  Successfully achieving bipedal locomotion remains challenging due to
real-world factors such as model uncertainty, random disturbances, and
imperfect state estimation. In this work, we propose a novel metric for
locomotive robustness -- the estimated size of the hybrid forward invariant set
associated with the step-to-step dynamics. Here, the forward invariant set can
be loosely interpreted as the region of attraction for the discrete-time
dynamics. We illustrate the use of this metric towards synthesizing nominal
walking gaits using a simulation-in-the-loop learning approach. Further, we
leverage discrete-time barrier functions and a sampling-based approach to
approximate sets that are maximally forward invariant. Lastly, we
experimentally demonstrate that this approach results in successful locomotion
for both flat-foot walking and multi-contact walking on the Atalante lower-body
exoskeleton.
