Force decomposition in cooperating manipulators using the theory of metric spaces and generalized inverses

The decomposition of forces on an object grasped by multiple manipulators is analyzed using the theory of metric spaces and generalized inverses. In general, the space of forces exerted on the object is nonhomogenous and suitable metrics must be used to decompose the space into motion-inducing and internal force subspaces. A common theoretical framework is proposed in this paper which solves the decomposition problem for rigid, palm-type, and frictional point-contact grasps. New solutions are derived for systems with palm-type and mixed grasps. Previous decompositions for the rigid and frictional point contact grasps are analyzed within the theoretical framework. It is shown that previous solutions in the rigid grasp case are equivalent to the minimization of a norm based on a kinetic energy metric associated with the object