Abstract

The problem of tracking the distance between two convex polyhedra is finding applications in many areas of robotics. The algorithm of Lin and Canny is a well-known fast solution to this problem, but by recasting the algorithms into configuration space we show that a minor modification to the earlier algorithm of Gilbert, Johnson and Keerthi also gives this algorithm the same expected cost. I. Introduction Methods for computing the minimum distance function between convex polyhedra have been known for some time. Here we wish to concentrate on two well-known algorithms for computing the exact (Euclidean) distance between two convex polyhedra. The first is the algorithm published by Gilbert, Johnson and Keerthi in 1988 [5], henceforth referred to as GJK. The second is the algorithm published by Lin and Canny in 1991 [6], which we will henceforth refer to as LC. (We may also use these abbreviations to refer to the authors.) Both algorithms have been extended in various ways, including the...

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