Model Predictive Path-Space Iteration for Multi-Robot Coordination

  • Omar A. A. Orqueda
  • Rafael Fierro
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 588)

Summary

In this work, two novel optimization-based strategies for multi-robot coordination are presented. The proposed algorithms employ a model predictive control (MPC) version of a Newton-type approach for solving the underlying optimization problem. Both methods can generate control inputs for vehicles with nonholonomic constraints moving in a configuration space cluttered by obstacles. Obstacle- and inter-collision constraints are incorporated into the optimization problem by using interior and exterior penalty function approaches. Moreover, convergence of the algorithms is studied with and without the presence of obstacles in the environment. Simulation results verify the validity of the proposed methodology.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Belta and V. Kumar. Optimal motion generation for groups of robots: A geometric approach. ASME Journal of Mechanical Design, 126:63–70, 2004.CrossRefGoogle Scholar
  2. 2.
    S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, Cambridge, UK, March 2004.MATHGoogle Scholar
  3. 3.
    J. Bullingham, A. Richards, and J. P. How. Receding horizon control of autonomous aerial vehicles. In Proceedings of the American Control Conference, pages 3741–3746, Anchorage, AK, May 2002.Google Scholar
  4. 4.
    J. Cortés, S. Martínez, T. Karatas, and F. Bullo. Coverage control for mobile sensing networks. IEEE Transactions on Robotics and Automation, 20(2):243–255, April 2004.CrossRefGoogle Scholar
  5. 5.
    R. Diestel. Graph Theory. Springer-Verlag, New York, 2000.Google Scholar
  6. 6.
    A. Divelbiss and J.T. Wen. Nonholonomic motion planning with inequality constraints. In Proceedings of the IEEE Conference on Decision and Control, pages 2712–2717, San Antonio, Texas, December 1993.Google Scholar
  7. 7.
    A.W. Divelbiss and J.T. Wen. A path space approach to nonholonomic motion planning in the presence of obstacles. IEEE Transactions on Robotics and Automation, 13(3):443–451, June 1997.CrossRefGoogle Scholar
  8. 8.
    W. B. Dunbar and R. M. Murray. Model predictive control of coordinated multi-vehicle formations. In Proceedings of the IEEE Conference on Decision and Control, pages 4631–4636, Las Vegas, NV, Dec. 10–13 2002.Google Scholar
  9. 9.
    J. T. Feddema, R. D. Robinett, and R. H. Byrne. An optimization approach to distributed controls of multiple robot vehicles. In Workshop on Control and Cooperation of Intelligent Miniature Robots, IEEE/RSJ International Conference. on Intelligent Robots and Systems, Las Vegas, Nevada, October 31 2003.Google Scholar
  10. 10.
    R. Fierro and K. Wesselowski. Optimization-based control of multi-vehicle systems. In V. Kumar, N.E. Leonard, and A.S. Morse, editors, A Post-Workshop Volume 2003 Block Island Workshop on Cooperative Control Series, volume 309 of LNCIS, pages 63–78. Springer, 2005.Google Scholar
  11. 11.
    C.J. Goh and K.L. Teo. Alternative algorithms for solving nonlinear function and functional inequalities. Applied Mathematics and Computation, 41(2):159–177, January 1991.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    T. Keviczky, F. Borrelli, and G.J. Balas. A study on decentralized receding horizon control for decoupled systems. In Proceedings of the American Control Conference, volume 6, pages 4921–4926, Boston, MA, June 2004.Google Scholar
  13. 13.
    J.J. Kuffner and S.M. LaValle. RRT-Connect: An efficient approach to singlequery path planning. In Proceedings of the IEEE International Conference on Robotics and Automation, pages 95–101, San Francisco, CA, April 2000.Google Scholar
  14. 14.
    J.C. Latombe. Robot Motion Planning. Kluwer Academic Publications, Boston, MA, 1991.Google Scholar
  15. 15.
    F.C. Lizarralde. Estabilização de sistemas de controle não lineares afins por um método do tipo Newton (in Portuguese). PhD thesis, Universidade Federal do Rio de Janeiro, COPPE, Río de Janeiro, RJ-BRASIL, September 1998.Google Scholar
  16. 16.
    D.Q. Mayne, J.B. Rawings, C.V. Rao, and P.O.M. Scokaert. Constrained model predictive control: Stability and optimality. Automatica, 36(6):789–814, June 2000.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    D-O. Popa. Path-Planning and Feedback Stabilization of Nonholonomic Control Systems. PhD thesis, Rensselaer Polytechnic Institute, Troy, NY 12180, April 1998.Google Scholar
  18. 18.
    C.W. Reynolds. Flocks, herds, and schools: A distributed behavioral model. Computer Graphics, 21(4):25–34, July 1987.CrossRefMathSciNetGoogle Scholar
  19. 19.
    R. Olfati Saber. Flocking for multi-agent dynamic systems: Algorithms and theory. Technical Report CIT-CDS 2004-005, Control and Dynamical Systems, Pasadena, Cal, June 2004.Google Scholar
  20. 20.
    N. Sadegh. Trajectory learning and output feedback control of nonlinear discrete time systems. In Proceedings of the 40th IEEE Conference on Decision and Control, pages 4032–4037, Orlando, Florida USA, December 2001, December 2001.Google Scholar
  21. 21.
    E.D. Sontag. Control of systems without drift via generic loops. IEEE Transactions. on Automatic Control, 40:413–440, 1995.Google Scholar
  22. 22.
    H.G. Tanner, A. Jabdabaie, and G.J. Pappas. Stable flocking of mobile agents, part I: Fixed topology. In Proceedings of the IEEE Conference on Decision and Control, pages 2010–2015, Maui, Hawaii, USA, December 2003.Google Scholar
  23. 23.
    J.T. Wen and S. Jung. Nonlinear model predictive control based on predicted state error convergence. In Proceedings of the American Control Conference, pages 2227–2232, Boston, MA, June 2004.Google Scholar
  24. 24.
    J.T. Wen and F. Lizarralde. Nonlinear model predictive control based on the best-step Newton algorithm. In Proceedings of the 2004 IEEE Conference on Control Applications, pages 823–829, Taipei, Taiwan, August 2004.Google Scholar
  25. 25.
    S. Zelinski, T.J. Koo, and S. Sastry. Optimization-based formation reconfiguration planning for autonomous vehicles. In Proceedings of the IEEE International Conference on Robotics and Automation, number 3, pages 3758–3763, September 2003.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Omar A. A. Orqueda
    • 1
  • Rafael Fierro
    • 1
  1. 1.MARHES Laboratory, School of Electrical and Computer EngineeringOklahoma State UniversityStillwaterUSA

Personalised recommendations