DOI QR코드

DOI QR Code

Nash equilibrium-based geometric pattern formation control for nonholonomic mobile robots

  • Received : 2013.03.06
  • Accepted : 2013.10.03
  • Published : 2014.01.25

Abstract

This paper deals with the problem of steering a group of mobile robots along a reference path while maintaining a desired geometric formation. To solve this problem, the overall formation is decomposed into numerous geometric patterns composed of pairs of robots, and the state of the geometric patterns is defined. A control algorithm for the problem is proposed based on the Nash equilibrium strategies incorporating receding horizon control (RHC), also known as model predictive control (MPC). Each robot calculates a control input over a finite prediction horizon and transmits this control input to its neighbor. Considering the motion of the other robots in the prediction horizon, each robot calculates the optimal control strategy to achieve its goals: tracking a reference path and maintaining a desired formation. The performance of the proposed algorithm is validated using numerical simulations.

References

  1. Balch, T. and Arkin, R.C. (1998), "Behavior-based formation control for multi-robot teams", IEEE Trans. Robot. Autom., 14(6), 926-939. https://doi.org/10.1109/70.736776
  2. van den Broek, T.H.A., van de Wouw, N. and Nijmeijer, H. (2009), "Formation control of unicycle mobile robots: a virtual structure approach", Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, December 16-18.
  3. Chen, C. (1999), Linear System Theory and Design, (3rd Edition), Oxford University Press.
  4. Chen, J., Sun, D., Yang, J. and Chen, H. (2010), "Leader-follower formation control of multiple nonholonomic mobile robots incorporating a receding-horizon scheme", Int. J. Robot. Res., 29(6), 727-747. https://doi.org/10.1177/0278364909104290
  5. Consolini, L., Morbidi, F., Prattichizzo, D. and Tosques, M. (2008), "Leader-follower formation control of nonholonomic mobile robots with input constraints", Automatica, 44(5), 1343-1349. https://doi.org/10.1016/j.automatica.2007.09.019
  6. Desai, J.P., Ostrowski, J.P. and Kumar, V. (2001), "Modeling and control of formations of nonholonomic mobile robots", IEEE Trans. Robot. Autom., 17(6), 905-908. https://doi.org/10.1109/70.976023
  7. Dierks, T., Brenner, B. and Jagannathan, S. (2013), "Neural network-based optimal control of mobile robot formations with reduced information exchange", IEEE Trans. Control Syst. Technol., 21(4), 1407-1415. https://doi.org/10.1109/TCST.2012.2200484
  8. Do, K.D. and Pan, J. (2007), "Nonlinear formation control of unicycle-type mobile robots", Robot. Auton. Syst., 55(3), 191-204. https://doi.org/10.1016/j.robot.2006.09.001
  9. Dong, W. and Farrell, J.A. (2008), "Cooperative control of multiple nonholonomic mobile agents", IEEE Trans. Autom. Control, 53(6), 1434-1448. https://doi.org/10.1109/TAC.2008.925852
  10. Dunbar, W.B. and Murray, R.M. (2006), "Distributed receding horizon control for multi-vehicle formation stabilization", Automatica, 42(4), 549-558. https://doi.org/10.1016/j.automatica.2005.12.008
  11. Egerstedt, M. and Hu, X. (2001), "Formation constrained multi-agent control", IEEE Trans. Robot. Autom., 17(6), 947-951. https://doi.org/10.1109/70.976029
  12. Engwerda, J.C. (2005), LQ Dynamic Optimization and Differential Games, Wiley.
  13. Fontes, F.A.C.C. (2001), "A general framework to design stabilizing nonlinear model predictive controllers", Syst. Control Lett., 42(2), 127-143. https://doi.org/10.1016/S0167-6911(00)00084-0
  14. Gross, J.L. and Yellen, J. (2004), Handbook of Graph Theory, CRC Press.
  15. Gu, D. and Hu, H. (2005), "A stabilizing receding horizon regulator for nonholonomic mobile robots", IEEE Trans. Robot., 21(5), 1022-1028. https://doi.org/10.1109/TRO.2005.851357
  16. Gu, D. (2008), "A differential game approach to formation control", IEEE Trans. Control Syst. Technol., 16(1), 85-93. https://doi.org/10.1109/TCST.2007.899732
  17. Jank, G. and Abou-Kandil, H. (2003), "Existence and uniqueness of open-loop Nash equilibria in linearquadratic discrete time games", IEEE Trans. Autom. Control, 48(2), 267-271. https://doi.org/10.1109/TAC.2002.808477
  18. Lewis, M.A. and Tan, K. (1997), "High precision formation control of mobile robots using virtual structures", Auton. Robot., 4(4), 387-403. https://doi.org/10.1023/A:1008814708459
  19. Meenakshi, A.R. and Rajian, C. (1999), "On a product of positive semidefinite matrices", Linear Alg. Appl., 295(1-3), 3-6. https://doi.org/10.1016/S0024-3795(99)00014-2
  20. Moshtagh, N., Michael, N., Jadbabaie, A. and Daniilidis, K. (2009), "Vision-based, distributed control laws for motion coordination of nonholonomic robots", IEEE Trans. Robot., 25(4), 851-860. https://doi.org/10.1109/TRO.2009.2022439
  21. Ou, M., Du, H. and Li, S. (2012), "Finite-time formation control of multiple nonholonomic mobile robots", Int. J. Robust Nonlinear Control, doi: 10.1002/rnc.2880. https://doi.org/10.1002/rnc.2880
  22. Sun, D., Wang, C., Shang, W. and Feng, G. (2009), "A synchronization approach to trajectory tracking of multiple mobile robots while maintaining time-varying formations", IEEE Trans. Robot., 25(5), 1074-1086. https://doi.org/10.1109/TRO.2009.2027384
  23. Tabuada, P., Pappas, G. J. and Lima, P. (2005), "Motion feasibility of multi-agent formations", IEEE Trans. Robot., 21(3), 387-392. https://doi.org/10.1109/TRO.2004.839224
  24. Tanner, H.G., Pappas, G.J. and Kumar, V. (2004), "Leader-to-formation stability", IEEE Trans. Robot. Autom., 20(3), 443-455. https://doi.org/10.1109/TRA.2004.825275