Near-Optimal Tracking Control of a Nonholonomic Mobile Robot with Uncertainties

Abstract

A combined kinematic/torque control law is developed by using a backstepping design approach for a nonholonomic mobile robot with two driving wheels mounted on the same axis to track a reference trajectory. The auxiliary velocity control inputs are designed for the kinematic steering system to make the posture error asymptotically stable. Next, a computed-torque controller is designed such that the mobile robot's velocities converge on the given velocity inputs in an optimal manner by converting the tracking control problem into the regulation problem whereby the uncertainties in the dynamics of mobile robots are considered. The proposed online and forward-in-time policy iteration (PI) algorithm based on approximate dynamic programming (ADP) is used to solve the optimal control problem with unknown internal dynamics by using single neural networks (NNs) to approximate the cost function. Afterwards, the near-optimal control policy can be computed directly according to the cost function, which removes the action network appearing in the ordinary ADP method. The stability of the dynamical extension system is demonstrated using Lyapunov methods. The simulation results are provided to demonstrate the effectiveness of the proposed approach.