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

TL;DR

The paper tackles safety guarantees for autonomous systems under limited actuation by bridging Hamilton-Jacobi reachability with control barrier functions. It introduces an online scheme that constructs an implicit CBF at every control cycle via reach-avoid differential dynamic programming in a receding-horizon framework, yielding smooth safety corrections with infinite-time enforcement. Key contributions include (i) a provably safe online method that maintains safety without the conservativeness of handcrafted CBFs, and (ii) demonstration on a Dubins car and a 5D bicycle showing smoother safety filtering than LR approaches while avoiding extreme interventions. The approach facilitates real-time safety-critical control by integrating reachability-based invariants with CBF-style safety guarantees for high-dimensional systems.

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.