Equilateral Three-Finger Caging of Polygonal Objects Using Contact Space Search

Abstract

Multifinger caging offers a robust object grasping approach. However, while efficient computation of two-finger caging grasps is well developed, the computation of three-finger caging grasps has remained a challenge. This paper 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 4-D, their contact space that represents all two and three finger contacts along the grasped object’s boundary forms a 2-D stratified manifold. The paper describes a caging graph that can be constructed in the hand’s relatively simple contact space. Starting from a desired immobilizing grasp of the polygonal object, the caging graph can be readily searched for the largest finger opening that maintains a three-finger cage about the object to be grasped. Any equilateral finger placement within the corresponding caging regions guarantees robust object grasping. Note to Practitioners —A commonly used industrial gripper is the parallel gripper. While it is well suited for grasping objects that have parallel edges, it is less suited for objects with more complicated geometries, and it relies on high coefficients of friction. This paper considers the robust grasping of polygonal objects using equilateral three-finger robot hands. Such hands are mechanically simple, and enable grasping objects with complicated shapes without relying on contact friction. To safely grasp an object, the hand is first brought to a caging configuration around the object. Once the object is caged, it cannot be accidentally ejected from the hand, and the fingers can be closed safely until an immobilizing grasp is reached. To reach a specific immobilizing grasp, the fingers are placed in the three caging regions associated with that grasp. This paper proposes a method that is both physically intuitive and computationally simple, to compute these caging regions. Although this paper considers grasping polygonal objects using frictionless point fingers, the proposed method can be used for grasping nonpolygonal objects using identical disc fingers, by expanding the object by the finger radius, and then approximating the expanded object by a polygon. Finger’s center can then be treated as a point finger. Frictional jamming of the fingers can overcome using rotating fingers or slightly vibrating the hand.