Distance computation between smooth convex objects

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 paper extends the computation of growth distance to smooth convex objects. Specifically, the authors introduce a formulation of the growth distance for smooth convex objects which is well suited for numerical computation. By modeling convex objects as the 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 which reduces the computational time significantly. In the case where the objects undergo continuous relative motion and the growth distances must be evaluated for a large number of closely spaced points along the motion, further reduction in computational effort is achieved. Numerical experiments with objects that are found in typical robot applications are also provided