A Comprehensive Review on Control Barrier Functions: Uncertainty Handling, Design Optimization, and Feasibility Analysis

Control barrier functions (CBFs) provide a rigorous framework for enforcing safety in control-affine systems by ensuring system states remain within predefined safe sets. However, practical deployment faces fundamental challenges that limit real-world applicability. This review analyzes recent progress in CBF methodologies across three interconnected domains: uncertainty handling, structural optimization, and feasibility assurance. For uncertainty, we distinguish strategies tailored to unknown dynamics, modeling discrepancies, and dynamic environments, spanning robust theoretical methods and learning-based approaches. For structural design, we examine class- $\mathcal {K}$ function selection, parameter tuning, and advanced modifications that jointly address conservatism and feasibility. For feasibility, we identify the root causes of CBF-QP infeasibility and survey solution strategies, including constraint relaxation, structural redesign, and mathematical guarantees. By synthesizing these directions into a unified framework, this review highlights key interdependencies and outlines future research opportunities for advancing CBF-based safety-critical control in robotics, autonomous systems, and beyond.