Boundary Sampling to Learn Predictive Safety Filters via Pontryagin's Maximum Principle
For autonomous systems requiring safety filters, this method improves learning efficiency by focusing data collection on safety-critical states.
The paper introduces a boundary sampling method guided by Pontryagin's Maximum Principle to improve data efficiency for learning safety filters in autonomous systems. Experiments show faster convergence, reduced failure rates, and improved safe set reconstruction with wall times around 3ms.
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.