Abstract
The foraging scenario is important in robotics, because it has many different applications and demands several fundamental skills from a group of robots, such as collective exploration, shortest path finding, and efficient task allocation. Particularly for large groups of robots emergent behaviors are desired that are decentralized and based on local information only. But the design of such behaviors proved to be difficult because of the absence of a theoretical basis. In this paper, we present a macroscopic model based on partial differential equations for the foraging scenario with virtual pheromones as the medium for communication. From the model, the robot density, the food flow and a quantity describing qualitatively the stability of the behavior can be extracted. The mathematical model is validated in a simulation with a large number of robots. The predictions of the model correspond well to the simulation.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arkin, R.C.: Motor schema based mobile robot navigation. International Journal of Robotics Research 8, 92–112 (1989)
Bonabeau, E., Thraulaz, G., Fourcassi, V., Deneubourg, J.: The phase-ordering kinetics of cemetery organization in ants. Technical Report 98-01008, Santa Fe Institute (1998)
Cole, B.J., Cheshire, D.: Mobile Cellular Automata Models of Ant Behavior: Movement Activity of Leptothorax allardycei. American Naturalist 148, 1–15 (1996)
Deneubourg, J.L., Aron, S., Goss, S., Pasteels, J.M.: The self-organizing exploratory pattern of the Argentine ant. Journal of Insect Behavior 3, 159–168 (1990)
Goss, S., Aron, S., Deneubourg, J.L., Pasteels, J.M.: Self-organized shortcuts in the Argentine ant. Naturwissenschaften 76, 579–581 (1989)
Jasmine Robot - Project Website (2006), http://www.swarmrobot.org/ .
Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. International Journal of Robotics Research 5, 90–98 (1986)
Klein, J.: Continuous 3D Agent-Based Simulations in the breve Simulation Environment. In: Proceedings of NAACSOS Conference (North American Association for Computational, Social, and Organizational Sciences) (2003)
Lerman, K.: A model of adaptation in collaborative multi-agent systems. Adaptive Behavior 12, 187–198 (2004)
Lerman, K., Galstyan, A.: Mathematical Model of Foraging in a Group of Robots: Effect of Interference. Autonomous Robots 13, 127–141 (2002)
Lerman, K., Jones, C., Galstyan, A., Mataric, M.: Analysis of Dynamic Task Allocation in Multi-Robot Systems. In: Int. J. of Robotics Research (2006)
Lerman, K., Martinoli, A., Galstyan, A.: A Review of Probabilistic Macroscopic Models for Swarm Robotic Systems. In: Sahin, E., Spears, W. (eds.) Swarm Robotics Workshop: State-of-the-art Survey, Springer, Heidelberg (2005)
Martinoli, A., Easton, K., Agassounon, W.: Modeling Swarm Robotic Systems: A Case Study in Collaborative Distributed Manipulation. In: Siciliano, B. (ed.): Special Issue on Experimental Robotics, Int. Journal of Robotics Research 23, 415–436 (2004)
Panait, L., Luke, S.: Ant Foraging Revisited. In: Pollack, J., Bedau, M., Husbands, P., Ikegami, T. (eds.) ALife IX Proceedings, MIT Press, Cambridge (2004)
Schweitzer, F.: Brownian Agents and Active Particles. On the Emergence of Complex Behavior in the Natural and Social Sciences. Springer, New York (2003)
Schweitzer, F.: Brownian Agent Models for Swarm and Chemotactic Interaction. In: Polani, D., Kim, J., Martinetz, T. (eds.) Fifth German Workshop on Artificial Life, Akademische Verlagsgesellschaft Aka, Berlin (2002)
Schweitzer, F., Lao, K., Family, F.: Active Random Walker Simulate Trunk Trail Formation by Ants. BioSystems 41, 153–166 (1997)
Seyfried, J., Szymanski, M., Bender, N., Estana, R., Thiel, M., Wörn, H.: The I-SWARM project: Intelligent Small World Autonomous Robots for Micro-manipulation. In: Sahin, E., Spears, W. (eds.) Swarm Robotics Workshop: State-of-the-art Survey, Springer, Heidelberg (2005)
Spears, W.M., Gordon, D.F.: Using Artificial Physics to control agents. In: IEEE International Conference on Information, Intelligence, and Systems, IEEE Computer Society Press, Los Alamitos (1999)
Sugawara, K., Kazama, T., Watanabe, T.: Foraging Behavior of Interacting Robots with Virtual Pheromone. In: Proceedings of 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, IEEE, Los Alamitos (2004)
Theraulaz, G., Gautrais, J., Camazine, S., Deneubourg, J.L.: The formation of spatial patterns in social insects: from simple behaviours to complex structures. Phil. Trans. R. Soc. Lond. A 361, 1263–1282 (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Hamann, H., Wörn, H. (2007). An Analytical and Spatial Model of Foraging in a Swarm of Robots. In: Şahin, E., Spears, W.M., Winfield, A.F.T. (eds) Swarm Robotics. SR 2006. Lecture Notes in Computer Science, vol 4433. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71541-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-71541-2_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71540-5
Online ISBN: 978-3-540-71541-2
eBook Packages: Computer ScienceComputer Science (R0)