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.