3-D Robust Stability Polyhedron in Multicontact

We propose algorithms to compute the three-dimensional (3-D) robust stability region in multicontact. It is well known that the stability region is a product of convex cones and, hence, is a convex polyhedron. Our stability region extends existing recursive two-dimensional (2-D) static stability approaches to 3-D by accounting for possible center-of-mass accelerations. We provide algorithms that construct the region of robust stability in a systematic way. We compare our algorithms and discuss possible computation of intermediary shapes using morphing. Finally, we provide an example of usage in generating robust static postures that can serve the purpose of multicontact planning.