Exact-Time Safety Recovery using Time-Varying Control Barrier Functions with Optimal Barrier Tracking
This addresses safety-critical control for autonomous vehicles, offering a more precise and less aggressive recovery method, though it is incremental as it builds on existing control barrier function techniques.
The paper tackles the problem of safety recovery for autonomous vehicles when safety is violated, by developing a framework that guarantees recovery to a safe set at a prescribed exact time, unlike conventional methods that only provide conservative bounds. It demonstrates improved feasibility and performance in simulations for roundabout traffic coordination of connected and automated vehicles.
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.