A Continuous Collision Detection Algorithm for Dubins Paths

This paper introduces a geometric algorithm for Continuous Collision Detection (CCD). It can be used for so-called Dubins paths, which are composed of arcs and straight lines. The CCD approach checks for an overlap between the area covered by the vehicle during a full arc and the polytopic obstacles. Previous work has already demonstrated the potential benefits over other methods, which perform collision checks at discrete sample points along the path. Compared to the previous CCD implementation, the proposed geometric algorithm requires only on elementary functions and does not depend on external libraries, e.g., for numerical optimization. A numerical study demonstrates the numerical speed-up, for elementary collision checks and in combination with a basic Rapidly-exploring Random Tree (RRT) path planner.