Sampling-Aware Control Barrier Functions for Safety-Critical and Finite-Time Constrained Control

TL;DR

This paper proposes Sampling-Aware Control Barrier Functions (SACBFs) to ensure safety and feasibility in sampled-data control systems, addressing limitations of existing methods under zero-order-hold implementations.

Contribution

It introduces SACBFs that incorporate sampling effects and high relative-degree constraints, providing guarantees for safety and finite-time reachability in practical sampled-data control.

Findings

SACBFs maintain safety under zero-order-hold control where traditional methods fail.

The relaxed variant r-SACBF improves feasibility with slack variables for multiple constraints.

Simulation results on a unicycle robot validate the effectiveness of SACBFs.

Abstract

In safety-critical control systems, ensuring both safety and feasibility under sampled-data implementations is crucial for practical deployment. Existing Control Barrier Function (CBF) frameworks, such as High-Order CBFs (HOCBFs), effectively guarantee safety in continuous time but may become unsafe when executed under zero-order-hold (ZOH) controllers due to inter-sampling effects. Moreover, they do not explicitly handle finite-time reach-and-remain requirements or multiple simultaneous constraints, which often lead to conflicts between safety and reach-and-remain objectives, resulting in feasibility issues during control synthesis. This paper introduces Sampling-Aware Control Barrier Functions (SACBFs), a unified framework that accounts for sampling effects and high relative-degree constraints by estimating and incorporating Taylor-based upper bounds on barrier evolution between sampling instants. The proposed method guarantees continuous-time forward invariance of safety and finite-time reach-and-remain sets under ZOH control. To further improve feasibility, a relaxed variant (r-SACBF) introduces slack variables for handling multiple constraints realized through time-varying CBFs. Simulation studies on a unicycle robot demonstrate that SACBFs achieve safe and feasible performance in scenarios where traditional HOCBF methods fail.