Distance computation for rotational and translational motions

A new technique for computing the minimum translational distance between two moving objects with rotational motions is presented in this paper. Separation or penetration distance is computed with no space and time discretization for constant-speed motions. Motions are constrained to two degrees of freedom. Objects and their motions are modeled by 3D spherically-extended polytopes. The distance-computation algorithm returns a set of parameters that characterizes the maximum approach positions and the corresponding instant of time. Additionally, this set of parameters also characterizes a new motion for one of the objects to come into contact with the other moving object.