Grasp analysis as linear matrix inequality problems

Three important problems in the study of grasping and manipulation by multi-fingered robotic hands are: 1) given a grasp characterised by a set of contact points and the associated contact models, determine if the grasp has force closure; 2) if the grasp does not have force closure, determine if the fingers are able to apply a specified resultant wrench on the object; and 3) compute "optimal" contact forces if the answer to problem (2) is affirmative. In this paper, based on an early result by Buss-Hashimoto-Moore (1996), 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. We perform simulation studies to show the simplicity and efficiency of the LMI formulation to the three problems.