Verification of safety critical control policies using kernel methods

TL;DR

This paper introduces a Gaussian process-based framework to model and manage errors in Hamilton-Jacobi reachability methods, enhancing safety guarantees in control policies by providing confidence metrics for switching controllers.

Contribution

It presents a novel approach to quantify and correct errors in safety-critical control using Gaussian processes, enabling safer hybrid control strategies.

Findings

Effective error modeling of value functions

Improved safety through confidence-based controller switching

Successful validation in pursuit-evasion scenarios

Abstract

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.