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.

In the field of research and development of grippers in object-handling applications, many research results in improving grippers' performances have been achieved, and many kinds of multifinger grippers have been developed. By using multifinger grippers, it is possible to grasp different objects of different shapes without changing grippers; and most importantly, it can manipulate the grasped object in the hand, under the condition that the object is controlled in real-time. Therfore, an object-pose controller with feedback from an object-pose sensor is presented in this paper.