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

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.在存在障碍物的空间中控制移动机器人，是机器人学领域广为人知的经典问题。其控制目标为使移动机器人在规避障碍物的前提下抵达目标点位。本文专门针对四轮移动机器人，深入研究其多障碍物避障问题。假设障碍物的形状与位置均为已知条件，本文提出一种非可微导航函数（nondifferentiable navigation function）的设计方法，该函数可引导车辆抵达期望目标点位。四轮移动机器人的控制律可通过该导航函数的扩展形式推导得到。由于四轮移动机器人受非完整约束（nonholonomic constraint）限制，无法实现横向移动，本文所提出的控制律通过引入控制李雅普诺夫函数（control Lyapunov function）的递减条件来解决该技术难题，且该控制律可适配带有转向限制的移动机器人。此外，该控制律可使车辆无需借助任何基于规则的决策逻辑或启发式方法，即可自动完成任意点位转向。在本文提出的控制律作用下，四轮移动机器人可从任意初始点位抵达目标点。本文末尾将展示我们基于小型四轮移动机器人开展的实验结果。