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 the use of discrete-time barrier functions to certify hybrid forward invariance of reduced step-to-step dynamics. The size of these invariant sets can then be used as a metric for locomotive robustness. We demonstrate an application of this metric towards synthesizing robust nominal walking gaits using a simulation-in-the-loop approach. This procedure produces reference motions with step-to-step dynamics that are maximally forward-invariant with respect to the reduced representation of choice. The results demonstrate robust locomotion for both flat-foot walking and multi-contact walking on the Atalante lower-body exoskeleton.

翻译：成功实现双足运动仍面临诸多实际挑战，包括模型不确定性、随机干扰以及不完善的状态估计。本研究提出利用离散时间势垒函数来验证简化步间动态的混合前向不变性，这些不变集的规模可作为衡量运动稳健性的指标。我们展示了该指标在仿真循环方法中的应用，用于合成稳健的名义步行步态。该流程能生成具有最大前向不变性（相对于所选简化表征）的步间动态参考运动。实验结果表明，该方法在Atalante下肢外骨骼上实现了平足行走和多接触行走的稳健运动。