Transverse-longitudinal Coupled Trajectory Tracking Control of Mobile Robots Based on Generalized Udwadia-Kalaba Equation

doi:10.3901/JME.2025.19.078

Abstract

Abstract: In the field of motion control, mobile robot systems usually need to satisfy a series of equations (including completeness and non-completeness) with inequality constraints in order to accomplish the target task. However, the current research mainly focuses on the trajectory tracking performance of mobile robots and lacks an in-depth study on the transverse-longitudinal coupling control during their motion. To this end, a transverse-longitudinal coupled constraint following control method based on the generalized Udwadia-Kalaba equation is proposed. First, for the longitudinal tracking task, a longitudinal trajectory tracking controller based on the servo-equivalent constraint theory is designed and its stability is proved by using the Lyapunov stability theory. Secondly, based on the inequality constraint information, the fixed constraints in the y-direction and the boundary constraints for linear and circular trajectories are established respectively. On this basis, a transverse-longitudinal coupling controller τ that can satisfy the boundary inequality constraints is proposed. Finally, the proposed method is verified by numerical simulation through Matlab simulation software. The simulation results show that, compared with the traditional PD control and model predictive control, the proposed controller can efficiently accomplish the target task with faster convergence speed and superior control performance while satisfying the inequality constraints. Meanwhile, the practical effectiveness of the proposed control method is verified based on the ROS mobile robot physics experimental platform, which realizes the fixed-point, linear and circular trajectory tracking control under the inequality constraints, and provides a new research idea in the field of transverse-longitudinal coupling control of mobile robots.

Key words: mechanical system, equation/inequality constraints, generalized Udwadia-Kalaba equation, Lyapunov stability, transverse-longitudinal coupled control

CLC Number:

TP242

ZHANG Jiale, LI Zhiyong, ZHANG Chuanwei, WEI Meng, JIAO Shengjie. Transverse-longitudinal Coupled Trajectory Tracking Control of Mobile Robots Based on Generalized Udwadia-Kalaba Equation[J]. Journal of Mechanical Engineering, 2025, 61(19): 78-90.

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