Three important problems in the study of grasping and manipulation by multifingered robotic hands are: (a) Given a grasp characterized by a set of contact points and the associated contact models, determine if the grasp has force closure; (b) If the grasp does not have force closure, determine if the ngers are able to apply a specified resultant wrench on the object; and (c) Compute "optimal" contact forces if the answer to problem (b) is affirmative. In this paper, based on an early result by Buss, Hashimoto and Moore, which transforms the nonlinear friction cone constraints into positive definiteness of certain symmetric matrices, we further cast the friction cone constraints into linear matrix inequalities (LMIs) and formulate all three of the problems stated above as a set of convex optimization problems involving LMIs. The latter problems have been extensively studied in optimization and control community and highly efficient algorithms with polynomial time complexity are now available for their solutions. We perform simulation studies to show the simplicity and efficiency of the LMI formulation to the three problems.

This paper formally introduces several stability characterizations of xtured three-dimensional rigid bodies initially at rest and in unilateral contact with Coulomb friction. These characterizations, weak stability and strong stability, arise naturally from the dynamic model of the system, formulated as a complementarity problem. Using the tools of complementarity theory, these characterizations are studied in detail to understand their properties and to develop techniques to identify the stability classications of general systems subjected to known external loads.