Control of Many Agents by Moving Their Targets: Maintaining Separation

  • Timothy Bretl

Summary

Consider a large group of agents chasing a small group of moving targets. Assume each agent moves at constant speed toward the closest target. This paper studies the problem of controlling the agents indirectly by specifying the motion of the targets. In particular, it considers the problem of maintaining a minimum separation distance between each pair of agents, something that is impossible to do with only one target. This paper shows that only two targets are necessary to maintain separation between four agents. It also shows results in simulation to support the conjecture that only two targets are necessary to maintain separation between any number of agents, given suitable initial conditions.

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References

  1. 1.
    Antonelli, G., Chiaverini, S.: Kinematic control of platoons of autonomous vehicles. IEEE Trans. Rebot. 22(6), 1285–1292 (2006)CrossRefGoogle Scholar
  2. 2.
    Bernhart, A.: Curves of pursuit. Scripta Mathematica 20(3-4), 125–141 (1954)MATHMathSciNetGoogle Scholar
  3. 3.
    Bernhart, A.: Curves of pursuit-II. Scripta Mathematica 23(1-4), 49–65 (1957)MathSciNetGoogle Scholar
  4. 4.
    Bernhart, A.: Curves of general pursuit. Scripta Mathematica 24(3), 189–206 (1959)MATHMathSciNetGoogle Scholar
  5. 5.
    Bernhart, A.: Polygons of pursuit. Scripta Mathematica 24(1), 23–50 (1959)MATHMathSciNetGoogle Scholar
  6. 6.
    Bruckstein, A.: Why the ant trails look so straight and nice. Mathematical Intelligencer 15(2), 59–62 (1993)MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Butler, Z., Corke, P., Peterson, R., Rus, D.: From robots to animals: virtual fences for controlling cattle. Int. J. Rob. Res. 25(5-6), 485–508 (2006)CrossRefGoogle Scholar
  8. 8.
    Caprari, G., Colot, A., Siegwart, R., Halloy, J., Deneubourg, J.-L.: Insbot: Design of an autonomous mini mobile robot able to interact with cockroaches. In: Int. Conf. Rob. Aut. (2004)Google Scholar
  9. 9.
    Cortés, J., Martínez, S., Bullo, F.: Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Trans. Automat. Contr. 51(8), 1289–1296 (2006)CrossRefGoogle Scholar
  10. 10.
    Davis, H.T.: Introduction to Nonlinear Differential and Integral Equations. Dover Publications, Inc., New York (1962)MATHGoogle Scholar
  11. 11.
    Freeman, R.A., Yang, P., Lynch, K.M.: Distributed estimation and control of swarm formation statistics. In: American Control Conference, Minneapolis, MN, pp. 749–755 (June 2006)Google Scholar
  12. 12.
    Gazi, V., Passino, K.M.: Stability analysis of swarms. IEEE Trans. Automat. Contr. 48(4), 692–697 (2003)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Contr. 48(6), 988–1001 (2003)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Leonard, N.E., Fiorelli, E.: Virtual leaders, artificial potentials and coordinated control of groups. In: IEEE Conf. Dec. Cont., Orlando, FL, pp. 2968–2973 (December 2001)Google Scholar
  15. 15.
    Low, D.J.: Statistical physics: Following the crowd. Nature 407, 465–466 (2000)CrossRefGoogle Scholar
  16. 16.
    Marshall, J.A., Broucke, M.E., Francis, B.A.: Formations of vehicles in cyclic pursuit. IEEE Trans. Automat. Contr. 49(11), 1963–1974 (2004)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Ogawa, N., Oku, H., Hashimoto, K., Ishikawa, M.: Microrobotic visual control of motile cells using high-speed tracking system. IEEE Trans. Rebot. 21(3), 704–712 (2005)CrossRefGoogle Scholar
  18. 18.
    Ogawa, N., Oku, H., Hasimoto, K., Ishikawa, M.: A physical model for galvanotaxis of paramecium cell. Journal of Theoretical Biology 242, 314–328 (2006)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Pan, X., Han, C.S., Dauber, K., Law, K.H.: Human and social behavior in computational modeling and analysis of egress. Automation in Construction 15(4), 448–461 (2006)CrossRefGoogle Scholar
  20. 20.
    Reif, J.H., Wang, H.: Social potential fields: A distributed behavioral control for autonomous robots. Robotics and Autonomous Systems 27, 171–194 (1999)CrossRefGoogle Scholar
  21. 21.
    Robinson, K.R.: The responses of cells to electrical fields: A review. Journal of Cell Biology 101(6), 2023–2027 (1985)CrossRefGoogle Scholar
  22. 22.
    Takahashi, K., Ogawa, N., Oku, H., Hashimoto, K.: Organized motion control of a lot of microorganisms using visual feedback. In: IEEE Int. Conf. Rob. Aut., Orlando, FL, pp. 1408–1413 (May 2006)Google Scholar
  23. 23.
    Tanner, H.G., Pappas, G.J., Kumar, V.: Leader-to-formation stability. IEEE Trans. Robot. Automat. 20(3), 443–455 (2004)CrossRefGoogle Scholar
  24. 24.
    Vaughan, R., Sumpter, N., Frost, A., Cameron, S.: Robot sheepdog project achieves automatic flock control. In: Int. Conf. on the Simulation of Adaptive Behaviour (1998)Google Scholar
  25. 25.
    Vaughan, R., Sumpter, N., Henderson, J., Frost, A., Cameron, S.: Experiments in automatic flock control. Robotics and Autonomous Systems 31, 109–117 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Timothy Bretl
    • 1
  1. 1.Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801 

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