Refining Control Barrier Functions through Hamilton-Jacobi Reachability

TL;DR

This paper introduces refineCBF, a method that uses Hamilton-Jacobi reachability and dynamic programming to iteratively improve control barrier functions, ensuring safer and less conservative control of autonomous systems.

Contribution

It presents a novel framework that refines candidate CBFs through formal verification, guaranteeing safety and convergence to valid CBFs in nonlinear control systems.

Findings

RefineCBF guarantees at least as much safety with each iteration.

The method reduces conservativeness of CBFs in simulations.

Demonstrated effectiveness on various nonlinear control systems.

Abstract

Safety filters based on Control Barrier Functions (CBFs) have emerged as a practical tool for the safety-critical control of autonomous systems. These approaches encode safety through a value function and enforce safety by imposing a constraint on the time derivative of this value function. However, synthesizing a valid CBF that is not overly conservative in the presence of input constraints is a notorious challenge. In this work, we propose refining a candidate CBF using formal verification methods to obtain a valid CBF. In particular, we update an expert-synthesized or backup CBF using dynamic programming (DP) based reachability analysis. Our framework, refineCBF, guarantees that with every DP iteration the obtained CBF is provably at least as safe as the prior iteration and converges to a valid CBF. Therefore, refineCBF can be used in-the-loop for robotic systems. We demonstrate the practicality of our method to enhance safety and/or reduce conservativeness on a range of nonlinear control-affine systems using various CBF synthesis techniques in simulation.