Generation of optimal-time trajectory for the two cooperating robot manipulators

Two robot manipulators grasping a common object are assumed to travel a specified Cartesian path, and a method for deriving the optimal-time solution is presented. The approach is based on parametrizing the corresponding path and utilizing the phase-plane technique for trajectory planning. The torques supplied by the actuators are assumed to have some constant bounds. The effectiveness of the approach is demonstrated by a computer simulation using a PUMA 560 manipulator. The scheme can be easily extended to more than two manipulators