Path constrained time-optimal motion of multiple robots holding a common object

This paper deals with a systematic analysis of the time-optimal motion of a multiple robot system carrying an object along a prescribed path. In our approach, the time-optimal motion planning problem is formulated in a concise form by employing a parameter describing the movement along the path and a vector representing the internal force. Various constraints governing the motion yield the so-called admissible region in the phase plane of the parameter. The orthogonal projection technique and the theory of multiple objective optimization make it possible to construct the admissible region, while taking into account the load distribution problem that is coupled with the motion. Furthermore, our approach provides a way of detailed investigation for the admissible region that is not simply connected. The resulting velocity profile of the path parameter and the internal force at every instant determine the optimal actuator torques for each robot.