An analytical method to detect collision between cylinders using dual number algebra

Cylinder, a common geometric entity has a discontinuity at the joining of cylindrical surface and circular-disks. Hence, collision detection between two cylinders in space is a difficult task and few have reported formulations to solve it. In this paper, a novel analytical methodology is proposed to detect collision or intersection between two cylinders. The configuration, i.e., position and orientation, between the cylinders was represented using the four Denavit-Hartenberg (DH) parameters plus two extra parameters. Dual Number Algebra was used to extract these six parameters. Tests involved in collision detection between the cylinders were between the lines and rectangles in a plane, thus considerably simplifying the problem of collision detection. As an illustration, an one-DOF arm modeled as a cylinder with cylindrical shaped obstacles were modeled and tested for their collisions. The results were validated with an analytical method available in the literature and a commercial software.