Continuous distance computation for motions with constant accelerations

A method for computing the distance between two mobile objects following linear or arc-like motions with constant accelerations is introduced in this paper. This distance is obtained without stepping or discretizing any object's motion. Objects are modeled by bi-dimensional convex hulls. The distance- computation algorithm obtains the instant in time when two mobile objects are at their minimum translational distance of separation or penetration. The distance and the instant in time are parallely computed. This method is so fast that can be run as frequent as new information from the world is received.