Obstacle avoidance control for non-holonomic vehicles on Lie group SE(2): a rotating attractive vector approach

Abstract

This paper studies the obstacle avoidance problem with the applications to set-point stabilization and trajectory tracking tasks in non-holonomic vehicles, whose kinematics evolve on the Special Euclidean group SE(2). At first, by rotating the attractive vector in the direction perpendicular to the repulsive vector, a novel strategy of obstacle avoidance is proposed to avoid the local minimum positions. Therefore, the relative angle and the distance to the obstacle are considered during the design of the switch signal. Then based on the proposed approach, the set-point stabilization controller and trajectory tracking controller are designed to avoid the obstacle, respectively, which can drive the vehicle to move to the goal position for any initial configuration. The stability analysis effectively validates the achievement of the obstacle avoidance strategy without locating in the local minimum positions, and it also proves that the set-point stabilization and trajectory tracking tasks can be achieved. In order to verify the theoretical results, two simulations are given where the initial condition exists the local minimum positions.