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Successfully achieving bipedal locomotion remains challenging due toreal-world factors such as model uncertainty, random disturbances, andimperfect state estimation. In this work, we propose the use of discrete-timebarrier functions to certify hybrid forward invariance of reduced step-to-stepdynamics. The size of these invariant sets can then be used as a metric forlocomotive robustness. We demonstrate an application of this metric towardssynthesizing robust nominal walking gaits using a simulation-in-the-loopapproach. This procedure produces reference motions with step-to-step dynamicsthat are maximally forward-invariant with respect to the reduced representationof choice. The results demonstrate robust locomotion for both flat-foot walkingand multi-contact walking on the Atalante lower-body exoskeleton.

Synthesizing Robust Walking Gaits via Discrete-Time Barrier Functions with Application to Multi-Contact Exoskeleton Locomotion