Comparison between safety methods control barrier function vs. reachability analysis

TL;DR

This paper compares control barrier functions and Hamilton-Jacobi reachability analysis in terms of their applicability, complexity, and computational cost using a Dubins car model.

Contribution

It provides a systematic comparison of two safety methods, highlighting their differences in generality, construction difficulty, and computational requirements.

Findings

Control barrier functions are more general for certain dynamics.

Hamilton-Jacobi reachability offers precise safety guarantees.

Computational costs vary significantly between methods.

Abstract

This report aims to compare two safety methods: control barrier function and Hamilton-Jacobi reachability analysis. We will consider the difference with a focus on the following aspects: generality of system dynamics, difficulty of construction and computation cost. A standard Dubins car model will be evaluated numerically to make the comparison more concrete.