Abstract
Aiming at the trajectory tracking problem of nonholonomic wheeled mobile robots (WMR) with bounded external disturbances and parameter uncertainties, a dual-loop attitude tracking robust controller is proposed for WMR. Firstly, a kinematic controller is designed to generate the virtual velocity based on the kinematic error model. Secondly, the sliding mode control with a modified reaching law is adopted to ensure the actual velocity can converge to the virtual velocity in finite time based on the dynamic model. Finally, the stability of the controller is verified through the Lyapunov function. Numerical simulation shows the robustness and effectiveness of the proposed dual-loop tracking controller.
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Z. Jiang and H. Nijmeijer, “Tracking control of mobile robots: a case study in backstepping,” Automatica, vol. 33, no. 7, pp. 1393–1399, February, 1997.
D. Kim and T. Oh, “Tracking control of a two-wheeled mobile robot using input-output linearization,” Control Engineering Practice, vol. 7, no. 3, pp. 369–373, July, 1999.
D. Chwa, “Sliding-mode control of nonholonomic wheeled mobile robots in polar coordinates,” IEEE Trans. on Control Systems Technology, vol. 12, no. 4, pp. 637–644, July, 2004.
O. Mofid and S. Mobayen, “Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties,” ISA Trans., vol. 72, pp. 1–14, January, 2018.
J. Zhai and Z. Song, “Adaptive sliding mode trajectory tracking control for wheeled mobile robots,” International Journal of Control, vol. 92, no. 10, pp. 2255–2262, October, 2019.
R. Fierro and F. Lewis, “Control of a nonholonomic mobile robot using neural networks,” IEEE Trans. on Neural Networks, vol. 9, no. 4, pp. 589–600, April, 1998.
B. Park, S. Yoo, J. Park, Y. Choi, “Adaptive neural sliding mode control of nonholonomic wheeled mobile robots with model uncertainty,” IEEE Trans. on Control Systems Technology, vol. 17, no. 1, pp. 207–214, January, 2009.
H. Du, J. Zhai, M. Chen, and W. Zhu, “Robustness analysis of a continuous higher order finite-time control system under sampled-data control,” IEEE Trans. on Automatic Control, vol. 64, no. 6, pp. 2488–2494, June, 2019.
S. Li, L. Ding, H. Gao, C. Chen, Z. Liu, and Z. Deng, “Adaptive neural network tracking control-based reinforcement learning for wheeled mobile robots with skidding and slipping,” Neurocomputing, vol. 283, pp. 20–30, December, 2017.
J. Y. Zhai and H. R. Karimi, “Universal adaptive control for uncertain nonlinear systems via output feedback,” Information Sciences, vol. 500, pp. 140–155, October, 2019.
J. Y. Zhai and H. R. Karimi, “Global output feedback control for a class of nonlinear systems with unknown homogenous growth condition,” International Journal of Robust and Nonlinear Control, vol. 29, no. 7, pp. 2082–2095, May, 2019.
G. Walsh, D. Tilbury, S. Sastry, R. Murray, and J. Laumond, “Stabilization of trajectories for systems with non-holonomic constraints,” IEEE Trans. on Automatic Control, vol. 39, no. 1, pp. 216–222, January, 1994.
S. Lee, Y. Cho, M. Hwang, B. You, and S. Oh, “A stable target-tracking control for unicycle mobile robots,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1822–1827, March, 2000.
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, pp. 1236–1241, November, 1991.
W. Chen, “Disturbance observer based control for nonlinear systems,” IEEE/ASME Trans. on Mechatronics, vol. 9, no. 4, pp. 706–710, April, 2004.
M. Hassana, E. Aljuwaiser, and R. Badr, “A new online observer-based controller for leader-follower formation of multiple nonholonomic mobile robots,” Journal of the Franklin Institute, vol. 355, no. 5, pp. 2436–2472, February, 2018.
D. Huang, J. Zhai, W. Ai, and S. Fei, “Disturbance observer-based robust control for trajectory tracking of wheeled mobile robots,” Neurocomputing, vol. 198, pp. 74–79, March, 2016.
S. Li and Y. Tian, “Finite-time stability of cascaded time-varying systems,” International Journal of Control, vol. 80, no. 4, pp. 646–657, April, 2007.
F. Pourboghrat and M. Karlsson, “Adaptive control of dynamic mobile robots with nonholonomic constraints,” Computers and Electrical Engineering, vol. 28, no. 4, pp. 241–253, April, 2002.
J. Huang, C. Wen, W. Wang, and Z. Jiang, “Adaptive stabilization and tracking control of a nonholonomic mobile robot with input saturation and disturbance,” System and Control Letters, vol. 62, no. 3, pp. 234–241, January, 2013.
I. Matraji, A. Durra, A. Haryono, K. Wahedi, and M. Khousa, “Trajectory tracking control of skid-steered mobile robot based on adaptive second order sliding mode control,” Control Engineering Practice, vol. 72, pp. 167–176, March, 2018.
Y. Wu, X. Yu, and Z. Man, “Terminal sliding mode control design for uncertain dynamic systems,” System and Control Letters, vol. 34, no. 5, pp. 281–287, March, 1998.
D. Wu, Y. Cheng, H. Du, W. Zhu, and M. Zhu, “Finite-time output feedback tracking control for a nonholonomic wheeled mobile robot,” Aerospace Science and Technology, vol. 78, pp. 574–579, July, 2018.
W. Ji, J. Qiu, and H. Karimi, “Fuzzy-model-based output feedback sliding mode control for discrete-time uncertain nonlinear systems,” IEEE Trans. on Fuzzy Systems, 2019. DOI: https://doi.org/10.1109/TFUZZ.2019.2917127
L. Hsu, T. Oliveira, J. Cunha, and L. Yan, “Adaptive unit vector control of multivariable systems using monitoring functions,” International Journal of Robust and Nonlinear Control, vol. 29, no. 3, pp. 583–600, February, 2019.
P. Pinto, R. Oliveira, and L. Hsu, “Sliding mode observer for fault reconstruction of time-delay and sampled-output systems — a Time Shift Approach,” Automatica, vol. 106, pp. 390–400, May, 2019.
A. Ilchmann and D. Owens, “Adaptive stabilization with exponential decay,” Systems and Control Letters, vol. 14, no. 5, pp. 437–443, January, 1990.
N. Sun, D. Liang, Y. Wu, Y. Chen, Y. Qin, and Y. Fang, “Adaptive control for pneumatic artificial muscle systems with parametric uncertainties and unidirectional input constraints,” IEEE Trans. on Industrial Informatics, vol. 16, no. 2, pp. 969–979, February, 2020.
T. Yang, N. Sun, H. Chen, and Y. Fang, “Neural network-based adaptive antiswing control of an underactuated ship-mounted crane with roll motions and input dead zones,” IEEE Trans. on Neural Networks and Learning System, vol. 31, no. 3, pp. 901–914, March, 2020.
N. Hoang and H. Kang, “Neural network-based adaptive tracking control of mobile robots in the presence of wheel slip and external disturbance force,” Neurocomputing, vol. 188, pp. 12–22, February, 2016.
J. Moreno, D. Negrete, V. Torres-Gonzalez, and L. Fridman, “Adaptive continuous twisting algorithm,” International Journal of Control, vol. 89, no. 9, pp. 1798–1806, July, 2016.
M. Boukattaya, N. Mezghani, and T. Damak, “Adaptive nonsingular fast terminal sliding mode control for the tracking problem of uncertain dynamical system,” ISA Trans., vol. 77, pp. 1–19, June, 2018.
S. Yi and J. Zhai, “Adaptive second-order fast nonsingular terminal sliding mode control for robotic manipulators,” ISA Trans., vol. 90, pp. 41–51, July, 2019.
S. Bhat and D. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM J. Control and Optimization, vol. 38, no. 3, pp. 751–766, March, 2000.
S. Mondal and C. Mahanta, “Adaptive second order terminal sliding mode controller for robotic manipulators,” Journal of the Franklin Institute, vol. 351, no. 4, pp. 2356–2377, April, 2014.
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Recommended by Associate Editor Quoc Chi Nguyen under the direction of Editor Myo Taeg Lim.
Hui Ye received her M.S. degree from College of Mathematics and Information Science, Jiangsu University, Zhenjiang, China. She is an associate professor at School of Science, Jiangsu University of Science and Technology. Her current research interests include robot control, stability analysis and fault tolerant control of switched systems.
Shuai Wang received her B.S. degree at Measurement and Control Technology and Instruments, University of Electronic Science and Technology of China, in 2017. She is currently pursuing her M.S. degree at the School of Automation, Southeast University. Her research interests include robot control and nonlinear systems.
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Ye, H., Wang, S. Trajectory Tracking Control for Nonholonomic Wheeled Mobile Robots with External Disturbances and Parameter Uncertainties. Int. J. Control Autom. Syst. 18, 3015–3022 (2020). https://doi.org/10.1007/s12555-019-0643-y
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DOI: https://doi.org/10.1007/s12555-019-0643-y