Abstract
This paper deals with a path following problem with collision avoidance for multiple robots. The path following aims to move the robots along reference paths with assigned velocities. When there are geometric errors between the robots' positions and the reference paths, or when the differences between their velocities and assigned velocities are not zero, we expect to reduce these errors. Unfortunately, if the multiple robots try to realize the exact path following, they may collide with one another in areas where the reference paths intersect. In this case, the robots have to avoid collision at the expense of the original paths. This paper introduces a value function including geometric and velocity errors, and proposes a new online collision avoidance method which constrains the value function. The proposed method minimizes the time derivative of the value function in each instance. Moreover, this method prevents deadlocks of the robots with the following strategy: design a time-varying function which moves slowly along the reference path for each robot, and append a penalty function to the value function which increases when the position of the robot becomes less than the time-varying function.
