Fast, Smooth, and Safe: Implicit Control Barrier Functions through Reach-Avoid Differential Dynamic Programming

TL;DR

This paper introduces an online method combining Hamilton-Jacobi reachability with differential dynamic programming to create implicit control barrier functions, enabling smooth, safe, and less conservative control in autonomous systems.

Contribution

It presents a novel receding-horizon approach to construct implicit CBFs via reach-avoid DDP, providing infinite-time safety guarantees with smooth control adjustments.

Findings

Successfully applied to Dubins car and bicycle models.

Achieves safety with smooth control without conservative handcrafting.

Demonstrates improved safety filtering in simulations.

Abstract

Safety is a central requirement for autonomous system operation across domains. Hamilton-Jacobi (HJ) reachability analysis can be used to construct "least-restrictive" safety filters that result in infrequent, but often extreme, control overrides. In contrast, control barrier function (CBF) methods apply smooth control corrections to guard the system against an often conservative safety boundary. This paper provides an online scheme to construct an implicit CBF through HJ reach-avoid differential dynamic programming in a receding-horizon framework, enabling smooth safety filtering with infinite-time safety guarantees. Simulations with the Dubins car and 5D bicycle dynamics demonstrate the scheme's ability to preserve safety smoothly without the conservativeness of handcrafted CBFs.