Refining Almost-Safe Value Functions on the Fly

2026-02-26

AI Summary

This work addresses the challenge of maintaining safety in complex dynamic environments where traditional control barrier functions (CBFs) struggle to adapt in real time to sudden obstacles or environmental disturbances. The authors propose an online optimization framework that integrates Hamilton-Jacobi (HJ) reachability analysis with a warm-start mechanism to locally and incrementally refine unsafe or approximate CBFs, thereby adaptively updating the safety value function. This approach achieves, for the first time, online local reconstruction of safety certificates grounded in HJ reachability, ensuring monotonic improvement of safety during adaptation while supporting seamless deployment from simulation to physical hardware. Experimental validation on ground vehicles and quadrotor drones demonstrates the framework’s effectiveness in handling unexpected obstacles and unmodeled wind disturbances, offering both real-time performance and formal safety guarantees.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Control Barrier Functions
• Hamilton-Jacobi Reachability
• online adaptation
• safety guarantees
• dynamic environments

Innovation

• Control Barrier Functions
• Hamilton-Jacobi Reachability
• Online Safety Adaptation
• HJ-Patch
• Real-time Verification