Scalable Learning of Safety Guarantees for Autonomous Systems using Hamilton-Jacobi Reachability

TL;DR

This paper introduces a set of techniques to significantly accelerate Hamilton-Jacobi reachability analysis, enabling real-time safety guarantees for high-dimensional autonomous systems like quadcopters in uncertain environments.

Contribution

It combines decomposition, warm-starting, and adaptive grids to speed up safety analysis, making it feasible for systems with higher dimensions than previously possible.

Findings

Safe set computation is accelerated by up to two orders of magnitude.

The framework enables real-time safety updates for 10D systems.

Validated on simulated quadcopters in windy conditions.

Abstract

Autonomous systems like aircraft and assistive robots often operate in scenarios where guaranteeing safety is critical. Methods like Hamilton-Jacobi reachability can provide guaranteed safe sets and controllers for such systems. However, often these same scenarios have unknown or uncertain environments, system dynamics, or predictions of other agents. As the system is operating, it may learn new knowledge about these uncertainties and should therefore update its safety analysis accordingly. However, work to learn and update safety analysis is limited to small systems of about two dimensions due to the computational complexity of the analysis. In this paper we synthesize several techniques to speed up computation: decomposition, warm-starting, and adaptive grids. Using this new framework we can update safe sets by one or more orders of magnitude faster than prior work, making this technique practical for many realistic systems. We demonstrate our results on simulated 2D and 10D near-hover quadcopters operating in a windy environment.