Two-Finger Caging of Polygonal Objects Using Contact Space Search

Multifinger caging offers a rigorous and robust object grasping approach. Focusing on two-finger caging, this paper describes an algorithm for finding all two-finger cage formations of planar polygonal objects based on contact-space formulation. The paper shows that two-finger cages have several useful properties in contact space. First, the critical points of the cage representation in the hand´s configuration space appear as critical points of the interfinger distance function in contact space. Second, these critical points can be graphically characterized directly on the object´s boundary. Third, contact space admits a natural rectangular decomposition such that all critical points lie on the rectangle boundaries, and the sublevel sets of contact space and free space are topologically equivalent. These properties lead to a caging graph that can be readily constructed in contact space. Starting from a desired immobilizing grasp of a polygonal object, the caging graph is searched for the minimal, intermediate, and maximal caging regions surrounding the immobilizing grasp. An example constructed from real-world data illustrates and validates the method.