Using Equilibria and Virtual Holonomic Constraints to Generate Families of Walking Gaits

We present a principled approach to generating walking gaits for point- and curved-feet, underactuated, multi-degree-of-freedom, 2D and 3D biped walkers subject to a biped’s hybrid dynamics and user-defined virtual holonomic constraints (constraints that are enforced through feedback control). Specifically, we combine numerical continuation methods (NCM) and the hybrid zero dynamics (HZD) framework to generate families of gaits starting from equilibria of the biped model that satisfy the hybrid dynamics and virtual holonomic constraints (VHC).