This paper presents a new method to solve the configuration problem on robotic hands:deter- mine 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 one presented here allows specifing such contacts 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. Experi- ments are included that illustrate the performance of the method in the particular case of the Schunk Anthropomorphic hand.

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