Path tracking control of Lagrange systems with obstacle avoidance

This paper addresses a path tracking problem with obstacle avoidance for Lagrange systems. The proposed method is based on field potential methods in combination with navigation functions for obstacle avoidance. First, it is shown that a simple combination of the navigation function with the conventional path tracking controller does not work. Therefore, in order to cope with this problem, a new feedback law is proposed for a path parameter which characterizes the reference path. It is proved that the proposed controller achieves both path following and collision avoidance. Moreover, since the method adopts bounded navigation functions, the proposed controllers generate bounded input signals even when target systems approach obstacles. Finally, an experimental evaluation is performed with a two-link manipulator to illustrate the effectiveness of the proposed method.