I. Introduction
Computing optimal and collision-free joint trajectories for robotic manipulators operating in the presence of static and dynamic obstacles remains an open and widely studied problem in the robotics literature. A key element in developing an optimization algorithm for generating collision-free trajectories is a means for evaluating the proximity of two potentially colliding objects. The Euclidean separation distance, or shortest line segment joining two objects, is a natural measure of this proximity [1]. Some of the most general and versatile algorithms for computing separation distance are based on the concept of bounding volumes [2], in which potentially colliding objects are modeled using simple geometric primitives. The notion of bounding volumes, especially spherical bounding volumes, has been extensively employed in the development of path planners for robotic manipulators (see for example [3]–[5]). Sphere-swept volumes, such as the line-swept sphere (LSS), give another approach for modeling the manipulator and obstacles with increased accuracy [6].