An analytical grasp planning on given object with multifingered hand

In this paper, an analytical approach is proposed for planning finger positions of grasping an object with a multifingered hand. First, a method is given to obtain which combination of the object edges is possible to be used for grasping. Then, a graspable finger position region (GFPR) on a combination of edges is defined where the object can be held successfully. It is shown that the region is bounded by several boundary hyperplanes. By combining these boundary hyperplanes, two propositions for analytically and exactly obtaining the GFPR are proposed. An algorithm is proposed to find a stable GFPR that contains the biggest inscribed hypersphere of GFPR and has the largest volume. Finally, a numerical example is performed to show the effectiveness of the proposed grasp planning approach.