Hybrid Zero Dynamics of Bipedal Robots Under Nonholonomic Virtual Constraints

This letter investigates the hybrid zero dynamics for planar bipedal robots with one degree of underactuation subject to nonholonomic virtual constraints (NHVCs). We first derive the closed-form expression of the bipedal robot zero dynamics under NHVCs. We next present conditions that make the NHVCs invariant with respect to rigid impacts with the ground. Lastly, a reduced dimensionality test, which is independent of the number of degrees of freedom of the bipedal robot, is proposed for checking existence and exponential stability of hybrid periodic orbits under NHVCs. Simulation results using the RABBIT biped robot demonstrate the robustness of the proposed NHVCs against a randomized horizontal push disturbance. A statistical significant difference between the mean number of steps until failure is shown between the NHVC and virtual holonomic constraint control schemes.