Dynamic surface control for omnidirectional mobile robot with full state constrains and input saturation

In this paper, we study the trajectory tracking problem of a three-wheeled omnidirectional mobile robot with full state constraints and actuator saturation. Firstly, we analyze a three-wheeled omnidirectional mobile robot and give control model with actuator saturation. By using tan-type Barrier Lyapunov Function and backstepping method, kinematic and dynamic controllers are built, which can ensure that the system full states will not violate the given constraints when the robot is performing trajectory tracking. Then, considering the differential explosion problem which occurs when solving the derivatives of the virtual control law, we use a second-order differential sliding mode surface to calculate it, so as to reduce the complexity of the operation. In addition, due to the output saturation problem of the robot drive motor, an auxiliary compensation system is adopted to compensate for the error generated by the saturation function. Finally, an experimental simulation is performed in MATLAB and the simulation results illustrate the effectiveness of the control algorithm proposed in this paper.

1. Kramer J., Scheutz M. Development environments for autonomous mobile robots: A survey. Autonomous Robots, 2007, vol. 22, no. 1, pp. 101–132. https://doi.org/10.1007/s10514-006-9013-8

2. Watanabe K., Shiraishi Y., Tzafestas S.G., Tang J., Fukuda T. Feedback control of an omnidirectional autonomous platform for mobile service robots. Journal of Intelligent and Robotic Systems, 1998, vol. 22, pp. 315–330. https://doi.org/10.1023/A:1008048307352

3. Kalmár-Nagy T., D’Andrea R., Ganguly P. Near-optimal dynamic trajectory generation and control of an omnidirectional vehicle. Robotics and Autonomous Systems, 2003, vol. 46, no. 1, pp. 47–64. https://doi.org/10.1016/j.robot.2003.10.003

4. Liu Y., Zhu J.J., Williams R.L. II, Wu J. Omni-directional mobile robot controller based on trajectory linearization. Robotics and autonomous Systems, 2008, vol. 56, no. 5, pp. 461–479. https://doi.org/10.1016/j.robot.2007.08.007

5. Huang H.C., Tsai C.C. Adaptive trajectory tracking and stabilization for omnidirectional mobile robot with dynamic effect and uncertainties. IFAC Proceedings Volumes, 2008, vol. 41, no. 2, pp. 5383–5388. https://doi.org/10.3182/20080706-5-KR-1001.00907

6. Alakshendra V., Chiddarwar S.S. Adaptive robust control of Mecanum-wheeled mobile robot with uncertainties. Nonlinear Dynamics, 2017, vol. 87, no. 4, pp. 2147–2169. https://doi.org/10.1007/s11071-016-3179-1

7. Lu X., Zhang X., Zhang G., Fan J., Jia S. Neural network adaptive sliding mode control for omnidirectional vehicle with uncertainties. ISA Transactions, 2019, vol. 86, pp. 201–214. https://doi.org/10.1016/j.isatra.2018.10.043

8. Zijie N., Qiang L., Yonjie C., Zhijun S. Fuzzy control strategy for course correction of omnidirectional mobile robot. International Journal of Control, Automation and Systems, 2019, vol. 17, no. 9, pp. 2354–2364. https://doi.org/10.1007/s12555-018-0633-5

9. Tee K.P., Ge S.S., Tay E.H. Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica, 2009, vol. 45, no. 4, pp. 918–927. https://doi.org/10.1016/j.automatica.2008.11.017

10. Xi C., Dong J. Adaptive neural network-based control of uncertain nonlinear systems with time-varying full-state constraints and input constraint. Neurocomputing, 2019, vol. 357, pp. 108–115. https://doi.org/10.1016/j.neucom.2019.04.060

11. Ding L., Li S., Liu Y.J., Gao H., Chen C., Deng Z. Adaptive neural network-based tracking control for full-state constrained wheeled mobile robotic system. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017, vol. 47, no. 8, pp. 2410–2419. https:// doi.org/10.1109/TSMC.2017.2677472

12. Dong C., Liu Y., Wang Q. Barrier Lyapunov function based adaptive finite-time control for hypersonic flight vehicles with state constraints. ISA Transactions, 2020, vol. 96, pp. 163–176. https://doi.org/10.1016/j.isatra.2019.06.011

13. Doyle J.C., Smith R.S., Enns D.F. Control of plants with input saturation nonlinearities. American Control Conference, IEEE, 1987, pp. 1034–1039. https://doi.org/10.23919/ACC.1987.4789464

14. Mofid O., Mobayen S. Adaptive finite-time backstepping global sliding mode tracker of quad-rotor UAVs under model uncertainty, wind perturbation, and input saturation. IEEE Transactions on Aerospace and Electronic Systems, 2022, vol. 58, no. 1, pp. 140–151. https://doi.org/10.1109/TAES.2021.3098168

15. Chen X., Jia Y., Matsuno F. Tracking control for differential-drive mobile robots with diamond-shaped input constraints. IEEE Transactions on Control Systems Technology, 2014, vol. 22, no. 5, pp. 1999–2006. https://doi.org/10.1109/TCST.2013.2296900

16. Yang C., Huang D., He W., Cheng L. Neural control of robot manipulators with trajectory tracking constraints and input saturation. IEEE Transactions on Neural Networks and Learning Systems, 2021, vol. 32, no. 9, pp. 4231–4242. https://doi.org/10.1109/TNNLS.2020.3017202

17. Gao Y.-F., Sun X.-M., Wen C., Wang W. Adaptive tracking control for a class of stochastic uncertain nonlinear systems with input saturation. IEEE Transactions on Automatic Control, 2017, vol. 62, no. 5, pp. 2498–2504. https://doi.org/10.1109/TAC.2016.2600340

18. Levant A. Higher-order sliding modes, differentiation and outputfeedback control. International Journal of Control, 2003, vol. 76, no. 9-10, pp. 924–941. https://doi.org/10.1080/0020717031000099029