On the Liapunov stability of multi-finger grasps

This paper deals with the stability of a rigid body under multiple contact forces. First, the problem is considered at the force planning level, and t he stability of a force distribution is formulated. For this problem, the s tiffness tensor is derived, and its basic properties are analyzed. Necessar y and sufficient conditions for stability of a force distribution are estab lished in an analytical form. These conditions, considered under unilateral frictional constraints, are studied on an illustrative example. Next, it i s shown that stabilization of an unstable force distribution can be done by a simple control law. The stability conditions for this control law are fo rmulated by transforming the stiffness tensor to the center of stiffness. F inally, conclusions on the contradiction between the Liapunov stability and the contact stability of the objects are drawn.