Spatial impedance realization by grasps with fingers in soft contact

Abstract

This paper characterizes the space of spatial impedance behaviors that can be realized by grasps having multiple fingers in soft contact with a held object. The dimension of the space of achievable impedance matrices is identified for each multi-finger case. Not all impedance matrices can be achieved by a soft-finger grasp regardless of the number of fingers used. For each multi-finger case, a set of necessary and sufficient conditions for impedance matrix realization is derived. For a grasp having 4 or fewer fingers, the space of realizable impedances is not only restricted by the number of fingers but also by the number of distinct object surface normals at the fingertip contact locations. A synthesis procedure for the realization of an arbitrary full rank impedance matrix in the realizable impedance subspace is developed for a minimum-finger grasp. Using this procedure, a specified grasp-realizable object impedance matrix can be achieved by a 3-finger grasp by properly selecting the locations of fingertips in contact with the held object and the fingertip impedance at each contact location.