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.
Also known as: MPC, model-predictive control, receding-horizon model predictive control
Updated
Replanning turns a predicted trajectory into feedback
The basic loop is to estimate the current state, optimise a future trajectory, execute its first action and repeat. Tedrake's treatment of MPC explains why this is a feedback policy even when the policy has no compact formula: the optimisation is solved again using the current state, rather than blindly replaying an earlier plan.
The optimisation needs a model of robot dynamics, a cost describing the desired behaviour, a planning horizon and any imposed constraints. A humanoid walking formulation might penalise deviation from a desired body velocity while constraining contact forces. That example describes a possible formulation, not a requirement that every MPC controller use the same state or contact model.
MPC is not synonymous with whole-body control
MPC describes how future decisions are planned and refreshed. Whole-body control describes coordination across the robot's joints, tasks and contacts. A system can use MPC on a reduced model and let a separate whole-body controller produce joint commands; another design can optimise a more detailed model directly. The two labels therefore answer different questions.
Similarly, using a model does not require learning that model with a neural network. Linear, nonlinear and learned dynamics can support different MPC formulations. The model and solver determine what can be predicted and computed within the available time.
Constraints in a solver are not a blanket safety guarantee
Tedrake distinguishes a feasible solution now from recursive feasibility: whether a feasible solution will still exist after the horizon shifts. His discussion of terminal conditions and stability shows that these properties require suitable assumptions and design; they do not follow from the name MPC alone. Model error, disturbances and computation deadlines also matter on hardware.
For demonstrations generated by MPC, preserve the state estimate available at each decision, model version, costs, constraints, horizon, replan interval and solver status. Record the action actually sent to the robot separately from the full predicted sequence. A planned future action that was replaced at the next update is not an executed training target, and control latency can make a timely-looking plan stale before execution.
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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
Robot dynamics
Robot dynamics describes the relationship between forces and torques acting on a robot and the motion they produce, accounting for mass, inertia, gravity, velocity-dependent effects and external contact. Forward dynamics predicts acceleration from applied forces; inverse dynamics computes forces or torques for a specified motion.
Hardware & control
State estimation
State estimation is the process of inferring variables that are not known exactly—such as a robot’s base pose, velocity, contact state or sensor bias—from noisy measurements, control inputs and a model of how the system evolves. An estimator should provide both an estimate and, where possible, a representation of its uncertainty.
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.
Hardware & control
Control latency
Control latency is the elapsed time between a relevant event or observation and the physical effect of the resulting robot command. It can include sensor exposure and transport, preprocessing, policy inference, network transfer, controller scheduling, actuator response, and communication back to a human operator. The measured boundary must be stated because each component has a different latency.