International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

Cooperative Path Planning of Dynamical Multi-Agent Systems Using Differential Flatness Approach

  • Lian, Feng-Li (Department of Electrical Engineering, National Taiwan University)
  • Published : 2008.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper discusses a design methodology of cooperative path planning for dynamical multi-agent systems with spatial and temporal constraints. The cooperative behavior of the multi-agent systems is specified in terms of the objective function in an optimization formulation. The path of achieving cooperative tasks is then generated by the optimization formulation constructed based on a differential flatness approach. Three scenarios of multi-agent tasking are proposed at the cooperative task planning framework. Given agent dynamics, both spatial and temporal constraints are considered in the path planning. The path planning algorithm first finds trajectory curves in a lower-dimensional space and then parameterizes the curves by a set of B-spline representations. The coefficients of the B-spline curves are further solved by a sequential quadratic programming solver to achieve the optimization objective and satisfy these constraints. Finally, several illustrative examples of cooperative path/task planning are presented.

Keywords

References

  1. D. Fox, W. Burgard, H. Kruppa, and S. Thrun, "A probabilistic approach to collaborative multirobot localization," Autonomous Robots, vol. 8, no. 3, pp. 325-344, June 2000 https://doi.org/10.1023/A:1008937911390
  2. W. Burgard, M. Moors, C. Stachniss, and F. E. Schneider, "Coordinated multi-robot exploration," IEEE Trans. Robot., vol. 21, no. 3, pp. 376-386, June 2005 https://doi.org/10.1109/TRO.2004.839232
  3. D. Hougen, S. Benjaafar, J. Bonney, J. Budenske, M. Dvorak, M. Gini, H. French, D. Krantz, P. Li, F. Malver, B. Nelson, N. Papanikolopoulos, P. Rybski, S. Stoeter, R. Voyles, and K. Yesin, "A miniature robotic system for reconnaissance and surveillance," Proc. IEEE Int. Conf. on Robot. Autom., pp. 501-507, San Francisco, CA, USA, April 2000
  4. R. R. Murphy, "Human-robot interaction in rescue robotics," IEEE Trans. Syst., Man, Cybern., C, Appl. Rev., vol. 34, no. 2, pp. 138-153, May 2004 https://doi.org/10.1109/TSMCC.2004.826267
  5. J. S. Jennings, G. Whelan, and W. F. Evans, Cooperative search and rescue with a team of mobile robots," Proc. IEEE Int. Conf. Advanced Robotics, Monterey, CA, USA, pp. 193-200, July 1997
  6. P. Varaiya, "Smart cars on smart roads: Problems of control," IEEE Trans. on Automatic Control, vol. 38, no. 2 pp. 195-206, Feb. 1993 https://doi.org/10.1109/9.250509
  7. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations," IEEE Trans. on Automatic Control, vol. 49, pp. 1465-1476, Sept. 2004 https://doi.org/10.1109/TAC.2004.834433
  8. R. Vidal, O. Shakernia, and S. Sastry, "Formation control of nonholonomic mobile robots omnidirectional visual servoing and motion segmentation," Proc. IEEE Conf. Robot. Autom., pp. 584-589, Taipei, Taiwan, Sep. 2003
  9. Mixed Initiative Control of Automa-teams program of DARPA at http://dtsn.darpa.mil/ixo/ mica.asp
  10. A. K. Das, R. Fierro, V. Kumar, J. P. Ostrowski, J. Spletzer, and C. J. Taylor, "A vision-based formation control framework," IEEE Trans. Robot. Autom., vol. 18, no. 5, pp. 813-825, Oct. 2002 https://doi.org/10.1109/TRA.2002.803463
  11. P. Tabuada, G. J. Pappas, and P. Lima, "Motion feasibility of multi-agent formations," IEEE Trans. Robot., vol. 21, no. 3, pp. 387-392, June 2005 https://doi.org/10.1109/TRO.2004.839224
  12. T. Balch and R. Arkin, "Behavior-based formation control for multirobot systems," IEEE Trans. Robot. Autom., vol. 14, no. 6, pp. 926-939, Dec. 1998 https://doi.org/10.1109/70.736776
  13. J. Fredslund and M. J. Mataric, "A general algorithm for robot formations using local sensing and minimal communication," IEEE Trans. Robot. Autom., vol. 18, no. 5, pp. 837-846, Oct. 2002 https://doi.org/10.1109/TRA.2002.803458
  14. J. R. T. Lawton, R. W. Beard, and B. J. Young, "A decentralized approach to formation maneuvers," IEEE Trans. Robot. Autom., vol. 19, no. 6, pp. 933-941, Dec. 2003 https://doi.org/10.1109/TRA.2003.819598
  15. H. G. Tanner, G. J. Pappas, and V. Kumar, "Leader-to-formation stability," IEEE Trans. Robot. Autom., vol. 20, no. 3, pp. 443-455, June 2004 https://doi.org/10.1109/TRA.2004.825275
  16. J. P. Desai, J. P. Ostrowski, and V. Kumar, "Modeling and control of formations of nonholonomic mobile robots," IEEE Trans. Robot. Autom., vol. 17, no. 6, pp. 905-908, Dec. 2001 https://doi.org/10.1109/70.976023
  17. P. Ogren, M. Egerstedt, and X. Hu, "A control Lyapunov function approach to multiagent coordination," IEEE Trans. Robot. Autom., vol. 18, no. 5, pp. 847-851, Oct. 2001 https://doi.org/10.1109/TRA.2002.804500
  18. S. S. Ge and C.-H. Fua, "Queues and artificial potential trenches for multirobot formations," IEEE Trans. Robot. Autom., vol. 21, no. 4, pp. 646-656, Aug. 2005 https://doi.org/10.1109/TRO.2005.847617
  19. M. B. Milam, K. Mushambi, and R. M. Murray, "A new computational approach to real-time trajectory generation for constrained mechanical systems," Proc. on IEEE Conf. Decision and Control, Sydney, Australia, Dec. 2000
  20. N. Petit, M. B. Milam, and R. M. Murray, "Inversion based constrained trajectory optimization," Proc. IFAC Symp. Nonlinear Control Systems Design, Saint-Petersburg, Russia, July 2001
  21. R. Olfati-Saber, W. B. Dunbar, and R. M. Murray, "Cooperative control of multi-vehicle systems using cost graphs and optimization," Proc. American Control Conference, Denver, CO, USA, June 2003
  22. M. Fliess, J. Levine, P. Martin, and P. Rouchon, "Flatness and defect of non-linear systems: Introductory theory and examples," International Journal of Control, vol. 61, no. 6, pp. 1327-1360, 1995 https://doi.org/10.1080/00207179508921959
  23. C. de Boor, A Practical Guide to Splines, Springer-Verlag, 1978
  24. P. Gill, W. Murray, M. Saunders, and M. Wright, User's Guide for NPSOL 5.0: A Fortran Package for Nonlinear Programming, System Optimization Laboratory, Stanford University, California, USA
  25. H. Choset, K. M. Lynch, S. Hutchinson, G. Kantor, W. Burgard, L. E. Kavraki, and S. Thrun, Principles of Robot Motion: Theory, Algorithms, and Implementations. MIT Press, 2005
  26. L. Cremean, W. B. Dunbar, D. van Gogh, J. Hickey, E. Klavins, J. Meltzer, and R. M. Murray, "The Caltech multi-vehicle wireless testbed," Proc. IEEE Conf. Decision and Control, Las Vegas, NV, USA, pp. 86-88, Dec. 2002
  27. F.-L. Lian and R. M. Murray, "Real-time trajectory generation for the cooperative path planning of multi-vehicle systems," Proc. IEEE Conf. Decision and Control, Las Vegas, NV, USA, pp. 3766-3769, Dec. 2002
  28. F.-L. Lian and R. M. Murray, "Cooperative task planning of multi-robot systems with temporal constraints," Proc. IEEE Int'l Conf. on Robot. Autom., Taipei, Taiwan, pp. 2504-2509, Sep. 2003.