Caging polygonal objects using equilateral three-finger hands

Multifinger caging offers a robust object grasping approach. While efficient computation of two-finger caging grasps is well developed, the computation of three-finger caging grasps has remained a challenging open problem. This letter considers the caging of polygonal objects with three-finger hands which maintain an equilateral triangle formation during the grasping process. While the c-space of such hands is four-dimensional (4-D), their contact space which represents all two and three finger contacts along the grasped object's boundary forms a 2-D stratified manifold. The letter describes a caging graph that can be constructed in the hand's relatively simple contact space. Starting from a desired immobilizing grasp of the object, the caging graph is searched for the largest finger opening that maintains a three-finger cage about the object. This finger opening determines the caging regions, and any equilateral finger placement within the caging regions guarantees a robust object grasping. The technique is illustrated with a detailed example and a video showing caging experiments with an equilateral robot hand.