Robot control
Control barrier function
Definition
A control barrier function is a mathematical function used to express a safe set for a dynamical system and constrain control inputs so the system remains inside that set. It is commonly used as a safety filter around a nominal robot controller.
Also known as: CBF, Control barrier functions
Updated
A boundary on admissible motion
A control barrier function assigns values to robot states so that an inequality, often written as h(x) >= 0, describes a safe set. The controller then chooses inputs that satisfy a condition on how h changes. Under the assumptions in the formulation, satisfying that condition makes the set forward invariant: a trajectory that starts in the set remains there. Ames and colleagues develop this relationship between barrier functions, control inputs, and forward invariance.
The function does not have to generate the robot's desired behaviour. A separate controller can request an action for tracking, navigation, or robotic manipulation, while the barrier condition limits which actions are admissible.
A quadratic program can act as a safety filter
One common construction puts the barrier inequality into a quadratic program. The program finds a control input close to the nominal command while satisfying the safety constraint. The same optimisation can combine a control barrier function with a control Lyapunov function that represents a performance objective, as demonstrated in the foundational CBF-QP paper.
Robotics applications can encode constraints such as separation from an obstacle or keeping a sensing trajectory out of a modelled collision region. A 2026 preprint called Splat-CBF reports using a risk-aware barrier constraint with a 3D Gaussian map while treating informative camera motion as a softer objective. That is evidence for the method studied in that system, not proof that every Gaussian map or barrier controller is safe.
The guarantee is conditional
A CBF certificate depends on the stated system dynamics, safe-set definition, state estimate, input limits, and numerical solution. Unmodelled contacts, delayed measurements, or a constraint that admits no feasible input can break the connection between the mathematical condition and the physical robot. A control barrier function is therefore not a general safety claim about a robot. It certifies a particular property only under its explicit assumptions.
Sources
Related terms
Model predictive control
Model predictive control repeatedly optimizes future actions using a system model, applies the next part of the solution, and replans from updated state information. It can account for objectives and constraints over a finite prediction horizon.
Motion planning
Motion planning finds a robot movement from an initial state to a goal while satisfying constraints such as collision avoidance. A planner may produce a geometric path, a timed trajectory, or a sequence of controls.
Trajectory optimization
Trajectory optimization finds a time-varying motion, and often control inputs, that minimizes an objective while satisfying specified constraints. Robot applications can include geometric, kinematic, and dynamic constraints.
Whole-body control
Whole-body control coordinates a robot’s joints and contacts to satisfy several motion and force objectives together. In humanoids, it commonly combines balance, foot motion, hand tasks, and posture subject to physical constraints.