Finding antipodal point grasps on irregularly shaped objects

The authors consider two-finger antipodal point grasping of arbitrarily shaped 2D and 3D objects. An object function which maps a finger contact space to the object surface is introduced. 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 at F. Optimization and/or continuation techniques are used to find these critical points. In particular, global optimization techniques are applied to find the maximal grasp. Modeling techniques for representing 2D and 3D objects using B-spline curves and spherical product surfaces are described