Hardware & control
Control barrier function
CBF
A control barrier function is a scalar function used to describe a safe set of system states and constrain control choices so trajectories remain inside that set. It is commonly enforced through an optimisation problem that modifies a nominal control input only when needed; its guarantee depends on the dynamics model, state estimate, constraints, and assumptions used to define the safe set.
Updated
A function draws the boundary of a safe set
In a common formulation, a scalar function h(x) describes a safe set through the condition h(x) >= 0, where x is the system state. The control problem is to choose inputs that stop the state from crossing that boundary. Ames and colleagues connect this idea to forward invariance: once the system begins inside the specified set, the controller should keep its future trajectory inside it under the formulation's assumptions.
The function does not discover safety by itself. Engineers choose the state, dynamics, constraints, and meaning of the boundary. A distance-based CBF might protect a keep-out region; another could describe speed, balance, actuator, or contact limits.
A CBF-QP changes a nominal command when required
Control barrier constraints are often placed inside a quadratic program. The objective stays close to a nominal command from a planner, policy, or human operator, while the inequalities require the result to remain inside or move towards the safe set. If the proposed command is already feasible, a minimum-intervention formulation can pass it through unchanged.
This differs from model predictive control. MPC explicitly optimises a sequence over a future horizon. A CBF condition can be enforced in a compact one-step optimisation, although predictive controllers can also include barrier constraints.
A mathematical safe set is not a complete robot guarantee
The guarantee covers the set that was actually encoded. Model mismatch, delayed or incorrect state estimates, unmodelled contacts, actuator saturation, numerical tolerances, and an incomplete hazard definition can all break the link between the optimisation and the physical robot.
CSF illustrates a newer semantic use. Safe and unsafe generated motions define affine margins, and a CBF-QP pushes the current motion estimate to the allowed side of those margins. The paper proves properties of that constructed motion-space set. It does not convert a semantic rule into a universal physical-safety guarantee.
For logged robot data, preserve the barrier definition, dynamics and state source, active constraints, nominal and filtered commands, solver result, tolerances, intervention magnitude, and measured outcome. Without those fields, a “CBF applied” label cannot explain what was protected or whether the hardware followed the filtered command.
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Related terms
Hardware & control
Feedback control
Feedback control is a closed-loop control method that measures a system’s current output or state, compares it with a target and adjusts the command using the resulting error. In robotics, feedback can correct joint, end-effector, balance or force errors as new sensor measurements arrive.
Hardware & control
Model predictive control
Model predictive control is a feedback-control method that uses a dynamics model to optimise a sequence of future actions, applies the first action or short part of that sequence, and replans from an updated state estimate. In receding-horizon MPC, the planning window moves forward at each update.
Data & collection
Robot state
Robot state is the set of variables used to describe a robot at a particular time, such as joint positions and velocities, base pose, end-effector pose, gripper state, actuator measurements, or estimated motion. In control theory, a complete state contains enough information to predict future evolution given an action; in robot datasets, “state” often means only the measured or estimated subset that was logged.
Hardware & control
Whole-body control
Whole-body control coordinates a humanoid’s full multibody state, actuated joints and environmental contacts to pursue several motion or force objectives while respecting constraints such as balance, joint limits and friction. It is a family of hierarchical or optimisation-based methods, not one algorithm; implementations may output joint positions, accelerations or torques.
Simulation & transfer
Collision detection
Collision detection determines whether geometric representations of a robot, itself, or its environment intersect or come within a specified distance. Robotics systems use it for self-collision checking, environment collision checking, motion planning, simulation, and safety monitoring, but its result depends on the geometry, poses, margins, and update timing supplied.