Trajectory Tracking Control for Wheeled Mobile Robots with Unknown Slip Rates Based on Improved Rapid Variable Exponential Reaching Law and Sliding Mode Observer

Aiming at the trajectory tracking control problem of wheeled mobile robots under unknown slip ratio conditions, this paper designs a trajectory tracking controller based on an improved rapid variable power reaching law and a sliding mode observer. First, a kinematic model of the wheeled mobile robot is established, explicitly considering the influence of slip ratio. Then, a sliding mode observer is developed for online estimation of the slip ratio, addressing the difficulty of direct slip ratio measurement. On this basis, a trajectory tracking controller is designed based on the improved rapid variable power reaching law, enabling fast tracking of multiple complex trajectories under slip conditions. Simulation and experimental results show that the proposed trajectory tracking controller not only effectively eliminates the influence of unknown slip disturbances on trajectory tracking, improving smoothness and tracking accuracy but also greatly accelerates the convergence process. The shortest convergence time is only 20.56% of that achieved by a fuzzy PID trajectory tracking controller and 61.43% of that achieved by a rapid double power reaching law trajectory tracking controller with a sliding mode observer.