On Computing Four-Finger Equilibrium and Force-Closure Grasps of Polyhedral Objects

Abstract

This article addresses the problem of computing stable grasps of three-dimensional polyhedral objects. We consider the case of a hand equipped with four hard fingers and assume point contact with friction. We prove new necessary and sufficient conditions for equilibrium and force closure, and present a geometric characterization of all possible types of four-finger equilibrium grasps. We then focus on concurrent grasps, for which the lines of action of the four contact forces all intersect in a point. In this case, the equilibrium conditions are linear in the unknown grasp parameters, which reduces the problem of computing the stable grasp regions in configuration space to the problem of constructing the eight-dimensional projec tion of an ll-dimensinnal polytope. We present two projection methods: the first one uses a simple Gaussian elimination ap proach, while the second one relies on a novel output-sensitive contour-tracking algorithm. Finally, we use linear optimization within the valid configuration space regions to compute the maximal object regions where fingers can be positioned inde pendently while ensuring force closure. We have implemented the proposed approach and present several examples.

On 2D 4-finger frictionless optimal grasps

“…One variation of the problem is the determination of independent regions on the object boundary such that a finger in each region ensures a form/force-closure grasp, thus dealing with some uncertainty in the finger positioning. The works of Ponce et al [12] and Nguyen [10] are remarkable in this line.…”

An overview of 3D object grasp synthesis algorithms

“…Based on these properties, grasp synthesis approaches dealing with polyhedral objects reduce the force-closure condition to a test of the angles between the face normals [10], or use the linear model to derive analytical formulation for grasp characterization [16][17][18]. Based on the property that each point on a plane face can be parameterized linearly with two parameters, Ponce et al [16,19] formulated necessary linear conditions for three and fourfinger force-closure grasps and implemented them as a set of linear inequalities in the contact positions. Finding all force-closure grasps is thus set as a problem of projecting a polytope onto a linear subspace.…”

Grasping bulky objects with two anthropomorphic hands

“…This area of research have been widely used in the synthesis of grasps for 2D [1], [2], [3] as well as for 3D objects [4], [5], [6]. Moreover, the concept of independent contact regions (ICRs) was introduced in order to provide robustness to the grasp in front of finger positioning errors [7], ensuring force-closure grasps independently of the exact position of the fingers within the ICRs.…”

“…Moreover, the concept of independent contact regions (ICRs) was introduced in order to provide robustness to the grasp in front of finger positioning errors [7], ensuring force-closure grasps independently of the exact position of the fingers within the ICRs. This concept has been developed by several researchers for 2D [8], [9] and 3D objects [10], [4], [11], [6] without considering whether they are reachable by an specific hand.…”