Before revision:  The main contribution of this paper is to provide a high-level overview of major categories of collision detection, provide insight into the need for accurate and computationally efficient collision detection, and provide methods of collision detection and anticipatory collision avoidance  that are both computationally efficient and exact -- that is, they will never yield false negative or false positive detections . Supplementary reference for mathematics behind collision detection .
After revision:  The main contribution of this paper is to provide a high-level overview of major categories of collision detection, provide insight into the need for accurate and computationally efficient collision detection, and provide methods of collision detection and anticipatory collision avoidance that are both computationally efficient and exact -- that is, they will never yield false negative or false positive detections .