Single Network Robust Adaptive Critic-Based Trajectory Tracking Control for Wheeled Mobile Robot with Wheel Sliding

In the trajectory tracking control problem of wheeled mobile robot with wheel sliding, the design process of traditional method is divided into two steps. This requires two controllers, which makes debugging difficult and error large. We propose one-step single network (OSSN), a method that combines backstepping and robust adaptive critic. Specifically, we use the backstepping with designed auxiliary variables to integrate the pose error and velocity error into a unified affine nonlinear system with disturbance term, which is convenient for tracking pose and velocity simultaneously. Then, the reward function including error, energy and disturbance information is specially designed. By solving the Hamilton–Jacobi–Bellman (HJB) equation, the optimal control is calculated. A Lyapunov function is designed to prove that under the effect of this special reward function, the optimal control can achieve the asymptotic stability of tracking errors. Besides, in order to reduce the training time, different from the traditional Actor-Critic structure, this paper uses the single network robust adaptive critic to approximate the optimal cost function from which the optimal control torques can be deduced. The simulation results show that this OSSN algorithm can realize good trajectory tracking performance of the wheeled mobile robot with wheel sliding.