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We propose an original formulation to describe the motion of a rolling object in contact with a flat surface, and propose a complete application of this model to generate optimal walk of a humanoid system. We derive an analytic formulation of the contact equations which does not require any numerical approximation. We then show how the model performs when applied to the simulation of bipedal locomotion: by replacing polyhedral models of the feet by ellipsoidal ones, the numerical algorithms run faster and provide higher quality results. Furthermore, as any convex shape may be approximated locally by an ellipsoid, the scope of the model goes beyond locomotion simulation.

An analytical model of rolling contact and its application to the modeling of bipedal locomotion