On the analysis of force closure and force optimization in fixtures and robotic manipulation

This paper deals with mechanical systems with passive contact elements, such as whole-hand grasps and fixture systems. The force closure problem in fixtures and manipulation systems with hybrid (active and passive) contacts is shown to be quite different from the pure active force closure in a multi-fingered robot hand. We discuss the conditions of active and passive force closure problems in such devices based on a rigid-body model with frictional contact. The contact force space is decomposed into three orthogonal subspaces: the space of external forces, the space of active internal forces, and the space of passive internal forces. The space of active internal force and the space of passive internal force play important roles in achieving the closure grasping. This paper presents an algorithm for computing the basis of each subspace. Based on this force decomposition, the force closure problem is formulated as linear matrix inequality feasibility problems, and minimization of the joint torque is also studied.