A Stable Switched-System Approach to Collision-Free Wheeled Mobile Robot Navigation

This paper presents a novel switched-system approach for obstacle avoidance by mobile robots. This approach does not suffer from common drawbacks of existing methods, such as needing prior knowledge of obstacles, or local minima or chattering in control laws. We define an attractive and an avoidance vector in obstacle-free and obstacle-avoidance regions, respectively. Next, we define an unified velocity vector, which represents either the attractive vector or the avoidance vector, and drives the robot away from the obstacle and ultimately towards the goal. The avoidance vector differs from the repulsive vector commonly used in potential field approaches, rather it is defined always perpendicular to such a repulsive vector and projects positively onto the attractive vector. The unified velocity vector enables the use of a common Lyapunov function in analyzing the stability of the system under arbitrary switching. Novel switching rules are proposed for obstacles that can be well bounded by a circle in the local subset of SE(2). To better handle large, non-circular obstacles, a separate switching signal is proposed. Through the choice of switching rule, we investigate the chattering problem that can hinder some switching controllers. We present two control laws, one with bounded inputs and one with no bounds on inputs. We prove both control schemes are asymptotically stable and guide the robot to the goal while avoiding obstacles. To verify the effectiveness of the proposed approach, as well as compare the control laws and switching rules, several simulations and experiments have been conducted.