Path-constrained motion planning for multi-manipulator systems

The paper presents a systematic approach to the minimum-energy collision-free motion planning of many redundant manipulators along prescribed paths. It is based on using a parametric-decomposition method and a negative formulation of the Pontryagin Maximum Principle which handles efficiently various control and/or state constraints imposed on the manipulators´ motions, which arise naturally out of joint limits and obstacle avoidance. In contrast to the penalty-function method, the proposed algorithm does not require an initial admissible solution and finds trajectories of a smaller cost than those generated by the penalty-function approach. A computer example involving two planar redundant manipulators of three revolute kinematic pairs is included to illustrate the discussed ideas.