Learn · Intermediate

Model predictive control: planning ahead, taking one step, then planning again

Model predictive control chooses actions by predicting several possible futures, executing only the first step of a selected plan, and planning again after a new observation. It matters because the world rarely follows a forecast exactly. Repeated replanning lets a controller combine anticipation with feedback, while explicitly accounting for limits such as speed, force or available resources.

A plan that is deliberately temporary

Consider a robot moving a cup around obstacles. It predicts what would happen under several sequences of motions over the next few seconds. It scores those sequences for reaching the destination, avoiding collisions and respecting motor limits. It selects a sequence, performs its first motion, observes where the cup actually moved and solves the planning problem again. The previous forecast informs the decision without becoming a promise to follow every step regardless of new evidence.

The same idea appears when a driver looks ahead while steering. The driver anticipates the bend, makes a small adjustment and then uses the updated view to correct the next one. A purely reactive rule has little foresight; a plan executed without feedback can persist after its assumptions become wrong. Model predictive control combines a finite look ahead with frequent correction. Its alternative name, receding-horizon control, describes the moving boundary of that forecast.

The four ingredients

First, the controller needs a model of change: given the current state and an action, what state is likely next? That model can be a physical equation or a learned predictor. It is related to the idea of a world model, but learning a model does not by itself specify how to choose actions. A controller supplies the decision procedure that uses the prediction.

Second, it needs a state estimate. A camera image may not directly reveal velocity, contact or hidden obstacles. The estimate summarizes what the controller currently believes about the system. Errors here can spoil an otherwise sensible plan. Today's Reflex paper, which separates visual estimation from humanoid control, illustrates why this boundary matters. Reflex is related context, not evidence that its authors implemented model predictive control.

Third, the controller needs an objective. In the cup example, it might penalize distance from the target, jerky motion and effort. A typical formulation adds predicted costs over a fixed horizon and may include a final-state cost. This formalizes a preference; it does not guarantee that the preference captures every consequence people care about. An objective that ignores spilling can recommend a fast motion that reaches the right coordinates with the wrong result.

Fourth, it needs constraints. These can bound joint positions, motor forces or acceptable clearances. They restrict the candidate plans before an action is selected. David Mayne, James Rawlings, Christopher Rao and Pierre Scokaert's foundational review, Constrained model predictive control: stability and optimality00214-9), explains why constraint handling and assumptions about stability are central to the method. Writing a limit into an optimizer is useful, but remains conditional on the model and state estimate being accurate enough.

Planning is not training

The controller solves a decision problem during operation. Its dynamics model can remain fixed while the plan changes at every step. That differs from reinforcement learning, where a policy is improved through training data and a reward signal. The methods can be combined: reinforcement learning can learn a model or useful controller components, while predictive control uses them to make a fresh decision.

Danijar Hafner and colleagues' Dream to Control is important related reading about learning behaviors through a latent world model. It helps explain why learning predictive structure is useful, but its imagination-trained policy should not be equated with repeatedly solving a constrained predictive-control problem at deployment. A learned predictor, a trained policy and an online optimizer are distinct objects even when they appear in the same system.

Why the horizon and clock matter

A short horizon may fail to see that an apparently easy move leads into a dead end. A long horizon sees more consequences, but increases computation and compounds prediction errors. The best horizon depends on the task and the model. Longer is not automatically better. The controller must also finish planning before its action deadline; a perfect solution returned after the robot has passed the interception point is unusable.

This is especially clear in catching a moving object. Observations arrive, the object keeps moving and the body has limits. Better perception cannot compensate for unlimited planning delay. Conversely, rapid replanning cannot rescue a systematically wrong estimate of the object's motion. The useful question is whether the complete loop predicts, decides and reacts at the required rate.

Model predictive control offers a disciplined pattern for acting under change: forecast, choose, take one step, observe and repeat. Its strongest claims require stated assumptions about prediction error, feasibility and stability. Replanning improves responsiveness; it does not make an uncertain model infallible or turn written constraints into unconditional safety guarantees.

Ground Truth. (2026, October 13). Model predictive control: planning ahead, taking one step, then planning again. Ground Truth. https://groundtruth.day/learn/model-predictive-control.html

@misc{groundtruth:model-predictive-control,
  title  = {Model predictive control: planning ahead, taking one step, then planning again},
  author = {{Ground Truth}},
  year   = {2026},
  month  = {oct},
  url    = {https://groundtruth.day/learn/model-predictive-control.html}
}

Topics: control · planning · robotics · world-models · fundamentals