Control

Control Barrier Function (CBF)

A control barrier function is a scalar function of the system state whose sublevel or superlevel set defines a safe region, together with a condition on its derivative ensuring the set is forward invariant under control, formalized by Ames et al. CBF constraints are typically enforced pointwise via quadratic programs that minimally modify a nominal controller's command, yielding real-time safety filters for collision avoidance, joint limits, and force bounds.

Why it matters for physical AI

CBF-based safety filters wrap learned policies with mathematically grounded runtime guarantees, letting neural controllers act freely inside a certified safe set while overriding them near its boundary.