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.

翻译：双足行走的成功实现仍面临模型不确定性、随机扰动及状态估计不完善等现实因素的挑战。本文提出一种步态鲁棒性的新型度量——与步步动态相关的混合前向不变集估计尺寸。此处，前向不变集可粗略理解为离散时间动态的吸引域。我们通过仿真-在环学习方法展示了该度量在名义行走步态合成中的应用。进一步，利用离散时间障碍函数与基于采样的方法近似最大前向不变集。最后，实验证明该方法在Atalante下肢外骨骼上实现了平足行走与多接触行走两种模式的成功步态。