Control Barrier Functions

Control barrier functions provide mathematical conditions for keeping systems inside safe sets, such as avoiding collisions or respecting actuator limits. A common approach adds barrier constraints to a quadratic program that minimally adjusts a nominal controller; other methods use high-order and discrete-time barriers, reachability, robust or probabilistic bounds, and learned safety functions. Researchers apply these tools to robotics, autonomous vehicles, multi-agent systems, and learning-based control, often combining them with perception, model predictive control, or reinforcement learning. A central challenge is making safety guarantees hold under uncertainty and limited control authority without making constraints infeasible or behavior overly cautious, while also preserving progress toward goals.