Is Your Safe Controller Actually Safe? A Critical Review of CBF Tautologies and Hidden Assumptions

TL;DR

This paper critically reviews the practical application of Control Barrier Functions in robotic safety, highlighting gaps between theory and implementation, and providing guidelines to ensure valid safety guarantees in real systems.

Contribution

It clarifies the distinction between candidate and valid CBFs, analyzes common misuses, and offers practical guidelines for constructing realizable safety arguments in robotic systems.

Findings

CBFs often assume safe controllers that are not constructively realizable in constrained systems

Many demonstrations only show passive safety, not active safety guarantees

Guidelines are provided for designing valid safety assurances in real-world systems

Abstract

This tutorial provides a critical review of the practical application of Control Barrier Functions (CBFs) in robotic safety. While the theoretical foundations of CBFs are well-established, I identify a recurring gap between the mathematical assumption of a safe controller's existence and its constructive realization in systems with input constraints. I highlight the distinction between candidate and valid CBFs by analyzing the interplay of system dynamics, actuation limits, and class-K functions. I further show that some purported demonstrations of safe robot policies or controllers are limited to passively safe systems, such as single integrators or kinematic manipulators, where safety is already inherited from the underlying physics and even naive geometric hard constraints suffice to prevent collisions. By revisiting simple low-dimensional examples, I show when CBF formulations provide valid safety guarantees and when they fail due to common misuses. I then provide practical guidelines for constructing realizable safety arguments for systems without such passive safety. The goal of this tutorial is to bridge the gap between theoretical guarantees and actual implementation, supported by an open-source interactive web demonstration that visualizes these concepts intuitively.