Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-14T05:22:17.111Z Has data issue: false hasContentIssue false
  • English
  • Français

A model predictive controller for robots to follow a virtual leader

Published online by Cambridge University Press:  19 January 2009

Dongbing Gu  and
Huosheng Hu
Dongbing Gu*
Affiliation:
School of Computer Science and Electronic Engineering, University of Essex, UK
Huosheng Hu
Affiliation:
School of Computer Science and Electronic Engineering, University of Essex, UK
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, we develop a model predictive control (MPC) scheme for robots to follow a virtual leader. The stability of this control scheme is guaranteed by adding a terminal state penalty to the cost function and a terminal state region to the optimization constraints. The terminal state region is found by analyzing the stability. Also a terminal state controller is defined for this control scheme. The terminal state controller is a virtual controller and is never used in the control process. Two virtual leader-following formation models are studied. Simulations on different formation patterns are provided to verify the proposed control strategy.

Keywords

Control of robotic systemsMobile robotsMulti-robot systemsRobot dynamicsNavigation
Type
Article
Information
Robotica , Volume 27 , Issue 6 , October 2009 , pp. 905 - 913
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Murray, R. M., “Recent research in cooperative control of multivehicle systems,” J. Dyn. Syst. Meas. Control 129 (5), 571–583 (2007).Google Scholar
2.Tanner, H. and Christodoulakis, D., “Decentralized cooperative control of heterogeneous vehicle groups,” Robot. Auton. Syst. 55 (11), 811–823 (2007).CrossRefGoogle Scholar
3.Hsieh, M. A., Loizou, S. and Kumar, V., “Stabilization of multiple robots on stable orbits via local sensing,” Proceedings of IEEE Conference on Robotics and Automation (Apr. 10–14, 2007).CrossRefGoogle Scholar
4.Zavlanos, M. and Pappas, G. J., “Distributed formation control with permutation symmetries,” Proceedings of IEEE Conference on Decision and Control, New Orleans, LA (Dec. 2007).CrossRefGoogle Scholar
5.Finke, J. and Passino, K. M., “Stable cooperative vehicle distributions for surveillance,” ASME J. Dyn. Syst. Meas. Control 129, 597–608 (2007).Google Scholar
6.Balch, T. and Arkin, R., “Behavior-based formation control for multi-robot teams,” IEEE Trans. Robot. Autom. 14 (6), 926–939 (1998).Google Scholar
7.Fredslund, J. and Mataric, M., “A general algorithm for robot formations using local sensing and minimal communication,” IEEE Trans. Robot. Autom. 18 (5), 837–846 (2002).Google Scholar
8.Giulietti, F., Pollini, L. and Innocenti, M., “Autonomous formation flight,” IEEE Control Syst. Mag. 18 (5), 34–44 (Dec. 2000).Google Scholar
9.Vidal, R., Shakernia, O. and Sastry, S., “Formation control of nonholonomic mobile robots with omnidirectional visual servoing and motion segmentation,” Proceedings of IEEE Conference on Robotics and Automation. (May 2003).Google Scholar
10.Egerstdt, M. and Hu, X., “Formation constrained multi-agent control,” IEEE Trans. Robot. Autom. 17 (6), 947–951 (2001).CrossRefGoogle Scholar
11.Fierro, R., Das, A., Kumar, V. and Ostrowski, J., “Hybrid control of formation of robots,” Proceedings of the 2001 IEEE ICRA, Korea (May 21–26, 2001) pp. 157–162.Google Scholar
12.Tanner, H., Pappas, G. and Kumar, V., “Leader-to-formation stability,” IEEE Trans. Robot. Autom. 20 (3), 433–455 (2004).CrossRefGoogle Scholar
13.Desai, J., Ostowski, J. and Kumar, V., “Modeling and control of formations of nonholonomic mobile robots,” IEEE Trans. Robot. Autom. 17 (6), 905–908 (2001).CrossRefGoogle Scholar
14.Lawton, J., Beard, R. and Young, B., “A decentralized approach to formation manoeuvres,” IEEE Trans. Robot. Autom. 19 (6), 933–941 (2003).Google Scholar
15.Egerstdt, M. and Hu, X., “A control Lyapunov function approach to multi-agent coordination,” IEEE Trans. Robot. Autom. 18 (5), 847–851 (2002).Google Scholar
16.Keerthi, S. S. and Gilbert, E. G., “Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations,” J. Optim. Theory Appl. 57, 265–293 (1988).Google Scholar
17.Rawlings, J. B. and Muske, K. R., “Stability of constrained receding horizon control,” IEEE Trans. Autom. Control 38 (10), 1512–1516 (1993).CrossRefGoogle Scholar
18.Chen, H. and Allgower, F., “A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability,” Automatica 34 (10), 1205–1217 (1998).Google Scholar
19.Nicolao, G. D., Magni, L. and Scattolini, R., “Stabilizing receding-horizon control of nonlinear time varying systems,” IEEE Trans. Autom. Control 43, 1030–1036 (1998).Google Scholar
20.Fontes, F. A. C. C., “A general framework to design stabilizing,” Syst. Control Lett. 42 (2), 127–143 (2001).CrossRefGoogle Scholar
21.Jadbabaie, A., Yu, J. and Hauser, J., “Stabilizing receding horizon control of nonlinear systems: A control Lyapunov function approach,” Proceedings of American Control Conference, San Diego, CA (1999).Google Scholar
22.Mayne, D. Q., Rawlings, J. B., Rao, C. and Scokaert, P., “Constrained model predictive control: Stability and optimality,” Automatica 36, 789–814 (2000).Google Scholar
23.Primbs, J., Nevistic, V. and Doyle, J., “A receding horizon generalization of pointwise min-norm controllers,” IEEE Trans. Autom. Control 45 (5), 898–909 (2000).Google Scholar
24.Scokaert, P., Mayne, D. and Rawlings, J., “Suboptimal model predictive control (feasibility implies stability),” IEEE Trans. Autom. Control 44, 648–654 (1999).CrossRefGoogle Scholar
25.Dunbar, W. and Murray, R., “Model predictive control of coordinated multi-vehicle formations,” Automatica 2 (4), 549–558 (2006).CrossRefGoogle Scholar
26.Wesselowski, K. and Fierro, R., “A dual-mode model predictive controller for robot formations,” Proceedings of the 42nd IEEE CDC, Hawaii (2003) pp. 3615–3620.Google Scholar
27.Das, A., Fierro, R., Kumar, V., Ostrowski, J., Spletzer, J. and Taylor, C., “A vision-based formation control framework,” IEEE Trans. Robot. Autom. 18 (5), 813–825 (2002).Google Scholar
28.Takahashi, H., Nishi, H. and Ohnishi, K., “Autonomous decentralized control for formation of multiple mobile robots considering ability of robot,” IEEE Trans. Ind. Electron. 51 (6), 1272–1279 (2004).CrossRefGoogle Scholar
29.Gu, D. and Hu, H., “A stabilizing receding horizon regulator for nonholonomic mobile robots,” IEEE Trans. Robot. 21 (5), 1022–1028 (2005).Google Scholar
30.Bleris, L., Vouzis, P., Arnold, M. and Kothare, M., “A co-processor FPGA platform for the implementation of real-time model predictive control,” Proceedings of American Control Conference, Minneapolis, MN (June 2006).Google Scholar