Global tracking control for car-like mobile robots with zero-crossing driving velocity

This work proposes a smooth time-varying con- troller to address the trajectory tracking problems of car-like mobile robots. Currently, literature does not suggest globally asymptotically stable controllers solving this problem. Unlike the prototypical method of transforming the model into a nonholonomic chained-form system, the proposed method is designed based on the original tracking error equation, and therefore our approach does not have singularities of chained- form transformations. Opposing current methods, our control law satisfactorily addresses the cases where the vehicle’s velocity passes through zero. In general, our redesigned control law has no singularities, which can satisfy the requirement that the vehicle’s velocity can cross zero and at the same time have a global attraction region. The design of the controller is mainly divided into two steps. Firstly, the linear velocity and steering angle of the robot are regarded as control inputs, which are designed by making the derivative of a positive definite Lyapunov-like function semi-negative definite. In the next step, another control input is designed by the backstepping approach. Furthermore, the global convergence of the state trajectory to the reference one is strictly proved by Barbalat’s Lemma. Finally, simulated and actual experiments on a car-like robot demonstrate the effectiveness of the proposed control scheme.