A general tracking control problem for mobile robots is proposed and solved using the backstepping technique. A global result is given for the kinematic steering system to make the tracking error approaching to zero asymptotically. Based on our efforts, the proposed controller can solve both the tracking problem and the regulation problem of mobile robots. In particular, mobile robots can now globally follow any differentiable with bounded velocities path such as a straight line, a circle and the path approaching to the origin using the proposed controller. Moreover, the problem of back-into-garage parking is also solved by our approach. Some interesting simulation results are given to illustrate the effectiveness of the proposed tracking control laws.

A computed torque controller for a dynamic model of nonholonomic mobile robots with bounded external disturbance is proposed to treat the adaptive tracking control problem using the separated design method. A velocity controller is first designed for the kinematic steering system to make the tracking error approaching to zero asympotically. Then, a computed torque controller is designed such that the true mobile robot velocity converges to the desired velocity controller. In each step, the controllers are designed independently, and this will simplify the design of controllers. A novel stability analysis involving the estimation of some differential inequalities is also given to guarantee the stability of the closed-loop system. Moreover, the regulation problem and the tracking problem will be treated using the proposed controller. In particular, the mobile robots can globally follow any path such as a straight-line, a circle and the path approaching to the origin. Furthermore, the problems of back-into-garage parking and the parallel parking problem can also be solved using the proposed controller. Some interesting simulation results are given to illustrate the effectiveness of the proposed tracking control law.