Minimum-time trajectories for two robots holding the same workpiece

The authors present an algorithm which minimizes the time for two robots holding the same workpiece to move along a given path. The method can be applied to any constrained robot system, including the case where one robot arm moves in contact with a surface. The unique feature of these systems is that they are redundantly actuated because they have more actuators then degrees of freedom. In addition to finding the optimum torque histories, the algorithm determines the contact force between each robot and the workpiece throughout the motion. Constraints on these internal forces are easily introduced into the algorithm. Examples are given for two planar arms holding a common workpiece. It is shown that arbitrary bounds on the internal forces of interaction on the workpiece may easily be imposed; this causes a reduction in the path traversal time. The motions found using this algorithm establish a performance limit on cooperating robot systems, and can be used to guide the analysis and design of such systems