Autonomous Robots

, Volume 13, Issue 2, pp 127–141 | Cite as

Mathematical Model of Foraging in a Group of Robots: Effect of Interference

  • Kristina Lerman
  • Aram Galstyan
Article

Abstract

In multi-robot applications, such as foraging or collection tasks, interference, which results from competition for space between spatially extended robots, can significantly affect the performance of the group. We present a mathematical model of foraging in a homogeneous multi-robot system, with the goal of understanding quantitatively the effects of interference. We examine two foraging scenarios: a simplified collection task where the robots only collect objects, and a foraging task, where they find objects and deliver them to some pre-specified “home” location. In the first case we find that the overall group performance improves as the system size grows; however, interference causes this improvement to be sublinear, and as a result, each robot's individual performance decreases as the group size increases. We also examine the full foraging task where robots collect objects and deliver them home. We find an optimal group size that maximizes group performance. For larger group sizes, the group performance declines. However, again due to the effects of interference, the individual robot's performance is a monotonically decreasing function of the group size. We validate both models by comparing their predictions to results of sensor-based simulations in a multi-robot system and find good agreement between theory and simulations data.

robotics foraging mathematical modeling 

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References

  1. Beckers, R., Holland, O.E., and Deneubourg, J.L. 1994. From local actions to global tasks: Stigmergy and collective robotics. In Proceedings of the 4th International Workshop on the Synthesis and Simulation of Living Systems Artificial Life IV, R.A. Brooks and P. Maes (Eds.), USA, MIT Press: Cambridge, MA, pp. 181-189.Google Scholar
  2. Fontan, M.S. and Matari?, M.J. 1996. A study of territoriality: The role of critical mass in adaptive task division. In From Animals to Animats 4: Proceedings of the 4th International Conference on Simulation of Adaptive Behavior, P. Maes, M.J. Matari?, J.A. Meyer, J. Pollack, and S. Wilson (Eds.), MIT Press: Cambridge, MA, pp. 553-561.Google Scholar
  3. Galstyan, A. and Lerman, K. 2001. A stochastic model of platoon formation in traffic flow. In Proceedings of the TASK Workshop, Santa Fe, NM. Google Scholar
  4. Gerkey, B.P., Vaughan, R.T., Sty, K., Howard, A., Sukhatme, G.S., and Mataric, M.J. 2001. Most valuable player: A robot device server for distributed control. In Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2001), Wailea, Hawaii. Available at http://www-robotics.usc.edu/player/.Google Scholar
  5. Goldberg, D. and Matari?, M.J. 1999. Coordinating mobile robot group behavior using a model of interaction dynamics. In Proceedings of the Autonomous Agents '99.Google Scholar
  6. Goldberg, D. and Matari?, M.J. 2000. Robust behavior-based control for distributed multi-robot collection tasks.Technical Report IRIS-00-387, USC Institute for Robotics and Intelligent Systems.Google Scholar
  7. Holland, O. and Melhuish, C. 2000. Stigmergy, self-organization and sorting in collective robotics. Artificial Life, 5(2).Google Scholar
  8. Lerman, K. and Galstyan, A. 2001. A general methodology for mathematical analysis of multi-agent systems. University of California, Information Sciences Institute, Technical Report ISI-TR529.Google Scholar
  9. Lerman, K., Galstyan, A., Martinoli, A., and Ijspeert, A. 2001. A macroscopic analytical model of collaboration in distributed robotic systems. Artificial Life, 7(4):375-393.Google Scholar
  10. Lerman, K. and Shehory, O. 2000. Coalition formation for large-scale electronic markets. In Proceedings of the International Conference on Multi-Agent Systems (ICMAS'2000), Boston, MA.Google Scholar
  11. Martinoli, A., Ijspeert, A.J., and Gambardella, L.M. 1999. A probabilistic model for understanding and comparing collective aggregation mechanisms. In Proceedings of the 5th European Conference on Advances in Artificial Life (ECAL-99), D. Floreano, J.-D. Nicoud, and F. Mondada (Eds.), volume 1674 of LNAI, Springer: Berlin, pp. 575-584.Google Scholar
  12. Matari?, M. 1992. Minimizing complexity in controlling a mobile robot population. In Proceedings of the 1992 IEEE International Conference on Robotics and Automation, Nice, France, pp. 830-835.Google Scholar
  13. Michel, O. 1998. Webots: Symbiosis between virtual and real mobile robots. In Proc. of the First Int. Conf. on Virtual Worlds, J.-C. Heudin (Ed.), Paris, France, Springer Verlag: Berlin, pp. 254-263. See also http://www.cyberbotics.com/webots/.Google Scholar
  14. Nitz, E., Arkin, R.C., and Balch, T. 1993. Communication of behavioral state in multi-agent retrieval tasks. In Proceedings of the 1993 IEEE International Conference on Robotics and Automation, Atlanta, GE, Vol. 3, L. Werner and Robert, O'Conner (Eds.), IEEE Computer Society Press, pp. 588-594.Google Scholar
  15. Østergaard, E.H., Sukhatme, G.S., and Matari?, M.J. 2001. Emergent bucket brigading—a simple mechanism for improving performance in multi-robot constrained-space foraging tasks. In Proceedings of the 5th International Conference on Autonomous Agents (AGENTS-01).Google Scholar
  16. Parker, L.E. 1994. Heterogeneous multi-robot cooperation. Massachusetts Institute of Technology, Technical Report AITR-1465.Google Scholar
  17. Parker, L. 1998. Alliance: An architecture for fault-tolerant multi-robot cooperation. IEEE Transactions on Robotics and Automation, 14(2):220-240.Google Scholar
  18. Sugawara, K. and Sano, M. 1997. Cooperative acceleration of task performance: Foraging behavior of interacting multi-robots system. Physica D, 100:343-354.Google Scholar
  19. Sugawara, K., Sano, M., and Yoshihara, I. 1997. Cooperative acceleration of task performance: Analysis of foraging behavior by interacting multi-robots. In Proc. IPSJ Int. Symp. on Information Systems and Technologies for Network Society, Fukuoka, Japan, pp. 314-317.Google Scholar
  20. Sugawara, K., Sano, M., Yoshihara, I., and Abe, K. 1998. Cooperative behavior of interacting robots. Artificial Life and Robotics, 2:62-67.Google Scholar
  21. Vaughan, R.T., Støy, K., Sukhatme, G.S., and Matari?, M.J. 2000a. Blazing a trail: Insect-inspired resource transportation by a robot team. In Proceedings of the 5th International Symposium on Distributed Autonomous Robotic Systems (DARS), Knoxville, TN.Google Scholar
  22. Vaughan, R.T., Støy, K., Sukhatme, G.S., and Matari?, M.J. 2000b. Whistling in the dark: Cooperative trail following in uncertain localization space. In Proceedings of the 4th International Conference on Autonomous Agents (AGENTS-00), C. Sierra, G. Maria, and J.S. Rosenschein (Eds.), ACM Press: New York, pp. 187-194.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Kristina Lerman
    • 1
  • Aram Galstyan
    • 1
  1. 1.University of Southern CaliforniaMarina del ReyUSA

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