Stable and Adaptive Control for Wheeled Mobile Platform
ABSTRACT
Most differential drive platforms are equipped with two independent actuators and casters. The positions of the gravity center and the rotation center often do not coincide. This position difference, combined with the effect of unbalanced actuator dynamics on the motion, makes it difficult to properly control the platform. We propose an adaptive nonlinear controller system based on the Lyapunov stability theory that greatly improves the trajectory tracking performance of such platforms. The asymptotically stable kinematic controller takes into account the position difference and the effect of the unbalanced actuator dynamics. The dynamic controller has the desirable property that it requires minimal knowledge of the platform physical parameters. Validation was performed through simulation and several experiments conducted on a rear driven powered wheelchair. Comparative experimental studies suggested that the proposed adaptive control system performs better than a similar method presented in the literature for linear as well as curvilinear trajectory tracking. Furthermore, the control system exhibits good tracking performance on inclined plans and non smooth surfaces.
KEYWORDS
Robotic Control; Lyapunov Stability; Nonholonomic Control; Differential Drive; Powered Wheelchair
Robotic Control; Lyapunov Stability; Nonholonomic Control; Differential Drive; Powered Wheelchair
Cite this paper
S. Kelouwani, C. Ouellette and P. Cohen, "Stable and Adaptive Control for Wheeled Mobile Platform," Intelligent Control and Automation, Vol. 4 No. 4, 2013, pp. 391-405. doi: 10.4236/ica.2013.44047.
S. Kelouwani, C. Ouellette and P. Cohen, "Stable and Adaptive Control for Wheeled Mobile Platform," Intelligent Control and Automation, Vol. 4 No. 4, 2013, pp. 391-405. doi: 10.4236/ica.2013.44047.
References
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[1] M. Deng, A. Inoue, K. Sekiguchi and L. Jiang, “TwoWheeled Mobile Robot Motion Control in Dynamic Environments,” Robotics and Computer-Integrated Manufacturing, Vol. 26, No. 3, 2010, pp. 268-272.
http://dx.doi.org/10.1016/j.rcim.2009.11.005 [2] W. Yu, O. Y. Chuy Jr., E. G. Collins Jr. and P. Hollis, “Analysis and Experimental Verification for Dynamic Modeling of a Skid-Steered Wheeled Vehicle,” IEEE Transactions on Robotics, Vol. 26, No. 2, 2010, pp. 340353. http://dx.doi.org/10.1109/TRO.2010.2042540 [3] D.-E. Ameddah and T. Benmokrane, “A Comparison of a Classical Pid and Sliding Mode: Traction Control for Fast Wheeled Mobile Robot,” International Journal of Automation and Control, Vol. 4, No. 1, 2010, pp. 65-83.
http://dx.doi.org/10.1504/IJAAC.2010.029839 [4] H. Wang and G. Li, “Motion Control and Trajectory Tracking Control for a Mobile Robot via Disturbance Observer,” WSEAS Transactions on Systems, Vol. 9, No. 1, 2010, pp. 31-41. [5] M. K. Bugeja, S. G. Fabri, and L. Camilleri, “Dual Adaptive Dynamic Control of Mobile Robots Using Neural Networks,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 39, No. 1, 2009, pp. 129-141.
http://dx.doi.org/10.1109/TSMCB.2008.2002851 [6] R. W. Brocket, “Asymptotic Stability and Feedback Stabilization,” In: R. W. Brockett, R. S. Millman and H. J. Sussmann, eds., Differential Geometric Control Theory, Birkhauser, Boston, 1983, pp. 181-208. [7] E. Noohi, S. S. Mahdavi, A. Baghani and M. N. Ahmadabadi, “Wheel-Based Climbing Robot: Modeling and Control,” Advanced Robotics, Vol. 24, No. 8-9, 2010, pp. 1313-1343.
http://dx.doi.org/10.1163/016918610X501453 [8] Y. Kanayama, Y. Kimura, F. Miyazaki and T. Noguchi, “A Stable Tracking Control Method for a Non-Holonomic Mobile Robot,” Proceedings of IEEE/RSJ International Workshop on Intelligent Robots and Systems ’91. Intelligence for Mechanical Systems, Osaka, 3-5 November 1991, pp. 1236-1241. [9] J. L. Avendano-Juarez, V. M. Hernandez-Guzman and R. Silva-Ortigoza, “Velocity and Current Inner Loops in a Wheeled Mobile Robot,” Advanced Robotics, Vol. 24, No. 8-9, 2010, pp. 1385-1404.
http://dx.doi.org/10.1163/016918610X501480 [10] A. Astolfi, “Exponential Stabilization of Nonholonomic Systems via Discontinuous Control,” Journal of Dynamic Systems, Measurement, and Control, Vol. 121, 1999, pp. 121-126.
http://dx.doi.org/10.1115/1.2802429 [11] Z.-G. Hou, A.-M. Zou, L. Cheng and M. Tan, “Adaptive Control of an Electrically Driven Nonholonomic Mobile Robot via Backstepping and Fuzzy Approach,” IEEE Transactions on Control Systems Technology, Vol. 17, No. 4, 2009, pp. 803-815.
http://dx.doi.org/10.1109/TCST.2009.2012516 [12] R. C. Luo, T. M. Chen, C.-Y. Hu and Z. H. Hsiao, “Adaptive Intelligent Assistance Control of Electrical Wheelchairs by Grey-Fuzzy Decision-Making Algorithm,” Proceedings of IEEE International Conference on Robotics and Automation, Vol. 3, 1999, pp. 2014-2019. [13] B. S. Park, S. J. Yoo, J. B. Park and Y. H. Choi, “Adaptive Neural Sliding Mode Control of Nonholonomic Wheeled Mobile Robots with Model Uncertainty,” IEEE Transactions on Control Systems Technology, Vol. 17, No. 1, 2009, pp. 207-214.
http://dx.doi.org/10.1109/TCST.2008.922584 [14] A. Venelinov Topalov, J.-H. Kim and T. Proychev, “Fuzzy-Net Control of Non-Holonomic Mobile Robot Using Evolutionary Feedback-Error-Learning,” Robotics and Autonomous Systems, Vol. 23, No. 3, 1998, pp. 187200. http://dx.doi.org/10.1016/S0921-8890(98)80013-4 [15] J. Wang, Z. Qu, M. Obeng and X. Wu, “Approximation Based Adaptive Tracking Control of Uncertain Nonholonomic Mechanical Systems,” Control and Intelligent Systems, Vol. 37, No. 4, 2009, pp. 204-211. [16] M. Egerstedt, X. Hu and A. Stotsky, “Control of Mobile Platforms Using a Virtual Vehicle Approach,” IEEE Transactions on Automatic Control, Vol. 46, No. 11, 2001, pp. 1777-1782.
http://dx.doi.org/10.1109/9.964690 [17] J. Chang and Q.-X. Meng, “Stabilization Control of Nonholonomic Wheeled Mobile Service Robots,” Key Engineering Materials, Vol. 419-420, 2010, pp. 593-596.
http://dx.doi.org/10.4028/www.scientific.net/KEM.419-420.593 [18] R. Mukherjee, D. Chen and G. Song, “Feedback Control Strategies for a Nonholonomic Mobile Robot Using a Nonlinear Oscillator,” Journal of Robotic Systems, Vol. 16, No. 4, 1999, pp. 237-248.
http://dx.doi.org/10.1002/(SICI)1097-4563(199904)16:4<237::AID-ROB4>3.0.CO;2-F [19] C. Samson, “Velocity and Torque Feedback Control of a Nonholonomic Cart,” Lecture Notes in Control and Information Sciences, Vol. 162, 1991, pp. 125-151.
http://dx.doi.org/10.1007/BFb0039269 [20] K. Tsuchiya, T. Urakubo and K. Tsujita, “Motion Control of a Nonholonomic System Based on the Lyapunov Control Method,” Journal of Guidance, Control, and Dynamics, Vol. 25, No. 2, 2002, pp. 285-290.
http://dx.doi.org/10.2514/2.4880 [21] W. Oelen, H. Berghuis, H. Nijmeijer and C. C. de Wit, “Hybrid Stabilizing Control on a Real Mobile Robot,” IEEE Robotics and Automation Magazine, Vol. 2, No. 2, 1995, pp. 16-23.
http://dx.doi.org/10.1109/100.392415 [22] T. Urakubo, K. Tsuchiya and K. Tsujita, “Motion Control of a Two-Wheeled Mobile Robot,” Advanced Robotics, Vol. 15, No. 7, 2001, pp. 711-728.
http://dx.doi.org/10.1163/15685530152744581 [23] C.-L. Hwang, “A Novel Takagi-Sugeno-Based Robust Adaptive Fuzzy Sliding-Mode Controller,” IEEE Transactions on Fuzzy Systems, Vol. 12, No. 5, 2004, pp. 676687.
http://dx.doi.org/10.1109/TFUZZ.2004.834811 [24] A. Rojko and K. Jezernik, “Sliding-Mode Motion Controller with Adaptive Fuzzy Disturbance Estimation,” IEEE Transactions on Industrial Electronics, Vol. 51, No. 5, 2004, pp. 963-971.
http://dx.doi.org/10.1109/TIE.2004.834945 [25] A. Fel’Dbaum, “Application of Theory of Statistical Solutions to Open and Closed-Loop Automatic Control Systems,” Engineering Cybernetics, No. 1, 1963, pp. 1-12. [26] Y. Ou and Y. Xu, “Gyroscopically Stabilized Robot: Balance and Tracking,” International Journal of Advanced Robotic Systems, Vol. 1, No. 1, 2004, pp. 23-32. [27] F. Mnif and A. Yahmadi, “Recursive Backstepping Stabilization of a Wheeled Mobile Robot,” Vol. 219, No. 6, 2005, pp. 419-429. [28] R.-J. Wai and C.-M. Liu, “Design of Dynamic Petri Recurrent Fuzzy Neural Network and Its Application to Path-Tracking Control of Nonholonomic Mobile Robot,” IEEE Transactions on Industrial Electronics, Vol. 56, No. 7, 2009, pp. 2667-2683.
http://dx.doi.org/10.1109/TIE.2009.2020077 [29] R. Fierro and F. Lewis, “Control of a Nonholonomic Mobile Robot: Backstepping Kinematics into Dynamics,” Proceedings of the 34th IEEE Conference on Decision and Control, Vol. 4, 1995, pp. 3805 -3810. [30] S. Kelouwani, C. Ouellette and P. Cohen, “Adaptive Nonlinear Controller Design for Differential-Drive Mobile Platforms,” 2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 6-9 July 2010, pp. 1238-1244. [31] J. Craig, Introduction to Robotics: Mechanics and Control. 1em plus 0.5em minus 0.4em Addison-Wesley, 1989. [32] R. DeSantis, “Dynamique des Systèmes Mécaniques Sous Contraintes Holonomes et Non Holonomes,”1em plus 0.5em minus 0.4em école Polytechnique de Montréal, 1989. [33] S. Sastry and M. Bodson, “Adaptive Control: Stability, Convergence, and Robustness,” 1em plus 0.5em minus 0.4em Prentice-Hall Advanced Reference Series (Engineering), 1994. [34] S. K. Vincent Zalzal, R. Gava and P. Cohen, “Acropolis: A Fast Prototyping Robotic Application,” International Journal of Advanced Robotic Systems, Vol. 6, No. 1, 2009, pp. 1-6. [35] L. Montesano, M. Diaz, S. Bhaskar and J. Minguez, “Towards an Intelligent Wheelchair System for Users with Cerebral Palsy,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, Vol. 18, No. 2, 2010, pp. 193-202.
http://dx.doi.org/10.1109/TNSRE.2009.2039592 [36] M. Elarbi-Boudihir and K. Al-Shalfan, “Adaptable Intelligent Robotic Wheelchair for Severely Disabled People,” Journal of Digital Information Management, Vol. 7, No. 4, 2009, pp. 252-260.