Designing Predictive Kinematic Control and Dynamic Robust Control for Path Tracking in a Wheeled Mobile Robot

Subject Areas : Renewable energy

Fahime Kordi ¹ , Hamid Reza Reza Alikhani ² , Javad Nikoukar ³

1 - Department of Electrical Engineering, Saveh Branch, Islamic Azad University, Saveh, Iran.
2 - Department of Electrical Engineering, Tafresh University, Tafresh, Iran
3 - Department of Electrical Engineering, Saveh Branch, Islamic Azad University, Saveh, Iran.

Received: 2022-05-07 Accepted : 2022-09-06 Published : 2024-08-22

Keywords: Wheeled mobile robot, Path Tracking, Adaptive Sliding Mode Control, hybrid controller, kinematic and dynamic model,

Abstract :

In this paper, we investigate a hybrid controller for wheeled mobile robots in the presence of external disturbances and parametric uncertainty. Robot models include kinematic and dynamic equations of motion. In this paper, in order to reach the final position, the wheeled moving robot must be controlled in such a way that it can follow a reference path. Many studies often use a motion control strategy for the wheeled mobile robot. In this study, the proposed control strategy has two stages including cinematic control and dynamic control. In this regard, first after introducing the kinematic model of the robot, we design a predictive controller for this part and prove it. Then, based on the nonlinear dynamic dynamics of the robot, an adaptive sliding mode dynamic controller is introduced to estimate the disturbances online, automatically adjust the gain of the control and eliminate the umbrella phenomenon completely. Then, the proposed design is analyzed and proved using Lyapanov's theory of stability. According to the proposed adaptive control law, optimal convergence and tracking performance of all signals are guaranteed and tracking errors can converge arbitrarily in finite time to the source. Simulation results have been performed to show the effectiveness of the proposed design using Matlab software.

References:

[1] Y. Koubaa, M. Boukattaya, T. Damak, "Adaptive sliding mode control for trajectory tracking of nonholonomic mobile robot with uncertain kinematics and dynamics", Applied Artificial Intelligence, vol. 32, no. 9-10, pp. 924-938, Sept. 2018 (doi.org/10.1080/08839514.2018.1519100).

[2] S. Peng, W. Shi, "Adaptive fuzzy output feedback control of a nonholonomic wheeled mobile robot", IEEE Access, vol. 6, pp. 43414-43424, Aug. 2018 (doi: 10.1109/ACCESS.2018.2862163).

[3] A. J. Muñoz-Vázquez, V. Parra-Vega, A. Sánchez-Orta, J.D. Sánchez-Torres, "Adaptive fuzzy velocity field control for navigation of nonholonomic mobile robots", Journal of Intelligent and Robotic Systems, vol. 101, no. 2, pp. 1-12, Dec. 2021 (doi: 10.1007/s10846-020-01306-w).

[4] A.V. Savkin, T.M. Cheng, Z. Xi, F. Javed, A.S. Matveev, H. Nguyen, "Decentralized coverage control problems for mobile robotic sensor and actuator networks", John Wiley and Sons, July 2015 (ISBN: 978-1-119-05816-8).

[5] S. Wang, J. Zhai, "A trajectory tracking method for wheeled mobile robots based on disturbance obse­rver", International Journal of Control, Automation and Systems, vol. 18, no. 8, pp. 21, 65-2169, Oct. 2019 (doi: 10.1007/s12555-019-0156-8).

[6] J. Wang, L. Zhao, L. Yu, "Reduced-order generalized proportional integral observer based continuous dynamic sliding mode control for magnetic levitation system with time-varying disturbances", Internati­onal Journal of Control, Automation and Systems, vol. 19, no. 1, pp. 439-448, April 2021 (soi: 10.10­07/s­1255­5-019-0387-8).

[7] Z. Chen, Y. Liu, W. He, H. Qiao, H. Ji, "Adaptive-neural-network-based trajectory tracking control for a nonholonomic wheeled mobile robot with velocity constraints", IEEE Trans. on Industrial Electronics, vol. 68, no. 6, pp. 5057-5067, June 2020 (doi: 10.1109/TIE.2020.2989711).

[8] X. Wu, P. Jin, T. Zou, Z. Qi, H. Xiao, P. Lou, "Backstepping trajectory tracking based on fuzzy sliding mode control for differential mobile robots", Journal of Intelligent and Robotic Systems, vol. 96, no. 1, pp. 109-121, Jan. 2019 (doi: 10.1007/s10846-019-00980-9).

[9] Y. Cheng, R. Jia, H. Du, G. Wen, W. Zhu, "Robust finite‐time consensus formation control for multiple nonholonomic wheeled mobile robots via output feedback", International Journal of Robust and Nonlinear Control, vol. 28, no. 6, pp. 2082-2096, April 2018 (doi: 10.1002/rnc.4002).

[10] M. Boukattaya, N. Mezghani, T. Damak, "Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems", ISA Transactions, vol. 77, pp. 1-19, April 2018 (doi: 10.1016/j.isatra.2018.04.007).

[11] N. Ali, I. Tawiah, W. Zhang, "Finite-time extended state observer based nonsingular fast terminal sliding mode control of autonomous underwater vehicles", Ocean Engineering, vol. 218, Article Number: 108179, Sept. 2020 (doi: 10.1016/j.oceaneng.2020.108179).

[12] Q. Cao, Z. Sun, Y. Xia, L. Dai, "Self-triggered MPC for trajectory tracking of unicycle-type robots with external disturbance", Journal of the Franklin Institute, vol. 356, no. 11, pp. 5593-5610, Mar. 2019 (doi: 10.1016/j.jfranklin.2019.03.015).

[13] X. Liu, W. Wang, X. Li, F. Liu, Z. He, Y. Yao, H. Ruan, T. Zhang, "MPC-based high-speed trajectory tracking for 4WIS robot", ISA Transactions, vol. 123, pp. 413-424, April 2022 (doi: 10.1016/j.i­sa­tra.2­021.05.018).

[14] D. Liu, M. Tang, J. Fu, "Robust adaptive trajectory tracking for wheeled mobile robots based on Gaussian process regression", Systems and Control Letters, vol. 163, Article Number: 105210, April 2022 (doi: 10.1016/j.sysconle.2022.105210).

[15] K. Shojaei, "A prescribed performance PID control of robotic cars with only posture measurements considering path curvature", European Journal of Control, vol. 65, Article Number: 100616, Jan. 2022 (doi: 10.1016/j.ejcon.2022.100616).

[16] T. Ding, Y. Zhang, G. Ma, Z. Cao, X. Zhao, B. Tao, "Trajectory tracking of redundantly actuated mob­ile robot by MPC velocity control under steering strategy constraint", Mechatronics, vol. 84, Article Number: 102779, Feb. 2022 (doi: 10.1016/j.mechatronics.2022.102779).

[17] J. Huang, C. Wen, W. Wang, Z.P. Jiang, "Adaptive stabilization and tracking control of a nonholonomic mobile robot with input saturation and disturbance", Systems and Control Letters, vol. 62, no. 3, pp. 234-241, Nov. 2013 (doi: 10.1016/j.sysconle.2012.11.020).

[18] H. Yang, M. Guo, Y. Xia, Z. Sun, "Dual closed‐loop tracking control for wheeled mobile robots via active disturbance rejection control and model predictive control", International Journal of Robust and Nonlinear Control, vol. 30, no. 1, pp. 80-99, Oct. 2020 (doi: 10.1002/rnc.4750).

[19] F. Korkmaz, "Performance improvement of induction motor drives with model-based predictive torque control", Turkish Journal of Electrical Engineering and Computer Science, vol. 28, no. 1, pp. 525-539, Jan. 2020 (doi: 10.3906/elk-1804-124).

[20] P. Wang, X. Feng, W. Li, X. Ping, W. Yu, "Robust RHC for wheeled vehicles with bounded disturbances", International Journal of Robust and Nonlinear Control, vol. 29, no. 7, pp. 2063-2081, Jan. 2019 (doi: 10.1002/rnc.4478).

[21] Z. Wu, F. Albalawi, Z. Zhang, J. Zhang, H. Durand, P. D. Christofides, "Control Lyapunov-Barrier function-based model predictive control of nonlinear systems", Automatica, vol. 109, Article Number: 10850, June 2019 (doi: 10.1016/j.automatica.2019.108508).

[22] H. Yang, M. Guo, Y. Xia, L. Cheng, "Trajectory tracking for wheeled mobile robots via model predictive control with softening constraints", IET Control Theory & Applications, vol. 12, no. 2, pp. 206-214, Jan. 2018 (doi: 10.1049/iet-cta.2017.0395).

[23] Z. Sun, L. Dai, Y. Xia, K. Liu, "Event-based model predictive tracking control of nonholonomic systems with coupled input constraint and bounded disturbances", IEEE Trans. on Automatic Control, vol. 63, no. 2, pp. 608-615, Feb. 2017 (doi: 10.1109/TAC.2017.2736518).

[24] H. Pan, G. Zhang, H. Ouyang, L. Mei, "A novel global fast terminal sliding mode control scheme for second-order systems", IEEE Access, vol. 8, pp. 22758-22769, Jan. 2020 (doi: 10.110­9/ACCE­SS.2­02­0.2969­665).

[25] T. Das, I. Kar, S. Chaudhury, "Simple neuron-based adaptive controller for a nonholonomic mobile robot including actuator dynamics", Neurocomputing, vol. 69, no. 16-18, pp. 2140-2151, Feb. 2006 (doi: 10.10­16/j.neu­com.2005.09.013).

[26] J.C. Alexander, J.H. Maddocks, "On the kinematics of wheeled mobile robots", The International Journal of Robotics Research, vol. 8, no. 5, pp. 15-27, Oct. 1989 (doi: 10.1177/027836498900800502).

[27] M. Asif, M.J. Khan, N. Cai, "Adaptive sliding mode dynamic controller with integrator in the loop for nonholonomic wheeled mobile robot trajectory tracking", International Journal of Control, vol. 87, no. 5, pp. 964-975, Dec. 2013 (doi: 10.1080/00207179.2013.862597).

[28] P. N. Dao, H. Q. Nguyen, T.L. Nguyen, X.S. Mai, "Finite horizon robust nonlinear model predictive control for wheeled mobile robots", Mathematical Problems in Engineering, vol. 21, no. 3, pp. 21-28, Jan. 2021 (doi: 10.1155/2021/6611992).

[29] H. Zhang, B. Li, B. Xiao, Y. Yang, J. Ling, "Nonsingular recursive-structure sliding mode control for high-order nonlinear systems and an application in a wheeled mobile robot", ISA Transactions, vol. 127, pp. 206-215, April. 2022 (doi: 10.1016/j.isatra.2022.04.021).

[30] Z. Zhu, Y. Xia, M. Fu, "Attitude stabilization of rigid spacecraft with finite‐time convergence", International Journal of Robust and Nonlinear Control, vol. 21, no. 6, pp. 686-702, Feb. 2011 (doi: 10.1002/rnc.1624).