Guaranteeing safe behavior on complex autonomous systems -- from cars to walking robots -- is challenging due to the inherently high dimensional nature of these systems and the corresponding complex models that may be difficult to determine in practice. With this as motivation, this paper presents a safety-critical control framework that leverages reduced order models to ensure safety on the full order dynamics -- even when these models are subject to disturbances and bounded inputs (e.g., actuation limits). To handle input constraints, the backup set method is reformulated in the context of reduced order models, and conditions for the provably safe behavior of the full order system are derived. Then, the input-to-state safe backup set method is introduced to provide robustness against discrepancies between the reduced order model and the actual system. Finally, the proposed framework is demonstrated in high-fidelity simulation, where a quadrupedal robot is safely navigated around an obstacle with legged locomotion by the help of the unicycle model.

翻译：针对从汽车到步行机器人等复杂自主系统，保证其安全行为具有挑战性，原因在于这些系统本质上具有高维特性，且对应的复杂模型在实践中可能难以确定。基于此动机，本文提出了一种安全关键控制框架，利用降阶模型来确保全阶动力学系统的安全性——即使这些模型受到扰动和有限输入（如执行器极限）的影响。为处理输入约束，在降阶模型框架下重新表述了备份集方法，并推导了全阶系统可证明安全行为的条件。随后，引入了输入到状态安全的备份集方法，以增强对降阶模型与实际系统间差异的鲁棒性。最后，通过高保真仿真验证了所提框架，其中借助独轮车模型，使四足机器人通过腿部运动安全地绕过障碍物。