Must a motion model include physical forces?

No. Kinematic models can describe movement using positions, velocities and geometric constraints without explicitly modeling forces.

Can motion models be learned from data?

Yes, but learned models still require validation, uncertainty assessment and attention to the conditions represented in training.

Why use a motion model when sensors are available?

It predicts between observations and helps combine noisy or incomplete measurements within a coherent state estimate.

AI Glossary / Statistics and probability / Intermediate

Motion model

Definition

A motion model describes how the state of a moving object or robot changes over time, often in response to control inputs. It may predict position alone or a state containing position, velocity, orientation and other quantities. A deterministic motion model gives a specified next state, while a probabilistic model describes uncertainty in that transition. Motion models support tracking, localization, navigation and planning. They describe expected movement under assumptions; they do not directly establish where an object actually is without accounting for observations and uncertainty.

What it means

A system needs a way to connect its present estimate with a future state. A simple model might assume constant velocity during a short interval. A more detailed model may include acceleration, turning constraints, wheel geometry or forces. The appropriate detail depends on the task, time scale and available information. A robot's command is not necessarily its realized motion because of slip, disturbances or imperfect control. A probabilistic model can represent those differences, but its usefulness depends on whether the uncertainty description reflects the actual operating conditions.

How it works

Choose a state representation, coordinate frame and time interval. Define a transition function using the previous state and any relevant controls. Include process noise or a transition distribution when movement is uncertain. Propagate the state estimate through this model, and propagate uncertainty using an appropriate estimation method. A sensor or observation model then relates the state to measurements, allowing a filter to update the prediction. Validate motion predictions against observed trajectories, including turns, stops and unusual conditions. Refine the model or uncertainty assumptions when systematic errors appear.

Three practical examples

Mobile robotics: predict a platform's new pose from commanded velocities or wheel-motion information.
Object tracking: forecast a moving object's next position so new detections can be associated with a track.
Simulation: evaluate candidate movements under stated dynamic constraints before execution. The model used for planning may differ from the model used for estimation, but their assumptions should be compatible with the actual system.

Think of it this way

Think of estimating where a cyclist will be a few seconds after you last saw them. Their current speed and direction offer a useful prediction, but they might brake or turn. A motion model formalizes that prediction and, when probabilistic, represents how uncertain it is. A new observation can correct the estimate rather than requiring the original prediction to have been exact.

Worked example

Consider one-dimensional constant-velocity motion over three seconds. The estimated initial position is 10 meters and velocity is 2 meters per second, so predicted position is 10 + 2 times 3 = 16 meters. Suppose initial position variance is 1 square meter, velocity variance is 0.25 square meters per second squared, their covariance is zero, and independent added displacement noise has variance 0.36 square meter. Predicted position variance is 1 + 3 squared times 0.25 + 0.36 = 3.61 square meters, giving standard deviation 1.9 meters. This original calculation uses a specified linear uncertainty model. If the object instead accelerates at 1 meter per second squared throughout the interval, its deterministic position from the same initial conditions is 10 + 6 + 4.5 = 20.5 meters. The mismatch shows why a constant-velocity approximation must be assessed over its intended time horizon.

Illustrative case study

In a fictional case, Ash Robotics tests a warehouse cart's localization system. A simple motion model predicts adequately on straight, dry aisles but accumulates errors during sharp turns on a slippery section. Engineers compare predicted motion with independent position measurements and identify conditions where uncertainty is understated. They revise the relevant movement model and evaluate the combined prediction-and-measurement update. The team does not treat a larger uncertainty allowance as a substitute for understanding persistent systematic errors.

Common misconceptions and mistakes

A motion model is not the same as a sensor model: one describes state changes, while the other describes measurements given a state. A control command is not guaranteed realized movement. Constant velocity is an approximation, not a claim that real objects never accelerate. Process noise and measurement noise represent different uncertainties and should not be confused. Independent-error assumptions can be wrong, especially when state components are correlated. A precise prediction from a poor model can be less useful than a well-calibrated uncertain prediction.

Business use

Businesses deploying tracking or robotic systems should evaluate motion models under representative operating conditions and time intervals. Record units, reference frames and timing conventions, since mismatches can create large errors despite correct equations. Measure prediction error and uncertainty calibration, not only final navigation outcomes. Examine transitions between operating modes such as stopping, turning and accelerating. Coordinate model changes with estimation and control components. The practical objective is a reliable representation of movement that supports the system's decisions without requiring unnecessary complexity or concealing known limitations.

Check your understanding

In a tracking system, does the equation predicting the next position from the current velocity describe the sensor or motion model?

Answer: The motion model. A separate observation model describes how a sensor measurement relates to the state.

Related terms

Kinematics
Kalman filter
Localization
Odometry
State transition
dynamics
process noise
observation model
trajectory prediction

Learn next

Review state-space representations and uncertainty propagation, then compare constant-position, constant-velocity and accelerating models on the same trajectory. Examine how sensor updates correct motion predictions.

State space

Sources

Dellaert and Hutchinson, Introduction to Robotics and Perception, Moving in 2D: https://www.roboticsbook.org/S42_logistics_actions.html Dellaert and Hutchinson, Motion Model for the Differential Drive Robot: https://www.roboticsbook.org/S52_diffdrive_actions.html

Previous: Motion-JPEG Next: Motion planning