From Space to Time: Enabling Adaptive Safety with Learned Value Functions via Disturbance Recasting

Abstract

Safe operation is essential for autonomous systems in safety-critical environments such as urban air mobility. Value function-based safety filters provide formal guarantees on safety, wrapping learned or planning-based controllers with a layer of protection. Recent approaches leverage offline learned value functions to scale these safety filters to high-dimensional systems. Yet these methods assume detailed prior knowledge of all possible sources of model mismatch, in the form of disturbances, in the environment -- information that is typically unavailable in real world settings. Even in well-mapped environments like urban canyons or industrial sites, drones encounter complex, spatially-varying disturbances arising from payload-drone interaction, turbulent airflow, and other environmental factors. We introduce Space2Time, which enables safe and adaptive deployment of offline-learned safety filters under unknown, spatially-varying disturbances. The key idea is to reparameterize spatial disturbances as a time-varying formulation, allowing the use of temporally varying precomputed value functions during online operation. We validate Space2Time through extensive simulations on diverse quadcopter models and real-world hardware experiments, demonstrating significantly improved safety performance over worst-case and naive baselines.