Advertisement

Laplacian Sheep: A Hybrid, Stop-Go Policy for Leader-Based Containment Control

  • G. Ferrari-Trecate
  • M. Egerstedt
  • A. Buffa
  • M. Ji
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3927)

Abstract

The problem of driving a collection of mobile robots to a given target location is studied in the context of partial difference equations. In particular, we are interested in achieving this transfer while ensuring that the agents stay in the convex polytope spanned by dedicated leader-agents, whose dynamics will be given by a hybrid Stop-Go policy. The resulting system ensures containment through the enabling result that under a Laplacian, decentralized control strategy for the followers, these followers will converge to a location in the convex leader polytope, as long as the leaders are stationary and the interaction graph is connected. Simulation results testify to the viability of the proposed, hybrid control strategy.

Keywords

Mobile Robot Target Location Interaction Graph Convex Polytope Stationary Leader 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Parker, L.E., Kannan, B., Fu, X., Tang, Y.: Heterogeneous mobile sensor net deployment using robot herding and line-of-sight formations. In: Proceedings of IEEE International Conference on Intelligent Robots and Systems, pp. 681–689 (2003)Google Scholar
  2. 2.
    Vaughan, R., Sumpter, N., Henderson, J., Frost, A., Cameron, S.: Experiments in automatic flock control. Journal of Robotics and Autonomous Systems 31, 109–117 (2000)CrossRefGoogle Scholar
  3. 3.
    Desai, J., Ostrowski, J.P., Kumar, V.: Controlling formations of multiple mobile robots. In: Proc. IEEE Int. Conf. Robot. Automat., pp. 2864–2869 (1998)Google Scholar
  4. 4.
    Ji, M., Muhammad, A., Egerstedt, M.: Leader-based multi-agent coordination: Controllability and optimal control. In: the American Control Conference, Minneapolis (submitted) (June 2006)Google Scholar
  5. 5.
    Tanner, H., Pappas, G., Kumar, V.: Leader to formation stability. IEEE Transactions on Robotics and Automation 20(3), 443–455 (2004)CrossRefGoogle Scholar
  6. 6.
    Tanner, H., Jadbabaie, A., Pappas, G.: Flocking in fixed and switching networks (submitted 2005), http://www.seas.upenn.edu/~pappasg/publications.html#journals
  7. 7.
    Saber, R.O.: A unified analytical look at Reynolds flocking rules. Technical Report CIT-CDS 03-014, California Institute of Technology (2003)Google Scholar
  8. 8.
    Muhammad, A., Egerstedt, M.: Connectivity graphs as models of local interactions. Journal of Applied Mathematics and Computation (to appear, 2005)Google Scholar
  9. 9.
    Egerstedt, M., Martin, C.: Conflict resolution for autonomous vehicles: A case study in hierarchical control design. International Journal of Hybrid Systems 2(3), 221–234 (2002)Google Scholar
  10. 10.
    Sussmann, H.: A maximum principle for hybrid optimal control problems. In: 38th IEEE Conference on Decision and Control (1999)Google Scholar
  11. 11.
    Ferrari-Trecate, G., Buffa, A., Gati, M.: Analysis of coordination in multiple agents formations through Partial difference Equations. Technical Report 5-PV, IMATI-CNR (2004), http://www-rocq.inria.fr/who/Giancarlo.Ferrari-Trecate/publications.html
  12. 12.
    Bollobás, B.: Modern graph theory. Graduate texts in Mathematics. Springer, Heidelberg (1998)CrossRefMATHGoogle Scholar
  13. 13.
    Bensoussan, A., Menaldi, J.L.: Difference equations on weighted graphs. Journal of Convex Analysis (Special issue in honor of Claude Lemaréchal) 12(1), 13–44 (2005)MathSciNetMATHGoogle Scholar
  14. 14.
    Ferrari-Trecate, G., Buffa, A., Gati, M.: Analysis of coordination in multi-agent systems through partial difference equations. Part I: The Laplacian control. In: 16th IFAC World Congress on Automatic Control (2005)Google Scholar
  15. 15.
    Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. on Automatic Control 48(6), 988–1001 (2003)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Olfati-Saber, R., Murray, R.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans on Autom. Control 49(9), 101–115 (2004)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Dautray, R., Lions, J.-L.: Mathematical analysis and numerical methods for science and technology. Evolution problems I-II, vol. 5-6. Springer-Verlag, Berlin (1992)MATHGoogle Scholar
  18. 18.
    Johansson, K., Egerstedt, M., Lygeros, J., Sastry., S.: Regularization of zeno hybrid automata. Systems and Control Letters 38, 141–150 (1999)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • G. Ferrari-Trecate
    • 1
    • 2
  • M. Egerstedt
    • 3
  • A. Buffa
    • 4
  • M. Ji
    • 3
  1. 1.INRIARocquencourt, Le ChesnayFrance
  2. 2.Dipartimento di Informatica e SistemisticaUniversitá degli Studi di PaviaPaviaItaly
  3. 3.School of Electrical and Computer EngineeringGeorgia Institute of TechnologyAtlantaUSA
  4. 4.Istituto di Matematica Applicata e Tecnologie Informatiche, C.N.R.PaviaItaly

Personalised recommendations