Tech Report: Efficient and Exact Collision Detection for Circular Agents

A common problem in multi-robot algorithms is collision detection. Many solutions exist, but often suffer from problems such as high computational cost or causing false negative or false positive detections. In practice, these problems can result in results that range from inefficiency and annoyance to catastrophic. 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.