Ray-Shooting Algorithms for Robotics

Ray shooting is a well-studied problem in computer graphics and also has applications in robotics such as collision detection and contact force optimization. Unfortunately, most ray-shooting algorithms developed for graphics applications only allow 3-dimensional (3-D) objects represented as triangle meshes, and therefore are not suited for objects with parametric surfaces or general convex sets in high-dimensional space which robotics applications often require. In contact force optimization, for example, the problem is in the 6-dimensional (6-D) wrench space and it is desirable to consider the nonlinear friction cone without approximating it by a pyramid. This paper discusses existing and novel geometry-based ray-shooting algorithms applicable to general convex sets, and compares their performances in two robotics applications: computing the distance between two convex objects and optimizing contact forces in grasping.