Survey Paper on Control Barrier Functions
Promit Panja
TL;DR
This survey addresses enforcing safety in cyber-physical systems by framing safety as forward invariance of a safe set and grounding it in Nagumo's condition and barrier certificates. It surveys Control Barrier Functions (CBFs) and their extensions—High-Order CBFs (HOCBFs) and Adaptive CBFs (aCBFs)—and shows how quadratic-programming-based safety filters can be integrated with performance objectives. Key contributions include formal definitions of CBFs/HOCBFs/aCBFs, derivations of corresponding safety constraints, and demonstrations across Adaptive Cruise Control, robotics, and quadrotor flight. The work highlights the practical impact of barrier-based safety in complex, uncertain, and high-degree-of-freedom systems, illustrating how safety can be maintained without sacrificing performance in real-world applications.
Abstract
Control Barrier Functions (CBFs) have emerged as a powerful paradigm in control theory, providing a principled approach to enforcing safety-critical constraints in dynamic systems. This survey paper comprehensively explores the foundational principles of CBFs, delves into the complexities of High Order Control Barrier Functions (HOCBFs), and extends the discussion to the adaptive realm with adaptive Control Barrier Functions (aCBFs). Through a systematic examination of theoretical underpinnings, practical applications, and the evolving landscape of research, this survey highlights the versatility of CBFs in addressing safety and stability challenges.