Design of a robust tracking controller for a nonholonomic mobile robot based on sliding mode with adaptive gain

This article propounds addressing the design of a sliding mode controller with adaptive gains for trajectory tracking of unicycle mobile robots. The dynamics of this class of robots are strong, nonlinear, and subject to external disturbance. To compensate the effect of the unknown upper bounded external disturbances, a robust sliding mode controller based on an integral adaptive law is proposed. The salient feature of the developed controller resides in taking into account that the system is MIMO and the upper bound of disturbances is not priori known. Therefore, we relied on an estimation of each perturbation separately for each subsystem. Hence, the proposed controller provides a minimum acceptable errors and bounded adaptive laws with minimum of chattering problem. To complete the goal of the trajectory tracking, we apply a kinematic controller that takes into account the nonholonomic constraint of the robot. The stability and convergence properties of the proposed tracking dynamic and kinematic controllers are analytically proved using Lyapunov stability theory. Simulation results based on a comparative study show that the proposed controllers ensure better performances in terms of good robustness against disturbances, accuracy, minimum tracking errors, boundness of the adaptive gains, and minimum chattering effects.