Refining Almost-Safe Value Functions on the Fly

TL;DR

This paper introduces methods for real-time refinement of control barrier functions to ensure safety in robotic systems, enabling online adaptation to environmental changes with formal safety guarantees.

Contribution

It presents refineCBF and HJ-Patch algorithms that allow safe value function updates during operation, bridging offline synthesis and online adaptation.

Findings

Successful real-time safety adaptation in simulation and hardware

Effective handling of environmental changes like obstacles and wind

Guarantees of safety recovery during online updates

Abstract

Control Barrier Functions (CBFs) are a powerful tool for ensuring robotic safety, but designing or learning valid CBFs for complex systems is a significant challenge. While Hamilton-Jacobi Reachability provides a formal method for synthesizing safe value functions, it scales poorly and is typically performed offline, limiting its applicability in dynamic environments. This paper bridges the gap between offline synthesis and online adaptation. We introduce refineCBF for refining an approximate CBF - whether analytically derived, learned, or even unsafe - via warm-started HJ reachability. We then present its computationally efficient successor, HJ-Patch, which accelerates this process through localized updates. Both methods guarantee the recovery of a safe value function and can ensure monotonic safety improvements during adaptation. Our experiments validate our framework's primary contribution: in-the-loop, real-time adaptation, in simulation (with detailed value function analysis) and on physical hardware. Our experiments on ground vehicles and quadcopters show that our framework can successfully adapt to sudden environmental changes, such as new obstacles and unmodeled wind disturbances, providing a practical path toward deploying formally guaranteed safety in real-world settings.