A numerical solution to the ray-shooting problem and its applications in robotic grasping

Based on the distance algorithm by Gilbert et al., this paper presents a numerical algorithm for computing the intersection of the boundary of a compact convex set with a ray emanating from an interior point of the set, which is known as the ray-shooting problem. Affinely independent points on the boundary of the convex set are also determined such that the intersection point can be written as their convex combination. Because of its high efficiency and other good qualities, this algorithm provides superior solutions to three fundamental problems in robotic grasping, i.e., force-closure test, contact force optimization, and grasp quality evaluation, which can be formulated as the ray-shooting problem.