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This paper presents an efficient algorithm to compute the minimum of the largest wrenches that a grasp can resist over all wrench directions with limited contact forces, which equals the minimum distance from the origin of the wrench space to the boundary of a grasp wrench set. This value has been used as an important grasp quality measure in optimal grasp planning for over two decades, but there has been no efficient way to compute it until now. The proposed algorithm starts with a polytope containing the origin in the grasp wrench set and iteratively grows it such that the minimum distance from the origin to the boundary of the polytope quickly converges to the aforementioned value. The superior efficiency and accuracy of this algorithm over the previous methods have been verified through theoretical and numerical comparisons.
Date of Publication: April 2013