Multiple obstacle avoidance of four-wheeled vehicle with steering limitation using nondifferentiable control Lyapunov function

Abstract

Controlling a mobile robot in a space with obstacles is a well-known problem in robotics. The control objective is for the mobile robot to reach a goal point with obstacle avoidance. In this paper, we specially consider the multiple obstacle avoidance problem for particularly a four-wheeled vehicle. Assuming that the shapes and locations of the obstacles are known, we propose a design method of a nondifferentiable navigation function, which guides a vehicle at the desired point. The control law for the four-wheeled vehicle is obtained from the extended function of the navigation function. As four-wheeled vehicles cannot move sideways because of their nonholonomic constraint, the proposed control law addresses this difficulty by considering a decrease in the control Lyapunov function, and can be applied to vehicles with steering limitations. Moreover, the control law makes it possible for the vehicles to achieve an -point turn automatically without the need for any rule-based decision-making or heuristic method. The four-wheeled vehicle can reach the goal point from any initial point under the proposed control law. Our experimental results with a small four-wheeled vehicle are presented at the end of this paper.