Minimum-time collision-free trajectory planning for dual-robot systems

Collision-free multirobot motion planning can be achieved in two steps: path planning and trajectory planning. Path planning finds for the robots geometric paths to avoid collision with static obstacles and trajectory planning determines how fast each robot must move along its geometric path to avoid collision with other moving robots. For a dual-robot system, a simple trajectory planning strategy is to let each robot move along its path as fast as possible and delay one robot at its initial position to avoid collision with the other robot. A sufficient condition under which this simple (thus easy to implement) strategy for dual-robot systems can achieve time optimality as well as collision avoidance, i.e., the two robots reach their final positions without colliding with each other in the minimum amount of time, is derived. A demonstrative example is presented, showing how this strategy can be used for loading and unloading applications