Ambiguous collision outcomes and sliding with infinite friction in models of legged systems

This work explores the collision process at foot contact in models of legged robots. In particular, we highlight that for legged systems the widely used assumption of no sliding of the contact points can yield inconsistent outcomes. For certain contact configurations and system parameters, neither the assumption of lift-off of the trailing foot nor the assumption that it stays fixed on the ground yield valid solutions. The foot will slide, even if an infinite coefficient of friction is assumed. In a related effect, we present configurations in which the solution of the collision process is ambiguous. These behaviors are examined for the models of a minimalistic biped, a passive dynamic walker, and the five-link bipedal robot RAMone. The paper provides background for these non-intuitive behaviors and investigates the influence of system parameters onto the collision behavior of a passive dynamic walker. By studying bipedal models that range from minimalistic to physically accurate, this paper establishes a bridge between the theoretical study of unilateral contact in multibody dynamic simulations and the application of these simulation methods in the modeling of ground contact in actual legged systems.