Adaptive Tracking Control of an Uncertain Nonholonomic Robot
ABSTRACT
In this paper, a new controller is proposed by using backstepping method for the trajectory tracking problem of nonholonomic dynamic mobile robots with nonholonomic constraints under the condition that there is a distance between the mass center and the geometrical center and the distance is unknown. And an adaptive feedback controller is also proposed for the case that some kinematic parameters and dynamic parameters are uncertain. The asymptotical stability of the control system is proved with Lyapunov stability theory. The simulation results show the effectiveness of the proposed controller. The comparison with the previous methods is made to show the effectiveness of the method in this article.
In this paper, a new controller is proposed by using backstepping method for the trajectory tracking problem of nonholonomic dynamic mobile robots with nonholonomic constraints under the condition that there is a distance between the mass center and the geometrical center and the distance is unknown. And an adaptive feedback controller is also proposed for the case that some kinematic parameters and dynamic parameters are uncertain. The asymptotical stability of the control system is proved with Lyapunov stability theory. The simulation results show the effectiveness of the proposed controller. The comparison with the previous methods is made to show the effectiveness of the method in this article.
Cite this paper
nullN. Hu and C. Wang, "Adaptive Tracking Control of an Uncertain Nonholonomic Robot," Intelligent Control and Automation, Vol. 2 No. 4, 2011, pp. 396-404. doi: 10.4236/ica.2011.24045.
nullN. Hu and C. Wang, "Adaptive Tracking Control of an Uncertain Nonholonomic Robot," Intelligent Control and Automation, Vol. 2 No. 4, 2011, pp. 396-404. doi: 10.4236/ica.2011.24045.
References
[1] R. W. Brockett, “Differential Geometric Control Theory,” Burkhauser, Boston, 1983. [2] R. M. Murray and S. S. Sastry, “Nonholonomic Motion Planning: Steering Using Sinusoids,” IEEE Transactions on Automatic Control, Vol. 38, No. 5, 1993, pp. 700-716. doi:10.1109/9.277235 [3] Y. P. Tian and S. Li, “Exponential Stabilization of Nonholonomic Dynamic Systems by Smooth Time-Varying Control,” Automatica, Vol. 38, No. 7, 2002, pp. 1139-1146. doi:10.1016/S0005-1098(01)00303-X [4] A. Teel, R. Murry and G. Walsh, “Nonholonomic Control Systems: From Steering To Stabilization with Sinusoids,” Proceeding of 31st IEEE Conference on Decision Control, Tucson, 16-18 December 1992, pp. 1603-1609. doi:10.1109/CDC.1992.371456 [5] A. Astolfi, “Discontinuous Control of Nonholonomic Systems,” Systems & Control Letters, Vol. 27, No. 1, 1996, pp. 37-45. doi:10.1016/0167-6911(95)00041-0 [6] A. M. Bloch and S. Drakunov, “Stabilization of a Nonholonomic Systems via Sliding Modes,” Proceeding of 33st IEEE Conference on Decision Control, Lake Buena Vista, 14-16 December 1994, pp. 2961-2963. doi:10.1109/CDC.1994.411342 [7] C. Canudas de Wit and O. J. Sordalen, “Exponential Stabilization of Mobile Robots with Nonholonomic Constraints,” IEEE Transactions on Automatic Control, Vol. 37, No. 11, 1992, pp. 1791-1797. doi:10.1109/9.173153 [8] O. J. Sordalen and O. Egeland, “Exponential Stabilization of Nonholonomic Chained Systems,” IEEE Transactions on Automatic Control, Vol. 40, No. 1, 1995, pp.35-49. doi:10.1109/9.362901 [9] P. Soueres, A. Balluchi and A. Bicchi, “Optimal Feedback Control for Line Tracking with a Bounded-Curvature Vehicle,” International Journal of Control, Vol. 74, No. 10, 2001, pp. 1009-1019. [10] I. I. Hussein and A. M. Bloch, “Optimal Control of Underactuated Nonholonomic Mechanical Systems,” IEEE Transactions on Automatic Control, Vol. 53, No. 3, 2008, pp. 668-682. doi:10.1109/TAC.2008.919853 [11] Z. Qu, J. Wang, C. E. Plaisted and R. A. Hull, “Global-Stabilizing Near-Optimal Control Design for Nonholonomic Chained Systems,” IEEE Transactions on Automatic Control, Vol. 51, No. 9, 2006, pp. 1440-1456. doi:10.1109/TAC.2006.880965 [12] Y. Haowen, S. Yang and G. S. Mittal, “Tracking Control of a Nonholonomic Mobile Robot by Integrating Feedback and Neural Dynamics Techniques,” Proceedings of the 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, Miami, 27-31 October 2003, pp. 3522- 3527. doi:10.1109/IROS.2003.1249701 [13] Y. Kanayama, Y. Kimura and T. Noguchi, “A Stable Tracking Method for an Autonomous Mobile Robot,” Proceedings of 1990 IEEE International Conference on Robotics and Automation, Cincinnati, 13-18 May 1990, pp. 384-389. doi: 10.1109/ROBOT.1990.126006 [14] R. Fierro and F. L. Lewis, “Control of a Nonholonomic Mobile Robot: Backstepping Kinematics into Dynamics,” Proceeding of the 34th Conference on Decision and Control, New Orleans, 13-15 December 1995, pp. 3805-3810. doi: 10.1109/CDC.1995.479190 [15] J. Yang and J. Kim, “Sliding Mode Motion Control of Nonholonomic Mobile Robots,” IEEE Control Systems, Vol. 19, No. 2, 1999, pp. 15-23. doi: 10.1109/37.753931 [16] T. Hu and S. X. Yang, “An Efficient Neural Controller for a Nonholonomic Mobile Robot,” Proceedings of 2001 IEEE International Conference on Robotics and Automation, Piscataway, 2001, pp. 461-466. doi:10.1109/CIRA.2001.1013245 [17] T. Fukao, H. Nakagawa and N. Adachi, “Adaptive Tracking Control of a Nonholonomic Mobile Robot,” IEEE Transaction on Robotics and Automation, Vol. 16, No. 5, 2000, pp. 609-615. doi:10.1109/70.880812 [18] J. B. Wu, G. H. Xu and Z. P. Yin, “Robust Adaptive Control for a Nonholonomic Mobile Robot with Unknown Parameters,” Journal of Control Theory and Applications, Vol. 7, No. 2, 2009, 212-218. doi:10.1007/s11768-009-7130-6 [19] M. Yan, Q. Wu and Y. He, “Adaptive Sliding Mode Tracking Control of Nonholonomic Mobile Robot,” Journal of System Simulation, Vol. 19, No. 3, 2007, pp. 579-581. [20] J. J. E. Slotine and W. P. Li, “Applied Nonlinear Control,” Prentice Hall, Upper Saddle River, 1991. [21] C. Samson, “Control of Chained Systems Application to Path Following and Time-Varying Point-Stabilization of Mobile Robots,” IEEE Transactions on Automatic Control, Vol. 40, No. 1, 1995, pp. 64-77. doi:10.1109/9.362899
[1] R. W. Brockett, “Differential Geometric Control Theory,” Burkhauser, Boston, 1983. [2] R. M. Murray and S. S. Sastry, “Nonholonomic Motion Planning: Steering Using Sinusoids,” IEEE Transactions on Automatic Control, Vol. 38, No. 5, 1993, pp. 700-716. doi:10.1109/9.277235 [3] Y. P. Tian and S. Li, “Exponential Stabilization of Nonholonomic Dynamic Systems by Smooth Time-Varying Control,” Automatica, Vol. 38, No. 7, 2002, pp. 1139-1146. doi:10.1016/S0005-1098(01)00303-X [4] A. Teel, R. Murry and G. Walsh, “Nonholonomic Control Systems: From Steering To Stabilization with Sinusoids,” Proceeding of 31st IEEE Conference on Decision Control, Tucson, 16-18 December 1992, pp. 1603-1609. doi:10.1109/CDC.1992.371456 [5] A. Astolfi, “Discontinuous Control of Nonholonomic Systems,” Systems & Control Letters, Vol. 27, No. 1, 1996, pp. 37-45. doi:10.1016/0167-6911(95)00041-0 [6] A. M. Bloch and S. Drakunov, “Stabilization of a Nonholonomic Systems via Sliding Modes,” Proceeding of 33st IEEE Conference on Decision Control, Lake Buena Vista, 14-16 December 1994, pp. 2961-2963. doi:10.1109/CDC.1994.411342 [7] C. Canudas de Wit and O. J. Sordalen, “Exponential Stabilization of Mobile Robots with Nonholonomic Constraints,” IEEE Transactions on Automatic Control, Vol. 37, No. 11, 1992, pp. 1791-1797. doi:10.1109/9.173153 [8] O. J. Sordalen and O. Egeland, “Exponential Stabilization of Nonholonomic Chained Systems,” IEEE Transactions on Automatic Control, Vol. 40, No. 1, 1995, pp.35-49. doi:10.1109/9.362901 [9] P. Soueres, A. Balluchi and A. Bicchi, “Optimal Feedback Control for Line Tracking with a Bounded-Curvature Vehicle,” International Journal of Control, Vol. 74, No. 10, 2001, pp. 1009-1019. [10] I. I. Hussein and A. M. Bloch, “Optimal Control of Underactuated Nonholonomic Mechanical Systems,” IEEE Transactions on Automatic Control, Vol. 53, No. 3, 2008, pp. 668-682. doi:10.1109/TAC.2008.919853 [11] Z. Qu, J. Wang, C. E. Plaisted and R. A. Hull, “Global-Stabilizing Near-Optimal Control Design for Nonholonomic Chained Systems,” IEEE Transactions on Automatic Control, Vol. 51, No. 9, 2006, pp. 1440-1456. doi:10.1109/TAC.2006.880965 [12] Y. Haowen, S. Yang and G. S. Mittal, “Tracking Control of a Nonholonomic Mobile Robot by Integrating Feedback and Neural Dynamics Techniques,” Proceedings of the 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, Miami, 27-31 October 2003, pp. 3522- 3527. doi:10.1109/IROS.2003.1249701 [13] Y. Kanayama, Y. Kimura and T. Noguchi, “A Stable Tracking Method for an Autonomous Mobile Robot,” Proceedings of 1990 IEEE International Conference on Robotics and Automation, Cincinnati, 13-18 May 1990, pp. 384-389. doi: 10.1109/ROBOT.1990.126006 [14] R. Fierro and F. L. Lewis, “Control of a Nonholonomic Mobile Robot: Backstepping Kinematics into Dynamics,” Proceeding of the 34th Conference on Decision and Control, New Orleans, 13-15 December 1995, pp. 3805-3810. doi: 10.1109/CDC.1995.479190 [15] J. Yang and J. Kim, “Sliding Mode Motion Control of Nonholonomic Mobile Robots,” IEEE Control Systems, Vol. 19, No. 2, 1999, pp. 15-23. doi: 10.1109/37.753931 [16] T. Hu and S. X. Yang, “An Efficient Neural Controller for a Nonholonomic Mobile Robot,” Proceedings of 2001 IEEE International Conference on Robotics and Automation, Piscataway, 2001, pp. 461-466. doi:10.1109/CIRA.2001.1013245 [17] T. Fukao, H. Nakagawa and N. Adachi, “Adaptive Tracking Control of a Nonholonomic Mobile Robot,” IEEE Transaction on Robotics and Automation, Vol. 16, No. 5, 2000, pp. 609-615. doi:10.1109/70.880812 [18] J. B. Wu, G. H. Xu and Z. P. Yin, “Robust Adaptive Control for a Nonholonomic Mobile Robot with Unknown Parameters,” Journal of Control Theory and Applications, Vol. 7, No. 2, 2009, 212-218. doi:10.1007/s11768-009-7130-6 [19] M. Yan, Q. Wu and Y. He, “Adaptive Sliding Mode Tracking Control of Nonholonomic Mobile Robot,” Journal of System Simulation, Vol. 19, No. 3, 2007, pp. 579-581. [20] J. J. E. Slotine and W. P. Li, “Applied Nonlinear Control,” Prentice Hall, Upper Saddle River, 1991. [21] C. Samson, “Control of Chained Systems Application to Path Following and Time-Varying Point-Stabilization of Mobile Robots,” IEEE Transactions on Automatic Control, Vol. 40, No. 1, 1995, pp. 64-77. doi:10.1109/9.362899