Leveraging Cone Double Description for Multi-contact Stability of Humanoids with Applications to Statics and Dynamics

We build on previous works advocating the use of the Gravito-Inertial Wrench Cone (GIWC) as a general contact stability criterion (a "ZMP for non-coplanar contacts"). We show how to compute this wrench cone from the friction cones of contact forces by using an intermediate representation, the surface contact wrench cone, which is the minimal representation of contact stability for each surface contact. The observation that the GIWC needs to be computed only once per stance leads to particularly efficient algorithms, as we illustrate in two important problems for humanoids: "testing robust static equilibrium" and "time-optimal path parameterization". We show, through theoretical analysis and in physics simulations, that our method is more general and/or outperforms existing ones.