Simplification of the ray-shooting based algorithm for 3-D force-closure test

This paper addresses a shortcut in the ray-shooting based algorithm proposed by Liu. His algorithm provides an efficient force-closure test of 3D frictional grasps, which is formulated as a linear programming (LP) problem. We prove that the optimal objective value of the LP formulation indicates the force-closure property of grasps directly. Thus computing Q, d₁, and d₂ can be omitted.