Two-finger caging of 3D polyhedra using contact space search

Multi-finger caging offers a robust approach to grasping. This paper describes an algorithm to find caging formations of a 3D polyhedron for two point fingers using a lower-dimensional contact-space formulation. The paper shows that contact space has several useful properties. First, the critical points of the cage in the hand´s configuration space are identical to the critical points of the interfinger distance in contact space. Second, contact space can be naturally decomposed into 4D regions having useful properties. A geometric analysis of the critical points of the interfinger distance function results in a catalog of grasps in which the cages change topology, leading to a simple test to classify critical points. These properties lead to an easily constructed caging graph whose nodes contain the critical points of contact space. Starting from an immobilizing grasp, this graph can be searched to find local, intermediate, and maximal caging regions around that initial grasp. An implemented algorithm demonstrates the method.