Boundary Sampling to Learn Predictive Safety Filters via Pontryagin's Maximum Principle

Abstract

Safety filters provide a practical approach for enforcing safety constraints in autonomous systems. While learning-based tools scale to high-dimensional systems, their performance depends on informative data that includes states likely to lead to constraint violation, which can be difficult to efficiently sample in complex, high-dimensional systems. In this work, we characterize trajectories that barely avoid safety violations using the Pontryagin Maximum Principle. These boundary trajectories are used to guide data collection for learned Hamilton-Jacobi Reachability, concentrating learning efforts near safety-critical states to improve efficiency. The learned Control Barrier Value Function is then used directly for safety filtering. Simulations and experimental validation on a shared-control automotive racing application demonstrate PMP sampling improves learning efficiency, yielding faster convergence, reduced failure rates, and improved safe set reconstruction, with wall times around 3ms.

This work has been submitted to the IEEE for possible publication