Trajectory tracking control of nonholonomic wheeled mobile robots

Nonholonomic wheeled mobile robot's posture error model denoted by Cartesian coordinates in local coordinates is established. A novel nonlinear state feedback trajectory tracking control law is proposed, which causes closed-loop system state space equation of robot to have isolated equilibrium state at origin. Through analysing the local uniform asymptotical stability at origin and the instability of isolated boundary equilibrium state at non-origin under the proposed trajectory tracking control law, the scale of control parameters is confirmed. By Lyapunov candidate function method, this paper concludes that the closed-loop system is globally uniformly asymptotically stable at origin. Simulation results show the effectiveness of the proposed control law.

I. Introduction

The wheeled mobile robot (WMR) has a far-ranging practical application background [1]–[3],[5]. In this system the rolling contact between the wheel and the floor must satisfy the nonholonomic constraint condition of pure rolling without slipping, therefore it is a typical nonholonomic dynamics system. The trajectory tracking control design is to control the linear velocity and angle velocity (or acceleration) of the WMR which track the reference trajectory. The target of control is to minimize the error between the reference trajectory and the real trajectory. Because of the existence of sliding, disturbing and sensor error, the tracking error is inevitable. In last two decades, extensive researches have been done on the trajectory tracking control of WMR [1]–[3],[7],[8]. Generally, the controlling methods can be divided into four types: linear method; nonlinear method; geometrical method and intelligent method [4].