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 the stability of a force distribution is formulated. For this problem, the stiffness tensor is derived, and its basic properties are analyzed. Necessary and sufficient conditions for stability of a force distribution are established in an analytical form. These conditions, considered under unilateral frictional constraints, are studied on an illustrative example. Next, it is shown that stabilization of an unstable force distribution can be done by a simple control law. The stability conditions for this control law are formulated by transforming the stiffness tensor to the center of stiffness. Finally, conclusions on the contradiction between the Liapunov stability and the contact stability of the objects are drawn.