Physically Plausible Wrench Decomposition for Multieffector Object Manipulation

When manipulating an object with multiple effectors such as in multidigit grasping or multiagent collaboration, forces and torques (i.e., wrench) applied to the object at different contact points generally do not fully contribute to the resultant object wrench, but partly compensate each other. The current literature, however, lacks a physically plausible decomposition of the applied wrench into its manipulation and internal components. We formulate the wrench decomposition as a convex optimization problem, minimizing the Euclidean norms of manipulation forces and torques. Physical plausibility in the optimization solution is ensured by constraining the internal and manipulation wrench by the applied wrench. We analyze specific cases of three-fingered grasping and 2-D beam manipulation, and show the applicability of our method to general object manipulation with multiple effectors. The wrench decomposition method is then extended to quantification of measures that are important in evaluating physical human-human and human-robot interaction tasks. We validate our approach via comparison to the state of the art in simulation and via application to a human-human object transport study.