Estimate of minimum distance between convex polyhedra based on enclosed ellipsoids

A tight estimate of upper and lower bounds of the distance between convex polyhedra based on the best ellipsoid fit is proposed. Estimated distance is mainly based on enclosed ellipsoids, instead of minimum volume enclosing ellipsoids. We provide an algorithm for computing the enclosed ellipsoid of a convex polyhedron by the use of its best fit enclosing ellipsoid. By this estimate, the collision-free region could be much larger than enclosing ellipsoids and the detection of potential collisions can be more accurate than that of using enclosing ellipsoids. A numerical example is presented to show the tightness of upper and lower distance estimates based on enclosed ellipsoids.