Exact-Time Safety Recovery using Time-Varying Control Barrier Functions with Optimal Barrier Tracking

TL;DR

This paper introduces an exact-time safety recovery method for control-affine nonlinear systems using time-varying Control Barrier Functions, ensuring safety within a prescribed time and optimizing recovery trajectories.

Contribution

It proposes a novel active barrier tracking approach that guarantees safety recovery at a specified time, transforming safety into a trajectory design problem.

Findings

Guarantees recovery to safe set at a prescribed time.

Optimizes recovery trajectories for better performance.

Demonstrates effectiveness in autonomous vehicle traffic scenarios.

Abstract

This paper is motivated by controllers developed for autonomous vehicles which occasionally result into conditions where safety is no longer guaranteed. We develop an exact-time safety recovery framework for any control-affine nonlinear system when its state is outside a safe region using time-varying Control Barrier Functions (CBFs) with optimal barrier tracking. Unlike conventional formulations that provide only conservative upper bounds on recovery time convergence, the proposed approach guarantees recovery to the safe set at a prescribed time. The key mechanism is an active barrier tracking condition that forces the barrier function to follow exactly a designer-specified recovery trajectory. This transforms safety recovery into a trajectory design problem. The recovery trajectory is parameterized and optimized to achieve optimal performance while preserving feasibility under input constraints, avoiding the aggressive corrective actions typically induced by conventional finite-time formulations. The safety recovery framework is applied to the roundabout traffic coordination problem for Connected and Automated Vehicles (CAVs), where any initially violated safe merging constraint is replaced by an exact-time recovery barrier constraint to ensure safety guarantee restoration before CAV conflict points are reached. Simulation results demonstrate improved feasibility and performance.