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Two-finger antipodal point grasping of arbitrarily shaped smooth 2-D and 3-D objects is considered. An object function is introduced that maps a finger contact space to the object surface. Conditions are developed to identify the feasible grasping region, F, in the finger contact space. A "grasping energy function", E, is introduced which is proportional to the distance between two grasping points. The antipodal points correspond to critical points of E in F. Optimization and/or continuation techniques are used to find these critical points. In particular, global optimization techniques are applied to find the "maximal" or "minimal" grasp. Further, modeling techniques are introduced for representing 2-D and 3-D objects using B-spline curves and spherical product surfaces.>
Chen et al. (Fri,) studied this question.