Computation of penetration between smooth convex objects in three-dimensional space

Abstract

There are many applications in robotics where collision detection, separation distance, and penetration distance between geometrical models of objects are required. Efficient numerical procedures for the computation of these proximal relations are important as they are frequently invoked. A new measure of penetration and separation called the growth distance has been introduced in the literature. It has been shown that the growth distance can be efficiently computed for convex polytopes. This article extends the computation of growth distance to smooth convex objects. Specifically, we introduce a formulation of the growth distance for smooth convex objects that is well suited for numerical computation. By modeling a convex object as union of convex subobjects, the growth distance of a wide family of objects can be computed. However, computation of growth distance for such object models may be expensive. A fast algorithm is introduced that reduces the computational time significantly. In the case where the objects undergo continuous relative motions and the growth distances must be evaluated for a large number of closely-spaced points along the motions, further reduction in computational effort is achieved. Numerical experiments with objects that are found in typical robot applications substantiate the claim. © 1996 John Wiley & Sons, Inc.