Computation of 3-D form-closure grasps

We address the problems of computing form-closure regions as well as computing optimal fingertip locations yielding n-finger form-closure grasps of three-dimensional (3-D) objects. Given grip points of k fingers not in form-closure, we propose a sufficient and necessary condition for the n-k fingers to achieve an n-finger form-closure grasp. Based on the condition, it is demonstrated that the problem of computing form-closure regions can be formulated as an existence problem of a solution for a set of inequalities. A sufficient condition is also proposed to simplify the computation of form-closure regions. As to searching for optimal fingertip locations, we transform the problem to a nonlinear programming problem subject to a set of constraints arising from that sufficient and necessary condition. Furthermore, a performance index is defined by measuring the distance between the center of mass of the grasped object and the center of the contact points. Finally, we have implemented the approach proposed and verified its efficiency by several numerical examples.