A grasp metric invariant under rigid motions

Consider the problem of quantifying the quality of a multifinger grasp. The “traditional” grasp quality measures, which are based on inscribing a sphere in the set of wrenches which a grasp can resist, suffer from being dependent on the coordinate system of the object being grasped. In fact, we show that by changing the coordinate system, one can make these measures arbitrarily small. In this paper we generalize these measures in a natural way, and propose a new measure which is invariant under rigid motions of the object coordinate system. It is based on a certain class of ellipsoids which captures the changes in wrench space that occur