An analytical approach is proposed for obtaining finger position regions of an object with a multi-fingered hand. First, a method to obtain which combination of the object edges is possible to be used for grasping, is given. Then, a graspable finger position region on a combination of edges is defined where the object can be held successfully. It is shown that the region is bounded by plural boundary hyperplanes. By combining these boundary hyperplanes, two propositions for exactly obtaining the graspable finger position region by using an analytical method, are proposed. Finally, numerical examples are performed to show the effectiveness of the proposed approach.
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