Minimum time trajectory planning for dual robot systems

The problem of planning minimum time collision-free trajectories for a dual robot system is addressed. It is shown that this problem can be solved by first planning the minimum time trajectory for each robot without considering the existence of the other and then combining the two individual trajectories. This combination is accomplished by delaying one of the two trajectories in such a way that the time required for the coordinated motion of the two robots is minimized while avoiding collision between them. The optimality of the method is rigorously proved, the practical aspects of its realization are discussed, and example is presented