Internal object loading for multiple cooperating robot manipulators

For an object being rigidly grasped and manipulated by multiple robotic mechanisms, the internal loading characteristics at a common coordinate set within the object are considered. It is demonstrated that representation of internal forces and moments in these common coordinates gives insight into force and load distribution schemes developed previously. In particular, it is shown how internal loads may be created in some end-effector force distribution schemes even when no component in the null-space of the grasp matrix is included. It is further shown that a particular pseudoinverse of the grasp matrix, which can be shown to be consistent with the kinematic constraints, may be used to eliminate this situation. The case of a two-arm system is used to illustrate the concepts introduced.