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Guaranteeing safe behavior on complex autonomous systems -- from cars towalking robots -- is challenging due to the inherently high dimensional natureof these systems and the corresponding complex models that may be difficult todetermine in practice. With this as motivation, this paper presents asafety-critical control framework that leverages reduced order models to ensuresafety on the full order dynamics -- even when these models are subject todisturbances and bounded inputs (e.g., actuation limits). To handle inputconstraints, the backup set method is reformulated in the context of reducedorder models, and conditions for the provably safe behavior of the full ordersystem are derived. Then, the input-to-state safe backup set method isintroduced to provide robustness against discrepancies between the reducedorder model and the actual system. Finally, the proposed framework isdemonstrated in high-fidelity simulation, where a quadrupedal robot is safelynavigated around an obstacle with legged locomotion by the help of the unicyclemodel.

Safety-Critical Control with Bounded Inputs via Reduced Order Models