LET THEM FALL WHERE THEY MAY - CAPTURE REGIONS OF CURVED OBJECTS AND POLYHEDRA

When a three-dimensional object is placed in contact with a supporting plane, gravitational forces move if to one of a finite set of stable poses. For each stable pose, there is a region in the part's configura tion space called a capture region; for any initial configuration with in the region, the object is guaranteed to converge to that pose. The problem of computing maximal capture regions from an object model is a nalyzed assuming only that the dynamics are dissipative; the precise e quations governing the system are unnecessary. An algorithm, based on Morse theory, is first developed for objects with smooth, convex hulls . The formulation is then extended to objects with piecewise-smooth hu lls using a catalog of critical points derived from stratified Morse t heory. Algorithms have been fully implemented for objects with smooth and polyhedral convex hulls. As examples from the implementation demon strate, calculating these regions from a geometric model is computatio nally practical.