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Grasp Analysis as Linear Matrix Inequality Problems
"... 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 th ..."
Abstract

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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.
Dikin~pe Algorithms for Dextrous Grasping
"... Force Optimization One of the central issues in dextrous robotic hand grasping is to balance external forces acting on the object and at the same time achieve grasp slability and minimum grasping effort. A companion paper shows that the nonlinear frictionforce limit constraints on grasping forces a ..."
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Force Optimization One of the central issues in dextrous robotic hand grasping is to balance external forces acting on the object and at the same time achieve grasp slability and minimum grasping effort. A companion paper shows that the nonlinear frictionforce limit constraints on grasping forces are equivalent to the positive definiteness of a certain matrix subject to linear constraints. Furthe ~ compensation of the external object force is also a linear constraint on this matrix. Consequently, the task of grasping force optimization can be formulated as a problem with semidefinite constraints. In this papec two versions of strictly convex costfanctions, one of them selfconcordant, are considered. These are twicecontinuously dl~erentiable functions thut tend to infinity at the bounday of positive definiteness, For the general class of such cost finctions, Dikin~pe algorithms are presented. It is shown that the proposed algorithms guarantee convergence to the unique solution of the semidefinite programming problem associated with dextrous grasping force optimization, Numerical examples demonstrate the simplicip of implementation, the good numerical properties, and the optimality of the approach, 1.