Reachability Analysis for Black-Box Dynamical Systems

TL;DR

This paper introduces a novel method for Hamilton-Jacobi reachability analysis tailored for black-box dynamical systems, enabling safety verification without explicit system models, demonstrated on robotic simulations.

Contribution

It develops a new approach to approximate Hamiltonian functions from samples, extending reachability analysis to black-box systems, which was previously limited to white-box models.

Findings

Accurately computes reachable sets for black-box systems.

Successfully applied to robotic simulations like slip-wheel car and quadruped.

Integrates with existing reachability tools for broader applicability.

Abstract

Hamilton-Jacobi (HJ) reachability analysis is a powerful framework for ensuring safety and performance in autonomous systems. However, existing methods typically rely on a white-box dynamics model of the system, limiting their applicability in many practical robotics scenarios where only a black-box model of the system is available. In this work, we propose a novel reachability method to compute reachable sets and safe controllers for black-box dynamical systems. Our approach efficiently approximates the Hamiltonian function using samples from the black-box dynamics. This Hamiltonian is then used to solve the HJ Partial Differential Equation (PDE), providing the reachable set of the system. The proposed method can be applied to general nonlinear systems and can be seamlessly integrated with existing reachability toolboxes for white-box systems to extend their use to black-box systems. Through simulation studies on a black-box slip-wheel car and a quadruped robot, we demonstrate the effectiveness of our approach in accurately obtaining the reachable sets for blackbox dynamical systems.