THESE. En vue de l'obtention du. Délivré par l'université Toulouse III - Paul Sabatier Discipline ou spécialité : Ethologie

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1 THESE En vue de l'obtention du DOCTORAT DE L UNIVERSITÉ DE TOULOUSE Délivré par l'université Toulouse III - Paul Sabatier Discipline ou spécialité : Ethologie Présentée et soutenue par Simon Garnier Le 19/11/2008 Titre : Décisions collectives dans des systèmes d'intelligence en essaim JURY Professeur Jean-Louis Deneubourg Professeur Philippe Gaussier Docteur Nicolas Franceschini Professeur Dario Floreano Professeur Richard Fournier Ecole doctorale : CLESCO Unité de recherche : CRCA Directeur(s) de Thèse : Dr Guy Theraulaz Rapporteurs : Professeur Jean-Louis Deneubourg et Professeur Philippe Gaussier

2 2008 Simon Garnier Tous droits réservés i

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4 A tous ceux qui m ont soutenu d une façon ou d une autre dans cette entreprise. A Grand-Père et à Mamou qui nous ont quitté cette année. iii

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6 Remerciements En tout premier lieu, parce que la tradition l exige certes, mais surtout parce qu il le mérite, je tiens à remercier mon directeur de thèse, Guy Theraulaz, pour m avoir donner l opportunité de pratiquer le métier de chercheur, métier qui me tient tant à coeur. Au cours de ces années passées à travailler sous ta direction, j ai pu mesurer à de nombreuses reprises la chance que j ai eu de débuter ma carrière à tes côtés. Tu t es toujours efforcé de me fournir le matériel et les ressources nécessaires à la bonne conduite de mes travaux. Tu m as encouragé à présenter mes résultats dans des conférences nationales et internationales. A travers ton réseau de relations, tu m as permis d établir des collaborations multiples dans des domaines aussi divers que l éthologie, la robotique, l informatique, la physique ou les mathématiques. Ces collaborations ont enrichi considérablement mon travail quotidien et l ont rendu plus passionnant que jamais. Enfin, tu as toujours su être présent pour discuter, pour me conseiller et pour me transmettre tes immenses connaissances sur l organisation des sociétés animales. Mon impulsivité n a pas dû te rendre la tâche facile tous les jours, et ta patience à mon encontre n en est que plus méritoire. Pour toutes ces raisons et bien d autres encore, je t adresse de nouveau un grand merci. Au cours de ces années, Christian Jost a été successivement mon professeur, mon directeur de DEA et mon référent pédagogique. Il s est acquitté de toutes ces tâches avec la ferveur qui caractérise l excellent enseignant qu il est. C est lui qui m a appris (presque) tout ce que je sais aujourd hui sur l analyse statistique et la modélisation en biologie. C est lui qui m a mis le pied à l étrier en m offrant l opportunité de réaliser mon premier stage dans le laboratoire lors de mon année de Maîtrise. C est lui enfin qui m a transmis l amour de l enseignement malgré mes fortes réticences initiales. Pour ta disponibilité, pour ta gentillesse et pour tes inimitables «suisseries», merci beaucoup Christian. Je tiens à remercier Jean-Louis Deneubourg et Philippe Gaussier d avoir accepté d évaluer mon manuscrit. Pour avoir évaluer quelques copies d examens, j imagine à quel point la fonction de rapporteur peut être gourmande en temps. Merci d avoir bien voulu consacrer le vôtre à mon travail de thèse. Je vous associe également aux remerciements que j adresse à Dario Floreano, v

7 Nicolas Franceschini et Richard Fournier pour avoir eu la gentillesse d accepter de participer à mon jury de thèse. Ma famille a toujours été d un grand soutien pour moi a cours de ces longues années d étude. Avec des moyens financiers restreints, mais surtout avec beaucoup d amour, mes parents ont toujours fait ce qu il fallait pour que leurs enfants suivent la voie qu ils s étaient choisis. J en suis arrivé là aujourd hui parce qu ils ne m ont jamais laisser penser que c était impossible. Autour d eux, mes frères et soeurs, mes grand-parents, mes oncles, mes tantes et tous mes cousins (et ils sont nombreux) ont entretenu un climat de bonne humeur permanente, dans les moments les plus joyeux comme au coeur des coups durs. Leur verve et leur bagou m ont appris à me sortir des joutes orales les plus difficiles, leur entêtement et leur force de caractère m ont appris à ne jamais renoncer. A vous tous qui êtes de ma famille, un grand merci. Comme ma famille, mes amis prennent une part importante dans la réussite de mon travail. Ils ont enrichi ma vie de leurs expériences et, pour cela, je remercie toutes ces personnes qui ont croisé plus ou moins longtemps mon chemin ces dernières années. Parmi elles, je voudrais adresser un merci spécial et chaleureux à Alexandre, Mehdi et Marie-Hélène qui ont partagé avec moi la passion de l étude des sociétés animales et m ont apporté aide, soutien et bonne humeur. Vous avez été les meilleurs collègues possibles pendant ces quatre années et vous resterez mes amis pour un long moment encore. Je tenais également à remercier les «p tits loups» et les «p tits monstres» du hand qui m ont permis de me défouler dans tous les gymnases de la région et avec qui j ai partagé mes plus beau fous rire. Merci aussi à Nathalie pour tout ce qu elle donne aux autres, merci à Jeanne pour son éternelle joie de vivre. Merci Lucile, Carole et Elodie. Vous avez partagé ma vie et m avez offert les moments les plus heureux de mon existence. La recherche scientifique est un travail d équipe et rien de ce qui est dans ce manuscrit n aurait pu voir le jour sans de multiples collaborations, conseils et coups de main. Merci donc à tous les membres de l équipe EMCC, titulaires et passagers, qui ont toujours su m apporter leur aide dans mon entreprise. Merci à Vincent, Raphaël, Pablo, Richard, Andrea, Jacques, Laurent, Grégory, Niriaska, Sébastien et Abel pour leur disponibilité et leurs conseils. Merci également à Audrey, il paraît que tu n y es pas pour rien dans mon arrivée au sein de l équipe. Merci à Aurélie et à Marjorie, les meilleures stagiaires du monde. Merci à Anne pour les heures de travail qu elle a consacré à mes travaux, merci à Gérard pour ses connaissances encyclopédiques sur l élevage des fourmis, merci à Maud pour tous les logiciels qu elle développe pour nos besoins spécifiques. Je remercie Gilles, Masoud, Fabien, Nikolaus et tous les membres des laboratoires de Roland Siegwart et Alcherio Martinoli pour l aide qu ils m ont apporté dans mon travail de robotique vi

8 et pour leur accueil chaleureux et efficace à l EPFL. Merci enfin à tous les membres du CRCA. L approche multi-échelle et multi-disciplinaire que vous développez est une source de richesse scientifique qu il est essentiel de préserver, la place privilégiée que vous accordez aux étudiants est un moteur d innovation rare et précieux. Merci à vous tous qui êtes cités ici, merci à ce que j aurais pu oublier. vii

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10 Il arrive que les grandes décisions ne se prennent pas, mais se forment d elles-mêmes. Henri Bosco. ix

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12 TABLE DES MATIÈRES TABLE DES MATIÈRES Table des matières Remerciements v 1 Introduction Intelligence en essaim Introduction et repères historiques Auto-organisation et propriétés des systèmes d intelligence en essaim Mécanismes Propriétés Etude des systèmes d intelligence en essaim Interactions et transferts d information dans les systèmes d intelligence en essaim Transfert indirect d information Transfert direct d information Direct vs indirect Fonctions assurées par les systèmes d intelligence en essaim Coordination Collaboration Délibération Intelligence en essaim dans les systèmes artificiels De l animal à l animat Intelligence artificielle Les Animats De l animat à l animal Applications de l intelligence en essaim Animation graphique : les Boids et leurs descendants Algorithmes d optimisation xi

13 TABLE DES MATIÈRES TABLE DES MATIÈRES Robotique collective Agrégation Ségrégation Exploration Déplacements coordonnés Manipulations coopératives Allocation de tâches Prises de décisions collectives Décisions collectives dans les systèmes biologiques d intelligence en essaim Prises de décisions dans les sociétés animales Qui décide dans le groupe? Comment les individus s accordent-ils sur un choix? Décisions collectives et intelligence en essaim Sélection d un chemin chez la fourmi Les points à retenir de l exemple des fourmis Sensibilité à l environnement Préférences individuelles et choix collectifs Modulation des comportements individuels et efficacité des choix collectifs Complexité individuelle vs complexité collective Objectifs Implémentation du comportement d agrégation de la blatte Blattella germanica dans un groupe de micro-robots Introduction Materials and methods The biological system : first-instar larvae of Blattella germanica The artificial system : micro-robots Alice Experimental set-up The behavioral model Implementation in the Alice robots Displacement Stopping behavior xii

14 TABLE DES MATIÈRES TABLE DES MATIÈRES 2.3 Analysis and Comparison to Cockroach behavior Path analysis for an individual robot Central zone Peripheral zone Spontaneous stopping times Interactions among robots Probabilities to join and to leave an aggregate Calibration of interaction parameters Collective behaviors Discussion Conclusion Le comportement d agrégation des blattes comme processus de décision collective pour des groupes de robots Introduction Self-organized aggregation Collective choice Conclusion Introduction Material and methods The micro-robots Alice The experimental set-up The behavioral model The experimental parameters Identical shelters Shelters of different sizes Numerical experiments Data analysis Experiments Sensitivity analysis Results Identical shelters Experiments xiii

15 TABLE DES MATIÈRES TABLE DES MATIÈRES Simulator validation Sensitivity analysis Summary of the identical shelters case Shelters with different sizes Experiments Simulator validation Sensitivity analysis Summary of the different shelters case Discussion Sensibilité de la fourmi d Argentine à la géométrie des bifurcations d un réseau Introduction Methods Biological material Experimental set-up and protocol Statistical analysis Results Foodbound trip (unfed ants) Foodbound trip (unfed ants) Discussion Sélection de chemin et efficacité de fourragement dans un réseau de transport chez la fourmi d Argentine Introduction Material and methods Biological material Individual behaviour Collective behaviour Experimental results Individual ant behaviour Collective behaviour Model Model description Comparison of the model output with the experimental results xiv

16 TABLE DES MATIÈRES TABLE DES MATIÈRES 5.5 Discussion Sélection de chemin par stigmergie dans un groupe de petits robots autonomes Introduction Materials and methods Robot Alice Base robot Trail following add-on Experimental setup Maze Tracking device Pheromone deposit device Behavioral model Simulations Data analysis and results Parameter estimation Two path maze Identical length condition Different length condition Network maze Three loop maze Four loop maze Discussion Conclusion Discussion et conclusion Discussion générale Comparaison qualitative des deux processus de décision collective Interactions directes vs interactions indirectes Sélection de place vs sélection de route Sensibilité à la taille du groupe Conclusion Implémentation du modèle biologique : objectifs et méthodologie L approche réaliste xv

17 TABLE DES MATIÈRES TABLE DES MATIÈRES L approche bio-inspirée Conclusion Structure de l environnement, modulation passive du comportement et parcimonie du traitement cognitif Structure de l environnement et modulation passive du comportement Structure de l environnement et parcimonie du traitement cognitif Perspectives Formation des réseaux de pistes chez la fourmi d Argentine Détection collective de caractéristiques environnementales Quel avenir pour la robotique en essaim? L absence d applications Polymorphisme, polyéthisme et modulation des comportements individuels Intégration dans les systèmes naturels Conclusion Bibliographie 227 A Les principes biologiques de l intelligence en essaim 257 B Transferts d information et comportements auto-organisés dans les foules et les essaims 289 C Extraction expérimentale de lois d interaction chez l Homme : le cas des piétons 325 xvi

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20 CHAPITRE 1. INTRODUCTION Chapitre 1 Introduction Dans la nature, les groupes et les sociétés animales sont fréquemment confrontés à des choix dont peut dépendre leur survie. Les singes hamadryas par exemple se dispersent tous les matins pour rechercher de la nourriture. Avant cela, ils décident autour de quel point d eau ils se retrouveront vers le milieu de la journée pour se reposer (Kummer, 1968). Dans la région semi-désertique où ces animaux vivent, les points d eau sont relativement rares. Le regroupement de l ensemble des singes autour de l un d entre eux facilite sa défense contre d éventuels compétiteurs, ainsi que la défense du groupe contre ses prédateurs. Tous les matins, ces singes doivent donc prendre une décision importante pour l avenir du groupe. Pour cela, ils votent... avec leurs pieds, c est à dire en se déplaçant. Pour indiquer leur point d eau préféré, certains mâles s éloignent de quelques mètres du groupe dans la direction de ce point d eau. Les autres mâles votent en rejoignant l un ou l autre, et des colonnes commencent à se former en direction des points d eau majoritaires. Les mâles peuvent également attirer l attention de leurs congénères pour les inciter à les rejoindre dans leur colonne. Pendant plus d une heure, ces colonnes se développent ou régressent en fonction des changements d opinions des individus. Finalement, l une d entre elles l emporte et l ensemble du groupe se met alors en mouvement dans la direction choisie (Sigg & Stolba, 1981). De manière générale, lorsqu un groupe d animaux fait face à un choix, l ensemble des individus doit adopter de concert la même alternative afin de limiter les risques de séparation. Par exemple, lorsqu une colonie d abeilles mellifères essaime vers un nouveau nid, les membres de l essaim doivent s accorder à l avance sur la localisation de leur futur nid parmi les multiples possibilités qui s offrent dans l environnement. Sans cet accord préalable, l essaim encoure le risque de se disperser (Seeley & Buhrman, 1999). Les animaux doivent donc établir un consensus auquel tous les membres du groupe vont se rallier. Le choix par consensus se retrouve également dans les sociétés humaines et s applique aussi aux systèmes artificiels conçus par l Homme comme les 1

21 CHAPITRE 1. INTRODUCTION robots. Par exemple, lorsque plusieurs robots coopèrent pour transporter une charge importante vers un objectif, il est nécessaire que les robots s entendent sur la direction à suivre ou la route à prendre pour atteindre cet objectif (Kube & Bonabeau, 2000; Campo et al., 2006). Dans un système naturel ou artificiel, il est donc essentiel que les agents qui le composent disposent de mécanismes leur permettant d établir un consensus. On distingue principalement deux grandes catégories de mécanismes : 1. Dans la première catégorie, le processus de décision repose sur la centralisation de l information acquise par le groupe. Ce regroupement de l information peut avoir deux origines différentes. La centralisation peut être le fait d un individu unique, un leader, ou d un petit groupe d individus qui se chargent de prendre la décision pour l ensemble du groupe. Dans ce cas, les autres membres du groupe ne participent pas à la décision et se contentent de suivre les directives du leader ou du sous-groupe dirigeant. Mais l information peut également être centralisée à travers l organisation d un vote. Dans ce cas, les opinions de chaque membre du groupe sont collectées et rassemblées pour être dénombrées. Le consensus est obtenu en suivant une règle établie au préalable, par exemple la règle de la majorité absolue, qui défini l alternative gagnante en fonction des votes exprimés. L ensemble des membres du groupe est alors tenu de suivre ce résultat, quelque qu ait été son vote personnel. 2. Dans la seconde catégorie, l information n est jamais centralisée au cours du processus de décision. Les individus se comportent en suivant leurs propres motivations. Ils ne se conforment pas à la décision d un leader ni à une opinion majoritaire. Cependant, leur comportement est influencé par celui des congénères avec qui ils interagissent. Plus précisément, ils tendent à adopter le même comportement qu eux. A travers ce mimétisme comportemental, les individus s accordent sans concertation sur une alternative à adopter. Ces mécanismes décentralisés permettant à des individus de prendre collectivement une décision s observent fréquemment dans les colonies d insectes sociaux. On les retrouve également chez de nombreuses autres espèces sociales, y compris chez l Homme. Le présent mémoire se veut une contribution à la connaissance et à la compréhension de ces mécanismes décentralisés de prise de décision dans les systèmes collectifs. D un point de vue théorique, ce travail se situe dans le cadre général de l étude des systèmes d intelligence en essaim. Ce champ de recherche s attache à comprendre et à concevoir des mécanismes décentralisés de résolution collective de problèmes, et s intéresse aussi bien aux systèmes biologiques qu aux systèmes artificiels (Bonabeau et al., 1999; Bonabeau & Theraulaz, 2000; Eberhart et al., 2001; 2

22 CHAPITRE 1. INTRODUCTION Garnier et al., 2007a). Il étudie plus particulièrement les comportements des individus et du groupe auquel ils appartiennent, et cherche avant tout à établir le lien causal qui les unit. Dans la nature, les mécanismes décentralisés de résolution de problèmes sont à l origine de certains des comportements collectifs les plus spectaculaires. De l organisation spontanée du trafic piétonnier chez l Homme à la construction de nids gigantesques chez les termites et les fourmis, de la répartition adéquate des tâches à accomplir chez les guêpes à la coordination du mouvement dans les vols d oiseaux et les bancs de poissons, ces mécanismes permettent aux sociétés animales d organiser de manière efficace l activité de grands groupes d individus. Ils ont également servi de source d inspiration pour la conception de plusieurs systèmes artificiels. Ils sont par exemple à l origine d un système très efficace pour optimiser le routage des marchandises et le transfert des paquets de données dans les réseaux de télécommunication (Dorigo et al., 1999; Bonabeau et al., 2000). Ils servent également dans l animation graphique pour générer le mouvement de foules virtuelles et leur donner un aspect réaliste (Reynolds, 1987). Enfin, ils ont contribué au développement d une nouvelle branche de la robotique qui s en inspire pour coordonner l activité de plusieurs robots afin qu ils accomplissent collectivement une tâche (Sahin & Winfield, 2008). Parmi tous ces phénomènes collectifs, les mécanismes décentralisés de prise de décision ont été l objet de très nombreuses études en biologie. Ils ont également servi de sources d inspiration pour concevoir de nouveaux algorithmes d optimisation dans le domaine de la recherche opérationnelle et en informatique. Cependant, leur application en robotique reste extrêmement marginale. A travers une approche combinant étroitement éthologie et robotique, expériences et simulations, ce travail se propose donc d étudier deux processus biologiques permettant à un groupe de prendre une décision et de les implémenter sur une plateforme robotique. Dans cette introduction, nous aborderons dans un premier temps le concept d intelligence en essaim (Section 1.1). Nous commencerons par le définir à travers un rapide historique (Section 1.1.1) qui nous permettra d en comprendre les multiples racines scientifiques. Cette section nous permettra également d appréhender les questions abordées par ce champ de recherches. Puis nous nous intéresserons plus particulièrement aux processus d auto-organisation qui sous-tendent le fonctionnement des systèmes d intelligence en essaim (Section 1.1.2). En particulier, nous passerons en revue les mécanismes (Section ) et les propriétés ( ) de ces processus, ainsi que la méthodologie générale qui permet de les étudier (Section ). Nous verrons que les processus d auto-organisation reposent sur de multiples interactions entre les individus 3

23 CHAPITRE 1. INTRODUCTION composant le groupe. La nature de ces interactions sera abordée dans la Section Nous distinguerons deux types d interactions, les interactions indirectes (Section ) et directes (Section ), dont nous comparerons les propriétés (Section ). Enfin, nous parlerons des fonctions que les systèmes d intelligence en essaim remplissent pour le groupe (Section 1.1.4). Nous en différencierons trois en particulier : la coordination (Section ), la collaboration (Section ) et la délibération (ou prise de décision collective, Section ). Dans un second temps, nous passerons en revue les systèmes artificiels d intelligence en essaim, et en particulier ce qu il est convenu d appeler la robotique en essaim (Section 1.2). Nous commencerons par faire des rappels historiques sur la transition entre l approche classique de l intelligence artificielle, et l approche adaptative (Section 1.2.1). Nous aborderons ces deux notions dans les Sections et Nous discuterons également l intérêt de l approche adaptative pour la connaissance des systèmes biologiques (Section ). Nous présenterons ensuite rapidement deux types d applications de l intelligence en essaim : l animation graphique de foules (Section ) et les algorithmes d optimisation (Section ). Nous nous focaliserons ensuite sur l application de l intelligence en essaim dans le domaine de la robotique collective (Section 1.2.3). Dans la troisième partie de cette introduction, nous aborderons en détails les processus de délibération par auto-organisation dans les sociétés animales (Section 1.3). Nous commencerons par replacer cette question dans un cadre théorique plus général, celui de la prise de décision par consensus. En particulier nous nous poserons les questions suivantes : qui dans un groupe d animaux peut prendre une décision? (Section ) Et comment les animaux s accordent-ils sur un choix commun? (Section ) A l intérieur de ce cadre théorique général, nous identifierons la place des processus de délibération par auto-organisation (Section 1.3.2). Puis à travers une série non exhaustive d exemples, nous expliquerons les mécanismes qui permettent à un groupe d individus de prendre collectivement une décision en ne se basant que sur une information locale et restreinte de l activité globale du groupe (Section et ). Nous évoquerons ensuite la sensibilité de ces mécanismes de délibération aux variations de l environnement (Section ) et aux préférences individuelles (Section ). Nous parlerons également de l effet des modulations du comportement des individus sur l efficacité du processus de décision (Section ). Pour finir, nous essaierons de comprendre comment la complexité comportementale de l individu peut modeler précisément le processus de décision à l échelle du groupe (Section ). Enfin, nous préciserons dans la dernière partie de cette introduction les objectifs de cette thèse ainsi que l organisation générale du reste du mémoire (Section 1.4). 4

24 CHAPITRE 1. INTRODUCTION 1.1 Intelligence en essaim 1.1. INTELLIGENCE EN ESSAIM Introduction et repères historiques L étude du comportement animal présente à divers égards des aspects aussi intrigants que passionnants. Parmi eux se trouvent les extraordinaires phénomènes collectifs (voir Figure??) que l on observe au sein de nombreuses sociétés animales (Camazine et al., 2001; Couzin & Krause, 2003; Sumpter, 2006). Tout le monde a un jour observé les surprenantes chorégraphies exécutées par des vols d oiseaux ou des bancs de poissons, chaque membre du groupe en parfaite coordination avec ses congénères au sein d une structure constamment changeante et pourtant toujours cohérente. Moins virevoltant mais tout aussi impressionnant est le spectacle offert chaque année dans la savane africaine du Serengeti par la migration d un troupeau gigantesque de gnous. Un million et demi de ces animaux, accompagnés par des milliers de zèbres et de gazelles, entament à chaque fin de saison humide un long périple collectif qui les mènera à leurs quartiers de saison sèche. Suivant les zones d herbes fraiches, le troupeau géant forme un immense front s étendant parfois sur plusieurs kilomètres (Gueron & A., 1993). Plus proches de nous, dans les rues bondées de nos centres-villes ou dans les couloirs de métro aux heures de pointe, les foules de piétons forment également d étonnantes structures : les personnes provenant de directions opposées se partagent spontanément la route, créant ainsi des files alternées d individus se déplaçant dans le même sens (Helbing et al., 2001). Plus petits, plus discrets dans la nature, les insectes sociaux sont néanmoins maîtres dans l art de l organisation des foules, de la construction de structures gigantesques et de la résolution des problèmes à l échelle de leur société toute entière (Bonabeau et al., 1997; Camazine et al., 2001; Detrain & Deneubourg, 2006). Leurs colonies, qui selon les espèces comptent quelques individus ou des millions, présentent une gamme très variée de comportements collectifs, qui allient l efficacité à la flexibilité et à la robustesse. Ces animaux à l apparence simple sont ainsi capables de construire des réseaux de transport et d échange (Theraulaz et al., 2003; Buhl et al., 2004, 2005) à l intérieur desquels le traffic des individus et du matériel est régulé (Couzin & Franks, 2003; Dussutour et al., 2004; Burd, 2006; Vittori et al., 2006) ; ils sont également à même de construire des édifices immenses comparés à leur petite taille (Grassé, 1984; Tschinkel, 2003, 2004) ; ils disposent de systèmes de division du travail permettant d allouer de manière dynamique les différentes tâches à effectuer pour le bon fonctionnement de la colonie (Deneubourg et al., 1987; Gordon, 1996; Bonabeau et al., 1998b; Beshers & Fewell, 2001) ; etc. Enfin, invisibles à nos yeux la plupart du temps, les amibes et les bactéries sociales sont ca- 5

25 1.1. INTELLIGENCE EN ESSAIM CHAPITRE 1. INTRODUCTION Figure 1.1: Exemples de comportements collectifs dans les sociétés animales et humaines. (a) Culture sur agar de la bactérie Bacillus subtilis. Le pattern formé par la colonie dépend à la fois du morphotype de la bactérie et des conditions environnementales (Ben-Jacob et al., 2000). (b) Colonne de chasse chez la fourmi légionnaire Eciton burchelli. Les individus au centre de la colonie se déplacent majoritairement en direction du bivouac de la colonie, alors que les individus sur les côtés se déplacent majoritairement vers le front de chasse. (c) Un banc de poissons formé par l alignement des individus sur une direction commune de déplacement. (d) Un phénomène similaire est à l origine de la formation des vols d oiseaux. (e) Migration d un troupeau géant de gnous à travers la savane du Serengeti. (f) Déplacement d une foule de piétons dans une rue commerçante. Les individus se séparent en deux flux de directions opposées (repris depuis Helbing et al., 2005). 6

26 CHAPITRE 1. INTRODUCTION 1.1. INTELLIGENCE EN ESSAIM pables de former d étonnantes structures spatio-temporelle (Ben-Jacob et al., 2000). Par exemple, lorsque les conditions environnementales deviennent rudes, en particulier quand les nutriments se font rares, l amibe Dictyostelium discoideum produit des bouffées d AMP cyclique qui, relayées de proche en proche par les autres cellules, produit des ondes en spirales. Pour finir, chez de nombreuses espèces de bactéries, le déplacement coordonné des cellules au cours de la croissance de la colonie conduit à la formation de structures tri-dimensionnelles régulières aux formes multiples. Depuis longtemps, ces étonnants comportements, ces colossales structures qui émergent au sein des sociétés animales fascinent les hommes. Artistes et naturalistes se sont demandés quelle force permettait à tant d animaux de se coordonner afin d atteindre les objectifs du groupe. Le poète belge Maurice Maeterlink par exemple prêtait aux insectes sociaux une forme d obéissance à une entité, un maître ignoré qu il appelait l esprit de la ruche (Maeterlinck, 1927). Plus récemment, Michael Crichton reprend dans son roman, La proie, une idée assez similaire, celle d une nuée de nanorobots formant une forme de super-organisme capable de prendre des décisions complexes et d anticiper des événements futurs (Crichton, 2002). De son côté, la littérature scientifique sur le sujet remonte au moins jusqu au XIX ème siècle. Les premières hypothèses pour expliquer ces phénomènes collectifs faisaient appel à une organisation hiérarchique et centralisée (voir par exemple Büchner, 1881; Forel, 1921). Les individus étaient supposés disposer de capacités cognitives suffisantes pour se représenter la globalité de l état de la société et de l environnement, pour évaluer la situation de la société par rapport à ses objectifs et pour prendre en conséquence des décisions appropriées (voir par exemple Thorpe, 1963). Dans ce schéma de pensée, la complexité de la structure produite ou du comportement réalisé par le groupe reflétait la complexité cognitive des individus composant le groupe, ou au moins de l un d entre eux. En particulier chez les insectes sociaux, la reine était considérée comme le superviseur de l activité de la colonie, surveillant l activité des ouvriers et leur donnant des ordres appropriés à chaque situation. Cependant, une telle approche ne peut pas rendre compte d un grand nombre des phénomènes collectifs observés dans les sociétés animales. Lorsque la taille du groupe est immense (certaines colonies de fourmis comportent plusieurs millions d individus), lorsque l espace à couvrir dépasse les capacités de communication des animaux (les troupeaux de gnous dans le parc du Serengeti peuvent s étendre sur plusieurs kilomètres), lorsque la structure produite par le groupe nécessite le travail d ouvriers sur plusieurs générations (c est le cas du nid chez certaines espèces de termites) ou lorsque des individus qui ne se perçoivent pas tous doivent changer de 7

27 1.1. INTELLIGENCE EN ESSAIM CHAPITRE 1. INTRODUCTION comportement à l unisson (par exemple lors de changements brusques de direction dans les bancs de poissons), il devient difficile d imaginer qu un seul individu, ou même un petit groupe d individus, puisse mettre en place efficacement une quelconque forme d organisation à une aussi grande échelle spatio-temporelle. L extraordinaire quantité d information à acquérir, à traiter et à restituer pour coordonner efficacement l activité globale du groupe semble bien souvent hors de portée des capacités cognitives des animaux considérés, être humain compris (Seeley, 2002). La conclusion s impose alors : une organisation collective, un ordre collectif peut émerger en l absence de supervision. Comprendre les mécanismes qui permettent l émergence de ces propriétés à l échelle du groupe revient à établir un lien entre deux niveaux d organisation : d un côté, le niveau macroscopique correspond au comportement du groupe lui-même, comme une entité propre réagissant aux stimuli environnementaux ; de l autre côté, le niveau microscopique correspond au comportement de chaque individu dans le groupe, en réaction à des stimuli locaux produits par l environnement proche ou par les individus voisins et qui construisent une perception partielle de la structure ou du comportement du groupe auquel ils appartiennent. La nature du lien qui unit ces deux niveaux d organisation a été étudié en premier lieu dans les systèmes physico-chimiques. Les travaux d Ilya Prigogine et de Grégoire Nicolis en particulier (Nicolis & Prigogine, 1977)ont conduit à la création d une théorie puissante, la théorie de l auto-organisation, qui permet d expliquer l émergence non supervisée (ou autonome) de structures, de régularités, à partir des interactions répétées entre les sous-unités d un système. Cette théorie a été transposée au cours des années 1970 à l étude des systèmes biologiques, et en particulier à l étude de l organisation des sociétés d insectes. Les travaux scientifiques menés depuis ont démontré que des processus d auto-organisation sont à l oeuvre dans de nombreux systèmes biologiques. Nous savons aujourd hui qu il n est pas toujours nécessaire de superviser les activités de chaque membre d un groupe pour que celui-ci s organise et réponde aux défis de son environnement. C est en réalité l activité de chacun des individus combinée à celle de tous les autres selon des principes d interaction souvent très simples qui fait émerger une organisation fonctionnelle à l échelle de la société. Nous détaillerons plus loin la nature de ces principes ainsi que leurs propriétés. Lorsque cette organisation permet de résoudre des problèmes, elle peut être assimilée à une forme d intelligence, qui apparaît seulement lorsque les individus sont en groupe. En référence à certaines espèces d insectes sociaux (en particulier les guêpes et abeilles), cette intelligence en groupe est appelée intelligence en essaim (swarm intelligence en anglais). 8

28 CHAPITRE 1. INTRODUCTION 1.1. INTELLIGENCE EN ESSAIM Aujourd hui, l intelligence en essaim est un champ de recherche scientifique, multidisciplinaire, qui s intéresse aux processus distribués (i.e. non supervisés) d organisation et de résolution de problèmes présents dans un certain nombre de sociétés animales et dans des systèmes artificiels qui en sont inspirés. Le terme d intelligence en essaim est apparu au cours de l année 1989 dans des publications de Beni, Hackwood et Wang portant sur les systèmes de robotique cellulaire. Dans ces automates cellulaires, des agents virtuels représentant des robots se déplaçaient dans des environnements uni- ou bi-dimensionnels en interagissant avec leurs voisins proches. Chaque interaction entraînait une modification du comportement de l agent selon des règles pré-établies. Selon le jeu de règles utilisé, des structures pouvaient éventuellement se former sans codage explicite ni supervision externe. Dans un article plus récent (Beni, 2005), Beni raconte que, lors d une conférence en 1988 où il présentait ses travaux de robotique cellulaire (Beni, 1988), Alexander Meystel qualifia son système de sort of swarm (genre d essaim). Trouvant l expression accrocheuse, il choisit de la conserver dans ses articles. Les robots cellulaires devinrent des essaims de robots, et l intelligence développée par ses essaims devint l intelligence en essaim. Par la suite en 1999, Bonabeau, Dorigo et Theraulaz étendirent le champ de l intelligence en essaim à toute tentative de conception d algorithmes ou de dispositifs de résolution distribuée de problèmes inspirés par le comportement collectif des colonies d insectes sociaux et des autres sociétés animales (Bonabeau et al., 1999). Enfin, il y a quelques mois seulement, lors du lancement de la revue Swarm Intelligence 1 (la première consacrée entièrement à l étude de l intelligence en essaim), son comité d édition a ajouté au champ d investigation l ensemble des études expérimentales et théoriques portant sur les systèmes collectifs en biologie. Ironiquement, la source d inspiration de la plupart des travaux dans ce domaine aura été la dernière a intégrer sa définition Auto-organisation et propriétés des systèmes d intelligence en essaim Bien que cela ne soit pas explicitement spécifié dans sa définition, l intelligence en essaim repose en grande partie sur des processus d auto-organisation. Il existe de nombreuses définitions de l auto-organisation dans la littérature. Celle que nous choisirons ici décrit l auto-organisation comme l émergence spontanée d une organisation à l échelle d un système, à partir des interactions locales entre les sous-unités composant ce système, et sans codage explicite de la structure produite au niveau de ces sous-unités (Camazine et al., 2001). Les processus d auto-organisation sont basés sur un ensemble d éléments et de mécanismes dynamiques qui assurent l apparition de la structure et sa stabilisation dans le temps. Dans les sections suivantes, nous décrirons

29 1.1. INTELLIGENCE EN ESSAIM CHAPITRE 1. INTRODUCTION rapidement ces mécanismes, ainsi que les propriétés collectives générales qui en résultent Mécanismes Les processus d auto-organisation reposent en particulier sur les quatre constituants suivants (voir Figure 1.2) : 1. Rétroaction positive. Il y a rétroaction positive lorsque la probabilité d apparition d un élément augmente avec le nombre d éléments similaires déjà présents. Ce mécanisme d amplification conduit à une augmentation non-linéaire de la quantité de ces éléments et sert de moteur à la création de nouvelles structures. Pour illustrer cette notion, prenons l exemple d une expérience portant sur l attention collective et réalisée par Stanley Milgram en 1969 (Milgram & Toch, 1969). Cette expérience consiste à demander à des personnes dans des groupes de taille variable de fixer un point précis situé sur la façade d un immeuble newyorkais. Pendant ce temps, on relève le nombre de passants naïfs qui regardent dans cette direction. Les résultats obtenus montrent qu une seule personne qui semble regarder un point d intérêt entraîne en moyenne 40% des passants à regarder dans la même direction. Lorsque cinq personnes observent un même point, ce pourcentage double et il atteint près de 90% lorsque le groupe de démonstrateurs est composé de quinze personnes. Dans cette expérience, une rétroaction positive est en jeu : la probabilité que des personnes naïves regardent dans une direction précise augmente avec le nombre de personnes qui regardent déjà dans cette direction. Cette amplification conduit à une propagation rapide du comportement de quelques individus dans la population. 2. Rétroaction négative. Il y a rétroaction négative lorsque la probabilité d apparition d un élément diminue avec le nombre d éléments similaires déjà présents. Ce mécanisme d atténuation s oppose à la rétroaction positive dans les sytèmes auto-organisés, et conduit à une stabilisation de la structure collective lorsqu un équilibre dynamique entre les deux types de rétroactions est atteint. Pour illustrer ce propos, prenons l exemple du recrutement alimentaire chez l abeille domestique Apis mellifera (Seeley et al., 1991). Chez cette espèce, une ouvrière qui découvre une source de nourriture rentre à sa ruche et entame à l intérieur une danse de recrutement. Cette danse, permet à l abeille de communiquer la direction, la distance et la qualité de la source de nourriture découverte aux ouvrières qui se trouvent autour d elle. Certaines d entre elles prendront alors leur envol pour aller exploiter cette source. A leur retour, elles entameront éventuellement une danse similaire afin de recruter de nouvelles butineuses. Le recrutement par danse des abeilles est un exemple classique de 10

30 CHAPITRE 1. INTRODUCTION 1.1. INTELLIGENCE EN ESSAIM rétroaction positive, une abeille en recrutant plusieurs qui à leur tour en recrutent plusieurs autres, etc. En l absence de toute régulation, ce recrutement conduirait inévitablement au regroupement de toutes les abeilles de la ruche sur la source de nourriture découverte. Dans la nature, cela n arrive jamais car la rétroaction positive est contrebalancée par un certain nombre de mécanismes réalisant une rétroaction négative : nombre limité d ouvrières recrutables pour le fourragement alimentaire, épuisement de la source de nourriture, compétition entre des sources de nourriture, etc. Lorsque la rétroaction positive et la rétroaction négative s équilibrent, cela conduit à une stabilisation du nombre d abeilles exploitant la source de nourriture. En général, les boucles de rétroaction négative sont plutôt associées à des facteurs non comportementaux (contraintes spatiales, évaporation du signal, etc.) alors que les boucles de rétroaction positive sont plutôt associées au comportement de l animal, 3. Fluctuations. Ce sont des hétérogénéités qui modifient le comportement des individus. Lorsque ces modifications sont soumises à un mécanisme de rétroaction positive, elles peuvent être amplifiées et donner naissance à une structure, qui sera éventuellement stabilisée par un mécanisme de rétroaction négative. Ces fluctuations peuvent être des hétérogénéités environnementales qui vont alors favoriser l émergence d une structure à un endroit plutôt qu à un autre. Mais elles peuvent également être dues à la variabilité des comportements individuels. Dans ce cas, une structure peut être initiée et amplifiée dans un environnement parfaitement homogène. 4. Interactions. Deux individus interagissent lorsqu au moins l un d eux est en mesure d acquérir de l information détenue par l autre et que cette information entraîne une modification de l état de l individu qui la reçoit. Si cette modification a pour effet d augmenter (respectivement de diminuer) la probabilité d apparition d un état particulier, alors la répétition de l interaction à l échelle de la population devient le support d un mécanisme de rétroaction positive (respectivement négative). La multiplication de ce type d interactions est donc à la base des processus d auto-organisation Propriétés De ces quatre constituants de base découlent plusieurs de propriétés qui caractérisent les processus d auto-organisation. En particulier, on distingue classiquement les cinq propriétés suivantes : 1. Ce sont des systèmes dynamiques. La mise en place d une organisation ainsi que son maintien dans le temps sont le fruit des interactions permanentes entre les individus qui com- 11

31 1.1. INTELLIGENCE EN ESSAIM CHAPITRE 1. INTRODUCTION Figure 1.2: Illustration des constituants de l auto-organisation à travers l exemple du recrutement alimentaire chez la fourmi. Au début de l expérience, les fourmis découvrent par hasard une source de nourriture. Le nombre de fourmis à cette source est alors très faible et fluctue de manière aléatoire (flèche verte). Lorsqu elles retournent à leur nid, ces fourmis déposent derrière elles une piste chimique qui leur permet d interagir avec les autres ouvrières. En particulier, cette piste stimule les autres ouvrières à rechercher de la nourriture et les guide vers la source découverte. Ces fourmis recrutées vont à leur tour déposer une trace chimique par-dessus la première piste à leur retour vers le nid. Elles amplifient ainsi le pouvoir attracteur de la piste. Cette rétroaction positive (flèche rouge) enclenche une croissance exponentielle du nombre de fourmis présentes à la source. Enfin, l évaporation de la piste chimique, sa saturation, l encombrement à la source ou sur la piste vont limiter le nombre maximal de fourmis qui pourront de rendre à la source. Cette rétroaction négative (flèche bleue) va contrebalancer l effet de la rétroaction positive, et le nombre de fourmis à la source va se stabiliser en fin d expérience. 12

32 CHAPITRE 1. INTRODUCTION 1.1. INTELLIGENCE EN ESSAIM posent le groupe. En conséquence, l état du système évolue au cours du temps et/ou en réponse à des perturbations. Le système peut éventuellement atteindre un état stable, mais celui-ci ne sera pas figé. Au contraire, il s agira d un équilibre dynamique qui résultera de la compétition ininterrompue entre les rétroactions positives et négatives. 2. Ce sont des systèmes redondants. A l intérieur du groupe, plusieurs individus (voire tous) peuvent accomplir une même tâche. En conséquence, l échec d un individu dans la réalisation d une tâche ou la disparition de cet individu du système peut être compensée par les autres membres du groupe. Cette redondance augmente la robustesse générale du système aux perturbations et aux variations de l environnement. 3. Ces systèmes présentent des propriétés émergentes. Le comportement du groupe ne peut être résumé à la simple addition des contributions de chaque membre du groupe. Il est le résultat d une combinaison non linéaire de ces contributions, grâce aux interactions entre les membres du groupe qui supportent des processus de rétroaction positive. La conséquence est l apparition à l échelle du groupe de nouvelles propriétés qui ne sont pas directement déductibles du comportement isolé de chaque individu. 4. Le comportement de ces systèmes présente des bifurcations. Lorsque certains paramètres du système évoluent, son comportement peut opérer une transition d un état stable vers un autre. Il s agit en fait d un changement qualitatif du comportement du groupe. Par exemple, lors de la construction de leur nid, les guêpes sociales Polistinae doivent prendre en charge trois activités différentes : récolter de la pulpe de bois, récolter de l eau et construire les cellules du nid. Lorsque la taille de la colonie est faible, chaque guêpe peut prendre en charge chacune de ces activités indifféremment. Mais si la taille de la colonie dépasse un certaine valeur seuil, alors il apparaît des spécialistes qui prennent en charge exclusivement l une de ces tâches (Karsai & Wenzel, 1998; Theraulaz et al., 1998). La taille de la colonie est donc un paramètre susceptible de provoquer un changement qualitatif (i.e., une bifurcation) dans l organisation de la colonie. 5. Enfin, ces systèmes peuvent être multi-stables. Pour des paramètres donnés, le système peut atteindre plusieurs états stables différents, Cela signifie que qu un groupe donné peut présenter plusieurs comportements collectifs différents, en fonction des conditions initiales ou de l historique des fluctuations aléatoires. 13

33 1.1. INTELLIGENCE EN ESSAIM CHAPITRE 1. INTRODUCTION Figure 1.3: Les quatres étapes de l étude des processus d auto-organisation Etude des systèmes d intelligence en essaim Pour comprendre l émergence d un phénomène d auto-organisation, il faut avant tout établir un lien causal entre le comportement des individus et celui du groupe auquel ils appartiennent. Une approche en quatre étapes permet l établissement de ce lien (voir Figure 1.3). 1. Dans la première étape, l étude porte sur la structure et la dynamique du groupe (i.e., l évolution de la structure au cours du temps). Cette étape permet de caractériser, d une part, l état d organisation du groupe, et d autre part, la ou les fonctions remplies par cette organisation particulière. Dans le premier cas, il s agit d identifier la présence d éléments récurrents (on parle également de patterns), non aléatoires, et qui sont le signe d une organisation sous-jacente. Dans le second cas, il s agit de comprendre quel défi de l environnement est solutionné par cette organisation. Il est également fréquent d étudier l impact de différentes conditions environnementales sur la structure et la dynamique du groupe. 2. Dans une deuxième étape, l étude s attache à identifier dans le comportement des individus composant le groupe et dans leurs interactions des mécanismes susceptibles d expliquer la dynamique observée à l échelle du groupe. Il s agit dans cette étape de caractériser finement les comportements des individus en fonction des conditions environnementales et sociales qu ils perçoivent. En particulier, l influence des congénères sur le comportement individuel doit faire l objet d une analyse précise. Par exemple, le degré de mimétisme comportemental des individus aura un impact très important sur la capacité du groupe à 14

34 CHAPITRE 1. INTRODUCTION 1.1. INTELLIGENCE EN ESSAIM opérer des choix collectifs. En général, le comportement des individus est décrit dans cette étape par des processus stochastiques, comme par exemple des probabilités de transition entre deux comportements donnés. Ce type de description permet à la fois de capturer le changement de comportement et la variabilité qui y est associé. 3. La troisième étape consiste à rassembler dans un cadre cohérent les observations obtenues au cours de l étape précédente. Il s agit de bâtir un modèle contenant l ensemble des comportements individuels susceptibles d expliquer l apparition d une organisation fonctionnelle (car elle répond à un problème) à l échelle du groupe. Ce modèle peut être basé sur des observations qualitatives des comportements individuels. Dans la mesure du possible, il est cependant préférable de disposer d une mesure quantitative de la valeur de chaque paramètre du modèle. 4. Enfin, la quatrième étape consiste à formaliser le modèle dans un langage permettant de l implémenter sur une plateforme de simulation. Ce langage est en général celui des équations mathématiques ou des algorithmes informatiques. La simulation du modèle permet d observer la structure et la dynamique collective théoriques obtenues à partir des éléments individuels décrits lors de l étape numéro 2. La comparaison de ces observations théoriques aux observations réalisées lors de l étape numéro 1 permet de confirmer ou d infirmer la validité du modèle proposé dans l étape numéro 3. La simulation du modèle est donc une étape cruciale pour établir le lien entre le niveau des individus et celui du groupe. Elle permet en outre de faire des prédictions sur de nouvelles conditions qui pourront être ensuite testées expérimentalement Interactions et transferts d information dans les systèmes d intelligence en essaim Les propriétés d auto-organisation d un système reposent principalement sur les interactions entre ses composants. Classiquement, les interactions au sein des systèmes auto-organisés sont divisées en deux catégories distinctes, qui représentent deux manières différentes pour les éléments d un système ou les individus d un groupe d échanger de l information Transfert indirect d information Le transfert indirect d information est basé sur une modification par un individu de l environnement dans lequel il vit. Cette modification peut en retour modifier le comportement de ce même individu ou de ses congénères lorsqu ils la perçoivent. Ce type d interactions reposant sur 15

35 1.1. INTELLIGENCE EN ESSAIM CHAPITRE 1. INTRODUCTION la formation d une trace dans l environnement est qualifié de stigmergique (Theraulaz & Bonabeau, 1999). Le concept de stigmergie a été introduit pour la première fois à la fin des années 1950 par le biologiste Pierre-Paul Grassé pour rendre compte de la coordination des activités lors de la construction du nid chez les termites (Grassé, 1959). Grassé montra que chaque acte de construction réalisé par les ouvriers était déterminé par la structure locale de l environnement qui est elle-même modifiée par l acte de construction. A travers cette boucle, les traces laissées par les actions présentes de chaque individu influencent le comportement futur des individus qui les percevront. La construction du nid chez les guêpes sociales Polistinae est un bon exemple de comportement basé sur un transfert stigmergique de l information (voir Figure 1.5a). Chez ces guêpes, la grande majorité des nids est constituée de rayons de cellules hexagonales construites à partir de fibres végétales et de sécrétions orales assemblées par mastication (Wenzel, 1991). Afin de déterminer l emplacement d une nouvelle cellule, ces insectes utilisent la configuration locale des cellules qui les entourent et qu ils perçoivent grâce à leurs antennes (Karsai & Theraulaz, 1995). En fonction de cette configuration, la probabilité de construire une cellule varie fortement. Par exemple, elle est élevée lorsque le site potentiel de construction est entouré de trois murs adjacents. Elle est au contraire très faible lorsqu il n existe qu un ou deux murs adjacents. Les constructions passées et leur résultat stocké dans l environnement ont donc une influence sur les actes de construction suivants. Ils permettent ainsi une coordination précise des activités individuelles. Dans ce cas c est l architecture qui contrôle indirectement de déroulement des activités bâtisseuses. Le transfert stigmergique d information n est pas uniquement porté par des modifications qualitatives des structures présentes dans l environnement. Toute trace durable déposée dans l environnement et qui peut être détéectée peut suffire à établir une interaction stigmergique entre des individus. Ainsi, de nombreuses espèces de fourmis communiquent entre elles au moyen d un signal chimique, une phéromone, qu elles déposent dans l environnement afin de marquer, par exemple, le chemin qu elles ont emprunté pour rejoindre une source de nourriture depuis leur nid (Hölldobler & Wilson, 1990). Ce signal chimique a la particularité d être attractif pour les fourmis passant à proximité. La piste chimique déposée par une première fourmi va alors augmenter la probabilité que d autres ouvrières empruntent le même chemin, et éventuellement renforcent le marquage de la piste par leurs propres dépôts chimiques, augmentant d autant plus son attractivité. On retrouve donc ici aussi des interactions stigmergiques qui vont induire un feedback positif. A long terme, le renforcement de cette trace phéromonale par les dépôts 16

36 CHAPITRE 1. INTRODUCTION 1.1. INTELLIGENCE EN ESSAIM successifs des fourmis peut conduire à l établissement d un trafic important d ouvrières entre leur nid et une source de nourriture, comme en par exemple les gigantesques colonnes de chasse des fourmis légionnaires qui peuvent parfois s étendre sur plusieurs centaines de mètres (Franks & Fletcher, 1983; Franks, 1989; Hölldobler & Wilson, 1990). Enfin, des interactions stigmergiques peuvent également avoir lieu dans des environnements sans dimension physique. Dans certaines communautés internet, par exemple sur le site Digg.com, l exposition d une nouvelle sur la page d entrée du site est directement reliée à sa popularité (Wu & Huberman, 2007). Chaque membre de cette communauté peut attribuer un point à chaque nouvelle qu il juge intéressante. Plus une nouvelle récolte de points dans un laps de temps donné, plus elle est mise en avant sur la page d entrée du site. Cette mise en avant augmente la probabilité que la nouvelle atteigne d autres membres naïfs de la communauté. Ces membres peuvent à leur tour, à la manière des dépôts chimiques chez les fourmis, renforcer la nouvelle en lui attribuant un nouveau point. Des interactions stigmergiques similaires sont également utilisées dans les réseaux sociaux pour assurer la promotion de certains produits (Leskovec, 2006) Transfert direct d information Contrairement aux interactions stigmergiques, les transferts directs d information ne se font pas par l intermédiaire d une trace durable laissée dans l environnement. Dans le cas d interactions directes, les individus tirent leurs informations de l observation du comportement de leurs congénères voisins (voir Figure 1.5b). L information peut circuler sous plusieurs formes (visuelle, tactile, auditive), mais elle ne perdure pas dans l environnement. De nombreux comportements auto-organisés reposent sur des interactions directes entre les membres d un groupe. Probablement l exemple le plus parlant est celui des bancs de poissons et des vols d oiseaux dans lesquels des milliers, voire même des millions, d individus se déplacent de manière cohérente, changeant de direction parfois brusquement mais toujours de manière synchrone (Partridge, 1982; Aoki, 1982; Parrish et al., 2002; Ballerini et al., 2008). Cette cohésion presque parfaite est le résultat d un fort mimétisme comportemental couplé à un transfert direct d information : chaque poisson, chaque oiseau adopte dans ces groupes la direction et la vitesse de déplacement de ses voisins. De proche en proche, chaque individu s aligne sur ses voisins qui euxmêmes s alignent sur les leurs : le groupe adopte ainsi une direction commune de déplacement sans concertation de ses membres ni supervision par l un d entre eux. Comme l information direction de déplacement n est pas imprimée dans l environnement, toute variation importante dans le déplacement de quelques individus en réponse à des facteurs externes au groupe va se 17

37 1.1. INTELLIGENCE EN ESSAIM CHAPITRE 1. INTRODUCTION Figure 1.4: A gauche, de 1 à 8, une séquence d images montrant l attaque d un prédateur sur un banc de poissons. A droite, de a à h, un banc de poissons simulés (n=1000) répondant à l attaque d un prédateur simulé. propager rapidement à l ensemble du groupe et entraîner un brusque changement de direction ou de configuration du groupe. Cela arrive par exemple lorsque qu un banc de poissons est attaqué par un prédateur. Les individus qui le perçoivent et tentent de le fuir déclenchent alors des vagues de mouvements de fuite qui parcourent l ensemble du groupe. Chez l homme, on retrouve un phénomène similaire lorsque, à la fin d un concert par exemple, la foule qui applaudie au départ de manière désordonnée adopte peu à peu un battement rythmique (Néda et al., 2000; Strogatz, 2003). Grâce à un signal acoustique, chaque spectateur communique à ses voisins son propre rythme de battement et perçoit celui des personnes qui l entourent. Comme chez oiseaux ou les poissons, les individus ajustent leur rythme sur celui de leurs voisins et la foule finit par adopter une fréquence d applaudissement consensuelle. Toujours sur le même principe, certaines espèces de lucioles sont capables de synchroniser leurs émissions lumineuses en adaptant leur fréquence propre d émission sur celle de leur voisins (Buck & Buck, 1976). 18

38 CHAPITRE 1. INTRODUCTION 1.1. INTELLIGENCE EN ESSAIM Figure 1.5: Deux exemples d interactions au sein de sociétés animales. (a) Lors de la construction de leur nid, les guêpes Polistes interagissent indirectement à travers la configuration des cellules du nid en cosntruction. (b) Chez l abeille mellifère, une ouvrière qui a découvert une source de nourriture informe directement ces congénères à travers une danse qui leur indique la direction et la distance à laquelle se trouve la source. Enfin, des interactions directes à courte distance sont à l origine de l organisation particulière du trafic dans les colonnes de chasse des fourmis légionnaires (Couzin & Franks, 2003). Lorsque deux fourmis se rencontrent sur ces pistes, elles se perçoivent à courte distance et amorcent une manoeuvre d évitement. Cependant, chaque fourmi ne s écarte pas de sa trajectoire de la même façon, selon qu elle provient du front de chasse ou du bivouac de la colonie. En particulier, les fourmis provenant du bivouac tournent de manière plus prononcée que les fourmis provenant du front. A chaque interaction, les premières ont une probabilité plus importante de se déporter vers le bord de la piste. La répétition de ce type d interaction directe à l échelle de la colonie conduit à une organisation du trafic selon trois flux distincts de fourmis (voir Figure??b) : un flux central composé majoritairement de fourmis provenant du front de chasse, flanqué de deux flux latéraux composés majoritairement de fourmis provenant du bivouac (Franks, 1985) Direct vs indirect Les interactions directes et indirectes (ou stigmergiques) peuvent cohabiter au sein des sociétés animales. Cependant les spécificités de ces deux formes de transferts d information leur confèrent des propriétés différentes à l intérieur des processus d auto-organisation. Lors de transferts indirects d information, la trace laissée par les individus confère une forme de stabilité temporelle à la solution trouvée par le groupe. Une fois que cette dernière est établie, elle reste imprimée dans l environnement pendant une durée qui peut parfois être très longue. Certaines espèces de fourmis des bois (Rosengren & Sundström, 1987; Chauvin, 1962), de fourmis coupeuses de feuilles (Weber, 1972; Shepherd, 1982; Vasconcelos, 1990) et de fourmis granivores (Hölldobler, 1976; Lopez et al., 1994; Detrain et al., 2000; Azcárate & Peco, 2003) forment des 19

39 1.1. INTELLIGENCE EN ESSAIM CHAPITRE 1. INTRODUCTION pistes qui peuvent durer plusieurs semaines à plusieurs mois, et peuvent même résister jusqu à la fin de la période d hibernation. De plus, les ouvrières nettoient la piste des débris et de la végétation qui s y trouvent, et peuvent dans certains cas construire des murs ou un tunnel autour (Shepherd, 1982; Kenne & Dejean, 1999; Anderson & Mcshea, 2001). Dans ces exemples, les pistes conduisent à des ressources persistantes dans l environnement et leur stabilité maintient ainsi la mémoire du chemin vers ces ressources. Les interactions indirectes sont donc le plus souvent associées à des solutions qui présentent une certaine robustesse aux perturbations. Cependant, cette robustesse implique parfois une moindre flexibilité. Par exemple, une fois que la piste vers une ressource est établie, il est difficile pour certaines espèces de fourmis d abandonner ensuite cette piste pour un chemin plus court ou une ressource de meilleure qualité (Beckers et al., 1990). Pour être plus précis, il existe une forme de compromis entre la robustesse et la flexibilité de la structure produite par le processus d auto-organisation. Et la valeur de ce compromis est régulée par la stabilité de la trace laissée par les individus. Par exemple, les piliers, les murs et les plafonds construits par les termites sont des traces très stables qui assurent la pérennité du nid pour plusieurs générations, même si les dimensions ou l organisation de certaines structures comme la chambre royale peuvent être adaptées au cours de la vie d une colonie (Bruinsma, 1979). Au contraire, les traces virtuelles déposées dans les communautés Internet sont plus volatiles, l intérêt des utilisateurs pour une information diminuant rapidement dans le temps. Cela assure le renouvellement quotidien des sujets traités sur le réseau. Les interactions directes permettent plutôt de créer des structures hautement réactives aux perturbations. Comme nous l avons évoqué un peu plus haut, les bancs de poissons ou les vols d oiseaux peuvent modifier leur déplacement de manière brusque lorsqu un prédateur se présente. La propagation de l information de proche en proche permet à celle-ci de traverser à grande vitesse l ensemble du groupe qui peut en conséquence réagir très rapidement. Cependant, cette grande flexibilité peut également avoir des conséquences négatives. Par exemple, une fluctuation aléatoire dans le comportement des individus peut soudainement être amplifiée et créer ainsi des déplacements inutiles et coûteux. Un compromis entre la flexibilité et la stabilité du groupe existe donc également dans le cas des processus d auto-organisation basés sur des interactions directes. La valeur de ce compromis est en général régulée par le nombre de congénères que l individu prend en compte pour ajuster son comportement. Plus ce nombre est élevé, moins les fluctuations aléatoires locales auront d impact sur la structure du groupe. 20

40 CHAPITRE 1. INTRODUCTION 1.1. INTELLIGENCE EN ESSAIM Figure 1.6: Exemple de coordination dans les systèmes d intelligence en essaim. Dans ce banc de poisson, les individus coordonnent leur déplacement afin de se diriger dans une même direction Fonctions assurées par les systèmes d intelligence en essaim Dans un contexte biologique, les processus d auto-organisation remplissent souvent des fonctions qui permettent au groupe ou à la société animale d appréhender les divers éléments de son environnement. Il est possible de regrouper ces fonctions au sein de trois grandes catégories, non exclusives l une de l autre et souvent combinées au sein d un même comportement collectif. Ces trois catégories sont la coordination, la collaboration et la délibération Coordination La coordination correspond à l organisation dans l espace et dans le temps des tâches requises pour résoudre un problème (Figure 1.6). Elle affecte la séquence temporelle et/ou la répartition spatiale des activités des individus. Par exemple, dans les essaims d abeilles (Janson et al., 2005) et de criquets (Buhl et al., 2006b), dans les vols d oiseaux (Ballerini et al., 2008)ou les bancs de poissons (Aoki, 1982), les individus alignent leur déplacement sur celui de leurs voisins. Ce comportement génère une synchronisation des changements individuels de direction (coordination temporelle) et l adoption d une direction commune de déplacement (coordination spatiale). D une manière générale, la coordination de l activité des individus est la conséquence principale des processus d auto-organisation qui sont au coeur des systèmes d intelligence en essaim. Les mécanismes de rétroaction positive, en favorisant la réalisation d une tâche à un endroit donné ou en propageant un comportement dans la population, conduisent nécessairement à une organisation spatio-temporelle des activités des individus. 21

41 1.1. INTELLIGENCE EN ESSAIM CHAPITRE 1. INTRODUCTION Figure 1.7: Exemple de collaboration dans les systèmes d intelligence en essaim. Lors de la construction du nid chez la fourmi tisserande Oecophylla longinoda, un premier groupe de fourmis assure la mise en place des feuilles, pendant qu un second groupe les connecte à l aide la soie produite par les larves Collaboration La collaboration correspond à la répartition adéquate des activités entre des individus ou des groupes d individus spécialisés dans la réalisation de l une de ces activités (Figure 1.7). On parle également de division du travail. Cette répartition des tâches peut s établir sur la base de différences morphologiques inter-individuelles : des individus aux capacités physiques différentes vont accomplir des tâches différentes. Un exemple bien connu est l existence de castes physiques chez certaines espèces d insectes sociaux. Chez les fourmis Atta coupeuses de feuilles par exemple, la taille des ouvrières est fortement corrélée aux tâches qu elles effectuent (Hölldobler & Wilson, 1990). Seules les ouvrières dont la tête dépasse 1,6 millimètres sont capables de couper les feuilles qui sont utilisées pour faire pousser le champignon qui sert de nourriture principale à la colonie. Cependant, la tête de ces ouvrières est trop grosse pour se glisser dans les galeries où pousse ce champignon. Seules les ouvrières dont la tête à une largeur d environ 0,5 millimètres en sont capables et prennent en charge la culture du champignon. La spécialisation des individus peut également être le fruit de leur expérience (Deneubourg et al., 1987; Bonabeau et al., 1998b). Des individus régulièrement confrontés à un stimulus particulier déclenchant la réalisation d une tâche particulière peuvent devenir plus sensibles à la présence de ce stimulus. Une stimulation moins importante suffira alors à déclencher la réalisation de la tâche. Tant que l intensité du stimulus reste suffisamment faible, seuls ces individus spécialistes accompliront la tâche associée. Ce mécanisme basé sur l expérience des individus semble être à l origine de l organisation du travail chez plusieurs espèces d insectes sociaux, et en particulier chez certaines guêpes sociales (Gadagkar & Joshi, 1983, 1984) et certaines espèces de fourmis (Ravary et al., 2007). 22

42 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS Figure 1.8: Exemple de délibération dans les systèmes d intelligence en essaim. Les fourmis ont accès depuis leur nid à une source de nourriture de l autre côté de ce pont dont les deux branches son de longueur identique. Elles sélectionnent cependant l une des branches sur laquelle elles établissent la majorité de leur trafic Délibération La délibération correspond à la sélection d une alternative parmi plusieurs possibilité offerte au système (Figure 1.8). On parle également de choix collectif ou de décision collective. Par exemple, l abeille mellifère Apis mellifera est capable de sélectionner la parcelle florale la plus productive grâce au recrutement d ouvrières inactives (Seeley et al., 1991). La fourmi Lasius niger est elle aussi capable de choisir parmi plusieurs sources de nourritures celle qui est la plus riche, et parmi plusieurs chemins conduisant à une source, celui qui est le plus court (Beckers et al., 1990, 1992b). Cette fonction faisant l objet du présent travail, elle sera traitée en détails dans la section 1.3 de ce mémoire. 1.2 Intelligence en essaim dans les systèmes artificiels La simplicité des principes d organisation à l oeuvre au sein des sociétés animales couplée à l importante gamme de problèmes qu ils sont capables de résoudre efficacement ont attiré depuis maintenant plus de 30 ans l attention d une communauté grandissante de chercheurs et d ingénieurs en recherche opérationnelle, en informatique ou encore en robotique. Dans cette section, nous allons plus particulièrement nous intéresser à l application de l intelligence en essaim dans les systèmes multi-robots. Avant cela, il nous semble nécessaire de faire quelques rappels historiques qui permettront de mieux positionner la robotique en essaim dans le champ plus large 23

43 1.2 SYSTÈMES ARTIFICIELS CHAPITRE 1. INTRODUCTION de l intelligence artificielle et de la robotique adaptative De l animal à l animat Intelligence artificielle Dès la fin de la seconde guerre mondiale, avec l avènement des premiers ordinateurs, est apparue une nouvelle discipline, l intelligence artificielle, dont l objectif était d étudier les conditions d émergence d une intelligence dans un système artificiel (McCarthy et al., 2006). Jusqu à la fin des années 90, cette discipline a été dominée par une approche computationnelle ou symboliste de l intelligence. En particulier, il était implicitement admis que des systèmes artificiels pouvaient se passer d organes sensoriels et moteurs pour développer des capacités cognitives aussi élaborées que celles de l être humain. La machine devait pouvoir raisonner à partir d un modèle symbolique de la tâche à accomplir ou du problème à résoudre. Cette approche s est révélée particulièrement productive, permettant le développement d applications spectaculaires. Parmi elles, on peut citer par exemple le programme GPS (pour General Problem Solver) capable de démontrer des théorèmes mathématiques complexes (Simon & Newell, 1963). Les programmes Dendral (Smith et al., 1974) et Mycin (Shortliffe, 1976) étaient quant à eux experts respectivement dans l identification de molécules chimiques et dans le diagnostique de maladies du sang. Ils étaient même susceptibles d expliquer leurs décisions, ce dont certains experts humains étaient parfois incapables. Cependant, cette approche a rapidement montré ses limites, et en particulier dans le cadre de la robotique autonome. Dès 1972, dans un livre qui fit l objet de controverses What computers can t do : The limits of Artificial Intelligence (Dreyfus, 1972), Hubert Dreyfus lui reprocha que les concepteurs devaient a priori fournir à la machine un grand nombre de connaissances humaines afin que celle-ci fonctionne correctement. De plus le sens attribué aux symboles manipulés par ces cerveaux artificiels était imposé par le programmeur qui souvent omettait des notions évidentes pour le commun, comme par exemple le fait de savoir qu un objet ne tient pas en l air tout seul ou que si l on coupe un morceau de beurre en deux, on en obtient deux, mais que si l on coupe une table en deux, on n obtient pas deux tables. Selon Dreyfus, ce sens commun s élabore sous l effet de l expérience qui ne peut être obtenu qu à travers l interaction entre les organes sensoriels, le cerveau et les organes moteurs de l organisme considéré. A la suite de cette controverse, les tentatives pour faire acquérir ce sens commun a des systèmes désincarnés (i.e., sans organe sensoriel et moteur) ont toutes échouées, car elles se sont confrontées à une augmentation exponentielle de la quantité d information à encoder. Pour cette 24

44 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS même raison, les robots (systèmes incarnés) utilisant l approche symboliste se sont révélés peu efficaces pour accomplir des tâches dans le monde réel. Le concepteur du robot devait en effet lui fournir a priori les informations nécessaires pour appréhender toutes les situations possibles du monde physique dans lequel il évoluait. Cette quantité d information était telle qu il devenait impossible dans la pratique de réaliser certaines des tâches les plus simples lorsque l environnement devenait trop bruité et imprédictible Les Animats A partir du début des années 80, une approche différente commence à se développer. Cette approche met en avant la nécessité de concevoir des systèmes capables d évoluer de manière autonome dans un environnement changeant. Pour cela, ces systèmes artificiels doivent avant tout être capables d assurer les fonctions essentielles à leur survie, comme par exemple le déplacement et l orientation dans l environnement, ou la recherche d une ressource vitale. L objectif de cette approche n est pas de concevoir des systèmes artificiels capables de raisonner à partir de symboles abstraits, mais plutôt des systèmes capables de se débrouiller dans le monde réel, comme le ferait n importe quel animal. L intelligence de tels systèmes ne repose pas sur leur capacité à résoudre formellement des problèmes. Elle réside dans la capacité de ces systèmes à atteindre leur but tout en s adaptant aux changements survenant dans l environnement. Elle se veut en cela plus proche de l éthologie et des neurosciences que l approche computationnelle, qui est, elle, plutôt liée aux sciences de l information et du calcul. Ce rapport étroit à la biologie animale a valu à ces systèmes adaptatifs qui s en inspirent explicitement le nom d Animats, pour Animaux Artificiels (Meyer & Guillot, 1991). L approche adaptative se distingue de l approche computationnelle essentiellement par le fait que le comportement du système artificiel est intimement lié à l environnement dans lequel il se déplace. On dit que de tels systèmes sont situés, c est à dire qu ils interagissent en permanence avec leur environnement. Pour cette raison, l approche adaptative met plus particulièrement en avant le couplage sensori-moteur comme le générateur principal du comportement du système. Les premiers exemples de tels systèmes remontent au début du 20ème siècle, bien avant l approche computationnelle de l intelligence artificielle. En 1912, les ingénieurs John Hammond Jr. et Benjamin Miessner conçoivent un chien électromagnétique capable de poursuivre une source lumineuse en mouvement (Hammond & Miessner, 1918). Ce robot est équipé de deux roues motrices à l avant et d une roue mobile à l arrière. Il porte également deux capteurs de lumière. Plus ces capteurs sont stimulés, plus les roues avant tournent vite. La roue arrière quant à elle 25

45 1.2 SYSTÈMES ARTIFICIELS CHAPITRE 1. INTRODUCTION s oriente de façon à ce que le robot tourne dans la direction du capteur le plus stimulé. Ce simple mécanisme de contrôle suffit à implémenter un phototropisme, c est à dire un déplacement vers une source de lumière, sans nécessiter le codage explicite de la notion de lumière ou de source ou de poursuite. Plus tard dans le siècle, en 1949 (soit un peu avant l émergence de l approche computationnelle de l intelligence artificielle), les tortues cybernétiques du neurophysiologiste William Grey Walter démontraient déjà que des mécanismes très simples permettaient de générer des comportements intelligents et relativement complexes (Holland, 2003). Grey Walter fabriqua deux exemplaires de ce qu il appelait des Machina speculatrix (machine qui cherche un but ), ELMER et ELSIE, la première étant le prototype de la seconde (Figure 1.9c). Elles possédaient toutes deux un capteur de luminosité, un capteur de choc, deux roues motrices à l arrière et une roue directionnelle à l avant. Grâce à un circuit électronique très simple, les robots cherchaient à maintenir la perception d une luminosité moyenne. Lorsque la luminosité est trop forte, les machines ralentissent ; lorsqu elle est trop faible, elles entament une exploration de leur environnement à la recherche d une source lumineuse. Ce comportement de base est combiné avec l état de charge des batteries des robots. Lorsque celles-ci sont pleines, l aversion pour la lumière est maximale ; elle diminue quand la charge baisse, et s inverse même lorsque les batteries doivent bientôt être rechargées. La zone de rechargement des batteries étant fortement éclairée, ce simple mécanisme conduit les machines à s en éloigner quand leurs batteries sont pleines et à y retourner quand il est temps de les recharger. Les robots sont donc autonomes dans la gestion de leurs réserves énergétiques. L apparente complexité de ce comportement contraste avec la simplicité du processus cognitif sous-jacent. Les robots fonctionnent selon un simple principe de stimulus-réponse qui maintient un équilibre dynamique (on parle aussi d homéostasie) entre l intensité lumineuse recherchée et la charge de la batterie. D autres machines fonctionnant sur les mêmes principes furent construites à cette époque (citons par exemple l Homeostat de William Ross Ashby ou Job, le renard électronique d Albert Ducrocq). Il semble cependant que la vague computationnelle naissante ait alors stoppé net leur carrière. Il faudra attendre 1984 pour que les véhicules de Valentino Braitenberg remettent au goût du jour de telles architectures de contrôle réactives (Braitenberg, 1984). Celui-ci a réalisé une série de 14 robots de conception très rudimentaire afin d expliquer comment certains comportements animaux pouvaient être le fruit de simples processus de type stimulus-réponse. Le plus simple d entre eux était équipé d une seule roue motrice reliée directement à un capteur de température. Le robot avançait donc d autant plus vite que la température augmentait. En 26

46 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS conséquence, il passait plus de temps dans les zones de faible température et semblait fuir les zones de haute température. En jouant sur le nombre et la position des moteurs et des capteurs, ainsi que sur le câblage entre les moteurs et les capteurs, Braitenberg pu ainsi obtenir une diversité étonnante de comportements. Enfin, les Animats prirent leur envol définitif en 1986 à la suite des travaux de Rodney Brooks (Brooks, 1986). Il développa une nouvelle façon de programmer les systèmes artificiels pour que ceux-ci agissent dans l environnement sans nécessiter la moindre représentation de concept. Au lieu de programmer des processus complexes de raisonnement à partir d une représentation symbolique de l environnement, il programme plutôt des modules comportementaux très simples et qui peuvent s activer en parallèle en fonction des données brutes reçues par les capteurs de la machine (Brooks, 1991). Il replace ainsi l interaction avec l environnement au coeur de la conception des systèmes artificiels. Il imposa finalement l idée qu un système artificiel pouvait avoir un comportement intelligent en l absence de toute représentation du monde dans lequel il évolue et sans le moindre concept des objets qu il rencontre. Aujourd hui, cette approche adaptative ou animat de l intelligence artificielle regroupe une communauté importante de chercheurs. En puisant dans les connaissances acquises en biologie sur les systèmes vivants, ils cherchent à développer des systèmes artificiels autonomes, adaptatifs et situés. Autonomes car ils doivent pouvoir atteindre leurs buts et satisfaire leurs besoins sans assistance extérieure. Adaptatifs car ils doivent pouvoir évoluer dans un environnement changeant et imprévisible. Et enfin situés car ils doivent agir dans l environnement et réagir aux stimulations que celui-ci procure De l animat à l animal L approche Animat puise largement son inspiration dans les résultats obtenus dans le domaine biologique pour concevoir des plateformes robotiques. Elle implémente donc, plus ou moins fidèlement, des modèles du fonctionnement biologique de l animal dont elle s inspire. Si cette implémentation est généralement tournée vers le développement d une application robotique, avec ses objectifs et ses contraintes propres, elle permet néanmoins de valider sur le principe les hypothèses biologiques sous-jacentes. Dans ce cas, les considérations biologiques sont secondaires par rapport aux considérations technologiques. Cependant, un certain nombre de travaux de robotique mettent au coeur de leur démarche la validation d une hypothèse biologique. L objectif premier est alors de tester un modèle biologique à travers son implémentation sur une plateforme robotique et de proposer éventuellement 27

47 1.2 SYSTÈMES ARTIFICIELS CHAPITRE 1. INTRODUCTION Figure 1.9: Six exemples d Animats. (a) Le robot Genghis développé par Rodney Brooks (Brooks & Flynn, 1989). (b) Le robot Sahabot développé par Lambrinos et al. (2000) pour tester les hypothèses sur la navigation de la fourmi Cataglyphis. (c) William Gray Walter et son robot ELSIE rentrant à son poste de rechargement (Holland, 2003). (d) Le robot Insbot développé dans le cadre du projet européen Leurre pour interagir avec un groupe de blatte Periplaneta americana (Halloy et al., 2007). (e) Le robot Octave développé dans le laboratoire de Nicolas Franceschini embarque un système de pilotage inspiré des capacités de navigation de la mouche (Franceschini et al., 2007). (f) Le robot Alice développé par Gilles Caprari (Caprari & Siegwart, 2005) et utilisé dans les travaux de cette thèse. 28

48 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS de nouvelles hypothèses sur le fonctionnement de l animal. Par exemple, les travaux robotique de Lambrinos et al. (1997, 2000) ont permis de vérifier la plausibilité d un certain nombre d hypothèses sur les mécanismes de navigation de la fourmi du désert Cataglyphis (voir Figure 1.9b). Ils ont notamment permis de tester l efficacité (1) pour la navigation à longue distance d un compas basé sur le pattern céleste de lumière polarisé et (2) pour la recherche du nid d une stratégie basée sur la mémorisation d instantanés photographiques comme points de repères. Dans chacun des cas (1) et (2), ces travaux ont conduit à la proposition de mécanismes alternatifs, plus simples ou plus efficaces, compatibles avec les connaissances sur cette espèce. Grâce à des plateformes robotiques, (Franceschini et al., 1992) ont testé la validité de leurs hypothèses concernant la circuiterie neuronale à l origine de la perception du mouvement chez la mouche. A l aide de divers robots mobiles (voir Figure 1.9e), ils ont pu ainsi montrer son efficacité dans la réalisation de tâches telles que l évitement des obstacles ou le maintien d une altitude. A partir de leurs résultats, ils ont également proposé une explication à certains comportements jusque-là inexpliqués chez cet insecte (Franceschini et al., 2007). Ces deux exemples, parmi beaucoup d autres, illustrent la capacité des systèmes robotiques à produire des résultats pertinents sur des questions biologiques. Néanmoins, d autres solutions existent pour implémenter et tester des modèles biologiques, comme la modélisation mathématique ou la simulation informatique. Il est alors légitime de se demander quelle peut être la valeur ajoutée de l expérimentation robotique? (Webb, 2000, 2001) Il n est pas question ici de rejeter une méthode ou de faire du prosélytisme aveugle pour une autre. Dans la réalité, leurs qualités et leurs défauts sont complémentaires, et pour cette raison elles sont bien souvent associées au sein d un même projet de recherche. L objectif de cette section est plutôt de dégager certaines qualités de l approche robotique des théories biologiques qui justifient son emploi en tant qu outil au service d une meilleure compréhension des systèmes vivants. Le robot est intégré dans un environnement réel Rodney Brooks disait que le monde est son meilleur modèle. Dans son contexte original, cette phrase signifiait qu un robot ne devait pas raisonner sur un modèle abstrait de son environnement, mais directement sur les entrées sensorielles en provenance de l environnement. Dans le contexte qui nous intéresse ici, cette phrase prend un sens nouveau. Un modèle mathématique ou une simulation informatique sont des abstractions à la fois de l animal étudié et de l environnement dans lequel il évolue. Bien souvent, le travail de modélisation se concentre principalement sur les caractéristiques de l animal (qui est l objet de l étude) et bien 29

49 1.2 SYSTÈMES ARTIFICIELS CHAPITRE 1. INTRODUCTION moins sur son environnement (qui ne l est pas). Il en résulte une très grande simplification de ce dernier : un modèle de fourragement alimentaire peut se trouver réduit à deux boîtes, l une pour le nid, l autre pour la nourriture, reliées par une double flèche correspondant au trajet entre les deux. Si pour un certain nombre de modèles, cette simplicité ne détériore pas ou peu leurs capacités explicatives et prédictives, pour d autres, cela peut se révéler critique, en particulier lorsque la forme de l individu est susceptible de modifier son interaction avec l environnement. Par exemple, un animal placé dans un courant d eau ou d air à la recherche de la source d une odeur perturbe fortement l écoulement du fluide autour de lui et donc la répartition de l odeur (Grasso et al., 2000; Hayes et al., 2002). Modéliser cette perturbation peut se révéler très difficile alors même qu elle joue un rôle majeur dans la capacité de l animal à retrouver la source de l odeur. L utilisation d un robot peut alors constituer un bon moyen de se dispenser de la modélisation de l environnement pour se concentrer uniquement sur la modélisation des mécanismes cognitifs que l animal met en place pour remonter l odeur et qui sont finalement l objet principal de l étude. Le robot nécessite une spécification complète Dans une simulation informatique, il est par exemple possible d utiliser les coordonnées cartésiennes de l environnement pour calculer rapidement la distance entre deux animaux virtuels. Il est également possible de simuler leur déplacement à l aide de translations et de rotations. Il n est donc pas nécessaire de préciser le processus par lequel chaque individu perçoit son environnement ou agit sur lui. De cette manière, la simulation permet de s affranchir des problèmes sensoriels et moteurs qui peuvent sembler superflus et se concentrer sur la spécification du comportement de l animal virtuel. Pour que le robot fonctionne en revanche, il est nécessaire de spécifier complètement ses capacités sensorielles, cognitives et motrices. Pour que le robot détecte la présence d un obstacle, il a besoin de capteurs de distance. La répartition de ses capteurs autour du corps du robot peut avoir une incidence sur la détection des obstacles : deux capteurs trop espacés par exemple créent un angle mort qui ne permet plus de détecter un obstacle situé dans cette zone (Maris & Boeckhorst, 1996). En conséquence, l organisation des capteurs, mais aussi leur qualité, ne permettent pas toujours d assurer des conditions optimales de mesure telles qu elles pourraient être obtenues en simulation. Les mêmes remarques s appliquent également à la partie motrice du robot. Le nombre de roues, le type de pattes ou la coordination des moteurs sont autant de facteurs qui peuvent affecter le comportement final du robot. A première vue, de tels arguments sont en défaveur de l utilisation des robots comme modèles d animaux. La spécification complète de toutes les parties du robot peut sembler une perte de 30

50 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS temps inutile par rapport à la souplesse d utilisation de la simulation. Cependant, il ne faut pas perdre de vue que cette obligation force le chercheur à concevoir le comportement du robot (et donc de l animal) comme une intégration de facteurs sensoriels, cognitifs et moteurs, le tout en interaction étroite avec la structure de l environnement comme il a été dit plus haut. En supportant cette vision intégrée du comportement, le robot rappelle que le traitement cognitif est couplé à des mécanismes sensoriels et moteurs, et que la nature de ce couplage peut être primordial dans l exécution d un comportement. Le robot peut interagir avec l animal Comme il a été souligné à plusieurs reprises, le robot est une incarnation d un modèle animal dans le monde réel. Il peut donc interagir avec les différents éléments de l environnement, y compris avec l animal dont il est le modèle. A la manière des leurres utilisés par Tinbergen pour étudier le comportement de l épinoche, le robot permet de tester des hypothèses particulières sur le comportement de l animal. Par exemple, un dispositif électromécanique imitant la danse de l abeille mellifère Apis mellifera a permis d étudier la nature des signaux critiques impliqués dans la communication de la position d une source de nourriture chez cet insecte (Michelsen et al., 1992). De la même façon, Böehlen (1999) ou plus récemment Fernandez-Juricic et al. (2006) ont utilisé de tels dispositifs mécaniques pour étudier la réponse de groupes d oiseaux à différent signaux. Enfin, Reaney et al. (2008) ce sont servis de modèles robotiques du crabe mâle Uca mjoebergi pour étudier les signaux de cour pris en compte par la femelle lors du choix de son partenaire sexuel. Chez l Homme, le récent développement de robots possédant des expressions et des traits humains a permis de tester des hypothèses sur la perception des émotions. Des études récentes suggèrent également que ce type de robots pourrait aider des enfants atteints de difficultés d apprentissage ou d autisme à former des relations et à développer des aptitudes sociales (Dautenhahn, 2003). Dans ces exemples, le robot est sous le contrôle d un opérateur humain qui décide de ses moindres actions. Mais des robots autonomes ont également été développés dans le but d interagir avec des groupes animaux et de modifier leur comportement. Le travail de Vaughan et al. (2000) a par exemple conduit à la création d un robot chien de berger capable de contrôler les déplacements d un troupeau d oies dans une arène expérimentale. Judicieusement camouflé, le robot peut également s infiltrer au sein d un groupe social et influencer son comportement de l intérieur. A cet égard, le récent projet Leurre en est pour l instant l illustration la plus aboutie (Caprari et al., 2005). Couvert par l odeur de la blatte 31

51 1.2 SYSTÈMES ARTIFICIELS CHAPITRE 1. INTRODUCTION Periplaneta americana, des petits robots autonomes, les Insbots (voir Figure 1.9d), sont capables d intégrer un groupe de ces insectes. En jouant sur le fort mimétisme de cet animal, ces robots peuvent modifier le choix d un abri par le groupe. Ils peuvent ainsi favoriser la sélection d un abri habituellement évité par les blattes (Halloy et al., 2007) Applications de l intelligence en essaim Pendant que l intelligence artificielle faisait sa révolution, les premiers travaux sur l intelligence collective des sociétés animales commençaient à s accumuler. Ils montraient qu une organisation complexe pouvait émerger des multiples interactions entre des individus au comportement simple. Ces observations biologiques ont tout naturellement reçu un écho dans la communauté Animat naissante. Plus largement, ils se sont diffusés dans la communauté informatique et robotique. Par leurs capacités à résoudre de façon décentralisée des problèmes a une échelle bien supérieure à celle de l individu, à s adapter de façon dynamique aux changements de l environnement et à optimiser leurs comportements, les groupes animaux ont rapidement attiré l attention des concepteurs de systèmes artificiels. En particulier, les résultats des travaux scientifiques à leur sujet sont devenus une source d inspiration pour le développement d applications nouvelles dans au moins trois domaines : l animation graphique, les algorithmes d optimisation et la robotique collective. Nous passerons rapidement sur les deux premiers, et nous nous étendrons plus longuement sur le troisième, en rapport direct avec mon travail de thèse Animation graphique : les Boids et leurs descendants L animation graphique a probablement été la première discipline à s inspirer des découvertes réalisées sur l organisation décentralisée des sociétés animales. Dès 1986, Craig Reynolds, s inspirant de résultats récents sur la formation des bancs de poissons et des vols d oiseaux, réalise une application graphique dans laquelle des agents, qu il appelle Boids (voir Figure 1.10), se déplacent de manière cohérente dans un environnement virtuel (Reynolds, 1987). Dans cette simulation, chaque Boid agit de manière autonome, et en fonction des stimuli qu il reçoit de son environnement proche. Le comportement d un Boid suit un jeu de règles très simples. Trop près d un autre Boid, il cherche à s en éloigner. Trop loin du groupe, il cherche à se rapprocher de ses plus proches voisins. Enfin, il cherche en permanence à ajuster sa vitesse de déplacement à la vitesse moyenne de ses voisins et à éviter les obstacles qui se présentent face à lui. A partir de ses 4 règles comportementales, Reynolds parvient à obtenir des animations graphiques dans lesquelles le comportement du groupe ressemble tantôt à celui d un vol d oiseau, tantôt à celui 32

52 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS Figure 1.10: Captures d écran montrant un essaim de Boids se déplaçant à travers un champ de colonnes (repris depuis Langton, 1987). d un banc de poisson, ou encore à celui d un troupeau de Mammifères en fonction du poids relatif de chaque règle. Grâce à leur simplicité et à la gamme étendue des comportements collectifs qu ils permettent, les principes utilisés par Reynolds pour concevoir ses Boids sont toujours utilisés de nos jours pour animer le déplacement de foules d animaux dans de nombreux films à grand succès. Citons pour l exemple Le Roi Lion et la trilogie du Seigneur Des Anneaux parmi les plus connus Algorithmes d optimisation Comme nous l avons vu précédemment, les sociétés animales sont capables de sélectionner l alternative la plus avantageuse pour le groupe dans un grand nombre de situations. Les fourmis par exemple sélectionnent le chemin le plus court qui relie leur nid à une source de nourriture. Ou bien encore, elles sélectionnent la source de nourriture la plus riche parmi un ensemble de sources disponibles. Elles réalisent tout cela grâce au dépôt d une trace chimique volatile le long de leur trajet. Ce principe très simple a été repris au début des années 90 par Marco Dorigo pour développer des algorithmes d optimisation de trajet et des algorithmes de routage dans des réseaux (Dorigo et al., 1996; Dorigo & Gambardella, 1997; Dorigo et al., 1999; Bonabeau et al., 33

53 1.2 SYSTÈMES ARTIFICIELS CHAPITRE 1. INTRODUCTION Figure 1.11: L algorithme «Ant System» appliqué au problème du voyageur de commerce permet de sélectionner un tour permettant de traverser chaque ville une seule fois, tout en minimisant la distance totale parcourue. 1999; Dorigo et al., 2000). Schématiquement, ces algorithmes fonctionnent tous de la manière suivante, avec des additions spécifiques en fonction du problème traité. Des fourmis virtuelles sont relâchées dans un réseau (réseau de télécommunication ou de villes par exemple) à la recherche d un chemin optimal (le plus rapide entre deux noeuds du réseau ou le plus court reliant tous les noeuds par exemple, voir Figure 1.11). Quand l une de ces fourmis découvre une solution possible, elle dépose le long du chemin suivi une quantité de phéromone virtuelle qui dépend de la qualité de la solution (par exemple, la durée totale du trajet). Les chemins optimaux recherchés seront donc en moyenne plus marqués que les autres. Les fourmis qui seront relâchées sur le réseau par la suite seront influencées par ces dépôts : plus le lien entre deux noeuds sera marqué, plus les fourmis virtuelles auront tendance à l emprunter et à le renforcer s il satisfait leurs critères. Un mécanisme d évaporation de la phéromone virtuelle vient compléter le processus. Il efface petit à petit les chemins les moins empruntés et renforce ainsi le contraste entre les bonnes et les mauvaises solutions. Entre autres, ces algorithmes dits d optimisation par colonie de fourmis ont été et sont encore utilisés pour optimiser le routage des télécommunications chez British Telecom et MCI-Worldcom, ou pour optimiser la planification des trajets des camions de transport d essence dans la partie italienne de la Suisse (Bonabeau et al., 2000). Les bancs de poissons et les vols d oiseaux ont également inspirés la conception des algorithmes dits d optimisation par essaim particulaires. Comme nous l avons vu précédemment, ces animaux se déplacent de manière cohérente au sein de grands groupes. Pour assurer cette cohérence, ils ajustent en permanence leur déplacement sur celui de leurs voisins, un peu à la manière des Boids de Reynolds. Nous avons vu également que la présence de quelques individus dont le déplacement est orienté vers un but précis peut suffire à conduire l ensemble du groupe vers ce but. Grâce au comportement d ajustement de la trajectoire, la direction suivie par ces individus 34

54 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS se propage à leur voisins puis de proche en proche à l ensemble du groupe. C est ce principe très simple qui a été exploité par Eberhart et Kennedy à partir de 1995 pour concevoir un algorithme d optimisation de fonctions non-linéaires (Kennedy & Eberhart, 1995; Eberhart et al., 2001). Ces algorithmes, proches sur le principe des méthodes d évolution artificielle, sont utilisés essentiellement pour rechercher les extrema d une fonction inconnue. Ils fonctionnent schématiquement de la manière suivante. Des particules mobiles sont relâchées aléatoirement à l intérieur de l espace des solutions de la fonction étudiée. Ces particules évaluent la qualité de la solution au point où elles se trouvent. Chacune d entre elles retient tout au long de son déplacement la meilleure solution rencontrée et sa position appelée p best, et a accès à la meilleure solution rencontrée par les particules voisines et à sa position l best. A chaque pas de temps, les particules modifient leur vecteur de déplacement en direction de la position de p best et de la position de l best. En général, les particules finissent par converger autour d un point qui correspond à la meilleure approximation de la solution recherchée. Les abeilles ont pour leur part inspiré un processus d optimisation pour l allocation dynamique de ressource. Lorsqu une abeille découvre une source de nourriture, elle rentre à sa ruche où elle entame une danse en forme de 8 (Lindauer, 1951, 1953, 1955). A travers cette danse, elle informe les abeilles voisines de la présence et de la localisation d une source de nourriture. Celles-ci peuvent alors s envoler pour aller exploiter la source. A leur retour, elles pourront éventuellement danser à leur tour pour recruter de nouvelles ouvrières. Comme chez les fourmis donc, un processus d amplification se met en place pour établir un pont aérien entre la ruche et la source de nourriture. Mais à la différence des fourmis, aucune trace chimique ne perdure dans le temps. Le nombre d abeilles recrutées vers une source de nourriture dépend uniquement du temps total passé par les recruteuses à danser. Et ce temps total est directement lié à la qualité de la source et à sa distance à la ruche. Lorsque plusieurs sources sont découvertes en même temps, ce mécanisme permet d allouer à chacune d entre elles une fraction des ouvrières disponibles en fonction de l intérêt de la source (Seeley, 1995). Un processus similaire a été mis en oeuvre récemment pour allouer de façon dynamique des serveurs à des sites internet, en fonction de la demande fluctuante des internautes (Nakrani & Tovey, 2004, 2007). Chaque site internet produit un avertissement qui attire les serveurs disponibles, et la durée de cet avertissement est, à l instar de la danse des abeilles, proportionnelle au nombre d utilisateurs connectés au site. Ainsi, la charge des serveurs est efficacement répartie entre les différents sites internet de manière à réduire les temps d attente sur les sites surchargés. Enfin, le mécanisme qui permet aux fourmis Leptothorax unifasciatus de trier leur couvain 35

55 1.2 SYSTÈMES ARTIFICIELS CHAPITRE 1. INTRODUCTION a inspiré la conception d un algorithme permettant d optimiser l exploration d une grande base de données afin de regrouper des éléments aux caractéristiques proches. A l intérieur de son nid, cette fourmi sépare les éléments du couvain en fonction de leur âge : elle regroupe les oeufs et les microlarves au centre d une surface donnée, les larves les plus âgées à la périphérie et les pupes et les prépupes entre les deux (Franks & Sendova-Franks, 1992). Une explication à ce phénomène serait la suivante : lorsqu une fourmi transporte un élément du couvain, elle le dépose préférentiellement auprès d éléments du même âge ; inversement, lorsqu elle ne transporte rien, elle aura tendance à attraper un élément du couvain s il est entouré d éléments plus jeunes ou plus âgés (Deneubourg et al., 1991). En s inspirant de ce principe très simple, Erik Lumer et Baldo Faieta ont conçu un outil capable de regrouper au sein d une base de données de clients par exemple ceux possédant des caractéristiques d âge, de sexe, de situation familiale, etc, similaires (Lumer & Faieta, 1994). Chaque individu dans la base donnée est représenté dans un espace bi-dimensionnel sur lequel des fourmis virtuelles se déplacent. Lorsqu elles rencontrent un utilisateur entouré d utilisateurs aux caractéristiques différentes, elles le déplacent vers des utilisateurs possédant des caractéristiques communes. Au final, les individus les plus ressemblants se retrouvent proches les uns des autres Robotique collective La robotique collective a pour objectif l étude des algorithmes de contrôle permettant d organiser l activité simultanée de plusieurs robots afin d atteindre un but. Cette coordination peutêtre atteinte par des processus centralisés. Les robots se réfèrent alors constamment à un coordinateur chargé d établir la stratégie pour atteindre le but fixé. Si cette approche s est révélée particulièrement efficace pour l organisation de petits groupes de robots, elle ne peut plus fonctionner lorsque le nombre de robots à contrôler devient trop important. La multiplication des transferts d information entre le coordinateur et les membres du groupe et l augmentation de la quantité totale d informations à traiter par le coordinateur réduit fortement les possibilités d un contrôle efficace en temps réel. Pour contourner ce problème, une partie des travaux de robotique collective se sont inspirés dès le début des années 90 des mécanismes de contrôle distribué à l oeuvre au sein des sociétés animales et plus particulièrement des sociétés d insectes. Cette branche de la robotique collective s appelle la robotique en essaim. Elle s intéresse plus largement aujourd hui à la coordination de robots à l aide de processus d auto-organisation. Ces processus possèdent plusieurs qualités qui les rendent attractifs. Premièrement, un comportement collectif complexe peut émerger de la combinaison des actions d individus relativement 36

56 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS simples. En robotique, cela permet d envisager l utilisation de robots peu sophistiqués, plus faciles à concevoir, éventuellement moins coûteux et susceptibles d être miniaturisés. Deuxièmement, les processus d auto-organisation mettent souvent en jeu de nombreux individus aux capacités proches, voire identiques. Cette redondance procure une certaine robustesse au système : si un robot n est pas en mesure d assurer une fonction ou s il disparait, il peut être remplacé facilement par un autre. De cette façon également, la performance du groupe ne sera pas affectée de façon brutale par des variations du nombre de robots. Depuis le début des années 90, la robotique en essaim s est développée en même temps que les connaissances sur l auto-organisation des sociétés animales. Elle a donc pu profiter des outils développés pour mieux comprendre l organisation des groupes animaux. En particulier, la modélisation et la simulation ont permis de faire avancer de manière significative les recherches dans ce domaine. Cependant, en robotique comme en biologie, la réalisation d expériences est essentielle pour valider les résultats issus de modèles numériques ou analytiques. En effet, ceux-ci peuvent facilement occulter des paramètres fondamentaux du système réel et compromettre ainsi le comportement global du groupe. En implémentant les algorithmes sur des plateformes réelles, on s assure du bien-fondé de l approche et de l efficacité du système dans un environnement réel. Dans ce but, plusieurs plateformes technologiques ont été développées, parmi lesquelles ont peut citer les plus miniaturisés que sont les robots Khepera 2, epuck 3, Jasmine 4 et Alice (utilisée dans les travaux de robotique de cette thèse, Caprari & Siegwart, 2005). L avancée des expérimentations est un indice significatif des progrès réalisés par le champ de la robotique en essaim. En conséquence, nous nous intéresserons plus particulièrement dans la suite de cette section aux travaux expérimentaux les plus représentatifs de la vitalité de ce champ de recherche. Nous traiterons ce sujet en séparant ces travaux selon le comportement collectif étudié : agrégation, ségrégation, dispersion, couverture spatiale, localisation de cibles, déplacements coordonnés, manipulations coopératives, allocation de tâches, fourragement et prises de décisions collectives Agrégation L agrégation correspond au regroupement d objets ou d individus initialement dispersés dans l environnement. Ce comportement a fait l objet d une expérience réalisée par Ralph Beckers en 1994 à l Université de Bielefeld et considérée comme fondatrice de la robotique en essaim (Beckers et al., 1994). Dans cette expérience, des robots mobiles équipés d un poussoir en forme de U se

57 1.2 SYSTÈMES ARTIFICIELS CHAPITRE 1. INTRODUCTION Figure 1.12: Illustrations des différentes tâches accomplies par des systèmes de robotique en essaim. (a) Aggrégation. Dans cette expérience de Beckers et al. (1994), les robots doivent regrouper des palets. (b) Ségrégation. Dans cette expérience de Melhuish et al. (2001), les robots ségrègent les disques en fonction de leur couleur, les noirs au centre, les blancs en périphérie et les noirs et blancs entre les deux. (c) Dispersion. Dans cette expérience de Schwager et al. (2006), la densité des robots en un point de l espace dépend de l intesité lumineuse perçue en ce point. (d) Couverture spatiale. Dans cette expérience de Correll et al. (2008), les robots doivent inspecter l ensemble des pâles d une turbine le plus rapidement possible. (e) Localisation de cibles. Dans cette expérience de Hayes et al. (2002), les robots coopèrent pour retrouver l origine d une source d odeur. (f) Déplacement coordonné. Dans cette expérience de Campo et al. (2006), les robots coordonnent leurs déplacements afin d amener un objet vers une cible. (g) Allocation de tâches. Dans cette expérience de Labella et al. (2006), les robots régulent leur probabilité de s engager dans une tâche de fourragement en fonction de la disponibilité dans l environnement des objets à récupérer. (h) Manipulations coopératives. Dans cette expérience de Martinoli (1999), deux robots coopèrent pour extraire une tige de bois d un trou. 38

58 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS déplacent dans une arène carrée contenant 81 palets circulaires dispersés de manière régulière. Lorsque le robot rencontre l un de ces palets, il le pousse devant lui. Lorsque trois palets au moins s accumulent au niveau du poussoir, un capteur de force placé derrière celui-ci déclenche une marche arrière suivi d une rotation selon un angle aléatoire (voir Figure 1.12a). De cette façon, les palets sont libérés du poussoir et le robot reprend sa marche en ligne droite. Ainsi, de petits agrégats de trois palets se forment rapidement en tout début d expérience. Lorsqu un robot poussant un ou deux palets rencontre l un de ces agrégats, le capteur de force est activé et le robot libère ses palets. L agrégat initial croît donc d une ou deux unités supplémentaires. Le nombre de palets solitaires diminue ainsi très rapidement. Les robots peuvent également retirer un ou deux palets à un agrégat. Cependant, seuls les palets en contact avec un petit nombre d autres palets voisins peuvent être retirés car ils ne sont pas susceptibles de déclencher le capteur de force. Plus les agrégats grandissent, plus les palets qu ils contiennent ont de chances d avoir des voisins. En conséquence, la probabilité qu un palet soit retiré d un agrégat par un robot diminue avec la taille de l agrégat. Inversement, la probabilité qu un palet soit ajouté à un agrégat grandi avec la taille de l agrégat. En effet, plus l agrégat est important, plus il est susceptible de déclencher le capteur de force du robot, et donc la libération des palets. On retrouve ici une double boucle de rétroaction positive : plus un agrégat est de grande taille, plus la probabilité qu un robot y dépose un palet augmente, et plus la probabilité qu un robot retire un palet diminue. L amplification qui résulte de ce processus stigmergique conduit à une compétition entre les agrégats formés en tout début d expérience. Très rapidement, cela conduit à la disparition d un grand nombre d entre eux dont les palets sont transportés vers des agrégats plus importants. Finalement, un seul agrégat composé des 81 palets de départ subsiste à la fin de l expérience. Deux ans plus tard, Maris & Boeckhorst (1996) ont montré que l agrégation d objets pouvait également être obtenu comme une conséquence de la forme des robots. Ils utilisent dans leurs expériences des robots Didabots possédant deux capteurs de distance à l avant-gauche et à l avant-droit, placés de telle sorte qu il existe un angle mort entre eux. Les robots ne présentent que deux comportements : rouler en ligne droite en absence de signal sur les capteurs de distance, et tourner pour éviter un obstacle si l un des capteurs de distance est activé. En raison de l angle mort entre les deux capteurs, tout objet placé à l intérieur de cet angle mort ne sera pas détecté et sera poussé par le robot. Si pendant que le robot déplace l objet, il détecte un autre objet, un mur ou un autre robot, il effectue une manoeuvre d évitement dont le résultat est la libération 39

59 1.2 SYSTÈMES ARTIFICIELS CHAPITRE 1. INTRODUCTION de l objet poussé. Si l objet poussé est libéré à côté d un autre objet, alors un agrégat se forme et peut éventuellement grandir selon des principes très proches de ceux décrits dans l expérience de Beckers et al. (1994). En fin d expérience, les robots finissent par agréger tous les objets en un seul tas, sans nécessiter un algorithme de contrôle complexe et comme la conséquence de la structure physique des robots. Les travaux de Gaussier & Zrehen (1994) fonctionnent selon le même type de principe. Pour conclure, il faut souligner que l étude de Beckers et al. (1994) démontra pour la première fois que les principes de l intelligence en essaim pouvaient être appliqués en robotique collective. Bien que le comportement étudié soit très simple, il présentait déjà toutes les caractéristiques des processus d intelligence en essaim : contrôle décentralisé, comportements individuels basés sur une information locale et partielle, et émergence d une structure par auto-organisation. Un grand nombre de travaux ont par la suite présentés des expériences basées sur les mêmes principes, permettant aujourd hui de considérer la robotique en essaim comme un champ de recherche à part entière Ségrégation La ségrégation correspond à la formation de groupes d objets ou d individus homogènes selon un ou plusieurs critères. Chez les insectes sociaux, on retrouve des comportements de ségrégation chez certaines espèces de fourmis qui séparent les éléments du couvain en fonction de leur stade de développement (Franks & Sendova-Franks, 1992; Sendova-Franks et al., 2004). Cette ségrégation peut conduire à la formation de plusieurs tas séparés contenant des éléments de même stade. On parle alors de ségrégation en patch. Elle peut également conduire à une structuration en forme d anneaux concentriques, avec les premiers stades de développement au centre du nid et les derniers en périphérie. On parle ici de ségrégation en anneaux. Ces deux types de ségrégation ont été explorés dans des expériences de robotique en essaim. La ségrégation en patch a été étudiée par Melhuish et al. (2001). Dans leurs expériences, les robots doivent séparer des palets de couleurs différentes en tas de couleur identique. Ces robots sont équipés d une sorte de mâchoire pour attraper les palets et de capteurs permettant de détecter la couleur du palet transporté et des palets rencontrés pendant le déplacement. Si un robot rencontre un palet, il l attrape pour le transporter. Au cours du transport, si le robot détecte un autre palet, il compare la couleur du palet transporté avec celle du palet rencontré. Si celles-ci sont différentes, alors le robot effectue une manoeuvre d évitement et s éloigne. Si elles sont identiques, alors il relâche le palet transporté et s éloigne. De cette manière, les palets de 40

60 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS même couleur sont peu à peu regroupés en petits agrégats homogènes. Comme dans l expérience d agrégation de Beckers et al. (1994), les agrégats de grande taille ont plus de chances de survivre que les agrégats de petite taille et une compétition entre les agrégats de même couleur conduit au final à la formation d autant d agrégats qu il y a de couleurs à trier. Dans l expérience de Melhuish et al. (2001), les robots sont ainsi capables de ségréger trois couleurs différentes (voir Figure 1.12b), mais des simulations montrent qu ils sont en théorie capables d en ségréger au moins sept différentes. La ségrégation en anneaux a été étudié dans Melhuish et al. (1998). Dans leurs expériences, ils utilisent un mécanisme très différent de la ségrégation en patch pour séparer les différents objets au sein d un même agrégat. Comme dans les expériences d agrégation précédentes, un robot libère un palet s il entre en contact avec un obstacle. Mais avant de relâcher le palet, il effectue une marche arrière dont la distance dépend de sa couleur : si le palet est rouge, le robot ne recule pas et le libère immédiatement ; s il est jaune, il recule sur une distance préalablement fixée puis relâche le palet. De cette manière, les palets rouges ont une probabilité plus importante de se retrouver au centre de l agrégat que les palets jaunes. Cette simple différence dans le comportement de dépôt des robots suffit à obtenir en fin d expérience un agrégat unique de palets, avec les palets rouges regroupés au centre et entourés à la périphérie par les palets jaunes. Plus tard, Wilson et al. (2004) ont perfectionné cet algorithme de ségrégation et ont montré qu il était possible d obtenir la séparation de plus de deux types d objets différents au sein d un même agrégat Exploration L exploration de l environnement est probablement l une des tâches les plus étudiées dans le champ de la robotique en essaim. Cette tâche peut être divisé en trois parties : dispersion, couverture et localisation de cibles. Dispersion La dispersion correspond à une répartition spatiale des robots afin de couvrir au mieux une aire donnée. En général, les algorithmes de dispersion sont utilisés pour établir un réseau de communication ou de senseurs robotiques distribués. La façon dont l aire est couverte par les robots peut varier avec le profil du terrain et la tâche à accomplir. Par exemple, dans une expérience récente de Schwager et al. (2006), la répartition de robots dans l environnement doit suivre la répartition d une caractéristique de l environnement (voir Figure 1.12c). L objectif est que la densité des robots soit plus importante dans les aires où cette caractéristique environnementale s exprime majoritairement. On peut voir cela comme une 41

61 1.2 SYSTÈMES ARTIFICIELS CHAPITRE 1. INTRODUCTION approximation de la fonction de densité de la caractéristique étudiée. Pour arriver à ce résultat, chaque robot est capable de calculer sa cellule de Voronoi (portion de territoire qui est plus proche de lui que de tout autre robot) à partir de l estimation de la position de ses voisins proches. Il calcule également la position du barycentre de sa cellule de Voronoi, et pondère cette position par une estimation de l intensité et du gradient de la caractéristique étudiée. Enfin, il se dirige vers ce barycentre. En itérant cette démarche sur plusieurs pas de temps, les robots ajustent leur position à celle de leur voisin. Ils finissent par se stabiliser autour d une position donnée et la mesure de la densité des robots s accordent alors avec la densité réelle de la caractéristique environnementale étudiée. De nombreux autres algorithmes de dispersion décentralisés existent et permettent d obtenir des configurations adaptées à une situation donnée. Dans McLurkin & Smith (2007) par exemple, un algorithme distribué est proposé pour obtenir une dispersion uniforme des robots dans des environnements complexes. Couverture spatiale La couverture correspond à l exploration systématique de l ensemble des points d une région. Les algorithmes de couverture trouvent leur utilité dans des tâches aussi diverses que le déminage, l inspection, le nettoyage ou encore la tonte du gazon. Dans un travail récent, Correll et al. (2008) propose et teste expérimentalement un algorithme auto-organisé permettant l inspection systématique des pales d une turbine par un groupe de petits robots autonomes (voir Figure 1.12d). A l intérieur de la turbine (en réalité une arène expérimentale qui mime l intérieur d une turbine), les robots se déplacent de manière aléatoire dans un premier temps. Lorsqu ils détectent une pale, ils commencent à tourner autour en suivant les bords puis la quitte au bout d un certain temps. Pendant qu un robot inspecte une pale, il émet dans le même temps un signal qui empêche les autres robots dans un rayon donné de commencer la détection d une pale. Ce signal favorise également le départ d autres robots qui inspecteraient éventuellement la même pale. Grâce à cette interaction répulsive, les robots se dispersent de manière plus homogène sur l ensemble des pales, ce qui réduit le temps nécessaire pour explorer l ensemble de la turbine. Localisation de cibles La localisation de cible est la dernière étape de l exploration de l environnement. Il s agit ici de retrouver un ou plusieurs objets dispersés dans l environnement. Cette tache peut avoir de nombreuses variantes, dépendantes de la nature de la cible et de la manière de la localiser. La plupart des travaux explorant cette question se sont pour le moment limités à l analyse de modèles numériques ou analytiques. Il n existe que peu d exemples d implémentation 42

62 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS dans des groupes de robots. Cependant, ce problème fait l objet d une étude expérimentale de Hayes & Dormiani-Tabatabaei (2002) concernant la localisation d une source d odeur par un essaim de robots (voir Figure 1.12e). Dans ce travail, les robots se déplacent dans leur environnement à la recherche d une trace odorante. Lorsque l un d entre eux détecte une odeur, il mesure la direction du vent et le remonte. S il perd la trace de l odeur, il entame de nouveau un cycle de recherche. Un robot qui a détecté une odeur émet également un signal qui attire vers lui ceux qui sont encore à la recherche d une trace odorante. Grâce à ce recrutement, la probabilité de retrouver la source de l odeur augmente Déplacements coordonnés Les robots doivent ici adopter une direction commune afin de se déplacer en groupe. Les travaux de simulation sur cette question ce sont largement basés sur les modèles théoriques des déplacements de bancs de poissons ou de vols d oiseaux, et en particulier sur les travaux de Reynolds (1987). Dans cette situation, les robots doivent être capables d estimer très fréquemment la direction de déplacement des autres membres du groupe afin que celui-ci reste cohérent. Cependant, la fréquence de rafraichissement et la précision des dispositifs actuels de positionnement relatif embarqués rend l implémentation de l algorithme de Reynolds très problématique. Un travail récent de Pugh & A. Martinoli (2006) est néanmoins parvenu à l utiliser en limitant la vitesse de leurs robots à 10 cm/s (les robots font 24 cm de diamètre). Une autre solution proposée dans le cadre du projet Swarm-Bot (Baldassarre et al., 2007) consiste à lier physiquement les robots les uns aux autres. De cette manière, la cohésion du groupe est assurée. Pour déterminer la direction de déplacement du groupe, les robots perçoivent la force de traction qui leur est imposée par le reste du groupe. Ils alignent alors leur châssis sur la direction de cette force qui est une bonne approximation de la direction générale de déplacement du groupe. Ainsi, tous les robots convergent rapidement vers une direction commune et la maintienne. Une solution intermédiaire aux deux précédentes a été proposée par (Campo et al., 2006). Les robots sont toujours physiquement connectés comme précédemment, mais ils indiquent par un jeu de lumière la direction de leur déplacement. Les robots étant équipés d une caméra panoramique, ils peuvent alors estimer la direction de chaque membres du groupe et ajuster leur déplacement (voir Figure 1.12f). 43

63 1.2 SYSTÈMES ARTIFICIELS CHAPITRE 1. INTRODUCTION Manipulations coopératives On parle de manipulation coopérative lorsqu au moins deux robots sont requis pour manoeuvrer un objet dans l environnement. Il peut s agir d un simple déplacement d objet trop volumineux pour être transporté par un seul robot (Kube & Bonabeau, 2000; Campo et al., 2006). Mais il peut également s agir de manipulations plus complexes. Par exemple, Martinoli et ses collaborateurs ont réalisé une expérience dans laquelle des robots doivent retirer d un trou une baguette qui s y trouve plongée (Martinoli & Mondada, 1995; Martinoli, 1999; Ijspeert et al., 2001). Ces robots, équipés d une pince mobile, n ont pas l amplitude de mouvement nécessaire pour retirer seuls la baguette du trou. Le robot qui détecte une baguette en premier se saisit d elle et la soulève au maximum. Pour la retirer complètement du trou, il doit attendre qu un second robot se présente et saisisse l extrémité inférieure la baguette, juste au-dessus du trou. La force que le second robot exerce sur la baguette pour tenter de la retirer complètement est un signal pour le premier robot qui la relâche instantanément. Le second robot peut alors retirer totalement la baguette du trou (voir Figure 1.12g) Allocation de tâches L allocation de tâches correspond à la répartition adéquate des activités entre les robots, en fonction de la charge de travail à accomplir ou des besoins du groupe. Il existe à l heure actuelle trois manières différentes d attribuer des tâches à l intérieur d un groupe de robots. En premier lieu, l attribution peut être déterministe : dans ce cas, chaque robot est programmé à priori pour réaliser un type de tâches plutôt qu un autre. L absence de d allocation dynamique des tâches rend ce type de systèmes peu flexible dans des environnements changeants. Eventuellement, un contrôleur central peut se charger d activer ou de désactiver les robots afin de s adapter à la charge de travail. L attribution des activités peut également se baser sur un système d enchères. Les robots reçoivent une monnaie virtuelle pour accomplir un travail et payent avec cette monnaie les ressources dont ils ont besoin. Comme dans un marché ou une place boursière, chaque robot entre en compétition avec les autres pour effectuer un travail donné ou acheter une ressource en posant des enchères. En fonction de ses moyens et de ses besoins, chaque robot essaye de maximiser son profit. Cette approche se montre très efficace pour répartir la charge de travail dans un groupe de robots (Dias et al., 2006), mais elle est relativement coûteuse en ressources de calcul et de communication car elle requiert la présence d un contrôleur central pendant la phase d enchères. 44

64 CHAPITRE 1. INTRODUCTION 1.2 SYSTÈMES ARTIFICIELS Enfin, l allocation des tâches peut être basée sur des seuils de réaction. Dans ce cas, chaque robot décide de s engager dans une tâche si la demande de main d oeuvre pour cette tâche dépasse un certain seuil. Cette demande est perçue par le robot comme la quantité de stimulation associée à la tâche en question. Le seuil de réponse peut être fixe ou dépendant de l expérience du robot. Cette méthode est la plus proche des principes de l intelligence en essaim puisqu elle est directement inspirée des résultats d études sur les processus distribués de division du travail chez certaines espèces d insectes sociaux. Malheureusement, elle est aujourd hui très peu employée dans le cadre d applications de robotique collective, bien qu une étude théorique récente montre sa plus grande robustesse aux perturbations ou aux informations partielles (Kalra & Martinoli, 2006). On peut néanmoins citer deux études expérimentales ayant implémenter des systèmes d allocation de tâches par seuils de réponse. Krieger et al. (2000) ont par exemple utilisé des seuils de réponse fixes (mais différents pour chaque robot) afin de réguler la quantité de robots impliqués dans une tâche de fourragement (exploration de l environnement, localisation de cibles et transport des cibles jusqu au point de départ des robots) en fonction de l état énergétique du groupe. Lorsque les réserves énergétiques du groupe sont importantes, seuls les robots avec un seuil de réponse très faible se lancent dans la recherche de nouvelles sources d énergie. Lorsque les réserves diminuent, un plus grand nombre de robots s activent car leur seuil de réponse est dépassé. Cela permet au groupe de robots d adapter en permanence son activité à ses besoins. Dans une étude plus récente, Labella et al. (2006) utilisent des seuils de réponse adaptatifs, également dans une tâche de fourragement (voir Figure 1.12h). Au départ de l expérience, tous les robots possèdent le même seuil d activation : la probabilité qu ils s engagent dans la tâche de fourragement est la même. Une fois engagé dans cette tâche, chaque robot qui la mène à bien voit son seuil d activation diminuer et donc sa probabilité de s engager de nouveau dans la tâche augmenter. En conséquence, la probabilité qu il réussise de nouveau à accomplir la tâche augmente. Au contraire s il échoue, son seuil d activation augmente et la probabilité qu il s engage de nouveau dans la tâche et qu il la réussisse diminue. Si la densité d objets dans l environnement est importante, la plupart des robots réussiront la tâche et auront tendance à s engager plus fréquemment dans la recherche de nouveaux objets. Au contraire, si la densité d objets est faible, les robots entreront en compétition pour les récupérer. Ceux qui échoueront trop souvent verront leur seuil d activation augmenter rapidement et ne s engageront plus que très rarement dans le fourragement, au profit des quelques-uns qui ont réussi. Grâce à ce mécanisme, le groupe est capable d adapter dynamiquement le nombre de robots impliqués dans le fourragement à la 45

65 1.3 DÉCISIONS COLLECTIVES CHAPITRE 1. INTRODUCTION densité d objets dans l environnement Prises de décisions collectives Dans le cadre de la robotique collective, les systèmes de contrôle permettant à plusieurs robots d établir un consensus ont été très étudiés d un point de vue théorique (voir pour revue Ren et al., 2005). Cependant, peu de travaux ont conduit à une exploration expérimentale de cette question, à l exception notable des expériences sur le déplacement coordonné de robots qui nécessite l établissement d un consensus sur la direction commune à adopter. L un des objectifs principaux de cette thèse est donc de contribuer à l étude expérimentale des processus de décision collective dans les systèmes de robotique en essaim. Afin de replacer cet objectif dans une perspective plus générale, nous détaillerons dans la section suivante les processus de prise de décision par auto-organisation dans les sociétés animales. 1.3 Décisions collectives dans les systèmes biologiques d intelligence en essaim Prises de décisions dans les sociétés animales Prendre une décision correspond à sélectionner une alternative dans un ensemble fini ou infini de possibilités. Si cette sélection peut s opérer sur la base du hasard, elle est motivée dans la plupart des situations par les préférences ou les buts du décideur. Celui-ci opère alors une sélection parmi les alternatives possibles, sur la base de leurs caractéristiques perceptibles et afin de satisfaire ses désirs ou ses besoins. La prise de décision est donc un processus qui requiert l acquisition et l intégration d informations portant à la fois sur les différentes options à trier et sur les motivations du décideur. Idéalement, celui-ci dispose de l ensemble de ces informations, aussi précisément que possible, afin de faire son choix. En réalité, l acquisition et le traitement des informations sont fortement contraints car le temps et les efforts nécessaires à leur réalisation sont limités. La grande majorité des décisions s opère donc sur la base d informations limitées, ce qui introduit un risque d erreur concernant l alternative choisie. Le décideur ne peut alors que chercher à réduire cette incertitude dans le temps et avec les moyens dont il dispose pour prendre la décision. Chez les animaux sociaux, la nécessité de maintenir la cohésion du groupe ajoute une contrainte supplémentaire aux décisions réalisées par les individus. Pour éviter l éclatement du groupe, la plupart des décisions doivent être prises de concert par tous les congénères. Les membres du 46

66 CHAPITRE 1. INTRODUCTION 1.3 DÉCISIONS COLLECTIVES groupe doivent s entendre pour sélectionner collectivement la même alternative, c est à dire qu ils doivent établir un consensus. Un consensus désigne un choix entre plusieurs alternatives auquel tous les membres du groupe se rallient. De nombreux exemples montrent que plusieurs espèces sociales sont en mesure d établir de tels consensus. Chez les abeilles (Seeley & Buhrman, 1999, 2001; Britton et al., 2002; Seeley & Visscher, 2003, 2004) ou les fourmis (Mallon et al., 2001; Pratt et al., 2002; Franks et al., 2003a,b, 2006, 2008; Dornhaus et al., 2004; Jeanson et al., 2004a) par exemple, le choix d un nouveau site de nidification requiert un consensus pour éviter l éparpillement de la colonie. Chez certaines espèces d oiseaux, la cohésion du vol nécessite un consensus concernant la route à suivre vers un site de nidification ou pendant une migration (Guilford & Chappell, 1996; Burt de Perera & Guilford, 1999; Biro et al., 2006). Enfin, chez certaines espèces de Mammifères (Leca et al., 2003; Gautrais et al., 2007), il est indispensable de s accorder sur le moment d initiation des activités pour ne pas risquer l éclatement du groupe. L identification d une décision consensuelle au sein d un groupe animal soulève les deux séries de questions suivantes : Quels sont les membres du groupe qui contribuent à la prise de décision? Quelles sont les conséquences du consensus pour les individus? Existe-t il des conflits d intérêts? Quels sont les coûts éventuels pour les individus? Par quel(s) mécanisme(s) le consensus est-il atteint? Comment les individus communiquentils entre eux pour l atteindre? Ces deux séries de questions sont au coeur de l article de revue de Conradt & Roper (2005). Dans la suite de cette section, nous nous appuierons essentiellement sur leur travail pour replacer les prises de décisions par consensus dans un cadre théorique cohérent Qui décide dans le groupe? Cette question est d une importance cruciale. La réponse qui est apportée influence à la fois les mécanismes de la prise de décision et les conséquences du consensus pour les individus. Selon Conradt & Roper (2005), il existe une forme de continuum entre des décisions partagées également et des décisions non partagées. Dans le premier cas, tous les individus participent de manière égale à la décision, quelque soit leur identité, leur qualité, leur âge ou leur statut social. L opinion de chaque individu compte autant que celle d un autre. Le consensus peut être atteint par quorum, c est à dire lorsqu une certaine fraction des individus adopte le même choix. En général, le quorum est utilisé lorsque le nombre d alternatives possibles est fini, comme par exemple dans le cas d une élection chez l Homme. Un consensus peut également être atteint en 47

67 1.3 DÉCISIONS COLLECTIVES CHAPITRE 1. INTRODUCTION moyennant les opinions de chacun des individus. La moyenne est utilisée lorsque le nombre d alternatives est infini, par exemple lors du choix d une direction de vol chez les oiseaux (Couzin et al., 2005). Dans le second cas, la décision est non partagée car elle est le fait d un seul individu auquel tous les autres se réfèrent. On retrouve ce type de décisions chez certains groupes de Mammifères à l intérieur desquels un individu dominant prend en charge l organisation des activités du groupe (Dunbar, 1983; Mech, 2000). Enfin, tous les intermédiaires entre les décisions partagées également et les décisions non partagées sont envisageables. On parle alors de décisions partiellement partagées. Dans ce cas là, un groupe plus ou moins important d individus décide pour l ensemble du groupe, ou tout du moins influence fortement sa décision. Dans une démocratie par exemple, les parlementaires reçoivent des citoyens le pouvoir de décider des lois qui s appliqueront à l ensemble de la population. L expérience et le nombre des individus décideurs affectent de manière importante la précision du consensus (i.e., sa déviation par rapport à la meilleure décision possible) et la vitesse à laquelle il est atteint (Franks et al., 2003a; Couzin & Krause, 2003). En théorie, plus la décision est partagée entre les membres d un groupe, plus la probabilité de prendre une décision avantageuse augmente (Simons, 2004; Conradt & Roper, 2005). Prenons par exemple un groupe d individus qui doit choisir entre deux alternatives dont l une est meilleure que l autre. Si chaque individu choisi trois fois sur quatre la meilleure alternative, une décision non partagée prise par un individu dominant conduirait le groupe à sélectionner la mauvaise option dans 25% des cas. Si la décision est partagée de manière égale (ou équitablement) entre les membres du groupe et avec un quorum à la majorité (la moitié des individus plus un), la probabilité de choisir la mauvaise option diminue alors avec la taille du groupe : elle sera de 0.16 pour trois individus, 0.10 pour cinq, 0.07 pour sept, etc (voir Figure 1.13). De la même manière, elle diminuera avec la taille du quorum : dans un groupe de cinq individus, si le quorum est fixé à quatre, la probabilité ne sera plus que de 0.02 au lieu des 0.07 dans l exemple précédent. L explication est simple : plus le nombre d individus et/ou le quorum à atteindre sont importants, moins il est probable que la mauvaise décision soit sélectionnée. En revanche, plus le nombre d individus impliqués dans la décision est important, plus la prise de décision sera longue car il faudra alors plus de temps pour collecter les opinions de chacun. Et plus le quorum est grand, plus le risque sera grand de ne pas parvenir à prendre une décision si un nombre insuffisant d individus est en faveur de chacune des alternatives. Il peut alors s avérer nécessaire pour le groupe d ajuster le nombre de décideurs et/ou la valeur du quorum afin d obtenir un bon compromis entre la probabilité d obtenir un consensus, sa vitesse d obtention et sa précision (Franks et al., 2003a). 48

68 CHAPITRE 1. INTRODUCTION 1.3 DÉCISIONS COLLECTIVES Probabilité de mauvais choix !!!!!!!!!!!!!!!!!!!!!!!!!! Décision non partagée!!!!!!! Décision partagée!!!!!!!!!!!!!!!!!! Nombre d'individus dans le groupe Figure 1.13: Evolution de la probabilité de réaliser un mauvais choix lorsque la taille du groupe augmente et lorsque la décision est partagée également (en bleu) ou non partagée (en rouge). Quelque soit le degré de partage de la décision, le nombre de décideurs ou la valeur du quorum, le consensus entraîne dans de nombreux cas des conflits entre les membres du groupe (Conradt & Roper, 2005). En effet, certains d entre eux peuvent se trouver lésés ou désavantagés par la décision finale du groupe. Les conflits d intérêts sont présents lorsque les individus dans le groupe ont des préférences différentes ou des rythmes d activités décalés. Le groupe peut alors décider de choisir une alternative ou une activité en contradiction avec les préférences et le rythme d un ou plusieurs individus. Pour ceux-ci, le ralliement au consensus entraîne un coût car ils auraient pu espérer mieux en choisissant seuls. Ce coût doit bien évidemment être mis en balance avec les avantages de la vie en groupe. Au final, l animal doit tenter d établir un compromis entre ces différentes contraintes. Chez certaines espèces cependant, le décalage entre les individus ou entre des groupes d individus est tel qu un consensus est difficile à établir. Cela conduit en général à l éclatement du groupe en sous-groupes composés d individus présentant des intérêts ou des rythmes d activité proches. Par exemple, le décalage des budgets d activité entre mâles et femelles chez certaines espèces d ongulés est à l origine d une ségrégation sociale basée sur le sexe des individus (Ruckstuhl & Neuhaus, 2002; Michelena et al., 2004). Le coût total de l obtention d un consensus dépend donc du décalage entre les intérêt des 49

69 1.3 DÉCISIONS COLLECTIVES CHAPITRE 1. INTRODUCTION individus qui composent le groupe. Mais il dépend également du type de décision qui est prise (Conradt & Roper, 2005). En théorie, un consensus sera en moyenne plus avantageux dans le cas d une décision partagée également, plutôt que dans le cas d une décision non partagée. En effet, les décisions partagées également tendent vers des choix moins extrêmes par rapport aux attentes des individus. La moyenne des opinions ou le quorum requis favorisent l adoption de l opinion majoritaire par le groupe, réduisant ainsi les écarts avec les opinions individuelles. Au contraire, les décisions non partagées peuvent être à l origine d inégalités très importantes, en particulier entre l individu dominant et le reste du groupe. L individu dominant peut éventuellement forcer le consensus, entraînant alors un coût de coercition. Ce dernier peut devenir très important, en particulier dans les grands groupes où la coercition devient inapplicable en pratique. Seul un compromis est alors envisageable Comment les individus s accordent-ils sur un choix? On peut séparer les différents mécanismes de prises de décisions collectives selon deux critères principaux. Le premier critère est la portée de la communication entre les individus (Conradt & Roper, 2005). La communication peut être globale. Dans ce cas, les décideurs peuvent envoyer des informations à l ensemble de la communauté, sans restriction. Les opinions de chacun peuvent être ainsi collectées directement et faire l objet d une discussion entre tous les décideurs. En conséquence, des comportements complexes de négociation ou de coalition peuvent se mettre en place au cours de la formation du consensus. Ce type de communication cependant est réservé à des groupes de taille relativement réduite, comme par exemple chez certains primates (Milton, 2000; Byrne, 2000), carnivores (Clutton-Brock et al., 2001) et ongulés (Ruckstuhl & Neuhaus, 2002; Conradt & Roper, 2003), à l intérieur desquels il est aisé et fréquent d interagir avec chacun des autres membres. On retrouve bien évidemment ce type de communication chez l Homme. La communication peut également être locale ou restreinte, auquel cas les décideurs ne peuvent communiquer qu avec un petit nombre de leurs congénères, en général des voisins proches dans le cas des groupes animaux (Conradt & Roper, 2005). Ce type de communication est en général présent dans les groupes composés de très nombreux individus, comme dans les vols d oiseaux (Ballerini et al., 2008), les bancs de poissons (Parrish et al., 2002), les grands troupeaux de Mammifères (Gueron & A., 1993; Gueron et al., 1996) ou dans les colonies d insectes sociaux (Bonabeau et al., 1997). Le nombre d individus est alors si important qu il n est plus possible de communiquer et de négocier un consensus. Pour parvenir à un consensus, ces animaux recourent en général à des processus d auto-organisation (Camazine et al., 2001). Dans ce type de proces- 50

70 CHAPITRE 1. INTRODUCTION 1.3 DÉCISIONS COLLECTIVES sus, les individus suivent un ensemble de règles comportementales basées sur les informations partielles qu ils perçoivent, et qui assurent la transmission de l information et la coordination des individus à l intérieur du groupe. Le second critère à prendre en compte est la dépendance des décideurs aux opinions de leurs congénères. Les décideurs peuvent être indépendants : leurs décisions sont fondées sur leurs préférences et sur les informations en leur possession, sans référence aux opinions des autres membres du groupe. Les votes à bulletins secrets pratiqués chez l Homme font (idéalement) partie de cette catégorie. Chaque citoyen glisse dans l urne le bulletin du candidat qu il a jugé le plus capable sur la base des informations qu il a pu obtenir à travers divers media d information. Sa décision est indépendante de celui des autres citoyens dont il ne peut connaître le choix. Le consensus est obtenu après collection de toutes les opinions anonymes et comptage des voix en faveur de chaque alternative. Les décideurs peuvent également tenir compte des avis déjà exprimés par d autres individus et éventuellement choisir d aller dans le même sens ou d exprimer une opinion différente. S ils ont tendance à suivre l opinion majoritaire, cela peut enclencher un phénomène d entraînement : plus une opinion est représentée dans la population, plus elle a de chance d être adoptée par de nouveaux individus et donc d être encore plus représentée dans la population. De cette manière, une opinion peut rapidement se propager au sein de la population. Les insectes sociaux en particulier utilisent ce mécanisme d entraînement pour établir un consensus. Il semblerait que les phénomènes de modes chez l Homme fonctionnent sur un principe similaire (Ball, 2004). Grâce à cette dépendance aux opinions précédemment exprimées, les coalitions et les groupes de pression peuvent démultiplier leur impact s ils arrivent à entraîner suffisamment d individus vers une alternative donnée. Le marketing viral par exemple est une technique de vente dans laquelle les commerçants incitent par des récompenses ou des réductions les consommateurs à recommander leurs produits (Leskovec, 2006). En jouant ainsi sur l influence des proches et des amis, ils espèrent entraîner un nombre grandissant de clients à choisir leurs boutiques Décisions collectives et intelligence en essaim Dans le cadre théorique précédent, les prises de décision dans les systèmes d intelligence en essaim sont toujours partagées (partiellement ou également). Elles sont basées sur une communication locale entre des individus dont le comportement dépend de celui de ses congénères proches. Dans cette section, nous allons exposer les principes sous-jacents à ces processus de choix à travers divers exemples biologiques. 51

71 1.3 DÉCISIONS COLLECTIVES CHAPITRE 1. INTRODUCTION Sélection d un chemin chez la fourmi La sélection d un chemin par une colonie de fourmi est souvent considérée comme le paradigme de l intelligence en essaim. Cet exemple possède toutes les caractéristiques classiques des processus distribués de décision collective. Nous l utiliserons donc pour introduire les différentes notions relatives à ces processus (voir Figure 1.8). Nous avons déjà évoqué brièvement les signaux chimiques utilisés par certaines espèces de fourmis pour marquer le chemin reliant le nid à une source de nourriture (Hölldobler & Wilson, 1990). Cette trace chimique est déposée en premier lieu par l ouvrière qui a découvert la source. C est une phéromone de recrutement qui stimule les autres ouvrières de la colonie à suivre le chemin tracé jusqu à la nourriture. Ces ouvrières recrutées peuvent à leur tour renforcer la piste d origine et renforcer de cette manière son pouvoir attracteur. Nous sommes ici en présence d une rétroaction positive : plus le nombre de fourmis qui empruntent une piste est important, plus cette piste devient attractive. Plusieurs rétroactions négatives vont contrebalancer cet effet d auto-amplification de la piste. En premier lieu, la volatilité du signal chimique conduit à une évaporation progressive de la piste si celle-ci n est pas régulièrement renforcée, par exemple lorsque les fourmis stoppent leur marquage parce que la source de nourriture est épuisée ou que sa capacité d accueil est atteinte. De la même manière, si le nombre de fourmis engagées initialement dans le fourragement est trop faible, le renforcement de la piste ne pourra avoir lieu, l évaporation de la trâce chimique prenant le pas sur la quantité de dépôts. La quantité totale d ouvrières disponibles pour fourrager est également un paramètre limitant l amplification du trafic sur la piste chimique. Le trafic total sur la piste ne pourra pas dépasser cette quantité, quelque soit l intensité du pouvoir attracteur de la piste. Enfin, plusieurs études montrent que le comportement de dépôt des fourmis peut changer au cours du fourragement. En particulier, la fréquence des dépôts et le nombre de fourmis marqueuses diminuent en général avec le temps, peut-être lorsque la piste atteint une saturation critique en phéromone (Aron et al., 1989; Beckers et al., 1992a, 1993). Lorsque les conditions sont réunies, le recrutement par piste chimique conduit rapidement à l établissement d une route très fréquentée reliant le nid de la colonie d un côté à la source de nourriture de l autre. Cependant, ce phénomène présente d autres propriétés intéressantes, et en particulier celle de produire des décisions collectives. Lorsqu une colonie de fourmis a accès à une source de nourriture par l intermédiaire de deux chemins identiques, l expérience montre qu au bout d un certain temps, le trafic de fourragement s établit majoritairement sur un seul des deux chemins (Deneubourg & Goss, 1989). Initialement 52

72 CHAPITRE 1. INTRODUCTION 1.3 DÉCISIONS COLLECTIVES Figure 1.14: Expérience de sélection d un chemin chez la fourmi Lasius niger. Au départ de l expérience, les deux branches sont parfaitement identiques et chaque fourmi sélectionne aléatoirement l une d entre elles. Le comportement de dépôt et de suivi de la piste chimique enclenche une compétition entre les deux branches, compétition qui se termine par la sélection de l une d entre elles par la majorité de la colonie (la branche A dans cette expérience). pourtant, chaque fourmi a une probabilité équivalente de sélectionner l un ou l autre des deux chemins parce qu ils sont identiques. Cependant, chaque fois qu une fourmi s engage sur l un d entre eux, elle y dépose un peu de phéromone, augmentant alors légèrement la probabilité que les fourmis suivantes s engagent également sur ce chemin. Si, par le jeu du hasard et des probabilités, l un des deux chemins vient à être significativement plus marqué que l autre, il va commencer à attirer un nombre plus élevé de fourmis. Une boucle de rétroaction positive est alors enclenchée qui amplifie cette fluctuation aléatoire, le chemin le plus marqué attirant plus d ouvrières qui renforcent d autant plus son marquage. L autre chemin finit par être abandonné par la majorité des fourrageuses. En d autres termes, le recrutement par piste chimique entraîne une compétition entre les deux chemins possibles, compétition qui est gagnée par celui sur lequel la trace phéromonale se renforce le plus vite (voir Figure 1.14) Les points à retenir de l exemple des fourmis Avant tout, la décision du groupe est le résultat d une compétition entre plusieurs boucles de rétroaction positive, chacune d entre elles étant associées à l une des alternatives disponibles. Ces boucles d amplification fonctionnent toutes sur le principe suivant : plus le nombre d individus qui choisissent une alternative est important, plus le degré d attractivité de cette alternative augmente. La blatte Blattella germanica utilise un processus d auto-organisation semblable pour former dans des endroits sombres des agrégats qui leur permettent de réduire leurs pertes hydriques en maintenant localement un niveau d humidité plus élevé que dans les alentours (Rust et al., 1995; Dambach & Goehlen, 1999). Cette agrégation est le produit d une double boucle de 53

73 1.3 DÉCISIONS COLLECTIVES CHAPITRE 1. INTRODUCTION rétroaction positive (Jeanson et al., 2005) : d une part les blattes en déplacement ont tendance à s arrêter plus fréquemment lorsqu elles rencontrent un groupe de grande taille et d autre part les individus arrêtés ont tendance à repartir plus tard lorsqu ils se trouvent dans un groupe de grande taille. Lorsque l on disperse des blattes à l intérieur d une arène dans laquelle est placé un abri sombre, ce processus conduit en général à la formation d un groupe stable sous l abri (Ledoux, 1945). Si deux abris exactement identiques sont présents, chacun d eux peut être le siège d un processus d amplification. S amorce alors entre eux une compétition qui conduira à la sélection d un seul abri par le groupe de blattes (Amé et al., 2006). Seule, la compétition entre les processus d amplification n est pas suffisante néanmoins pour assurer l émergence d une décision. Pour opérer le basculement vers l une des alternatives, son pouvoir attracteur doit devenir significativement plus important que celui des autres alternatives. Par significativement, j entends que l influence relative de l alternative en question devient plus importante que la variabilité comportementale des individus. Cette variabilité comportementale est une composante essentielle pour expliquer la dynamique de ces choix collectifs. En son absence, le choix final du groupe se résumerait à la première décision prise par l un des membres du groupe 5. La variabilité des comportements individuels atténue en quelque sorte l impact des premières décisions individuelles. Elle offre ainsi au groupe une certaine latence avant le choix final qui lui permet d explorer chacune des alternatives qui lui sont offertes. Au fur et à mesure que le temps passe et que les décisions individuelles s accumulent, la stochasticité du comportement des individus peut pousser le système hors de son point d équilibre et conduire ainsi à la sélection de l une des alternatives possibles. Ainsi, le système parvient à faire un choix, même lorsque toutes les alternatives en présence sont identiques ou très proches. Ce type de processus a par exemple été évoqué en économie pour expliquer en partie au moins la sélection de normes d enregistrement audiovisuelles parmi un panel de normes sensiblement équivalentes. La guerre entre les formats VHS et Betamax à la fin des années 70 (Arthur, 1989, 1990), ou plus récemment entre les formats Blu-Ray et HD-DVD en seraient autant d illustrations. Enfin, si le groupe réalise un choix entre deux alternatives équivalentes, il faut noter que ce choix est quant à lui complètement imprévisible. Si l expérience de sélection d un chemin par une colonie de fourmis est répétée plusieurs fois, chaque chemin sera sélectionné en moyenne dans la moitié des expériences (Deneubourg & Goss, 1989). Les deux chemins étant identiques, la nature du processus d amplification sera la même sur chacun d entre eux et la variabilité 5. Dans le cas où les différentes alternatives ont initialement le même pouvoir attracteur, aucun individu ne peut en théorie prendre une décision, et le groupe reste bloqué dans une situation de non choix. 54

74 CHAPITRE 1. INTRODUCTION 1.3 DÉCISIONS COLLECTIVES comportementale responsable du basculement vers l un ou l autre des chemin sera parfaitement aléatoire. D une expérience à l autre, aucune alternative ne sera donc favorisée au départ par rapport à l autre. De la même manière, la sélection d un abri par un groupe de blatte conduira, si l expérience est répétée, à une proportion équivalente de choix en faveur de chaque abri présent (Amé et al., 2006) Sensibilité à l environnement La conclusion précédente a un corollaire particulièrement intéressant pour la compréhension des processus de décision collective dans les systèmes d intelligence en essaim. En effet, tout phénomène qui biaise la variabilité comportementale vers l une des alternatives ou qui influence l intensité de l amplification au niveau de l une des alternatives modifie l équilibre des choix observés sur plusieurs réplications. Le groupe peut donc répondre à des modifications de l environnement dans lequel il évolue (Detrain et al., 2001). Si l on présente à une colonie de fourmis d Argentine Linepithema humile deux chemins dont l un est deux fois plus long que l autre, alors on observe que la grande majorité des expériences se termine par le choix du chemin le plus court (Goss et al., 1989). Au départ de l expérience, chaque chemin est emprunté de manière égale, les fourmis n ayant pas la capacité d estimer à priori la longueur du parcours à venir. Les fourmis qui se sont engagées par hasard sur le chemin court arriveront en moyenne deux fois plus vite à destination. Elles seront donc les premières à marquer puis à renforcer les zones où les deux chemins se séparent. Cet avantage temporel introduit donc un biais dans le choix des fourmis suivantes qui auront tendance à suivre et à renforcer de nouveau le chemin court. Celui-ci a donc plus de chances d être le vainqueur de la compétition (voir Figure 1.15). Dans quelques cas cependant, le choix peut se porter sur le chemin long, si dans les premiers temps de l expérience, le hasard a conduit un nombre significativement plus grand d ouvrières sur le chemin long. Malgré l avantage temporel en faveur de la branche courte, l amplification sur la branche longue sera plus forte et celle-ci l emportera. Il faut noter cependant que ce mécanisme de sélection de la branche la plus courte ne vaut que pour un dépôt de phéromone dans les deux directions (du nid vers la source, et de la source vers le nid) comme c est le cas chez la fourmi d Argentine. Lorsque le dépôt de phéromone ne se fait que dans une direction, comme chez la fourmi Lasius niger, il est nécessaire de recourir à des mécanismes supplémentaires, en particulier la présence de demi-tours, pour expliquer la sélection du chemin court (Beckers et al., 1992b; Camazine et al., 2001). Dans cette situation, la colonie sélectionne la plupart du temps la solution la plus avantageuse 55

75 1.3 DÉCISIONS COLLECTIVES CHAPITRE 1. INTRODUCTION Figure 1.15: Expérience de sélection d un chemin chez la fourmi Linepithema humile. Lorsque les deux branches du pont n ont pas la même longueur, les fourmis sélectionnent dans la plupart des expériences la branche la plus courte. sans nécessiter un traitement cognitif important de la part des fourmis. En effet, les fourmis n ont pas besoin individuellement d estimer la longueur du chemin sur lequel elles se déplacent ni même de comparer les deux chemins entre eux. Le couplage entre la structure de l environnement et le processus d amplification suffit à lui seul à déplacer l équilibre vers le chemin court. Cependant, la structure de l environnement ne favorise pas systématiquement la solution la plus avantageuse. Le déséquilibre créé par des facteurs abiotiques peut être sans relation aucune avec les intérêts ou les besoins du groupe. Par exemple, Jeanson et al. (2003b) ont montré que la vitesse de disparition d une piste chimique chez la fourmi Monomorium pharaonis dépendait de la nature du substrat sur lequel elle avait été formée. Ils ont pu estimer que la demi-vie de la piste était d environ 9 minutes sur un substrat plastique et de seulement 3 minutes sur un substrat papier. Il est aisé d imaginer l impact d une telle différence si une colonie de fourmis devait choisir entre deux chemins, l un en plastique, l autre en papier. Le choix final se porterait massivement sur le substrat plastique sans procurer d avantage particulier à la colonie. Il faut noter également qu une différence relativement faible de la nature du substrat peut être suffisante pour orienter la colonie sur un chemin plutôt qu un autre, comme l ont montré Detrain et al. (2001) Préférences individuelles et choix collectifs Dans de très nombreux cas cependant, les individus jouent un rôle actif dans le processus de sélection et favorisent par leur comportement l une des alternatives. Loin d être des systèmes purement réactifs, les animaux sociaux sont d une part sensibles aux conditions qui règnent dans leur environnement local et expriment d autre part des préférences pour certaines de ces 56

76 CHAPITRE 1. INTRODUCTION 1.3 DÉCISIONS COLLECTIVES conditions (Menzel & Giurfa, 2001; Seeley, 2002; Sumpter, 2006). Dans une situation de choix, ils peuvent donc modifier activement l équilibre initial entre les différents choix possibles. Comme précédemment, l amplification de ce déséquilibre conduit le groupe à sélectionner dans la majorité des cas l alternative pour laquelle les animaux expriment une préférence. Par exemple, nous avons vu précédemment que la blatte Blattella germanica était capable de réaliser un choix collectif entre deux abris identiques. Une autre espèce de blatte, Periplaneta americana, est également capable d effectuer un tel choix. Dans une expérience récente, Halloy et al. (2007) ont confronté des individus de cette espèce à un choix binaire entre deux abris de luminosité différente. Cet insecte qui vit principalement la nuit préfère vivre dans les endroits sombres et le choix du groupe de blattes s est porté majoritairement vers lui (dans 73% des cas) au cours de ces expériences. Le couplage entre le processus auto-organisé d agrégation et la préférence pour les endroits sombres a conduit les blattes à sélectionner dans l environnement le lieu qui satisfait au mieux leurs préférences individuelles. Les fourmis Messor barbarus préfèrent également les endroits sombres pour établir leurs nids. Lorsque plusieurs endroits dans l environnement sont aptes à les accueillir, la colonie doit en sélectionner une, de préférence la plus sombre possible. Dans une expérience de choix binaire, Jeanson et al. (2004a) ont proposé à une colonie de cette espèce deux lieux potentiels de nidification : un tube en plastique sombre et un tube transparent, tous deux équidistants du point d entrée des fourmis. Ils montrent que les fourmis recrutant vers le tube sombre déposent une trace chimique plus fréquemment et plus intensément que celles recrutant vers le tube transparent. Elles biaisent donc le choix final de la colonie vers ce tube. Ils montrent également que, parmi les premières fourmis qui explorent chacun des tubes et qui vont amorcer le recrutement, seules 5% visitent les deux alternatives. Dans la majorité des cas, les fourmis ne comparent donc pas directement les deux tubes. Malgré cela, elles sont capables de faire basculer le choix vers une solution plutôt qu une autre en modifiant seulement l intensité d un comportement en fonction de leur perception individuelle de la qualité d une ressource Modulation des comportements individuels et efficacité des choix collectifs L expression de préférences à travers la modulation des comportements individuels joue un rôle majeur dans l efficacité du choix réalisé par le groupe. Chez les fourmis par exemple, la présence simultanée de deux sources de nourriture de qualités égales et équidistantes du nid va conduire à la sélection aléatoire de l une d entre elle par la colonie, selon le même principe qui régit la sélection d un chemin vers une source unique. Si maintenant l une des deux sources 57

77 1.3 DÉCISIONS COLLECTIVES CHAPITRE 1. INTRODUCTION Figure 1.16: Dans cette simulation, une source de nourriture est placée dans l environnement et un banc de poissons de taille variable (10 à 200 individus) doit la retrouver. Cette figure montre la précision du groupe dans cette tâche en fonction du pourcentage d individus dans le groupe informés de la position de la source (Couzin et al., 2005). est plus riche en nourriture que l autre, et en absence de modulation du comportement par la qualité de la source, les fourmis devraient sélectionner dans la moitié des expériences la source la moins avantageuse. En effet, rien dans l environnement n avantagerait de manière passive une source plutôt que l autre. Dans la réalité, les fourmis modulent leur comportement de dépôt de phéromone en fonction de la qualité de la source, comme elles le font pour la qualité du nid. Plus la source est riche en nourriture, plus la fréquence et la durée des dépôts augmentent. Elles font ainsi basculer le choix vers la solution la plus avantageuse dans la majorité des cas (Beckers et al., 1993). Plus intéressant encore, il n est pas nécessaire que la modulation du comportement individuel soit de grande amplitude pour conduire le groupe à la sélection quasi systématique de l alternative la plus avantageuse. Il n est même pas indispensable que tous les individus modulent leur comportement. Dans les bancs de poissons par exemple, les individus se déplacent en adoptant une direction proche de celles de leur voisins. Ce comportement suffit à maintenir la cohésion entre les membres du banc et à adopter une direction commune de déplacement. En absence de biais comportemental, la direction de déplacement adoptée au final par le banc est complètement aléatoire. Des travaux théoriques récents montrent que la présence dans le banc de quelques individus (moins de 10%, voir Figure 1.16) dont le déplacement est orienté vers un but particulier, par exemple une source de nourriture dont ils connaissent l emplacement, suffit à diriger l ensemble du banc dans cette direction (Couzin et al., 2005). La direction privilégiée de ces quelques 58

78 CHAPITRE 1. INTRODUCTION 1.3 DÉCISIONS COLLECTIVES Figure 1.17: Dans cette expérience, des colonies de fourmis Lasius niger ont accès à une source de nourriture par deux chemins de même longueur. Dans l expérience contrôle (à gauche), les chemins sont parfaitement identiques au début de l expérience et les fourmis choisissent autant de fois la branche gauche que la branche droite. Dans l expérience test (à droite), l un des deux chemins est bordé par un mur. La majorité des expériences se terminent alors par la sélection de ce chemin (Dussutour et al., 2005a). individus se propagent à l ensemble du groupe grâce au comportement d alignement. Cela permet au groupe entier de profiter des connaissances de quelques-uns d entre eux seulement. Si cette prédiction reste théorique, elle démontre néanmoins qu un biais dans le comportement de quelques individus peut entraîner le groupe à sélectionner très majoritairement une alternative plutôt qu une autre. Ceci a été vérifié expérimentalement chez la fourmi Lasius niger Dans une expérience de choix binaire, Dussutour et al. (2005a) offrent à des ouvrières le choix entre un chemin bordé d un mur et un chemin ouvert de chaque côté. Les deux chemins sont de longueurs égales et ils conduisent tous les deux à la même source de nourriture. Lorsque la colonie entière a accès aux deux chemins, 84% des expériences se terminent par le choix du chemin qui longe le mur (voir Figure 1.17). Pourtant, lorsque les fourmis sont testées individuellement, seulement 66% d entre elles choisissent spontanément ce chemin. Cette préférence individuelle est amplifiée au niveau de la colonie grâce au processus de recrutement de masse, ce qui explique l écart observé entre la préférence exprimée par les individus et celle exprimée par la colonie Complexité individuelle vs complexité collective Dans les exemples traités précédemment, il apparaît clairement que des comportements individuels très simples peuvent conduire le groupe à prendre une décision particulièrement bien adaptée à la situation environnementale présente. Grâce à des processus d auto-organisation, des informations complexes et subtiles sur l état du groupe et de l environnement, parfois dispersées 59

79 1.3 DÉCISIONS COLLECTIVES CHAPITRE 1. INTRODUCTION sur des échelles spatio-temporelles importantes, sont intégrées pour produire un choix efficace dans la plupart des situations. Il n est alors pas nécessaire aux individus de déployer des capacités cognitives importantes pour obtenir à l échelle du groupe un choix sophistiqué. Cependant il serait bien évidemment réducteur de penser que les animaux sociaux ne disposent que de faibles ressources cognitives que les processus d auto-organisation permettraient de magnifier. En réalité, ces animaux sont des entités complexes, dont le comportement est le résultat d une combinaison souvent insaisissable de facteurs génétiques et environnementaux multiples. Même chez des animaux de très petite taille, comme par exemple chez les insectes, il peut exister une diversité comportementale conséquente. Ainsi, malgré leurs neurones, les abeilles mellifères utilisent pas moins de 17 signaux de communication différents pour échanger des informations (voir pour revue Seeley, 1998). Elles sont également capables d ajuster leur comportement individuel en réponse à la variation de plus de 34 facteurs différents (voir pour revue Seeley, 1998). Il n est donc pas question ici de nier la complexité de l individu. Il est légitime néanmoins de se poser la question suivante : dans quelle mesure la complexité individuelle trouve-t elle sa place à l intérieur des processus d auto-organisation en biologie? Comme nous l avons vu précédemment, une simple modulation comportementale en réponse à un seul facteur environnemental est suffisante pour faire basculer le choix d une population vers une alternative privilégiée. Sachant que les animaux sociaux, des plus frustes au plus sophistiqués, disposent pour la plupart d une palette importante de réponses à de nombreuses variations de l environnement, il est très probable que cette complexité comportementale influence d une manière ou d une autre la dynamique collective du choix. La sélection d un nouveau nid par les fourmis du genre Temnothorax (voir Figure 1.18) est un comportement collectif qui a été étudié ces dernières années tant du point de vue de la complexité comportementale individuelle que de la complexité comportementale du groupe (Mallon et al., 2001; Pratt et al., 2002; Pratt, 2005; Pratt et al., 2005). Lorsque le nid de ces fourmis est détruit, elles migrent après quelques heures vers un nouveau lieu de nidification qui a fait l objet d une sélection attentive. Dans ces petites colonies (entre 50 et 500 individus), environ 30% des individus prennent part à la sélection du nouveau nid. Cette sélection s opère de la manière suivante. Un premier lot d ouvrières entame une exploration de l environnement à la recherche de cavités qui sont autant de sites de nidification potentiels pour cette espèce. Quand l une d entre elle en découvre un, elle évalue de manière indépendante sa qualité sur des critères aussi variés que l aire totale de la cavité, sa hauteur, la taille de l entrée ou le niveau de luminosité (Pratt & Pierce, 2001; Franks et al., 2003a,b). Si la fourmi trouve le site acceptable, 60

80 CHAPITRE 1. INTRODUCTION 1.3 DÉCISIONS COLLECTIVES Figure 1.18: Un nid de fourmis Temnothorax formé par l agrégation de petits grains de sable entre deux plaques de verres (40x40 mm) séparées de 1mm l une de l autre. elle commence une première phase de recrutement en tandem : elle invite une autre ouvrière restée au nid à la suivre jusqu au futur nid potentiel. La fourmi recrutée réalise à son tour une évaluation indépendante du site et peut à son tour recruter de nouvelles ouvrières si elle le juge acceptable. Le recrutement en tandem est un recrutement lent, car il exige que la recrutée suive attentivement la recruteuse. Dans un premier temps donc, le nombre de fourmis présentes à chaque site potentiel de nidification augmente lentement. Lorsque la population dans l un de ces sites potentiels atteint un quorum donné, les fourmis présentes à ce site entament une deuxième phase de recrutement par transport des ouvrières et du couvain restés dans l ancien nid (voir Figure 1.19a et b). Cette phase de recrutement étant trois fois plus rapide que la première, le nouveau site est rapidement choisi. Comme dans les exemples précédents, la sélection du nid chez cette espèce de fourmis est réalisée grâce à un processus d auto-organisation. Deux processus d amplification successifs (le premier lent, le second rapide) assurent une compétition entre les différents sites potentiels de nidification, compétition qui se conclue par le choix de l un d entre eux par l ensemble de la colonie. Au cours du processus de choix, chaque ouvrière évalue la qualité de l un des sites découverts pendant l exploration. Pour cela, elle intègre plusieurs critères différents et décide individuellement de recruter, ou non, vers le site en question. De plus, la durée de son évaluation est inversement proportionnelle à la qualité estimée du site : la fourmi commencera à recruter plus tard si la qualité du site lui semble moins bonne (Mallon et al., 2001). Elle peut donc moduler très finement son comportement de recrutement (pas seulement en tout ou rien ) en fonction 61

81 1.3 DÉCISIONS COLLECTIVES CHAPITRE 1. INTRODUCTION Figure 1.19: Illustrations du mécanisme de sélection d un nouveau site de nidification par les fourmis du genre Temnothorax. (a) Evolution du mode de recrutement en fonction du nombre moyen de fourmis présent au nouveau nid. Lorsque le nombre est faible, la probabilité qu un fourmi recrute par transport est presque nulle. Lorsque ce nombre dépasse une certaine valeur (le quorum), la probabilité qu un fourmi recrute par transport se situe aux alentours de 1. Les fourmis recruteuses opèrent donc un changement qualitatif de leur comportement lorsque la population au nouveau nid atteint une certaine valeur (Pratt, 2005). (b) Estimation de la population du nouveau nid à partir de laquelle une fourmi donnée abandonne le recrutement en tandem pour le recrutement de groupe. Les extrémités de chaque barre noire indiquent les valeurs minimales et maximales déclenchant ce changement pour une ouvrière donnée. Les lignes pointillées représentent la médiane des valeurs minimales et maximales respectivement (Pratt et al., 2002). (c) Evolution du seuil de déclenchement du changement de recrutement en fonction des conditions environnementales. Dans chaque cadran, B représente des conditions normales et H des conditions dégradées. Dans tous les cas, les fourmis déclenchent le recrutement par transport plus tôt lorsque les conditions environnementales sont dégradées (Franks et al., 2003a). 62

82 CHAPITRE 1. INTRODUCTION 1.3 DÉCISIONS COLLECTIVES de sa perception des différentes qualités d un site. De cette manière, chaque fourmi peut jouer localement sur la vitesse de l amplification et le choix final de la colonie pourra ainsi être très finement ajusté aux conditions locales présentes à chaque site potentiel de nidification. Chaque fourmi peut également moduler la valeur du quorum requis pour débuter le recrutement rapide par transport (Pratt et al., 2002; Franks et al., 2003a,b). Ce paramètre a un impact particulier sur le choix final de la colonie. Lorsque le quorum est bas, il peut être atteint très rapidement. Dans ce cas, le choix de la colonie sera rapide. Cependant, la probabilité que le recrutement rapide par transport débute sur plusieurs sites au même moment est importante et donc la colonie a de fortes chances de se diviser. Au contraire, lorsque le quorum est plus élevé, la colonie a moins de chances de se diviser, mais le choix prendra plus de temps à s établir 6. De plus, le choix du nid sera plus précis car il intègrera les évaluations indépendantes d un plus grand nombre de fourmis. Une étude récente a montré que les fourmis du genre Temnothorax sont capables de moduler la valeur de ce quorum en fonction de la dureté des conditions environnementales (voir Figure 1.19c). Lorsque l environnement est défavorable et qu il est donc urgent pour la colonie de trouver un nouveau nid, elles utilisent une valeur de quorum plus petite qui permet d entamer la migration plus tôt, au risque de voir la colonie se séparer en plusieurs sous-ensembles. En absence de pression particulière sur la migration, une autre étude montre que ces fourmis sont également capables d augmenter la valeur du quorum afin d obtenir une comparaison plus précise des différents sites potentiels de nidification. Cet exemple illustre donc parfaitement comment un mécanisme très simple de sélection par amplification peut être modulé très précisément par les multiples variations du comportement des individus. D un côté, la simplicité du mécanisme de sélection permet à celui-ci d être robuste, c est à dire de produire un choix dans une vaste gamme de conditions. De l autre, la sensibilité des individus aux variations des conditions locales permet d ajuster en permanence le choix du groupe à ses besoins et à ses contraintes. Au final, la combinaison entre le processus d auto-organisation et la complexité comportementale des individus procure au groupe un registre comportemental très fourni lui permettant de s adapter en permanence aux incertitudes de son histoire. 6. Si le quorum était trop élevé, il pourrait ne pas être atteint et la colonie ne ferait alors pas de choix. Chez ces fourmis, le quorum se situe entre 9 et 17 ouvrières dans des conditions normales et il augmente légèrement avec la taille de la colonie. 63

83 1.4. OBJECTIFS CHAPITRE 1. INTRODUCTION 1.4 Objectifs Ce thèse se veut une contribution à la connaissance et à la compréhension des mécanismes décentralisés de prise de décision dans les systèmes collectifs naturels et artificiels. Dans la nature, ces mécanismes sont principalement basés sur un mimétisme comportemental fort qui pousse les individus appartenant à un groupe à opérer les mêmes choix que leurs congénères. Il s en suit le plus souvent l établissement d un consensus qui permet de maintenir la cohérence du groupe et de concentrer son activité sur l une des alternatives disponibles. Malgré l efficacité de ces processus biologiques de décision collective, très peu d études ont tenté de les transposer dans le domaine de la robotique collective, discipline qui s attache à concevoir des systèmes de contrôle capables de coordonner l activité de robots au sein d un groupe. L un des objectifs principaux de cette thèse est donc de réaliser cette transposition et d étudier les propriétés de ces processus de décision collective à travers une série d expériences sur la plateforme robotique Alice. En particulier, nous nous sommes concentrés sur les points suivants : 1. Lorsqu un robot est utilisé pour étudier le comportement d un animal, il est souhaitable qu il capture les propriétés essentielles du comportement étudié, sans introduire de nouveaux comportements qui pourrait rendre difficile l interprétation biologique du résultat. Dans le cadre des processus d auto-organisation, cette précaution est d autant plus importante que les mécanismes d amplification sous-jacents pourraient aggraver au niveau collectif les petites différences comportementales individuelles qui existent entre l animal et le robot. Cependant, il est rarement envisageable de disposer d un robot possédant les mêmes caractéristiques sensorielles et motrices que l animal dont il est le modèle. Il est donc essentiel avant toute étude d identifier les différences entre le système naturel et le système artificiel et de disposer d une méthode permettant d implémenter le modèle comportemental de telle sorte que le comportement du robot ne puisse pas être distingué de celui de l animal. Nous aborderons cette question dans le Chapitre Bien qu un seul principe général permet d expliquer la formation d une décision collective dans un système décentralisé, des variations dans le processus d amplification sous-jacent peuvent générer une grande diversité de processus de choix distincts. Pour cette raison, nous nous sommes attachés au cours de notre travail à étudier deux mécanismes différents de prises de décision. D un côté, nous nous sommes intéressés à un processus de sélection de place basé sur des interactions directes entre les individus (Chapitre 3). De l autre, nous 64

84 CHAPITRE 1. INTRODUCTION 1.4. OBJECTIFS avons étudié un processus de sélection de route basé sur des interactions indirectes entre les individus (Chapitre 6). 3. Chacun de ces deux processus de décision collective est construit à partit d un modèle comportemental issu de l étude d un système biologique. Le processus de sélection de place est basé sur le comportement d agrégation de la blatte Blattella germanica. Le modèle sur lequel nous nous sommes appuyés a été conçu par Jeanson et al. (2003a, 2005) à partir d une étude détaillée du comportement de cet insecte. Ce modèle d agrégation est également celui qui est implémenté dans le Chapitre 2 dans le but de se confondre avec le modèle biologique. En conséquence, nous interprèterons les résultats obtenus dans le Chapitre 3 du point de vue robotique comme du point de vue biologique. Le processus de sélection de route à l intérieur d un réseau est quant à lui inspiré de travaux expérimentaux que nous avons mené au cours de cette thèse sur la fourmi d Argentine (Chapitre 4 et 5). Le modèle implémenté dans les robots ayant été adapté aux contraintes du système robotique, nous interpréterons les résultats du Chapitre 6 essentiellement du point de vue robotique, bien que le comportement du robot semble expliquer certains aspects du comportement de la fourmi. Au-delà de ce travail de bio-robotique, ce mémoire de thèse se veut également une contribution plus générale à l étude des mécanismes décentralisés de décision collective. Les systèmes naturels et artificiels que nous étudions, c est à dire les insectes sociaux et les essains de robots, sont des entités réelles qui interagissent avec le monde physique qui les entoure. Ces interactions avec l environnement peuvent avoir un impact très important sur la décision finale rendue par le groupe (voir Section ). Pour cette raison, nous avons souhaité analyser l impact de la structure de l environnement sur le comportement des systèmes collectifs que nous avons étudié. 1. Dans le Chapitre 3, consacré au processus de sélection de place par agrégation, nous évaluerons l influence de l espace (1) à explorer et (2) disponible pour l agrégation sur la décision finale opérée par un groupe de robots. 2. Dans le Chapitre 4, nous étudierons le comportement individuel de la fourmi d Argentine Linepithema humile lorsqu elle traverse une bifurcation dans un réseau de galleries. En particulier, nous évaluerons l impact de la géométrie de la bifurcation sur la probabilité de sélectionner l une ou l autre des branches et sur sa probabilité d opérer des demi-tours. 3. Dans le Chapitre 5, nous étudierons comment les modifications comportementales observées dans le Chapitre 4 modifient l exploitation du réseau de gallerie par une colonie de fourmis dans une tâche de fourragement alimentaire. 65

85 1.4. OBJECTIFS CHAPITRE 1. INTRODUCTION 4. Dans le Chapitre 6, nous examinerons comment la géométrie des bifurcations influence également la sélection par un groupe de robots d une route dans un réseau de galleries. Enfin, la dernière partie de ce mémoire (Chapitre 7) sera consacrée à une discussion générale autour des résultats obtenus au cours de cette thèse et autour des prolongements envisageables des travaux présentés dans ce document. 66

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88 CHAPITRE 2. Chapitre 2 Implémentation du comportement d agrégation de la blatte Blattella germanica dans un groupe de micro-robots L un des intérêts de l utilisation de robots dans des études biologiques repose sur leur capacité à interagir avec le monde réel, et en particulier avec des animaux (Webb, 2000; Holland & McFarland, 2001). Il devient alors envisageable d infiltrer dans des sociétés animales des agents artificiels dont on contrôle le comportement. De telles sociétés mixtes offrent au moins deux intérêts. Premièrement, la modification du comportement de l agent artificiel permet de tester in vivo des hypothèses sur le fonctionnement du groupe. Ces robots sont en quelque sorte une version améliorée, réactive et interactive des leurres utilisées dans de nombreuses études sur le comportement animal (De Schutter et al., 2001; Caprari et al., 2005; Halloy et al., 2007). Deuxièmement, l influence de ces leurres robotiques, à travers leur influence sur le comportement du groupe, ouvrent d interessantes perspectives sur le contrôle des troupeaux d animaux par exemple (Vaughan et al., 2000; Butler et al., 2006), ou sur la gestion adaptative du trafic automobile chez l Homme (Gershenson, 2007; Schönhof et al., 2007). Pour qu un robot soit considéré par un animal comme son congénère, il n est pas toujours nécessaire qu il ressemble parfaitement à son modèle biologique. La présence de certains stimuli pertinents pour l animal suffit bien souvent à induire chez lui un comportement spécifique (De Schutter et al., 2001). Cependant, dans les groupes animaux qui coordonnent leurs activités grâce à des processus d auto-organisation, il peut s avérer nécessaire de reproduire parfaitement le comportement individuel de l animal. En effet, des travaux théoriques suggèrent fortement que la présence dans un tel groupe de quelques individus dont le comportement diffèrent de celui des autres membres peut entraîner des modifications importantes du comportement global du 69

89 CHAPITRE 2. groupe (Gautrais et al., 2004; Couzin et al., 2005). Dans ce chapitre, nous nous intéresserons donc à la question de la reproduction d un comportement animal sur une plateforme robotique. A travers l étude d un cas concret, nous identifierons un certain nombre de différences entre le robot et l animal qui peuvent affecter fortement le comportement global du groupe. Nous proposerons également quelques solutions permettant de contourner ces différences afin d obtenir du robot un comportement individuel et collectif aussi proche que possible de son modèle animal. Le système biologique utilisé dans cette étude est le comportement d agrégation de la blatte Blattella germanica. Un modèle détaillé de ce comportement a été développé par Jeanson et al. (2003a, 2005). Nous réaliserons l implémentation de ce modèle dans un groupe de robots miniatures, les robots Alice (Caprari & Siegwart, 2005), et nous nous servirons des résultats expérimentaux de Jeanson et al. (2003a, 2005) comme base de comparaison pour le comportement individuel et collectif de ces robots. 70

90 CHAPITRE 2. The embodiment of cockroach aggregation behavior in a group of micro-robots Simon Garnier, Christian Jost, Jacques Gautrais, Masoud Asadpour, Gilles Caprari, Raphaël Jeanson, Anne Grimal and Guy Theraulaz Simon Garnier, Christian Jost, Jacques Gautrais, Raphaël Jeanson, Anne Grimal and Guy Theraulaz Centre de Recherches sur la Cognition Animale, CNRS-UMR 5169, Université Paul Sabatier, Bât IVR3, Toulouse cedex 9, France. Masoud Asadpour Robotics and AI Lab, ECE Dept, University of Tehran, IRAN Gilles Caprari Autonomous Systems Lab, ETH Zürich, ETH Zentrum CLA E31, Tannenstrasse 3, CH-8092 Zürich, Switzerland Article published in Artificial Life, vol. 14(4), pp DOI : /artl

91 2.1. INTRODUCTION CHAPITRE 2. Abstract In this paper we report the faithful reproduction of the self-organized aggregation behavior of the German cockroach Blattella germanica with a group of robots. We describe the implementation of the biological model provided by Jeanson et al. (2003a, 2005) in Alice robots and we compare the behaviors of the cockroaches and the robots using the same experimental and analytical methodology. We show that the aggregation behavior of the German cockroach was succesfully transferred to the robot Alice despite strong differences between robots and animals at the perceptual, actuatorial and computational levels. This paper highlights some of the major constraints one may encounter during such a work and proposes general principles to ensure that the behavioral model is accurately transfered to the artificial agents. Keywords : Collective robotics, Autonomous robots, Self-organization, Bio-mimetic robotics, Aggregation. 2.1 Introduction Collective behaviors in social animals can be very impressive. They range from the coordinated displacement of thousands of individuals (Dussutour, 2004; Partridge, 1982) to the building of complex structures (Grassé, 1984; Lüscher, 1961) or to the proper allocation of tasks between the members of a group (Bonabeau et al., 1999; Deneubourg et al., 1987; Jeanne, 1996). During the last forty years, a growing body of studies was interested in understanding the mechanisms underlying these biological systems. We now know that most of these collective behaviors can be seen as decentralized systems made of autonomous units that are distributed in the environment and that can be described as following simple probabilistic stimulus-response behaviors (Camazine et al., 2001). This peculiar mode of organization, often based on self-organized processes, combines efficiency with flexibility, robustness and distributedness (Bonabeau et al., 1999). For about twenty years, such features have attracted people who are working on research topics far from the study of animal behavior (Camazine et al., 2001). Probably the best known example is the development during the 90 s of the so called ant algorithms for routing optimization by Dorigo and his colleagues (Dorigo et al., 2000; Dorigo & Gambardella, 1997). But other research fields are now tightly linked with the study of collective behaviors in social animals, collective robotics being one of them (Arnaud, 2000). Aiming at controlling the behaviors of groups of robots, swarm robotics was often inspired by the collective abilities demonstrated by social animals, and particularly by social insects (Sahin, 2005). Indeed, social animals represent promising models for the decentralized organisation and coordination of many autonomous robots (Bonabeau et al., 1999). For fifteen years, several studies have used bio-inspired robot controllers to deal with collective behaviors as manifold as aggregation (Martinoli et al., 1999), foraging (Sugawara & Sano, 1997), task allocation (Krieger et al., 2000), stick pulling (Ijspeert et al., 2001) or site selection (Garnier et al., 2005). Nevertheless, robotics also offers interesting tools for the study of animal behavior (Webb, 2000). A recent review by Webb (2001) lists several works that studied animal behavior through robotics embodiments and argues that a robotics implementation of a biological mechanism provides a strong proof in principle (stronger than any computer simulation) that this mechanism really works as suggested. Most of these works are interested in motor and sensorimotor control, navigation or learning in animals. Only few of them dealt with biological self-organized behaviors or addressed questions about collective behaviors in animals. For instance, Beckers et al. (1994); Holland & Melhuish (1999); Melhuish et al. (2001) led a series of studies about ant-inspired object clustering and sorting by groups of robots. Their main goal was to design robot controllers but they also discuss 72

92 CHAPITRE INTRODUCTION their results in the context of biological stigmergic processes (stigmergy is a coordination process in which the result of the previously accomplished work guides the animal s next tasks (Grassé, 1959; Theraulaz & Bonabeau, 1999)). The work by Kube & Bonabeau (2000) about cooperative transport of objects by a group of robots can certainly be considered as more biology-oriented. Though their results did not display a very effective collective transport, their robotic embodiment nevertheless was intended to display the first formalized model of cooperative transport of prey by ants. Finally, whatever the main purpose of a robotic embodiment of an animal collective behavior is, it remains an interesting mean to test and to explore its properties since it shares with the animal the physics, constraints and opportunities of the real world (Webb, 2000, 2001). In the context of collective behaviors a robotics embodiment may fulfill an additional function. Embodied agents could be used to infiltrate groups of animals and influence their individual and collective behaviors (De Schutter et al., 2001). Some recent works point in that direction. For instance, Michelsen et al. (1992) designed a mechanical model of a dancing bee to investigate the role of various components of the waggle dance in the transfer of information to follower bees. Böehlen (1999) performed a cohabitation experiment between a robot and three chickens and identified cues that can be used to increase the acceptance of the robot by the birds. As an other example, Vaughan et al. (2000) proposed a behavioral algorithm for a robot that is able to control the displacement of a group of ducks inside a closed arena. Fernandez-Juricic et al. (2006) used bird-like robots to manipulate the behaviour of individuals and study the responses of flock members under different ecological and social conditions. As a last example, the recent Leurre project 1 has proposed to provide a general methodology toward the design and control of mixed societies made up of real animals and autonomous artificial agents (Caprari et al., 2005). Getting a robot to become accepted by an animal as its conspecific does not necessarily require a perfect matching between the artificial and the biological agents. An artificial decoy mimicking some particular stimuli is often sufficient to induce a specific behavior in the animal (De Schutter et al., 2001). However, in the case of a mixed society that relies on self-organized behaviors, it can be necessary to accurately imitate with robots the relevant individual and collective animal behaviors in a qualitative as well as in a quantitative sense. Indeed, in a recent theoretical study, Gautrais et al. (2004) showed that it is sufficient to modify the quantitative behavior of five individuals within a group of twenty cockroaches in order to change profoundly their self-organized aggregation pattern. This result emphasizes the need for a precise adequacy between animal s and artificial agent s individual behaviors. In this paper, we thus address the problem of accurately reproducing a self-organized biological behavior with a group of small autonomous robots. We choose to study a grouping behavior, which is probably the most common collective behavior among living organisms. Grouping occurs in a wide range of taxa, including bacteria, arthropods, fish, birds and mammals (Deneubourg et al., 2002; Parrish & Edelstein- Keshet, 1999; Parrish & Hamner, 1997). More precisely, we report here a detailed description of the quantitative reproduction of the self-enhanced aggregation behavior of the German cockroach Blattella germanica with groups of ten and twenty robots. The behavioral model we used to perform this embodiment was described by Jeanson et al. (2003a, 2005). They characterized the individual and collective behaviors of B. germanica within a descriptive framework that considers almost all behaviors as probabilistic. This descriptive methodology is common in studies of self-organized behaviors in biology (Camazine et al., 2001) and offers a great advantage for our work : because it describes the behavioral output of animals, it is independant of the perceptual and cognitive process underlying such output. It therefore becomes possible to implement a self-organized behavior in an artificial system with perceptual and cognitive abilities that can be very different from the biological model, provided that the artificial system has access to the information required for the behavioral model to work

93 2.2. MATERIALS AND METHODS CHAPITRE 2. In this paper, we will first summarize the biological model of aggregation we used and then explain in detail how this model was implemented in mini-robots Alice (Section 2.2). We will also emphasize the difficulties encountered during the embodiment process and the solutions applied to solve these problems. In a second part, we will report the experimental validation of this implementation (Section 2.3). In particular we will compare the measurements of individual and collective behaviors of robots with the same measurements made by Jeanson et al. (2003a, 2005) in cockroaches. We will precisely describe the analytical tools used to quantify behaviors in both insects and robots. Finally, we will discuss the general problems we encountered when porting the animal behavior to the robots. 2.2 Materials and methods In this section, we summarily describe the biological and artificial systems used in our work, followed by an overview of our experimental setup and a detailed description of the behavioral model of aggregation and its implementation in the robots The biological system : first-instar larvae of Blattella germanica The German cockroach, Blattella germanica, is a worldwide spread urban pest which lives in close association with humans (Rust et al., 1995). It can be commonly found in kitchens, restaurants or supermarkets. This species presents a rudimentary type of social organization and thus could be qualified as presocial. B. germanica commonly forages at night. During the day, this insect rests hidden (under kitchen appliances, sinks, behind baseboards,...), forming mixed and dense aggregates of individuals of both sexes and all developmental stages especially at low external humidity (Dambach & Goehlen, 1999; Ledoux, 1945). The behavioral model was developed from experiments conducted with first-instar larvae of B. germanica (24-hours old). At this developmental stage, the body is about 3 mm long (excluding the antennae), 2 mm wide and the antennae length is 3 mm. The individuals do not present any polymorphism (i.e. the existence of two or more forms of individuals within the same animal species) or any sexual attraction. See (Jeanson et al., 2003a, 2005) for more details about the origin and the breeding of the animals The artificial system : micro-robots Alice The Alice micro-robots were designed at the EPFL (Lausanne, Switzerland) (Caprari & Siegwart, 2005). They are very small robots (22 mm x 21 mm x 20 mm) with a maximum speed of 40 mm s 1. They are equipped with two watch motors with wheels and tires. Four infrared sensors and transmitters are used for obstacle detection and local communication among Alices. Energy is provided by a NiMH rechargeable battery allowing an autonomy of about six hours in the configuration used during this study. The Alice robots have a microcontroller PIC16LF877 with 8K Flash EPROM memory, 368 bytes RAM and no built-in float operations. The implementation of the behavioral model should thus be as parsimonious as possible, rely on integer operations and avoid floating point operations. Programming is done with the IDE of the CCS-C compiler and the compiled programs are downloaded in the Alice memory with the PIC-downloader software Experimental set-up The behavioral model was built from experiments performed in a uniform environment to

94 CHAPITRE MATERIALS AND METHODS avoid any spatial heterogeneities that might bias the behavior of the cockroaches. The experimental set-up used with cockroaches consisted of a circular arena with diameter 11 cm and height 3 mm, covered by a glass plate (see (Jeanson et al., 2003a, 2005) for further details). Experiments with robots were conducted in the same kind of experimental set-up. At this point we have to consider the scale difference that exists between a cockroach larva and the robot. A cockroach larva is about 3mm long, while the Alice has 22mm length. Also, cockroaches move at approximately 10 mm s 1 while the Alice have a maximal speed of 40 mm s 1. We choose to scale up from the experimental system used with coackroaches by a factor of 4 : Alice move at maximal speed, the arena has a diameter of 50 cm and all parameters with length units will be corrected by a factor 4. Note that on this scale the Alice are still double the size of a cockroach The behavioral model This section summarizes the individual behavioral model reported in Jeanson et al. (2003a, 2005). For further details, refer to the cited papers. The radial distribution of cockroaches during the experiments showed that the larvae (that were dropped in the centre of the arena) tended to reach the periphery of the arena and stay in an external ring (0.5 cm wide) for more than 50% of their time (see Figure 2.1). This is an example of thigmotactic behavior, that is a tendency to decelerate upon contact with the arena wall and remain in antennal contact with it. We can thus subdivide the arena into a central zone and a peripheral zone. The analysis in Jeanson et al. (2003a) showed that cockroaches move at approximately constant speed in the central zone. Their movement in that zone is a correlated random walk characterized by a constant rate per unit time to change direction and a forward oriented turning angle distribution. In the peripheral zone, cockroaches follow the arena wall at approximately constant speed with a constant rate to leave and re-enter into the central zone. In addition, cockroaches can stop at any moment, stay motionless for some time and then move again. Most of these processes have a memory-less property, that is the cockroaches have a constant probability per unit time to change state (moving straight to turning, moving to stopping, leaving the periphery) : in other words, the probability to change from state a to state b between time t and time t + dt is constant and independent of the time already spent in state a. Thus, the time to remain in a given state is exponentially distributed and the rate of change can be estimated by survival curve analysis (Haccou & Meelis, 1992). A survival curve analysis consists in plotting on log-linear scale the proportion of individuals that remain in a given state as a function of the time (or distance) elapsed since the beginning of this state. On this log-linear scale (provided that the process truly has a memory-less property) the decay of the proportion will follow a straight line (see Figure 2.2) : f(t) = log(e kt )= kt. The slope k of this straight line will give us the rate of changing state and the inverse of the slope 1 k will give us the mean time (or distance) to remain in this given state. In contrast to the simple exponential distributions mentioned above, the stop times (either in the center or in the periphery) followed a distribution which can be described as the sum of two exponential distributions (we will name this particular distribution a bi-exponential distribution). On a log-linear scale the decay of the proportion of individuals that remain stopped is described by (see Figure 2.3) : f(t) = log(pe k 1t + (1 p)e k 2t ). 75

95 2.2. MATERIALS AND METHODS CHAPITRE 2. Density Distance to the centre of the arena(%) Figure 2.1: Radial distribution of Alice robots (black line) and cockroaches (grey polygon) in the arena during 60 minutes of free walking. log(proportion) Wall following time (s) Figure 2.2: Survival curve of the Alice wall-following times with the fitted regression line (solid) and the original cockroach regression line (dashed). 76

96 CHAPITRE MATERIALS AND METHODS log(proportion) Stop time (s) Figure 2.3: Survival curve of the Alice stop times with the fitted regression line (solid) and the original cockroach regression line (dashed). These stop times are for a single Alice (without neighbors). This distribution can be explained by the cockroach to be in either one of two stop states, a short one (with mean stop time 1 k 1, the animal shows some activity) and a long one (with mean stop time 1 k 2, the animal does not display any activity) with probability p to be in the short state (Jeanson et al., 2003a, 2005). Interactions between individuals were studied in Jeanson et al. (2005). The stop behavior of a cockroach was obtained by analysing the fraction of moving cockroaches that stopped when encountering a group of N stopped cockroaches (1 N 3). Note that the moving cockroach only perceives its conspecifics in its immediate neighborhood. The fraction of stops increased with the number of stopped cockroaches in the neighborhood. The spontaneous rate to start moving for a cockroach stopped in a cluster was deduced from the survival curves of aggregate life-times. These life-times also followed a bi-exponential distribution (again interpreted as two stop states), and the rates to leave an aggregate (k 1 and k 2 ) as well as the probability to be in a short stop state (p) decreased with the number of neighbors. The model (see Figure 2.4 for a schematic description of the behavioral model and Tables 2.1 and 2.2 for parameter values) was first implemented in computer simulations. Details about the simulation can be found in (Jeanson et al., 2003a) for the individual movement and in (Jeanson et al., 2005) for the collective implementation. In few words, a spatially explicit individual based model was designed to explore model predictions by Monte Carlo simulations. In order to assess the model validity, comparison between model predictions and real experiments were done. Collective behaviors were studied by putting 10 or 20 cockroaches into an experimental arena. A camera placed above the arena was coupled with a computer and an image-processing software computed the position of each individual every 10 seconds during 60 min. Two cockroaches were assumed to belong to the same aggregate if their interindividual distance was less or equal to 1 77

97 2.2. MATERIALS AND METHODS CHAPITRE 2. Figure 2.4: The behavioral model of cockroach displacement. Parameters are: speed in the centre v c, speed in the periphery v p, mean free transport path l, rate to quit the periphery q p, rate to stop in the centre s c or periphery s p, probability to be in the short stop state p s,n with mean short stopping time τ s,n and mean long stopping time τ l,n (as a function of the N stopped neighbors). The transition probability from moving in the centre to moving in the periphery is not directly encoded in the model since it is a direct consequence of the random walk in the centre. The parameter values for the cockroaches (Jeanson et al., 2003a, 2005) are listed in Tables 2.1 and 2.2. cm. The experimental data and the simulation data were then processed to obtain the size of the largest aggregate every 10 seconds. The comparison between experimental results and simulation results showed a good agreement between the model and the biological system on the individual level as well as on the collective level (Jeanson et al., 2003a, 2005) Implementation in the Alice robots The implementation of the behavioral model described above may be broken down into two parts : displacement and stopping behavior. In the displacement part, we describe the behaviors involved in the dispersal of the robots inside the arena, while the stopping behavior part contains a description of the core of the self-organized aggregation process Displacement The correlated random walk used to describe the cockroach displacements (Jeanson et al., 2003a) is characterized by a series of straight moves (also called free paths) and turning angles. The lengths of straight moves are exponentially distributed with a mean free path of length l. The distribution of turning angles was found to be bell shaped. One could implement this random walk in the Alice by drawing repeatedly a random free path from an exponential distribution of mean l, with a random turning angle from a fitted bell shaped curve. 78

98 CHAPITRE MATERIALS AND METHODS Parameter Cockroach Alice v c (cm s 1 ) 1.1 ± ± 0.01 v p (cm s 1 ) 1.06 ± ± 0.01 s c (s 1 ) ± ± s p (s 1 ) ± ± l (cm) p s, ± ± τ s,0 (s) 5.87 ± ± 0.28 τ l,0 (s) 700 ± ± 103 τ exit (s) ± ± Table 2.1: Individual displacement parameters of the cockroaches (Jeanson et al., 2003a) and their estimation from the analysis of the Alice s paths (mean ± s.e.m.). A indicates that the standard error was estimated from a non-parametric bootstrap (200 iterations). A indicates that the standard error was computed from the measured fraction and the sample size with the formula given in Zar (1999). Parameter Cockroach Alice F Stop, ± 0.03 F Stop, ± 0.05 F Stop, (0.72) τ s,1 (s) 16 ± ± 1.75 τ l,1 (s) 1248 ± ± 150 p s, ± ± 0.07 τ s,2 (s) 18.5 ± ± 9.90 τ l,2 (s) 1062 ± ± 94 p s, ± ± 0.12 τ s,3 (s) 34.1 ± 10.2 (6.64) τ l,3 (s) 1719 ± 956 (910) p s, ± 0.06 (0.09) Table 2.2: Interaction parameters among cockroaches (Jeanson et al., 2005) and their estimation from the analysis of the Alice s interactions (mean ± s.e.m.). Each parameter is given for the three tested group sizes (2, 3 and 4). A indicates that the standard error was estimated from a non-parametric bootstrap (200 iterations). A indicates that the standard error was computed from the α-trimmed (α =0.05) values. 79

99 2.2. MATERIALS AND METHODS CHAPITRE 2. However since the final goal will be experiments with several robots at the same time, there is a simpler solution. In fact, when averaged over many individuals and after a few diffusive events, a random walk as described above is equivalent to one where the turning angles are distributed uniformly in [ 180; 180] degrees (isotropic distribution) and the straight moves are exponentially distributed with mean l (Case & Zweifel, 1967). l corresponds to the transport mean free path and is computed from l and the asymetry parameter g ( 1, 1) by the equation l = l 1 g. The value l represents the distance for which the random walk becomes uncorrelated. g corresponds to the mean of the cosine of the turning angles. It characterizes the tendency of the individual to continue in a same general direction (majority of turning angles in [0; +90[ and ] 90; 0] degrees, 1 g>0) or to make U-turns (majority of turning angles in ] + 90; +180] and [ 180; 90[ degrees, 1 g<0). See (Jeanson et al., 2003a) for a more detailed description. Given the limited computing capacities of the Alice robots we choose to implement this simplified random walk. Uniform random numbers were generated with a Quick & Dirty algorithm (Press et al. (1992)). Exponential random numbers with mean l were created from a uniform random number r (0, 1) transformed to log(r)l with an algorithm using only integers (see Ahrens & Dieter (1972) for the algorithm). Letting the Alice move or turn at maximum speed we computed from these random numbers the time (in ms, which is the unit of the internal clock in the Alice) that it should move straight forward or turn. This random walk is continued until the Alice detects with its infra-red sensors an arena wall. When the Alice detects a wall, it switches into wall-following behavior (provided with the pre-programmed sensory-motor behaviors of Alice robots, see Caprari (2003)). The time an Alice follows the wall is also exponentially distributed with mean τ Exit (Jeanson et al., 2003a) and was computed as described above. Upon completion of this wall-following path the Alice returns to the central zone with a random angle drawn uniformly between 17 and 78 degrees (as an approximation to the log-normal angle distribution measured in (Jeanson et al., 2003a)) Stopping behavior The rate to stop is constant per unit time (memory-less process), the above displacement is thus interrupted every 500 ms and a random number uniformly distributed between 0 and 100 is drawn to decide whether or not the Alice should stop. This probability is different when the Alice is in the centre (s c ) than when it is in the periphery (s p ). It also varies with the number N of neighbors that an Alice detects through its local infra-red communication (s N, 0 N 3). Each robot broadcasts with its infrared emitters two robot-specific identification numbers : an odd one if it is moving (movement number) and an even one if it is stopped (stop number). This emission can be read by other robots up to a distance of 4 cm. Each Alice can thus detect the number of stopped robots in its immediate neighborhood. In agreement with the behavioral model, the maximum number of stopped robots that an Alice could detect at the same time was limited to 3 (Jeanson et al., 2005). The stop duration has a bi-exponential distribution that varies according to the number N of neighbors an Alice can detect (1 N 3, see above). This bi-exponential distribution is generated by the superposition of two exponential distributions, one for short stops and one for long stops. The robot thus first draws a random number uniformly distributed between 0 and 100 to decide whether it will be a short stop (probability p s,n ) or a long stop, and then draws an exponential stop time that is either short (mean τ s,n ) or long (mean τ l,n ). If the number of stopped neighbors changes during a robot s stop, this latter has to modify the duration of its halt according to the new number of neighbors. Because we deal with a memory-less process, the time the robot has to remain stopped is independent of the time it already spent in this state. Consequently when the number of stopped neighbors changes the 80

100 CHAPITRE ANALYSIS AND COMPARISON TO COCKROACH BEHAVIOR robot only draws a new stop time from the appropriate exponential distribution. Note that the robot retains whether the stop state is short or long. Once the stop time is elapsed the Alice continues its displacement either with a random walk (centre) or a wall-following behavior (periphery). 2.3 Analysis and Comparison to Cockroach behavior In order to validate the implementation of the cockroach aggregation behavior in Alice robot, we performed the analysis of robot behaviors in conditions similar to those used for the characterization of cockroach behaviors. This analysis is broken down into three differents parts. The first (behavior of isolated robot) and second (local interactions) parts validate the implementation at the individual level while the third part focuses on the collective output of the system. In each of these parts, the data collected with robots are compared with the data collected with cockroaches in (Jeanson et al., 2003a, 2005) Path analysis for an individual robot Individual displacements of robots were studied by letting a single individual move during 60 min in the experimental arena. This experiment was repeated ten times with ten different robots. Displacements were recorded with a high definition camera (Sony CDR-VX 2000 E) and the paths were digitized with an automatic tracking software (Ethovision, version 1.90, Noldus Information Technology, 1 pixel = x cm). Sampling rate was chosen according to Tourtellot et al. (1991) : the time interval between two successive points should let an individual move approximately its own body length. Thus, the sampling rate was set to one point every 0.48 s for the robots. The analysis of the different paths followed the procedures explained in (Jeanson et al., 2003a). These procedures were implemented in the open-source software R (R Development Core Team, 2006) (scripts can be obtained from the authors upon request). The paths over a whole hour were divided into the pieces in the central zone and the pieces in the peripheral zone (all coordinates within less than 2.75 cm from arena walls). Then these pieces were again subdivided into sub-pieces where the Alice robot moved and where it was at a stop (defined as less than 7 mm distance between two successive coordinates for at least 0.96 s (Collins et al., 1995)). Standard errors for all parameters were estimated by a non-parametric bootstrap method (Efron & Tibshirani, 1993) Central zone Speed in the centre was computed as the total length of a path sub-piece divided by the total time it took the Alice to pass through it. The mean (v c ) of these velocities gave 3.97 ± 0.01 cm s 1 (mean ± s.e.m.). To assess the random walk of the robots in the central zone, we computed the transport mean free path l. One could compute this value by means of the equation l = given in Section But to compute l and g, one would need an unbiased criterion to compute the distribution of turning angles, that is to establish accurately at which moment the individual significantly changed the direction of its path (Tourtellot et al., 1991; Turchin, 1998). To compute the value of l we rather used the same method as in Jeanson et al. (2003a) which does not require the characterization of the distribution of turning angles. The net squared displacement of a moving individual is given by (Kareiva & Shigesada, 1983) : <R 2 n > n l 2 p(l)dl l 1 g

101 2.3. ANALYSIS AND COMPARISON TO COCKROACH BEHAVIOR CHAPITRE 2. where p(l)dl is the probability that the length of each path has a value between l and l + dl. <R 2 n > corresponds to the square of the straight line distance between the beginning of a path and the position of the individual after n consecutive steps. In the case of a diffusive random walk, assuming an exponential distribution of the path lengths with a characteristic length l : p(l) = 1 l (el/l ) Then, <R 2 n > n + Assuming that the velocity v is constant, at time t : and substituting Equation (5.1) in Equation (5.2) we finally get 0 l 2 1 l (el/l )dl 2n(l ) 2 (2.1) n = tv l (2.2) <R 2 n > 2v c l t l <R2 n > 2vt For each path and each time step, we calculated the square of the distance, R n, between the beginning of the path (x 0,y 0 ) and the position (x n,y n ) of the robot after n steps : <R 2 n >= (x n x 0 ) 2 +(y n y 0 ) 2 Figure 2.5 shows the average squared distance <R 2 n > as a function of time for all paths recorded in the central zone of the arena. During the diffusive regime, the mean squared net displacement increases linearly with time and reaches a plateau due to the finite space provided by the arena that prevents robots to diffuse further away. Fitting the initial linear part of the curve to get the slope, we obtained (Figure 2.5) : (2.3) <R 2 n >= 90.14t , r=0.998 (2.4) With v c =3.97 cm s 1, equations (2.3) and (2.4) predict a transport mean free path l cm, which is of the same order as the expected value of 9.28 cm corresponding to the transport mean free path of cockroaches, 2.32 cm, scaled by a factor 4 (see Section 2.2.3). To assess the probability for a robot to spontaneously stop (that is without any interactions with another robot) in the central zone we used only the paths of the robots that started in the peripheral zone of the arena and that either spontaneously stopped in the central zone or returned to the periphery. We computed the fraction F Stop,c of paths that ended by a spontaneous stop in the central zone. Assuming that the speed v c in the centre of the arena is constant, knowing the diameter d of the central zone and using a recent result from Blanco & Fournier (2003) the probability for a robot to spontaneously stop in the central zone can be computed from the following equation (see (Jeanson et al., 2003a) for the detailed mathematics) : s c = 4v c(f Stop,c ) πd In the central zone of the arena, the fraction F Stop,c was 22.7% (n=616) for the robots. Thus, the probability per unit time to spontaneously stop in the central zone of the arena is s c =0.026 s 1 ± for the robots. 82

102 CHAPITRE ANALYSIS AND COMPARISON TO COCKROACH BEHAVIOR Net squared displacement (cm!) Time (seconds) Figure 2.5: Mean net square displacement (< R 2 n >) of robots as a function of time. Each dot represents the mean ± s.e.m. The dashed line represents the linear regression based on the linear part of the curve (< R 2 n >= 90.14t , r 2 =0.998). 83

103 2.3. ANALYSIS AND COMPARISON TO COCKROACH BEHAVIOR CHAPITRE Peripheral zone Speed in the periphery was computed as detailed above, giving a mean speed v p =3.68±0.01 cm s 1. The rates to spontaneously stop in or to quit the periphery were estimated together by first drawing the survival curve of all the times during which an Alice followed the arena wall before either spontaneously stopping or quitting it (see Figure 2.2). Given the proportion of these wall-following path pieces that ended by a spontaneous stop in the periphery one can decompose the slope of this survival curve into the rate to quit the periphery (q p =1/τ Exit ) and the rate to spontaneously stop (s p =1/τ Stop ) in it (see Jeanson et al. (2003a) for the details). This procedure gave a rate to quit of ± s 1 and a rate to spontaneously stop of ± s Spontaneous stopping times Spontaneous stopping times were also analyzed as a survival curve and they showed, as the cockroach data, a bi-exponential distribution (see Figure 2.3). We estimated the probability p s,0 for a spontaneous stop to be of the short type and the mean duration of short (τ s,0 ) and long (τ l,0 ) stops by fitting the following equation to the fraction of robots F (t) still motionless at time t (using the least squares method) : F (t) =p s,n e t τ s,n + (1 p s,n )e t τ l,n,n =0 (2.5) The best fit was obtained with p s,0 =0.94±0.01, τ s,0 =7.52±0.28 seconds and τ l,0 = 626±103 seconds Interactions among robots In order to quantify interactions among robots we must determine when an individual detects another robot. This was done by estimating the detection area of a single robot. A robot A was programmed to report the presence of neighbors in its vicinity. Another robot B was drawn near to A from several different directions and orientations : parallel to the incoming direction with the front side toward A, parallel to the incoming direction with the back side toward A and perpendicular to the incoming direction (Figure 2.6). For each of these directions and orientations we then measured the maximal distance from which robot A detected the approaching robot B. This gave us an estimation of the neighbor detection area of robot A for each orientation of B (Figure 2.6). We finally defined the maximal detection area of robot A as the superimposition of the previous detection areas. In the rest of the analysis we considered that a stopped robot was a neighbor of another one, and hence belongs to the same aggregate, if its body crossed the maximal detection area of the other Alice, whatever its incoming orientation Probabilities to join and to leave an aggregate To analyse the interactions among individuals, that is to determine the behavioral rules based on local information, we introduced several aggregates of N stopped robots in the arena (1 N 3) and then we let a single robot move between them. Forty experiments lasting 60 min were performed. The probability to stop in an aggregate is defined in (Jeanson et al., 2005) as follows : P Stop,N = v(log(1 F Stop,N)) d with v the speed of the cockroach (either v c or v p depending on the position of the animal 84

104 CHAPITRE ANALYSIS AND COMPARISON TO COCKROACH BEHAVIOR Figure 2.6: Left box: Estimated neighbor detection areas (units are in cm) of a single robot A for different orientations of the neighbor B. From the left to the right: neighbor front side, neighbor back side and neighbor side aim at the robot A. Right box: the estimated maximum neighbor detection area corresponds to the superimposition of the three previous estimated neighbor detection area. in the arena), d the distance a moving cockroach could perceive a stopped one and F Stop,N the fraction of cockroaches that stopped when encountering N (1 N 3) stopped neighbors. d strongly depends on the size and shape of the maximal detection area of the cockroach that was defined as a disk of diameter 6 mm centered on the head of the animal. This disc corresponds to the area around the head of the cockroaches within which an antennal contact with another cockroach can happen (antennae are 3 mm long). Because the maximal detection area measured in robots does not match the size and shape of the one of cockroaches, we did not compute P stop,n in robots, but we rather chose F Stop,N to compare robots stopping behavior with cockroaches stopping behavior. We thus counted the number of encounters a moving robot made with N stopped robots within its maximal detection area and the number of these encounters that ended by a stop of the moving robot. Once a robot was stopped near N robots we computed the duration of that stop. We then drew log-linear plots of the stop times survival curve for each group size (2 to 4 by counting the observed robot). As with the cockroaches all the survival curves showed a bilinear pattern (bi-exponential on normal scale). Since in our set-up only one Alice could leave the aggregate we could estimate the stopping parameters for each group size (probability to be in short stopping state p s,n, mean duration of short stops τ s,n and mean duration of long stops τ l,n ) by directly fitting equation (2.5) Calibration of interaction parameters Interactions among robots and neighbor detection are based on local communication through infra-red transmitters and sensors. However, the quality of this IR local communication is somewhat restricted, particurlarly in the case of bad alignement or multiple robots emitting at the same time in the same place (Caprari, 2003). In our experiments, a robot could obtain the following false identification numbers : a stop number from a moving robot, a movement number from a stopped robot or two different numbers from the same robot (identification numbers are sent every 50 milliseconds and stored in memory at most during one second). This noisy perception of the number of stopped neigbours had to be taken into account during the implementation of the behavioral model. 85

105 2.3. ANALYSIS AND COMPARISON TO COCKROACH BEHAVIOR CHAPITRE 2. At the behavioral level, the major consequence was a discrepancy between the probability (estimated by F Stop,N ) and time (estimated by p s,n, τ s,n and τ l,n ) to stop measured in experiments and those coded in robot s controller. Thus, the hardware constraints have altered the behavioral output of the robot in comparison to the programmed behavioral algorithm. To hedge this hardware issue, we decided to calibrate the interaction parameters programmed in the robots by a modified bisection method. More precisely, we ran a first set of 40 experiments to assess the initial discrepancy between implemented and observed interaction values. If this discrepancy was negative (implemented < observed), the implemented value was excessively increased ; if this discrepancy was positive, the implemented value was excessively decreased. Another set of 40 experiments gave us a new assessment of the discrepancy with an opposite sign : positive if it was formerly negative and negative if it was formerly positive. This gave us a first interval that contains the set of implementation parameters that would result in the correct behavioral values (those of cockroaches). We then reduced this interval by a dichotomous process. For each parameter we computed the mean of the upper and lower bound of the interval and implemented it in the robots controller. We then ran a new set of 40 experiments and we checked whether the correct behavioral values were below or above this mean. If the correct values were under this mean, it became the upper bound of the interval. Otherwise, it became the lower bound. This process was repeated until no statistical difference was observed between robots and cockroaches interaction behaviors. After the last set of 40 experiments, we obtained interaction parameter values with robots in agreement with those found in cockroaches, except for N =3: stop events in these experiments with at least 3 robots inside the maximal detection area were too scarce to confidently estimate the interaction values. Thus, the values of the different interaction parameters for more than two neighbors are given without any confidence interval and will be displayed between brackets. F Stop,N, the fraction of cockroaches that stopped when encountering N (1 N 3) stopped neighbors increased with the number of stopped neighbors (Table 2.2). Thus, the probability for a robot to join an aggregate increased with the number of neighbors as in cockroaches. Regarding p s,n, τ s,n and τ l,n, the results (see Figure 2.7, Tables 2.1 and 2.2) indicated that stop times, either short (τ s,n ) or long (τ l,n ), remained inside the confidence interval of cockroach values. The probability to belong to short stop durations (p s,n ) decreased as the number of neighbors increased and remained in the confidence interval of cockroach values Collective behaviors For the final validation of our implementation of the cockroach aggregation behavior in Alice robots we compared the collective structures that resulted from this self-organized clustering process between robots and cockroaches. The movement of 10 robots (10 replications) or 20 robots (10 replications) was recorded during 60 minutes with a high definition camera (Sony CDR-VX 2000 E). Every minute, we computed three collective behavioral measurements : the number of aggregates, the size of the largest one and the number of isolated robots. An example experiment can be seen in Figure 2.8. The results of the collective experiments with the robots were compared to the results of the same experiments made with 10 (20 replications) or 20 (22 replications) cockroaches by Jeanson et al. (2005). This comparison is shown in Figure 2.9. Note that the cockroaches are introduced at the centre of the experimental arena under CO 2 narcosis (Jeanson et al., 2003a, 2005). After recovery from this narcosis, cockroaches first ran around in an excited way. Furthermore, all the cockroaches in a group introduced into the arena did not wake up simultaneously. Therefore, to compare the dynamics of aggregation, one should not take into account the first five minutes of the experiments with cockroaches. Qualitatively, the curves of robots and cockroaches display a similar shape whatever the 86

106 CHAPITRE DISCUSSION log(proportion) Stop time (s) Figure 2.7: Survival curves of Alice stop times near 0 (round), 1 (cross) or 2 (triangle) neighbors with their fitted regression lines. observed measure. All the curves have reached a stationary state after 40 minutes. We then computed for each experiment and each behavioral measurement the mean over the last 20 minutes and compared with an exact Wilcoxon rank sum test for non paired data the set of experiments with robots to the set of experiments with cockroaches. Regarding the number of aggregates, experiments with 10 agents resulted in ± robot aggregates versus ± cockroach aggregates (NS, W = 134.5, p = 0.13). Experiments with 20 agents resulted in ± robot aggregates versus ± cockroach aggregates (NS, W = 158, p =0.051). In experiments with 10 agents, the size of the largest cluster was ± in robots and ± in cockroaches (NS, W = 109, p =0.71). In experiments with 20 agents, the size of the largest cluster was ± in robots and ± in cockroaches (NS, W = 74, p =0.15). At last, the number of isolated individuals in experiments with 10 agents was ± in robots and ± in cockroaches (NS, W = 60, p =0.08). The number of isolated individuals in experiments with 20 agents was ± in robots and ± in cockroaches (significant difference, W = 53, p = 0.02). Quantitatively, experiments with 10 robots showed a very good agreement with the biological system all along the experiment. Experiments with 20 robots also showed a good agreement with the cockroaches, except for the number of isolated individuals which is significantly higher in cockroaches compared to robots. 2.4 Discussion To build a realistic representation of an animal behavior with robots raises several problems. 87

107 2.4. DISCUSSION CHAPITRE 2. Figure 2.8: An example of a collective experiment with 20 robots that ends with a single large aggregate. Snapshots were done at the beginning of the experiment (a), after 20 min (b), 40 min (c) and at the end of the experiment (d). 88

108 CHAPITRE DISCUSSION Figure 2.9: Dynamics of aggregation in robots (black dots) and cockroaches (white dots, data from (Jeanson et al., 2005)). Data points represent the mean ± s.e.m. Row 1 represents experiments with 10 individuals (10 replications with robots, 20 replications with cockroaches). Row 2 represents experiments with 20 individuals (10 replications with robots, 22 replications with cockroaches). Column A represents the mean number of aggregates as a function of time. Column B represents the mean size of the largest aggregate as a function of time. Column C represents the mean number of isolated individuals as a function of time. 89

109 2.4. DISCUSSION CHAPITRE 2. The very first of them is to determine which level of description is required to catch the main explanatory mechanisms underlying a given behavior. Should we study the group level, the individual level, the cognitive level, the physiological level? Actually, this problem is not specific to a robotics model of animal behaviors. It is rather a general concern for all people involved in modeling animal behavior, whatever their analytical and modeling tools are. Yet, it can have major implications for the design of the robot architecture and controller. This level of description conditions what part of the biological model has to be faithfully reproduced and what part permits a less accurate implementation since it is only weakly linked with the studied behavior. For instance, Lambrinos et al. (2000) have tested their hypothesis about the navigation behavior of the Saharan ant Cataglyphis with a mobile robot called Sahabot. Their main purpose was to gain insights about the way this insect uses the polarized-light pattern of the sky to find its way back home after a foraging trip. Thus, they concentrated their efforts on the robotics embodiment of the detection and the treatment of the polarized light as made by this ant. On the contrary the other parts of the robot were designed without care about the biological realism : the robot was much larger than ants, it had wheels instead of legs, it moved on a soft synthetic material in Zürich rather than on sand in the middle of the Sahara desert. However, their Sahabot correctly reproduced the characteristic homing trajectories of the ant Cataglyphis and thus strengthened the hypothesis about the major role of the polarized-light pattern of the sky in the navigation abilities of this desert ant. In the case of a self-organized behavior the level of description focuses on the interactions between the agents, and between the agents and their environment. More precisely, the behavioral hypotheses mainly concentrate on the two following questions : 1. How does an agent s activity evolve in space and/or time in a homogeneous environment and in the absence of other agents? 2. How is this evolution modified by the presence of environmental discontinuities? How is it modified by the activities or the result of the activities of the other agents? In most cases it is possible to answer these two questions without making any hypothesis about the physiology of the agents, but rather by performing a statistical description (i.e. in terms of mean, confidence interval and/or probability) of the observable output of the agent, that is its behavior. For instance, question (1) applied to the aggregation behavior studied in this paper is answered by simply tracking the successive positions of the animal in order to obtain characteristic measurements of its displacement : length of free paths, distribution of turning angles, duration of spontaneous stops. These three measurements are sufficient to reproduce with any moving agent the dispersal of cockroaches in space and time. No additional information is required for example about walking mechanisms. Question (2) can be answered as well by simply measuring the modification of stop duration if the animal is in the presence of a given number of conspecifics. Here again no additional hypotheses are needed about the way the animal estimates the neighbor density. One can thus reproduce the cockroach aggregation behavior with any agent able to estimate this density. This is in fact what we did with Alice robots and one could do it again with any kind of robots able to move, to stop and to detect its conspecifics in a rather limited range. Of course these actions have to be performed with space and time scales accordingly adapted to the size and speed of the robots, so that the dynamics of the self-organized behavior remain the same. More generally the models of self-organized animal behaviors can often be considered as independant of the animal s physiology. Their implementation in artificial agents only requires that these latter are able to accomplish the actions stated in the model with corresponding space and time scales. However, if the model is independent of the animal s physiology, its 90

110 CHAPITRE DISCUSSION implementation remains conditioned by the artificial agent s physiology, that is everything that is involved in the agent functioning : hardware, firmware, operating system, etc. The problem of the unstable detection of neighbors met in Section well illustrates that point. The infrared local communication between robots was noisy and introduced non desired fluctuations in the neighbor count. Noise of course exists in nature and its creative role in selforganized biological systems was already emphasized in many studies (see for instance (Camazine et al., 2001; Deneubourg et al., 1983; Detrain & Deneubourg, 2006; Helbing et al., 2000)). But in our case, the variability of cockroach behavior was already considered in the model. Indeed the description of the animal behavior in terms of probabilities or in terms of means and confidence intervals integrated the biological noise. Therefore, the noisy infrared communication added an artificial fluctuation over the fluctuations already included in the biological model. This additional fluctuation could have deeply modified the collective output of the model and in such a manner could have jeopardized our main objective which was to quantitatively reproduce the self-organized aggregation of cockroaches with a group of robots. Indeed we already knew that the self-organized aggregation process implemented in this paper can produce a wide variety of aggregation patterns depending on the balance between the tendencies to join and to leave an aggregate (Gautrais et al., 2004). Thus, the physiology of the robots can have an important influence on the realistic implementation of a biological model. To achieve this realistic implementation, it is necessary to control the effects of the robot s physiology on the output of the biological model. First the differences between the biological model and its robotics implementation must be evaluated. This has to be done with exactly the same protocol as the one applied to study the animal behavior and to build the biological model. The study of the robot behavior must be done with an experimental environment, an observation methodology and a procedure of analysis identical to the one used with the animal model. This ensures the realism of the implementation and facilitates the detection of discrepancies. All along the work presented in this paper, we took care of this principle, which allowed us to detect the implementation flaw introduced by the communication channel of the Alice robots. After the difference between the model and the robot behavior has been established, it has to be reduced as far as possible. However, this problem has to be handled on a case-by-case basis since it strongly depends on the hardware part of the robot that is used : two different kinds of robots with different hardware (or physiology ) but endowed with the same model can display different behavioral output. As regards our work, the effect of the noisy infrared communication on the stop and restart behavior was counterbalanced thanks to a dichotomous calibration of stop and restart probabilities implemented in the robot controller. Although this method looks rather rough and time consuming, it turned out to be efficient in finding the good set of stop and restart parameters. Moreover it saved us an exhaustive analysis of infrared communication noise which could have eventually cost more time. Once all the mechanisms that constitute the biological model have been correctly reproduced, the last step of the work is to verify that the final output of the implementation acts as the animal does. This final stage is of great importance since it validates that the model is compatible with the real phenomenon and that its implementation does not suffer a flaw. In the case of selforganized behavior, the final output corresponds to the collective behavior of the agents. In our work, this collective behavior resulted in an aggregation of the robots which was defined through three dynamic measurements : number of robots remaining alone, number of clusters formed and number of robots in the largest cluster. Here again, these measurements were obtained in the same experimental conditions as for cockroaches and allowed a direct comparison between the collective behavior of animals and robots. The results displayed in Section show a good qualitative agreement between cockroaches and Alice robots for the three measurements. 91

111 2.5. CONCLUSION CHAPITRE 2. Quantitatively, this agreement remains good, except for an increased tendency of the cockroaches to remain isolated. Thus, robots seem to slightly over-aggregate. This could be consistent with the results in Jeanson et al. (2005) that show a higher aggregation intensity in simulated cockroaches than in real ones. However, the discrepancy observed between the simulations and the cockroaches is much more significant than the small discrepancy observed between the cockroaches and the robots. The simulations in (Jeanson et al., 2005) did not implement a physical occlusion between the simulated cockroaches. As a consequence a simulated cockroach passing near a given cluster could perceive the cockroaches at the periphery of the cluster as well as those inside. Therefore, the resulting aggregation was faster and more stable. Experiments with robots, on the contrary, took naturally into account the physical occlusion. It explains why the collective behavior of the robots was closer to the collective behavior of the cockroaches. It also emphasized the effect of physical constraints on the regulation of aggregation in cockroaches, and more generally their role in self-organized behaviors as a potential source of negative feedbacks. Another reason for the slight over-aggregation of robots could be the difference between the maximal perception area of robots and cockroaches. The perception area of cockroaches was estimated by Jeanson et al. (2005) as a 6 mm diameter disc around the head of the cockroach. Scaled by four to match the robot size, this area corresponds to 4.5cm 2. The perception area of the robots as described in Figure 2.6 corresponds to 30.7cm 2. As stated in Martinoli et al. (2004), the probability for a moving agent to encounter a conspecific inside a closed arena grows with its perception area. Moreover, with a macroscopic implementation (difference equations) of the aggregation model used in this paper, Correll & Martinoli (2007) showed that the number of agents in clusters grows with the encountering probability. Together, this could easily explain why robots in our experiments had a tendency to remain more clustered than cockroaches. This also highlights the potential effect of small physiological differences in agents on the dynamic of self-organized behaviors. 2.5 Conclusion In conclusion, we report in this paper the implementation of a self-organized aggregation behavior in a group of small autonomous robots. The main originality of this work lies in the nature of this implementation. Most of the works about self-organized behaviors in collective robotics focus on the design of controllers that solve or that optimize the solving of multi-robot coordination problems (see Matarić (1995) for a general discussion ; see Baldassarre et al. (2003) and Dorigo et al. (2004) for examples of self-organized aggregation of robots). On the contrary, our purpose was to realistically reproduce with a group of Alice mini-robots the self-organized aggregation behavior of a social animal, namely the German cockroach Blattella germanica. Thus, this work comes close to other biology-oriented studies like those reviewed by Webb (2000, 2001), even if these studies are mostly dedicated to the understanding of individual animal behaviors. To reach our goal, we have used a behavioral model of this biological phenomenon previously studied in Jeanson et al. (2003a, 2005) that described the individual behaviors of the animals in a stochastic framework. Such a description makes the model independent of the animal s physiology and thus allows its implementation in a wide variety of artificial agents. However, at least if the artificial agent is a robot, it should be noted that its physiology can have some non desired effects on its individual behaviors that may strongly modify the collective behavior of the group. If these effects cannot be eliminated with a hardware or firmware solution, they can be 92

112 CHAPITRE CONCLUSION lowered thanks to a careful implementation of the model driven by an experimental assessment of the behavioral differences. At last, the present work provides a basic framework for further thinking and experimental studies about the realistic implementation of biological models in collective robotics : 1. Because it highlights the main constraints that one may encounter during the realistic implementation of self-organized behaviors in groups of robots. 2. Because it proposes general principles to ensure that the behavioral model is accurately and faithfully transfered to the artificial agents. It can thus be considered as an important step in the process linking the study of self-organized animal behaviors to their control by groups of bio-mimetic robots as proposed in Caprari et al. (2005). Acknowledgements We thank Jean-Louis Deneubourg, Nikolaus Correll and three anonymous reviewers for helpful advices. This work was partly supported by a European community grant given to the Leurre project under the Information Society Technologies Programme ( ), contract FET- OPEN-IST of the Future and Emerging Technologies arm and by the Programme Cognitique from the French Ministry of Scientific Research. Simon Garnier is supported by a research grant from the French Ministry of Education, Research and Technology. 93

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114 CHAPITRE 3. Chapitre 3 Le comportement d agrégation des blattes comme processus de décision collective pour des groupes de robots Nous avons vu dans le chapitre précédent qu un mécanisme d amplification basé sur un mimétisme comportemental fort permettait l agrégation de robots dans un environnement homogène. Ce comportement reproduisait fidèlement celui d un groupe de blatte de l espèce Blattella germanica placé dans des conditions expérimentales similaires (Jeanson et al., 2005). Dans la nature cependant, l environnement est rarement homogène, et certains endroits se révèlent plus attractifs pour les blattes que d autres. Par exemple, les blattes s agrègent préférentiellement dans les endroits sombres (Rust et al., 1995). De manière très intéressante, plusieurs études expérimentales montrent que lorsque deux endroits sombres ou plus sont présents dans l habitat de ces insectes, alors les blattes opèrent une sélection : parmi tous les abris disponibles, elles choisissent de s agréger sous un seul d entre eux (Ledoux, 1945; Amé et al., 2006). Dans ce chapitre, nous testons l hypothèse selon laquelle cette sélection est le résultat d une restriction du comportement d agrégation vu précedemment à certaines zones de l environnement. Si le comportement d agrégation se met en place essentiellement sous les abris, alors le processus d amplification sous-jacent devrait conduire à une compétition entre les agrégats formés sous chacun des abris. Comme nous l avons vu dans l introduction de ce mémoire, cette compétition est susceptible de conduire l ensemble des individus opérer le même choix et donc à se regrouper sous le même abri. Pour tester cette hypothèse, nous reprenons le dispositif expérimental utilisé dans le chapitre précédent et auquel nous rajoutons deux abris sombres séparés. Nous modifions légèrement l implémentation précédente des robots en restreignant les arrêts à ces abris sombres. En dehors des abris, les robots ne peuvent donc s arrêter. Dans les deux articles qui composent ce chapitre, nous 95

115 CHAPITRE 3. montrons que cela est suffisant pour obtenir de la part du groupe de robots la sélection de l un des deux abris. Nous montrons également que le choix final du groupe est influencé par la différence de taille entre les abris : le groupe de robots choisit préférentiellement l abri le plus grand des deux. Dans le premier article, nous discutons d un point de vue robotique cette capacité du groupe à évaluer cette différence physique entre les deux alternatives. Dans le second article, qui est une version étendue du premier, nous explorons plus en détails les propriétés de ce choix collectif à l aide de simulations informatiques. Nous montrons en particulier que le choix final du groupe est sensible également à l espace disponible pour s agréger ainsi qu à l espace total à explorer. Nous montrons également que le nombre d individus impliqués dans la tâche de sélection influence de manière critique la capacité du groupe à sélectionner un abri. Une interprétation de ces résultats d un point de vue biologique révèle qu ils rendent compte de plusieurs observations du comportement de sélection des blattes dans des conditions naturels et expérimentales. 96

116 CHAPITRE 3. Aggregation behaviour as a source of collective decision in a group of cockroach-like-robots Simon Garnier, Christian Jost, Raphaël Jeanson, Jacques Gautrais, Masoud Asadpour, Gilles Caprari and Guy Theraulaz Simon Garnier, Christian Jost, Raphaël Jeanson, Jacques Gautrais and Guy Theraulaz Centre de Recherches sur la Cognition Animale, CNRS-UMR 5169, Université Paul Sabatier, Bât IVR3, Toulouse cedex 9, France. Masoud Asadpour Robotics and AI Lab, ECE Dept, University of Tehran, IRAN Gilles Caprari Autonomous Systems Lab, ETH Zürich, ETH Zentrum CLA E31, Tannenstrasse 3, CH-8092 Zürich, Switzerland Article published in Advances in Artificial Life, Volume 3630 of Lecture Notes in Artificial Intelligence, pp DOI : / _18. 97

117 3.1. INTRODUCTION CHAPITRE 3. Abstract In group-living animals, aggregation favours interactions and information exchanges between individuals, and thus allow the emergence of complex collective behaviors. In previous works, a model of a self-enhanced aggregation was deduced from experiments with the cockroach Blattella germanica. In this work, this model was implemented in micro-robots Alice and successfully reproduced the agregation dynamics observed in a group of cockroaches. We showed that this aggregation process, based on a small set of simple behavioral rules and interaction among individuals, can be used by the group of robots to select collectively an aggregation site among two identical or different shelters. Moreover, we showed that the aggregation mechanism allow the robots as a group to estimate the size of each shelter during the collective decision-making process, a capacity which is not explicitly coded at the individual level. 3.1 Introduction Since the last 15 years, collective robotics has undergone a considerable development (Wagner & Bruckstein, 2001). In order to control the behavior of a group of robots, collective robotics was often inspired by the collective abilities demonstrated by social insects (Bonabeau et al., 1997, 1999; Camazine et al., 2001). Indeed, nature has already developed many strategies that solve collective problems through the decentralized organisation and coordination of many autonomous agents by self-organized mechanisms (Camazine et al., 2001) : for instance trail formation (Pasteels et al., 1987), food source selection (Seeley et al., 1991), division of labor (Bonabeau et al., 1998a), collective defense (Millor et al., 1999), etc. Among all these self-organized behaviours, aggregation is one of the simplest. But it is also one of the most useful. For instance, it allows an individual to transmit an information in a very efficient way to many other conspecifics at the same time. It thus favours recruitment processes during food source exploitation (Camazine et al., 2001) or territory defense (Detrain & Pasteels, 1992). Aggregation also facilitates the interactions among individuals, leading to complex collective behaviors such as nest construction (Franks & Deneubourg, 1997), nest-site selection (Jeanson et al., 2004b), traffic regulation (Dussutour, 2004), etc. To sum up, aggregation is a step toward much more complex collective behaviours because it favours interactions and information exchanges among insects, leading to the emergence of complex and functional self-organized structures. As such it plays a keyrole in the evolution of cooperation in animal societies (Deneubourg et al., 2002). 98

118 CHAPITRE INTRODUCTION Self-organized aggregation processes were regularly used in collective robotics. For instance, foraging tasks (i.e. clustering of objects scattered in the environment) were used to study the impact of the group size (Martinoli & Mondada, 1995) or of a simple form of communication (Sugawara & Sano, 1997) on the harvest efficiency. But even more complex consequences of aggregation processes were studied with group of robots. For instance, Agassounon & Martinoli (2002) showed that division of labor can emerge in a group of foraging robots when the size of the group grows. Holland & Melhuish (1999) showed that an object clustering paradigm based on stigmergy (Grassé, 1959) can lead a group of robots to order and assemble objects of two different types. In this paper we address a new collective behavior that is also based on self-organized aggregation of robots themselves. We show that a self-enhanced aggregation process, which leads groups of cockroaches to a quick and strong aggregation (Jeanson et al., 2005), can be used by a group of mini-robots Alice to select collectively an aggregation site among two identical or different shelters. We show that, even though these robots have limited sensory and cognitive abilities, they are still able to perform a collective decision. It has already been shown that such self-enhanced mechanisms are used by insects to make collective decisions : for instance in food source selection in bees (Seeley et al., 1991) or in nest site selection in ants (Jeanson et al., 2004b). This collective choice appears each time through the amplification of small fluctuations in the use of two (or more) targets. These fluctuations arise from behavioral randomness and/or from natural preferences of animals (in the case of different targets), and are amplified by recruitment process (through pheromone deposits in ants for instance) (Camazine et al., 2001). Here we propose that a biological model of aggregation of first instar larvae of the cockroach Blattella germanica (Jeanson et al., 2003a, 2005) can lead a group of robots Alice to the collective choice of a rest site (or shelter). We show that a very simple self-enhanced mechanism underlying this aggregation process is sufficient to make the group of robots aggregate under one of two identical shelters, instead of equally splitting between them. If the two shelters are different (here in size), we also show that robots preferentially choose the biggest of the two, without being individually able to measure the size of each shelter. In this paper, we first describe the biological model of aggregation we have used and the way this model was implemented in a group of mini-robots Alice. We then show that this implementation indeed results in a collective aggregation behavior that is quantitatively indistinguishable from cockroach aggregation. Finally, we show that, when this aggregation behavior is restricted 99

119 3.2. SELF-ORGANIZED AGGREGATION CHAPITRE 3. to certain zones in the environment (for instance by natural preferences for dark places as in cockroaches (Rust et al., 1995)), the robots preferentially aggregates in one of these zones, i.e. they collectively choose a single rest site. The results of our experiments were also used to calibrate a computer simulation of robots Alice that will allow us to deeply explore this collective decision model in further studies. 3.2 Self-organized aggregation The aggregation process cited above is directly inspired by a biological model of displacement and aggregation developed from experiments with first instar larvae of the german cockroach Blattella germanica (Jeanson et al., 2003a, 2005). This model was built by quantifying individual behaviors of cockroaches, that is their displacement, interactions among individuals and with the environment in a homogeneous circular arena (11 cm diameter). Each of these individual behaviors was described in a probabilistic way : we measured experimentally the probability distribution for a given behavior to happen. The model is precisely described in Jeanson et al. (2003a, 2005), its main features being that the probability for an individual to stop increases with the number of stopped conspecifics just around him (i.e. within range of antenna contact in cockroaches), and that the probability for an individual to restart decreases with this number. Thus, this dual positive feedback leads to the quick and strong formation of aggregates (as can be seen in Fig. 3.1). The first part of our work was to implement this biological model of aggregation in the microrobots Alice. These robots were designed at the EPFL (Lausanne, Switzerland) Caprari et al. (2002). They are very small robots (22mm x 21mm x 20mm) equipped with two watch motors with wheels and tires allowing a maximum speed of 40 mm s 1. Four infra-red sensors are used for obstacle detection and local communication among Alices (up to 4 cm distance). Robots have a microcontroller PIC16LF877 with 8K Flash EEPROM memory, 368 bytes RAM but no built-in float operations. To determine the number of neighbors (which is the basis of the aggregation process), each robot owns a specific identification number and counts the number of nearby neighbors in a distance less than 4 cm) with a different id number. Intrinsic differences between the perception area of robots and cockroaches and imperfect neighbor count due to noise in IR device required some fine-tuning of the behavioral parameters in order for the behavioural output of the robots to correctly match the cockroach individual behaviors. This behavioral output of 100

120 CHAPITRE COLLECTIVE CHOICE robots was measured using the same experimental methods (10 to 30 experiments depending on the studied behavior) as those used to characterize the individual behavior of cockroaches (see Jeanson et al., 2003a, 2005 for a detailed description of these methods). However individual behaviors are not aggregation behavior, and the true validation of model implementation must be done at the collective level by comparing aggregation behavior of robots to aggregation behavior of cockroaches. To this aim, we ran the following aggregation experiment : groups of robots (10 or 20 individuals) were put into a homogeneous white circular arena (50 cm diameter) during 60 minutes. This experiment is similar to the one done by Jeanson et al. (2005) with cockroaches. To draw a parallel between cockroach aggregation behavior and robot aggregation behavior, we scaled the dimensions of robot arena so that it matches scale differences between robot and cockroach sizes. The experiment was repeated 10 times for each group size (10 or 20 robots). The aggregation dynamic was obtained through three kind of measurements (sampled every minute) : size of the largest aggregate, number of aggregates and number of isolated individuals (see Jeanson et al., 2003a, 2005 for a detailed description of these measurements). For each of these three dynamics, experimental results showed a very good agreement between robots and cockroaches, confirming that the cockroach aggregation process was well implemented in the robots Alice (see Fig. 3.1). 3.3 Collective choice This aggregation process implemented in robots can occur in the whole experimental arena, without any preference for a given location. Actually, in nature some places are more attractive for cockroaches, thus promoting aggregation in particular sites. For instance, cockroaches preferentially aggregate in dark places (Rust et al., 1995). Experimentally, if one puts a dark shelter in a lighted arena (as the one used for the study of cockroach aggregation), one can observe that cockroaches strongly aggregate under this shelter. And if two or more dark shelters are placed in the arena, one can observe that a majority of cockroaches aggregates under only one of these shelters, rather than evenly spreading their population among all the aggregation sites (Ledoux, 1945). Thus cockroaches are able to perform a collective choice for a given aggregation site, even if these sites are identical. Though the mechanisms leading to this collective choice are not yet fully understood, we suggest that this choice could strongly rely on the self-enhanced aggregation process described 101

121 3.3. COLLECTIVE CHOICE CHAPITRE 3. Figure 3.1: Aggregation dynamic: size of the largest aggregate. A: experiments with 10 individuals. B: experiments with 20 individuals. Black dots represent data for robots; white dots represent data for cockroaches. Each dot represents the mean ± standard error (s.e.). Differences between starting points of robot and cockroach dynamics are solely due to the way cockroaches have to be brought in the arena as explained in Jeanson et al. (2005). 102

122 CHAPITRE COLLECTIVE CHOICE above and tested with robots. Indeed such self-enhanced mechanisms are already known to lead groups of animals to collective decisions, such as the collective choice of a food source (Seeley et al., 1991) and of a target (Millor et al., 1999) in bees, or of a nest site in ants (Jeanson et al., 2004b). To test our hypothesis, we ran three sets of experiments during which a group of robots was faced to the choice between two potential aggregation sites. Besides proving that collective decision in robots can appear from a simple aggregation process, these experiments were used to calibrate a simulation tool which will be used in further studies to identify the behavioral parameters that control collective choice. The first set of experiments was designed to ascertain whether the cockroach aggregation behavior is able to lead a group of robots to a collective choice between two identical targets. To that aim, we put a group of 10 robots in the same arena as the one used for aggregation experiments, except that we added just above the arena two dark shelters. These shelters were of the same size (14 cm diameter) and each of them can house the whole population of robots. Robots used the same behavioral algorithm as the one previously tested for its aggregation ability, except that, now, robots only stop under dark shelters (that is when IR light intensity falls under a given threshold). 20 experiments were performed, each lasting 60 minutes. The number of stopped robots under each shelter was measured every minute to characterize the aggregation dynamic under each shelter. At the end of each experiment, we also measured the percentage of stopped robots under each shelter to characterize the collective choice of the robots. From this last measurement, we derive what we call a choice distribution. For a given shelter, this choice distribution corresponds to the number of experiments ending with a given percentage of stopped robots under this shelter (the choice distribution being symmetrical for the other shelter). For instance, how many experiments ended with 0 to 20 percent of stopped robots under shelter number 1? Or with 20 to 40 percent, etc. In the case of each robot randomly choosing a shelter during experiments (i.e. without any influence of its conspecifics), the result will follow a binomial law with parameters n =5(number of percentage classes : 0-20, 20-40, 40-60, and percent) and p = 0.5 (equiprobability to choose a given shelter because of any difference between the two shelters). The resulting choice distribution displays a centered peak as can be seen in Fig. 3.2 B.1, meaning that a majority of experiments ended with no choice for one shelter. Contrary to the binomial resulting choice distribution, the choice distribution obtained in experiments with two identical shelters displays two peaks at each side (see Fig. 3.2 B.2). A 103

123 3.3. COLLECTIVE CHOICE CHAPITRE 3. chi square test shows a strong difference between the binomial and experimental distributions (χ 2 = 42.2, df =4, p<0.0001). Similar results are obtained with simulations (see Fig. 3.2 B.3). This U-shape distribution corresponds to two different populations of experiments, each of them preferentially ending with the choice of a given shelter. Furthermore, in this case with two identical shelters, the symmetry of the U-shape means that each shelter is randomly chosen from an experiment to another. The dynamic of this choice can be seen in Fig. 3.3 B.1 and B.2. It shows that the choice occurs very rapidly from the first minutes of the experiments. It also shows that this choice is very strong, since 75.5 ± 1.9% (mean±s.e., n = 20) of the population of robots is under the chosen shelter at the end of the experiments (78 ± 2.2%, n = 1000, in simulations). Thus this set of experiments clearly shows that the aggregation process described above (with a very simple individual behaviors) can lead a group of robots to perform a collective choice between two aggregation sites. The two other sets of experiments were designed to assess the impact on the collective choice of a qualitative difference between the two shelters. As in the previous set of experiments, a group of 10 robots faced a choice between two shelters. But this time, one of the shelters was kept constant according to the previous experiment, while the size of the other was altered. In a first set of 20 experiments, we confronted a 14 cm diameter shelter (able to house the whole robot population) with a 10 cm diameter shelter (just too small to house the whole population of robots). As can be seen in Fig. 3.3 A.1 and A.2, robots quickly and strongly choose the shelter able to house their whole population. Thus, at the end of the experiments, 68 ± 1.9% (mean±s.e., n = 20) of the population is under the 14 cm diameter shelter (72.7±3.2%, n = 1000, in simulations). The choice distribution shows a strong shift toward the 14 cm diameter shelter (see Fig. 3.2 A.2). This shift is the result of more than the simple difference between the area of the two shelters. Indeed, a comparison between experimental distribution and a binomial distribution (Fig. 3.2 A.1) taking into account this deviation (p =0.66) shows a strong difference (χ 2 = 74.1, df =4, p<0.0001). Similar results are obtained with simulations (see Fig. 3.2 A.3). The disappearance of the U-shape of the distribution means that it remains only one population of experiments preferentially ending with the choice of the 14 cm diameter shelter, i.e. the one able to house the whole population of robots. In a second set of 20 experiments, we confronted a 14 cm diameter shelter with a 18 cm diameter shelter. This two shelters are able to house the whole population of robots. As can be seen in Fig. 3.3 C.1 and C.2, robots choose the 18 cm diameter shelter. Thus, at the end of the 104

124 CHAPITRE COLLECTIVE CHOICE Figure 3.2: Choice distributions. In these distributions, each block represents a number of experiments ending with a given percentage (0-20, 20-40, 40-60, and percent) of robots under one of the two shelters. Top: binomial distributions (random choice). Middle: experimental distributions (n = 20). Bottom: simulation distributions (n = 1000). Columns A and C represent choice distributions for the 14 cm diameter shelter against either the 10 cm diameter shelter (column A) or the 18 cm diameter shelter (column C). For each of these distributions, blocks on the right means choice of the 14 cm diameter shelter and blocks on the left means choice of the other shelter (either 10 or 18 cm diameter). Column B represents choice distribution for a 14 cm diameter shelter against an other 14 cm shelter. 105

125 3.3. COLLECTIVE CHOICE CHAPITRE 3. Figure 3.3: Choice dynamics: number of robots aggregated under each shelter. Top: experimental data (n = 20). Bottom: simulation data (n = 1000). In column A and C, black dots represent data for the 14 cm diameter shelter; white dots represents data for either the 10 cm diameter shelter (column A) or the 18 cm diameter shelter (column C). In column B, black dots represent data for the chosen shelter (i.e. the shelter which is chosen at the end of each experiment); white dots represent data for the not chosen shelter. In all cases, each dot represents the mean ± s.e. 106

126 CHAPITRE CONCLUSION experiments, 70.5 ± 4.3% (mean±s.e., n = 20) of the population is under the 14 cm diameter shelter (61±4.6%, n = 1000, in simulations). The choice distribution shows a shift toward the 18 cm diameter shelter (see Fig. 3.2 C.2). This shift is the result of more than the simple difference between the area of the two shelters. Indeed, a comparison between experimental distribution and a binomial distribution (Fig. 3.2 C.1) taking into account this deviation (p =0.38) shows a strong difference (χ 2 = 77.5, df =4, p<0.0001). Similar results are obtained with simulations (see Fig. 3.2 C.3). But on the contrary of the previous experiment, the U-shape of the distribution does not have disappeared and the two populations of experiments still exist : one that preferentially ended by a choice of the 14 cm diameter shelter, the other that preferentially ended by a choice of the 18 cm diameter shelter, the latter prevailing on the former. From the two latter sets of experiments, we can conclude that the group of robots will choose a shelter if it is sufficiently large to house all its members. But when the group is confronted to two sufficiently large shelters, the self-enhanced aggregation mechanism can lead the group to two stable choices, one being more expressed if the two shelters are of different sizes. This implies that the group of robots is able to sense and compare the size of the shelters during the collective decision process, a performance that is beyond the direct scope of the simple aggregation process used in these experiments and that is not explicitly implemented in individual robots. 3.4 Conclusion In this work, we achieved a collective decision process from a simple biological model of aggregation. We showed that a self-enhanced aggregation process associated with a preference for a given type of environmental heterogeneity (here a preference for dark places) can lead a group of robots to a collective choice for an aggregation site. Furthermore, this choice can be related to a collective ability to sense and compare the sizes of the aggregation sites. The most interesting aspect is that individual robots are unable to perform such behaviors (sensing the size of the shelters and choosing one of them) because of their very limited perception apparatus and computing power, and also because of the simplicity of their individual behaviors. But, as it has already been shown in insects (Camazine et al., 2001; Dussutour, 2004) and robots (Holland & Melhuish, 1999; Agassounon & Martinoli, 2002), this simplicity is not a limit to the appearance of complex collective behavior. Division of labor (Agassounon & Martinoli, 2002), object ordering (Holland & Melhuish, 1999) and even collective decisions can emerge from the numerous interactions between artificial agents with some very simple behavioral rules. 107

127 3.4. CONCLUSION CHAPITRE 3. We now plan to complete our experimental results by performing choice experiments with more than 10 robots to better tune our simulation tool. Indeed, we also plan to explore this collective choice model by performing simulation experiments in order to find behavioral parameters able to influence this choice. Previous simulation work about this aggregation model shown that small modifications of stop and start probabilities can deeply alter aggregation patterns. What is more interesting is that these alterations appear even if only 20% of the population has modified probabilities (Gautrais et al., 2004). Thus we think that modifying these probabilities can also modify the collective choice, allowing us to control group decision through the introduction of some modified robots. Moreover this work already opens some interesting perspectives for collective robotics. Such a collective choice could be associated, for instance, with a construction behavior, allowing a group of robots to choose a place to build a nest adapted to the size of their population or having some specific environmental properties (for instance light intensity, humidity, etc.). It could also be associated with the ordering behavior described in Holland & Melhuish (1999), allowing robots to assemble objects of different types in different places. We argue that such associations are new challenges to take up if this collective robotics, based on self-organized mechanisms and/or biologically inspired behaviors, must become an efficient way to achieve complex tasks with groups of numerous small autonomous robots. Acknowledgements This work was partly supported by a European community grant given to the Leurre project under the IST Programme ( ), contract FET-OPEN-IST of the Future and Emerging Technologies arm and by the Programme Cognitique from the French Ministry of Scientific Research. The authors would like to thank Jean-Louis Deneubourg for all its very helpful advices about this work. 108

128 CHAPITRE CONCLUSION Self-organized aggregation triggers collective decision-making in a group of cockroach-like robots Simon Garnier, Jacques Gautrais, Masoud Asadpour, Christian Jost and Guy Theraulaz Simon Garnier, Jacques Gautrais, Christian Jost, and Guy Theraulaz Centre de Recherches sur la Cognition Animale, CNRS-UMR 5169, Université Paul Sabatier, Bât IVR3, Toulouse cedex 9, France. Masoud Asadpour Robotics and AI Lab, ECE Dept, University of Tehran, IRAN Article submitted to Adaptive Behavior. 109

129 3.5. INTRODUCTION CHAPITRE 3. Abstract Self-amplification processes are at the origin of several collective decision phenomena in insect societies. Understanding these processes requires to link the individual behavioral rules of insects to a choice dynamics at the colony level. In an homogeneous environment, the German cockroach Blattella germanica displays such a self-amplified aggregation behavior. In an heterogeneous environment where several shelters are present, groups of cockroaches collectively select one of them. In this paper, we demonstrate that the restriction of the self-amplified aggregation behavior to distinct zones in the environment can explain the emergence of a collective decision at the level of the group. This hypothesis is tested with robotics experiments and dedicated computer simulations. We show that the collective decision is influenced by the available space to explore and to aggregate, by the size of the population involved in the aggregation process and by the probability to encounter these places while the robots explore the environment. We finally discuss these results both from a biological and a robotics point of view. Keywords : Self-organization, Aggregation, Collective decision, Blattella germanica, Swarm robotics 3.5 Introduction Decision-making mechanisms are of crucial importance for any animal. They allow it to behave differently according to its needs and according to the environmental situation : the decision results from the integration over time of what the animal perceives and what it aims at. The elucidation of such mechanisms is therefore central to understand how an animal deals with heterogeneous environments. If decision-making mechanisms are essential for a single individual, they are also crucial for the organization of animal groups. In particular collective decision-making (i.e. the ability for the group s members to reach a consensus on a common action to carry out) is a cornerstone for the organization of animal societies (Camazine et al., 2001; Conradt & Roper, 2005; Couzin et al., 2005; Garnier et al., 2007a). It is involved at different stages of the group s life, from the choice of a place to live to the selection of a profitable food source or of a direction to follow. In order to reach a consensus the group members may refer to one or a few leaders that decide for the whole community. Such behavior can be observed in certain animal groups where few individuals guide the activities of the others. However in social insects collective decisionmaking relies on a different principle. Their collective choices are often based on self-organization 110

130 CHAPITRE INTRODUCTION processes (Camazine et al., 2001; Couzin et al., 2005; Sumpter, 2006; Garnier et al., 2007a), as for instance in target selection in bees (Millor et al., 1999) or in food source (Beckers et al., 1990) and path selection (Beckers et al., 1992b) in ants. In each of these cases, some insects discover independently different opportunities in the environment and recruit other nest mates towards these opportunities. The recruited nest mates can, in turn, recruit other nest mates, and so on. This is a self-amplification process : the more individuals that signal an opportunity, the more likely other individuals will join them. Because the number of individuals that can be recruited is limited (e.g. because of the size of the colony), a competition arises between the different opportunities to attract the greatest number of individuals. Eventually, the winning opportunity is the one with a faster self-amplification process than the other. The decision is not taken by one or a few individuals in the group but rather emerges from the numerous interactions among the members of the group. Such self-organization processes present several interesting features for the achievement of multi-robot tasks : the individual behaviors are often simple compared with the complex colony output ; the colony is flexible to changing environmental conditions ; the redundancy makes the colony tolerant to individual failures (Bonabeau et al., 1999; Sahin, 2005). This has encouraged the development of swarm robotics, a branch of collective robotics, which has made an explicit use of bio-inspired self-organization to coordinate group of robots in various contexts : dispersion (McLurkin & Smith, 2007), aggregation (Beckers et al., 1994; Garnier et al., 2008), segregation/sorting (Wilson et al., 2004), coordinated movement (Baldassarre et al., 2007), coverage (Correll et al., 2008), target localization (Hayes & Dormiani-Tabatabaei, 2002), task allocation (Labella et al., 2006), cooperative manipulation (Kube & Bonabeau, 2000; Martinoli et al., 2004) and foraging (Krieger et al., 2000). Because swarm robotics is mainly a bio-inspired discipline dealing with artificial systems, its results can be interpreted from different points of view. From an engineer s point of view it displays alternative mechanisms to organize the activities of groups of autonomous robots. From a biologist s point of view it is an interesting tool to formulate and to test hypotheses about the organization of animal societies. In this paper our goal is to investigate a self-organized decisionmaking process from both points of view thanks to a collective robotics implementation. On one hand we want to test whether the self-organized aggregation behavior of the German cockroach Blattella germanica may account for its ability to select places in heterogeneous environments. And on the other hand we want to show that this self-organized process may be used as a place selection mechanism for groups of autonomous mini-robots. 111

131 3.5. INTRODUCTION CHAPITRE 3. In recent works, Jeanson et al. (2003a, 2005) have demonstrated that the aggregation behavior displayed by the German cockroach Blattella germanica relies on a self-organization process : for a given moving cockroach, the larger the number of staying neighbors, the more likely the animal is to stop and stay beside them. This leads the cockroaches to quickly aggregate in dense clusters in a homogeneous environment. The natural habitat of B. germanica is however heterogeneous : some places are more attractive for cockroaches, thus promoting aggregation in particular sites. For instance, cockroaches preferentially aggregate in dark places (Rust et al., 1995). If one puts a dark shelter in a bright arena, one will observe that cockroaches strongly aggregate under this shelter. If two or more dark shelters are placed in the arena, a majority of the cockroaches will aggregate under a single shelter rather than evenly spreading among all resting sites (Ledoux, 1945). The group therefore selects a place to aggregate among several available in its environment. In this paper, we propose that this collective choice of a single resting site is a consequence of self-amplification process that triggers aggregation in cockroaches. If the occurrence of the aggregation behavior is restricted to or favored in several spatially distinct areas, a competition should arise between the potential aggregation sites which should end with the collective selection of only one of them. This hypothesis is supported by a recent paper by Amé et al. (2006) which showed that this collective choice can be explained by a modulation of the individual staying time under a dark shelter by the number of nest mates already present under this shelter : the more cockroaches there are, the longer time a cockroach will stay under this shelter. Their mean-field model assumes that this modulation of the individual behavior is linked to the overall density of cockroaches under the shelter. Therefore cockroaches should have a global perception of the number of conspecifics under the shelter they occupy. Here, we rather propose that this modulation is achieved thanks to a local perception of the proximate neighbors as described in the cockroach aggregation model by Jeanson et al. (2005). To investigate this hypothesis, we use an approach mixing both robotics experiments and computer simulations. On the one hand the robotics implementation allows the testing of the behavioral model in practice and in context, that is in terms of real problems in real environments. It is the proof-of-concept that the aggregation behavior can be used as a place selection mechanism for groups of autonomous robots. It is also a validation of our biological hypothesis that the aggregation behavior of B. germanica actually drives its place selection behavior (for a review of the robotics approach to animal behaviour, see Dean, 1998; Webb, 2000, 2001). Note that this robotics approach has been successfully employed to study individual animal behaviors related with motor or sensorimotor control (see for instance Franceschini et al., 1992; Pfeiffer 112

132 CHAPITRE INTRODUCTION et al., 1995), navigation (see for instance Lambrinos et al., 2000; Srinivasan et al., 1999) or learning (see for instance Voegtlin & Verschure, 1999). In a collective behavior context, it has been applied to study aggregation (May et al., 2006; Garnier et al., 2008), stigmergic processes (Beckers et al., 1994; Holland & Melhuish, 1999; Melhuish et al., 2001), cooperative transport (Kube & Bonabeau, 2000), the influence of task allocation and group size on foraging efficiency (Krieger et al., 2000; Krieger & Billeter, 2000) or the influence on collective place selection of robotic lures in animal groups (Halloy et al., 2007). On the other hand the computer simulations approach aims at exploring more systematically the properties of the behavioral model. They allow the investigation of the collective selection mechanism in an extended set of environmental conditions. They thus bring additional information about the collective behavior of the robotics system. Seen from a biological point of view this information may also open interesting insights about the collective behavior of our biological model. To ensure the coherence between the virtual implementation and the physical embodiment of the behavioral model, the computer simulations are calibrated according to the robotics experiments. With this dual approach, we first test whether the self-amplified aggregation behavior of the German cockroach is capable of triggering a collective choice between two identical opportunities. In a recent work, we have implemented this aggregation behavior in a group of small autonomous robots, and we have successfully reproduced the aggregation dynamics displayed by B. germanica in a homogeneous circular arena (Garnier et al., 2008). Here, we introduce heterogeneities in the circular arena in the form of two identical dark shelters. We also restrict the occurrence of the aggregation behavior to these dark shelters (robots are programmed not to stop outside the shelters). If our hypothesis is correct, the robots should aggregate under a single shelter. We further investigate with computer simulations whether this choice between equal opportunities is sensitive to the available space for aggregation. Keeping the number of virtual robots constant, we vary the radius of the shelters, from shelters too small to house the whole group of robots to shelters much bigger than the required size to house all the robots. We repeat these virtual experiments with different numbers of robots in order to evaluate how the response scales with the group size. In a second step we test how the collective decision mechanism deals with physically different opportunities. Collective choices are known to be sensitive to the physical differences between opportunities that are in competition. In particular, any constraint that modulates the speed of the self-amplification process at one of the different opportunities can lead that opportunity to 113

133 3.6. MATERIAL AND METHODS CHAPITRE 3. win, or lose, its competition against the other ones (Camazine et al., 2001; Jost et al., 2007). In this paper, we assess the influence of a difference between the radii of the two shelters on the final choice. To that purpose, we run two sets of robotics experiments, each time with one shelter bigger than the other one. In the first set of experiments, the smaller shelter can hardly house the whole group of robots while the bigger one can do it. In the second set of experiments, the two shelters are large enough to house the whole group of robots. These two situations differ from each other only by the influence of the physical obstruction to enter the smaller shelter. When some other robots are already there the new arrivals are less likely to enter the smaller shelter in the first situation only. We therefore expect that the group behaves differently between these two nearly identical situations. In order to study in more detail the influence of the ratio between the sizes of the two shelters on the final choice, we use computer simulations where we confront a group of ten virtual robots with one shelter of constant size and one shelter which size varies between simulation runs. We finally discuss the results of both robotics experiments and computer simulations from our dual point of view. We examine in particular how the collective decision model tested in this paper may account for various observations of cockroach collective behavior in both experimental and natural contexts. We also consider the interest for collective robotics of the properties displayed by this embodied model. 3.6 Material and methods The micro-robots Alice The Alice micro-robots (see figure 3.4) were designed at the EPFL (Lausanne, Switzerland) (Caprari & Siegwart, 2005). They are very small robots (22 mm x 21 mm x 20 mm) with a maximum speed of 40 mm s 1. They are equipped with two watch motors with wheels and tires. Four infrared sensors and transmitters are used for obstacle detection and local communication among Alices. Energy is provided by a NiMH rechargeable battery allowing an autonomy of about six hours in the configuration used during this study. The Alice robots have a micro-controller PIC16LF877 with 8K Flash EPROM memory, 368 bytes RAM and no built-in float operations. Programming is done with the IDE of the CCS-C compiler and the compiled programs are downloaded in the Alice memory with the PIC-downloader software

134 CHAPITRE MATERIAL AND METHODS Figure 3.4: A robot Alice heading towards the left side The experimental set-up The experimental setup consists of a circular arena (25 cm radius) covered with a glass plate and two freely suspended semi-transparent dark discs that act as shelters. A 60 watts glow light is suspended 60 cm above the arena to generate a background infrared light of homogeneous intensity (the robots only detect infrared light). All other light sources are eliminated. This experimental setup aims at reproducing the one used in Amé et al. (2006). Three shelter sizes are used : small (radius r small = 5cm), medium (radius r medium = 7cm) and large (radius r large =9cm). In theory, these three kinds of shelters are all sufficiently large to house the whole population of robots : the minimal known radius of the circle required to house 10 packed squares measuring 2.1 cm on each size is r 10 =4.45 cm (Friedman, 2007). However, the 10 robots cannot aggregate under the small shelter if they do not adopt a particular configuration. In practice, physical obstruction prevents the whole group to house under the small shelter. Experiments are conducted with groups of ten robots and they last 60 minutes each. In order to record robot behaviors, a high definition camera (Sony CDR-VX 2000 E) is attached above the arena The behavioral model The behavioral model we use in this work is an extension of the aggregation model described in Jeanson et al. (2003a, 2005) and implemented in robots by Garnier et al. (2008). The original behavioral model is developed from experiments with first instar larvae of the German cockroach, Blattella germanica. In its natural environment, B. germanica forms dense aggregates of individuals of both sexes and all developmental stages especially at low external humidity (Ledoux, 1945; Dambach & Goehlen, 1999). The original behavioral model accounts for the self-organized 115

135 3.6. MATERIAL AND METHODS CHAPITRE 3. mechanism that leads to this aggregation behavior. The complete aggregation model and its implementation are described in Garnier et al. (2008) and outlined in the supplementary material of this paper. In summary, each robot explores the experimental arena by a correlated random walk in the absence of obstacles or by a wall-following behavior in the presence of large obstacles. Each robot can stop its displacement at any time. The decision to stop is taken according to a memory-less process : it is independent of the previous experience of the robot, therefore the probability to stop moving per unit time (stop rate) is constant in time. However it depends on the number of stopped robots that a robot perceives in its direct neighborhood (up to 4cm distance). The stop rate of a robot grows with this number and it reaches a maximum for three neighbors or more. Once stopped, the robot decides whether the stop is of short or long mean duration. The probability for the stop to be a short one decreases with the number of neighbors, with a minimum for three of more neighbors. The decision to restart is also taken according to a memory-less process. The rate to restart is therefore constant in time. However it depends on the state of the stop (short or long) and on the number of neighbors. It is maximal for a short stop with no neighbor, and minimal for a long stop with three or more neighbors. In the extended model used in this paper, this aggregation behavior is restricted to dark places in the environment. A robot can only stop if it perceives a significant drop in the background infrared light intensity that it detects with its infrared sensors. This drop informs the robot that it enters a shelter. This rule restricts the aggregation behavior to the dark places and is the only addition to the original aggregation model from Jeanson et al. (2005) and Garnier et al. (2008) The experimental parameters Identical shelters In a first set of twenty experiments, the robots are put into an arena with two shelters of the same size (medium size, radius r medium =7cm). The goal of this situation is to demonstrate the ability of the behavioral model to trigger a collective choice, even if the two offered opportunities are equivalent. At the beginning of each experiment, ten robots are evenly spread within the arena. We then suspend two medium shelters and let the robots aggregate during sixty minutes Shelters of different sizes In this second set of experiments, the robots are put into an arena with two shelters of different radius. The goal of this situation is to study whether a difference between the two 116

136 CHAPITRE MATERIAL AND METHODS opportunities would bias the collective choice. Two situations are tested : a shelter of small size (radius r small =5cm) versus a shelter of medium size (radius r medium =7cm), and a shelter of medium size versus a shelter of large size (radius r large =9cm). For each situation, twenty experiments are performed. At the beginning of each experiment, ten robots are evenly spread in the arena and we let them aggregate during sixty minutes Numerical experiments In addition to the robotic experiments, we run several sets of spatially explicit individual based simulations to further explore the model properties. The simulator takes into account the spatial obstruction between the individuals in order to reproduce the physical exclusion of the robots under crowded shelters. For the purpose of computing efficiency, the spatial obstruction is not obtained thanks to a physics engine but rather by mimicking the avoidance behavior of the robot observed in experiments after a collision with another robot (slightly go backward and wobble). This simulator has already been validated for the aggregation behavior in Garnier et al. (2008). We also validate the simulator against experimental results for the collective choice behavior in order to ensure the coherence between robotics and virtual experiments. With the simulations we address in particular two questions. The first one is : how does the collective choice scale with group size and with changing available space for aggregation (that is the space covered by the two shelters)? To answer this question we vary the radius of the two shelters simultaneously from 0 to 5 times (in steps of 0.1) the minimal known radius r n of the circle required to house n packed squares, with n =5, 10, 20, 50 robots and r 5 =3.32 cm, r 10 =4.45 cm, r 20 =6.08 cm and r 50 =9.26 cm (Friedman, 2007). The radius of the arena is chosen such that the ratio between the surface of the arena and the cumulated surface of the shelters remains constant. We run 1000 replications by size step and each simulation corresponds to 60 minutes in real time. The second question is : how does a difference between the sizes of the two shelters bias the collective choice? To answer this question we fix the radius of one shelter (7 cm, medium size shelter) while we vary the radius of the other one from 1 cm to 50 cm (i.e., from 0.14 to 7.14 times the radius of the constant shelter) by steps of 1 cm. The idea is to extend the range of radius values tested in the robotics part of the work. We look in particular for specific values for which the collective choice could change qualitatively. The size of the arena is varied in order to fix the ratio between the surface of the arena and the cumulated surface of the shelters. We run 1000 replications by radius size and each simulation corresponds to 60 minutes. This sensitivity 117

137 3.6. MATERIAL AND METHODS CHAPITRE 3. analysis is performed for a group of 10 robots Data analysis All analyses are made with the free statistical software R (R Development Core Team, 2006) Experiments For each kind of experiment, we count at each minute the number of stopped robots under each shelter. For convenience, we name the shelters subsequently S 1 and S 2. For each experiment, we thus obtain m s1 (the number of robots stopped under shelter S 1 ), m s2 (the number of robots stopped under shelter S 2 ) and m tot (the total number of robots). In the robotics experiments, we have m tot = 10. For the experiments with identical shelters, we define in each replication the chosen shelter as the one that contains the largest number of stopped robots at the end of the experiment. We then compute the mean number of robots under the chosen and the not chosen shelters minute by minute. We also compute the fraction of the stopped robots which are under shelter S 1 at m the end of each experiment as F Stop,S1 = S1 m S1 +m S2. From this last statistics we derive what we call a choice distribution which corresponds to the distribution of the F Stop,S1 over all the replications. Note that a robot can be in three different locations at the end of an experiment : under one of the two shelters or outside the shelters. In the case of each robot choosing randomly a shelter (i.e., without any influence of its conspecifics), the result follows a trinomial law with parameters m tot = 10 (number of robots), p a = (mtot m S 1 m S2 ) m tot (probability for a robot to be outside the rs shelters, estimated from the experiments), p S1 = (1 p a )( 2 1 ) (probability for a robot to rs 2 +r 2 1 S 2 be under shelter S 1 ; r S1, radius of shelter S 1 ; r S2, radius of shelter S 2 ) and p S2 =1 p S1 p a (probability for a robot to be under shelter S 2 ). The choice distribution resulting from this trinomial law is obtained through Monte Carlo simulations (10000 simulations of 20 replications). We compare this random choice distribution with the experimental choice distribution by means of a chi square test. For the experiments with different shelters, we always consider the medium shelter as shelter S 1 and either the small or the large shelter as shelter S 2. We compute every minute the mean number of robots under shelters S 1 and S 2. We also compute the choice distribution in the two different situations. The resulting choice distributions are compared with the corresponding trinomial distributions with a chi square test and with the choice distribution of the identical 118

138 CHAPITRE MATERIAL AND METHODS shelters case with a Fisher s exact test. To ensure the coherence between the robotics and the virtual experiments, three sets of simulations corresponding to the three experimental situations described in section are analyzed with the same methods as those described above. Additionally, the choice distributions of these three sets of simulations are compared with the corresponding experimental choice distribution thanks to Fisher s exact test Sensitivity analysis The goal of the sensitivity analysis is to assess how the collective choice depends on either the sizes of the two shelters (identical shelters case) or the ratio between the two shelter sizes (different shelters case). We therefore define the control parameter for the sensitivity analysis in the identical shelters case as the ratio r S rn, with r S the radius of the two shelters and r n the size of the minimal known radius of the circle required to house n packed squares measuring 2.1 cm on each side (with n =5, 10, 20, 50). In the different shelters case we define the control parameter as the ratio r S 2 r S1, with r S2 the radius of the shelter whose size varies (S 2 ) and r S1 the radius of the shelter whose size remains constant and corresponds to a medium shelter (S 1 ). To measure the variation of the collective choice, we compute for each replication the fraction of robots stopped under shelters S 1 and S 2 at the end of each experiment as F S1 = m S 1 m tot and F S2 = m S 2 m tot. These fractions are slightly smaller than the fraction F Stop,S1 of stopped robots which are under shelter S 1 since they also take into account the number of robots that remain moving at the end of the replication. In the experimental part, this number can be neglected (most of the robots are stopped under a shelter at the end of each experiment) and thus F Stop,S1 is used. However the number of robots still moving at the end of the replication cannot be neglected in the sensitivity analysis since the available space for aggregation should have an influence on the total number of stopped robots. In the identical shelters case we also compute the fraction F S 0.8 of replications that end with either F S1 0.8 or F S2 0.8 : this corresponds to the fraction of experiments that ends with at least 80% of the robots under one of the two shelters. In the different shelters case, we compute in the same manner the fraction F S1 0.8 of replications that end with F S1 0.8, the fraction F S2 0.8 of replications that end with F S2 0.8 and the fraction F S 0.8 = F S F S2 0.8 of replications that end with either F S1 0.8 or F S

139 3.7. RESULTS CHAPITRE 3. Figure 3.5: Typical temporal evolution of the collective decision process in a robotics experiment (top row) and a simulation run (bottom row). Robots under the dark shelters (top row) are visualized by white squares. 3.7 Results Figure 3.5 displays typical spatio-temporal dynamics of the collective choice of a single shelter in both robotics and simulated experiments with identical shelters Identical shelters Experiments Figures 3.6a and 3.6c summarize the experimental results for the case with two identical shelters. Figure 3.6a describes the temporal dynamics of the number of aggregated robots under the chosen and the discarded shelters. These dynamics display two distinct phases. The first phase lasts approximately 10 minutes and displays a linear growth of the number of aggregated robots under the chosen shelter. At the end of this first period, about 50% of the overall population of robots is aggregated under the chosen shelter, while less than 10% is aggregated under the discarded one. The second phase lasts until the end of the experiment. It also displays a linear growth of the number of aggregated robots under the chosen shelter, but with a smaller rate. At the end of the experiments, 75.5 ± 3.36% (mean ± standard error) of the overall population is aggregated under the chosen shelter, while 12 ± 3.44% (mean ± s.e.) is aggregated under the discarded one. 120

140 CHAPITRE RESULTS Figure 3.6c describes the experimental choice distribution for shelter S 1. This choice distribution displays a U shape which is a typical signature of self-organized binary choices (see for instance Beckers et al., 1992b; Amé et al., 2006). 60% of the experiments end with more than 80% of the aggregated robots under a single shelter. 85% of the experiments end with more than 60% of the aggregated robots under a single shelter. The comparison of this experimental choice distribution with a random choice distribution shows a highly significant difference (χ 2 = 134.8, p<0.0001, p-value simulated with replications) Simulator validation Figures 3.6b and 3.6d summarize the simulation results for the case with two identical shelters. As for the robotics experiments (see figure 3.6a), the choice dynamics display in the first minutes a quick linear growth of the number of aggregated robots under the chosen shelter, followed by a slower growing phase during the remaining time. At the end of the simulations, 77.9 ± 0.52% (mean ± s.e.) of the overall population is aggregated under the chosen shelter (68 ± 3.2% in the experiments), while ± 0.48% (mean ± s.e.) is aggregated under the discarded one (12 ± 3.44% in the experiments). Moreover, the comparison between the simulated (see figure 3.6d) and the experimental (see figure 3.6b) choice distributions shows no significant differences (Fisher s exact test, p =0.5759) Sensitivity analysis Figure 3.7 summarizes the sensitivity analysis in the identical shelters case. It represents the fraction of replications ending with at least 80% of the robots aggregated under the same shelter (F S 0.8 ) as a function of the ratio between the radius of the shelters and the minimal known radius of the circle required to house the whole group of robots ( r S rn ). The curves for 5, 10, 20 and 50 robots display a common pattern. Below a threshold ratio r S rn, no replication ends with at least 80% of the robots aggregated under the same shelter. This corresponds to ratio values for which r S is too small to house 80% of the robots, therefore a trivial case. After this initial part, F S 0.8 quickly grows with r S rn until reaching a plateau, and finally decreases as r S becomes much larger than r n. This final decrease is mainly due to the increase of the available space as a consequence of the constant ratio between the surface of the arena and the cumulated surface of the shelters (see section 3.6.5). As r S grows the available space under each shelter and outside the shelters grows. This decreases the probability for a robot to encounter an aggregate and therefore reduces the probability to obtain a large and stable cluster 121

141 3.7. RESULTS CHAPITRE 3. Mean number of stopped robots Chosen shelter Unchosen shelter Chosen shelter Unchosen shelter Time (min) Time (min) Number of replicates Number of replicates F Stop,S F Stop,S1 Figure 3.6: Results of the robotics experiments and the simulations with two identical shelters. Top: number of robots aggregated under each shelter per minute. (a): experimental data (n = 20). (b): simulation data (n = 1000). White dots represent data for the chosen shelter (i.e. the shelter which is chosen at the end of each experiment); black dots represent data for the discarded shelter. Each dot represents the mean ± s.e. (note that in the simulations the s.e. became too small to be seen on the graph). Bottom: choice distributions. In these distributions, each block represents the number of experiments ending with a given percentage (0-20, 20-40, 40-60, and percent) of stopped robots under shelter 1 (independently of whether it was chosen or not). (c): experimental distributions (n = 20). (d): simulation distributions (n = 1000). 122

142 CHAPITRE RESULTS F S! robots 10 robots 20 robots 50 robots r S r n Figure 3.7: Identical shelters case. Fraction of simulation replications that end with at least 80% of the robots aggregated under the same shelter (F S 0.8 ) as a function of the ratio between the radius of the two identical shelters (r S ) and the minimal known radius of the circle required to house the whole group of robots (r n ) simulation replications have been performed for each value of r S rn and for each group size (5, 10, 20 and 50 robots). under one of the two shelters. Despite this common pattern, the sensitivity analysis displays a difference between the different group sizes. This difference is an obvious decrease of the values of F S 0.8 as the number of robots increases. For instance, the maximal value of F S 0.8 varies from 0.73 for 5 robots to 0.19 for 50 robots. At the plateau, this means that more than 70% of the replications with 5 robots end with at least 80% of the robots under one of the two shelters. This percentage of replications drops below 20% with 50 robots : few replications with 50 robots ends with a clear choice for one of the two shelters. With 50 robots, it is likely that several large aggregates (10 robots or more) appear during the collective choice process. The time spent by a robot in an aggregate is maximal when this robot is surrounded by at least three neighbors. In a group of 10 or more robots, it is likely that several robots are surrounded by at least three neighbors. As a consequence, such aggregates are very stable. If one large aggregate forms under each shelter, it is therefore likely that the competition between them lasts a long time (more than the 60 minutes of the experiment) before one of them captures most of the robots and the collective decision occurs. Additional simulations (data not shown) support this idea : even after 120 minutes the stationary state is not reached with 50 robots (i.e the mean number of robots under the chosen shelter continues to increase). 123

143 3.7. RESULTS CHAPITRE Summary of the identical shelters case Experimentally, when the group of robots faces two identical shelters, most of the experiments end with a choice of either shelter S 1 or shelter S 2. The German cockroach aggregation behavior is therefore able to trigger a collective choice, even if the different opportunities are equivalent. The sensitivity analysis reveals that the group of robots cannot perform a collective choice if the two shelters are very large or if the size of the group is too important. In the first case, the collective choice is prevented by a dilution effect that restricts the possibilities for the robots to interact and therefore to aggregate. In the second case, the large number of individuals interferes with the collective decision process because of the formation of several stable aggregates which delay the choice beyond the experiment s duration and might even prevent it. Finally, these results suggest that there exist a range of shelter sizes and group sizes for which a collective decision can emerge from the cockroach aggregation behavior Shelters with different sizes Experiments Medium versus small shelters. Figures 3.8a and 3.8c summarize the experimental results for the case with a medium and a small shelter. Figure 3.8a describes the temporal dynamics of the number of aggregated robots under the medium and the small shelters. As in the previous section, these dynamics display two distinct phases. The first linear growth phase lasts approximately 15 minutes and ends with approximately 70% of the overall population of robots aggregated under the medium shelter, while only 5% is aggregated under the small one. During the second phase the percentage of robots under the medium shelter remains rather stable around 70%. At the end of the experiments, 68 ± 3.2% (mean ± s.e.) of the overall population is aggregated under the medium shelter, while 1.5 ± 1.1% (mean ± s.e.) is aggregated under the small one. Figure 3.8c describes the experimental choice distribution for shelter S 1 (i.e., the medium shelter). This choice distribution displays a single peak. 95% of the experiments end with more than 80% of the aggregated robots under the medium shelter. 100% of the experiments end with more than 60% of the aggregated robots under the medium shelter. The comparison with a random choice distribution shows a highly significant difference (χ 2 = 87.16, p =0.0002, p-value simulated with replications). The comparison with the distribution of the identical shelters case shows also a highly significant difference (Fisher s exact test, p<0.0001). 124

144 CHAPITRE RESULTS Mean number of stopped robots Medium shelter Small shelter Time (min) Medium shelter Small shelter Time (min) Number of replicates Number of replicates F Stop,S F Stop,S1 Figure 3.8: Results of the experiments and the simulations with a normal size and a small shelter. Top: number of robots aggregated under each shelter per minute. (a): experimental data (n = 20). (b): simulation data (n = 1000). Black dots represent data for the small shelter (radius of 5 cm) and white dots those for the normal shelter (radius of 7 cm). Each dot represents the mean ± s.e. Bottom: choice distributions (see figure 3.6). (c): experimental distributions (n = 20). (d): simulation distributions (n = 1000). 125

145 3.7. RESULTS CHAPITRE 3. Medium versus large shelters. Figures 3.9a and 3.9c summarize the experimental results for the case with a medium and a large shelter. Figure 3.9a describes the temporal dynamics of the number of aggregated robots under the medium and the large shelters. As aforementioned, these dynamics display two distinct phases. The first linear growth phase lasts approximately 15 minutes and ends with approximately 60% of the overall population of robots aggregated under the medium shelter, and 25% under the small one. During the second phase the percentage of robots under the medium shelter remains rather stable around a plateau at 60%. At the end of the experiments, 70.5 ± 7.6% (mean ± s.e.) of the overall population is aggregated under the large shelter, while 17.5 ± 7.1% (mean ± s.e.) is aggregated under the medium one. Figure 3.9c describes the experimental choice distribution for shelter S 1 (i.e., the medium shelter). This choice distribution displays a biased U shape, with 75% of the experiments ending with more than 80% of the aggregated robots under the large shelter and 15% of the experiments ending with more than 80% of the aggregated robots under the medium shelter. The comparison with a random choice distribution shows a highly significant difference (χ 2 = , p<0.0001, p-value simulated with replications). The comparison with the distribution of the identical shelters case shows also a highly significant difference (Fisher s exact test, p<0.0282) Simulator validation Medium versus small shelters. Figures 3.8b and 3.8d summarize the simulation results for the case with a medium and a small shelter. As for the robotics experiments (see figure 3.8a), the dynamics of the choice displays in the first minutes a quick linear growth of the number of aggregated robots under the medium shelter, followed by a plateau in the rest of the simulation. At the end of the simulations, ± 0.8% of the overall population is aggregated under the medium shelter (75.5 ± 3.36% in the experiments), while ± 0.5% is aggregated under the small one (1.5 ± 1.1% in the experiments). Moreover, the comparison between the simulated (see figure 3.8d) and the experimental (see figure 3.8b) choice distributions shows no significant differences (Fisher s exact test, p = ). Medium versus large shelters. Figures 3.9b and 3.9d summarize the simulation results for the case with a medium and a large shelter. As for the robotics experiments (see figure 3.9a), the dynamics of the choice displays during the first minutes a quick linear growth of the number of aggregated robots under the large shelter, followed by a plateau during the remaining time. At the end of the simulations, ± 1.11% of the overall population is aggregated under the large 126

146 CHAPITRE RESULTS Mean number of stopped robots Medium shelter Large shelter Medium shelter Large shelter Time (min) Time (min) Number of replicates Number of replicates F Stop,S F Stop,S1 Figure 3.9: Results of the experiments and the simulations with a normal size and a large shelter. Top: number of robots aggregated under each shelter per minute. (a): experimental data (n = 20). (b): simulation data (n = 1000). Black dots represent data for the large shelter (radius of 9 cm) and white dots those for the normal shelter (radius of 7 cm). Each dot represents the mean ± s.e. Bottom: choice distributions (see figure 3.6). (c): experimental distributions (n = 20). (d): simulation distributions (n = 1000). 127

147 3.7. RESULTS CHAPITRE 3. shelter (70.5±7.6% in the experiments), while 29.29±1.07% is aggregated under the medium one (17.5 ± 7.1% in the experiments). Moreover, the comparison between the simulated (see figure 3.9d) and the experimental (see figure 3.9b) choice distributions shows no significant difference (Fisher s exact test, p =0.5351) Sensitivity analysis Figure 3.10 summarizes the sensitivity analysis in the different shelters case with 10 robots. It represents the fraction of replications ending with at least 80% of the robots aggregated under the shelter with a constant radius (F S1 0.8), under the shelter with a varying radius (F S2 0.8) or under both shelters (F S 0.8 ) as a function of the ratio between the radius of the varying shelter and the radius of the constant shelter ( r S 2 r S1 ). As r S 2 r S1 grows from 0 to 7, F S1 0.8 monotonically decreases, approximately following an exponential decay from to 0. F S2 0.8 is equal to 0 for r S 2 r S1 < 0.71, that is when r S2 is inferior to the minimal known radius of the circle required to house 8 robots (i.e., 80% of the whole group). It then grows and reaches a plateau around 0.55 for 1.5 r S 2 r S Finally, F S2 0.8 decreases as r S 2 r S1 increases. At last, F S 0.8 (the sum of F S F S2 0.8) initially follows the same decay as F S1 0.8 until r S 2 r S1 < It then switches to a plateau around 0.6 before continuing the decay for r S 2 r S1 > 2.7. Together, these three curves lead to the following scenario. For small ratios, the varying shelter S 2 is too small to house 8 robots ( r S 2 r S1 < 0.71), the constant shelter S 1 is therefore selected in most of the experiments. During this first part, the decrease of F S1 0.8 is a consequence of the increase of r S2. As the available space under S 2 increases, the competition between S 1 and S 2 is amplified and the probability for a replication to end with 80% of the robots under S 1 decreases. Once S 2 is sufficiently large to house 8 robots ( r S 2 r S1 0.71), F S2 0.8 starts to grow while F S1 0.8 continues to decrease. F S 0.8 reaches a plateau from this point : the decrease of F S1 0.8 is balanced by the increase of F S The two curves cross at r S 2 r S1 =1(the two shelters have the same size). Beyond r S 2 r S1 =1, F S1 0.8 decreases towards zero while F S2 0.8 reaches a maximum before also decreasing. Interestingly, F S1 0.8 and F S2 0.8 are not symmetrical before and after r S 2 r S1 =1. F S1 0.8 starts from a value near 1 and goes down to 0, while F S2 0.8 starts from 0 but only grows until around 0.6 before decreasing. As in the identical shelters case, this final decrease of F S2 0.8 is mainly due to the increase of the available space as a consequence of the constant ratio between the surface of the arena and the cumulated surface of the shelters. As r S2 grows the available space 128

148 CHAPITRE RESULTS F Si! F S! r S2 r S r S2 r S1 Figure 3.10: Different shelters case. Dashed line: fraction of simulation replications that end with at least 80% of the robots aggregated under the shelter 1 (F S1 0.8) as a function of the ratio between the radius of the shelter 2 (which size varies, r S2 ) and the radius of the shelter 1 (which size remains constant, r S1 ). Solid line: fraction of simulation replications that end with at least 80% of the robots aggregated under the shelter 2 (F S2 0.8) as a function of the ratio between r S2 and r S1. Inset: fraction of simulation replications that end with at least 80% of the robots aggregated under the same shelter (F S 0.8 = F S F S2 0.8) as a function of the ratio between r S2 and r S1. For each value of r S 2 r S simulation replications have been performed with a group of 10 robots). under shelter S 2 and outside the two shelters grows. This decreases the probability for a robot to encounter an aggregate and therefore reduces the probability to obtain a stable cluster under shelter S Summary of the different shelters case If one of the two shelters is bigger than the other, the aggregation behavior is also able to trigger a collective choice. However this collective choice favors one of the opportunities. In the case of the medium versus the large shelter, the two shelters can be chosen by the robots, but more experiments end with a choice of the large one. In the case of the medium versus the small shelter, the group only chooses the medium one and never chooses the small one. The sensitivity analysis confirms that the choice is biased towards the larger shelter which probability to be encountered by a robot is greater. Moreover, the larger shelter is more often selected if the smaller shelter is not sufficiently large to house the whole population of robots. As in the identical shelters case, there exists a range of shelter sizes for which a collective decision can 129

149 3.8. DISCUSSION CHAPITRE 3. emerge from the cockroach aggregation behavior. 3.8 Discussion The restriction to two distinct but identical shelters of the self-organized aggregation behavior described in Jeanson et al. (2005) enables a group of robots to collectively select one of them. The dynamic of this choice (the evolution of the number of robots under each shelter) is similar to the dynamics of other self-organized decision-making processes (Camazine et al., 2001). This shows that the local amplification that triggers the aggregation behavior works also as a mechanism for the collective choice of a shelter : the higher the size of an aggregate under a shelter, the higher the probability for a robot to join this cluster and to rest under the shelter. As time goes on, the decreasing number of moving robots (Garnier et al., 2007b) brings the global dynamics to a standstill with a majority of the robots clustered under only one of the two available aggregation places. A disparity between the two shelters can be amplified by the collective choice mechanism. The presence of a slight size difference between the shelters biases the final choice towards the bigger one. Interestingly, a similar result has recently been found in a set of experiments with groups of 10, 20 and 30 real cockroaches : they preferentially choose to aggregate under the larger of two shelters (Terramorsi et al., 2007). This strengthens the validity of the biological model used in our study to explain the emergence of the collective choice in cockroaches from their aggregation behavior. From the robotic point of view, this implies that the group of robots is able to sense and compare the size of the shelters during the collective decision process. The group acts as a larger place detector, a performance that is beyond the direct scope of the simple aggregation process used in these experiments and that is not explicitly implemented in individual robots. Such an influence of a physical characteristic on the final choice has already been reported for other self-organized decision-making processes. For instance, Dussutour et al. (2005a) showed that the presence of a wall along one of the paths linking the nest and a food source induces a collective selection of this path by the ant Lasius niger. The natural tendency of this ant to follow edges enhances the positive feedback and thus leads to the choice of paths passing along spatial heterogeneities. As another example, the ants Messor barbarus preferentially select a dark rather than a light place to aggregate (Jeanson et al., 2004a). In this case, ants modulate their recruitment behavior as a function of the quality (dark/light) of the place : the intensity 130

150 CHAPITRE DISCUSSION of the recruitment towards dark places being stronger than towards light places, the former is preferentially selected. But a physical property of the environment can also have an influence through the collective dynamics and without any modulation of the individual behavior. For example, this is what happens when the ant Linepithema humile preferentially selects the shortest path between its nest and a food source (Goss et al., 1989; Aron et al., 1990; Vittori et al., 2006). Here, ants following the shortest path need less time to go back and forth between the source and the nest. Therefore, they replicate the pheromone trail on the shortest path more often than ants following longer ones. The amplification of the pheromone trail is thus faster on the shortest path which is finally chosen. The bias in the collective choice of a shelter by the robots (shown here) and the cockroaches (Terramorsi et al., 2007) pertains to this last category. The physical properties of the shelters do not trigger any modulation of the individual behavior that could favor preferential choice of the larger shelter. Rather, individuals have a greater probability to encounter this latter because its periphery is larger, and they spend more time moving under it also because its surface is larger. Together, these two points increase the probability that an aggregate is first initiated and amplified under the larger shelter. At last, the preference for the larger shelter is increased when the radius of the smaller shelter is close to the minimal known radius of the circle required to house the 10 robots. The experimental results show that the small shelter, which radius is close to the limit, is never chosen when opposed to a medium shelter, while the medium shelter is sometimes chosen when opposed to a large shelter. The small shelter can house the 10 robots only if they are placed according to some particular configurations. Otherwise a part of the robots are prevented from entering under the shelter by physical obstruction. It is therefore unlikely that the 10 robots aggregate at the same time under the small shelter. As a consequence, even if a majority of the robots choose initially to aggregate under the small shelter, a part of them is almost always available to initiate a cluster in the other shelter. This makes the choice of the small shelter an unstable solution in most of the situations and enhances again the existing bias towards the choice of the larger shelter. Computer simulation results are statistically similar to those obtained with the robotics experiments. The sensitivity analysis indicates a range of group sizes and shelter radii that favors the occurrence of a collective decision when the two shelters are of equal size. As in the robotics experiments, the choice is biased towards the larger shelter in the case of shelters with different radii. The choice of the larger shelter is enhanced if the smaller shelter is not sufficiently 131

151 3.8. DISCUSSION CHAPITRE 3. large to house all the robots. The sensitivity analysis also reveals that the collective decision mechanism is hindered if the available space inside or outside the shelters is too important. The probability for a robot to encounter an aggregate diminishes with the area to explore which prevents the self-amplification of the cluster size. Aggregation and hence a collective choice are thus unlikely to occur because the density of individuals inside the experimental arena is too small. A similar density dependent effect is obtained with the deterministic mathematical model proposed in Amé et al. (2006) for a similar experimental setup. An extended analysis of this model (shown in the supplementary material) predicts that the robots will not perform a collective choice if the two shelters are much larger than the minimal size required to house the whole population. Whatever the model used, such a dilution effect raises the following question : is the collective choice of a shelter likely to occur in nature where the available space to explore is more important than in our experiments? The dilution effect may be explained by the experimental conditions used by Jeanson et al. (2005) to study the aggregation behavior of B. germanica and to build the behavioral model that is used in our work. Experiments with German cockroaches were performed in unknown and clean arenas. Therefore the observed exploratory behavior was a random walk with the consequence that the probability to encounter other individuals diminishes rapidly with the size of the area to explore. In nature, German cockroaches mark their home range with aggregation reinforcing pheromones contained in their feces (Rust et al., 1995) and they mark trails that orient their displacements in preferential directions (Miller & Koehler, 2000; Miller et al., 2000; Jeanson & Deneubourg, 2006). They also use visual landmarks and idiothetic cues to establish familiar routes to food sources in their home range (Durier & Rivault, 1999, 2000, 2001; Rivault & Durier, 2004). Together these points suggest that the random exploratory behavior is less frequent in nature than in Jeanson et al. s (2005) model and that, as a consequence, the individual dispersal is more directed than in our experiments. This should increase the number of interactions between individuals and favor the occurrence of a collective choice of a place to aggregate, provided that several shelters are present and that they are linked by scent trails or not too far from each other. This observation has an important consequence for the utilization of this collective place selection behavior in groups of robots : it must be coupled with a mechanism that favors interactions between individuals. As all self-organized processes its properties mainly rely on the repeated interactions that happen between the lower level components of the system (Camazine et al., 2001). Its efficiency will therefore be decreased if the amount of interactions is not maintained 132

152 CHAPITRE DISCUSSION at a sufficient level. The second point revealed by the sensitivity analysis is a delayed collective decision as the number of involved individuals increases. The higher the number of robots, the more likely occurs the formation of several large and therefore long lasting clusters (more than 10 individuals). The competition between these clusters delays the collective decision process in most of the replications with a large number of robots beyond the experiment s duration of 60 minutes. It is even possible that no collective decision occurs with groups larger than 40 individuals. An exhaustive analysis of the cockroach aggregation model shows that at stationary state the mean number of aggregates formed by 40 cockroaches is 2 (data not shown). It is therefore likely that a large population of cockroaches (40 or more individuals) preferentially splits between the different shelters, even if each of the shelters is sufficiently large to house the whole population. This is consistent with several observations regarding the number of B. germanica forming a cluster : depending on the kind, size and quality of the shelters, an aggregate can include usually between 10 and 30 individuals (Rust et al., 1995). Thus, the collective choice mechanism used in our study well explains the distribution of cockroaches in a natural population. Moreover it has been shown that aggregation increases the survival rate of cockroaches, especially at low humidity levels (Dambach & Goehlen, 1999), and also increases rates of both nymphal development and oothecae production in B. germanica (Lihoreau & Rivault, 2008). However there is a limit : group and individual developmental experiments have shown that overcrowding decreases the survival rate as well as the growth rate of B. germanica (Rust et al., 1995). Therefore the collective choice mechanism could also have an adaptive value for this insect since it favors the splitting of large populations under different shelters and consequently avoids overcrowding in only one aggregation place. In a robotics context such a population size dependent splitting behavior will affect the ability of large groups to select a place in the environment. However this lack of choice could be turned into a simple yet efficient means to spontaneously distribute a large population of robots into subgroups that would simultaneously perform a collective task at different places in the environment. Moreover we suggest that the tuning of the aggregation parameters should influence the mean size of these subgroups. One could therefore control more or less precisely the number of robots allocated to the different places of interest. Nevertheless preserving the collective selection behavior in large groups of robots may remain a desirable property that would require a modification of the current individual behavioral model. Interestingly, the splitting behavior depending of the group size is absent from the mathematical 133

153 3.8. DISCUSSION CHAPITRE 3. mean field model proposed in Amé et al. (2006). This latter rather predicts that the behavior of the group at steady state does not depend on its size. The difference between our model and the Amé et al. (2006) model lies in the individual behavior that triggers the self-amplification mechanism. In our model, the probability to leave a cluster depends on the number of perceivable neighbors, that is limited to three neighbors. As stated before (see section ), if several sufficiently large clusters appear (which is likely in large populations), they should be very stable. As a consequence, it is unlikely that only one of them eventually captures all the individuals. Such an occurrence of several stable aggregates has also been demonstrated with very similar behavioral models (Theraulaz et al., 2002; Nicolis, 2007). In the model of Amé et al. (2006) however, the probability to leave a shelter depends directly on the density of all individuals under this shelter. Therefore the most stable situation occurs when all the individuals are clustered under only a single shelter. The formation of subgroups is hence unlikely to occur with this model, whatever the size of the population. To obtain the same behavior with a large group of robots, these latter should hence be able to individually estimate the density under a shelter. This could easily be performed by counting the number of contacts with other robots encountered while exploring the shelter. Indeed the rate of encounters with another robot under a shelter is likely to grow with the density of robots under this shelter. For instance the ant Temnothorax albipennis successfully uses such a strategy to assess the number of conspecifics in its nest (Pratt, 2005). Note however that switching from the counting of the local number of individuals to the estimation of the density under the entire shelter may affect the selection behavior when the group faces two shelters of different radius. As previously seen, cockroaches (Terramorsi et al., 2007) as well as robots implemented with our model preferentially choose the larger of two shelters to aggregate, because the probability to encounter this shelter is more important and favors the initiation of a cluster. Amé et al. s (2006) model rather predicts that the individuals should aggregate under the shelter that allows them to reach a maximal density, provided that the two shelters are sufficiently large to house the whole population (Jean-Louis Deneubourg, personal communication). Then, this model predicts that the group should select the smaller of two shelters. In conclusion, our robotics experiments show that a model initially designed to understand the aggregation behavior of the German cockroach Blattella germanica also accounts for their collective ability to select a place to aggregate among several opportunities scattered in their environment. In a uniform environment, the modulation of the probability to join a cluster and of the time to stay in the cluster by the number of proximate neighbors leads to the aggregation of 134

154 CHAPITRE DISCUSSION the cockroaches (Jeanson et al., 2005) and the robots (Garnier et al., 2007b). In a heterogeneous environment where certain places favor the clustering of the individuals, the same amplification mechanism leads our robots to aggregate at only one of these places. Moreover, the collective decision is influenced by the available space at the different places and by the probability to encounter these places while the robots explore the environment. A set of simulations calibrated from the robotics experiments reveals that this collective choice behavior is sensitive to both the available space to explore and to aggregate, and the size of the population involved in the aggregation process. Interestingly, these results match well several observations about the real collective behavior of this cockroach species and about its dispersion in natural environments. Acknowledgments We thank Jean-Louis Deneubourg, Alexandre Campo and the members of the EMCC workgroup in Toulouse for helpful and inspiring discussions. This work was partly supported by the Programme Cognitique from the French Ministry of Scientific Research and a European community grant given to the Leurre project under the Information Society Technologies Programme ( ), contract FET-OPEN-IST of the Future and Emerging Technologies arm. Simon Garnier is supported by a research grant from the French Ministry of Education, Research and Technology. 135

155 3.8. DISCUSSION CHAPITRE 3. Supplementary material Behavioral model The behavioral model we use in this work is an extension of the aggregation model described in Jeanson et al. (2003a, 2005) and implemented in robots by Garnier et al. (2007b). The original behavioral model is developed from experiments with first instar larvae of the German cockroach, Blattella germanica. In its natural environment, B. germanica forms dense aggregates of individuals of both sexes and all developmental stages especially at low external humidity (Ledoux, 1945; Dambach & Goehlen, 1999). The original behavioral model accounts for the self-organized mechanism that leads to this aggregation behavior. In the extended model, the aggregation behavior is restricted to dark places in the environment. The detailed description of the extended model can be broken down into two parts : displacement and stopping behavior. See figure 3.11 for a schematic description of the behavioral model. All model parameter values are listed in table 3.1. Displacement The experimental arena is subdivided into two zones : a central zone and a peripheral zone. The peripheral zone is an external ring inside which a robot detects the arena wall. The central zone corresponds to the rest of the arena. In the central zone, a robot moves at speed v c according to a random walk, that is a series of straight moves which lengths follow an exponential distribution of mean l, interrupted by rotations which angles are uniformly distributed in [ 180; 180] degrees (isotropic distribution). Uniform random numbers were generated with a Quick & Dirty algorithm (Press et al., 1992). Exponential random numbers with mean l were created from a uniform random number r (0, 1) transformed to log(r)l with an algorithm using only integers (see Ahrens & Dieter, 1972, for the algorithm). Letting the robot move or turn at maximum speed we computed from these random numbers the time (in ms, which is the unit of the internal clock in the Alice) that it should move straight forward or turn. This random walk is continued until the Alice detects an arena wall with its infra-red sensors. When a robot detects a wall and enters the peripheral zone, it switches into a wall-following behavior (provided with the pre-programmed sensory-motor behaviors of Alice robots, see Caprari, 2003). The robot aligns its body with the wall and moves at speed v p in order to keep contact with the wall. The time a robot follows the wall is also exponentially distributed with 136

156 CHAPITRE DISCUSSION mean τ Exit and was computed as described above. Upon completion of this wall-following path the robot returns to the central zone with a random angle drawn uniformly between 17 and 78 degrees. During its displacement, a robot can enter a shelter. The shelter triggers a significant drop in the background infrared light intensity detected by the robot. This drop informs the robot that it is under a shelter. The robot will not modify its moving characteristics and continue its displacement according to the random walk rules. However, when under a shelter, the robot can decide to stop, which is prevented outside. This rule restricts the aggregation behavior to the dark places and is the only addition to the original aggregation model from Jeanson et al. (2005) and Garnier et al. (2008). Stopping behavior The stopping behavior only possible under a shelter depends on the number N of neighbors that a robot detects through its local infra-red communication (s N, 0 N 3). Each robot broadcasts with its infrared emitters two robot-specific identification numbers : an odd one if it is moving (movement number) and an even one if it is stopped (stop number). This emission can be read by other robots up to a distance of 4 cm. Each robot can thus detect the number of stopped robots in its immediate neighborhood. The rate to stop is constant per unit time (memory-less process), the above displacement is thus interrupted every 500 ms and a random number uniformly distributed between 0 and 1 is drawn to decide whether or not the robot should stop. If this number is inferior to a given threshold (s c if the robot is in the center, s p if it is in the periphery, s N if the robot perceives N neighbors), then the robot stops. Once stopped, the robot decides whether the duration of the stop is short or long. The probability p s,n to perform a short stop varies according to the number N of neighbors a robot can detect (0 N 3, the probability to perform a long stop is equal to 1 p s,n ). The robot thus draws a random number uniformly distributed between 0 and 1 to decide whether it will be a short stop (number inferior to p s,n ) or a long stop (number superior to p s,n ). The stop time follows an exponential distribution with a mean depending on N and on the state of the stop (short stop, mean stop time τ s,n ; long stop, mean stop time τ l,n ). If the number of stopped neighbors changes during a robot s stop, this latter has to modify the duration of its halt according to the new number of neighbors. Because we deal with a memory-less process, the time the robot has to remain stopped is independent of the time it 137

157 3.8. DISCUSSION CHAPITRE 3. Figure 3.11: Schematic representation of the behavioral model. Parameters are: speed in the center v c, speed in the periphery v p, mean free path l, rate to quit the periphery q p, rate to stop in the center s c or periphery s p, probability to be in the short stop state p s,n with mean short stopping time τ s,n and mean long stopping time τ l,n (as a function of the N stopped neighbors). The transition probabilities from moving in the center to moving in the periphery and between moving in the center or the periphery and moving under a shelter are not directly encoded in the model since they are direct consequences of the individual displacement. Moving and stopping under a shelter in the periphery are displayed in gray because these situations are taken into account in the model, but cannot occur inside our experimental setup. The parameter values are listed in table 3.1. already spent in this state. Consequently when the number of stopped neighbors changes the robot only draws a new stop time from the appropriate exponential distribution. Note that the robot retains whether the stop state is short or long. Once the stop time is elapsed the Alice continues its displacement either with a random walk (center) or a wall-following behavior (periphery). Bifurcation diagram for the binary choice of a shelter in robots Amé et al. (2006) give a system of differential equations describing the dynamical choice of a shelter in cockroaches. This system yields different qualitative collective behaviors, depending on the number and size of available shelters. In case of a binary choice between two shelters of the same size, Amé et al. (2006) provide the bifurcation diagram of the collective choice predicted by the model. Taking the reference shelter size as the size that can hold the whole group, they explored the collective choice for shelter sizes ranging from 0 to 2.5 times the reference size. They showed that all individuals gather under a unique shelter, provided that the shelter size is larger than the reference size (Amé et al., 2006, fig. 1). Here, we extend this diagram to greater size differences of the shelters, and show that the collective choice eventually collapses for bigger shelters. This collapse can be attributed to the decreasing density of individuals under the shelters, which becomes too low to trigger the auto-catalytic process. Let P i be the proportion of individuals under the shelter i, and P e the proportion of indi- 138

158 CHAPITRE DISCUSSION Parameter Value v c (cm s 1 ) 3.97 v p (cm s 1 ) 3.68 s c (s 1 ) s p (s 1 ) l (cm) τ exit (s) τ s,0 (s) 7.52 τ l,0 (s) 626 p s, s 1 (s 1 ) 0.30 τ s,1 (s) τ l,1 (s) 733 p s, s 2 (s 1 ) 0.40 τ s,2 (s) 9.98 τ l,2 (s) 713 p s, s 3 (s 1 ) 0.41 τ s,3 (s) 6.64 τ l,3 (s) 910 p s, Table 3.1: Individual behavioral parameters of the robots Alice as measured in Garnier et al. (2007b). viduals outside the shelters. Following Amé et al. (2006), the dynamics of the collective choice between two identical shelters follows : ( dp i dt = µp e 1 P ) i S 1=P 1 + P 2 + P e θp i 1+ρ ( Pi S ) n i =1, 2 with S the carrying capacity of the shelters (ratio of shelter sizes over the reference size), µ the maximal kinetic constant for entering a shelter, θ representing the shelter quality, and ρ a reference surface ratio for estimating carrying capacities. The stationary states are found by simply solving (see details in Amé et al., 2006) : dp i dt =0 i =1, 2 139

159 3.8. DISCUSSION CHAPITRE 3. P S Figure 3.12: Bifurcation diagram for the collective choice between two identical shelters. P 1 is the proportion of individuals under the shelter 1 and S is the normalized carrying capacity of the shelters (which corresponds to the ratio of shelter size over the reference size). Only stable stationary states are reported. Note that a collective choice only occurs between S =1and S =5. Setting µ =0.001 s 1 θ =0.01 s 1 ρ = 1667 n =2 we found the complete bifurcation diagram shown in figure 3.12 which shows that no collective choice occurs for S>6. 140

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162 CHAPITRE 4. Chapitre 4 Sensibilité de la fourmi d Argentine à la géométrie des bifurcations d un réseau De nombreuses espèces de fourmis forment au cours de l exploration et de l exploitation de leur environnement des réseaux de pistes (Hölldobler & Wilson, 1990). Chez certaines espèces, ces réseaux présentent une structure géométrique particulière : à une bifurcation, l angle moyen formé par les deux branches les plus éloignées du nid est compris entre 50 et 60 degrés (Atta sexdens, A. capiguara, A. laevigata and Messor Barbarus :Acosta et al., 1993 ; Monomorium pharaonis : Jackson et al., 2004). En conséquence, une fourmi venant du nid et se dirigeant vers la périphérie du réseau rencontre principalement des bifurcations symétriques : les deux branches qui suivent la bifurcation dévient approxamitevemnent de 30 de la direction d arrivée de la fourmi. Inversement, une fourmi en provenance de la périphérie du réseau et se dirigeant vers le nid rencontre principalement des bifurcations asymétriques : la branche menant au nid dévie moins (30 ) de la direction d arrivée de la fourmi que la branche qui l en éloigne (120 ). Jackson et al. (2004) ont montré que cette polarisation des bifurcations étaient utilisées par la fourmi Monomorium pharaonis pour s orienter correctement sur le réseau, en absence de tout autre indice de navigation. Une fourmi en provenance du nid et à la recherche de nourriture opérait plus fréquemment un demi-tour lorsqu elle atteignait une bifurcation asymétrique, qui indique qu elle se dirige vers le nid. Inversement, une fourmi nourrie opérait plus fréquemment un demi-tour lorsqu elle atteignait une bifurcation symétrique, qui indique qu elle s éloigne du nid. Chez la fourmi d Argentine Linepithema humile, une étude de Vittori et al. (2006) suggère que la géométrie des bifurcations pourrait également avoir un impact sur la capacité de cet insecte à naviguer dans un réseau complexe de galleries. Dans ce chapitre, nous évaluons cette capacité à travers une série d expériences. Nous confrontons des fourmis à jeun puis nourries à 143

163 CHAPITRE 4. des bifurcations symétriques et asymétriques sur leur trajet aller jusqu à une source de nourriture et sur leur trajet retour jusqu au nid. Contrairement à la fourmi Monomorium pharaonis (Jackson et al., 2004), nos résultats montrent que la fourmi d Argentine n utilise pas activement la géométrie des bifurcations pour naviguer dans un réseaux de galleries. Cependant, nous montrons que cette fourmi est tout de même sensible à la géométrie des bifurcations. Quelque soit leur direction de déplacement, une fourmi qui atteint une bifurcation asymétrique emprunte préférentiellement la branche qui dévie le moins de sa trajectoire initiale et opère plus fréquemment des demi-tours après s être engagée sur la branche qui en dévie le plus. Nous verrons dans le chapitre suivant que cette sensibilité peut modifier grandement le pattern d exploitation d un réseau de galleries par une colonie de fourmis de cette espèce. 144

164 CHAPITRE 4. Are ants sensitive to the geometry of tunnel bifurcation? Grégory Gerbier, Simon Garnier, Cécile Rieu, Guy Theraulaz and Vincent Fourcassié Grégory Gerbier, Simon Garnier, Cécile Rieu, Guy Theraulaz and Vincent Fourcassié Centre de Recherches sur la Cognition Animale, CNRS-UMR 5169, Université Paul Sabatier, Bât IVR3, Toulouse cedex 9, France. Article published online in Animal Cognition. DOI : /s

165 4.1. INTRODUCTION CHAPITRE 4. Abstract The ability to orient and navigate in space is essential for all animals whose home range is organized around a central point. Because of their small home range compared to vertebrates, central place foraging insects such as ants have for a long time provided a choice model for the study of orientation mechanisms. In many ant species, the movement of individuals on their colony home range is achieved essentially collectively, on the chemical trails laid down by their nest mates. In the initial stage of food recruitment, these trails can cross each other and thus form a network of interconnected paths in which ants have to orient. Previous simulation studies have shown that ants can find the shortest path between their nest and a food source in such a network only if there is a bias in the branch they choose when they reach an asymmetrical bifurcation. In this paper, we studied the choice of ants when facing either a symmetrical or an asymmetrical bifurcation between two tunnels. Ants were tested either on their way to a food source or when coming back to their nest, and either in the presence or in the absence of a chemical trail. Overall, our results show that the choice of an ant at a tunnel bifurcation depends more on the presence/absence of a trail pheromone than on the geometry of the bifurcation itself. Keywords : Ants, Argentine ant, Linepithema humile, Orientation, Trail network. 4.1 Introduction Ant colonies use a variety of foraging strategies to exploit the food sources present in their foraging area (Beckers et al., 1989; Traniello, 1989). In some species, food collection is achieved exclusively by solitary individuals, while in others it is achieved mostly collectively, by thousands of workers travelling along well-defined foraging trails (Hölldobler & Wilson, 1990). These trails emerge from a succession of pheromone deposits, first by the scouts that have discovered the food source and that have returned to the nest, then by the workers that are recruited by these scouts from inside the nest. In species of ants forming large colonies, such as army ants, leaf-cutting ants or seed-harvesting ants, simultaneous mass recruitment to several food sources can lead to the emergence of a system of dendritic foraging trails centered on the nest (Hölldobler & Möglich, 1980; Vasconcelos, 1990; Gotwald, 1995; Kost et al., 2005). In some species, the workers lay a chemical trail more or less permanently and a network of interconnected exploratory trails can also emerge as a result of mass recruitment to a new area (Linepithema humile : Aron et al., 1989 ; Monomorium pharaonis : Fourcassié & Deneubourg, 1994). While moving within a network of chemical trails, ants are faced with a succession of bifurca- 146

166 CHAPITRE INTRODUCTION tions, and at each of these bifurcations they have to make a choice as to which trail they will take next. As several trails can sometimes lead to the same food source, at least in the initial stage of a network, the length of the path followed by an ant within a network depends on the choice it makes at each bifurcation. Using an artificial network of galleries in which several interconnected paths can be used to reach a single food source, Vittori et al. (2006) have shown that ants choose one of the shortest possible paths in the network with a probability that is significantly much higher than that given by a random orientation. Computer simulations show that the choice of one of the shortest paths in such a network can emerge only if an intrinsic bias, i.e. a bias in the absence of a chemical trail, is introduced in the choice of the ants when they face asymmetrical bifurcations (Vittori et al., 2006) : ants should preferentially choose the branch that deviates less from their initial direction, which is actually what is observed in real experiments (Vittori et al., 2006). This means that ants are able to measure in one way or another the deviation they make from their initial direction when choosing a branch. This has indeed been demonstrated by Jackson et al. (2004) in an elegant experiment on the Pharaoh s ant Monomorium pharaonis. These authors have shown that the workers of this species can use the differences in the geometry of the bifurcations they face to orient within a network of foraging trails. In a system of dendritic foraging trails centered on the nest, an ant exiting the nest and moving to the food sources located at the periphery of the network generally faces symmetrical bifurcations, i.e. the two trails that follow a bifurcation deviate by the same angle from the original direction of the ant. An ant coming back to its nest on the other hand face asymmetrical bifurcations : the trail leading to the nest that follows the bifurcation deviates less from the original direction of the ant than that leading to another food source. This geometric property of trail networks is used by ants to find their way in a network : when unfed ants going to a food source face an asymmetrical bifurcation, they have a high tendency to make a U-turn and come back to their point of departure, while fed ants coming back to the nest do the same when they face a symmetrical bifurcation. This paper describes a simple experiment carried out in order to understand the mechanisms that generate the bias observed in ants at asymmetrical bifurcation when they orient in a system of multiple interconnected galleries such as that used in Vittori et al. (2006). As in Jackson et al s (2004) experiment, we tested the behaviour of ants at a symmetrical or asymmetrical bifurcation in two different motivational contexts : either when they were unfed and exploring the environment, or when they had just fed and were returning to their nest. We assumed that if ants use the geometry of the bifurcations to orient in a network of foraging trails, as shown by Jackson et al. (2004), they should be more sensitive to the geometry of a tunnel bifurcation in the presence 147

167 4.2. METHODS CHAPITRE 4. than in the absence of trail pheromone. We thus tested ants in two different experimental set-ups (in the presence and in the absence of a trail pheromone signal) and compared their orientation performance. The aim of our study was not to replicate, in the Argentine ant, Jackson et al s (2004) experiment on the measurement of the geometry of trail bifurcation by the Pharaoh s ant. The experimental set-up we used was indeed completely different from that used by Jackson et al. (2004). In our experiment, ants moved in an enclosed tunnel system, whereas in Jackson et al s (2004) experiment, ants moved on strips of paper and could leave the trail at any moment. Our aim was specifically to investigate the origin of the orientation bias observed in Argentine ant when workers reach an asymmetrical bifurcation in a tunnel network. 4.2 Methods Biological material A total of 15 experimental colonies of the Argentine ant Linepithema humile (Formicidae, Dolichoderinae), each containing 2,000 workers without queen or brood were used in the experiments. The ants were collected near Narbonne on the French Mediterranean coast where L. humile is considered as an invasive species with unicolonial habit (the species forms a gigantic colony extending along the Mediterranean coast from Italy to Portugal and individuals mix freely among physically separated nests : Giraud et al., 2002). The ants were housed in artificial plaster nests (Ø=10cm) and had access to an external foraging area. They were reared in an experimental room at a constant temperature of 25 C under L : D 12 : 12 conditions and fed twice a week with a mixture of eggs, carbohydrates and vitamins (Bhatkar & Whitcomb, 1970) and with Musca domestica maggots Experimental set-up and protocol The orientation of the Argentine ant workers was tested in a series of alternatively inverted Y-mazes whose branches deviated by an angle of 60 (Fig. 4.1). The PVC plate in which these mazes were carved could slide between two other PVC plates that were fixed. A transparent PVC plate fixed on the two lateral plates and covering the whole set-up prevented the ants from escaping the maze. Small access galleries were carved in one of the fixed plate, while in the other fixed plate small circular chambers (Ø=20mm), each with a 15mm long and 5mm wide access gallery, were carved. The depth of the galleries and chambers were 5mm. During a test, the central plate of the set-up was slit so that each branch of a maze coincided with one access. To 148

168 CHAPITRE METHODS prevent the use of external visual cues, the whole set-up was surrounded by white tissue, which also ensured an indirect and diffuse lighting. On its way to the food an ant could face either a symmetrical (S) or an asymmetrical bifurcation (A), and on its way back it could face again either a symmetrical (S) or an asymmetrical (A) bifurcation. This makes four combinations of tests possible for the foodbound and nestbound trip : S S, A A, S A and A S. A test was started by collecting an ant in the foraging area of its colony and by gently depositing it in a small Petri dish placed in front of an access gallery ( START in Fig. 4.1). A food source (a small piece of cotton soaked with a 1M solution of sucrose) was placed in each circular chamber (during symmetrical foodbound tests) or in only one of them (during asymmetrical foodbound tests). We waited until the ant found the food source and, after it had fed on it, until it went back to its point of departure. Each ant was thus tested successively in an unfed (foodbound trip) and then in a fed (nestbound trip) state. For both trips, the following data were recorded : Initial choice : the first branch chosen after the ant crossed the bifurcation for the first time. A branch was considered as chosen when the ant reached and moved beyond an area we called decision area (Fig. 4.1). Note that an ant could enter the decision area and make a U- turn to go back toward its point of departure. In that case, the initial choice of the ant corresponded to the branch by which it entered the maze. Final choice : the first branch extremity reached. Whether or not the ant made a U-turn on the branch chosen after crossing the bifurcation for the first time. Spontaneous U-turns occurring before an ant reached the bifurcation for the first time were not considered. We made two series of tests : one with an unmarked set-up and the other with a marked one. In the first series of tests, ants were tested in mazes in which no chemical trail had been deposited before. The bottom of the galleries was made of PVC. Each maze was used once and then washed with alcohol before being reused. Ants were thus tested in different mazes on their way to the food and back to the nest. Therefore, had the ants laid down a pheromone trail during their outbound trip, this manipulation should prevent them from using it when returning to the nest. In the second series, pieces of paper on which a fresh chemical trail had been deposited were placed before the tests at the bottom of the maze galleries. To avoid the effect of trail decay, the same pieces of papers were used during only 20min. The trail pheromone duration of L. humile is indeed estimated to be close to 30min (Deneubourg et al., 1990). This allowed us to test on average three ants. The six pieces of paper (three for the access galleries and one for each branch 149

169 4.2. METHODS CHAPITRE 4. Figure 4.1: Experimental set-up. The mazes used in the experiment were carved in a PVC plate that could slide between two other PVC plates that were Wxed. A transparent PVC plate Wxed on the two lateral plates and covering the whole set-up prevented the ants from escaping the maze. Small access galleries were carved in one of the Wxed plates, while in the other Wxed plate small circular chambers (Ø=20mm) in which food was placed were carved. The depth of the galleries and chambers were 5mm and the width of the galleries 5mm. During the test, the central plate of the set-up was slit so that each branch of a maze coincided with one access on the lateral plates of the maze) that were used to cover the bottom of the maze were cut from a piece of paper that had been marked during 30min by workers of a colony of the Argentine ant travelling between their nest and a food source (1M saccharose solution). This duration was sufficient to ensure that the paper was marked homogeneously. When ants were tested in marked set-ups with a different type of bifurcation in their foodand nestbound trips, the same maze was used, whereas when they were tested with the same type of bifurcation on both trips, two adjacent mazes were used. If ants lay down a trail during their outbound trip, they could theoretically use it during their return trip when the same maze was used. However, the pieces of paper that were placed at the bottom of the tunnels had been marked by ants during 30min. They were thus saturated by trail pheromone and it is highly unlikely that ants could be able to perceive their own trail against this saturated background to orient on it during their return trip. Besides, no individual trail idiosyncrasy has ever been shown in the Argentine ant. When two adjacent mazes were used, the pieces of paper that were placed in the two mazes were marked by two different experimental colonies. Since the Argentine ant is unicolonial (Tsutsui et al., 2000; Giraud et al., 2002) workers of one colony readily follow a trail laid by another colony. Two adjacent mazes were used in both cases during tests in unmarked set-ups. A total of 50 ants were tested in each set-up (marked and unmarked) for each combination of 150

170 CHAPITRE RESULTS bifurcations an ant could encounter on its way to the food and back to the nest (S-S, S-A, A-S, A-A). Each ant was tested once and was excluded from the experimental colonies after being tested Statistical analysis A χ 2 test for contingency tables was used to compare the proportion of ants choosing each of the three branches of the set-up in their initial and final choice. A binomial test was used to test the random character of the initial and final orientation of the ants between the two branches they faced after crossing the bifurcation. A χ 2 test for contingency tables was used to compare the proportion of ants making U-turns in the three branches of the mazes. A Yates correction was applied to all χ 2 statistics. 4.3 Results The results are presented graphically in Fig There were four combinations of bifurcation types an ant could face on its outbound and nestbound trip during a test : S S, S A, A S and A A. Since there were no significant differences in the performance of the ants when they faced the same type of bifurcation, either in their foodbound or their nestbound trip, the data for each identical bifurcation in the foodbound and nestbound trip were pooled. For example, the data for the symmetrical bifurcation faced by ants in their outbound trip in the S S and the S A tests were pooled. This increased the sample size to 100 ants for each type of bifurcation for the foodbound and nestbound trip Foodbound trip (unfed ants) Independent of whether the set-up was unmarked (Fig. 4.2a) or marked (Fig. 4.2b), both the initial (binomial test : P=1 and P=0.84, respectively) and the final (P=0.54 and P=1, respectively) choice of the unfed ants that crossed a symmetrical bifurcation were not different from random. In the unmarked set-up, however, one-third of the unfed ants that faced a symmetrical bifurcation went back to their point of departure to exit the maze (Fig. 4.2a), while this proportion decreased to 7% in the marked set-up (Fig. 4.2b ; χ 2 =22.61, df=2, P<0.001). The results for asymmetrical bifurcations differed between the two set-ups. In the unmarked set-up, unfed ants chose equally between the two branches that followed the bifurcation (binomial test : P=0.66), while their final choice was slightly, but not significantly, biased towards the branch 151

171 4.3. RESULTS CHAPITRE 4. that deviates the less from their direction of origin (binomial test : P=0.06). In the marked setup, ants expressed a significant preference in their initial and final choice for the branch that deviated by an angle of 30 over the branch that deviated by an angle of 120 (binomial test : P<0.001 for both choices). The proportion of ants that went back to their point of departure to exit the maze was also higher in the unmarked set-up than in the marked set-up (χ 2 =29.33, df=2, P<0.001). In both set-ups, when unfed ants faced a symmetrical bifurcation, the proportion of U-turning ants was not significantly different on the two branches that follow the bifurcation (χ 2 =0.18, P=0.67 ; χ 2 =0.04, P=0.84, for the unmarked and marked set-up, respectively ; df=1). When unfed ants faced a U-turns in the three branches of the mazes, a much greater proportion of ants made one or several U-turns on the branch of the bifurcation that deviated by an angle of 120 than on the branch that deviated by an angle of 30 (χ 2 =31.29, P<0.001, df=1) Foodbound trip (unfed ants) In the unmarked set-up, fed ants facing a symmetrical bifurcation did not choose randomly between the two branches of the bifurcation : the right branch was initially preferred (binomial test : P=0.02). In the final choice, however, no preference was expressed (binomial test : P=0.12). In the marked set-up on the other hand, ants did not express a significant preference for either branch they faced at a symmetrical bifurcation, both in their initial and final choice (binomial test : P=0.31, P=0.18, respectively). As in the foodbound trips, more ants came back to their point of departure to exit the maze in the unmarked set-up than in the marked set-up (χ 2 =9.05, df=2, P=0.011). In both set-ups, fed ants facing an asymmetrical bifurcation chose preferentially the branch that deviated less from their initial direction. A slightly higher proportion of ants exited the maze by the branch that deviated by 120 in the marked set-up than in the unmarked set-up (χ 2 =6.37, df=2, P=0.041). In both set-ups, the proportion of fed ants that made one or several U-turns after crossing an asymmetrical bifurcation was higher on the branches that deviated by 120 than on the branch that deviated by 30 (χ 2 =20.68, P<0.001 and χ 2 =15.51, P<0.001 for the unmarked and marked set-up, respectively ; df=1). To further test the effect of the bifurcation geometry on the ants behaviour, we categorized the final choice of the ants as correct or incorrect according to the criterion defined by Jackson et al. (2004). This criterion is based on the geometry of the bifurcation unfed and fed ants should 152

172 CHAPITRE RESULTS Figure 4.2: Proportion of ants selecting each branch of the maze in their initial choice (numbers in italic) and in their final choice (numbers in bold) in (a) an unmarked set-up (b) a marked set-up. The proportion of ants making a U-turn on each branch of the maze after reaching a bifurcation for the first time is indicated by underlined numbers. For asymmetrical bifurcations, the data for the two possible branches of departure have been collapsed on the same branch. The movement of the ants is always from bottom to top. N=100 ants for each bifurcation. 153

173 4.4. DISCUSSION CHAPITRE 4. encounter in a network of natural foraging trails. Unfed ants that faced a symmetrical bifurcation (i.e. the correct geometry in natural trail network), made a U-turn and exited by the entrance branch of the maze were considered as making an incorrect choice. Similarly, fed ants that faced an asymmetrical bifurcation, made a U-turn and exited by the entrance branch of the maze or by the branch that deviated by 120 were also considered as making an incorrect choice. Conversely, unfed ants that faced an asymmetrical bifurcation, made a U-turn and exited the maze by the entrance branch of the maze or by the branch that deviated by 120 were considered as making a correct choice. The same was true for fed ants making a U-turn at a symmetrical bifurcation and exiting the maze by the entrance branch. We then computed the ratio of correct to incorrect choice for each set-up (marked and unmarked). A confidence interval for this ratio was computed by a non-parametric bootstrap method (Manly, 1991). We found a ratio of correct to incorrect reorientation of 1.22 (±CI ) for the unmarked set-up and a ratio of 0.60 (±CI ) for the marked set-up. Both ratios are not significantly different from unity, which means that workers of the Argentine ant made as many correct as incorrect choices in the set-ups in relation to the geometry of natural trail network. 4.4 Discussion Overall, our results confirm the fact observed by Vittori et al. (2006) that the workers of the Argentine ant do make biased choice at asymmetrical bifurcations : ants chose preferentially the branch that deviates less from their original direction. This was true in all cases except for unfed ants exploring an unmarked set-up for which the bias was only marginally significant. In the unmarked set-up, the ant dispersion was generally more important than in the marked set-up. More ants came back to their point of departure. This is particularly true for unfed ants that tended to exit the maze evenly by the three branches of the maze. The difference between unfed and fed ants could be explained by the fact that unfed ants could be more prone to exploration than fed ants. Unfed ants initially chose equally between the two branches that follow a bifurcation. However, about a third of them on average made a U-turn after crossing the bifurcation and came back to their point of departure. Fed ants on the other hand had a higher forward tendency and their behaviour was close to that observed for both unfed and fed ants in a marked set-up. In the marked set-up, independent of whether they were unfed or fed, ants had a high forward tendency. Few ants made a U-turn at the bifurcation and came back to their point of departure. 154

174 CHAPITRE DISCUSSION When facing an asymmetrical bifurcation, they initially tended to choose the branch that deviated less from their original direction. Moreover, those ants that chose the branch that deviated more had a high tendency to make a U-turn. The fact that the number of ants making one or several U-turns was always much higher on the branch that deviated the more in asymmetrical bifurcations is intriguing. How did ants sense that they made too high a deviation from their original direction? The first mechanism one could think of is based on the use of the external visual cues that ants find in their surroundings. However, this mechanism can be dismissed because we took care to place the set-up in an environment as featureless and homogenous as possible, in terms of visual cues, contrast as well as lighting conditions. Besides, the Argentine ant is known to have poor visual discrimination capabilities (Aron et al., 1993). Ants could also use a compass to assess the deviation of their course. In the absence of a visual compass such as that provided by the sun or the polarized light of the sky (Müller & Wehner, 2007), the only compass that could be used by the ants in our experiment is the magnetic compass. However, although the use of magnetic cues for orientation has been demonstrated in a few species of ants (Formica rufa : Camlitepe & Stradling, 1995 ; Oecophylla smaragdina : Jander & Jander, 1998 ; Atta colombica : Banks & Srygley, 2003) no evidence of magnetic orientation has hitherto been provided in the Argentine ant. Finally, ants could be able to integrate their course deviations by using an egocentric system of reference, based on the idiothetic (kinaesthetic) cues they perceive while they change their walking direction. This type of orientation has already been described in other ant species (Cataglyphis fortis : Bisch-Knaden & Wehner, 2001). Additional experiments in darkness and in the absence of magnetic field should be performed to test this hypothesis. Our results show that fed and unfed workers of the Argentine ant, contrary to those of the Pharaoh s ants (Jackson et al., 2004), did not react differentially to the geometry of the bifurcations. Whereas Jackson et al. (2004) found a ratio of correct to incorrect reorientation of 5.80 for a bifurcation with two trails diverging by an angle of 60, the values we found for the same bifurcation angle for Argentine ants moving in tunnels were not significantly different from unity, independently of whether ants travelled on a marked or an unmarked set-up. In the marked set-up, 77% of unfed ants arrived at the food source, although they had to cross an asymmetrical bifurcation to do so. In the same way, 96% of fed ants crossed a symmetrical bifurcation without making a U-turn and chose one of the two branches that followed the bifurcation. In both cases, had the ants reacted to the geometry of the tunnel bifurcation in the same way as the Pharaoh s ants on natural foraging trails in Jackson et al. s (2004) experiment, they should have made a 155

175 4.4. DISCUSSION CHAPITRE 4. U-turn and come back to their point of departure. There are at least two explanations that can be provided for the discrepancy observed between our results on the Argentine ant and those of Jackson et al. (2004) on the Pharaoh s ant. One may be due to a difference in the experimental set-ups that were used and the other to a difference in the foraging behaviour of the two species. In Jackson et al. (2004) ants moved on plane strips of paper, whereas in our experiments they moved within galleries carved in a PVC plate. This could make a difference in the choice of the ant in front of a bifurcation. First, because of their natural wall-following tendency (Dussutour et al., 2005a), the forward tendency of the ants moving within the galleries could be accentuated. Second, ants may be able to assess more easily the angle of a bifurcation when moving on a plane surface than when moving within tunnels, by rotating their body and scanning the ground with their pairs of antennae. Finally, an alternative explanation for the discrepancy between the Argentine ant and the Pharaoh s ant behaviour could be that the Argentine ant, contrary to the Pharaoh s ant, does not use a network of foraging trails, or that the networks formed by the two species in their natural settings have different geometry. Preliminary experiments show that foragers of the Argentine ant, in the same way as those of the Pharaoh s ants (Fourcassié & Deneubourg, 1994), are able to form spontaneously networks of exploratory trails. Whether or not these networks have the same characteristics as those of the Pharaoh s ant, however, remains to be investigated. 156

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178 CHAPITRE 5. Chapitre 5 Sélection de chemin et efficacité de fourragement dans un réseau de transport chez la fourmi d Argentine Dans le chapitre précédent, nous avons mis en évidence un biais dans le comportement de la fourmi d Argentine lorsqu elle atteint une bifurcation asymétrique. La fourmi a tendance à emprunter la branche qui dévie le moins de sa trajectoire initiale et à opérer plus de demi-tours après s être engagée sur la branche qui en dévie le plus. Une colonie de fourmis d Argentine peut être composée de plusieurs milliers d individus dont une bonne partie s engage régulièrement dans une activité de fourragement. Il est donc intéressant de se demander quel peut être l impact de ce biais individuel à l échelle de la colonie. Dans un travail récent, Vittori et al. (2006) montrent dans un modèle théorique que ce biais est essentiel pour reproduire en simulations le pattern d exploitation d un réseau de galleries emprunté par les foumis pour rejoindre une source nourriture. Plus précisément, l absence de ce biais entraînerait une perte de la capacité de la colonie à sélectionner un chemin dans ce réseau. Dans ce chapitre, nous testons cette hypothèse à travers une approche mêlant étroitement expériences et modèlisation informatique. En premier lieu, nous réalisons une série d expériences dans lesquelles nous confrontons une colonie de fourmis à un réseau de galleries lui permettant de rejoindre une source de nourriture par 14 chemins de longueurs différentes. Nous testons deux types de réseaux différents : le premier type de réseaux est composé uniquement de bifurcations symmétriques, alors que le second type est contient des bifurcations asymétriques qui polarisent le réseau. Nous montrons que dans le réseau non polarisé, les fourmis se dispersent plus largement que dans le réseau polarisé, et que leur capacité de sélection d un chemin sont altérées. Dans un second temps, nous avons quantifié le comportement de fourmis lorsqu elles croisent des bifurcations polarisées (symétriques dans une direction, asymétriques dans l autre) et non 159

179 CHAPITRE 5. polarisées (symétriques dans dans les deux directions). Nous montrons, comme dans le chapitre précédent, que les fourmis ont tendance à suivre la direction qui dévie le moins de leur trajectoire initiale. Nous montrons également que la probabilité pour une fourmi d opérer un demi-tour après avoir franchi la bifurcation augmente avec l angle entre la branche d arrivée et de départ de la fourmi. Nous avons implémenté ces comportements dans un modèle informatique prenant également en compte l effet du recrutement par piste de phéromone très actif chez cette espèce de fourmis. Nous montrons que l amplification par le recrutement chimique du biais comportemental observé lorsqu une fourmi croise une bifurcation asymétrique est suffisant pour expliquer les différences de performance dans les deux types de réseaux. 160

180 CHAPITRE 5. Path selection and foraging efficiency in Argentine ant transport networks Simon Garnier, Aurélie Guérécheau, Maud Combe, Vincent Fourcassié and Guy Theraulaz Simon Garnier, Aurélie Guérécheau, Maud Combe, Vincent Fourcassié, Guy Theraulaz Centre de Recherches sur la Cognition Animale, CNRS-UMR 5169, Université Paul Sabatier, Bât IVR3, Toulouse cedex 9, France. Article submitted to Behavioral Ecology and Sociobiology. 161

181 5.1. INTRODUCTION CHAPITRE 5. Abstract We experimentally investigated the individual and collective behaviour of the Argentine ant Linepithema humile while crossing symmetrical and assymetrical bifurcations in gallery networks. Ants preferentially followed the branch that deviated less from their coming direction and their probability to perform a U-turn after a bifurcation increased with the turning angle at the bifurcation. At the collective level, the performance of the colony to find the shortest path linking the nest to a food source was better in a polarized network where bifurcations were symmetrical from one direction and assymetrical from the other than in a network where all bifurcations were symmetrical. A model of individual behaviour is proposed and a set of simulations showed that the preference to follow the less deviating path that is amplified by the ant mass chemical recruitment well account for the difference between polarized and non polarized networks when many ants travel through them. Moreover after only fifteen minutes the foraging efficiency measured in the simulations was three times higher in polarized than in non polarized networks. We conclude that measures of transport network efficiency requires to take into account both the structural properties of the network and the behaviour of the network users. Keywords : Transport networks, Argentine ant, Linepithema humile, Path selection, Bifurcation geometry, Foraging efficiency 5.1 Introduction Transport networks play a crucial role in the distribution of materials and information at all scales of the biological world. A lot of such networks have been studied so far, ranging from the internal 3D vascular systems of plants or animals (West et al., 1997, 1999a,b; Banavar et al., 1999, 2002) to the external 2D road networks built by human societies (Buhl et al., 2006a; Gastner & Newman, 2006), or even to the shape of certain organisms such as slime mould (Nakagaki et al., 2004b,a) or fungi (Bebber et al., 2007). Among the most striking examples of biological transport networks are those created by social insects. The nests of termites and ants for instance are typically composed of several chambers interconnected by a network of galleries that exhibit species-specific architectures (Darlington, 1997; Cassill et al., 2002; Tschinkel, 2003; Mikheyev & Tschinkel, 2004; Perna et al., 2008). Outside the nest, some species of ants draw dendritic networks of chemical and/or physical trails that radiate out from the nest and that are used during the exploration of their environment or while they exploit food sources (Anderson & Mcshea, 2001). 162

182 CHAPITRE INTRODUCTION Recent studies on transport networks in social insects have mostly focused on structure and measured the topological and/or geometrical relationships between the components of the network in order to identify its structural invariants or to estimate its efficiency and robustness. For instance, Perna et al. (2008) have shown that nests of Cubitermes termite display an excellent compromise between efficient connectivity within the nest and defence against attacking predators from outside the nest. In the ant Messor sancta, Buhl et al. (2004) have shown that the gallery networks achieve a near optimal compromise between a highly efficient network and a highly robust one. Less is known however about the way insects use their transport networks and how they distribute themselves within, for instance when they travel within the subterranean network of their nest or within a foraging network on the surface. Yet the transport network efficiency directly depends on the way a network is used. While moving within their networks ants often lay down a pheromone trail which is followed by other ants which in turn lay down additional pheromone deposits that attract more ants. At a given bifurcation in a network this positive feedback may eventually lead most of the traffic to establish itself on one single branch (Deneubourg & Goss, 1989) if certain conditions of traffic and ant density are present. In species where individuals are mainly guided by pheromone trail and do not use environmental cues to orient, any error on the branch selected at one bifurcation will propagate over the following bifurcations and ants may eventually get trapped into sub-optimal pathways or network loops. One solution for ants to navigate efficiently within their networks would be to use polarized trails that could indicate to the workers whether they are walking in the same general direction or whether they are going back to their point of departure. It has recently been suggested that the geometry of the bifurcations in a network could act as such a polarization cue (Jackson et al., 2004). Indeed it has been shown that in foraging trail networks the mean angle between trail bifurcations as they branch out from the nest is (Atta sexdens, A. capiguara, A. laevigata and Messor Barbarus :Acosta et al., 1993 ; Monomorium pharaonis : Jackson et al., 2004 ; Formica aquilona : Buhl et al., submitted). Therefore an ant exiting the nest and moving to the food sources located at the periphery of the network generally faces symmetrical bifurcations, i.e. the two trails that follow a bifurcation deviate by approximately 30 from the original direction of the ant. An ant coming back to its nest on the other hand faces asymmetrical bifurcations : at a bifurcation, the trail leading to the nest that follows the bifurcation deviates less ( 30 ) from the ant original direction than the other trail ( 120 ) that lead away from the nest. Jackson et al. (2004) have demonstrated on a pheromone trail network that when unfed M. pharaonis 163

183 5.1. INTRODUCTION CHAPITRE 5. ants going to a food source face an asymmetrical bifurcation (that is more likely to occur in the journey back to the nest) they have a high tendency to make a U-turn and come back to their point of departure. Fed ants coming back to the nest do the same when they face a symmetrical bifurcation. Therefore ants use the geometry of the bifurcation to orient themselves correctly in the network. In the ant Linepithema humile Gerbier et al. (2008) have shown in artificial gallery networks that workers that return to the nest with food and reach an asymmetrical bifurcation preferentially select the path that deviates less from their current heading (and which is likely to lead to the nest) and perform more U-turns on the path that deviates more (which is likely to move away from the nest). As a consequence, the less deviating path should be marked with a greater amount of pheromone and should be more likely to be selected by ants. Because this path is more likely to lead to the nest in natural networks, one would expect that an Argentine ant colony should be more prone to select the most direct path between a food source and its nest. Moreover one would expect that a colony would loose this ability if the workers are forced to encounter only symmetrical bifurcations. This hypothesis has been formulated and theoretically tested in a previous paper (Vittori et al., 2006) but has so far never received an experimental validation. In this paper we investigate this hypothesis with laboratory experiments at both the individual and the collective level. We assess the global behaviour of Argentine ant colonies when given access to two relatively complex artificial networks of galleries in which several possible interconnected paths can lead the insects from their nest to a food source. The first network presents a polarized geometry : the bifurcations are symmetrical from one walking direction and asymmetrical from the other one. Conversely the second network is not polarized : the bifurcations are symmetrical from every walking direction. We also observe and quantify the behaviour of ants while they cross a polarized bifurcation (symmetrical from one walking direction, asymmetrical from the other one) or a non polarized one (symmetrical from either direction). Based on these observations, we then build an individualbased model of the ants displacements to investigate the link between the individual behaviour of ants at bifurcations and the global behaviour of the colony in the two networks. The model also help us to estimate the foraging efficiency of the colony in each type of network. 164

184 CHAPITRE Material and methods 5.2. MATERIAL AND METHODS Biological material We used colonies of the Argentine ant Linepithema humile (Formicidae, Dolichoderinae) collected near Narbonne on the French Mediterranean coast. At this location the Argentine ant is considered as an invasive species with unicolonial habit (the species form a gigantic colony extending along the Mediterranean coast from Italy to Portugal and individuals mix freely among physically separated nests (Giraud et al., 2002)). Ants were housed in artificial plaster nests (Ø = 10 cm) without queen or brood and had access to an external foraging area. Twenty nests containing 2,000 workers each were used for the investigation of individual behaviour and twenty nests containing 500 workers were used for the investigation of collective behaviour. The ants were reared in an experimental room at a constant temperature of 25 C under L : D 12 : 12 conditions and fed twice a week with a mixture of eggs, carbohydrates and vitamins (Bhatkar & Whitcomb, 1970) and with Musca domestica maggots. The colonies were starved for three days before each experiment Individual behaviour The individual behaviour of the Argentine ant workers at bifurcations was tested in a series of alternatively inverted Y-mazes (see Figure 5.1, left). The PVC plate in which the mazes were carved could slide between two other PVC plates that were fixed. A transparent PVC plate fixed on the two lateral plates and covering the whole setup prevented the ants from escaping the maze. Small access galleries were carved in one of the two fixed plates, while in the other fixed plate small circular chambers (Ø = 20 mm), each with a 15 mm long and 5 mm wide access gallery, were carved. The depth of the galleries and chambers were 5 mm. During a test, the central plate of the setup was slit so that each branch of a maze coincided with one access. To prevent the use of external visual cues, the whole setup was surrounded by a white tissue, which also ensured an indirect and diffuse lighting. We tested the behaviour of the Argentine ant workers in two different types of Y-mazes : polarized ones (P-mazes, Figure 5.1, top left) and non polarized ones (NP-mazes, Figure 5.1, bottom left). In P-mazes, the angle between the three branches is not the same. According to the position of the access branch an ant could face either a symmetrical (each exit branch deviates by 30 from the access one) or an asymmetrical bifurcation (one exit branch deviates by 30 while the other deviates by 120 from the access branch). In NP-mazes, the angle between the three 165

185 5.2. MATERIAL AND METHODS CHAPITRE 5. Individual behaviour Collective behaviour Food zone 2 A Polarized Fixed parts 60 Decision area Mobile part N cm B Start zone Food zone 2 A Non polarized Fixed parts 120 Decision area Mobile part N cm B Start zone (a) Experiments Figure 5.1: Schematic description of the experimental setups. Left: experimental setups for testing the individual behaviour of the ants at a bifurcation. Right: experimental setups for testing the collective behaviour of the ants in a network of galleries. Top: polarized condition (P-mazes). Bottom: non polarized condition (NP-mazes). N corresponds to the nest, and A and B to the chambers in which the food was placed. 166

186 CHAPITRE MATERIAL AND METHODS branches is the same. Whatever the position of the access branch, an ant faces only symmetrical bifurcations with each exit branches deviating by 60 from the access branch. In each type of maze ants were tested successively in a single trip from the nest to the source (unfed ants, foodbound trip) and in a single trip from the source to the nest (fed ants, nestbound trip). In P-mazes four situations were tested : unfed ants with symmetrical bifurcation, unfed ants with asymmetrical bifurcation, fed ants with symmetrical bifurcation and fed ants with asymmetrical bifurcation. Hundred ants were tested in each situation. In NP-mazes two situations were tested : unfed ants and fed ants. Fifty-five ants were tested in each situation. A test started by collecting an ant in the foraging area of its colony and by gently depositing it in a small Petri dish placed in front of an access gallery. A food source (a small piece of cotton soaked with a 1 M solution of sucrose) was placed in each circular chamber (during symmetrical foodbound tests) or in only one of them (during asymmetrical foodbound tests). We waited until the ant found the food source and, after it had fed on it, until it went back to its point of departure. For each situation, the following data were recorded : Initial choice : the first branch chosen after the ant crossed the bifurcation for the first time. A branch was considered as chosen when the ant reached and moved beyond an area we called decision area (see Figure 5.1, left). Note that in rare cases (8 cases over 510 tests) an ant could enter the decision area and make a U-turn to go back toward its point of departure. In that case, the initial choice of the ant was not taken into account. Whether or not the ant made a U-turn on the branch chosen after crossing the bifurcation for the first time. Spontaneous U-turns occurring before an ant reached the bifurcation for the first time were not considered. For each of the six tests, pieces of paper on which a fresh chemical trail had been deposited were placed before the tests at the bottom of the maze galleries. To avoid the effect of trail decay, the same pieces of papers were used during only 20 min. The trail pheromone duration of L. humile is indeed estimated to be close to 30 min (Deneubourg et al., 1990). This allowed us to test on average three ants. The six pieces of paper (three for the access galleries and one for each branch of the maze) that were used to cover the bottom of the maze were cut from a piece of paper that had been marked during 30 min by workers of a colony of the Argentine ant travelling between their nest and a food source (1 M saccharose solution). This duration was sufficient to ensure that the paper was marked homogeneously. When ants were tested with a different type of bifurcation in their food- and nestbound trips, the same maze was used, whereas when they were tested with the same type of bifurcation on 167

187 5.2. MATERIAL AND METHODS CHAPITRE 5. both trips, two adjacent mazes were used. If ants lay down a trail during their outbound trip, they could theoretically use it during their return trip when the same maze was used. However, the pieces of paper that were placed at the bottom of the tunnels had been marked by ants during 30 min. They were thus saturated by trail pheromone and it is highly unlikely that ants could be able to perceive their own trail against this saturated background to orient on it during their return trip. Besides, no individual trail idiosyncrasy has ever been shown in the Argentine ant. When two adjacent mazes were used, the pieces of paper that were placed in the two mazes were marked by two different experimental colonies. Since the Argentine ant is unicolonial (Tsutsui et al., 2000; Giraud et al., 2002) workers of one colony readily follow a trail laid by another colony. A total of 50 ants were used in each test combination in the P-mazes and 55 ants were used in the NP-mazes. Each ant was tested once and was excluded from the experimental colonies after being tested. Note that the experimental results for the P-mazes have already been published in Gerbier et al. (2008) Collective behaviour The collective behaviour of the Argentine ant workers was tested in a maze carved in a PVC plate. The maze was composed of four identical hexagons assembled together (see Figure 5.1, right). We tested the collective behaviour of the Argentine ants in two different types of mazes : polarized ones (P-mazes, Figure 5.1, top right) and non polarized ones (NP-mazes, Figure 5.1, bottom right). In NP-mazes, the six angles of each hexagon are equal to 120. As a consequence, all the bifurcations in the network are symmetrical : at a bifurcation each branch deviates by a 60 angle from the other two. In P-mazes, two of the six angles of each hexagon (the closest from the nest and the closest from the food source) are equal to 60, while the other four are equal to 150. As a consequence, all the bifurcations are symmetrical from one branch and assymetrical from the other two. Each maze also included an entrance gallery connected to the nest of an ant colony and two circular chambers (Ø = 20 mm, A and B on Figure 5.1, right) in which food (a piece of cotton soaked with a 1 M solution of sucrose) could be placed. The maze galleries had a 5 mm square section. The whole setup was surrounded by a white tissue to prevent the use of any directional cues by the ants and to ensure an indirect and diffuse lighting. A transparent PVC plate covering the whole maze prevented the ants from escaping. Ten of the experimental colonies were tested in P-mazes while the other ten were tested in the NP-mazes. For half of the colonies in each 168

188 CHAPITRE MATERIAL AND METHODS type of mazes the food source was located in one chamber and for the other half, in the other chamber. Experiments with P-mazes and NP-mazes were alternated to randomize a potential effect of uncontrolled climatic variations (such as pressure or seasonal effect for instance). An experiment began when the first ant entered the network and then lasts 15 min. The whole experiment was recorded continuously with a high definition digital camera (Sony CDR-VX 2000 E) placed above the setup. We extracted one frame per second from the video recording plus one reference image of the network while it was empty. For each extracted frame, we computed the grey level difference between each pixel and the corresponding pixel in the reference image. If the absolute value of this difference was superior to a given threshold (here fixed to 30), the pixel was turned black. Otherwise it was turned white. We then counted the number of black pixels in each gallery of the network. For each experiment we estimated the mean number of pixels covered by one ant by counting the number of black pixels and the corresponding number of ants on thirteen different frames picked up every 70 seconds. From this we eventually computed the number of ants present in each gallery of the network for each second of the experiment and we applied a moving average over a period of 30 seconds to reduce the noise introduced by the picture analysis process. For each type of maze we computed the following data : Mean number of ants in the network as a function of time. Mean number of used galleries as a function of time. A gallery is considered as used if the density of ants is superior to 0.22 ants cm 1. For a given frame, we also specified the path selected by ants as follows. Starting from the entrance gallery we followed at each network bifurcation the gallery with the highest density of ants until we reached either a bifurcation followed by two empty galleries or a previously visited bifurcation or the food source. If we reached a bifurcation followed by two empty galleries we defined the selected path as pertaining to the no path category. If we reached a previously visited bifurcation we defined the selected path as pertaining to the loop category. There exists 14 possible paths to reach the food source without using twice the same gallery. These paths can be classified in five categories according to their length : 27 cm, 36 cm, 45 cm, 54 cm and 63 cm. Thus we defined the path selected by the ants to reach the food source as pertaining to the category corresponding to its length. By repeating this process on each frame of each experiment, we obtained the time sequence of path selection events. We defined a path selection event as all consecutive frames resulting in the same selected path category. We then computed the following data for each type of maze : 169

189 5.3. EXPERIMENTAL RESULTS CHAPITRE 5. Mean number of selection events. Mean duration of selection events for each selected path category. 5.3 Experimental results Individual ant behaviour Initial choice Independent of whether the ants crossed an asymmetrical bifurcation or a symmetrical bifurcation in either the P-mazes and NP-mazes, there was no significant difference in the performance of fed and unfed ants (Fisher exact test : P =0.367, P =0.396 and P =1, respectively). We therefore pooled the data for foodbound and nestbound ants for the three types of bifurcation tested. At the symmetrical bifurcation of P-mazes and NP-mazes, ants chose equally between the two branches that followed the bifurcation (binomial test : P = and P = 0.505, respectively). At the asymmetrical bifurcation of P-mazes however, ants expressed a significant preference in their initial choice for the branch that deviated by an angle of 30 over the branch that deviated by an angle of 120 (binomial test : P<0.001). The proportion of ants that selected the branch that deviated by an angle of 30 was U-turns The proportion of ants making a U-turn after crossing a symmetrical bifurcation was not statistically different between the two branches that followed the bifurcation and between foodbound and nestbound ants in both P-mazes and NP-mazes (Cochran-Mantel-Haenszel exact conditional test of independence in 2 x 2 x k contingency tables (Agresti, 2002) : P =0.368 and P = respectively). We therefore pooled the data for the two branches and for the foodbound and nestbound ants for the symmetrical bifurcations of P-mazes and NP-mazes respectively. A significant difference was found between P-mazes and NP-mazes for the proportions of ants making a U-turn after crossing a symmetrical bifurcation (Fisher exact test : P =0.007). While these two kinds of bifurcations are symmetrical, they deviated from the original direction of the ants by a different angle (30 in P-mazes and 60 in NP-mazes). This indicated that the proportion of U-turns is related to the angle between the former and the new direction followed by the ants. In the asymmetrical bifurcations of the P-mazes there was no statistically significant difference between foodbound and nestbound ants for the branch that deviated by an angle of 30 and for the branch that deviated by an angle of 120 (Fisher exact test : P =1and P =

190 CHAPITRE EXPERIMENTAL RESULTS Mean number of ants (a) Used segments NP P (b) Used segments Time (sec) Time (sec) (a) Experiments Figure 5.2: Mean number of ants in the network (main figures) and mean number of used segments (insets, density of ants superior to 0.22 ants cm 1 ) as a function of time. Left: experimental results. Right: simulation results. Plain curves represent data for polarized networks. Dashed curves represent data for non polarized networks. Each curve represents the mean±standard error (ligth and dark grey polygons). respectively). However, the proportion of ants making a U-turn was significantly dependent on the angle by which the branch deviated (Cochran-Mantel-Haenszel exact test : P>0.001). In P-mazes no significant difference was found in the proportion of U-turns between ants crossing a symmetrical bifurcation (and deviating from their original direction by an angle of 30 ) and ants choosing the branch that deviated by an angle of 30 in an asymmetrical bifurcation. As mentioned previously this indicated that the proportion of U-turns is related to the angle between the former and the new direction followed by the ants. We therefore pooled the data for 30 deviations in symmetrical and asymmetrical bifurcations in P-mazes. After all data pooling has been done, we finally computed the proportion of ants making a U-turn after a deviation of 30, 60 and 120 and we obtained ( 0.10), ( 0.57) respectively. ( 0.26) and Collective behaviour General network use The mean number of ants in the network at each time frame followed a sigmoidal growth for both P-mazes and NP-mazes (Figure 5.2, left). However while the value 171

191 5.4. MODEL CHAPITRE 5. in P-mazes reached a plateau around 40 ants, in NP-mazes it increases up to 60 ants. Each tested colony was randomly assigned to a type of maze and P-mazes and NP-mazes were tested alternatively. Thus the amount of ants involved in the exploration of the environment at the start of the experiments was likely to be equivalent between the two types of mazes. This is confirmed in the first 300 seconds of the experiments were the values for P-mazes and NP-mazes are indistinguishable. The mean number of used segments followed the same general dynamics (Figure 5.2, left inset). It also displayed a quantitative difference between the two types of mazes, the mean number of used segments being higher in NP-mazes than in P-mazes in the second half of the experiments. Therefore ants were less dispersed in P-mazes than in NP-mazes. Path selection A significant difference was found between P-mazes and NP-mazes in the mean number of selection events (two-sample Wilcoxon test with continuity correction, W = 14.5, P =0.008). In P-mazes the number of selection events was lower than in NP-mazes : once ants selected a path in P-mazes they were less likely to switch to another path than ants in NP-mazes (Figure 5.3, left inset). Moreover a two-way ANOVA revealed a significant difference between the different path categories (F =8.976, P<0.001) and between the two types of mazes (F =9.989, P =0.002) for the mean duration of a selection event, and a significant interaction between these two factors (F =3.116, P =0.015). In particular when ants in P-mazes selected a shorter path (one of the 27 cm paths), they used it for a significantly longer time than ants in NP-mazes (Tukey HSD test, P<0.001, see Figure 5.3, left). 5.4 Model Model description According to Camazine et al. (2001) the flow of ants leaving the nest and entering the network at each time step can be modeled as follows in the case of the Argentine ants : F entrance = k 0(k 1 + C entrance ) m k 2 +(k 1 + C entrance ) m C entrance corresponds to the total quantity of pheromone deposited by the ants at the entrance of the network ; k 0 corresponds to the maximal number of ants that can enter the network at each time step ; k 1 corresponds to the spontaneous tendency of ants to explore a new environment ; k 2 and m are parameters that depend on the time step (here fixed to one second). 172

192 CHAPITRE MODEL Mean time (sec) (a)! P!! NP Selection events ! P NP Network type!!! (b)!!! Selection events ! P NP Network type!!! Loop No path 27 cm 36 cm 45 cm 54 cm 63 cm Path category Loop No path 27 cm 36 cm 45 cm 54 cm 63 cm Path category (a) Experiments Figure 5.3: Mean duration of selection events for each path category (main figures) and mean number of selection events (insets). Left: experimental results. Right: simulation results. Black curves and bars represent data for polarized networks. Grey curves and bars represent data for non polarized networks. Each point and bar represents the mean±standard error. Once an ant has entered a gallery i of the network, the time t i required to travel the gallery is computed as follows : t i = d i v with d i the length of the gallery in centimeters and v the speed of the ant drawn from a normal distribution with mean v mean and standard deviation v sd. At each symmetrical intersection an ant has to choose between two branches a and b. The probability p a for an ant to choose the branch a and p b to choose the branch b at a symmetrical bifurcation are modeled as follows : p a = (k + C a ) n (k + C a ) n +(k + C b ) n (5.1) p b =1 p a (5.2) with k the intrinsic attractivity of branches a and b, C a and C b the quantity of pheromone on branches a and b respectively and n the degree of nonlinearity of the choice. At an asymmetrical bifurcation, about 2/3 of the ants choose the branch deviating less from 173

193 5.4. MODEL CHAPITRE 5. their original direction, whether the two branches are equally saturated by pheromone (as in our study) or unmarked (as in Gerbier et al., 2008). We computed the the probability p a to select the branch a and p b to select the branch b at an asymmetrical bifurcation as follows : p a = p a + p pref p b =1 p a with p pref = l( 4p 2 a +4p a ) l corresponds to the tendency of an ant to follow a path. It is positive if branch a deviates by a 30 angle from the ant s original direction and negative if it deviates by a 120 angle. When p a is equal to 0.5 (i.e., C a = C b ), then p pref is equal to l. Because the two branches are equally marked by pheromone, the ant choice is influenced only by the geometry of the bifurcation. Conversely when one of the two branches becomes more marked with pheromone, then the ant choice becomes influenced by the trail. Because this ant species is mainly guided by their pheromone trails, we assume that the influence of the bifurcation geometry progressively decreases as the difference in pheromone concentration between the two branches increases. Therefore when p a tends to 1 (C a C b ) or 0 (C a C b ), p pref tends to 0. Once the ant has crossed a bifurcation, it has a probability p α to make a U-turn before reaching the end of the selected branch. The probability value depends on the angle α (either 30, 60 or 120 ) the ant has rotated to enter the branch. An ant going to the food source deposits a quantity q of pheromone on the branch it comes from, just before reaching the bifurcation, and a quantity q on the branch it chooses, just after the bifurcation. An ant coming from the food source and going back to the nest deposits a quantity Q of pheromone at each of these points. As an approximation we considered that all ants in the simulations lay a trail whereas in experiments with L.humile the percentage of trail-laying ants is close to 90% (Deneubourg et al., 1990). Since the average lifetime of the trail pheromone in L. humile is long (20-30 min (Deneubourg et al., 1990)) compared to the duration of the simulation (15 min), we neglected the evaporation of the pheromone in our simulations. One can also assume that the air in the galleries is rapidly saturated by the trail pheromone during an experiment. For this reason, we also considered that the diffusion of the trail pheromone in the 174

194 CHAPITRE MODEL Parameters Value k 0 ; k 1 ; k ; ; 48 m 1.2 v mean ± v sd 1.1 ± 0.25ms 1 k 60 n 2.6 l p 30 ; p 60 ; p ; 0.26 ; 0.57 q ; Q 0.94 ; 9.2 τ 179.9sec Table 5.1: Parameters of the model. : parameters estimated experimentally. : parameters estimated experimentally in Vittori et al. (2006). : parameters estimated by genetic optimization. network was negligible and thus did not implement a diffusion function in our simulations. No crowding effect, either in the galleries or at the food source, that could influence the dynamics of the recruitment or the path choice were considered in the simulations. Finally, the time spent by an ant at the food source was modeled by a negative exponential law with a characteristic time τ as measured in (Vittori et al., 2006). The model was implemented in C++ and the simulations were run for 900 time steps of 1 second. Thousand simulations were run with the parameters given in Table 5.1. The parameters that had not been measured experimentally were estimated thanks to a genetic optimization algorithm designed to minimize the difference between simulations and observations, on the basis of the average number of ants in the network and the mean duration of selection events in the P-mazes. Note that the optimization was applied only to the P-maze condition and not to the NP-maze one. Thus free parameters were not optimized to reproduce the differences observed in experiments between the two conditions Comparison of the model output with the experimental results The simulation results were computed in the same manner as in the experiments. Note that, because of the 100-fold difference in sample size between the simulations and the experiments, we did not perform any statistical test to compare the results of the simulations to those of the experiments. The statistical power of such tests would indeed be too low to be meaningful. General network use As in the experiments, the mean number of ants in the network followed a sigmoidal growth in both P-mazes and NP-mazes and the plateau reached in NP-mazes was greater than that reached in P-mazes (Figure 5.2, right). The mean number of used segments in 175

195 5.5. DISCUSSION CHAPITRE 5. simulations followed a qualitatively different dynamics than in experiments, but it displayed a difference between the two types of mazes similar to the one observed in the experiments, the mean number of used segments being higher in NP-mazes than in P-mazes in the second half of the simulations (Figure 5.2, right inset). Path selection As in the experiments, a significant difference was found between P-mazes and NP-mazes for the mean number of selection events (two samples Wilcoxon test with continuity correction, W = , P<0.001) : once virtual ants had selected a path in P-mazes they are less likely to switch to another path than virtual ants in NP-mazes (Figure 5.3, right inset). A two-way ANOVA revealed a significant difference between the path categories (F = , P<0.001) and between the types of mazes (F = , P<0.001) for the mean duration of a selection event, and a significant interaction between these two factors (F = , P < 0.001). In particular when virtual ants in P-mazes selected a shorter path (one of the 27 cm paths), they used it for a significantly longer time than virtual ants in NP-mazes (Tukey HSD test, P<0.001, see Figure 5.3 on the right). These observations were similar to those obtained in the experiments. Foraging efficiency The foraging efficiency of the colony is difficult to evaluate in experiments because it requires to make a clear distinction between fed and unfed ants coming back to the nest. We therefore used the model to evaluate the foraging efficiency in each types of mazes. We defined the foraging efficiency as the ratio between the total number of fed ants returning to the nest over the total number of ants returned to the nest since the beginning of the virtual experiment. After only 900 seconds the foraging efficiency in P-mazes was more than three times higher than in NP-mazes (0.318 ± versus ± 0.001, two samples Wilcoxon test with continuity correction, W = , P < 0.001). 5.5 Discussion Our results show that individual ants behave differently according to the geometry of the bifurcations they encounter during their foraging trips. In particular we confirm the observations made by Vittori et al. (2006) that the workers of the Argentine ant do make biased choice at asymmetrical bifurcations : in our experiments, 66% of the ants chose the branch that deviated less from their original direction when the two branches were equally marked with pheromone. In addition our results indicate that the individual probability for an ant to perform a U-turn 176

196 CHAPITRE DISCUSSION increased with the turning effort the ant produced after crossing a bifurcation : the more its new walking direction diverged from its original direction, the more likely it was to perform a U-turn on the selected branch. A similar behaviour has been found in Lasius Niger ants : their probability to perform a U-turn increases with the angle between their walking direction and the nest direction (Beckers et al., 1992b; Dussutour et al., 2006). At the collective level, our experiments reveal that Argentine ants were more dispersed and less capable of selecting a path in networks that did not present a geometrical polarization. Our model simulations confirm that the differences between the individual behaviours of ants at symmetrical and assymetrical bifurcations are sufficient to explain the discrepancies observed at the collective level between polarized and non polarized networks. Additional sets of simulations (see Appendix 5.5) reveal that the improvement of the foraging efficiency and of the path selection ability in polarized networks was mainly due to the tendency of ants to follow the branch that deviated less from their original direction when reaching a bifurcation. On the contrary, the greater probability to perform a U-turn on the branch that deviated more seemed to slightly favour the dispersion of ants inside the network. In polarized networks, ants that went back to their nest and reached an assymetrical bifurcation preferentially selected the branch that deviated less from their original direction. This branch was therefore more marked with pheromone and attracted more ants. Owing to the amplification of this individual tendency, the colony was more likely to select this branch. Because the less deviating branch at each bifurcation of the polarized networks converged to the nest, ants had better opportunities to select one of the shortest paths than in non polarized networks. As a consequence, the absence of polarization cues in non polarized networks dramatically decreases the food income : after only fifteen minutes the foraging efficiency estimated by simulations was three times lower than in polarized networks. Amplification processes are widespread in group-living species and they are at the origin of some of the most impressive collective behaviours in social animals (see reviews in Camazine et al., 2001; Krause & Ruxton, 2002; Couzin & Krause, 2003; Detrain & Deneubourg, 2006; Garnier et al., 2007a). They are based on a very simple principle : the more individuals perform a given behaviour, the more likely other individuals will perform the same behaviour. This explains why a slight difference in the tendency of individual animals to perform a given action is likely to propagate in the population so that soon the majority of individuals performs the same behaviour. The amplification of behavioural differences by pheromonal recruitment in ants is responsible of several biased collective decisions during foraging (Beckers et al., 1993; Sumpter 177

197 5.5. DISCUSSION CHAPITRE 5. & Beekman, 2003; Dussutour et al., 2005a) or the selection of a new nest (Jeanson et al., 2004a). As illustrated by our work, the existence of such behavioural biases and their amplification can significantly modify the use and the functional efficiency of ants transport networks. This latter results from the interaction between the networks structure on one hand and the behaviour of the ants on the other hand. Amplification processes can have positive effects on foraging efficiency, but they can also have some drawbacks. In particular, when the positive feedback driving the amplification process is strong, it can lead the colony to persist in a sub-optimal choice. When a L. niger colony is offered two food sources with different qualities, it usually selects the best one. If the rich source is discovered after the poor one however, it remains unexploited (Beckers et al., 1990). The ants trapped into the recruitment trail toward the poor source are unable to revert their initial choice. The same phenomenom occurs when L. niger (Beckers et al., 1992b) and L. humile (Goss et al., 1989) ants use a path between their nest and a food source and discover a shorter route afterwards. This effect can have important negative consequences on the efficiency of ant colonies in foraging networks, in particular in L. humile ants that strongly rely on their pheromone trails (Aron et al., 1993). They can get easily stuck into loops or long paths in the absence of other orientating cues. Moreover the concentration of ants on a single path (short or long) virtually disconnects some sections of the network (Stickland et al., 1995)and therefore decreases its robustness from a topological point of view. Note however that this ant can switch to other solution when its first choice is disrupted after the pheromone trail is well established. When an obstacle blocks their path in a gallery network, ants are able to readily find another path toward their goal (Vittori et al., 2004). We conclude that biased individual behaviours coupled with amplification processes can have a major impact on the patterns of exploitation of transport networks in ants. Evaluating the efficiency of their transport networks on the basis of their structural properties may not fully reflect the actual performance of the colony. Understanding the coupling between ant behaviours and network structures is therefore essential to accurately evaluate the efficiency of their nest galleries or their foraging trails. In a more general context we emphasize the role of the behaviour of network users in the functional efficiency of transport networks. In road networks for instance, differences between drivers prefered speed is at the origin of spontaneous traffic jams that occur at car density far below the theroretical capacity of the road (Helbing & Huberman, 1998; Helbing, 2001). The functional efficiency of a transport network is the product of the structural properties of the network and of the network users behaviours, and it should be evaluated as 178

198 CHAPITRE DISCUSSION such. Acknowledgements We thank the members of the EMCC workgroup in Toulouse for helpful and inspiring discussions. Simon Garnier is supported by a research grant from the French Ministry of Education, Research and Technology. 179

199 5.5. DISCUSSION CHAPITRE 5. Supplementary material Sensitivity analysis We assessed the sensitivity of the model to the following parameters : the size of the colony, the number of bifurcations, the probability to perform a U-turn on the most deviating path (p α ) and the tendency to follow the less deviating path (p pref ). For each value of the tested parameter, we computed the time spent on shorter paths and the foraging efficiency after 900 seconds. One thousand realizations of the simulation were run Ffor each value of the parameters tested. Size of the colony (Figure 5.4a) We varied the number of virtual ants from 50 to We tested the virtual ants in both P-mazes and NP-mazes. The time spent on the shorter paths increases with the size of the colony in the two kind of mazes. But it increases faster in P-mazes than in NP-mazes. The foraging efficiency remains low and relatively constant with the colony size in NP-mazes while it grows up with the number of ants in P-mazes and eventually reaches a plateau for large colonies. Note however that no crowding effect that could affect the collective behaviour of the ants was implemented in the model. Number of bifurcations (Figure 5.4b) We increased the number of bifurcations in the network by adding extra triplets of hexagons at the end of the network. The total length of the network was kept constant and we tested virtual ants in P-mazes and NP-mazes. As the number of bifurcations increases both the time spent on the shorter paths and the foraging efficiency drop down in P-mazes and NP-mazes. However the decrease is slower in P-mazes than in NP-mazes. Probability to perform a U-turn on the most deviating path (Figure 5.4c) We fixed l to zero (no tendency to follow the less deviating path) and we varied p 120 from 0.1 to 1 while p 30 was kept equal to 0.1. The time spent on the shorter paths displayed only a small tendency to decrease as the probability to perform a U-turn on the most deviating branch increased while the efficiency of the colony decreased more clearly with increasing value of p 120. This effect is a consequence of the continuous pheromone laying of the ants. After crossing a bifurcation the ant lays down a trail on the branch it has chosen. If it decides to perform a U-turn on this branch, it gets over the trail it has just laid and therefore it reinforces it again. The choice of the next ant coming to the bifurcation is therefore slightly biased toward this branch. Because in this sensitivity analysis p 120 p 30, the most deviating branch is therefore more likely to be reinforced by U-turning ants than the less deviating one. Counterintuitively, the higher 180

200 CHAPITRE DISCUSSION Mean time spent on short paths Colony size Efficiency (a) (b) Efficiency Number of bifurcations Mean time spent on short paths Colony size Number of bifurcations Mean time spent on short paths p! Efficiency (c) (d) Efficiency p pref Mean time spent on short paths p! p pref (a) Colony size Figure 5.4: Mean time spent on shorter paths (main figure) and mean foraging efficiency (inset) as a function of: (a) the size of the colony; (b) the number of bifurcations in the network; (c) the probability p α to perform a U-turn on the most deviating branch after crossing a bifurcation; (d) the probability p pref to select the less deviating path at a bifurcation. Each curve represents the mean±the standard error (ligth and dark grey polygons). In (a) and (b) plain curves represent data for polarized networks and dashed curves represent data for not polarized networks. 181

201 5.5. DISCUSSION CHAPITRE 5. probability to perform a U-turn on the most deviating branch favours the dispersion of the ants in the network. Note that the efficiency grows up once p 120 becomes close to one because in this case a very few number of ants are able to reach the end of the most deviating branch (almost all of them perform a U-turn before) and the only escape way is the less deviating one. Tendency to follow the less deviating path (Figure 5.4d) We fixed p α to 0 (no U-turn) and we varied l from 0.25 (virtual ants preferentially selecting the most deviating branch) to 0.25 (virtual ants selecting the less deviating branch). As l increases both the time spent on the shorter paths and the foraging efficiency increases. For large values of l the foraging efficiency reaches a plateau. 182

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204 CHAPITRE 6. Chapitre 6 Sélection de chemin par stigmergie dans un groupe de petits robots autonomes Le mécanisme général du recrutement par piste chimique que l on retrouve chez de nombreuses espèces de fourmis a prouvé à maintes reprises son efficacité pour sélectionner des routes dans les réseaux naturels et artificiels de transport ou dans les réseaux de télécommunications (Dorigo & Gambardella, 1997; Dorigo et al., 1999, 2000; Bonabeau et al., 2000; Camazine et al., 2001). Malgré cela, les processus d auto-organisation basés sur l utilisation de pistes chimiques restent très peu étudiés dans le domaine de la robotique collective. Leur capacité à sélectionner une route parmi plusieurs alternatives possibles n a jamais été à notre connaissance étudiée dans un contexte robotique. L une des raisons principales de cet absence d étude repose sur la difficulté d utilisation des signaux chimiques en robotique. Dans ce chapitre, nous présentons un dispositif expérimental qui permet d implémenter dans des groupes de robots la logique sous-jacente du recrutement par piste de phéromone. Ce dispositif contourne le problème des signaux chimiques en utilisant à la place des signaux lumineux projetés sur l arène expérimentale. Les robots utilisés sont équipés de capteurs leur permettant de détecter cette trâce lumineuse et de la suivre. Ils sont également équipés d une balise lumineuse qu ils allument lorsqu ils souhaitent déposer un trâce sur leur passage. Cette balise est détectée par un système automatique de trajectométrie couplé à un vidéo-projecteur qui projette une trâce lumineuse derrière le robot. Si ce dispositif ne permet pas une utilisation dans des conditions naturelles, il permet cependant d explorer les propriétés de systèmes robotiques utilisant la logique du recrutement chimique. Nous utilisons ici ce dispositif pour étudier expérimentalement la sélection par un groupe de robots d un chemin à l intérieur de réseaux de galleries de complexité croissante. Au départ de l expérience, les robots sont regroupés dans leur nid et ils doivent réaliser des allers-retours 185

205 CHAPITRE 6. entre ce nid et une source placée quelque part dans le réseau. Nos résultats montrent tout d abord que le groupe de robots est capable de choisir un chemin lorsque deux alternatives identiques lui sont proposées, comme le font les fourmis (Deneubourg & Goss, 1989). La qualité de ce choix dépend largement du nombre de robots impliqués dans la tâche. Plus il est petit ou plus il est élevé, moins le groupe sera capable de sélectionner un chemin. Il existe donc une valeur optimale de la taille du groupe qui permet d obtenir un choix dans la grande majorité des cas. De plus, lorsque les deux routes alternatives ne sont pas de même longueur, le groupe sélectionne comme chez les fourmis (Deneubourg & Goss, 1989) la plus courte des deux dans la majorité des cas. Nous avons également testé le comportement du groupe dans deux réseaux plus complexes, offrant respectivement 7 et 14 chemins différents pour relier le nid à la source. Dans les deux cas, nous montrons que le groupe est capable de sélectionner le chemin le plus court dans le réseau. Nous montrons également que leur performance peut être grandement améliorée si l on introduit à chaque bifurcation du réseau un biais physique qui dévie légèrement la trajectoire des robots vers la branche menant préférentiellement au nid ou à la source. L effet de ce biais physique est amplifié par le recrutement chimique et augmente très fortement la probabilité que le chemin court soit sélectionné de façon stable par le groupe. 186

206 CHAPITRE 6. Stigmergic self-organization as a distributed path selection mechanism for groups of small autonomous robots Simon Garnier, Fabien Tâche, Maud Combe, Christian Jost and Guy Theraulaz Simon Garnier, Maud Combe, Christian Jost, Guy Theraulaz Centre de Recherches sur la Cognition Animale, CNRS-UMR 5169, Université Paul Sabatier, Bât IVR3, Toulouse cedex 9, France. Fabien Tâche Autonomous Systems Lab, ETHZ, Zurich, Switzerland Article in preparation 187

207 6.1. INTRODUCTION CHAPITRE Introduction Social insects are considered as the canonical example of a decentralized organization (Camazine et al., 2001). Using self-organization principles, these relatively simple animals can develop efficient collective behaviours without supervision or leadership. Self-organization is set of processes in which the solution to a problem emerges solely from the repeated interactions among the lower-level components of the system. These components interact with each other without reference to the global problem the group deals with, and rather behave according to the information they gather in their local environment. This distributed organisation of insect societies presents several interesting features for the achievement of multi-robot tasks : the individual behaviours are simple compared with the complex colony output ; the colony is flexible to changing environmental conditions ; the redundancy makes the colony tolerant to individual failures. This has encouraged the development of swarm robotics, a branch of the collective robotics, which has made an explicit use of self-organization to coordinate group of robots in various contexts : dispersion (Schwager et al., 2006), aggregation (Beckers et al., 1994; Garnier et al., 2008), segregation (Holland & Melhuish, 1999), coordinated movement (Pugh & A. Martinoli, 2006; Campo et al., 2006), coverage (Correll et al., 2008), target localization (Hayes et al., 2002), task allocation (Krieger et al., 2000; Labella et al., 2006), cooperative manipulation (Martinoli, 1999; Kube & Bonabeau, 2000; Ijspeert et al., 2001) and decision-making (Garnier et al., 2005). In most of the above examples, self-organized processes are supported by direct interactions : robots behave according to their perception of the immediate actions of their neighbours. Fewer studies however have investigated the use of indirect interactions for the organization of robotic groups. Indirect interactions correspond to the ability of individuals to modify the environment in which they evolve, and to respond in turn to such changes. In Biology, this is also refered as stigmergy (Grassé, 1959; Theraulaz & Bonabeau, 1999). As direct interactions, stigmergy can be used to achieve the coordination of many agents in order to find efficient solutions to a problem, as attested by numerous biological studies. Within collective robotics, the pioneering works by Beckers et al. (1994), Holland & Melhuish (1999) and Martinoli et al. (1999) for instance have made an explicit use of stigmergic coordination to assemble or sort objects with teams of robots. But compared to direct communication, stigmergic communication leaves in the environment a more or less persistent imprint of the agents behaviours. This imprint can in turn influence the agents future behaviours. In this sense, stigmergy can be regarded as an external collective memory. This has the advantages to stabilize the collective solution found by the group and 188

208 CHAPITRE INTRODUCTION to require no encoding of data in the agents individual memory. Ant pheromone trails are probably the best known example of such stigmergic self-organization. In several ant species, these chemical trails are involved in foraging behavior, and more precisely in recruitment of nestmates and navigation between nest and food sources. This is achieved through a simple stigmergic process which results in the formation and reinforcement of a chemical trail linking these different areas. Several experimental and theoretical studies showed that this self-enhanced communication process can lead an ant colony to interesting collective behaviors such as the selection of the most rewarding food source (Goss et al., 1989) or the selection of a single path between the nest and a food source (the shortest one if the alternatives are of unequal length, one of the alternatives at random if they are of equal length, Deneubourg & Goss, 1989). During the 1990 s, a growing number of studies proved that this pheromone-based process is an efficient method to solve path optimization problems such as re-routing traffic in busy telecommunication networks or dealing with the traveling salesman problem (finding the shortest route by which to visit a given number of cities, each exactly once, Bonabeau et al., 1999; Dorigo et al., 2000). These studies were the first evidences that the pheromone logic can be effectively applied to artificial systems. Despite these results, pheromone-based self-organization remains largely underinvestigated within the field of collective robotics. In particular, the path selection mechanism used by ants has never received an experimental assessment in a robotics context. In this contribution, we introduce the first implementation of this mechanism in a group of miniature robots. We also present an experimental investigation of this robotics system in various conditions, from simple binary choices to navigation in complex networks. To achieve our study, we need a handy way to deal with the pheromone signal. Despite significant progresses in odour detection and plume tracing (Grasso et al., 2000; Hayes et al., 2002), using chemicals (as in Russell, 1999) would not be sufficiently flexible for our exploratory investigation since extinction of pheromone can not be easily controlled. Some alternatives to chemicals have been proposed in previous works : e.g. (1) heat applicators and sensors (Russell, 1997), virtual pheromones stored either by (2) an external computer (Pearce et al., 2003) or by (3) each robot in the group (Payton et al., 2005), (4) ultraviolet sensitive glowpaint (Blow, 2005). Solution (1) (Russell, 1997) is not efficient to establish a long-lasting trail. In solution (2) (Pearce et al., 2003), perception of pheromone and control decisions are all performed by an external computer, thus severely limiting the autonomy of the robots. Solution (3) (Payton et al., 2005), even if really promising in terms of applications, rather resembles to path formation thanks 189

209 6.2. MATERIALS AND METHODS CHAPITRE 6. to robot chains as already suggested in (Goss & Deneubourg, 1992) than to the stigmergic path formation used by ants. At last, solution (4) has fairly the same lack of flexibility as chemicals. In the present work, we propose to use another method to study in laboratory conditions the properties of a robotic system using ant trail laying and trail-following behaviors. We suggest to substitute pheromones with light projected on the ground thanks to a video projector as proposed in Sugawara et al. (2004) and Siegrist (2005). This video projector is controlled by a tracking setup which detects a red LED on top of the robots. This LED is switched on only when the robot decides to lay down pheromone. According to this information, the tracking setup computes the location and strength of the light trail deposit. At last, robots detect and follow light trails thanks to two simple photoreceptors. Of course, this system does not solve the autonomous trail laying problem but the behaviour of individual robots remains independent of a central planner. Above all, our setup s purpose is not to become a real life application but rather to provide a cheap and very easy to handle laboratory tool to test pheromone algorithms with robots that perceive their environment and adapt their behavior in a fully autonomous way. 6.2 Materials and methods Robot Alice Base robot The micro-robots Alice were designed at the EPFL (Caprari et al., 2002, see the base robot on the right of Figure 6.1). They are very small robots (22mm x 21mm x 20mm) with a maximum speed of 40 mm s 1. They are equipped with two watch motors with wheels and tires. Four infrared (IR) sensors and transmitters are used for communication and obstacle detection. Energy is provided by a NiMH rechargeable battery allowing an autonomy of about 3.5 hours in our experimental conditions. The robots have a microcontroller PIC16LF877 with 8K Flash EPROM memory, 368 bytes RAM and no built-in float operations. Programming is done with the IDE of the CCS-C compiler allowing to use assembler and C commands at the same time, and the compiled programs are downloaded in the Alice memory with the PIC-downloader software Trail following add-on An add-on module has been built to allow light path detection by the robots and robot detection by a tracking device. This module is plugged into the top connector of the Alice 1. http :// 190

210 CHAPITRE MATERIALS AND METHODS (a) (b) Figure 6.1: (a): Robot Alice with (left) and without (right) the additional module for light detection. (b): Three robots Alice pursuing a luminous trail. robot, as can be seen on the left of Figure 6.1a. This add-on is equipped with two photodiodes pointing upwards which let the robot detect the trail. It also carries a red LED (Light Emitting Diode) to permit an easy and reliable tracking in conditions of changing background brightness. Additionally, the LED provides a very simple solution to indicate to the tracking device the robot s state : with the LED turned on, the robot does lay pheromones and thus must be videotracked, with the LED turned off the robot is only exploring without trail laying and no tracking is necessary. Technical details about this add-on can be found in Siegrist (2005) Experimental setup The experimental setup has three parts : a maze, a robot tracking device and a pheromone deposit device. The whole setup is held by a 2m x 1.5m x 3m aluminium cage with three opaque walls to avoid robots or tracking device being disturbed by external light. The fourth wall is left open and points towards a direction with no light source. All experiments are videotaped with a Sony 3CCD DCRTRV950E video camera Maze The maze is built with white cardboard (5mm thick, wall height of 2.5cm). It lies on the ground of the cage. Each extremity of the maze is an octagonal area which represents either the nest or the source. In each of these areas, two infrared transmitters built into the walls continuously emit a signal (different for each area) which allows the robots to know if they are 191

211 6.2. MATERIALS AND METHODS CHAPITRE 6. (a) Two path maze (equal lengths). (b) Two path maze (different lengths). (c) Three loop maze (polarized). (d) Three loop maze (non-polarized). (e) Four loop maze with removable deflectors. Figure 6.2: Blueprints of the experimental setups. 192

212 CHAPITRE MATERIALS AND METHODS in the nest or the source. Three types of mazes were used and for each type of mazes two different conditions were tested. Blueprints of the different type of mazes and conditions are shown in Figure 6.2. Two path mazes Nest and source are linked by two paths either of the same length (Figure 6.2a) or of different lengths (Figure 6.2b). In the equal length condition, the path are 85 cm long. In the different length condition, the short path is 85 cm long while the long path is 210 cm long (about 2.5 times the length of the short path). In order to asses the effect of the size of the group on the ability of the group to perform a choice, we test groups of 1, 2, 3, 5 and 10 robots in the equal length condition. We test a group of 10 robots in the different length condition. Three loop mazes Nest and source are linked by a network made of three diamond-shaped loops (Figure 6.2c and Figure 6.2d). In such network, it exists 7 possible paths of different lengths that robots can use to go from the nest area to the source area without using twice the same branch. We test the collective behaviour of the robots in two different types of mazes : polarized one (P-maze, Figure 6.2c) and non polarized one (NP-maze, Figure 6.2d). In the NP-maze, the six angles of each hexagon are equal to 120. As a consequence, all the bifurcations in the network are symmetrical : at a bifurcation each branch deviates by a 60 angle from the other two. In P-mazes, two of the six angles of each hexagon (the closest from the nest and the closest from the food source) are equal to 60, while the other four are equal to 150. As a consequence, all the bifurcations are symmetrical from one branch and assymetrical from the other two. We test a group of 10 robots in both conditions. Four loop mazes Nest and source are linked by a network made of four diamond-shaped loops (Figure 6.2e). In such network, it exists 14 possible paths of different lengths that robots can use to go from the nest area to the source area without using twice the same branch. We test the collective behaviour of the robots in two different types of mazes : polarized one (P-maze) and non polarized one (NP-maze). The polarization of the network is achieved by adding removable deflectors as shown in Figure 6.2e to mimic the presence of asymmetrical bifurcations as in the previous type of maze. A four loop maze with bifurcations polarized as those of the previous three loop maze would have been too large for the pheromone deposit device. We test a group of 10 robots in both conditions. 193

213 6.2. MATERIALS AND METHODS CHAPITRE Tracking device The goal of the tracking device is to detect the red LED on the top of each trail laying robot. The tracking device is made up with a firewire digital video camera Unibrain Fire-i400 (resolution 640x480) hung about 1.5m above the maze and connected to a laptop computer Dell Latitude D810 thanks to a 1394a PCMCIA card. Image acquisition is done with the open source CMU 1394 Digital Camera Driver (Robotics Institute, Carnegie Mellon University 2 ) and image treatment is done with the open source OpenCV library (Intel 3 ). Usually a picture is stored with the three channels RGB (Red, Green, Blue). If one would just look at the red channel, he could see the robot s LED as a bright spot, but also all virtual pheromone trails. Additionally, the red portion of the LED changes if the robot is in a dark or in a bright area. A better way for detection is to calculate the HSV channels (Hue, Saturation and Value) from the RGB channels. The resulting H value is the angle in a color circle. If the red color does get brighter or darker, the H value will stay the same. Once the H-channel is extracted, white noise is removed thanks to morphological opening (erosion followed by dilatation) with a 3x3 matrix. Then a maximum and minimum threshold are applied to turn the resulting image into a binary one and a fit ellipse function returns the centre positions of the robots. The described tracking function has proven to be very stable. The HSV decomposition is a reliable way to track the red spot. Even with room light turned on, or bad camera settings, the program can still track the robots in most situations Pheromone deposit device Once the position of a robot emitting pheromones is known, light has to be sent to this location (see Figure 6.1b). An output image (800 x 600 pixels) with luminous trails is produced and displayed in a window. This window is running in full screen mode on the enhanced desktop of Windows XP the video projector (Sony VPL-CX5) is connected to. To obtain a sufficiently large image to cover the whole maze, the video projector is hung 3m above it. The image is composed with uniformly blue spots (blue is chosen to contrast with the red LED of robots), each of them centred on the successive positions of robots, but without overlapping between the successive spot of a given robot. The light intensity of the blue spot is used to simulate the intensity of the pheromone deposit. Positions of pheromone spots are also corrected to take into account camera lens distortion (thanks to the Camera Calibration Toolbox for Matlab 4 ) and 2. http :// iwan/1394/ 3. http ://sourceforge.net/projects/opencvlibrary/ 4. http :// 194

214 CHAPITRE MATERIALS AND METHODS misaligning of the tracking camera and the trail laying video projector. Each point has a 6cm diameter. This diameter was chosen to allow two robots to cross each other and thus to reduce traffic jam on the trail. At last, if no other deposit is done at a given point, light intensity (I) decreases following an exponential decay to simulate pheromone evaporation : I(t) =I(t t) exp((log(1/2)/t c ) t) With t, the current time, t, the period between two evaporation time-steps and t c the characteristic evaporation time. To lower the processing charge (the previous computation is applied to each pixel in the image), evaporation is triggered every 5 seconds. All treatments included, the tracking and trail laying software allows an effective speed of about 5 images per second. This is sufficient for our needs Behavioral model The behavioral model is a generic and simplified model of trail laying and trail-following behaviors in ants. It aims at capturing the essential features needed to achieve a path selection as ants do. In the absence of light pheromones, a robot (laying a trail or not) moves according to a correlated random walk, with a strong tendency to continue in the same general direction. This behavior is called exploratory behavior. If the robot detects an obstacle, it tries to avoid it by turning in the opposite direction. This behavior is called avoidance behavior. If the robots detects a luminous trail with its photoreceptors, it tries to turn towards the one receiving more light. This behavior is called trail following behavior. Each of these behaviors triggers the computation of a movement vector. The three vectors are summed together with different weights to obtain the new direction at each time step (50ms). The exploratory vector points ahead of the robot and changes randomly between 90 and 90 after a time drawn in a decreasing exponential distribution. The avoidance vector is the sum of four vectors, each of them pointing in the opposite direction of one of the four proximity IR sensors of the robot. Their intensity grows with the intensity of the signal received by their respective sensor. At last, the trail following vector aims either to the right or the left of the robot. Its direction and intensity are controlled by the difference between light intensities perceived by the right and the left photoreceptor. 195

215 6.3. DATA ANALYSIS AND RESULTS CHAPITRE 6. The robot triggers its trail laying behavior (i.e. it switches on its red LED) each time it leaves either the nest or the source area (i.e. when it loses the IR nest or source signals). It then stops trail laying (i.e. switches off the red LED) when it enters either the nest or the source area (i.e. when it detects the IR nest or source signals) Simulations Before any experiment, a set of 8100 simulations was done with the Webots software (version 5.1.9) with physics engine switched on (Michel, 1998) on a Power Mac G5 2x2.3 GHz with Mac OS X In the simulations, pheromone deposits were gray spots laid on the ground by the simulated robots. The gray level (0=white, 1=black) was chosen to represent the intensity of the pheromone deposit. Simulated robots followed the pheromone trail thanks to light sensors installed under their body. Simulations were used to assess the influence of three parameters of the model : the number of robots (1, 2, 3, 5 and 10), the intensity of the pheromone deposit (six different intensities were tested between 0.03 and 0.5) and the characteristic evaporation time t c (see above, 9 different times were tested, varied between 60 and 3600 seconds). For each combination of parameters, 30 simulation runs were done. They were intended to estimate the parameters to use in experiments with real robots so as to obtain stable decisions. 6.3 Data analysis and results Parameter estimation For each minute of each simulation run (real time period of 60 minutes), we observe the number of robots coming from the source and entering each arm, that we call for the sake of simplicity A1 (n A1 ) and A2 (n A2 ). We then computed the proportion P i of robots entering arm A1 over a sliding time window of ten minutes. For each minute i [0 : 50], we computed : P i = i i+10 (n A1) i i+10 (n A1 + n A2 ) We thus obtain the temporal dynamics of the probability for the robots to choose each arm of the maze. At the beginning of the experiment (i =0), P 0 is set to 0.5. In order to evaluate the efficiency of each combination of parameters we must define a criterion representative of a stable choice. We first define a choice event each time the probability P i becomes superior to 196

216 CHAPITRE DATA ANALYSIS AND RESULTS 0.75 (A1 chosen) or inferior to 0.25 (A2 chosen). For each simulation, we count the number and the duration of these choice events. For each set of parameters, we compute the mean duration of choice events. This mean duration is a good indicator of a stable choice : if its value is low, it means that either no choice is made (the probability stays between 0.25 and 0.75) or the choice is not stable (many choice events of short duration). A high value indicates a strong and stable choice. The results for our simulations are shown in Figure 6.3. This figure clearly illustrates the three following points : Whatever the number of robots, the highest mean duration values occur only with long characteristic evaporation times (1200 to 3600 seconds). If evaporation is too fast, no stable choice can take place. When the number of robots grows, the pheromone deposit intensity needed to obtain a stable choice decreases. In other words, the individual cost of pheromone production decreases with the size of the group. At last, the highest mean duration (i.e. the maximum in each plot) grows with the number of robots, reach a maximum with 5 robots and then drop for 10 robots. This is due to the saturation in pheromone of both arms of the maze that occurs more frequently when the number of robots grows. The same analysis for robots coming from the nest gave similar results. Thus these results are not shown. To obtain the best experimental results according to the simulation data, we chose to work with a group of 5 robots, a deposit intensity of 0.12 and a characteristic evaporation time of 1800 seconds. However, a first set of experiments showed that these parameters in our experimental setup led the system to a pheromone saturation of the whole maze. The intensity of pheromone deposit (in simulations and experiments) varies between 0 and 1 according to a scale with 256 steps (256 gray levels in simulations, 256 blue levels in experiments). But the dynamic range, i.e. the number of undertones of a given color, our video projector is able to display is below this number. Therefore, the luminous trail intensity grows faster in experiments than in simulations. To counterbalance this effect, we lowered in experiments the characteristic evaporation time to 600 and the intensity of the pheromone deposit to We used the same parameters in every set of experiments. 197

217 6.3. DATA ANALYSIS AND RESULTS CHAPITRE 6. Figure 6.3: Mean duration of a choice event (gray levels, in minutes) as a function of the intensity of the pheromone deposit, the characteristic evaporation time t c and the number of robots. Proportion of successful experiments !!!!! Number of robots Figure 6.4: Proportion of successful experiments (P i > 0.75) as a function of the number of robots involved in the collective selection task Two path maze Identical length condition For each experiment in each group size, we compute P i over the last ten minutes of the experimental run. We then count for each group size the number of successful experiments, that is experiments that end with P i > Results are shown in Figure 6.4. This figure clearly shows that the ability of the group to perform a choice increases at first with group size and then decreases after an optimal group size. This is consistent with the simulation results and can be explained as well by the saturation in pheromone of both arms of the maze that occurs more frequently when the group size grows. 198

218 CHAPITRE DATA ANALYSIS AND RESULTS Proportion of experiments Proportion of individuals on short path Figure 6.5: Distribution of P i obtained over the last ten minutes of each experimental run in the different length condition. The strong right shift of the distribution indicates that a majority of the experiments end with a clear selection of the shorter path Different length condition We consider A1 as the short arm and A2 as the long one. For each experiment, we compute P i over the last ten minutes of the experimental run. We then draw the distribution of P i values in Figure 6.5. This distribution clearly shows that all the experiments end with more than 50% of the robots on the short arm and that most of the experiments (8 over 10) end with more than 75% of the robot on the short path Network maze At each second we specify the path selected by robots as follows. Starting from the source exit gallery we followed at each network bifurcation the gallery with the highest density of pheromone until we reach either a bifurcation followed by two empty galleries or a previously visited bifurcation or the nest area. If we reach a bifurcation followed by two empty galleries we define the selected path as pertaining to the no path category. If we reach a previously visited bifurcation we define the selected path as pertaining to the loop category. There exists 7 possible paths to reach the food source without using twice the same gallery in the three loop maze, and 14 in the four loop maze. These paths can be classified in a restrain number of categories according to their length in terms of number of segments (all segments have the same length). Thus we define the path selected by the ants to reach the food source as pertaining 199

219 6.3. DATA ANALYSIS AND RESULTS CHAPITRE 6. to the category corresponding to its length. By repeating this process at each second of each experiment, we obtain the time sequence of path selection events. We define a path selection event as all consecutive frames resulting in the same selected path category. We then compute the following data for each type of maze : Mean number of selection events. Mean duration of selection events for each selected path category Three loop maze Results for the three loop maze are displayed in Figure 6.6. Significantly less selection events are observed in the polarized network than in the non polarized one (two samples Wilcoxon test with continuity correction, W = 72, P<0.048) : once robots selected a path in P-mazes they were less likely to switch to another path than robots in NP-mazes (Figure 6.6a). A two-way ANOVA revealed a significant difference between the path categories (F =9.91, P < 0.001) and between the types of mazes (F =8.40, P < 0.005) for the mean duration of a selection event, and a marginally significant interaction between these two factors (F =2.53, P =0.06). In particular, robots always spent more time on a path of the shortest category than on a path of any other category whatever the type of the network. But when robots in P-mazes selected a path of the shortest category, they used it for a significantly longer time than robots in NP-mazes (Figure 6.6b) Four loop maze Results for the four loop maze are displayed in Figure 6.7. Significantly less selection events are observed in the polarized network than in the non polarized one (two samples Wilcoxon test with continuity correction, W = 20.5, P<0.027) : once robots selected a path in P-mazes they were less likely to switch to another path than robots in NP-mazes (Figure 6.7a). A two-way ANOVA revealed a significant difference between the path categories (F = 29.27, P < 0.001) and between the types of mazes (F = 10.31, P < 0.002) for the mean duration of a selection event, and a significant interaction between these two factors (F =7.31, P < 0.002). As in the three loop maze, robots always spent more time on a path of the shortest category than on a path of any other category whatever the type of the network. And when robots in P-mazes selected a path of the shortest category, they used it for a significantly longer time than robots in NP-mazes (Figure 6.7b). 200

220 CHAPITRE DATA ANALYSIS AND RESULTS Mean selection time for each path category Mean number of path change Mean time (sec) !!!!! Polarized network Non polarized network!!! Polarized Non polarized Loop No path Network type (a) Path category (b) Figure 6.6: Mean number of selection events (a) and mean duration of selection events for each path category (b) in the three loop maze. Blue curves and bars represent data for polarized networks. Red curves and bars represent data for non polarized networks. Each point and bar represents the mean±standard error. Mean selection time for each path category Mean number of path change Mean time (sec) !!!!!!! Polarized network Non polarized network!!! Polarized Non polarized Loop No path Network type (a) Path category (b) Figure 6.7: Mean number of selection events (a) and mean duration of selection events for each path category (b) in the four loop maze. Blue curves and bars represent data for polarized networks. Red curves and bars represent data for non polarized networks. Each point and bar represents the mean±standard error. 201

221 6.4. DISCUSSION CHAPITRE Discussion In this paper, we present a cheap and easy to handle experimental setup to test in laboratory conditions the applicability of the trail laying and trail following behaviors of ants to control a group of small autonomous robots. Preliminary computer simulations show that in such a system, a collective choice occurs only if the speed of pheromone evaporation is not too fast. Results also suggest that an optimal number of robots is required to get a quick and stable collective choice. At last, it seems that while the number of robots in the system grows, the quantity of pheromone needed to obtain a choice decreases : the individual cost of laying pheromone decreases with the size of the group. Such an exploration of system s parameters (whatever the method used, simulations, artificial evolution, etc) is useful to estimate the combination of factors that would give the best results in real experiments and avoid losing too much time finding them experimentally. It is also useful to gain some insight about the way the system behaves. However, at least in the context of biological based robotics, we think that experimental validation is the best proof that a given control algorithm works as it was hypothetized (Webb, 2000, 2001) and that simulation only remains a representation of the reality with all its lacks and simplifications. Therefore the proof of concept is done thanks to a very simple experiment in which a group of robots has to choose between two identical paths that link their nest to a food source. Experimental results show that the ability of the group to efficiently select one of the two paths depend on its size. They also show that an optimal number of robots can be found to maximize the decision-making strength, as predicted by simulations. This result is consistent with other works about self-organized collective behaviors in robotics (Krieger et al., 2000; Agassounon & Martinoli, 2002). We believe that this optimal number strongly depends on the configuration of the experimental setup : length of path between nest and source, width of arms of the maze, etc. In an unknown environment however, it would be hard to estimate this optimal number. A promising challenge would be to provide some control algorithms such that the group is able to adapt dynamically the number of robots to changing environmental conditions in a fully autonomous way. To increase group size, robots coming back from the source should recruit other robots. This could be easily done by letting these robots emit a signal (I.R. signal for instance) stimulating robots in the nest to start moving. Here again, recruitment processes used by ants could be used as a source of inspiration. For instance, it was showed in Krieger et al. (2000) that an ant-inspired 202

222 CHAPITRE DISCUSSION tandem recruitment increase the foraging efficiency of groups of 3 to 12 robots. Recruitment processes should also be counterbalanced by mechanisms able to reduce group size. This is necessary to avoid the system to overshoot the optimal group size, and thus to become less efficient. These mechanisms could act on different parts of robot behavior : robots could stop laying pheromone or reduce the quantity of deposited pheromone ; they could stop recruiting ; or they could stop foraging. But they should all rely on a less intuitive mechanism able to evaluate the number of robots currently involved in the task. The most promising way to evaluate such a number could again come from the ants. Indeed, ants are able to evaluate the density of their nestmates thanks to the rate of antennae contacts between them and to use this information to regulate their traffic organisation (Gordon et al., 1993; Burd & Aranwela, 2003; Dussutour, 2004). Such contacts between robots could then be used to estimate the local density of agents. And then, if this density goes above a threshold value, trigger one or several of the group size limiting behaviors mentioned above. In a second experiment, the group of robots has to choose between two paths, one of them being longer than the other one. As it is observed in ants (Deneubourg & Goss, 1989), the group preferentially select the shorter path. Robots that follow the shorter path link the nest and the food source quicker than robots that follow the longer path. Thus they reinforce the pheromone trail faster. This slightly biases the robots next choices toward the shorter path that is therefore more likely to be reinforced again. This amplification process that is more likely to occur on the shorter path leads the group to select the shorter path in most of the experiments. Interestingly, the robots do not need to evaluate or to compare individually the length of the two paths to select the most advantageous one. The coupling between the amplification of the pheromone trail and the structure of the environment is sufficient to achieve this efficient decision, with very few cognitive requirement at the robot level. This situation remains however very simple. Robots only choose among two alternatives. For this reason, we then test the ability of the group to select the shorter path in a more complex situation. Robots have to navigate across two networks that offer respectively 7 and 14 different paths of different lengths and at least three binary choices before a robot can arrive to either the source or the nest. The multiplication of the number of binary choices increases the probability that robots select a longer path or even get trapped into loops : any error at one choice point is likely to propagate over the following choice points. Results show that robots are able to preferentially select the shorter path in each of the two types of networks. They also show 203

223 6.5. CONCLUSION CHAPITRE 6. that this ability can be significantly improved if network bifurcations display an appropriate geometrical asymmetry. In the absence of pheromones or obstacles, a robot moves according to a correlated random walk, with a strong tendency to continue in the same general direction. As a consequence, when a robot reaches a bifurcation, its displacement inertia favors the selection of the branch that deviates less from the moving direction of the robot. Moreover its avoidance behavior favors the selection of the branch that is less obstructed. At a given bifurcation, if the branch that more directly leads to the nest or to the food source deviates less from the moving direction of the robots or is less obstructed than the other branch, thus robots will more likely follow it. This bias can be amplified by the pheromone trail laying trail following behavior, leading to the preferential selection of this branch. At the network scale, if all the bifurcations display such an asymmetry, this favors the selection of the shorter path between the nest and the source. In two studies about Argentine ant foraging behavior in network galleries, we show that when this ant reaches a bifurcation it preferentially follows the branch that deviates less from its moving direction (Gerbier et al., 2008) and that this individual bias favors the selection by the colony of the shortest path of the network (Garnier et al., in preparation). Our robotics study, despite the fact that robots follow a very simple and generic model of trail laying and trail following behaviors, suggests that this bias could be a simple consequence of the ant s displacement inertia. 6.5 Conclusion To conclude this paper, we would like to emphasize two particular points. First, the pheromone logic provides very interesting opportunities in terms of control algorithms for groups of autonomous robots. Its ability to efficiently select the shorter path in complex environnement should find potential applications in adaptative car traffic management or network exploration and exploitation by groups of robots (sewer, piping, landmine, etc). Second, the efficiency of self-organized behaviors in groups of robots can be significantly improves by an appropriate use of the structure of the environment. Through an appropriate exploitation of the constraints applied by the environment on the behavior of the robot, it becomes possibe to improve and to complexify the behavior of the group with minimum cognitive requirements at the level of the individual robot. 204

224 CHAPITRE CONCLUSION Acknowledgement We would like to thank Nikolaus Correll for designing the Webots model of the robot Alice, Olivier Michel for his help in programming our simulator and Jacques Gautrais for his helpful advices. Many thanks to all ASL members for their nice welcome and their technical help. Simon Garnier is partly funded by an ATUPS grant of the University Paul Sabatier. 205

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226 CHAPITRE 7. DISCUSSION ET CONCLUSION Chapitre 7 Discussion et conclusion Au cours de ce travail de thèse, nous avons examiné deux mécanismes d auto-organisation permettant aux individus appartenant à un même groupe de réaliser un consensus. Pour étudier ces deux mécanismes, nous avons adopté une approche mêlant étroitement éthologie et robotique. Ethologie d abord, parce que ces deux mécanismes ont en premier lieu fait l objet d un travail de caractérisation et de modélisation chez l animal, la blatte Blattella germanica d une part et la fourmi d Argentine Linepithema humile d autre part. Robotique ensuite, parce que ces modèles biologiques ont été implémentés sur une plateforme robotique, à savoir le mini-robot Alice. A travers cette double approche, nous avons essayé de contribuer à la fois à la compréhension générale des processus décentralisés de décision collective et à leur application dans des systèmes artificiels. Dans la suite de ce chapitre, nous présenterons dans un premier temps une discussion générale des résultats obenus (Section 7.1). Nous nous attacherons en particulier à réaliser une comparaison qualitative du fonctionnement et des propriétés de chacun des deux modèles étudiés (Section 7.1.1). Nous aborderons ensuite la question de l implémentation de ces modèles sur une plateforme robotique (Section 7.1.2). En effet, ces deux modèles n ont pas fait l objet du même traitement lors de leur implémentation. Nous discuterons les raisons de ces différences. Enfin, nous traiterons plus en détails les relations entre la structure de l environnement et le choix collectif réalisé par le groupe (Section 7.1.3). Dans un second temps, nous aborderons les prolongements possibles de ce travail de thèse (Section 7.2). Nous discuterons par exemple de la formation des réseaux de pistes chez la fourmi d Argentine (Section 7.2.1). Nous considèrerons également la possibilité de concevoir à partir de ces processus de décision collective des systèmes distribués de détection de caractéristiques environnementales (Section 7.2.2). Enfin, nous terminerons en traitant de perspectives générales concernant la robotique en essaim (Section 7.2.3), avant de conclure ce mémoire (Section 7.3). 207

227 7.1. DISCUSSION GÉNÉRALE CHAPITRE 7. DISCUSSION ET CONCLUSION 7.1 Discussion générale Comparaison qualitative des deux processus de décision collective Les deux processus de décision collective étudiés au cours de ce travail de thèse fonctionnent selon un même principe général : plus le nombre d individus qui choisissent une alternative est important, plus le degré d attractivité de cette alternative augmente. L application de ce principe conduit à une amplification du nombre d individus choisissant chacune des alternatives. Ces processus d amplification entrent alors en compétition les uns avec les autres. Le résultat de cette compétition désignera l alternative choisie par le groupe. Bien que fonctionnant selon le même principe général, ces deux processus présentent néanmoins des disparités notables. Dans la suite de cette section, nous allons discuter ces différences et nous attacher à comprendre comment elles affectent le fonctionnement et les propriétés du principe général évoqué plus haut Interactions directes vs interactions indirectes La première différence existant entre les deux processus étudiés est imputable au type d interactions mises en jeu. Le modèle d agrégation et de sélection d abri chez la blatte Blattella germanica est basé sur des interactions directes entre les individus, par le biais très probablement de signaux tactiles chez cet insecte ou par le biais de signaux infrarouges chez son pendant robotique. Au contraire, le modèle de sélection de route chez la fourmi d Argentine est basé sur des interactions indirectes, par le biais du dépôt d une trace chimique pour cet insecte ou d une trace lumineuse pour les robots. La nature et les propriétés de ces deux types d interactions dans les systèmes naturels ont déjà été largement discutées dans l introduction de ce mémoire. Nous ne reviendrons donc pas là-dessus. Nous aborderons plutôt les avantages et les inconvénients de ces deux types d interactions pour une utilisation en robotique collective. Aujourd hui, la majorité des applications de robotique collective utilisent des interactions directes pour coordonner l activité d un groupe de robots. Les technologies disponibles permettent de couvrir un champ très vaste de canaux sensoriels différents : ondes radios, vision, contact, infrarouges, etc... Pour fonctionner de manière optimale, ces signaux requièrent une ligne de vue dégagée entre les robots. Dans des environnements complexes, intriqués, il est parfois difficile de pouvoir maintenir la communication entre les individus, en particulier lorsque leur nombre est réduit par rapport à la surface à couvrir. L utilisation d interactions indirectes, par modification de la structure de l environnement ou 208

228 CHAPITRE 7. DISCUSSION ET CONCLUSION 7.1. DISCUSSION GÉNÉRALE dépôt d une trace persistante, pourrait permettre de contourner ces problèmes de communication. Cependant, l utilisation de telles interactions se heurte pour le moment à des difficultés pratiques et technologiques. Ainsi, la modification de la structure de l environnement n est pas toujours envisageable dans un environnement réel car elle pourrait entraîner des dégradations non désirées. On notera également les difficultés actuelles pour reproduire les propriétés d une communication chimique à l aide de robots. Ces difficultés limitent pour le moment l application en robotique des principes de sélection de route observés chez les fourmis Sélection de place vs sélection de route Dans le premier cas, il s agit d un processus de sélection de place. Les individus, blattes ou robots-blattes, identifient dans l environnement des endroits susceptibles de les accueillir. Le mécanisme de choix les conduit à ne sélectionner que l un d entre eux pour s y regrouper. Dans le second cas, il s agit d un processus de sélection de route. Les individus, fourmis ou robotsfourmis, réalisent une navette entre deux endroits répartis dans l environnement. Le processus de choix les conduit à sélectionner un seul des chemins qui relient ces deux endroits. En partant d un principe général identique, on peut altérer son fonctionnement pour obtenir des processus de sélection s appliquant à des catégories d objets différentes. Pour cela, on peut jouer à la fois sur la nature de l interaction et/ou sur la réaction de l individu à l interaction. Dans les deux cas cependant, le processus de choix conduit à une augmentation de la densité des individus dans une zone particulière de l espace. Le modèle de sélection de place conduit au regroupement des individus sous l un des abris disponibles, et le modèle de sélection de route conduit au regroupement des trajectoires des individus sur l un des chemins disponibles. Cette augmentation de la densité peut aider à remplir certaines fonctions, comme la défense contre les prédateurs ou les compétiteurs chez la fourmi, ou bien encore la lutte contre la dessication chez la blatte. Elle augmente également la probabilité d interactions entre les individus et favorise ainsi l émergence de nouveaux comportements collectifs (Deneubourg et al., 2002), comme par exemple l organisation du trafic sur les pistes chimiques chez la fourmi Sensibilité à la taille du groupe Enfin, les deux processus ne se comportent pas de la même manière lorsque la taille du groupe varie. Dans le cas de la sélection d une route, il a été possible d obtenir un choix avec un groupe de 5 robots comme avec une colonie de 500 fourmis. De plus, des résultats de simulations suggèrent que la sélectivité du groupe pour le chemin le plus court augmenterait encore pour des tailles de 209

229 7.1. DISCUSSION GÉNÉRALE CHAPITRE 7. DISCUSSION ET CONCLUSION colonies plus importantes, et en l absence de phénomènes d encombrements liés à la largeur des galeries utilisées. Dans le cas de la sélection de place en revanche, les simulations montrent une taille critique du groupe au-delà de laquelle il ne parvient plus à faire un choix. L origine de cette différence est à rechercher dans la nature du processus d amplification utilisé dans chaque modèle. Dans le modèle de sélection de place, l intensité maximale de l amplification est atteinte lorsque l individu rencontre au moins trois individus. En conséquence, des groupes de taille relativement faible (à partir de 10 individus) sont très stables, c est à dire que les individus qui les composent ont une très faible probabilité de les quitter pour rejoindre un autre groupe. La compétition entre les agrégats est en conséquence très fortement ralentie, voire négligeable, et les individus ne parviennent plus à se regrouper en un seul agrégat. Dans cette situation, lorsque la taille de la population augmente, la probabilité d établir un consensus diminue rapidement. De manière très intéressante, ce phénomène rend cependant compte d observations sur la taille des agrégats de blattes dans la nature. Dans le modèle de sélection de route, chaque fourmi qui atteint une bifurcation va être influencée dans son choix personnel par la quantité de phéromone présente sur chaque branche. Lorsqu elle emprunte une branche, elle renforce son marquage chimique et la rend ainsi plus attractive pour les fourmis suivantes. Si un nombre trop faible de fourmis se présente à cette bifurcation, l évaporation du marquage chimique rendra tout consensus impossible à établir car l information sur le choix des individus précédents aura disparu. Au contraire, si ce nombre est très élevé, la compétition entre les deux branches basculera rapidement d un côté ou de l autre. Dans un tel système, la probabilité de réaliser un consensus augmente donc avec le nombre d individus. Il faut cependant pondérer cette affirmation par deux remarques importantes. Premièrement, cette affirmation n est vraie que si l on ne tient pas compte des phénomènes d encombrement. En effet, si le chemin sélectionné par les fourmis est surpeuplé, les nombreux encombrements au niveau de la bifurcation auront tendance à faire basculer une partie du trafic sur la branche initialement délaissée (Dussutour et al., 2004, 2005b, 2006). Deuxièmement, il est possible d obtenir de bons résultats de sélection avec un petit nombre d individus en jouant sur l intensité du dépôt de phéromone et sur sa vitesse d évaporation. L expérience de sélection de route par les robots Alice présentée dans ce mémoire permet d obtenir la sélection d un chemin avec des groupes de 5 ou 10 robots grâce à une optimisation de ces paramètres. 210

230 CHAPITRE 7. DISCUSSION ET CONCLUSION 7.1. DISCUSSION GÉNÉRALE Conclusion Ces quelques différences soulignent la robustesse du mécanisme général sous-jacent. La sélection d une alternative par mimétisme comportemental permet au groupe d établir un consensus dans des conditions d application très différentes. A l opposé, la richesse des choix obtenus est une conséquence de la richesse des conditions d application. La nature des signaux échangés, le comportement des animaux ou encore les conditions environnementales façonnent une diversité étonnante de processus de sélection à partir d un seul principe très simple : chaque individu tend à adopter le comportement de ses voisins Implémentation du modèle biologique : objectifs et méthodologie Au cours de ce travail de thèse, nous avons réalisé l implémentation de deux modèles biologiques dans des groupes de robots Alice. Les méthodologies d implémentation employées pour chacun de ces modèles ont cependant été radicalement différentes. D un côté, le comportement d agrégation de la blatte Blattella germanica a fait l objet d une implémentation stricte du modèle dans le but de reproduire au mieux les caractéristiques comportementales individuelles de cet insecte. De l autre, le comportement de dépôt et de suivi de phéromone de la fourmi d Argentine Linepithema humile a fait l objet d une implémentation plus libre, s inspirant des principes de fonctionnement du modèle sans chercher à en reproduire les détails comportementaux. Dans la suite de cette section, nous allons discuter de l intérêt de chacune des deux approches en fonction de leurs contraintes et de leurs objectifs respectifs L approche réaliste L approche employée pour implémenter le comportement d agrégation de la blatte Blattella germanica peut être qualifiée de réaliste. L objectif premier de cette démarche était de disposer de robots dont le comportement individuel (déplacement, arrêts) et collectif (agrégation) était indiscernable de celui de son modèle biologique. La motivation d une telle démarche est double. En premier lieu, la proximité entre le comportement individuel du robot et celui de l animal renforce la validité du résultat obtenu lorsque les comportements collectifs du système naturel et du système artificiel sont comparés. Si cette comparaison est satisfaisante, cela confirme la plausibilité des hypothèses sous-jacentes au modèle. Plus intéressant, cela renforce également la confiance dans les extrapolations du modèle. Par exemple, dans ce travail de thèse, le modèle initial avait été conçu par Jeanson et al. (2005) pour expliquer le mécanisme d agrégation de cette espèce de blatte. Nos résultats ont montré dans un premier temps qu il suffisait de restreindre 211

231 7.1. DISCUSSION GÉNÉRALE CHAPITRE 7. DISCUSSION ET CONCLUSION l exécution de ce mécanisme à certaines zones de l espace pour entraîner la sélection de l une de ces zones par un groupe de robots. Dans un second temps, nous avons exploré expérimentalement les propriétés de ce modèle. En particulier, nous avons confronté le groupe à des zones de tailles différentes. Le résultat principal prédisait une sélection privilégiée de la plus grande zone. Cette prédiction a par la suite été confirmée dans une étude chez Blattella germanica (Terramorsi et al., 2007), démontrant ainsi l intérêt de notre implémentation réaliste et sa capacité à produire des résultats biologiques pertinents. Il faut noter cependant que ce qui vient d être dit s applique de manière générale à toutes les formes d implémentation d un modèle biologique, et pas seulement à un implémentation robotique. La seconde motivation de l approche réaliste est plus spécifique à l implémentation robotique. Ce travail a pu être mené à bien grâce au soutien du programme Cognitique ( ) et du projet européen Leurre ( ). L objectif principal de ces projets était d insérer des robots à l intérieur d un groupe d animaux afin d en contrôler les comportements collectifs. En contrôlant ces robots et en observant leur influence sur le comportement du groupe, il devient possible de tester dans la réalité la validité des hypothèses sur les processus de coordination à l oeuvre dans les sociétés animales. Pour atteindre cet objectif, il était nécessaire de disposer de robots possédant les caractéristiques comportementales et chimiques leur permetttant d être perçus et identifiés comme des congénères par les animaux étudiés. Parmi ces caractéristiques nécessaires, le comportement des individus joue un rôle très important. Comme plusieurs études l ont montré, la présence d individus dont le comportement diffèrent de celui de ses congénères peut suffire à perturber fortement le comportement global d un groupe (Gautrais et al., 2004; Couzin et al., 2005). Dans une telle situation, il est primordial de disposer d une implémentation réaliste du comportement des animaux étudiés. Cette implémentation réaliste peut alors servir de base pour introduire des modifications dans le comportement des robots et tester leur impact sur le comportement du groupe. L emploi de l approche réaliste nécessite une connaissance détaillée de l animal et du robot. En particulier, leurs différences perceptuelles et motrices doivent être prises en compte lors de l implémentation du robot. En modifiant les entrées et les sorties du modèle comportemental, elles peuvent affecter fortement le comportement individuel du robot. L emploi d outils statistiques pour évaluer l effet de ces différences est primordial. Ils permettent de détecter les variations du comportement qui sont dues à ces différences. En facilitant leur identification, ils facilitent leur correction. C est principalement pour identifier ces contraintes que ce travail a été entrepris. 212

232 CHAPITRE 7. DISCUSSION ET CONCLUSION 7.1. DISCUSSION GÉNÉRALE L approche bio-inspirée L approche employée pour implémenter le comportement de sélection de chemin chez la fourmi d Argentine Linepithema humile peut être rangée dans la catégorie des approches bio-inspirées. La motivation principale d une démarche bio-inspirée est d explorer de nouvelles méthodes de contrôle pour des systèmes artificiels, en prenant comme point de départ les principes de fonctionnement du monde vivant. Contrairement à la démarche réaliste, la reproduction fidèle du comportement de l animal n est pas un objectif prioritaire de la démarche bio-inspirée. La référence fidèle et exclusive au comportement de l animal peut même s avérer contre-productive. En effet, le système artificiel étudié possède rarement les mêmes caractéristiques que le système biologique qui sert de source d inspiration. Il est donc nécessaire dans la plupart des cas d adapter le modèle biologique aux contraintes du système artificiel. Par exemple, il a été nécessaire d ajuster l intensité du dépôt de lumière et sa vitesse de disparition pour être en mesure d obtenir un choix de la part des robots. Cet ajustement a été réalisé sans référence au système biologique, en particulier parce que le nombre de robots que nous avons utilisé (10 au maximum) est très largement inférieur à la taille des colonies de fourmis d Argentine (entre 500 et 2000 individus dans nos expériences, jusqu à plusieurs milliers dans une colonie naturelle). De la même manière, les algorithmes d optimisation par colonie de fourmis sont très largement modifiés par rapport au modèle biologique original afin de s adapter à la structure particulières des réseaux de transport et de télécommunication dans lesquels ils sont utilisés (Dorigo et al., 1996; Bonabeau et al., 1999; Dorigo et al., 2000). L emploi de l approche bio-inspirée nécessite donc avant tout une bonne connaissance du système artificiel étudié. Le modèle biologique sert ici de guide pour proposer de nouvelles méthodes de contrôle. Eventuellement, il est possible de se servir de plusieurs modèles biologiques différents comme sources d inspiration Conclusion Comme on peut le constater, l approche réaliste et l approche bio-inspirée n adressent pas les mêmes questions. L approche réaliste cherche avant tout à expliquer le comportement de l animal à travers l implémentation d un modèle. L approche bio-inspirée cherche quant à elle à concevoir un système fonctionnel et efficace en s inspirant des réalisations de la nature. Pour l informaticien ou le roboticien, la stricte dépendance à un modèle comportemental de l approche réaliste peut constituer un frein lors de son travail de conception. Inversement, les altérations du modèle dans l approche bio-inspirée peuvent diminuer l intérêt des résultats pour 213

233 7.1. DISCUSSION GÉNÉRALE CHAPITRE 7. DISCUSSION ET CONCLUSION le biologiste. Cependant, ces deux approches sont intimement liées l une à l autre à travers les problèmes qu elles abordent de deux points de vue différents Structure de l environnement, modulation passive du comportement et parcimonie du traitement cognitif La structure de l environnement, sa physique, son organisation, peuvent être exploitées de manière particulière au cours du processus de choix. Dans l introduction de ce mémoire, nous avons déjà évoqué l influence de la structure de l environnement sur le résultat d un choix collectif par auto-organisation. Nous avions alors pris l exemple du choix d un chemin par une colonie de fourmis. Nous avions vu que la longueur du chemin ou la nature du substrat, en modifiant la vitesse du processus d amplification, suffisait à faire basculer le choix du groupe vers l une ou l autre des alternatives. Les expériences présentées dans ce mémoire montrent des phénomènes semblables. Dans l expérience de sélection de place par exemple, la largeur de l abri modifie la probabilité que celuici soit découvert par les robots au cours de leur exploration de l environnement. En conséquence, si l un des deux abris est plus grand que l autre, la probabilité qu un agrégat se forme en premier sous cet abri sera plus importante que sous l autre. Cette légère différence initiale, amplifiée par le mécanisme d agrégation, conduit à la sélection préférentielle de l abri le plus grand par le groupe de robot. Dans l expérience de sélection d un chemin dans un réseau de galeries, les fourmis et les robots tendent à adopter la trajectoire qui dévie le moins de leur trajectoire initiale. A une bifurcation donnée, cette inertie dans le déplacement favorise la sélection de la branche qui dévie le moins par rapport à la brance d arrivée. L amplification de ce biais par la piste de phéromone peut alors modifier fortement le pattern d exploitation du réseau si celui-ci présente de nombreuses bifurcations asymétriques Structure de l environnement et modulation passive du comportement Au-delà de l effet sur le résultat du choix collectif, une question intéressante se pose sur la façon dont l animal ou le robot exploite la structure de l environnement. Dans les exemples qui viennent d être cités, l individu tient un rôle passif par rapport à la structure de l environnement. Il ne modifie pas activement son comportement en réponse à la détection d une caractéristique particulière de l environnement, et il ne détecte pas de manière explicite la caractéristique environnementale qui influence son comportement. Dans l exemple du choix d un abri, aucun robot n est programmé pour mesurer la taille de 214

234 CHAPITRE 7. DISCUSSION ET CONCLUSION 7.1. DISCUSSION GÉNÉRALE l abri sous lequel il se trouve. Il détecte seulement s il se trouve ou non sous un abri. La taille de l abri influence pourtant de manière implicite le comportement du robot. Si la taille d un abri est importante, la probabilité qu un robot le rencontre sera plus élevée. De la même manière, le temps moyen passé à se déplacer sous l abri sera plus important. Cela suffit à augmenter (même légèrement) la probabilité globale que le robot s arrête sous cet abri. Sans posséder aucune connaissance ni aucun indice sur la structure de l abri, le robot module néanmoins son comportement en fonction de la largeur de l abri. L expérience de sélection d un chemin dans un réseau de galeries permet d arriver à des conclusions similaires. Dans cette expérience, le robot est programmé pour se déplacer globalement toujours dans la même direction, sauf s il rencontre une piste ou un obstacle. Lorsqu il arrive au niveau d une bifurcation, le robot a une probabilité plus importante d emprunter la branche qui dévie le moins de sa trajectoire initiale. Pourtant, il n est pas programmé pour détecter la présence de la bifurcation ou pour mesurer la déviation des branches qui en partent. En réalité, le robot emprunte préférentiellement cette branche car elle offre moins de contraintes à l inertie de son déplacement. Il s agit d un phénomène purement physique. En quelque sorte, le déplacement du robot est guidé par la structure du réseau dans lequel il évolue, par la disposition des obstacles dans l environnement. Encore une fois, l individu module passivement son comportement en fonction d une caractéristique de l environnement qu il ne perçoit pas de manière explicite. Réitérer cette conclusion dans le cas de la même expérience chez la fourmi d Argentine appelle néanmoins un peu de prudence. Tout d abord, le comportement de cette fourmi lorsqu elle atteint une bifurcation est difficile à interpréter. Parfois elle s arrête quelques instants, passant sa tête dans l une ou l autre des deux branches avant de s engager. Ce comportement pourrait être interprété comme une évaluation active de chacune des deux alternatives. A d autres moments cependant, elle traverse la bifurcation sans même marquer un ralentissement, laissant supposer que son choix est dépendant de la géométrie de la bifurcation. D autre part, la mesure de la probabilité d effectuer un demi-tour une fois la bifurcation franchie montre que cette probabilité augmente avec l angle de rotation effectué par la fourmi à la bifurcation. En l absence de repères externes lui permettant de s orienter, cette observation suggère que la fourmi d Argentine possède un mécanisme lui permettant d évaluer son changement de direction à la bifurcation. Cependant, le demi-tour s effectue après la bifurcation. Il est donc difficile de dire si la fourmi a évalué son changement de direction à la bifurcation, par une détection explicite de la déviation de chaque branche, ou après la bifurcation, grâce par exemple à des informations proprioceptives. Dans le premier cas, la fourmi possèderait une connaissance explicite de la structure de la bifurcation. 215

235 7.1. DISCUSSION GÉNÉRALE CHAPITRE 7. DISCUSSION ET CONCLUSION Dans le second cas, elle ne détecterait que la conséquence de la structure de la bifurcation sur son comportement (en l occurrence, son déplacement). Les expériences de robotique suggèrent que la connaissance préalable de la structure de la bifurcation n est pas nécessaire pour obtenir le biais observé dans le choix individuel des fourmis Structure de l environnement et parcimonie du traitement cognitif Dans les exemples précédents, la structure de l environnement conduit les individus à adopter préférentiellement un comportement plutôt qu un autre. Plus précisément, c est le couplage entre le déplacement de l individu et la structure de l environnement qui favorise une alternative plutôt qu une autre lors du choix des individus. L amplification de ce biais environnemental conduit le groupe à sélectionner dans la plupart des cas l alternative favorisée par l environnement. D un point de vue cognitif, cette stratégie est particulièrement économe. Les individus, animaux ou robots, n ont pas besoin d évaluer la qualité de chaque alternative et de les comparer entre elles. C est en quelque sorte la structure de l environnement qui favorise l une des solutions en modulant la probabilité de présence des individus en un point de l espace. Dans le cas du choix d une route par les fourmis, cela leur procure même un avantage adaptatif en favorisant la sélection du chemin le plus court. Quoiqu il en soit, tout cela illustre bien la possibilité pour les processus évolutifs naturels comme pour les concepteurs de systèmes multi-robots d utiliser la structure de l environnement comme un élément déterminant le comportement collectifs d un groupe d agents. Cela permet dans bien des situations de faire l économie d un traitement cognitif plus élaboré pour atteindre le même objectif. En robotique, cette économie est particulièrement intéressante lorsqu on tient compte du fait que les capacités de calcul de robots miniatures tels que les Alices sont extrêmement faibles. En exploitant judicieusement les contraintes exercées par l environnement sur le comportement de l individu, il est ainsi possible d ajouter une couche supplémentaire de complexité au comportement du groupe sans rajouter une ligne de code au programme interne du robot. L avènement probable de la nano-robotique nécessitera probablement l emploi de méthodes de contrôle aussi parcimonieuses en ressources de calcul pour spécifier le comportement de ces nano-machines. 216

236 CHAPITRE 7. DISCUSSION ET CONCLUSION 7.2 Perspectives 7.2. PERSPECTIVES Formation des réseaux de pistes chez la fourmi d Argentine Notre étude portant sur l orientation des fourmis d Argentine dans un réseau de galeries a mis en évidence l impact important de la géométrie des bifurcations du réseau sur l efficacité de leur fourragement et sur leur capacité à sélectionner un chemin. Les réseaux que nous avons employés étaient, pour les besoins de l expérience, artificiels. Grâce à cela, nous pouvions contrôler la géométrie des bifurcations rencontrées par les fourmis. Une question que nous n avons pu aborder cependant concerne la formation naturelle des réseaux de pistes par cette espèce de fourmis. Des études précédentes montrent que plusieurs espèces de fourmis, dont la fourmi d Argentine, forment naturellement des réseaux de pistes (Linepithema humile Aron et al. (1989) ; Monomorium pharaonis (Fourcassié & Deneubourg, 1994)). Chez certaines de ces espèces, la structure et la géométrie des bifurcations ont été étudiés, montrant une polarisation générale du réseau semblable à celle des réseaux artificiels utilisés lors de nos expériences (Atta sexdens, A. capiguara, A. laevigata and Messor Barbarus :(Acosta et al., 1993) ; Monomorium pharaonis : (Jackson et al., 2004)). Les réseaux de pistes formés par la fourmi d Argentine n ont pour l instant fait l objet d aucune étude similaire. Pour cette raison, nous avons récemment entamé une série d expériences dans le but de caractériser la structure topologique et géométrique des réseaux de pistes que ces fourmis forment spontanément au cours de l exploration de leur environnement (voir Figure 7.1). Nous nous attendons à ce que, comme pour les autres espèces citées plus haut, ces réseaux présentent une polarisation qui facilite le retour vers le nid des ouvrières dispersées dans l environnement. Si cette prédiction se confirme, il sera alors intéressant d étudier les comportements individuels qui permettent l émergence de bifurcations asymétriques et la polarisation du réseau de pistes. Il existe déjà plusieurs modèles concernant la formation et le suivi de pistes chez diverses espèces de fourmis (Edelstein-Keshet, 1994; Edelstein-Keshet et al., 1995; Watmough & Edelstein-Keshet, 1995; Schweitzer et al., 1997). Aucun d entre eux cependant ne s est intéressé spécifiquement à l émergence de bifurcations asymétriques et à leur impact sur la répartition des individus sur le réseau de pistes. Notre hypothèse concernant cette question est la suivante. Lorsqu une colonie a accès à un nouvel environnement, les fourmis entament son exploration en diffusant de manière centripète depuis l entrée du nid. Ces fourmis déposent de la phéromone tout au long (ou presque) de leur déplacement. Elles forment donc rapidement un réseau de pistes qui s entremêlent et se croisent 217

237 7.2. PERSPECTIVES CHAPITRE 7. DISCUSSION ET CONCLUSION Figure 7.1: Réseau de pistes formé par une colonie de fourmis d Argentine Linepithema humile. Cette image est une superposition de 300 images correspondant à la position des fourmis dans l arène toutes les secondes pendant 5 minutes. aléatoirement. Ces bifurcations aléatoires seraient par la suite redessinées au fur et à mesure que des fourmis les traversent. La modification appliquée par les fourmis reste à déterminer. Elle est probablement le résultat d une balance entre le comportement de suivi de la piste et l inertie du déplacement de la fourmi, et les propriétés d évaporation et de diffusion de la phéromone. Nous prévoyons actuellement une série d expériences afin de déterminer la manière dont les fourmis d Argentine redessinent les bifurcations de leur réseaux. En particulier, nous souhaitons caractériser précisément le déplacement des fourmis à l approche d une bifurcation, au moment de sa traversée et après sa traversée. Enfin, des observations préliminaires tendent à montrer que l introduction d une source de nourriture après la formation du réseau d exploration conduit à une redistribution des individus sur une seule piste reliant le nid à la source. La dynamique de cette redistribution, ainsi que la reformation éventuelle d un réseau d exploration après la disparition de la source de nourriture sont des questions que nous souhaiterions aborder dans le futur. Toutes ces questions se placent dans le cadre plus général de la formation et de l utilisation des réseaux de transport (Boccaletti et al., 2006). Une des conclusions importantes de notre travail sur la sélection de chemin dans un réseau souligne le fait que l efficacité fonctionnelle d un réseau de transport est le produit de sa structure et de l usage qui en est fait par ses utilisateurs. A cet égard, il nous semble que les réseaux d exploration et de fourragement formés par les fourmis 218

238 CHAPITRE 7. DISCUSSION ET CONCLUSION 7.2. PERSPECTIVES sont un excellent modèle pour étudier l interaction entre le comportement des individus et la structure du réseau Détection collective de caractéristiques environnementales Les processus de décision collective auto-organisés permettent à un groupe d individus de sélectionner une alternative dans l environnement en fonction de ses caractéristiques. Ainsi, les robots-blattes sélectionnent l abri le plus large. Les fourmis et les robots-fourmis sélectionnent le chemin le plus court. D autres expériences montrent également que les blattes choisissent préférentiellement l abri le plus sombre (Halloy et al., 2007) ou que les fourmis et les abeilles sélectionnent la source de nourriture la plus riche (Beckers et al., 1990; Seeley et al., 1991). Lors de la sélection du nid chez les fourmis, plusieurs caractéristiques sont prises en compte par les ouvrières pour le choix final (Pratt & Pierce, 2001; Franks et al., 2003a,b; Jeanson et al., 2004a). Au cours du processus de choix, le groupe a donc pu estimer et comparer les différentes alternatives, et il a fixé en général son choix final sur celle qui satisfaisait le plus à certains critères. Ces critères pouvaient être dictés par l environnement, comme nous l avons vu dans une section précédente (Section 7.1.3), mais également par les préférences des individus, comme nous l avons signalé dans l introduction. On peut donc considérer ces processus de décision collective comme des détecteurs distribués de caractéristiques environnementales. Ces systèmes ont l avantage de permettre l exploration en parallèle de nombreuses alternatives avant de fixer leur choix sur l une d entre elles en particulier. De cette façon, une comparaison exhaustive des différentes alternatives peut être réalisée dans un temps relativement court. De tels senseurs distribués pourraient trouver une application par exemple lors de campagnes de prospection. Par leur capacité à explorer rapidement l environnement et à se regrouper dans les zones présentant une ou plusieurs caractéristiques désirables, ils pourraient grandement faciliter la détection de zones présentant un intérêt particulier. Dans cette optique-là, nous avons récemment entamé avec Alexandre Campo de l IRIDIA (Bruxelles, Belgique) un travail portant sur la mise au point d un essaim de robots capables de sélectionner dans l environnement un abri adapté à sa taille : plus le nombre de robots présents dans l essaim est important, plus la taille de l abri sélectionné est importante. Ce travail est actuellement en cours d achèvement. Dans ce travail, nous nous sommes inspirés du modèle de sélection d abri proposé par Amé et al. (2006), qui diffère sensiblement de celui proposé par Jeanson et al. (2005) utilisé dans ce mémoire de thèse. Dans le modèle de Amé et al. (2006), la probabilité pour qu une blatte quitte un abri diminue avec la densité d individus sous cet abri, alors que dans le modèle de Jeanson et al. 219

239 7.2. PERSPECTIVES CHAPITRE 7. DISCUSSION ET CONCLUSION (2005), cette probabilité diminue avec le nombre d individus entourant la blatte. Cette petite différence, densité au lieu de nombre, confère au modèle de Amé et al. (2006) une propriété intéressante pour le problème qui nous occupe. Avec le modèle de Jeanson et al. (2005), comme nous l avons vu dans le travail présenté dans ce mémoire, le groupe sélectionne préférentiellement l abri le plus grand car il est plus probable d y former un agrégat. Avec le modèle de Amé et al. (2006), cet effet est contrebalancé par la moindre densité que cet abri permet en comparaison à des abris plus petits. Le groupe sélectionne donc préférentiellement l abri qui lui permet de maintenir la densité la plus élevée. Nous avons implémenté ce modèle dans des robots e-pucks de la façon suivante. Au départ de l expérience, les robots se déplacent de manière aléatoire dans l environnement. S ils pénètrent sous un abri, ils tentent de s y maintenir en effectuant un demi-tour à chaque fois qu ils en détectent le bord. Pendant ce temps-là, ils comptent le nombre de collisions avec d autres robots. Ce nombre de collisions est un bon estimateur de la densité de robots sous l abri. Nous nous sommes inspirés ici de résultats concernant la fourmi Temnothorax albipennis montrant qu elle pourrait utiliser cette information pour estimer le nombre de congénères dans son nid (Pratt, 2005). En fonction du nombre de collisions détectées pendant une durée 30 secondes, les robots décident de quitter ou non l abri avec une certaine probabilité. Cette probabilité diminue avec le nombre de collisions. Les premiers résultats expérimentaux et les premières simulations sont encourageants. Lorsqu un groupe de robots est confronté à un abri de taille adaptée à la taille du groupe et à un abri plus grand ou plus petit, il choisit systématiquement l abri de taille adaptée. Si l on augmente la taille du groupe, la taille de l abri sélectionné par le groupe augmente dans des proportions similaires. Nous pouvons donc contrôler la taille de l abri recherché simplement en modifiant le nombre de robots impliqués dans la tâche. Nous avons pour le moment testé des groupes de 10 à 100 robots en simulation, et jusqu à 20 robots en expériences. L augmentation de la taille du groupe pose cependant un problème : plus le groupe est important, plus le temps nécessaire à la sélection de l abri est important. Nous travaillons actuellement sur une modification de l algorithme actuel qui pourrait nous permettre de sélectionner une taille d abri désirée avec un groupe de taille constante. En particulier, nous allons étudier une modification de la courbe de réponse des robots à la variation du nombre de collisions perçues. 220

240 CHAPITRE 7. DISCUSSION ET CONCLUSION 7.2. PERSPECTIVES Quel avenir pour la robotique en essaim? L absence d applications Les succès les plus connus de l intelligence en essaim se trouvent principalement dans le domaine de la recherche opérationnelle, de l optimisation et de l animation graphique de foules. Comparativement, la robotique en essaim peine à développer des applications qui sortent du cercle restreint des laboratoires spécialisés. Malgré le développement important des recherches et une compréhension accrue des processus décentralisés d organisation des systèmes naturels et artificiels, aucune application industrielle ou commerciale n a à notre connaissance été développée autour de la robotique en essaim. Deux raisons principales peuvent expliquer cet état de fait. Tout d abord, la robotique en essaim n a pas encore été capable dans une tâche particulière de prouver sa supériorité sur des approches centralisées plus classiques. Les algorithmes d optimisation par colonie de fourmis ou par essaim particulaires ont pris leur essor lorsqu ils ont été capables d apporter une telle preuve face à des systèmes concurrents. Aujourd hui, la plupart des démonstrations expérimentales de robotique en essaim utilisent des petits groupes de robots, en général inférieurs à 50 unités. Les technologies actuelles de transmission et de traitement de l information permettent de développer des algorithmes plus efficaces de contrôle centralisé pour de telles tailles de groupes. La robotique en essaim deviendra compétitive lorsque des applications nécessiteront l emploi de grands groupes de robots, c est à dire lorsque les méthodes classiques de planification se heurteront à l accroissement exponentiel de la quantité d informations à gérer simultanément. A cet égard, la nanorobotique semble être le champ idéal pour l application des principes de la robotique en essaim. La seconde raison majeure qui limite le développement d applications de robotique en essaim est l absence de véritables outils de synthèse. Par outil de synthèse, nous entendons un ensemble de méthodes permettant de concevoir un système multi-robots dans le but d atteindre un objectif fixé au préalable. Depuis les débuts de la robotique en essaim, les capacités des systèmes biologiques auto-organisés ont largement contribué au développement d applications dont les contraintes propres étaient proches de celles des modèles naturels. Depuis quelques années, l utilisation de processus d apprentissage ou de méta-heuristiques telles que les algorithmes génétiques ont permis de développer des systèmes robotiques auto-organisés à partir de contraintes et d objectifs fixées à l avance (par exemple Dorigo et al., 2004; Floreano et al., 2007). Les solutions produites par ces méthodes sont cependant difficiles à analyser, limitant ainsi la possibilité de prouver formellement leur efficacité. Cette absence de preuve formelle est probablement ce qui 221

241 7.2. PERSPECTIVES CHAPITRE 7. DISCUSSION ET CONCLUSION rebute aujourd hui le monde industriel à investir dans ces systèmes robotiques distribués. Ce constat ne doit cependant pas faire oublier que la robotique en essaim est une discipline très jeune (l expérience fondatrice de Beckers date de 1994 seulement) qui n a probablement pas fini d explorer toutes ses potentialités. Outre les promesses de la nanorobotique, deux pistes particulièrement prometteuses à notre avis devrait faire l objet d études plus approfondies dans les prochaines années Polymorphisme, polyéthisme et modulation des comportements individuels Comme nous l avons évoqué dans l introduction de ce mémoire, les animaux sociaux sont capables de moduler leurs comportements individuels en fonction de la variation de nombreux stimuli environnementaux. A travers cette modulation, ils répondent ainsi individuellement aux changements de leur environnement local. A l échelle de la société, ces réponses individuelles se couplent aux processus d auto-organisation, conférant à ces derniers une plus grande capacité d adaptation aux besoins et aux contraintes du groupe. Nous avions illustré ceci en détaillant le processus de sélection d un nouveau nid chez la fourmi Temnothorax albipennis, qui est capable à travers ce couplage de prendre en compte des facteurs aussi divers que le degré d urgence de la migration et les qualités de chacun des sites potentiels de nidification. Jusqu à présent, la robotique en essaim a très peu exploré cette facette de l auto-organisation. La majorité des expériences conduites dans le domaine implémentent des robots purement réactifs, sans capacités réelles d adaptation de leur comportement aux variations locales de l environnement. Par exemple, l utilisation d algorithmes d apprentissage, très étudiés avec des robots individuels, est relativement récente dans le cadre de la robotique en essaim. Quelques travaux récents ont pourtant montré la capacité de ces algorithmes à favoriser l adaptativité du groupe dans des situations non prévisibles. On peut citer en particulier les travaux de Labella et al. (2006) sur l émergence d une division du travail par modulation du seuil d activation pour une tâche donnée, ou encore les travaux de Pugh & Martinoli (2006) sur des processus d apprentissage non supervisé dans des groupes de robots par optimisation par essaim particulaire. Dans le même esprit, la formation de groupes de robots mixtes est une piste largement inexplorée. Par mixte, nous entendons que les robots composant le groupe possèdent des caractéristiques physiques et/ou comportementales différentes. En biologie, plusieurs études théoriques et expérimentales montrent que la présence d individus possédant un comportement différent du reste de la société peut entraîner des modifications importantes du comportement global du groupe (Gautrais et al., 2004; Couzin et al., 2005; Halloy et al., 2007). Peu d études de robotique 222

242 CHAPITRE 7. DISCUSSION ET CONCLUSION 7.2. PERSPECTIVES en essaim (mais voir Krieger et al., 2000) ont jusqu à présent exploré cette voie de recherche. De la même manière, peu d études de robotique en essaim s intéressent à l intégration, au sein d un même groupe, de robots possédant des caractéristiques physiques différentes. Ce polymorphisme est pourtant répandu chez les animaux sociaux, et en particulier dans les colonies de fourmis dans lesquelles ont peut trouver une importante diversité de castes physiques. Récemment cependant, le projet européen Swarmanoid 1 s est fixé comme objectif de réussir une telle intégration Intégration dans les systèmes naturels Une seconde voie très prometteuse pour la robotique en essaim est celle ouverte par les travaux des projets Cognitique et Leurre. L intégration dans des sociétés animales de plateformes robotiques capables de percevoir le comportement des animaux et d y répondre de manière adaptée ouvre de nombreuses perspectives pour l avenir. Deux idées retiennent particulièrement notre attention. En premier lieu, la possibilité d interagir avec des systèmes sociaux grâce à des leurres autonomes pourrait permettre de développer de nouveaux outils pour identifier les règles comportementales qui sous-tendent l organisation des sociétés animales (Halloy et al., 2007). Grâce à la comparaison des comportements de groupes naturels et mixtes (i.e., composés à la fois d animaux et de robots), il devrait être possible de tester dans la réalité des hypothèses sur les processus de coopération à l oeuvre chez les animaux sociaux. Enfin, la capacité de tels systèmes à influencer le comportement d un groupe d animaux ébauche les prémices de systèmes capables de contrôler les mouvements de foules d animaux. En modulant les processus d auto-organisation existant dans les sociétés animales, des agents artificiels, au premier rang desquels on trouverait les robots, pourrait modifier l organisation de groupes sociaux ou favoriser l émergence de comportements collectifs particulier. Quelques travaux font actuellement état du développement de tels systèmes pour la conduite de troupeaux (Vaughan et al., 2000; Butler et al., 2006). De tels systèmes pourraient également voir le jour au sein des sociétés humaines. En effet, de nombreux comportements de foules humaines peuvent être expliqués à l aide de processus d auto-organisation. Par exemple, dans des travaux récents mêlant expériences et simulations (voir Annexe C), nous avons mis en évidence que des processus d auto-organisation amplifiant une légère tendance à éviter les obstacles par la droite pouvaient expliquer la structuration particulière des flux de piétons observés dans des rues piétonnes. De la même manière, plusieurs

243 7.3. CONCLUSION CHAPITRE 7. DISCUSSION ET CONCLUSION études suggèrent que l organisation du trafic automobile sur les autoroutes s explique en grande partie par des processus d auto-organisation. Des travaux récents proposent par exemple la création de systèmes embarqués sur les voitures, capables de détecter un ralentissement et de communiquer cette information aux voitures voisines, qui elles-mêmes le répercuteront à leur voisines Schönhof et al. (2007). Couplé à un système GPS, cela devrait permettre de détecter en temps réel la présence d un bouchon de circulation et de déclencher la planification d un nouvel itinéraire. Dans sa thèse, Carlos Gershenson propose un système auto-organisé de feux tricolores qui adaptent leur signalisation en fonction du flux de voitures perçu localement (Gershenson, 2007). Le gouvernement Flamand pourrait financer une étude pilote sur ce système dans les mois à venir. Enfin, des signalétiques et des structures capables de s adapter de manière autonome aux déplacements des piétons pourraient être utilisées pour réguler les mouvements de foules lors des grands rassemblements sportifs, culturels ou religieux. Par exemple, les travaux théoriques de Batty (1997) suggèrent que l architecture intérieure d un bâtiment pourrait avoir un impact important sur la répartition de la foule. La conception de structures architecturales adaptative pourrait permettre d optimiser en permanence cette répartition, afin de limiter par exemple les afflux importants de personnes dans une même zone. 7.3 Conclusion A travers une approche mêlant tout à la fois expériences chez l animal, simulations informatiques et implémentations robotiques, ce travail de thèse nous a permis d explorer les propriétés de deux processus biologiques de prise de décision collective : la sélection d un abri par un groupe de blattes Blattella germanica et la sélection d un chemin dans un réseau complexe de galeries par la fourmi d Argentine Linepithema humile. Dans chacun de ces deux cas, le mimétisme comportemental conduit à une amplification du nombre d individus qui sélectionnent l une des alternatives en présence. Le résultat final est l établissement d un consensus par auto-organisation. Les deux processus étudiés au cours de ce travail présentaient toutefois plusieurs différences, en particulier à propos de la nature des interactions responsables du processus d amplification sous-jacent. Ces différences ont affecté profondément les propriétés de chacun de ces processus, montrant ainsi la diversité des choix collectifs qu il est possible d obtenir à partir d un même principe de fonctionnement général. Une part importante de ce travail a également été consacrée à l étude de l impact des pro- 224

244 CHAPITRE 7. DISCUSSION ET CONCLUSION 7.3. CONCLUSION priétés physiques de l environnement sur le résultat de ce consensus. Il apparaît clairement que de petites variations dans la taille de l abri chez la blatte et dans la géométrie des bifurcations du réseau chez la fourmi modifient profondément le choix final opéré par le groupe. Dans le premier cas, cela conduit à la sélection préférentielle de l abri de plus grande taille. Dans le second cas, la présence d une asymétrie dans la répartition des branches d une bifurcation introduit une polarisation du réseau qui facilite la sélection du chemin le plus court entre deux points du réseau. De manière intéressante, ce biais introduit dans le choix du groupe par la structure de l environnement ne nécessite pas pour se mettre en place l utilisation de capacités cognitives supplémentaires de la part des individus. Cette parcimonie du traitement cognitif met en avant la possibilité pour les processus évolutifs naturels comme pour les concepteurs de systèmes multirobots de s appuyer sur les propriétés physiques de l environnement pour modeler les processus d auto-organisation. 225

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274 BIBLIOGRAPHIE BIBLIOGRAPHIE Webb, B. (2000). What does robotics offer animal behaviour? Animal Behaviour, 60(5) : Webb, B. (2001). Can robots make good models of biological behaviour? Behavioral and Brain Sciences, 24(6) : ; discussion Weber, N. A. (1972). The Fungus-culturing Behavior of Ants. American Zoologist, 12(3) : doi : /icb/ Wenzel, J. (1991). The social biology of wasps, chap. Evolution of nest architecture, pp Cornell University Press, NY, NY, USA. West, G. B., Brown, J. H., &Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science, 276(5309) : doi : /science West, G. B., Brown, J. H., & Enquist, B. J. (1999a). The fourth dimension of life : Fractal geometry and allometric scaling of organisms. Science, 284(5420) : doi : /science West, G. B., Brown, J. H., & Enquist, B. J. (1999b). A general model for the structure and allometry of plant vascular systems. Nature, 400(6745) : doi : / Wilson, M., Melhuish, C., Sendova-Franks, A. B., & Scholes, S. (2004). Algorithms for building annular structures with minimalist robots inspired by brood sorting in ant colonies. Autonomous Robots, 17(2) : Wu, F. & Huberman, B. A. (2007). Novelty and collective attention. Proceedings of the National Academy of Sciences, p doi : /pnas Zar, J. H. (1999). Biostatistical analysis. Prentice Hall, New Jersey. 255

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276 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Annexe A Les principes biologiques de l intelligence en essaim 257

277 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: 3 31 DOI /s y The biological principles of swarm intelligence Simon Garnier Jacques Gautrais Guy Theraulaz Received: 6 February 2007 / Accepted: 21 May 2007 / Published online: 17 July 2007 Springer Science + Business Media, LLC 2007 Abstract The roots of swarm intelligence are deeply embedded in the biological study of self-organized behaviors in social insects. From the routing of traffic in telecommunication networks to the design of control algorithms for groups of autonomous robots, the collective behaviors of these animals have inspired many of the foundational works in this emerging research field. For the first issue of this journal dedicated to swarm intelligence, we review the main biological principles that underlie the organization of insects colonies. We begin with some reminders about the decentralized nature of such systems and we describe the underlying mechanisms of complex collective behaviors of social insects, from the concept of stigmergy to the theory of self-organization in biological systems. We emphasize in particular the role of interactions and the importance of bifurcations that appear in the collective output of the colony when some of the system s parameters change. We then propose to categorize the collective behaviors displayed by insect colonies according to four functions that emerge at the level of the colony and that organize its global behavior. Finally, we address the role of modulations of individual behaviors by disturbances (either environmental or internal to the colony) in the overall flexibility of insect colonies. We conclude that future studies about self-organized biological behaviors should investigate such modulations to better understand how insect colonies adapt to uncertain worlds. Keywords Swarm intelligence Social insects Stigmergy Self-organization collective behaviors 1 Introduction Swarm intelligence, as a scientific discipline including research fields such as swarm optimization or distributed control in collective robotics, was born from biological insights about the incredible abilities of social insects to solve their everyday-life problems (Bonabeau S. Garnier ( ) J. Gautrais G. Theraulaz Centre de Recherches sur la Cognition Animale, UMR-CNRS 5169, Université Paul Sabatier, Bât 4R3, 118 Route de Narbonne, Toulouse cedex 9, France simon.garnier@cict.fr 258

278 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 4 Swarm Intell (2007) 1: 3 31 et al. 1999). Their colonies ranging from a few animals to millions of individuals, display fascinating behaviors that combine efficiency with both flexibility and robustness (Camazine et al. 2001). From the traffic management on a foraging network (Burd 2006; Couzin and Franks 2003; Dussutour et al. 2004; Vittori et al. 2006), to the building of efficient structures (Buhl et al. 2004, 2005; Theraulaz et al. 2003; Tschinkel, 2003, 2004), along with the dynamic task allocation between workers (Beshers and Fewell 2001; Bonabeau et al. 1998; Deneubourg et al. 1987; Gordon 1996), examples of complex and sophisticated behaviors are numerous and diverse among social insects (Bonabeau et al. 1997; Camazine et al. 2001; Detrain and Deneubourg 2006). For example, in their moving phase, the neotropical army ants Eciton burchelli may organize large hunting raids which may contain more than workers collecting thousands of prey, be 15 m or more wide and sweep over an area of more than 1500 m 2 in a single day (Franks 1989; Franks and Fletcher 1983; Hölldobler and Wilson 1990). As another example, African termites of the species Macrotermes bellicosus build mounds that may reach a diameter of 30 m and a height of 6 m (Grassé 1984). These biological skyscrapers result from the work of millions of tiny (1 2 mm long) and completely blind individuals. Even more fascinating than the size of these mounds is their internal structure. Nests of the species Apicotermes lamani are probably one of the most complex structures ever built in the animal kingdom (Desneux 1956, see Fig. 1(a)). Over the outside surface of the nest, there exists a whole set of micro structures that ensure air conditioning and gas exchanges with the outside environment. Inside these nests, that are about 20 to 40 centimeters high, we find a succession of chambers connected together with helical ramps. These helical ramps arise from the twisting and soldering of successive floors. There are several stairs at each floor and some of these stairs go through the whole nest. Even distant chambers are in connection through these shortcuts. Surprisingly, the complexity of these collective behaviors and structures does not reflect at all the relative simplicity of the individual behaviors of an insect. Of course, insects are elaborated machines, with the ability to modulate their behavior on the basis of the processing of many sensory inputs (Menzel and Giurfa 2001; Detrain and Deneubourg 2006). Nevertheless, as pointed out by Seeley (2002), the complexity of an individual insect in terms of cognitive or communicational abilities may be high in an absolute sense, while remaining not sufficient to effectively supervise a large system and to explain the complexity of all the behaviors at the colony scale. In most cases, a single insect is not able to find by itself an efficient solution to a colony problem, while the society to which it belongs finds as a whole a solution very easily (Camazine et al. 2001). Behind this organization without an organizer are several hidden mechanisms which enable insect societies, whose members only deal with partial and noisy information about their environment, to cope with uncertain situations and to find solutions to complex problems. The present paper aims at reviewing these mechanisms that are by now a stimulating source of inspiration, especially when it comes to design distributed optimization algorithms in computer science or control algorithms in collective robotics (Bonabeau and Theraulaz 2000). Implementations in artificial systems of this swarm intelligence logic are nowadays numerous: discrete optimization (Dorigo et al. 1996, 1999), graph partitioning (Kuntz et al. 1999), task allocation (Campos et al. 2000; Krieger et al. 2000), object clustering and sorting (Melhuish et al. 2001; Wilson et al. 2004), collective decision making (Garnier et al. 2005), and so on. All these examples rely on mechanisms known to occur in social insects. However, if social insects remain the original source of inspiration for artificial swarm intelligent systems it is important to notice that other biological systems share similar collective properties 259

279 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: Fig. 1 Classification of collective behaviors in social insects. a An external view and a cross section of an Apicotermes lamani nest resulting from the coordination of workers building activities. b Collective selection of one foraging path over a diamond-shaped bridge leading to a food source by workers in the ant Lasius niger. c Weaver ant (Oecophylla longinoda) workers cooperate to form chains of their own bodies, allowing them to cross wide gaps and pull leaves together. d An example of division of labor among weaver ant workers (Oecophylla longinoda). When the leaves have been put in place by a first group of workers, both edges are connected with a thread of silk emitted by mature larvae held by a second group of workers. CNRS Photothèque Gilles Vidal and Guy Theraulaz such as colonies of bacteria or amoeba (Ben-Jacob et al. 1994, 2000), fish schools (Grünbaum et al. 2005; Parrish et al. 2002), bird flocks (Reynolds 1987), sheep herds (Gautrais et al. 2007) or even crowds of human beings (Helbing et al. 2001). Among them, the motions of fish schools and bird flocks have for instance partly inspired the concept of particle swarm optimization (Kennedy and Eberhart 1995). Nevertheless, we will restrict this review to collective behaviors of social insects for at least two reasons: (1) they represent the 260

280 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 6 Swarm Intell (2007) 1: 3 31 largest research corpus from both a theoretical and an experimental point of view; (2) their underlying principles are very close to those found or hypothesized in other animal species. In this paper, we first describe in an historical perspective the basic mechanisms that explain the amazing collective abilities of insect societies. This part is illustrated with wellknown examples and introduces the major concepts underlying the swarm intelligence research field: decentralization, stigmergy, self-organization, emergence, positive and negative feedbacks, fluctuations, bifurcations. It also highlights the nature of the relation between the behavior of the individual and the behavior of the group, an idea of great importance for understanding the third part of the paper. In a second part, we introduce a categorization of these collective behaviors. This categorization is based on the interplay of four components that emerge at the level of the group from the interactions and behaviors of the insects. We name these four components: coordination, cooperation, deliberation and collaboration. We illustrate their role in the organization of a colony s activities through various examples taken from the literature published over the last 40 years. The third part is dedicated to a problem which is central to swarm intelligence: the adaptation of the group to changes in the environment or in the composition of the group itself. We argue that this adaptation can be the result of an active modulation of individual insects behaviors. In support of this argumentation, we provide three examples that cover three different kinds of swarm intelligent problem solving: division of labor, morphogenesis and collective decisions. We show in each case how small behavioral modifications participate to the overall adaptation of the colony to changeable life conditions. Finally, the last part opens a discussion about the need to better understand the role of individual behavioral modulations in relation with the diversity of collective structures that a colony of insects is able to produce. It also provides some keys that could inspire further developments in the swarm intelligence research field. 2 The underlying mechanisms of complex collective behaviors For a long time, the collective behavior of social insects has remained a fascinating issue for naturalists. Everything happens as if there was some mysterious virtual agent inside the colony that would coordinate the individuals activities. Even today, success novelists like Michael Crichton have revived the old idea of the spirit of the hive (which was originally introduced by the Belgian poet Maurice Maeterlinck 1927); in his novel Prey, Crichton describes a swarm of artificial insect-like nanorobots which is governed by such a collective mind, allowing them to take complex decisions and even to anticipate future events (Crichton 2002). Of course, we know that there is no such spirit in the hive. Reality is less trivial, and also much more interesting. The quest for the mechanisms underlying insects collective behaviors started more than a century ago and the first hypothesis put forward were clearly anthropomorphic (see for instance Büchner 1881; Forel 1921). Individual insects were assumed to possess something like a representation of the global structure to be produced and then they were supposed to use that representation to make appropriate decisions (see, for instance, Thorpe 1963). In other words, people were thinking that there was some direct causal relationship between the complexity of the decisions and patterns observed at the colony level and the behavioral and cognitive complexity that was supposed to be required at the individual level to produce these decisions and patterns. In particular, the queen was supposed to gather and monitor all the information coming from its colony and then supervise the work done by the workers, 261

281 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: giving them appropriate orders. For instance, Reeve and Gamboa (1983, 1987) have argued that in colonies of the paper wasp Polistes fuscatus the queen functions as a central pacemaker and coordinator of workers activities. However, recent findings by (Jha et al. 2006) demonstrated that indeed this original statement was wrong. The kind of organization that was supposed to rule the society was hierarchical and centralized. Nevertheless, most of the works that have been done in the last 40 years revealed a completely different organization (Theraulaz et al. 1998a). We now know that individual insects do not need any representation, any map or explicit knowledge of the global structure they produce. A single insect is not able to assess a global situation, to centralize information about the state of its entire colony and then to control the tasks to be done by the other workers. There is no supervisor in these colonies. A social insect colony is rather like a decentralized system made of autonomous units that are distributed in the environment and that may be described as following simple probabilistic stimulus-response behaviors (Deneubourg et al. 1983). The rules that govern interactions among insects are executed on the basis of local information that is without knowledge of the global pattern. Each insect is following a small set of behavioral rules. For instance, in ants each individual is able to perform 20 different elementary behaviors on average (Wilson 1971). Organization emerges at the colony level from the interactions that take place among individuals exhibiting these simple behaviors. These interactions ensure the propagation of information through the colony and they also organize the activity of each individual. Thanks to these sophisticated interaction networks, social insects can solve a whole range of problems and respond to external challenges in a very flexible and robust way. 2.1 Stigmergy The first serious theoretical explanation to the organization of social insects activities was provided 40 years ago by French biologist Pierre-Paul Grassé, who introduced the concept of stigmergy to explain building activity in termites (Grassé 1959; see Theraulaz and Bonabeau 1999 for an historical review). Grassé showed that the coordination and the regulation of building activities do not depend on the workers themselves, but are mainly achieved by the nest structure. In other words, information coming from the local environment and the work in progress can guide individual activity. For instance, each time a worker performs a building action, the shape of the local configuration that triggered this action is changed. The new configuration will then influence other specific actions from the worker or potentially from any other workers in the colony. This process leads to an almost perfect coordination of the collective work and may give us the impression that the colony is following a welldefined plan. A good example of stigmergic behavior is provided by nest building in social wasps. The vast majority of wasp nests are built with wood pulp and plant fibers that are chewed and cemented together with oral secretions (Wenzel 1991). The resulting paper is then shaped by the wasps to build the various parts of the nest: the pedicel, which is a stalk-like structure connecting the comb to the substrate, the cells or the external envelope. Building activities are driven by the local configuration of cells detected by the wasps on the nest (Karsai and Theraulaz 1995). Indeed, the architecture by itself provides enough information and constraints to ensure the coordination of the wasp building activity. To decide where to build a new cell, wasps use the information provided by the local arrangement of cells on the outer circumference of the comb. They perceive these configurations of cells with their antennae. Potential building sites on the comb do not have the same probability to be chosen by wasps when they start to build a new cell. Wasps have a greater probability 262

282 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 8 Swarm Intell (2007) 1: 3 31 Fig. 2 A model of stigmergic nest construction in wasps. Simulation of collective building on a 3D hexagonal lattice (right). This architecture is reminiscent of natural Chartergus wasp nests (left) and exhibits a similar design. A portion of the external envelope has been partly removed to show the internal structure of the nest to add new cells to a corner area where three adjacent walls are already present, while the probability to start a new row, by adding a cell on the side of an existing row, is very low (Camazine et al. 2001). The consequences of applying these local rules on the development of the comb and its resulting shape can be studied thanks to a model in which wasps are represented by agents (Theraulaz and Bonabeau, 1995a, 1995b). These virtual wasps are asynchronous automata that move in a three-dimensional discrete hexagonal space, and that behave locally in space and time on a probabilistic stimulus-response basis. They only have a local perception of their environment where a virtual wasp perceives the first twenty six neighboring cells that are adjacent to the cell she occupies at a given time, and of course, this virtual wasp does not have any representation of the global architecture she is supposed to build. Each of these virtual wasps uses a set of construction rules. As they move in space, they will sometimes come into contact with the nest structure and at this moment they will perceive a local configuration of cells. Some of these configurations will trigger a building action, and as a consequence, a new cell will be added to the comb at the particular place that was occupied by the wasp. In all the other cases no particular building action will take place and the wasp will just move toward another place. These construction rules are probabilistic, so it is possible to use in the model the probability values associated with each particular configuration of cells that have been measured in the experiments with the real wasps. Nest architectures obtained by simulations show that the complexity of the structures that are built by social insects does not require sophisticated individual behavioral rules (see Fig. 2). 2.2 From stigmergy to self-organization: path selection in ant colonies Another example of stigmergic behavior is food recruitment in ants (Hölldobler and Wilson 1990). Ants communicate with each other through the use of pheromones. These pheromones are chemical substances that attract other ants. For instance, once an ant has found a food source, she quickly comes back to the nest and lays down a pheromone trail. This trail will then guide other workers from the nest toward the food source. When the recruited ants come back to the nest, they lay down their own pheromone on the trail and reinforce the pathway. The trail formation therefore results from a positive feedback: the 263

283 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: more ants use a trail, the more attractive the trail becomes. Of course the trail will disappear after some time if the reinforcement is too slow, which may occur when the food source becomes exhausted. The interesting thing is that this trail recruitment system is not only a mechanism used to quickly assemble a large number of foragers around a food source, it also enables a colony to make efficient decisions such as the selection of the shortest path leading to a food source. In the beginning of the 1990s, Jean-Louis Deneubourg and his collaborators have designed a simple and elegant experiment showing that information can be amplified and selected by ant colonies using pheromone trails (Deneubourg and Goss 1989). In the experiment, an ant nest was connected to a food source with a binary bridge whose branches were of equal length. After a certain period of time, they observed that most traffic occurs on a single branch. The choice was random with approximately 50% of the experiments in which one branch was selected and 50% in which the other branch was selected. Initially, the ant s choice is made at random because there is no pheromone on the branches. As time goes by, the stochasticity of individual decisions causes a few more ants to choose one branch. The greater number of ants on this branch induces a greater amount of pheromone, which in turn, stimulates more ants to choose the branch. This is a positive feedback which amplifies an initial random fluctuation. In the end, most traffic will take place on a single branch, chosen randomly (see Fig. 1(b)). Today, we know that most collective decisions in social insects arise through the competition among different types of information that can be amplified in various ways. In the case of path selection by ants, the information is conveyed by the pheromone trail. However, environmental constraints, such as the distance between the nest and the food source, affect this positive feedback. In particular, any constraint that modulates the rate of recruitment or the trail concentration on a branch can lead that branch to lose, or win, its competition against the other one (Detrain et al. 2001; Jeanson et al. 2003). Thus, an efficient decision can be made without any modulation of individual behavior and without any sophisticated cognitive processing at the individual level. This occurs, for example, when a colony of ants is presented with a short path and a long path leading to a food source (Goss et al. 1989). Using the trail-laying trail-following behavior, the shortest branch is selected in most cases. The first ants use both paths to reach the food source. When they come back to the nest, the ones that take the shortest path reach the nest first. The shorter path is thus slightly more marked with pheromone, and is therefore, more attractive to the ants that leave the nest to go to the food source. In this case, the positive feedback amplifies an initial difference induced by the path geometry. This simple experiment shows that geometrical constraints can play a key role in the collective decision-making processes that emerge at the collective level. The colony as a whole is able to produce an efficient collective response that far exceeds the scale and abilities of a single individual ant. 2.3 Principles and properties of self-organizing processes These collective decisions in ants rely on self-organization that appears to be a major component of a wide range of collective behaviors in social insects, from the thermoregulation of bee swarms to the construction of nests in ants and termites (Bonabeau et al. 1997; Camazine et al. 2001). Self-organization is a set of dynamical mechanisms whereby structures appear at the global level of a system from interactions among its lower-level components, without being explicitly coded at the individual level. It relies on four basic ingredients: 264

284 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 10 Swarm Intell (2007) 1: 3 31 (1) The first component is a positive feedback that results from the execution of simple behavioral rules of thumb that promote the creation of structures. For instance, trail recruitment to a food source is a kind of positive feedback which creates the conditions for the emergence of a trail network at the global level. (2) Then we have a negative feedback that counterbalances positive feedback and that leads to the stabilization of the collective pattern. In the example of ant foraging, negative feedback may have several origins. It may result from the limited number of available foragers, the food source exhaustion, and the evaporation of pheromone or a competition between paths to attract foragers. (3) Self-organization also relies on the amplification of fluctuations by positive feedbacks. Social insects are well known to perform actions that can be described as stochastic. Such random fluctuations are the seeds from which structures nucleate and grow. Moreover, randomness is often crucial, because it enables the colony to discover new solutions. For instance, lost foragers can find new, unexploited food sources, and then recruit nest mates to these food sources. (4) Finally, self-organization requires multiple direct or stigmergic interactions among individuals to produce apparently deterministic outcomes and the appearance of large and enduring structures. In addition to the previously detailed ingredients, self-organization is also characterized by a few key properties: (1) Self-organized systems are dynamic. As stated before, the production of structures as well as their persistence requires permanent interactions between the members of the colony and with their environment. These interactions promote the positive feedbacks that create the collective structures and act for their subsistence against negative feedbacks that tend to eliminate them. (2) Self-organized systems exhibit emergent properties. They display properties that are more complex than the simple contribution of each agent. These properties arise from the nonlinear combination of the interactions between the members of the colony. (3) Together with the emergent properties, non linear interactions lead self-organized systems to bifurcations. A bifurcation is the appearance of new stable solutions when some of the system s parameters change (see Appendix 1). This corresponds to a qualitative change in the collective behavior. (4) Last, self-organized systems can be multi-stable. Multi-stability means that, for a given set of parameters, the system can reach different stable states depending on the initial conditions and on the random fluctuations. 3 Categorizing the collective behaviors of social insects From the previously described self-organizing processes may emerge a wide variety of collective behaviors that are intended to solve a given problem. Such diversity may give the impression that no common point exists at the collective level between for instance the construction of the relatively simple nest of the ant Leptothorax albipennis made up with a single wall of debris and the construction of the seemingly more complex nest of the termite Macrotermes bellicosus with its intricate network of galleries and chambers. Nevertheless, it is possible to break down all these collective behaviors into a limited number of behavioral components. For example, Anderson and Franks (2001) have proposed to separate the collective behaviors accomplished by an insect colony into four task types: individual, group, team and 265

285 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: partitioned tasks. Following that categorization of social insects behaviors, Anderson et al. (2001) have proposed that every global task in a colony (for instance nest construction) can be broken down in a hierarchical structure of subtasks of the previous types. Their method can be seen as the deconstruction of a problem into the basic tasks required to solve it. Another way to deconstruct the collective behaviors of social insects goes through the functions that organize the insects tasks. We identified four functions of that kind: coordination, cooperation, deliberation and collaboration (see Fig. 1). They are not mutually exclusive but rather contribute together to the accomplishment of the various collective tasks of the colony. In the following sections, we first provide a definition of each and then illustrate their respective role in some examples of social insects collective behaviors. 3.1 Coordination Coordination is the appropriate organization in space and time of the tasks required to solve a specific problem. This function leads to specific spatio-temporal distributions of individuals, of their activities and/or of the results of their activities in order to reach a given goal. For instance, coordination occurs in the organization of the displacement in bee and locust swarms (Buhl et al. 2006; Janson et al. 2005). In this case, the interactions between individuals generate synchronized (temporal organization) and oriented (spatial organization) movements of the individuals toward a specific goal. Coordination is also involved in the exploitation of food sources by pheromone trail laying ants. They build trail networks that spatially organize their foraging behavior between their nest and one or more food sources (Hölldobler and Wilson 1990; Traniello and Robson 1995; Wilson 1962). As a last example, coordination is at work in most of the building activities in insect colonies. During nest building in certain species of social wasps (Downing and Jeanne, 1988, 1990; Karsai and Theraulaz 1995; Wenzel 1996) or termites (Bruinsma 1979; Grassé 1959), the stigmergic process described in Sect. 2.1 favors the extension by an individual of structures (spatial organization) previously (temporal organization) achieved by other individuals. 3.2 Cooperation Cooperation occurs when individuals achieve together a task that could not be done by a single one. The individuals must combine their efforts in order to successfully solve a problem that goes beyond their individual abilities. Cooperation is obvious in large prey retrieval, when a single individual is too weak to move a food item. Many cases of cooperative transport of prey were reported for several ant species such as weaver ants Oecophylla longinoda (Wojtusiak et al. 1994), army ants Eciton burchelli (Franks 1986) or Formica wood ants (Chauvin 1968; Sudd 1965). Such cooperative transport of prey can be a very efficient way to bring back food to the nest. For example, in the ant Pheidologeton diversus, it was reported that ants engaged in the cooperative transport of a prey can hold at least ten times more weight than did solitary transporters (Moffett 1988). Cooperation can also be involved in other tasks than prey retrieval. For instance, it is at work in chain formation in the weaver ant Oecophylla longinoda. In this ant species individuals hang to each other to form chains allowing the bridging of empty space between two branches or the binding of leaves during nest construction (Deneubourg et al. 2002; Hölldobler and Wilson 1990; Lioni et al. 2001). 266

286 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 12 Swarm Intell (2007) 1: 3 31 A last example of cooperation occurs when a long wood stick is plug into the entrance of an ant nest (Chauvin 1971). In such situation, ants combine their efforts to pull out the stick from the hole. Some of the ants lift the stick up while others slip their head inside the hole, in order to prevent the stick to fall back. Eventually, the combined efforts lead the group to remove the stick from the nest entrance. 3.3 Deliberation Deliberation refers to mechanisms that occur when a colony faces several opportunities. These mechanisms result in a collective choice for at least one of the opportunities. For instance, honeybees (Apis Mellifera) select the more productive floral parcels thanks to the recruitment of unemployed workers by the waggle dance performed by foragers returning from a food source (Seeley et al. 1991). When ants of the species Lasius niger have discovered several food sources with different qualities or richness, or several paths that lead to a food source, they generally select only one of the different opportunities. In this case, the deliberation is driven by the competition between the chemical trails leading to each opportunity (see Sect. 2.2). In most cases, ants will forage at the richer food source and travel along the shorter path toward the food source (Beckers et al. 1990, 1992; Goss et al. 1989). 3.4 Collaboration Collaboration means that different activities are performed simultaneously by groups of specialized individuals, for instance foraging for prey or tending brood inside the nest (Gordon, 1989, 1996; Wilson 1971). This specialization can rely on a pure behavioral differentiation as well as on a morphological one and be influenced by the age of the individuals. The most conspicuous expression of such division of labor is the existence of castes. For instance, in leaf cutter ants workers may belong to four different castes and their size is closely linked to the tasks they are performing (Hölldobler and Wilson 1990). Only the workers whose head size is larger than 1.6 millimeters are able to cut the leaves that are used to grow a mushroom that is the main food source of these colonies. On the contrary, only the tiny workers whose head size is about 0.5 millimeters are able to take charge of the cultivation of the mushroom. Differently, all workers in Indian paper wasps Ropalidia marginata and Ropalidia cyathiformis, look alike. But they do not work to the same extent and they do not perform the same kind of tasks. Some of the workers are foragers and take most of the burden of going out of the colony in search of food and building materials. Others specialize in staying and working at the nest. Among these, some are more aggressive towards their nest mates and they are called fighters. The other wasps staying at home are called sitters and spend most of the time just sitting and grooming themselves (Gadagkar and Joshi 1983, 1984). 3.5 Organizing collective behaviors Most of the collective behaviors in social insects can be understood as a combination of at least two of the four functions of organization defined in the previous sections. To better illustrate this point, we quickly describe in this section two examples of insects collective behaviors and we break them down as coordination, cooperation, deliberation and collaboration functions. 267

287 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: House hunting in the honeybee When a bee colony outgrows its hive, the mother queen and nearly half of the workers usually leave their nest. They temporarily form a cluster (called a bivouac) on a tree branch from which they start a complex procedure for finding a new nest site (reviewed by Seeley and Visscher 2004). First, scout bees (about 5% of the bees at the bivouac) explore the environment and search for suitable places to build a new hive. Once a scout bee finds such a place, it comes back to the bivouac where it recruits some other scout bees by performing a waggle dance. In turn, these recruited scouts assess the potential nest site and may possibly perform the waggle dance to recruit other scouts. Thus, a competition arises between different groups of scout bees recruiting for different potential nest sites. Once a site is visited by a sufficient number of scout bees, these latter advertise the rest of the cluster that it is time to warm up their flight muscles and to prepare for the liftoff toward the new nest site. They use three distinct signals to that purpose: the shaking signal that activates the quiescent bees, the piping signal that initiates the warm-up of the flight muscles and the buzz running signal that prepares bees for the liftoff (Seeley and Tautz 2001). At least three organization functions participate to the migration of honeybees toward a new nest site. First, collaboration occurs since bees split in two different functional groups: scout bees that search for potential nest site and clustered bees that remain quiescent and conserve the colony s energy reserves. Second, a self-organized deliberation process leads to the choice of a suitable place for nesting among several opportunities. And third, the quasi simultaneous liftoff of all bees in the cluster obviously results from a coordination function mediated by the three liftoff preparation signals Nest construction in the weaver ant Nest in the weaver ant Oecophylla longinoda are made of leaves stuck together (Hölldobler and Wilson 1990; Ledoux 1950). The nest construction requires the repetition of two stages: assembling two leaves and gluing them. In the first stage, workers line up in a row along the margin of a leaf and pull together to bring closer the two leaves (see Fig. 1(c)). If the gap between the two leaves is longer than a single ant, workers form a chain with their own bodies. Then, they pull together as one individual to bring them closer. In the second stage, when the leaves have been put in place, other workers carry mature larvae and use the silk they produce to glue the leaves together (see Fig. 1(d)). Nest construction in the weaver ant requires several functions of organization to be successfully achieved. It first needs a coordination function to ensure that leaves are put together before being glued. It also needs two cooperation functions. The first one occurs when workers pull together the leaves since this task can not be performed by a single one. The second arises during the gluing of the leaves: workers that do not produce silk require larvae that can not move alone. At last, a collaboration function distributes the tasks between different groups of individuals: workers that pull and maintain the leaves appropriately, workers that carry the larvae and larvae that produce the silk for gluing the leaves Conclusion As exemplified in the two previous subsections, the organization of collective behaviors in social insects can be understood as the combination of the four coordination, cooperation, deliberation and collaboration functions. Each of these functions emerges at the collective level from the unceasing interactions between the insects. They support the information processing abilities of the colony according to two main axes: 268

288 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 14 Swarm Intell (2007) 1: 3 31 (1) Coordination and collaboration shape the spatial, temporal and social structures that result from the colony s work. The coordination function regulates the spatio-temporal density of individuals while the collaboration function regulates the allocation of their activities. (2) Cooperation and deliberation provide tools for the colony to face the environmental challenges. The deliberation function represents the mechanisms that support the decisions of the colony, while the cooperation function represents the mechanisms that overstep the limitations of the individuals. Together, the four functions of organization produce solutions to the colony problems and may give the impression that the colony as a whole plans its work to achieve its objectives. 4 Modulation of self-organized behaviors In the preceding sections, we have seen that the organization of the collective behaviors in social insects arises from four functions that emerge from the activities of a dense network of interactions. These interactions take place among the members of a colony and between them and their environment. Because the colony and its environment permanently evolve in time, they can be considered as coupled dynamic systems. However, inside a colony of insects, some features seem to be actively maintained constant and thus get out from the dynamic evolution of the colony. For instance, a humidity drop can be life-threatening for cockroaches that could die as a consequence of desiccation. To avoid the death, cockroaches maintain locally a sustainable humidity level thanks to an increase of their tendency to aggregate (Dambach and Goehlen 1999). As another example, when their colony size varies, ants of the species Leptothorax albipennis are able to maintain their nest size so that each adult worker has about 5 mm 2 of floor area in the nest (Franks et al. 1992). In these two cases, the colony modifies its behavior in order to counterbalance the effects of a potentially harmful perturbation. The insect colony is thus an adaptive system. Now the question is: what are the mechanisms that underlie collective adaptation in insects societies? The only way for a colony to adapt its collective behavior is through the modulation of individual insect behaviors. With the term modulation we suggest that the probability for a given behavior to occur varies according to the disturbance. Each individual is able to sense the variation thanks to local cues and it slightly modifies its behavior in response. These behavioral modifications affect the interaction network, and hence the global structure, through a new balancing of positive and negative feedbacks. 4.1 Factors that modulate self-organized behaviors Two kinds of perturbations modulate self-organized biological behaviors. The first ones are produced by changes in the environment. We call them outer colony factors because they arise independently of the insect colony. These factors comprise climatic parameters such as temperature, humidity or wind, and ecological parameters such as food distribution or predator presence. We call inner colony factors the second kind of perturbations affecting self-organized biological behaviors. These factors are directly linked to the colony or its components: the size (i.e., the total number of individuals that belong to the colony), the morphological differences between insects (i.e., the ratio of the different physical castes), learning, etc. 269

289 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: Inner and outer factors both influence insect behavior. And the result of the insects activities can, in return, influence outer and inner factors. For example, air flows modulate the corpse clustering behavior of the ant Messor sanctus and are, in return, deviated by the insects construction (Jost et al. 2007). The successful achievement of a task can improve the experience of an individual which, in return, may favor the future achievement of the same task (Theraulaz et al. 1991). Thus, a subtle network of interacting influences regulates individual behaviors and provides to the colony a real-time solution to a real-time problem. 4.2 Three examples of modulation Whatever the nature of the perturbation, one must answer the two following questions to identify the mechanisms that underlie a collective adaptation to a given perturbation in an insect colony. (1) How does the perturbation modulate the individual behaviors of the interacting animals? Does it stimulate animals to perform a particular behavior or task or does it prevent them from doing so? (2) How does the modulation of the individual behavior shape the properties at the collective level? What changes does it trigger in the interaction network? What new structures does it elicit when the group behavior is considered? In order to better illustrate the previous questions, we present in the rest of this section, three examples of self-organized biological behaviors and their modulation by inner and/or outer factors. In each case we describe the mechanism in terms of individual behaviors, its result at the collective level and the impact of the modulation of individual behaviors by one or several factors Corpse clustering in ants Numerous ant species carry their dead out of the nest and aggregate them near the nest entrance (Ataya and Lenoir 1984; Haskins and Haskins 1974; Howard and Tschinkel 1976). This behavior has been studied in the lab under controlled conditions with Messor sanctus ants. When corpses are spread over the whole surface of an arena, ants collect and aggregate the corpses within a few hours. In the beginning, several clusters are formed and compete with each other to attract ants carrying corpses, and in the end only the piles that succeed to grow faster than the others will persist (Theraulaz et al. 2002). To build these structures, ants pick-up and drop a corpse as a function of the density of corpses they detect in their local neighborhood. We can have an estimate of these probabilities by looking at the behavior of ants when they come into contact with corpse piles of increasing size. The greater the size of a pile, the less likely the ant will pick up a corpse on that pile. On the other hand, the dropping probability increases rapidly as a function of the size of the pile. Thus, a positive feedback results from the combination of both enhancement of the dropping behavior and inhibition of the picking up behavior. This process is similar to the one that led to the formation of foraging trails, with the difference that here the negative feedback results from the depletion of isolated corpses that prevents the formation of other clusters in the neighborhood of a cluster already in place. In laboratory conditions with stable environmental factors, this corpse picking-up and dropping behavior results in few persisting piles with a circular shape. Interestingly, in the presence of a continuous laminar low speed air flow the form of the piles drastically changes. From an almost circular shape they switch to an elliptic one: piles are elongated to create 270

290 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 16 Swarm Intell (2007) 1: 3 31 Fig. 3 Spatio-temporal dynamics of corpse clustering by ants Messor sanctus without (a) and with (b) air currents. Black dots are ant corpses and black arrows indicate the air flow direction (from Jost et al with permission) parallel walls in the same direction as the wind (see Fig. 3). Note that the air flow is too weak (around 1 cm s 1 ) to move a single corpse and thus cannot explain pile elongation by its own. Something must have changed in the behavior of corpse carrying ants. A recent work has investigated these individual behavioral changes and has linked them to the observed shape modification in the presence of an air flow (Jost et al. 2007). Jost and his collaborators have shown that the probability to pick up a corpse from a pile grows with air flow speed while the probability to drop a corpse decreases with it. They, therefore, conclude that the lower the wind speed, the higher the amplification of corpse clustering. This leads ants to clear corpses from areas of high wind speed and to aggregate them in areas of low wind speed. In addition, they showed with numerical simulations that corpse piles modify the air flow around them: they slow it down on the side facing the wind (front side) and on the lee side; they accelerate it on the other sides. Together with the previous result, this explains why corpse piles lengthen in the same direction as the wind: amplification of clustering is stronger at the front and lee side of the piles. Consequently, a pile will grow from these two sides and will be elongated in the same direction as the wind. This example illustrates the modulation of a self-organized behavior by an outer colony factor through the modification of individual behavior. Ants aggregate corpses in piles that locally modify air flow. This modification triggers a modulation of individual probabilities to pick-up and drop corpses around the piles. The result is the appearance of a new spatial structure Division of labor in wasps Self-organized processes are also a major component of the division of labor in a colony. For instance in Polistes wasps, division of labor is based on behavioral castes, and the task allocation process results from a complex set of interactions among insects and the brood state (Theraulaz et al., 1991, 1992). In the Polistinae, sudden changes occur in the organization of work when colony size increases (Karsai and Wenzel 1998). We have experimental evidence showing that each insect has different response thresholds for each of the different tasks to be done (see for instance Deneubourg et al for ants; Robinson 1992 and Pankiw et al for bees; Weidenmüller 2004 for bumblebees). These response thresholds control the probability for a wasp to perform a task. It depends both on the threshold value and the stimulus level associated with the task at a given time. 271

291 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: Moreover, these response thresholds change with the wasp s experience (Theraulaz et al. 1991). The more an individual works on a task, the lower becomes the threshold for that task. As a consequence, the wasp will be more responsive to small variations of the stimuli. This is another example of a positive feedback loop. Conversely, if the wasp is not performing the task, because she is working on a different task or doing nothing, the threshold will increase. This means that the wasp will be less responsive to the stimuli and the probability to perform the task will be lower. This induces a negative feedback. Similar processes have been described in bumblebees in the context of nest thermoregulation (Weidenmüller 2004). So, when several insects are in competition to perform a task, the combination of the response threshold reinforcement and the competition among insects to perform the task induces the differentiation of individuals and thus the division of labor at the colony level (Theraulaz et al. 1998b). This mechanism creates not only a differentiation among individuals, but it also ensures the adjustment of the ratio of workers engaged in the various tasks and then plasticity of the division of labor. Now, why do we observe an increase of differentiation among individual activity levels when colony size is increasing? In other words, how does colony size (inner colony factor) modulate the individual behavior of wasps so that the allocation of building tasks strongly differs between small and large colony? Theoretical results have shown that when the total amount of workload is proportional to the size of the colony (that is, when the mean workload per individual remains constant), there exist large fluctuations of the task associated stimuli in a small colony (see Fig. 4, Appendix 1). As a consequence the positive feedback loops are impeded by the high level of noise and individuals do not differentiate. On the contrary, the greater is the colony size, and thus the higher is the absolute value of the number of tasks to be done, the smaller become the fluctuations of the stimuli, and therefore, the greater are the chances that some of the individuals develop in hard workers (Gautrais et al. 2002). The whole process does not only induce a differentiation in the activity levels among insects, it also induces the specialization of the hard workers in specific tasks. For instance in wasps, the normal sequence of tasks involved in nest building first starts with collecting water, then the wasp searches for wood pulp and finally she comes back to the nest where she molds the pellet and builds a cell. What has been noticed is a general tendency for each wasp to be specialized in the execution of one of these three tasks as the colony size is increasing (Karsai and Wenzel 1998). This means that wasps specialized in water or pulp retrieval must exchange their collected material with cell-building wasps when they come back to the nest. Thus, besides the specialization of workers, the colony size increase also promotes a higher degree of coordination between individuals. In wasp colonies, division of labor and task specialization result from a combination of a reinforcement process and a competition among individuals to perform the tasks. With these processes the organization of division of labor is automatically adapted when colony size is changing. When the total workload is high, which is the case in a large colony, it is better to have specialized workers whose performance in task execution will be optimal instead of having generalist workers with a lower performance. On the contrary, when the total amount of work is small, which is the case in a small colony, it might be more relevant to have generalist workers. Indeed, it would be too costly to keep specialized workers because these specialists would not work frequently and so they would not be used in an optimal way. So with this self-organized process, a colony is able to collectively optimize the division of labor, with a minimal complexity of the behaviors and cognitive processes which are required to achieve this regulation. 272

292 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 18 Swarm Intell (2007) 1: Nest choice in ants When the nest is destroyed or does not fulfill its requirements anymore (size, humidity, temperature, etc.), ant colonies hunt for new opportunities to settle in their environment. Scout ants seek for suitable places and then recruit their nest mates toward these locations. If several suitable places exist, the colony has to make a choice between the alternatives. This collective decision is done through the recruitment process. Two different recruitment mechanisms toward a new nest location are well studied in ants: mass recruitment and quorum sensing. Ants of the species Messor barbarus use a mass recruitment mechanism to select a new nest site (Jeanson et al. 2004). This mechanism is similar to the one described in Sect. 2.2 in the context of foraging: nest location is selected thanks to a differential amplification of the pheromone trails leading to the different places. The final choice of the colony can be modulated by the quality of the potential nest sites. For instance, dark places are strongly favored against light ones. Interestingly, this choice does not rely on a direct comparison of the different opportunities by ants: facing two different potential nest locations, only 5% of the scout ants that discover one of the two alternatives visit the other one (Jeanson et al. 2004). In fact, the modulation of this collective choice relies on the modulation of the individual trail laying behavior of ants: dark places increase intensity and frequency of trail laying. This modulation of the individual behavior of ants paired with the amplification process of the pheromone trail bias the final collective decision toward the choice of a dark place. However, this situation differs from the differential choice of the shortest path toward a food source seen in Sect In the case of nest choice, no environmental constraint acts on the collective decision of the colony, this latter being only influenced by a natural preference for dark places expressed by ants in the form of a variation of trail laying behavior. Ants of the species Leptothorax albipennis use a completely different recruitment process for choosing a new nest location. This recruitment process called quorum sensing takes place in two successive steps (Pratt et al. 2002). First, scout ants that discover a suitable place come back to the old nest and recruit a nest mate by leading a tandem run: the recruiter slowly leads a single recruit from the old nest to the potential new nest. Here the recruited ant assesses by itself the qualities of the potential nest place before recruiting a further nest mate by leading its own tandem run. The quality of the nest modulates the duration of the assessment period: a better nest is assessed more rapidly. It then induces a traffic flow which grows more rapidly. Thanks to this modulation, the numbers of ants in the different potential nest sites slowly diverge. Second, when the number of nestmates in one of the potential nest sites rises above a quorum (i.e., the minimal number of individuals that must be present in order for a decision to be taken) the recruitment behavior of ants in this place switches from tandem runs to direct transport by simply carrying the passive nestmates from the former nest. This recruitment by transport is three times faster than recruitment by tandem runs (Pratt et al. 2002). The amplification of the initial choice is so important that the old nest is moved to the new site before other potential sites reach the quorum. Therefore, the collective choice of a nest site in Leptothorax albipennis is based on a threshold-based amplification (also called quorum sensing) by the modulation of the individual recruitment behavior. In the two examples of nest choice described above, modulation of individual behavior by outer or inner colony factors deeply modifies the outcome at the collective level. In the case of ants Messor barbarus the modulation of the trail laying behavior by environmental conditions ensures that the colony as a whole compares the different opportunities and chooses the best nest site whereas a very small number of ants actually visited all the alternatives. Without such a modulation, the colony would remain able to choose a nest site but only at random. 273

293 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: In quorum sensing by ants Leptothorax albipennis, the modulation of recruitment behavior by the number of nestmates in the new nest is an essential part of the mechanism of the decision: it provides the amplification process required to make the decision once the potential nest site was evaluated and approved of by a sufficiently large number of nestmates. Interestingly, this amplification mechanism can be also modulated to adapt the decision making process of the colony to different environmental conditions. By decreasing the quorum value, these ants are able to quicken the choice of a nest if the pressure for emigrating is high (Franks et al. 2003). Conversely, if no particular pressure for emigrating exists, these ants increase the quorum value and thus make more accurate the comparison between the nests (Dornhaus et al. 2004). 5 Managing uncertainty and complexity with swarm intelligent systems We have seen that complex colony-level structures and many aspects of the so-called swarm intelligence of social insects can be understood in terms of interaction networks and feedback loops among individuals. These are the basic elements that allow the emergence of dynamic patterns at the colony level. These patterns can be material (e.g., corpse clustering, nest building) or social (e.g., division of labor) and lead the colony to structure its environment (e.g., during nest building) and solve problems (e.g., collective decision). The most interesting properties of these self-organized patterns are robustness (the ability for a system to perform without failure under a wide range of conditions) and flexibility (the ability for a system to readily adapt to new, different, or changing requirements). Robustness results from the multiplicity of interactions between individuals that belong to the colony. This ensures that, if one of the interactions fails or if one of the insects misses its task, their failure is quickly compensated by the other insects. This also promotes stability of produced patterns whereas individual behaviors are mostly probabilistic. Flexibility of self-organized systems is well illustrated by the ability of social insects to adapt their collective behaviors to changing environments and to various colony sizes (Deneubourg et al. 1986). These adaptations can occur without any change of the behavioral rules at the individual level. For instance, in the case of the selection of the shortest path in ants, a geometrical constraint applied on one of the two alternative paths increases the time needed by the ants to come back to their nest through this path and thus biases the choice toward the other path without any modification of the insects behaviors. But flexibility can also rely on the modulation of the individual behavioral rules by some factors produced by the environment or by the activity of the colony. For instance, the presence of an air flow modifies the probability for an ant to pick up and drop corpses of dead ants. This subtle modification of behavioral probabilities deeply modifies the shape of the piles resulting from the ants aggregating activity (see Sect ). As another example, the modulation of the trail laying behavior as a function of the food source profitability in the ants Lasius niger (Beckers et al. 1993) and Monomorium pharaonis (Sumpter and Beekman 2003) leads the colony to efficiently select the most rewarding food source if several opportunities are discovered simultaneously. The nutrient demand of the colony can modify the behavior of scout ants and can result in an adjustment of the harvesting strategy in the ant Lasius niger (Portha et al., 2002, 2004). The ability of a single worker to retrieve a prey modifies its recruiting behavior and generates a diversity of collective foraging pattern in the ant Pheidole pallidula (Detrain and Deneubourg 1997). Last, the presence of environmental heterogeneities can modulate the behavior of an insect and thus bias the behavior of the colony toward a particular solution (Dussutour et al. 2005). 274

294 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 20 Swarm Intell (2007) 1: 3 31 All these behavioral modulations provide the opportunity for a colony to develop a wide range of collective behaviors and can also be a powerful lever for evolution to shape and optimize these behaviors in a highly adaptive way. Thanks to the sensitivity of individuals to variations (either environmental or triggered by the colony itself), the colony as a whole is able to perceive these changes and can thus react appropriately in almost every situation. For the sake of simplicity, previous models of self-organized behaviors in insect societies often assumed that animals follow some kind of fixed behavioral rules and that new collective structures appear after the system has reached a bifurcation point. If such a viewpoint is of great interest to understand the mechanisms underlying a given collective behavior, one must keep in mind that the natural context in which it occurs can vary from day to day (or even from hour to hour) and that insect colonies have to permanently adapt their behavior to changing conditions. For this reason, future studies in social insects should emphasize the role of individual behavioral modulations in the flexibility of self-organized behaviors. Indeed these modulations trigger new interesting questions about the way insect societies deal with unpredictable and complex environments. For instance, it would be interesting to know how many modulated individuals are required to significantly influence the collective output (Couzin et al. 2005; Gautrais et al. 2004) or how much time is needed for the system to adapt its global behavior to the perturbations. These quantities can be viewed as the sensitivity and reactivity of the system to the perturbations. It would also be interesting to question at which conditions individual behavioral modulations are efficient to produce flexible responses at the level of the colony (see Appendix 2). Switching from a collective structure to another one which is better suited to the current situation requires at least that this switch is indeed possible. The following example illustrates the problem. The black garden ant Lasius niger and the honey bee Apis mellifera both recruit their nest mates toward newly discovered food sources. Scout ants use a pheromone trail to lead uninformed workers to the food source while scout bees indicate its location thanks to their well-known waggle dance. If one provides a bee or an ant colony with two different food sources, a poor one and a rich one, at the same time, then ants and bees will be able to select the richest one. But if one provides the poor source first, lets the colonies establish a recruitment toward this source and then introduces the rich source, then only the bees will be able to switch their recruitment toward this new source (Camazine and Sneyd 1991). Ants will continue to preferentially forage on the less rewarding food source (Beckers et al. 1990). The parameters of their recruitment mechanism do not allow them to change their collective behavior to a more profitable one, as bees do. This problem of ants being stuck in a less favorable collective behavior was addressed in (Bonabeau 1996). Bonabeau showed with the help of a simple model of cooperative foraging that the parameters of the recruitment behavior can lead to an efficient and flexible behavior only if the corresponding stable state is on the one hand close to a bifurcation point and on the other hand in a region where structures can appear and last. If the system at its stable state is too far from a bifurcation point, it becomes hard to make it behave differently and it may remain stuck in a sub-profitable solution. Thereby it should be relevant for a colony to have a mechanism that keeps the collective output at the edge of a bifurcation, not too close so that structures appear and are maintained, but also not too far so that they remain readily adaptive (see Appendix 2). This could be the purpose of the modulations of individual behaviors. 275

295 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: Conclusions Understanding how self-organization works in social insects has already inspired numerous algorithms to control the collective behavior of artificial systems (Bonabeau et al. 1999). However, the recent discoveries about the role individual behavioral modulations play in the adaptive abilities of insect colonies suggest us that the biological study of swarm intelligent systems should provide new sources of inspiration for the design of control algorithms. In particular, giving to artificial agents the ability to modulate their individual behaviors according to cues partially reflecting at the individual level the modifications that occur at the level of the colony would make this artificial colony better prepared to deal with uncertain worlds. Such agents would be able to collectively anticipate negative side effects due to the evolution of their own colony or to counterbalance the impact of hazardous environmental changes. The transition from self-organization to self-organization plus self-adaptation should trigger an increase of complexity in the tasks or the environments an artificial colony could deal with. The addition of self-adaptation to self-organization multiplies the number of group patterns and collective behaviors that can be potentially displayed by the artificial colony. Interestingly, this does not necessarily mean that the behavioral complexity required at the agent level is also dramatically increased. Actually, the major modification of the individual behavioral controller should be a transition from fixed probabilities to accomplish tasks to varying ones. This variation would be an appropriate function of a local cue that correlates with the perturbation the global system would face. In conclusion, the increased flexibility of collective structures in an insect colony triggered by simple modulations of the individual behavior opens interesting ways toward the design of self-adaptive artificial swarm intelligent systems. The pursuance of experimental investigations in biological systems and the development of new theoretical frameworks about the adaptive role of these modulations should encourage the emergence of new applied studies. This lets us believe that the potential of swarm intelligence is far from being exhausted. Appendix 1 Bifurcations in self-organized behaviors The dynamics of self-organized biological systems are shaped by the amplification of random fluctuations through positive feedback loops. Such dynamical systems can display bifurcations in the space of solutions, depending on a driving parameter. Above a critical value, the system can reach new stable states whereas the old solution becomes unstable. In social insects, the dynamics of collective behaviors are intrinsically stochastic and discrete but in some cases they can be approximated by a system of non-linear differential equations, such as in the collective choice of a foraging path in ants. Let us consider ants leaving their nest and facing a choice between two bridges leading to the same food source. In the absence of clues, each ant will choose either of these bridges with equal probability. If, however, preceding ants have left some pheromone on the bridge they took, then the incoming ants prefer to walk on the bridge over which the pheromone concentration is higher. This is a positive feedback loop: the more a bridge is chosen, the more likely it will be chosen by ants. For the very first ants facing the choice, the concentrations of pheromone on both bridges are very low and their difference is difficult to assess. Hence, their choices are still more or less equal between the two bridges. When the fluxes of ants reach a critical value, this 276

296 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 22 Swarm Intell (2007) 1: 3 31 difference becomes significant and triggers the positive feedback loop. Here, the flux of incoming ants acts as a driving parameter. Let C 1 and C 2 be the concentrations in pheromone on bridges 1 and 2. An ant leaving the nest will face the two bridges and choose the bridge C i with probability: p(c i C 1,C 2 ) = (k + C i ) α (k + C 1 ) α + (k + C 2 ) α, i = 1, 2 where k and α are parameters specific to the ant species and the actual set-up. If we assume the simplification that an ant deposits one unit of pheromone each time it takes a bridge, C i represents the flux of ants on the bridge i. The dynamics can thus be approximated by: dc i dt = Φp(C i C 1,C 2 ) µc i, i = 1, 2 where Φ is the total flux of ants leaving the nest, and µ the characteristic time of pheromone evaporation. This equation can be adimensionalized using: yielding dc i dt Hence, at the equilibrium, dc i dt C i kc i, t τ/µ, φ Φ/(kµ) (1 + c i ) α = φ (1 + c 1 ) α + (1 + c 2 ) c i, i = 1, 2. α = 0, i = 1, 2, we have: (1 + c i ) α c i = φ, i = 1, 2. (1 + c 1 ) α + (1 + c 2 ) α Experimental studies estimated α = 2 and k = 4 in Lasius niger (Beckers et al. 1990, 1992, 1993). Using these parameters, and c 1 + c 2 = φ, solutions are such that: (c i φ/2) ( c 2 i φc i + 1 ) = 0, i = 1, 2 which yields three equilibrium states: ( φ (c 1,c 2 ) = 2, φ ), 2 (1) ( 1 ( (c 1,c 2 ) = φ + φ2 4 ), 1 ( φ φ2 4 )), 2 2 (2) ( 1 ( (c 1,c 2 ) = φ φ2 4 ), 1 ( φ + φ2 4 )). 2 2 (3) The solution (1) corresponds to an equal use of the two bridges: this is a no-choice solution, whereas solutions (2) and (3) correspond to an asymmetrical use of the bridges: they are a collective choice (Fig. 4A, B). There is a bifurcation because solutions (2) and (3) only exist for φ >

297 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: Fig. 4 A The stable solutions for the flux C 1 of ants on the bridge 1 (plain dots) as a function of the incoming total flux φ. The system exhibits a bifurcation at φ c = 2 beyond which the no-choice solution becomes unstable (open dots) and the fluxes become asymmetrical, either at a high level on bridge 1, or at a high level on bridge 2. B The differentiation of the flux on the two bridges occurs only above the critical total incoming flux φ c = 2. The differentiation was computed as the absolute value of the relative difference of the fluxes on each bridge shown in subfigure (A) above. C The distribution of individual working times W (y-axis) for increasing colony sizes (x-axis). In small colonies, all individuals work at the same rate (about 40% of their time are devoted to the task), whereas for large colonies only a few individuals work at a high rate (75%) while the others do not work much (20%). For each colony size, the distribution is an average over 1000 simulations for time steps. D The differentiation W of the working times occurs only above a critical colony size (N = 20 30). For each simulation used for subfigure (C) above, the differentiation W (dots) was computed as the difference of working time between the most working and the less working individuals in the colony. The lines indicate the mean differentiation levels among the undifferentiated colonies ( W 0) and the highly differentiated colonies ( W 0.3) Hence φ = 2 is the critical flux which elicits a bifurcation in the space of solutions: if the total flux of ants leaving the nest is too low, the dynamics can not yield the collective choice solutions. Furthermore, beyond this critical value, the no-choice solution (1) becomes unstable. Hence, the random fluctuations around the equal use of bridges will trigger the positive feedback loop and lead the system to one of the two collective choice solutions. Since ants 278

298 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 24 Swarm Intell (2007) 1: 3 31 are actually a discrete system, one can be sure that the fluctuations are always sufficient for destabilizing this no-choice solution. Note that the adimensionalized variable representing the flux φ is such that the corresponding critical flux Φ is proportional to the evaporation rate of the pheromone: the faster the pheromone evaporates, the greater the minimal flux to yield a collective choice. As a whole, the collective choice emerges provided that the flux of ants is sufficient to compensate the pheromone evaporation. In this first example, the bifurcation process leads the colony to drive all the individuals to make eventually the same choice. As far as the individual behaviors are concerned, this is a bifurcation which homogenizes the individual choices. In other cases, the bifurcation can lead by contrast to break the homogeneity of the behaviors, as it is the case in a model of the division of labor in wasps colonies (Gautrais et al. 2002). In this model, the colony has to perform work for tackling a task T. Individuals can engage in doing the task, performing α units of work per unit of time. The task has an associated stimulus S that can be perceived by all individuals. If no wasp is currently working, the task spontaneously increases at a constant rate σ. Hence: ds = (σ K(t)α)dt, S(0) = 0 where K(t) is the number of workers devoted to the task at time t. To simplify the comparison between different colony sizes, σ is kept proportional to the colony size N. For each individual i, the decision to perform the task is stochastic and depends on an internal threshold Θ i, according to: S2 P (i engages) =. S 2 + Θi 2 If the threshold is low, Θ i S, individual i is very prone to engage in the task. Once engaged in the task, the individual stops working at a constant rate p. If all individuals have random threshold, the allocation of work among the workers would simply reflect the underlying distribution of thresholds. However, this distribution would have to be well-shaped for the system to fulfill the basic requirement of allocating the right number of workers to the task and keep the stimulus at a minimal level. This well-shaped distribution would depend on the balance between the increase of the amount of work to be done (σ ), the individual parameters (p and α) and the number of available workers, that is, the size of the colony (N). Designing this distribution on an individual basis would require that insects had access to global information (N, and the threshold of others) which is hardly conceivable. We proposed a mechanism of adaptive threshold that can produce such a distribution, using only the information provided by the stimulus level. Thresholds adapt according to the following rule: an individual engaged in the task gets a lower threshold for the task whereas an idle individual gets a higher threshold for the task. This positive feedback is expressed as: dθ i = ( ξi i + ϕ(1 I i ) ) dt where I i = 1 if i is engaged in the task, 0 otherwise. (ξ, ϕ) are, respectively, thresholds reinforcement and forgetting parameters. Thresholds are kept in a limited range from 0 to Θ max that acts as a negative feedback which stabilizes the process. 279

299 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: With this simple individual rule, a suitable distribution of thresholds spontaneously emerges in a colony starting with all individuals having the same initial threshold (0). For some values of (ξ, ϕ), the system can furthermore exhibit a striking property of the division of labor in social insects, namely that the individuals differentiate their working time only in large colonies (Fig. 4C, D). This size-induced bifurcation originates in the granularity of the stimulus fluctuations that can trigger or not the positive feedback on the thresholds. In small colonies, the amounts σ of work to be done, and α of work done by one individual are of the same order so that the variation of the number of working individuals induces great variations of the stimulus. As a consequence, even the workers with high thresholds have a significant probability to perform the task when by chance the stimulus becomes low. On the contrary, in large colonies the impact of the work done by one worker becomes negligible so the stimulus weakly fluctuates around a constant value. As a consequence, the individuals with high thresholds have a vanishing probability to perform the task (and their thresholds become even higher), and only those workers that have a low threshold can be enrolled (and their thresholds stabilize at a low value). Appendix 2 Modulation of individual behaviors and collective response tuning In the first approximation of the collective choice by ants presented in Appendix 1, the individual choice function takes for granted that individuals can perceive pheromone levels with no restriction: (k + qc 1 ) 2 p(c 1 ) = (4) (k + qc 1 ) 2 + (k + qc 2 ) 2 where q represents the amount of pheromone left by an individual, c 1, c 2 the fluxes on the two bridges, and k a constant related to the perceptual discriminative power for pheromones. However, we know that in general perceptual devices only respond to a limited range of stimuli, and can saturate when the stimulus becomes too high. In the present case, this can be taken into account by considering that the individuals estimate the flux on bridge c 1 through a saturating function of the actual amount of pheromone qc 1. This function can be modeled as: qc 1 c 1 = 2c s(qc 1 ) 2 cs 2 + (qc (5) 1) 2 where c s represents the saturating value (Fig. 5A). Plugging (5) into (4) yields: dc i dt = Φ (k + 2cs (qc i ) 2 cs 2 +(qc i ) 2 )2 (k + 2cs (qc 1) 2 cs 2 +(qc 1 ) 2 )2 + (k + µc i, i = 1, 2 (6) 2cs (qc 2) 2 cs 2 +(qc 2 ) 2 )2 which can have up to five real stationary solutions depending on the total adimensionalised flux φ = Φ/µ. Interestingly, for low values of φ, the system with perceptual saturation behaves similarly as in the first approximation with no saturation, including the bifurcation to the collective choice above a critical lower flux φ m (compare Fig. 5B with Fig. 4A, Appendix 1). However, for higher fluxes the perceptual saturation at the individual level prevents the emergence of a collective choice at the colony level because both bridges appear equally attracting even 280

300 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 26 Swarm Intell (2007) 1: 3 31 Fig. 5 A Estimation c 1 of the actual flux c 1 when the perceptual device is saturating at c s (arbitrarily fixed to 10). Since the saturation pertains to the pheromone, c 1 depends on the amount of pheromone q that each individual ant lays down. For higher values of q, the saturation occurs for lower values of the flux (from left to right, q = 4, 1.5, 1, 0.5). B The stable solutions for the flux C 1 on the bridge 1 (plain dots) as a function of the incoming total flux φ. The system exhibits the collective choice (asymmetrical fluxes) only for a range of φ. The solutions presented correspond to q = 1.5, marked as bold line in (A). C The ranges of fluxes that elicit a collective choice as a function of the individual deposit q. The collective response (z-axis) is indicated by the asymmetry of the fluxes on the two bridges c = c 1 c 2 c 1 +c. c>0 indicates the emergence of the collective 2 choice if the actual fluxes are not similar. Hence, there exists a critical upper flux φ M above which the collective choice vanishes. From a computational point of view, the collective choice can be considered as a response of the colony to the environmental conditions, either external (as in the case of bridges of different length) or internal such as the number of foragers. 281

301 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM Swarm Intell (2007) 1: In the simplest case with no perceptual saturation, the system behaves as a high-pass filter (it responds only to high incoming fluxes). Introducing the saturation constraint on individual perceptual ability enables the system to behave like a bandpass filter: it responds then to a specific range φ m φ M of the total flux φ. The bandwidth of this collective response depends non-linearly on the amount of pheromone q left by each individual (Fig. 5C). For high values of q, the system exhibits a collective choice for lower values of φ, but saturates quickly. Correspondingly, for a given flux φ, the collective choice can emerge only for a limited range of q. This range shrinks for higher values of φ: an increasing number of individuals at play increases the accuracy of the response. The collective response of the colony can thus be tuned by modulating individual parameters. From a functional point of view, the collapse of the collective choice for higher flux values might be an unwanted side effect of the perceptual saturation. This collapse can be prevented by an on-line modulation of the amount of pheromone q which is laid down by ants. If the optimal regime is the one that maintains a collective choice for any flux values, then a high value of q at the beginning of the recruitment process when the flux is low would favor the emergence of the collective choice but it should decrease progressively as the flux increases. This seems to be the strategy adopted by ants Lasius niger (Beckers et al. 1992). Note the counter-intuitive trick of decreasing on-line the information left by each individual in order for the colony to maintain its choice. Acknowledgements We thank all the members of the EMCC group in Toulouse for many helpful discussions and comments. We also thank the three anonymous reviewers for their useful advices. Simon Garnier is supported by a grant from the French Ministry of Education, Research and Technology. References Anderson, C., & Franks, N. R. (2001). Teams in animal societies. Behavioral Ecology, 12(5), Anderson, C., Franks, N. R., & McShea, D. W. (2001). The complexity and hierarchical structure of tasks in insect societies. Animal Behaviour, 62(4), Ataya, H., & Lenoir, A. (1984). Le comportement nécrophorique chez la fourmi Lasius niger L. Insectes Sociaux, 31, Beckers, R., Deneubourg, J. L., Goss, S., & Pasteels, J. M. (1990). Collective decision making through food recruitment. Insectes Sociaux, 37, Beckers, R., Deneubourg, J. L., & Goss, S. (1992). Trail laying behaviour during food recruitment in the ant Lasius niger (L.). Insectes Sociaux, 39, Beckers, R., Deneubourg, J. L., & Goss, S. (1993). Modulation of trail laying in the ant Lasius niger (Hymenoptera: Formicidae) and its role in the collective selection of a food source. Journal of Insect Behavior, 6, Ben-Jacob, E., Schochet, O., Tenenbaum, A., Cohen, I., Cziròk, A., & Vicsek, T. (1994). Generic modelling of cooperative growth patterns in bacterial colonies. Nature, 368(6466), Ben-Jacob, E., Cohen, I., & Levine, H. (2000). Cooperative self-organization of microorganisms. Advances in Physics, 49, Beshers, S. N., & Fewell, J. H. (2001). Models of division of labor in social insects. Annual Review of Entomology, 46(1), Bonabeau, E. (1996). Marginally stable swarms are flexible and efficient. Journal de Physique I, 6, Bonabeau, E., & Theraulaz, G. (2000). Swarm smarts. Scientific American, 282(3), Bonabeau, E., Theraulaz, G., Deneubourg, J. L., Aron, S., & Camazine, S. (1997). Self-organization in social insects. Trends in Ecology and Evolution, 12(5), Bonabeau, E., Theraulaz, G., & Deneubourg, J. L. (1998). Fixed response threshold and the regulation of division of labor in insect societies. Bulletin of Mathematical Biology, 60, Bonabeau, E., Dorigo, M., & Theraulaz, G. (1999). Swarm intelligence from natural to artificial systems. Oxford: Oxford University Press. 282

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304 ANNEXE A. LES PRINCIPES BIOLOGIQUES DE L INTELLIGENCE EN ESSAIM 30 Swarm Intell (2007) 1: 3 31 Jost, C., Verret, J., Casellas, E., Gautrais, J., Challet, M., Lluc, J., Blanco, S., Clifton, M. J., & Theraulaz, G. (2007). The interplay between a self-organized process and an environmental template: corpse clustering under the influence of air currents in ants. Journal of the Royal Society Interface, 4, Karsai, I., & Theraulaz, G. (1995). Nest building in a social wasp: postures and constraints. Sociobiology, 26, Karsai, I., & Wenzel, J. W. (1998). Productivity, individual-level and colony-level flexibility, and organization of work as consequences of colony size. Proceeding of the National Academy of Sciences, 95(15), Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of the IEEE international conference on neural networks (pp ). Washington: Bureau of Labor Statistics. Krieger, M. J. B., Billeter, J. B., & Keller, L. (2000). Ant-like task allocation and recruitment in cooperative robots. Nature, 406(6799), Kuntz, P., Snyers, D., & Layzell, P. (1999). A stochastic heuristic for visualising graph clusters in a bidimensional space prior to partitioning. Journal of Heuristics, 5(3), Ledoux, A. (1950). Recherche sur la biologie de la fourmis fileuse (Oecophylla longinoda Latr.). Annales des Sciences Naturelles et Zoologiques, 11, Lioni, A., Sauwens, C., Theraulaz, G., & Deneubourg, J. L. (2001). Chain formation in Oecophylla longinoda. Journal of Insect Behavior, 14, Maeterlinck, M. (1927). The life of the white ant. London: Allen & Unwin. Melhuish, C., Wilson, M., & Sendova-Franks, A. (2001). Patch sorting: multi-object clustering using minimalist robots. In Proceedings of the 6th European conference on advances in artificial life (pp ). London: Springer. Menzel, R., & Giurfa, M. (2001). Cognitive architecture of a mini-brain: the honeybee. Trends in Cognitive Sciences, 5, Moffett, M. W. (1988). Cooperative food transport by an Asiatic ant. National Geographic Research, 4, Pankiw, T., Waddington, K. D., & Page, R. E. (2001). Modulation of sucrose response thresholds in honey bees (Apis mellifera L.): influence of genotype, feeding, and foraging experience. Journal of Comparative Physiology A, 187(4), Parrish, J. K., Viscido, S. V., & Grünbaum, D. (2002). Self-organized fish schools: an examination of emergent properties. Biological Bulletin, 202(3), Portha, S., Deneubourg, J. L., & Detrain, C. (2002). Self-organized asymmetries in ant foraging: a functional response to food type and colony needs. Behavioral Ecology, 13(6), Portha, S., Deneubourg, J. L., & Detrain, C. (2004). How food type and brood influence foraging decisions of Lasius niger scouts. Animal Behaviour, 68(1), Pratt, S. C., Mallon, E. B., Sumpter, D. J. T., & Franks, N. R. (2002). Quorum sensing, recruitment, and collective decision-making during colony emigration by the ant Leptothorax albipennis. Behavioral Ecology and Sociobiology, 52(2), Reeve, H. K., & Gamboa, G. J. (1983). Colony activity integration in primitively eusocial wasps: the role of the queen (Polistes fuscatus, Hymenoptera: Vespidae). Behavioral Ecology and Sociobiology, 13, Reeve, H. K., & Gamboa, G. J. (1987). Queen regulation of worker foraging in paper wasp: a social feedback control system (Polistes fuscatus, Hymenoptera: Vespidae). Behaviour, 106, Reynolds, C. W. (1987). Flocks, herds and school: a distributed behavioral model. Computer Graphic, 21(4), Robinson, G. E. (1992). Regulation of division of labor in insect societies. Annual Review of Entomology, 37(1), Seeley, T. D. (2002). When is self-organization used in biological systems? Biological Bulletin, 202(3), Seeley, T. D., Camazine, S., & Sneyd, J. (1991). Collective decision-making in honey bees: how colonies choose among nectar sources. Behavioural Ecology and Sociobiology, 28, Seeley, T. D., & Tautz, J. (2001). Worker piping in honey bee swarms and its role in preparing for liftoff. Journal of Comparative Physiology A, 187, Seeley, T. D., & Visscher, P. K. (2004). Group decision making in nest-site selection by honey bees. Apidologie, 35, Sudd, J. H. (1965). The transport of prey by ants. Behaviour, 25, Sumpter, D. J. T., & Beekman, M. (2003). From nonlinearity to optimality: pheromone trail foraging by ants. Animal Behaviour, 66(2), Theraulaz, G., & Bonabeau, E. (1995a). Coordination in distributed building. Science, 269(5224), Theraulaz, G., & Bonabeau, E. (1995b). Modeling the collective building of complex architectures in social insects with lattice swarms. Journal of Theoretical Biology, 177,

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308 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Annexe B Transferts d information et comportements auto-organisés dans les foules et les essaims 289

309 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS 1 2 Information transfer and self-organized behavior in swarms, flocks and crowds Mehdi Moussaid 1, 2, Simon Garnier 2, Guy Theraulaz 2, and Dirk Helbing 1 1 ETH Zurich, Swiss Federal Institute of Technology, Chair of Sociology, UNO D11, Universitätstrasse 41, 8092 Zurich, Switzerland. 2 Centre de Recherches sur la Cognition Animale, UMR-CNRS 5169, Université Paul Sabatier, Bât 4R3, 118 Route de Narbonne, Toulouse cedex 9, France. Abstract The spontaneous organization of collective activities in animal groups and societies is a fascinating phenomenon. This emergent coordination often permits group-living species to achieve collective tasks that are beyond single individuals capabilities. In particular, a key benefit lies in the integration of partial knowledge of the environment at the group level. In this contribution we look at various expression of self-organization processes in animal swarms and human crowds from the point of view of information exchange among individuals. In particular we provide a general description of collective dynamics across species and introduce a classification of these dynamics not only with respect to the way information is transferred among individuals, but also regarding how the knowledge is processed at the collective level. Finally, we highlight the fact that the individuals ability to learn from past experiences can have a feedback effect on the collective dynamics, as experienced with the development of behavioral conventions in pedestrian crowds

310 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Introduction In nature, many group-living species - such as social arthropods, fish or humans - display collective order in space and time (see figure 1). In fish schools, for instance, the motion of each single fish is perfectly integrated into the group, so that the school often appears to move as a single coherent entity. In response to external perturbations, the whole school may suddenly change the swimming pattern, adopt a new configuration, or simply switch its direction of motion in perfect unison. In case of predator attack, fish fled almost simultaneously, seemingly all aware of the danger at the same moment (see e.g. Partridge 1982). Similar coordinated collective behaviors can be found in humans (Helbing et al. 2001). Flows of people moving in opposite directions in a street, spontaneously organize in lanes of uniform walking direction, in this way enhancing the overall traffic efficiency by reducing the number of avoidance maneuvers. A major characteristic of this collective organization lies in the fact that it emerges without any external control. No particular individual supervises the activities nor broadcasts relevant information to all the others and no blueprint or schedule is followed. This non-supervised order holds a puzzling question: By what means do hundreds or even thousands of individuals manage to coordinate their activity in such an extent without referring to a centralized control system? Answering this question comes down to establish a link between two distinct levels of observation: on the one hand, seen from a macroscopic level, the group displays a surprisingly robust and coherent organization that often favors an efficient use of the environment. But on the other hand, from the microscopic point of view of a given individual, the situation is perceived at a local scale: the pedestrians like the fish do not have a complete picture of the overall structure they create. They rather react according to partial information available in their local environment or provided by other nearby group members. The nature of the link between the individual and the aggregate level is investigated in this contribution. More specifically, the problem of how local interactions among individuals yield to efficient collective organizations is addressed by studying how information is transferred among individuals. Indeed, the contrast between the limited information owned by single individuals and the global knowledge required to coordinate the group s activity is often remarkable. The unexpected birth - or emergence - of new patterns out of interactions between numerous subunits was first established in physico-chemical systems (Nicolis & Prigogine 1977). Since then, it was many times demonstrated that spontaneous order can appear in such systems because of the non-linear interactions among chemicals. Because the order emerges without external control these 2 291

311 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS non-linear phenomena were labeled as self-organized. Self-organization mechanisms are not a specificity of physical and chemical systems. During the last 30 years, they have also been identified in various living systems, such as cellular structures (Shapiro 1988; Ben-Jacob et al. 2000; see Karsenti 2008 for a review), animal societies (Camazine et al. 2001; Couzin & Krause 2003; Sumpter 2006; Garnier et al. 2007) or human crowds (Helbing et al. 1995; Ball 2004). Their comprehension is among today s most essential challenges: first, because they are responsible for a significant part of the organization of animal and human societies; and second, because they are often the source of problems, such as vehicular traffic jams (Helbing 1998), the spread of diseases (Newman 2002), or the clogging of people fleeing away from a danger (Helbing 2000). The present study focuses on such behaviors in living beings: humans, like pedestrians, customers or Internet users, and animals, like insect colonies, vertebrate schools or flocks. Despite wide differences among these systems (in terms of the number of units, size or cognitive abilities of the individuals), human and animal systems can exhibit similar collective outcomes, suggesting the presence of common underlying mechanisms. For instance, bidirectional flows of pedestrians get organized in lanes (Helbing et al. 1995), as well as some species of ants or termites (Couzin & Franks 2002; Jander & Daumer 1974); an audience of people may collectively synchronize their clapping (Neda et al. 2000) as fireflies synchronize their flashing (Buck & Buck 1976); many insect species build trail systems in their environment, and so do humans (Hölldobler & Wilson 1990; Helbing et al. 1997). Moreover, we choose to consider humans and animal systems because, unlike molecules involved in physical or chemical self-organized systems, living beings exchange and process information (of any kind) when interacting with each other. This information influences and often determines the living being s next actions. In addition, the collective integration of individual knowledge often allows the group to produce efficient behavioral answers to their environment. Thus, studying the way individuals respond to information and how this information spreads among them constitutes an essential step to understanding the organizational abilities of many group-living species. The following sections of our contribution are organized as follow: First, we start with a description of the major principles behind the concept of self-organization. Then, in section 3, we review various self-organization phenomena occurring in animal or human populations. Most of the discussed systems have been previously studied in the literature but the novelty of this paper is its focus on the exchanges of information among individuals. That means, we highlight the internal mechanisms that allow the group to integrate and process this knowledge and to achieve various tasks, such as sorting items, optimizing activities or making collective decisions. Accordingly, section 4 presents a generalized view of the dynamics on the microscopic and macroscopic levels of description, and a classification of the collective outcomes

312 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Self-organized behavior in social living groups Since our purpose is to investigate the features of self-organized behaviors, our first concern is to properly define this term and to bring major principles underlying such phenomena into the picture. A self-organization process can be defined as the spontaneous emergence of large-scale structure out of local interactions between the system's subunits. Moreover, the rules specifying interactions among the system s components are executed, using only local information, without reference to the global pattern (Bonabeau et al. 1997). The distributed organization implies that no internal or external agent is supervising the process and that the collective pattern is not explicitly coded at the individual level. The emerging structures are in essence more complex than the addition of each agent s contribution. Self-organization is a key concept to understand the relationship between local inter-individual interactions and collective group patterns. A self-organized process relies on four basic elements: 1. A positive feedback loop, which makes the system respond to a perturbation by increasing it. Positive feedbacks often lead to an explosive amplification of a perturbation and promote the creation of new structures. Typically if the probability for an individual to perform a given action is somehow increased by other individuals in the neighborhood already performing the same action, the group is very likely to display a positive feedback loop. As an illustration, let us refer to a wellknown experiment performed by Stanley Milgram in the streets of New York (Milgram et al. 1969): Milgram noticed that, when someone seems to look at something interesting in a particular direction, people around him tend to look in the same direction. More detailed studies showed that the tendency to imitate this behavior is approximately proportional to the number of surrounding people already looking in the same direction: a single person looking at a given point triggers 40% of naive by-passers to follow his or her gaze. This percentage grows to 80% and up to 90% with five and fifteen persons, respectively looking into the same direction. A positive feedback loop is in play: the higher the number of people looking in a given direction - let's say up in the air- the more likely surrounding walkers will look up in turn, increasing again the attractiveness of the looking-up behavior and so forth. This reinforcement dynamics usually leads to a non-linear propagation of a given behavior in the population. 2. The non-linear amplification of such a snowball effect itself could eventually lead a system into a destructive state. Therefore, in self-organized systems, a negative feedback loop typically sets in at 4 293

313 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS larger perturbation amplitudes, and counterbalances the reinforcement effect of the positive feedbacks, eventually leading to the stabilization of the collective pattern. For instance, why did the previous experiment not make the whole city of New York to look up? Simply because human attention is not unlimited. Usually, after a few seconds of looking in the related direction, people tend to lose interest in the looking-up behavior and continue their walking. Therefore, a more or less significant group of people looking up will form and stabilize, depending on the quality and relevance of information provided. In most cases however, the negative feedback effect is rather provided by physical constraints of the system, like the limited number of individuals present. 3. Self-organizing processes also rely on the presence of fluctuations. Random fluctuations constitute the initial perturbations triggering growth by means of positive feedbacks. People walking straight ahead toward their destination would never discover any point of interest in their environment, and a collective looking-up behavior would never appear. Instead, a weak tendency to check out the neighborhood may catch the attention of a few walkers, triggering the amplification loop and spreading the information into their neighborhood. The unpredictability of exact individual behavior may also be the origin of the great flexibility of the system. As individuals do not deterministically respond to a given stimuli, there is a chance to discover alternative sources of information and other ways to solve a problem. In such a case, a positive feedback effect allows the system to leave a given state in favor of a better one. 4. Finally, self-organizing processes require multiple direct or indirect interactions among individuals to produce a higher-level, aggregate outcome. Permanent interactions among group members are the heart of any self-organized dynamics. Direct interactions imply some kind of direct communication between individuals (like visual or acoustic signals or physical contacts), while indirect interactions imply a physical modification of the environment that can be sensed later by other individuals. New York's by-passers unintentionally exchange information by means of direct interactions, namely by the visual signal they transmit when looking toward a particular direction. On the basis of these four ingredients, it has been possible to describe and explain numerous collective behaviors observed in social insects and animal societies (Camazine et al. 2001, Couzin & Krause 2003). Therefore, the concept of self-organization helps to elucidate the non-intuitive relationship between the apparent behavioral simplicity of group members and the complexity of the collective outcomes that emerge from their interactions. We will now look at various case studies involving self-organized behaviors both in humans and animals groups, and describe them by means of the mechanisms introduced above. In doing so, we emphasize the distinction between the individual and the collective levels of observation, to better understand the relationships between both levels. Finally, we choose to classify the described 5 294

314 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS systems according to the nature of the information transfered between individuals (i.e. either direct or indirect), because this difference has some further implications when studying the collective information processing, as discussed in the last section Case studies Indirect information transfer Indirect communication between individuals (also called stigmergic communication) is a frequent property of biological systems with many interacting agents. It refers to the ability of the individuals to modify the environment in which they live, and to respond in turn to such changes in specific ways. Stigmergy was initially introduced by French biologist Pierre-Paul Grassé at the end of the fifties to account for the coordination of building behavior in termites (Grassé 1959). Indeed, group-living insects often lay chemical signals in their environment to mark a particular location like a food source or to inform other group members of a recent change like a new construction stage in nest building. Signals exchanged in this way can be of different nature, such as chemical or physical with an alteration of the environment. In humans, the signals exchanged can also be virtual. Indeed, interactions within communities of people that have lately flourished on the Internet often go along with virtual signals left in blogs or forums. An interesting and simple example of such indirect information exchange involving virtual signals can be studied at the interactive website called digg.com, which we will focus on now

315 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Case 1 : The Online Social Network digg.com Digg.com is a website over which people can discover and share contents found elsewhere on the web. It allows its users to submit news stories they find while they browse the Internet. Each new story can be read by other community members. If they find it interesting, they can add a digg to it. A digg is a virtual signal associated to a given story that can be seen by other users. The more diggs a story received in a given period of time, the more it becomes visible to the visitors. Most popular news eventually reach the website s frontpage. The system actually provides a powerful decentralized way to efficiently share information across a community, since interesting stories are widely spread among the community members at the expense of old or non-interesting ones. Moreover, stories are also dynamically sorted with respect to their relevance: the greater the number of diggs a story has at a given moment of time, the more it is considered as interesting. Interactions between users take place by means of indirect communication. Each user is capable of leaving a trace (the digg) in a virtual common environment, characterized by a multitude of more or less interesting stories. The behavioral rules of a given user can be summarized as follow: each user initially moves almost randomly through the environment provided by the website. In a neutral environment (i.e. in the absence of digged stories), each user has an approximately equally weak probability to read a given news, according to his or her own liking and interests. If the user encounters a story he or she finds relevant, he or she may deliberately modify the environment and mark the story for the attention of other members of the community Since popular stories are presented in an attractive way and easily accessible, the probability for another user to read a given story increases with the number of diggs the story has received. Therefore, a positive feedback loop can be identified here: the more a story is popular (that is to say considered relevant by users), the more likely it is to be paid attention to and to further increase its popularity. Consequently, interesting information is spread over the group in a non-linear way and the level of propagation of relevant stories increases exponentially with time. But such an exploding dynamics itself would lead a few stories to be so attractive that the great majority of the available information would remain unexplored. As described in the previous section, a negative feedback is needed to limit the self-amplification. Wu and Huberman observed that this negative feedback was driven by the decay in novelty of the news: the older a news, the less it captures the attention of people (Wu & Huberman 2007). After a certain period of time, a given news will receive less and less diggs, and as a consequence its propagation will slow down and it will finally be replaced by newer stories (figure 2)

316 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Interestingly, it has been shown that the pattern of propagation of a novel information and the subsequent decay of attention depend on many factors, such as the time of the day it has appeared or the story's topic. This implies that the resulting sorting of the stories is somehow linked to the global environment: stories related to current events propagate faster than others. In terms of selforganizing mechanisms, this can be expressed by the fact that individuals tend to modulate their 'digging' behavior, with respect to the media-related context. Environmental specificities can thus induce a weak bias in the behavior of the users that would potentially result in a major change of the collective outcome. This sensitivity of the system provides a great flexibility in achieving the sorting task: different communities of people would sort the body of information in different ways, according to their interests, background and cultural environment

317 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Case 2 : Trail formation in ants In animal world, one of the best studied examples of indirect communication is probably the trail formation in ant colonies. Many species of ants have the ability of laying chemicals, called pheromones, in their environment (Hölldobler & Wilson 1990). Pheromones are a typical chemical support for information exchange in insect societies and can be used for various purposes such as alarming for a danger, mating communication, or indicating the location of a food source (Wyatt 2003). In particular, ants can deposit pheromone trails to mark the route from their nest to a newly discovered food source and share this crucial information with the rest of the colony. One can easily observe such a foraging behavior by setting out a piece of sugar in the neighborhood of a nest. After some time, an increasing number of foragers appear at the food source, and soon an important flow of ants sets in between nest and piece of sugar (see figure 1a). How does the colony manage to establish such a foraging trail? The process starts when a single ant finds a food source during a phase of random exploration. After feeding, the ant returns to the nest and drops small amounts of pheromones at regular intervals on its way back. This incipient trail has an attractive influence on other nestmates. Thus, although unaware of the food source location, nearby ants tend to modulate their random exploration behavior toward a trail-following behavior and may find the food source in turn. The greater the pheromone concentration, the higher the probability of an ant to follow the trail. Each new recruited ant finding the source reacts in the same way, returning to the nest and reinforcing the chemical trail with its own pheromones. This establishes a positive feedback: the more ants are recruited, the more attractive the trail becomes, increasing again the number of ants engaged in the process, and so forth. This leads to an exponential increase of the number of ants on the trail. However, pheromones are highly volatile chemicals. Thus, the evaporation of the trail can counterbalance its increasing attractiveness, leading the system to a stable state in which a constant flow of ants moves over the trail. A negative feedback occurs by other factors as well: it may result from the limited number of available foragers, from a competition between trails, or from the depletion of the food source. In any case, the negative feedback acts against the reinforcement loop, and a balance between opposite effects helps the system to stabilize in a new state, leading to a constant flow of ants on the trail (figure 3) This ability of ants to leave marks in their environment constitutes a powerful means for efficiently spreading novel information. Interestingly, the way in which knowledge is processed at the group level provides many other benefits to the colony. In particular, controlled experiments reproducing ants trail formation in the laboratory revealed that ants also carry information about the quality of the food source. Indeed, the workers tend to modulate their trail-laying intensity as a function of the quality of the discovered food (Beckers et al. 1993). From this behavioral modulation follows the ability of the colony to concentrate its effort toward the most profitable options. For example, if two 9 298

318 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS food sources are available, the trail toward the richest one will be initially slightly more concentrated in pheromones than the others, and thus will attract a little more foragers at the beginning. However, as the number of workers involved increases, the difference in pheromone concentration between the trails grows as well, since the reinforcement operates faster on the path leading to the richest source. The feedback is further reinforced by the evaporation of the pheromones so that, finally, the competition between rich and poor sources directs the colony activity toward the most profitable option. If the selected food source runs out, ants stop laying pheromones and the trail vanishes, allowing the exploitation of other food sources. Based on the same reinforcement mechanisms, ants also manage to select the shortest route among several possibilities to reach a given food source (Beckers et al. 1990). In contrast to the mechanisms in play at Digg.com, ants do not sort the different foraging alternatives according to their preference, but the colony rather selects the best option and focuses exclusively on it, almost ignoring all the others. The collective choice is decentralized: ants make no overall comparison of the different alternatives. The efficiency of the collective activities lies in the integration of information owned by single ants at the colony level, driving the group toward a consensus for the best foraging strategy

319 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Case 3 : Trail formation in pedestrians Humans are also often generating trail systems when walking through open natural space. One may observe such patterns imprinted in grassy areas in parks or meadows (figure 1d). The trails are caused by people walking off the originally planned ways, little by little trampling down the vegetation under their feet. The so-formed trail networks usually exhibit smooth curvy intersections and do not necessarily follow the shortest path between entry and exit points. Recent research highlighted that these trail systems result from a typical self-organization process (Helbing et al. 1997; Goldstone and Roberts, 2006). Unlike ants or digg.com users, pedestrians do not deliberately cooperate to build up an efficient trail system. They are simply goal-oriented agents, each having its own starting point and destination, but all pursuing the same aims: walking comfortably and avoiding detours as much as possible. Moreover, each walker unintentionally prints his or her own solution through the environment and thereby shares it with the other pedestrians. Indirect communication among people is achieved altering the ground via the walkers' footsteps. The subsequent walkers spontaneously reconcile their goal-oriented behavior with a preference for walking on previously used and more comfortable ground to walk. The system, therefore, has a reinforcement mechanism: trails attract walkers that in turn improve the trails and increase their attractiveness. Over time, and by using trails frequently, the system evolves toward a compromise between various direct trails. This enhances the walking comfort at minimum average detours. Helbing et al. developed an individual-based model of trail formation (the active walker model) (Helbing et al. 1997). The model is based on two intuitive behavioral rules: in a plain environment, each walker simply moves directly toward his or her destination point. However, such a movement prints a slight trail on the ground. If a pedestrian perceives such a trail on his or her way, he or she feels attracted toward this trail with an intensity proportional to the trail's closeness and visibility. The walker model is complemented by a dynamic ground structure that is modified by walking pedestrians (to reflect the trampling down of vegetation, or footprints in snow, for example). This alteration of the ground is limited by a maximum trail intensity, to take into account the effect of saturation. The ground structure also changes in time owing to the regeneration of vegetation, leading to the slow but permanent restoration of the environment.simulations made with a steady stream of pedestrians, all coming from and going to a few destinations at the periphery, gave rise to the formation of trails similar to those observed in urban grassy areas. Ants and pedestrians trail formation are different in principle: while ants deliberately cooperate to build up an efficient trail and gather food, pedestrians are expected to behave selfishly and not to pursue a collective benefit. Despite this major difference, the underlying mechanism remains the

320 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS same. People modify their environment by means of their footsteps and, at the same time, feel attracted by this modification. Incipient trails are reinforced by a positive feedback loop that finally gives rise to persistent patterns. Evaporating pheromones in ants play the same role as regenerating vegetation in pedestrians, by counterbalancing the previous amplification effect. Pedestrians also take advantage of the trails they produce. Without any overall view of their environment, people collectively find a good compromise in terms of short, but comfortable ways linking several entry and exit points. 3.2 Direct Information Transfer Information transfer in populations of living-beings can also occur through direct interactions. In this case, no modification of the environment (either real or virtual) is needed. Individuals rather behave according to the actions of their neighbors. The information exchanged in that way can be of different nature, ranging from visual signals to acoustic ones, or physical contacts. This kind of interactions is at the origin of various spatio-temporal coordinated behaviors. In the following, we examine the dynamic of coordinated movements in fish schools, the emergence of temporal coordination in a clapping audience and the emergence of spatial coordination such as the formation of lanes observed in some species of ants as well as pedestrians. Case 1: Fish Schools The coordinated motion of schools of thousands or even millions, of individuals, all moving cohesively as a single unit, constitutes an interesting case to study. Various group-living animal species exhibit this remarkable ability to move in highly coherent groups, such as bird flocks (May 1979; Higdon & Corrsin 1978) or fish schools (Shaw 1962; Partridge 1982). We choose to focus on the abilities of fish to coordinate their movements in groups, primarily because they have been well studied both, from an empirical and a theoretical point of view. Fish schools possess particular group-level properties. The observation of numerous individuals, all moving in parallel in the same direction and suddenly switching direction, implies that all individuals have somehow acquired the same turning information at almost the same moment. In case of a predator attack for example, the few individuals that perceive the danger trigger a wave of fleeing reactions that rapidly spreads across the school. Another feature of fish schooling is the variety of movement patterns that can be adopted. Spatial structures like mills, balls or vacuoles are examples of observable emerging organizations, the scales of which always exceed the size of a single individual by far (Parrish et al. 2002; figure 1b). Considering the enormous number of individuals involved, a centralized organization is hard to conceive. The most likely explanation of these group behaviors is self-organization

321 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Early experimental studies demonstrated that fish apply two different means of interaction: vision, used to acquire information about the motion of other fish, and the so-called lateral line system, a sense organ located along the side of the fish that responds to water movement, providing information about the distance of neighboring fish. First individual-based models have been developed on the basis on these observations (Aoki 1982; Huth & Wissel 1992). Huth and Wissel suggested that each fish within a school follows a set of simple rules to determine its next position: First, in the absence of interaction (i.e. when neither visual nor lateral line systems provide information about other fish, i.e. when the individual is isolated), the fish simply moves randomly to restore contact with the group. In response to interactions with other group members, the fish can display repulsive, attractive or alignment behaviors, as a function of the distance of the other individual it is interacting with. The distances at which fish adopt one of these behaviors are parameters of the model. These parameters are usually set so that the repulsion occurs at short distances, alignment at intermediate distances, and attraction at larger distances. Simultaneous interactions are determined by calculating the arithmetic mean response to the N nearest neighbors. A random term is also added in order to reflect the imperfect sensing and responses of fish. Simulations based on such simple behavioral rules generate convincing schooling with no need of any additional supervision. Any sudden move of a fish is imitated by its close neighbors. The higher the number of fish adopting a given behavior, the faster this behavior propagates among previously uninformed individuals. This reinforcement process leads to an exponentially increasing number of fish responding to new information. The negative feedback here is simply given by the limited number of individuals Results from this behavioral model demonstrate the power of self-organization mechanisms. For example, Couzin et al. (Couzin et al. 2002) showed that the range of alignment behavior has a critical effect on the configuration of fish schools. In particular, the study shows that a short, intermediate or large range of the alignment behavior yields packed stationary swarms, mills (where individuals circle around their center of mass) and parallel motions of the entire group into a common direction, respectively. This implies that individuals may adapt their interaction rules in a context-dependent way. In case of danger, stronger attraction and alignment make the group more sensitive to external perturbations and provide fast answers to external threats. In other contexts, however, weaker interactions can be more efficient, since the group does not systematically respond to each small fluctuation. Given a small alignment range, only the most relevant information is amplified, which allows the school to ignore stimuli of lower intensity. The exploration of the model also highlights the ability of the school to move cohesively toward a pertinent destination (for example the location of a food source). A small proportion of fish that possesses particular information, such as a migration route or the direction of a resource, and exhibiting a biased behavior toward that destination, is enough to yield a collective consensus on the swimming direction (Couzin et al. 2005). Interestingly, the proportion of informed individuals

322 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS required to achieve the consensus decreases with increasing group size. This last result follows directly from the reinforcement mechanism described above. In large groups, the interaction rate among individuals is increased. Hence, information propagates faster, and less than 5% of informed fish are enough to drive a school of 200 individuals toward a relevant destination. The system is all the more efficient, as it does not require individuals to recognize those who are informed Case 2 : Synchronized Clapping of an Audience Self-organizing mechanisms can also lead to the emergence of collective temporal coordination. The next case focuses on emerging synchronous activity that can be found in humans, when an audience showing its appreciation after a good performance suddenly turns from incoherent clapping into coordinated rhythmic applause. Although no particular rhythm is imposed by any supervisory control, a common clapping frequency and phase emerges from the interaction between people. Audience members interact by means of the acoustic signal produced by each clap and heard by other audience members. In such a way, people communicate their clapping rhythm to their neighbors, and acquire information about the rhythm adopted by the others around. Similarly to fish behavior in schools, people tend to adjust their activity with respect to the average information they get from their nearby environment. In the beginning, small clusters of synchronized individuals may appear by chance. This locally stronger information, then, produces a positive feedback loop: the more individuals locally agree on a clapping rhythm, the stronger is their influence on other audience members. This results in the spread and amplification of common rhythmic activity among the spectators, and the whole audience finally achieves a consensus on their clapping rhythm. This reinforcement process is widespread in other natural systems (Strogatz 2003). On the basis of similar mechanisms, some species of fireflies can achieve flashing synchronization (Buck & Buck, 1976). However, a quantitative analysis of recordings of audiences in Eastern European theaters and concert halls revealed a major difference compared to other animal synchronous activities. Néda et al. (2000) identified a particular common pattern characterized by an initial phase of incoherent but loud clapping, followed by a transition to synchronized clapping, which was again replaced by unsynchronized applause, and so on. Such a dynamics has not been observed in fireflies for example, although the underlying mechanisms are similar (individuals are adjusting to the average rhythm of their neighbors). In order to interpret this alternation of ordered and disordered states, the authors relied on a model of coupled oscillators, originally suggested by Kuramoto (Kuramoto 1975). The model is well adapted to audience behavior and shows that a large number of oscillators coupled together (continually adjusting their frequency to be nearer to the average) will finally oscillate synchronously, provided

323 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS that the distribution of initial frequencies of oscillators is not greater than a critical value (Kuramoto 1984). As pointed out by the authors, however, this model does not explain the wave-like aspect of synchronized clapping: a large dispersion of the initial clapping frequency would not lead to any synchronized state, while a smaller one would produce a persistent rhythmic applause as in fireflies, but the alternation between the two regimes is not theoretically expected. Interestingly, experimental observations of individual clapping behaviors reveal two possible modes of clapping: a loud and fast clapping mode, characterized by a large frequency distribution, and a slower one, characterized by a smaller dispersion of frequencies. An interpretation of the wave-like synchronization directly follows from these observations: the first mode is initially adopted by the audience and leads to a random applause regime, as expected by Kuramoto s model. Then, depending on the quality of the performance, the mood of the audience, or even cultural aspects of such behavior, a majority of the spectators may switch to the second clapping mode and give rise to coordinated applause. The resulting outcome is synchronized, but less noisy. The theoretical impossibility for an audience to combine loud and synchronized clapping leads to what the authors call the frustration of the system. Therefore, it may happen that the lower sound level which goes with coordinated clapping motivates enthusiastic audience members to clap louder, increase the frequency of clapping beyond a critical limit, where rhythmic coordination is possible, which causes an intermediate loss of collective coordination, until the slow mode re-establishes again. The example shows how the emerging collective pattern can be sensitive to particularities of the group members behavior. Compared to the coordination of fireflies exhibiting a continuous coordinated regime, people s behavior is subtler and the context of the situation influences the homogeneity of the clapping frequency, leading to the observed wave-like pattern. Interestingly, in addition to the rhythmic information transferred among people, this example exhibits a second kind of information communicating the intention to start rhythmic applause. A sufficient amount of people switching to the second clapping mode propagates this intention of coordinated clapping to the rest of the audience and carries them along in a collective expression of enthusiasm. Similarly to fish schools that are capable of adjusting their behaviors in a contextdependent way, audience members modulate their clapping behavior to achieve a particular collective outcome. In humans however, the process appears to be highly cultural, as synchronous clapping appears very often in Eastern Europe, while the phenomenon is rare in North America Case 3 : Lane Formation in Ants We have previously seen and discussed how ant colonies manage to build pheromone trails, i.e. some sort of invisible highways between their nest and a relevant point of their environment (typically a food source). Throughout the description of the phenomenon we assumed that only

324 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS indirect interactions between ants play a role. In certain species of ants however, the traffic over these trails may become so crowded that ants encounter frequent physical contacts and need to evade each other. In such a case, direct interactions also come into play as well. These are the origin of another emergent pattern called lane formation. A similar phenomenon was observed in humans (Helbing 1991) As described in the previous section, many ant species create chemical trail networks for exploration, emigration or transportation of resources. The functioning of such a system strongly depends on an effective management of traffic along the trails. In the neotropical army ants Eciton burchelli, the flow of traffic along trails is known to be particularly important (Schneirla 1971). Colonies of this species organize large hunting raids that may involve more than individuals. The main foraging trail is composed of two flows of ants: one corresponding to individuals moving from their nest to the end of the trail and the other corresponding to ants carrying prey and returning to the nest. Observations show that the bidirectional traffic in army ants organizes into lanes (Franks 1985): ants returning to the nest occupy the center of the trail, while ants leaving the nest predominantly use both margins of the trail, in this way protecting prey from enemies. How do the lanes emerge in this system? First, as described in the previous section, a dense traffic is established along the trail by means of indirect interactions via pheromones. This can be observed in many other ant species, so it does not explain the emergence of lanes itself. In case of army ants, an additional mechanism based on direct interactions is responsible for the spatial structuring. A single ant can perceive other ants at short distance and tends to turn away from them within this shortrange interaction zone. This kind of avoidance behavior can account for the formation of lanes in any kind of oppositely driven particles, as a simple result of physical interactions: individuals meeting others head on tend to move aside as a result of the repulsive effect. But as soon as they happen to move behind each other in the same direction, a more stable state has formed, in which side movements are no longer needed. The reinforcement of this incipient organization is based on the fact that the probability of an individual to leave an existing lane decreases as a function of the lane size. Therefore, a positive feedback loop supports the formation of lanes across the population. The theory predicts that the number and shape of lanes are functions of the available space, the inand outflows, and the fluctuation level (Helbing and Molnar 1995; Helbing and Vicsek 1999). However, traffic in army ants exhibits a fixed three-lanes structure regardless of external parameters. The reason for this unexpected configuration lies in the characteristics of ant behavior. Measurements of the turning rate of individual ants show a quantitative difference between the behavior of ants leaving the nest and those returning to it: the former exhibit a higher turning angle during avoidance maneuvers than the latter (Couzin & Franks 2002). This difference in the individual behavior of ants can potentially be explained by the fact that most of the ants returning to the nest are burdened with prey: due to their greater inertia, their turning requires more effort than

325 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS for unloaded ants leaving the nest. Simulations showed that this behavioral heterogeneity in the ant population is enough to make the system organize in three lanes: outbound ants moving along both margins of the trail and returning ants using the center (figure 4). Moreover, Couzin and Franks demonstrated that this spatial configuration vanishes when the population becomes homogeneous. Interestingly, the case of army ants demonstrates that, beyond the typical mechanism of lane formation, a simple behavioral specificity may result in significant characteristics of the collective pattern. Here, the difference between outbound and returning ants produces a slight asymmetry, when two ants of opposite flows interact. Although very weak, the bias gets reinforced, and individuals with a higher turning rate finally end up on the sides of the trail Case 4 : Lane Formation in Pedestrians Under everyday conditions, pedestrians walking in opposite directions also tend to organize in lanes of uniform walking direction (Milgram & Toch 1969; figure 1c). In terms of traffic efficiency, this segregation phenomenon reduces the number of encounters with oppositely moving pedestrians and enhances the walking comfort. Here, people interact by means of visual cues. The information exchanged between walkers is somehow related to the most comfortable area to walk through in order to avoid unnecessary speed decreases and avoidance maneuvers. Indeed, a pedestrian within a crowd tends to adjust his or her normal goal-oriented behavior with respect to other people perceived in the neighborhood. Based on such simple assumptions regarding the behavior of walkers, individual-based models of pedestrian behavior have contributed to develop an understanding of the collective dynamic of people within a crowd. In particular, the so-called social force model (Helbing 1991; Helbing and Molnar. 1995) was one of the first successful simulation models of self-organization in humans and has proved to be capable of capturing many complex patterns of motion, like the phenomena of lane formation, oscillations at bottlenecks and clogging effects (Helbing et al. 2005). The concept behind the model consists in considering that a given pedestrian moves toward his or her destination at a desired walking speed in the absence of other pedestrians, and that the pedestrian adjusts the normal behavior in case of visual interactions with other walkers: The pedestrian behaves as if he or she was repelled or attracted by other people or elements of the environment. The psychological motivation to move in a particular direction is captured by means of different kinds of forces: 1. a driving force, which lets the pedestrian move in his or her desired direction at the desired speed, 2. a set of repulsive forces, which makes him or her avoid other pedestrians and obstacles, and 3. a set of attractive forces responsible for the formation of pedestrian groups. At any moment, simulated pedestrians are subject to the sum of all forces simultaneously influencing him or her

326 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Although these behavioral rules appear simplistic compared to the wide variety of human behaviors, they are sufficient to cope with various unexpected crowd behaviors. The social force model was the first to reproduce the formation of lanes in simulations (figure 5). It predicts that the number of lanes emerging in bidirectional flows is influenced by various factors such as the street width and length, the pedestrian density, and the variance of walking speeds. However, the previous case of lane formation in ants showed how some behavioral characteristics are very likely to shape the resulting pattern into a particular spatial configuration. Are there any similar features in the motion of pedestrians? In fact, people are often reported to have a preferred side of walking. In continental Europe for example, lanes form more often on the right-hand side, while in Japan or Korea pedestrians are reported to walk on the left-hand side (figure 1c shows asymmetrical lane formation in London, biased toward the right-hand side). Game-theoretical models suggest that an emerging behavioral convention could be at the origin of this asymmetric configuration (Helbing 1991). According to this, it is more efficient to avoid someone on the side that is preferred by the majority. For such reasons, any random slight majority will cause further reinforcements, which ends up with a quite pronounced majority of people using the same avoidance strategy. This model implicitly assumes imitative strategy changes. One may also formulate this in terms of learning: Initially, pedestrians avoiding each other would have the same probability to choose the right or left-hand side. However, successful avoidance maneuvers would cause a more frequent use of the individual avoidance strategy. It turns out that such a reinforcement learning model eventually leads to an emergent asymmetry in the avoidance behavior, i.e. the probability to choose that side again on the following interactions is increased. Simulations actually predict that different side preferences would emerge in different regions of the world, as observed (Helbing et al. 2001) Two different levels of emergent behaviors are involved here at the same time. On short time scales, the way people avoid each other leads to the formation of lanes, which enhances the overall traffic efficiency. This phenomenon does not require any learning or memory about past interactions. In parallel, on longer time-scales, repeated interactions between pedestrians coupled to human learning abilities result in a further optimization of the traffic by establishing asymmetric avoidance behavior. This self-organization mechanism acts at the level of the population and induces a common bias in the people s behavior, which shapes the lanes into a particular configuration Discussion 4.1 General dynamics In this paper we have considered various features of self-organization processes in human and animal systems. In all examples of collective behaviors, the description of the individuals

327 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS behavioral rules and the related feedback mechanisms allowed us to better grasp the underlying dynamics. In particular, the separate analysis of individual and collective levels of observation could highlight a common scheme of description of these systems. From the microscopic point of view, the behavior of a single individual can be characterized by providing answers to the following questions: 1. How does a single individual behave in the absence of information about the perceived environment? 2. What kind of information does it acquire in its neighborhood? 3. How does it respond to this information? 4. How this information is transferred to other group members? Correspondingly, a model of the dynamics on the individual level can be constructed. First, each individual moves in its environment according to its spontaneous behavior. Here, we call spontaneous behavior the way in which group members move in the absence of new information regarding other individuals. For example, pedestrians usually have a spontaneous goal-oriented behavior. Without interactions, they simply move straight toward their next destination. Characteristics of this behavior are the speed of motion, the spontaneous probability to perform a given action, or environmental specificities that make the individual behave in a particular way. At the same time, an individual may acquire information about its local neighborhood. This can happen by means of direct or indirect information transfer. As a result, the individual produces a behavioral response that stimulates or inhibits a particular behavior. This behavioral change is often proportional to the intensity or the quality of the acquired information. Finally, this adjustment results in a local spreading of the information (intentionally or not). Once other individuals acquire the information, they adjust their behaviors in turn and propagate the information through the system. Table 1 summarizes the answers to the previous questions in the different examples discussed before. From the local interactions between individuals, one can derive the aggregate dynamics of such systems, thereby connecting the macroscopic and microscopic levels of observation. In the beginning, the group often remains in a disorganized state, until a weak perturbation appears within the system. A perturbation is the occurrence of novel information within the group (like the discovery of a food source, a new digged story or a predator strike), or could also have a random origin. Then, depending on the size of the group and the nature of information exchange among the individuals, a positive feedback loop can establish: the number of individuals sharing the new information and modulating their behavior accordingly increases in a non-linear way. Typically,

328 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS when an individual acquires the information "There is something above", it tends to look up, increasing the probability of other individuals to gain the information in turn and so forth. Eventually, negative feedback loops come into play (often induced by physical constraints like the limited number of individuals), and counterbalance the previous reinforcement. This helps to keep the amplification under control and yields a stabilization of a particular spatio-temporal pattern in the system. 4.2 Sensitivity to behavioral traits On the basis of the discussed cases, two features of individual-level behaviors often induce significant changes at the collective level: the specificities of the spontaneous behavior of individuals and those of the behavioral response to new information (which correspond to the questions 1 and 3 above) A key factor that may affect the spontaneous behavior of an individual is the presence of heterogeneity in its environment. The impact of such environmental specificities can turn out to be crucial, because a slight bias in individual behavior can be amplified through reinforcement loops and lead to major changes in the resulting pattern of behavior. For example, many animal species are strongly affected by the presence of physical heterogeneities in their environment (such as walls or edges). In fact, animals often search to maximize the amount of body area in contact with a solid surface, which in particular provides protection against potential predators. This individual sensitivity to the environment has, for example, a strong influence on trail formation in ants: it has been demonstrated that the final shape of the trail formed between two points is strongly biased by the presence of a wall (Dussutour et al. 2005). Owing to an individual ant s tendency to move along a boundary, the positive feedback loop is likely to reinforce this bias and to be triggered faster in the neighborhood of a wall. Consequently, the resulting pattern is often unbalanced with respect to the wall's location. Likewise, temperature variation (Challet et al. 2005) or local air flows (Jost et al. 2007) can shape the outcome of the colony in a very different way. Similar environment-induced biases are likely to play an important role in the formation of trails in humans. In fact, according to the related model, the spatial distribution of the pedestrians destination points directly determines the resulting trail network topology. In the same way, the presence of attractive or repulsive areas in the environment may shape the final trail system asymmetrically, even in case of symmetrical origin-destination flows. Similarly, the influence of public media is likely to induce biases in the behavior of digg.com users. The initial probability to read a new story can, therefore, become affected, slightly favoring actual events and pushing this news to propagate faster across the community. 36 In the same manner, specificities of the behavioral response of group members to new information

329 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS can create completely different emergent patterns. Several examples of this effect have been given in case of lane formation. Segregated lane patterns emerge both, in bidirectional traffic of pedestrians and certain species of ants. The study of these phenomena showed that the number of emerging lanes in pedestrians is variable, depending on the density of people, the width of the street or heterogeneity in walking speeds. In ants, however, there is a fixed three-lane configuration (two lanes along the margin of the trail and one in the center, regardless of external parameters. The underlying segregation mechanism in ants and pedestrians are the same. However, in ants one of the two flow directions is restricted by heavy loads and, thus, cannot flexibly respond to interactions. The limited turning capabilities of such ants produce an asymmetry in the system and finally lead to the observed three-lane configuration. Such a phenomenon is conceivable in humans as well, for example in situations where heavily loaded pedestrians walk in one direction and unloaded one moves in the opposite direction (e.g. observable at railway stations). Similarly, we have underlined the fact that pedestrian lanes have a preferred side of the street. This could be interpreted as result of a bias in pedestrian avoidance behavior during local interactions (Helbing 1995). This illustrates, again, how a small change in the way individuals respond to interactions can lead to major qualitative differences in the resulting collective pattern Collective information processing The above-described self-organization mechanisms constitute a powerful means by which a large number of individuals can achieve specific tasks that are often beyond the single individual s abilities, particularly when talking about animals. Although each group member acquires and spreads information locally, and this information is often limited and unreliable, the system as a whole fulfills higher-level tasks as if it had a global knowledge of the environment. Among the cases described before, three kinds of collective outcomes can be identified: sorting, optimization and consensus formation. Sorting: The dynamics underlying the website digg.com constitutes a typical example of a selforganized sorting procedure. The more relevant a story, the more often it is digged. Therefore, the number of diggs a story gets attests for its rank at a given moment of time. The website thus acts as an information sorting system. The sorting is dynamic: the relevance of a given story is a subjective feature that depends on the users interests, who choose to digg it or not. Consequently, according to the system s sensitivity to individual behaviors, the emerging classification of the stories is likely to vary between different communities, with respect to their cultural background, interests or goals. Various other self-organized systems generate such sorting of elements present in the environment. In some species of ants, for example, eggs are sorted out by workers according to their developmental stage and grouped into heaps of the same category. In this system, a positive

330 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS feedback loop arises from the tendency of ants to deposit the egg they carry closer to a heap of elements of the same size (Deneubourg et al. 1991). In human populations, the segregation of people of different origins, social class or opinions follows a similar kind of non-linear dynamics (Schelling 1969), and exhibits the main characteristics of a self-organized process. In that case, the sorting process acts on the involved individuals themselves rather than on external elements of the environment. Reaching consensus: Self-organized processes can also yield a group to reach a consensus. Achieving consensus on a given behavior is an essential aspect of collective organization, since it allows the individuals to act cohesively and prevents the group from splitting. Moreover, in most cases the consensus points toward the best alternative, which is often referred as the wisdom of crowds and based on an efficient collective integration of information (Surowiecki 2004). In the case of foraging ants, the mechanisms underlying the recruitment of new workers leads the colony to choose among foraging strategies of different profitability. The presence of several alternatives (e.g. several food sources or several paths toward a given food source) systematically results in a common decision about which option the colony will concentrate its activity on. The solution that is amplified faster is finally chosen at the expense of the others. In particular, if a given solution provides a higher benefit to the colony (e.g. a richer food source), signal modulation favors information related to this option, and the entire colony finally focuses on it. Similarly, the large number of fish that constitutes a school reaches a collective consensus on the swimming direction. In particular, models show that the larger a school, the more it will be receptive to the information provided by a small percentage of informed individuals, which finally induce the schools to move toward a relevant destination. The emergence of synchronized applause in an audience is another illustration, where numerous people achieve a consensus on their clapping rhythm Optimization: Finally, the third collective task highlighted by the case studies is the optimization of the group s activities. The formation of lanes in the bidirectional movements of ants and pedestrians is a form of traffic optimization. In both systems, repeated encounters with other individuals moving in opposite direction constitute a serious disturbance of efficient and collective motion. The organization into lanes reduces the interaction frequency and the number of necessary braking or avoidance maneuvers. In such a way, the traffic efficiency is optimized. In humans, the additional emergence of walking conventions, such as a common preferred side of avoidance, further enhances again the traffic efficiency (Helbing et al. 2001). Likewise, the occurrence of trail systems allows pedestrians to optimize their walking comfort in two ways: first, because trails are created by trampling vegetation and, thus, provide flat ground over which the ease of walking is increased. And second, because it appears that the topology of the trail network emerging between several entry and exit points comes close to an optimal way system in terms of minimizing the percentage of detours of paths. Interestingly, the resulting trail network is related to the environment configuration: the

331 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS more a way is frequented, the most it becomes comfortable and the shorter are the paths toward other points (i.e. the smaller are the compromises). Throughout this paper, we differentiate direct and indirect information transfer. In the accomplishment of consensus, sorting and optimization tasks, both kinds of communication can be used. This implies questions regarding the specificities of the two communication methods in the execution of the different tasks. The examples of news sorting at digg.com, path selection in ants and trail formation in pedestrians illustrate the usage of indirect information transfer in the achievement of the different kinds of tasks. The prime specificity of indirect communication is that the collective solution to a given problem is somehow printed in the environment. Diggs popularity distribution, pedestrian trails and pheromone paths remain in the environment for a relatively long period of time, even after the activity has ceased. Therefore, solutions emerging from indirect interactions are characterized by a high level of robustness to external perturbations. It is known, for example, that Pharaoh s ants make use of long lasting pheromones that remain attractive for several days to locate persistent food sources and ensure their exploitation from day to day, even when the foraging activity has to temporarily cease (Jackson 2006). However, robustness to changes also implies lower flexibility. This shortcoming can be illustrated by the fact that, once an ant colony has selected a food source and built a trail toward it, it is usually not able to redirect its activity toward a better source that would appear afterward, and stays stuck in a suboptimal solution (Pasteels et al. 1987). In such a way, indirect communication turns out to be particularly well adapted to stable environments with relatively persistent sources of information. For example, human trails are usually strongly imprinted on the ground, which is suitable to shape urban green spaces, since entry and exit points barely evolve in time In contrast, direct information transfer rather provides higher reactivity to external changes and appears more adapted to volatile information sources. The consensus on the swimming direction adopted by fish schools is likely to suddenly change in response to the occurrence of novel information, such as a predator strike. Unlike indirect communication, information directly spreads from one individual to its neighbors, and the spatial proximity of the individuals allows the information to travel rapidly among them. In pedestrians, direct interactions allow people to optimize their movements in many regards, and lead to adapted collective answers to environmental perturbations such as obstacles or bottlenecks (Helbing et al. 2005). On the other hand, this higher flexibility often implies a lower level of selection of information, since weak random fluctuations can be amplified at the group level. In fish schools, for example, this may create useless movements that can be costly (Couzin 2007). In general, the higher the interaction range, the less sensitive is the system to small perturbations, since information is locally integrated among a larger number of individuals. In audiences, for example, the acoustic nature of clapping signals exchanged between individuals facilitates a large interaction range and allows people to keep a constant common

332 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS 1 2 clapping rhythm during the synchronized phase, regardless of the local clapping imprecision. 4.4 Self-Organized dynamics and individual complexity Throughout this paper, we relied on various human and animal populations to explore the mechanisms underlying the emergence of collective patterns. The described systems differ in many regards, and in particular in terms of cognitive abilities of the individuals. When investigating selforganization processes, however, it is common to reduce the level of complexity of group members to a set of simple rules. Therefore, the question of the relevance of this approach for sophisticated individuals (such as humans) arises. Moreover, which additional features can result from higher cognitive abilities at the level of the individual? Obviously, the presence of common fundamental feedback mechanisms attests that some collective processes exhibited in human populations can be explained without invoking complex decisionmaking abilities at the level of the individual. The success of simplified behavioral models in reproducing many emergent behaviors in crowds demonstrates that higher cognitive abilities are not required to capture the self-organized dynamics (Ball 2004). In most cases, people react to wellknown situations in a more or less automatic manner, promoting relatively predictable collective patterns similar to those produced in animal societies. However, considering the wide variety of potential behavioral responses of complex beings, it is likely that individual complexity may play a role in the collective dynamics. Individual learning is a feature that can interfere with the collective dynamics. Human beings for example, can quickly learn from past experiences, and adapt to new situations. As an illustration, we previously highlighted that pedestrian interactions may be biased by a side preference. This can be explained by considering the emergence of a behavioral convention, due to the ability of people to learn avoidance strategies from repeated interactions. As a result, what individuals learn affects the configuration of the emerging pattern. Since the learning process can be affected by numerous factors, behavioral conventions develop in different ways, depending on the geographical area: while Western European populations learned that avoidance on the right-hand side is preferable, some Asian countries similarly developed a left-hand preference. Such learning processes play a role in animal societies as well, since many individual animals can also learn from their past experiences. Examples of learning involved in self-organized processes can be seen in the case of specialization of workers in insect societies. The more an individual performs a given task, the more it gets used to it and the faster it responds to this task in the future, leading to the emergence of specialized workers (Theraulaz et al. 1998). Learning is not a specificity of human beings, but people are more prone to this kind of adaptation and new behavioral biases can evolve on shorter time scales, and for a large variety of different settings. Interestingly, behavioral conventions are themselves self-enforcing and can spread across the population in a non-linear way, with no need of central authority (Helbing 1992; Young 1996). In terms of self-organized dynamics,

333 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS such a learning process induces a common behavioral bias among individuals (by acting on the socalled spontaneous behavior, or on the behavioral response). Although weak, such a bias, affecting all individuals, is amplified through reinforcement loops, eventually resulting in a qualitative change of the collective answer (see section 4.2) Conclusion In this contribution, we showed how a wide set of self-organized phenomena can be described and understood by means of local interaction mechanisms. Repeated interactions among individuals, random fluctuations, reinforcement loops and negative feedbacks are the basis of self-organization processes. The fact that a common approach can describe and explain the dynamics of various emerging collective behaviors strengthens the idea that these have a similar root, although the individuals involved differ in size, aims or cognitive capacities. The discussion of various cases highlighted that individuals exchange their knowledge by mean of direct or indirect interactions. This local exchange of information is integrated at the scale of the group by mean of feedback loops and produces adapted collective answers to various kinds of problems. In such a way, self-organization processes allow single individuals to gain higher capabilities in terms of perceptual range, knowledge about the environment and cognitive abilities. Swarms and crowds consequently manage to take advantage of their numbers to cope with their complex environment and achieve sorting tasks, optimize their activities or reach consensual decisions. Furthermore, through learning processes, individuals can develop behavioral specificities that may have additional effects on the collective dynamics. In humans for example, the emergence of behavioral conventions can induce a common behavioral bias in the population that enhances in turn the self-organized dynamics

334 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS 1 References Aoki I A simulation study on the schooling mechanism in fish. Bulletin of the Japanese Society of Scientific Fisheries 40: Ball P The physical modelling of human social systems. Complexus. 1: Ball, P Critical Mass: How one thing leads to another. William Heinemann, London. Beckers R. Deneubourg J.L. Goss S. and Pasteels J.M Collective decision making through food recruitment. Insectes Sociaux 37: Beckers R. Deneubourg J.L. and Goss S Modulation of trail laying in the ant Lasius niger (Hymenoptera: Formicidae) and its role in the collective selection of a food source. Journal of Insect Behavior 6: Ben-Jacob E. Schochet O. Tenenbaum A. Cohen I. Cziròk A. and Vicsek T Generic modelling of cooperative growth patterns in bacterial colonies. Nature 368: Bonabeau E. Theraulaz G. Deneubourg J. L. Aron S. and Camazine S Self-organization in social insects. Trends in Ecology and Evolution 12: Buck J. and Buck E Synchronous fireflies. Scientific American. 234:74-85 Camazine S. Deneubourg J.L. Franks N.R. Sneyd J. Theraulaz G. and Bonabeau E Selforganization in biological systems. Princeton University Press, Princeton. Challet M. Jost C. Grimal A. Lluc J. and Theraulaz G How temperature influences displacements and corpse aggregation behaviors in the ant Messor sancta. Insectes Sociaux 52: Couzin I.D Collective minds. Nature 445:715 Couzin I.D. and Franks N.R Self-organized lane formation and optimized traffic flow in army ants. Proceedings of the Royal Society B Biological Sciences. 270: Couzin I. D. and Krause J Self-organization and collective behavior in vertebrates. Advances in the Study of Behavior 32:1 75. Couzin I.D. Krause J. James R. Ruxton G.D. Franks N.R Collective memory and spatial sorting in animal groups. Journal of theoretical Biology. 218:1-11 Couzin I.D. Krause J. Franks N.R. Levin S.A Effective leadership and decision-making in animal groups on the move. Nature 433: Deneubourg J.L. Goss S. Franks N. Sendova-Franks A. Detrain C. and Chrétien L The dynamics of collective sorting: robot-like ants and ant-like robots. in From Animals to Animals: Proceedings of the First International Conference on Simulation of Adaptive Behavior, J.-A. Meyer and S. Wilson, eds. MIT Press, Cambridge, MA. Dussutour A. Deneubourg J.L. and Fourcassié V Amplification of individual preference in a social context: the case of wall-following in ants. Proceedings of the Royal Society B 272:

335 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Franks N.R Reproduction, foraging efficiency and worker polymorphism in army ants. In: Experimental behavioural ecology (eds. M. Lindauer & B. Hölldobler). Fischer-Verlag,Stuttgart and New York. Garnier S. Gautrais J. and Theraulaz G The biological principles of swarm intelligence, Swarm Intelligence 1:3-31 Goldstone R.L. and Roberts M.E Self-organized trail systems in groups of humans. Complexity. 11:43-50 Grassé P.P La reconstruction du nid et les coordinations interindividuelles chez Bellicositermes netelensis et Cubitermes sp. La théorie de la stigmergie: essai d interpretation du comportement des termites constructeurs. Insectes Sociaux 6:41-83 Helbing D A mathematical model for the behavior of pedestrians. Behavioral science 36: Helbing D A mathematical model for behavioral changes by pair interactions. In Haag G. Mueller U. and Troitzsch K.G. (eds.) Economic Evolution and Demographic Change Springer, Berlin. Helbing D. Molnar P. Farkas I. and Bolay K Self-organizing pedestrian movement. Environment and planning B 28: Helbing D. and Molnar P Social force model for pedestrian dynamics. Physical review E. 51: Helbing D. and Huberman B Coherent moving states in highway traffic. Nature. 396: Helbing D. Farkas I. and Vicsek T Simulating dynamical features of escape panic. Nature. 407: Helbing D. Keltsch J. Molnar P Modelling the evolution of human trail systems. Nature. 388: Helbing D Quantitative sociodynamics: Stochastic Methods and Models of Social Interaction Processes. Kluwer Academic, Dordrecht. Helbing D. and Vicsek T Optimal self-organization. New Journal of Physics 1: Helbing D. Buzna L. Johansson A. Werner T Self-organized pedestrian crowd dynamics: Experiments, simulations, and design solutions. Transportation science 39:1-24 Higdon J.J.L. and Corrsin S Induced drag of a bird flock. American Naturalist 112: Hölldobler B. and Wilson E.O The ants. Harvard University Press. Huth A. & Wissel C The simulation of the movement of fish schools. Journal of theoretical biology 156: Jackson D.E. and Ratnieks L.W Communication in ants. Current Biology 16: Jander R. and Daumer K Guide-line and gravity orientation of blind termites foraging in the open. Insectes Sociaux 21:45-69 Jost C. Verret J. Casellas E. Gautrais J. Challet M. Lluc J. Blanco S. Clifton MJ. and Theraulaz G The interplay between a self-organized process and an environmental template: corpse

336 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS clustering under the influence of air currents in ants - Journal of the royal society interface 4: Karsenti E Self-organization in cell biology: a brief history. Nature 9: Kuramoto, Y Self-entrainment of a population of coupled oscillators. In Int. Symp. On Mathematical Problems in Theoretical Physics, vol.39. Berlin:Springer. Kuramoto, Y Chemical oscillationes, waves and turbulence. Berlin:Springer May R.M Flight formations in geese and other birds. Nature 282: Milgram S. Bickman L. and Berkowitz L Note on the drawing power of crowds of different size. J. Pers. Soc. Psychol. 13:79-82 Milgram S. & Toch H Collective behaviour: crowds and social movements. In The handbook of social psychology (ed. G.Lindzey & E.Aronson), vol. IV. Neda Z. Ravasz E. Vicsek T. Brechet Y. Barabasi A.L Physics of the rythmic applause. Physical Review E. 61: Newman M.E.J Spread of epidemic disease on the networks. Physical Review E 66: Nicolis G. and Prigogine, I Self-organization in nonequilibrium systems. Wiley, New-York Shapiro J.A Bacteria as multicellular organisms. Scientific American 258:82-89 Parrish J.K. Viscido S.V. and Grünbaum D Self-organized fish schools: An examination of emergent properties. Biol Bull. 202: Partridge B.L The structure and function of fish schools. Scientific American 246: Pasteels J.M. Deneubourg J.L. and Goss S Self-organization mechanisms in ant societies I.: the example of food recruitment. In J.M. Pasteels and J.L. Deneubourg, eds., From Individual to Collective behaviour in Social Insects. Basel: Birkäuser Verlag. Schelling T.C Models of segregation. The American Economic Review 59: Schneirla T.C Army ants: a study in social organization. W. H. Freeman, San Francisco. Shaw E The schooling of fishes. Scientific American, 205: Strogatz S Sync: The Emerging Science of Spontaneous Order. Hyperion, New York. Sumpter D.J.T The principles of collective animal behaviour. Philosophical Transactions of the Royal Society B 361:5 22 Surowiecki J The wisdom of crowds. Doubleday, New York Theraulaz G. Bonabeau E. and Deneubourg J.L Response thresholds reinforcement and division of labor in insect societies. Proceedings of the Royal Society of London Series B- Biological Sciences, 265: Wu F. and Huberman B Novelty and collective attention. Proceedings of the National Academy of Sciences. 104: Wyatt T.D Pheromones and animal behaviour: communication by smell and taste. Cambridge University Press. Young P The economics of convention. Journal of economic perspectives 10:

337 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Figures & Table Table 1: Summary of case studies 4 5 SYSTEM People looking up (Milgram experiment) SPONTANEOUS BEHAVIOR Weak probability to look up RELATED INFORMATION "Direction of a point of interest" Digg.com Read random stories "Interesting news" Foraging ant trails Pedestrians trails Fish schooling Clapping synchronization Lane formation in ants Lane formation in pedestrians Random move Biased by environment (e.g. borders, walls) Goal-oriented motion Biased by environment (attractive places) Turns randomly Potentially biased toward attractive places (food source, migration route) Clap at own rhythm Goal-oriented motion along a pheromone trail Goal-oriented motion "Location of a food source" "Short and comfortable path" "Moving direction" Clapping rhythm "Faster moving area" "Faster and comfortable walking area" BEHAVIORAL RESPONSE - Increased probability to look up - Weighted by the number of people looking up - Increased probability to read the news - Weighted by the number of diggs - Attraction along the trail -Weighted by concentration of pheromone - Attraction toward the trail - Weighted by trail visibility - Move in the average perceived direction. - Adjust clapping to perceived average - Change moving direction - Weighted by amount of load - Move away from perceived people INFORMATION SUPPORT - Direct information transfer - Visual signals - Indirect information transfer - Virtual signals (diggs) - Indirect information transfer - Chemical signals (pheromones) - Indirect information transfer - Physical signals (alteration of the ground) - Direct information transfer - Visual signals combined with water displacement - Direct information transfer - Acoustic signals - Direct information transfer - Physical contacts - Direct information transfer - Visual signals

338 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Figure 1: Examples of self-organized phenomena in human and animal populations. a) Trail formation and collective path selection in ants. The figure refers to an experiment with a two-paths-bridge linking the nest and a food source. b) Emergence of a torus structure in a school of fish, consisting of individuals circling around an unoccupied core (picture bought from istockphoto.com) c) Segregation of a bidirectional flow of pedestrians into lanes of people with a common walking direction (from Helbing et al. 2005) d) Human trails formed on the university campus of Stuttgart-Vaihingen (from Helbing et al. 1997)

339 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Figure 2: Observed dynamics for a story on digg.com during one day Top: Observed digg-rate for a given story. The sudden amplification of interest after 5 hours is due to the reinforcement effect of increasing the number of diggs, while the following decay results from the decreasing attention of users. Bottom: Cumulated number of diggs illustrating the antagonist effects of positive and negative feedbacks (same dataset)

340 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Figure 3: Recruitment dynamics in ants Linepithema humile. Observation of number of ants involved in a foraging task, illustrating the emergence of a trail between the nest and a food source (experimental data). While an increasing pheromone concentration attracts more and more ants along the trail during the first moments, the jamming that occurs around the food source at higher density counterbalances the previous amplification and stabilizes the flow of ants at a constant level

341 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Figure 4: Lane formation in a simulation of bidirectional traffic of army ants Eciton burchelli Left: Snapshot of simulation (after Couzin and Franks 2002). The blue arrows represent ants loaded with prey and going back to the nest, while red arrows represent ants leaving the nest. Right: Distribution of ants of the two flows with respect to the trail center, illustrating the spatial segregation of inbound and outbound ants

342 ANNEXE B. TRANSFERTS D INFORMATION ET COMPORTEMENTS AUTO-ORGANISÉS DANS LES FOULES ET LES ESSAIMS Figure 5: Lane formation in pedestrians Snapshot of a simulation of bidirectional flows of pedestrians, reproducing the emergence of lanes (after Helbing and Molnar 1995)

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344 ANNEXE C. EXTRACTION EXPÉRIMENTALE DE LOIS D INTERACTION CHEZ L HOMME : LE CAS DES PIÉTONS Annexe C Extraction expérimentale de lois d interaction chez l Homme : le cas des piétons 325

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346 ANNEXE C. EXTRACTION EXPÉRIMENTALE DE LOIS D INTERACTION CHEZ L HOMME : LE CAS DES PIÉTONS tions, we have investigated the nature of the interaction mechanisms at work when two pedestrians approach each other. For this, subjects were video-recorded in an experimental corridor in three different experimental conditions: (1) individual motion of a single pedestrian (Fig. 1a), (2) individual motion in response to a pedestrian standing in the middle of the corridor (Fig. 2a), and (3) individual motion of two pedestrians moving in opposite directions and evading each other in the middle of the corridor (Fig. 2b). The first condition was mainly used to calibrate the measurement method, which included a correction for the angular distortion of the cameras [34] and an appropriate projection of three-dimensional pedestrian motion on the two-dimensional area of the corridor. The accuracy of the measurement was high enough to determine the lateral oscillations related with each single stride, which have afterwards been smoothed out for a better estimation of the trajectories (see Materials & Methods). The behavioral rules derived from the above experiments were finally implemented in a binary interaction model, the predictions of which have been compared to the experimental result and to empirical data of pedestrian flows recorded in a crowded street. Results Behavioral mechanisms. According to the social force concept, the observed velocity change of pedestrians results as the sum of three different components: (1) the internal acceleration behavior f i 0 of the reference pedestrian i, (2) the effects of the corridor walls f i wall on this pedestrian, and (3) the force f ij reflecting the reaction of pedestrian i to another pedestrian j, which serves to reach a smooth avoidance behavior without collisions. The experimental condition 1 was used to calibrate the internal acceleration behavior. Reference [11] suggested the acceleration equation f i 0 (t) = d vi dt = v0 i e i 0 v i(t), [1] τ describing the adaptation of the current velocity of pedestrian i to a desired speed vi 0 and a desired direction of motion e i 0 (given by the direction of the corridor). According to Fig. 1, this equation describes the acceleration behavior well. The desired velocities vi 0 are normally distributed with an average value of 1.29±0.19m/s (mean ± std. dev.), and the relaxation time amounts to τ =0.54 ± 0.05 seconds (see Fig. 1b). Conditions 2 and 3 were then used to determine the exact trajectories when avoiding a standing or moving pedestrian. By f i(t) = d vi dt f 0 i (t), [2] we have then determined the combined effects of interactions with the other pedestrian j and the corridor walls. Based on the findings in Ref. [21], we have specified the interactions with the corridor walls in an exponential way, as a function of the distance d perpendicular to a wall: fi wall (d )=ae d /b, with a = 3 and b =0.1 (see Materials & Methods). This finally allowed us to extract the pedestrian repulsive force f ij resulting from the interaction with the other pedestrian j via f ij(t) = f i(t) f i wall (t). [3] Figure 3 shows the vector field f ij obtained by averaging over all pedestrian interactions in condition 2. It is visible that removing the effects of acceleration and walls yields a clearly structured vector field which can be interpreted as interpersonal repulsive interaction force. In contrast to previous heuristic specifications, however, the interaction force is not the gradient of an interaction potential, otherwise the curl function of the vector field would have to vanish exactly [35]. While this is approximately the case to the sides of pedestrian i, it turns out that there is an area in front of the pedestrian, where the curl function has finite values (Fig. 3b). This is the area where pedestrians decelerate and choose the side on which they want to pass. Outside of it, they mainly adjust their direction to avoid collisions while continuing at their previous speed. For this reason, we interpret this area as decision area: for head-on encounters, it is necessary to take a binary decision, whether to evade the other pedestrian on the left-hand side or on the right-hand side. Remarkably, our experiments show that the resulting choice of pedestrians is biased. Pedestrians avoiding a static obstacle have a slight preference for the right-hand side,but the asymmetry is significantly more pronounced if both pedestrians are moving (see blue bars in Fig. 4). This shows that the mutual adjustment of motion of two interacting pedestrians intensifies the individual left/right bias. Modeling inter-individual interactions. The binary-decision nature of avoidance maneuvers is actually the reason for the fact that potential forces cannot work well. It calls for another representation, based on forces f v and f θ, respectively, describing the deceleration along the interaction direction t ij and directional changes along n ij, where n ij is the normal vector of t ij oriented to the left [36]. We define the interaction direction by t ij(t) = D ij/ D ij(t) with D ij(t) =λ( v i v j)+ e ij to take into account both, the direction ( v i v j) of relative motion and the direction e ij =( x j x i)/ x j x i, in which pedestrian j is located, where x i(t) is the location (center of mass) of pedestrian i at time t (see figure 6 in Supp. Info. for a descriptive sketch). The weight λ reflects the relative importance of the two directions, and has been estimated to be λ =2.0 ± 0.2 (see Materials & Methods). If d ij = x j x i denotes the distance between two pedestrians i and j and θ ij the angle between the interaction direction t ij and the vector ( x j x i) pointing from i to j, we can cast the results of our experiments into the mathematical functions f v(d, θ) = Ae d/b (n Bθ) 2 [4] and f θ(d, θ) = AKe d/b (nbθ)2 [5] (see Fig. 3). We have dropped the indices i and j, K = θ/ θ is the sign of θ, and A, B, n, n are model parameters. Equation (4) represents an exponential decay of the decelerating force with distance d. The decay is faster for large values of θ, i.e. towards the sides of the pedestrian. Therefore, the deceleration effect is strongest in front, in accordance with the decision area described above. Through the 2 Footline Author 327

347 ANNEXE C. EXTRACTION EXPÉRIMENTALE DE LOIS D INTERACTION CHEZ L HOMME : LE CAS DES PIÉTONS dependence on B =0.35 D, it is increased in the interaction direction by large relative speeds v i v j, while the repulsion towards the sides is reduced. This reflects the fact that fast relative motions require evading decisions in a larger distance, which also means that the same amount of displacement to the side (basically the shoulder width plus some safety distance) can be gained over a longer way, requiring a weaker sideward force (compare Fig. 2a with 2b). Note that Eq. (5) is analogous to Eq. (4) for the angular force, just with another parameter n < n, which corresponds to a larger angular interaction range. The prefactor K = θ/ θ takes into account the discontinuity in the angular motion, reflecting the binary decision to evade the other pedestrian either to the left or to the right. The effect becomes clearer, if we sum up over all terms contributing to the interaction force f ij, resulting in f ij(d, θ) = Ae d/bh e (n Bθ) 2 t + θ i 2 θ e (nbθ) n. [6] Accordingly, we have an exponential decay of the repulsive force with the pedestrian distance d, where the interaction range B depends on the relative speed. The angular dependence and anisotropy of the interactions is reflected by the θ-dependence. Model parameters were estimated as A =4.5 ± 0.4, n =2.0 ± 0.3 and n =3.0 ± 0.6 (see Materials & Methods). Finally, we have to represent the observed asymmetry in the avoidance behavior, which is reflected by the somewhat higher proportion of pedestrians evading on one side. The simplest model reproducing this observation replaces the angle θ in equation (6) by θ + Bɛ, where ɛ =0.005 > 0 corresponds to a preference for the right-hand side. The dependence on B reflects the fact that pedestrians make a faster side choice when the relative speed increases. Note that in other countries like Japan, the traffic can organize on the left-hand side [29], which would be characterized by a negative value of ɛ. Comparison of model predictions and observations. After the above model was fitted to the experimental data, we have tested it through a series of computer simulations involving two pedestrians in situations similar to conditions 2 and 3. Our results show that the shape of the trajectories during an avoidance maneuver, as well as the side choice proportions are in good agreement with the empirical data collected in our experiments (Fig. 4). This demonstrates that the repulsive force and the side preference have been well specified. The non-trivial reinforcement of the side preference observed in condition 2 and 3 is also well-reproduced by the model. We then used the model to study the interaction of larger numbers of pedestrians, with many simultaneous interactions. It was assumed that the force applied to each pedestrian is simply given by the sum of all interactions with other pedestrians, but restricting the number of interaction partners a pedestrian responds to did not improve our results significantly for the above model (while the situation is different for other force specifications). The superposition of binary interaction forces allowed us to compare computer simulations of pedestrian counterflows with empirical data of people moving in opposite directions in a pedestrian zone (see Materials & Methods and Fig. 5a ). We observed that the empirical flows, as well as the simulated ones, exhibit a very pronounced left-right asymmetry in street usage (Fig. 5b). In contrast, simulations for a uni-directional flow generate a uniform distribution of pedestrians (see the inset in Fig. 5b). We also found an almost uniform distribution for bidirectional pedestrian flows of low density, which supports the idea that a minimum amount of interactions is necessary for the flow separation to emerge (see Fig. 7 in Supp. Info.). Discussion Beyond explaining collective behaviors as self-organization phenomena based on individual interactions, we advocate for an experiment-driven rather than heuristic modeling of human interactions. Our experimentally well-controlled tracking study of pedestrian motion has revealed detailed mechanisms and functional dependencies of pedestrian interactions in space and time. While the concept of a social force turned out to be applicable in principle, some revisions of previous assumptions were needed: (1) Potential forces must be replaced by the superposition of a deceleration force with an angular force. The deceleration force applies to head-on encounters, when a binary decision between the right-hand and the lefthand side must be made, while directional adjustments apply otherwise and afterwards. (2) A slight bias in evading maneuvers towards one side supports a symmetry-breaking in the binary decision situation of head-on encounters. The left/right bias may be viewed as behavioral convention, emerging due to the fact that coordination between pedestrians during avoidance maneuvers is alleviated, if individuals prefer to choose the same passing side [33]. Our results show that the amplification of the side preference at the crowd level requires the combination of asymmetric behavior with frequent interactions to quantitatively reproduce our empirical data on side preference. Therefore, the left/right bias is much more pronounced when people have to mutually adjust to each other (see condition 3). This also explains the unexpected observation of higher efficiency in some situations of counterflows [37, 29]. Our findings may be used to assess the suitability of pedestrian facilities and escape routes under various conditions, such as the movement of homogeneous as compared to multinational crowds with different side preferences (e.g. during international sports events). This could significantly affect the efficiency of pedestrian flows during mass events or the functionality of heavily frequented buildings such as railway stations, if not taken into account in the planning of events and the dimensioning of public spaces and facilities. Even more importantly, our paper demonstrates the potential of experiment-driven modeling techniques for the discovery of human interaction laws and collective phenomena emerging from them. Note that a multivariate linear regression approach would not be able to identify laws resulting in selforganized collective behaviors, as these require non-linear interactions. Therefore, it is necessary to quantitatively extract the nonlinear dependencies from the data. In a similar way, one could address a multitude of other problems like the simultaneous interaction with several other people, or communication and decision-making behaviors that may explain phenomena from collective attention [38] over collective opinion formation [39] up to social activity patterns [40]. Footline Author PNAS Issue Date Volume Issue Number 3 328

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350 ANNEXE C. EXTRACTION EXPÉRIMENTALE DE LOIS D INTERACTION CHEZ L HOMME : LE CAS DES PIÉTONS Figure legends Fig. 1. (a) Snapshot of the experimental setup. Red circles indicate the location of cameras. (b) Calibration of the driving force on the basis of average time-dependant pedestrian velocity in the absence of interactions. The fitted curve (blue) is given by the acceleration equation (1). The parameters were estimated as τ = 0.54 ± 0.05 s and vi 0 =1.29 ± 0.19 m/s after a reaction time of 0.35s. Fig. 2. Observed trajectories in condition 2 (N=148) and condition 3 (N=123). One of the pedestrians (moving from left to right) is represented in blue, while the other one (either standing in (a) or moving in opposite direction in (b) ) is represented in red. Fig. 3. Data processing. The area in front of pedestrian i is first partitionned into a squared grid. The repulsive force f ij, reflecting the interaction of pedestrian i with pedestrian j is calculated according to Eq. (3). (a2) The average value f ij of all measurements for a given square is finally represented by a vector originating from the center of this square. (b) The final force field for condition 2 is determined by applying the above procedure to a 15x25 grid. The color coding indicates the absolute curl value of the force field. (c) For a given angle θ, the function f θ (d, θ) decreases exponentially with d, providing the equation f θ = A(θ)e bd, where b is a parameter to be fitted. (d) A(θ) can then be approximated by the equation ake (cθ)2, where K is the sign of θ and a, c are fit parameters. Fig. 4. Computer simulations as compared to experimental observations during conditions 2 and 3. In (a) and (b), the blue lines correspond to the average observed trajectories, with pedestrians moving from left to right. The blue dashed lines indicate the standard deviation. Red lines correspond to the average trajectories obtained after 1000 simulations (with parameter values A =4.5, n =2, n =3and ɛ =0.005). Bars in (c) and (d) indicate the proportions of choosing the left- or right-hand side in an avoidance maneuver during the experiment (blue) or in our simulations (red). Fig. 5. Asymmetry of bidirectionnal pedestrian traffic. As sketched in (a), six areas were distinguished for the measurements: 1) left sidewalk, 2) and 3) left side of the walkway, 4) and 5) right side of the walkway and 6) right sidewalk. Left and Right are presented with respect to the walking direction. The sidewalks were occupied by a small number of standing pedestrians. The blue bars in (b) show the proportion of observed pedestrians walking in each area, while the red bars are simulation results (with same parameter values as in Fig.4). The inset illustrates the symmetric simulation results obtained for a unidirectional flow for comparison. Supplementary Information Fig. 6. Description of the model framework. (a1) Pedestrian i with velocity vector v i interacts with pedestrian j with velocity vector v j. (a2) Two components have to be taken into account: the vector e ij giving the direction in which j is located, and the vector v i v j delineating the relative motion of pedestrians. (a3) Finally, the interaction direction t is the normalized vector taking into account both components : t = D/ D with D = λ( v i v j)+ e ij. The vector n is perpendicular to t, oriented to the left and (d, θ) are the polar coordinates of j in the so-defined frame of reference. Fig. 7. Effect of the density on the asymmetry of bidirectional traffic in simulations. (a) For a small flow value (0.1 ped/s in each walking direction), the distribution of pedestrians in the street is almost uniform. (b) A higher flow value (0.65 ped/s) genetrates a pronounced asymmetry in street usage. The six zones correspond to those sketched in Fig. 5a. The results are given after 50 simulation runs of 10 minutes each. 6 Footline Author 331

351 Speed (m/s) ANNEXE C. EXTRACTION EXPÉRIMENTALE DE LOIS D INTERACTION CHEZ L HOMME : LE CAS DES PIÉTONS Figure 1 a b Data+std. dev. Simulation Time (s) Figure 2 1 a Condition b Condition Footline Author PNAS Issue Date Volume Issue Number 1 332