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A stable switched-system approach to obstacle avoidance for mobile robots in SE(2)

In this paper, we propose a novel approach for obstacle avoidance. The configuration space of a nonholonomic mobile robot in the special Euclidean group SE(2). Therefore, we divide the whole configuration space into two sub-regions (i.e., a safe region and an obstacle avoidance region). We have derived two functions to define the robot's behavior in each region, which generate velocity vectors that drive the robot away from the obstacle and always towards the goal. We consider the existence of a switching surface between these two sub-regions, and specifically define this switching surface as a local subset of SE(2), i.e. the switching surface includes orientation, defined by the relative angle between the robot heading and bearing to the obstacle. Two different switching signals are proposed based on the switching surface. Lyapunov stability analysis proves the robot will converge to a goal position. To verify the effectiveness of the proposed approach, several simulations and experiments have been conducted.