Sampling-Aware Control Barrier Functions for Safety-Critical and Finite-Time Constrained Control
This addresses safety-critical control for practical deployment in robotics and autonomous systems, though it is incremental as it builds on existing CBF frameworks.
The paper tackled the problem of ensuring safety and feasibility in sampled-data control systems by introducing Sampling-Aware Control Barrier Functions (SACBFs), which guarantee continuous-time safety and finite-time reach-and-remain sets under zero-order-hold control, as demonstrated in simulations where traditional methods fail.
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.