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

2026-04-14

AI Summary

This work addresses the inefficiency of learning-based safety filters in high-dimensional autonomous systems, which stems from a scarcity of high-quality data near safety boundaries. To overcome this limitation, the study introduces the first application of Pontryagin’s Maximum Principle to actively sample boundary trajectories that just avoid constraint violations, thereby directing data collection toward safety-critical states. The resulting learned control barrier value function can be directly deployed for real-time safety filtering. Evaluated in both simulation and real-world shared-control racing experiments, the approach demonstrates significantly improved learning efficiency and generalization, achieving faster convergence, lower failure rates, and more accurate reconstruction of safe sets, all with a runtime latency of approximately 3 milliseconds.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Learning to Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• safety filters
• data sampling
• high-dimensional systems
• safety-critical states
• constraint violation

Innovation

• Boundary Sampling
• Pontryagin's Maximum Principle
• Safety Filter
• Hamilton-Jacobi Reachability
• Control Barrier Value Function