An adaptive variable structure controller for the trajectory tracking of a nonholonomic mobile robot with uncertainties and disturbances
Keywords:nonholonomic mobile robot, trajectory tracking, kinematic model, uncertainties and disturbances, adaptive variable structure controller, neural networks, Lyapunov method
In this paper, a trajectory tracking control for a nonholonomic mobile robot subjected to uncertainties and disturbances in the kinematic model is proposed. An adaptive variable structure controller based on the sliding mode theory is used, and applied to compensate these uncertainties and disturbances. To minimize the problems found in practical implementation using classical variable structure controllers, and eliminate the chattering phenomenon as well as compensate disturbances a neural compensator is used, which is nonlinear and continuous, in lieu of the discontinuous portion of the control signals present in classical forms. The proposed neural compensator is designed by a modeling technique of Gaussian radial basis function neural networks and does not require the time-consuming training process. Stability analysis is guaranteed with basis on the Lyapunov method. Simulation results are provided to show the effectiveness of the proposed approach.
 P. Morin, and C. Samson, “Motion Control of Wheeled Mobile Robots,” in B. Siciliano and O. Khatib (Eds.), Handbook of Robotics, Springer-Verlag: Berlin, Heidelberg, Germany, pp. 799-826, 2008.
 V. Utkin, J. Guldner, and J. Shi, “Sliding Mode Control in Eletro-Mechanical Systems,” 2 nd Edition, CRC Press, Boca Raton, Florida, USA, 2009.
 J. Y. Hung, W. Gao, and J. C. Hung, “Variable Structure Control: A Survey,” IEEE Trans. Industrial Electronics, vol. 40, no. 1, pp. 2-22, 1993.
 W. Gao, and J. C. Hung, “Variable Structure Control of Nonlinear Systems: A New Approach,” IEEE Trans. Industrial Electronics, vol. 40, no. 1, pp. 45-55, 1993.
 P. Shuwen, S. Hongye, H. Xiehe, and C. Jian, “Variable Structure Control Theory and Application: A Survey”, Proc. World Congress Intelligent Control and Automation, pp. 2977-2981, 2000.
 O. Kaynak, K. Erbatur, and M. Ertugrul, “The Fusion of Computationally Intelligent Methodologies and Sliding Mode Control - A Survey,” IEEE Trans. Industrial Electronics, vol. 48, no. 1, pp. 4-17, 2001.
 S. Seshagiri, and H. K. Khalil, “Output Feedback Control of Nonlinear Systems using RBF Neural Networks,” IEEE Trans. Neural Networks, vol. 11, no. 1, pp. 69-79, 2000.
 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 Trans. Control Systems Technology, vol. 17, no. 1, pp. 207-214, 2009.
 Y. Li, L. Zhu, Z. Wang, and T. Liu, “Trajectory Tracking for Nonholonomic Wheeled Mobile Robots based on an Improved Sliding Mode Control Method”, Proc. Int. Colloquium on Computing, Communication, Control, and Management, vol. 2, pp. 55-58, 2009.
 J. H. Lee, C. Lin, H. Lim, and J. M. Lee, “Sliding Mode Control for Trajectory Tracking of Mobile Robot in the RFID Sensor Space,” Int. Journal of Control, Automation, and Systems, vol. 7, no. 3, pp. 429-436, 2009.
 D. Chwa, “Sliding-Mode Tracking Control of Nonholonomic Wheeled Mobile Robots in Polar Coordinates,” IEEE Trans. Control Systems Technology, vol. 12, no. 4, pp. 637- 644, 2004.
 D. Chwa, J. H. Seo, P. Kim, and J. Y. Choi, “Sliding Mode Tracking Control of Nonholonomic Wheeled Mobile Robots”, Proc. American Control Conference, vol. 5, pp. 3991-3996, 2002.
 J.-M. Yang, and J.-H. Kim, “Sliding Mode Control for Trajectory Tracking of Nonholonomic Wheeled Mobile Robots,” IEEE Trans. Robotics and Automation, vol. 15, no. 3, pp. 578-587, 1999.
 J.-M. Yang, J.-H. Kim, “Sliding Mode Motion Control of Nonholonomic Mobile Robots,” IEEE Control Systems Magazine, vol. 19, no. 2, pp. 15-23, 1999.
 M.-B. Cheng, and C.-C. Tsai, “Robust Backstepping Tracking Control using Hybrid Sliding-Mode Neural Network for a Nonholonomic Mobile Manipulator with Dual Arms”, Proc. IEEE Conf. on Decision and Control, and the European Control Conf., pp. 1964-1969, 2005.
 N. A. Martins, D. W. Bertol, W. C. Lombardi, E. R. De Pieri, and E. B. Castelan, “Trajectory Tracking of a Nonholonomic Mobile Robot with Parametric and Nonparametric Uncertainties: A Proposed Neural Control,” Int. Journal of Factory Automation, Robotics and Soft Computing, vol. 2, pp. 103-110, 2008.
 S. S. Ge, “Robust Adaptive NN Feedback Linearization Control of Nonlinear Systems,” Int. Journal Systems Science, pp. 1327-338, 1996.
 Y. Li, S. Qiang, X. Zhuang, and O. Kaynak, “Robust and Adaptive Backstepping Control for Nonlinear Systems using RBF Neural Networks,” IEEE Trans. Neural Networks, vol. 15, no. 3, pp. 693-701, 2004.
 C. de Sousa Jr., E. M. Hemerly, and R. K. H. Galvao, “Adaptive Control for Mobile Robot using Wavelet Networks,” IEEE Trans. Systems, Man, and Cybernetics, Part B, vol. 32, no. 4, pp. 493-504, 2002.
 M. Defoort, J. Palos, T. Floquet, A. Kokosy, W. Perruquetti, “Practical Stabilization and Tracking of a Wheeled Mobile Robot with Integral Sliding Mode Controller,” Proc. IEEE Conference on Decision and Control, pp. 1999-2004, 2007.