Nonholonomic Virtual Constraint Design for Variable-Incline Bipedal Robotic Walking

Abstract

This letter presents a method of designing relative-degree-two nonholonomic virtual constraints (NHVCs) that allow for stable bipedal robotic walking across variable terrain slopes. Relative-degree-two NHVCs are virtual constraints that encode velocity-dependent walking gaits via momenta conjugate to the unactuated degrees of freedom for the robot. We recently introduced a systematic method of designing NHVCs, based on the hybrid zero dynamics (HZD) control framework, to achieve hybrid invariant flat ground walking without the use of dynamic reset variables. This work addresses the problem of walking over variable-inclined terrain disturbances. We propose a methodology for designing NHVCs, via an optimization problem, in order to achieve stable walking across variable terrain slopes. The end result is a single controller capable of walking over variable-inclined surfaces, that is also robust to inclines not considered in the optimization design problem, and uncertainties in the inertial parameters of the model.