In this paper we present a new method to solve the configuration problem on robotic hands: determining how a hand should be configured so as to grasp a given object in a specific way, characterized by a number of hand—object contacts to be satisfied. In contrast to previous algorithms given for the same purpose, the method presented here allows such contacts to be specified between free-form regions on the hand and object surfaces, and always returns a solution whenever one exists. The method is based on formulating the problem as a system of polynomial equations of special form, and then exploiting this form to isolate the solutions, using a numerical technique based on linear relaxations. The approach is general, in the sense that it can be applied to any grasping mechanism involving lower-pair joints, and it can accommodate as many hand—object contacts as required. Experiments are included that illustrate the performance of the method in the particular case of the Schunk Anthropomorphic hand.
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