Deadlock-free Path-following Control for Collision Avoidance of Multiple Robots

This paper deals with a collision avoidance problem for path-following of multiple holonomic 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 path-following completely, 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 path-following. This paper defines a cost function evaluating the geometric and velocity errors, and proposes a new online collision avoidance method which constrains the cost function. The proposed method minimizes the time-derivative of the cost function in each instance. Moreover, this method prevents the robots from deadlocking by introducing a penalty function for each robot into the cost function. Finally, the effectiveness of our proposed method is demonstrated by simulations for three mobile robots.