e-journal
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. Note to Practitioners—We describe efficient and accurate algorithms for ray-shooting problem, i.e., finding the intersection between a ray (a line emanating from a point) and a convex object.
Its major applications in robotics include computation of the distance between two convex objects and optimization of contact forces for multifingered grasping and multilegged locomotion.
The algorithms are efficient because they employ geometry-based iterations instead of general-purpose numerical optimization such as the active-set algorithm in MATLAB. They are accurate because we do not have to apply polygon approximation to object shapes in distance computation or to friction cones in contact force optimization. In distance computation, for example, this fact means that we can directly use the parametric representation of the object surfaces such as NURBS.
Index Terms—Collision detection, contact force optimization, distance measure, ray shooting, support function.
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