Abstract
In this paper, we present discrete-time, nonspatial, macroscopic models able to capture the dynamics of collective aggregation experiments using groups of embodied agents endowed with reactive controllers. The strength of the proposed models is that they have been built up incrementally, with matching between models and embodied simulations verified at each step as new complexity was added. Precise heuristic criteria based on geometrical considerations and systematic tests with one or two embodied agents prevent the introduction of free parameters into the models. The collective aggregation experiments presented in this paper are concerned with the gathering and clustering of small objects initially scattered in an enclosed arena. Experiments were carried out with teams consisting of one to ten individuals, using groups of both constant and time-varying sizes. In the latter case, the number of active workers was controlled by a simple, fully distributed, threshold-based algorithm whose aim was to allocate an appropriate number of individuals to a time-evolving aggregation demand. To this purpose, agents exclusively used their local perception to estimate the availability of work. Results show that models can deliver both qualitatively and quantitatively correct predictions and they represent a useful tool for generalizing the dynamics of these highly stochastic, asynchronous, nonlinear systems, often outperforming intuitive reasoning. Finally, in addition to discussions of small prediction discrepancies and difficulties in generating quantitatively correct macroscopic models, we conclude the paper by reviewing the intrinsic limitations of the current modeling methodology and by proposing a few suggestions for future work.
Similar content being viewed by others
References
Agassounon, W., Martinoli, A., and Goodman, R.M. 2001. A scalable, distributed algorithm for allocating workers in embedded systems. In Proc. IEEE Int. Conf. on System, Man and Cybernetics, Tucson, AR, pp. 3367-3373.
Agassounon, W. and Martinoli, A. 2002. Efficiency and robustness of threshold-based distributed allocation algorithms in multi-agent systems. In Proc. First Int. Joint Conf. on Autonomous Agents and Multi-Agent Systems, Bologna, Italy, pp. 1090-1097.
Agassounon, W. and Martinoli, A. 2002. A macroscopic model of an aggregation experiment using embodied agents in groups of time-varying sizes. In Proc. IEEE Int. Conf. on System, Man and Cybernetics, Hammamet, Tunisia.
Beckers, R., Holland, O.E., and Deneubourg, J.-L. 1994. From local actions to global tasks: Stigmergy and collective robotics. In Proc. Fourth Workshop on Artificial Life, R. Brooks and P. Maes (Eds.), Boston, MA, pp. 181-189.
Beshers, S.N. and Fewell, J.H. 2001. Models of division of labor in social insects. Annual Review of Entomology, 46:413–440.
Beni, G. and Wang, J. 1989. Swarm intelligence. In Proc. Seventh Annual Meeting of the Robotics Society of Japan, Tokyo, Japan, pp. 425-428.
Bonabeau, E., Theraulaz, G., and Deneubourg, J.-L. 1998. Fixed response thresholds and regulation of division of labour in insect societies. Bulletin of Mathematical Biology, 60:753–807.
Bonabeau, E., Dorigo, M., and Theraulaz, G. 1999. Swarm Intelligence: From Natural to Artificial Systems, SFI Studies in the Science of Complexity, Oxford University Press: New York, NY.
Camazine, S., Deneubourg, J.-L., Franks, J., Sneyd, E., Bonabeau, E., and Theraulaz, G. 2001. Self-Organization in Biological Systems. Princeton University Press: Princeton, NJ.
Cicirello, V.A. and Smith, S.F. 2004.Wasp-like agents for distributed factory coordination. J. of Autonomous Agents and Multi-Agent Systems, 8:237–266.
Chrétien, L. 1996. Organisation spatiale du matériel provenant de l'excavation du nid chez Messor Marbarus et des cadavres chez Lasius Niger (Hymenopterea: Formicidea), Ph.D. Dissertation, Université Libre de Bruxelles, Belgium.
Gerkey, B.P. and Matari?, M.J. 2002. Sold!: Auction methods for multirobot coordination. Special issue on advances in multi-robot systems. T. Arai, E. Pagello, and L.E. Parker (Eds.), IEEE Trans. on Robotics and Automation, 18(5):758–768.
Gordon, D.M. 1999. Ants at Work: How an Insect Society is Organized, The Free Press, Simon & Schuster Inc.: New York, NY.
Hayes, A.T., Martinoli, A., and Goodman, R.M. 2002. Distributed odor source localization. Special issue on artificial olfaction. H.T. Nagle, J.W. Gardner, and K. Persaud (Eds.), IEEE Sensors, 2(3):260-271.
Holland, O.E. and Melhuish, C. 1999. Stigmergy, self-organisation, and sorting in collective robotics. Artificial Life, 5:173–202.
Ijspeert, A.J., Martinoli, A., Billard, A., and Gambardella, L.M. 2001. Collaboration through the exploitation of local interactions in autonomous collective robotics: The stick pulling experiment. Autonomous Robots, 11(2):149–171.
Kazadi, S., Abdul-Khaliq, A., and Goodman, R.M. 2002. On the convergence of puck clustering systems. Robotics and Autonomous Systems, 38(2):93–117.
Krause, J. and Ruxton, G.D. 2002. Living in Group, Oxford University Press: New York, NY.
Krieger, M.J.B. and Billeter, J.-B. 2000. The call of duty: Self-organised task allocation in a population of up to twelve mobile robots. Robotics and Autonomous Systems, 30(1/2):65–84.
Kube, C.R. and Bonabeau, E. 2000. Cooperative transport by ants and robots. Robotics and Autonomous Systems, 30(1/2):85–101.
Labella, T.H., Dorigo, M., and Deneubourg, J.-L. 2004. Efficiency and task allocation in prey retrieval. In Proc. First Int.Workshop on Biologically Inspired Approaches to Information Technology, A.J. Ijspeert and M. Murata (Eds.), Lausanne, Switzerland, Lecture Notes in Computer Sciences, pp. 32-47.
Lerman, K., Galstyan, A., Martinoli, A., and Ijspeert, A.J. 2001. A macroscopic analytical model of collaboration in distributed robotic systems. Artificial Life, 7(4):375–393.
Lerman, K. and Galstyan, A. 2002. Mathematical model of foraging in a group of robots: Effect of interference. Autonomous Robots, 13:127–141.
Martinoli, A. 1999. Swarm intelligence in autonomous collective robotics: From tools to the analysis and synthesis of distributed control strategies. Unpublished doctoral manuscript, EPFL Ph.D. Thesis Nr. 2069, Lausanne, Switzerland. Downloadable at: http://www.coro/caltech/edu/people/alcherio/am pub.
Martinoli, A. and Easton, K. 2003a. Modeling swarm robotic systems. In Proc. Eighth Int. Symp. on Experimental Robotics, B. Siciliano and P. Dario (Eds.), Sant'Angelo d'Ischia, Italy. Springer Tracts in Advanced Robotics, pp. 285–294.
Martinoli, A. and Easton, K. 2003b. Optimization of swarm robotic systems via macroscopic models. In Proc. of the Multi-Robot Systems Workshop, A. Schultz, L. Parker, and F. Schneider (Eds.), Naval Research Laboratory, Washington, DC, pp. 181–192.
Martinoli, A., Easton, K. and Agassounon, W. 2004. Modeling swarm robotic systems: A case study in collaborative distributed manipulation. Int. Journal of Robotic Research, 23(4):415–436.
Martinoli, A., Ijspeert, A.J., and Mondada, F. 1999a. Understanding collective aggregation mechanisms: From probabilistic modelling to experiments with real robots. Robotics and Autonomous Systems, 29:51–63.
Martinoli, A., Ijspeert, A.J., and Gambardella, L.M. 1999b. A probabilistic model for understanding and comparing collective aggregation mechanisms. In Proc. Fifth European Conf. on Artificial Life, D. Floreano, F. Mondada, and J.-D. Nicoud (Eds.), Lausanne, Switzerland, Lectures Notes in Computer Science, pp. 575-584.
Martinoli, A. and Mondada, F. 1995. Collective and cooperative group behaviours: Biologically inspired experiments in robotics. In Proc. Fourth Int. Symp. on Experimental Robotics, O. Khatib and J.K. Salisbury (Eds.), Stanford, CA, Lecture Notes in Control and Information Sciences, pp. 3-10.
Michel, O. 1998. Webots: Symbiosis between virtual and real mobile robots. In Proc. First Int. Conf. on Virtual Worlds, J.-C. Heuding (Ed.), Paris, France, pp. 254-263. See also http://www.cyberbotics.com/webots/.
Mollison, D. 1977. Spatial contact models for ecological and epidemic spread. Royal Statist. Soc., B 39:283–326.
Mondada, F., Franzi, E., and Ienne, P. 1993. Mobile robot miniaturization: A tool for investigation in control algorithms. In Proc. Third Int. Symp. on Experimental Robotics, T. Yoshikawa and F. Miyazaki (Eds.), Kyoto, Japan, Lecture Notes in Control and Information Sciences, pp. 501-513.
Nouyan, S. 2002. Agent-based approach to dynamic task allocation. In Proc. Third Int.Workshop on Ant Algorithms, M. Dorigo, G. Di Caro, and M. Samples (Eds.), Brussels, Belgium, Lecture Notes in Computer Sciences, pp. 28-39.
Pacala, S.W., Gordon, D.M., and Godfray, H.C.J. 1996. Effects of social group size on information transfer and task allocation. Evolutionary Ecology, 10:127–165.
Parrish, J.K. and Hamner, W.M. (Eds.). 1997. Animal Groups in Three Dimensions, Cambridge University Press: Cambridge, UK.
Sugawara, K. and Sano, M. 1997. Cooperative accelleration of task performance: Foraging behavior of interacting multi-robots system. Physica D, 100:343–354.
Sugawara, K., Sano, M., Yoshihara, I., and Abe, K. 1998. Cooperative behavior of interacting robots. Artificial Life and Robotics, 2:62–67.
Theraulaz, G., Bonabeau, E., and Deneubourg, J.-L. 1998. Response threshold reinforcement and division of labour in insect societies. In Proc. Royal Society of London, Series B, vol. 265, pp. 327–332.
Wilson, E.O. 1984. The relation between caste ratios and division of labour in ant genus pheidole (Hymenoptera: Formidacea). Behav. Ecol. Sociobiol., 16:89–98.
Rights and permissions
About this article
Cite this article
Agassounon, W., Martinoli, A. & Easton, K. Macroscopic Modeling of Aggregation Experiments using Embodied Agents in Teams of Constant and Time-Varying Sizes. Autonomous Robots 17, 163–192 (2004). https://doi.org/10.1023/B:AURO.0000033971.75494.c8
Issue Date:
DOI: https://doi.org/10.1023/B:AURO.0000033971.75494.c8