Verification of safety critical control policies using kernel methods
This work addresses safety verification for control systems, particularly in robotics or autonomous vehicles, but is incremental as it builds on existing reachability methods by adding error modeling.
The paper tackles the problem of ensuring safety in control policies by modeling errors in Hamilton-Jacobi reachability value functions using a Gaussian process, resulting in a hybrid control law that switches between controllers based on confidence metrics, tested in a pursuit-evasion example.
Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies that occur due to uncertainty in the underlying dynamics and environment as well as the induced numerical errors. To this end, we propose a framework for modeling the error of the value function inherent in Hamilton-Jacobi reachability using a Gaussian process. The derived safety controller can be used in conjuncture with arbitrary controllers to provide a safe hybrid control law. The marginal likelihood of the Gaussian process then provides a confidence metric used to determine switches between a least restrictive controller and a safety controller. We test both the prediction as well as the correction capabilities of the presented method in a classical pursuit-evasion example.