Motion Model

A motion model is a mathematical description of how a robot’s inputs (like wheel speeds or motor commands) translate into changes in its state (position and orientation) over time.

Given coordinate frames:

• Reference frame; $\{s\}$ with axes $(X_S,Y_S)$
• Moving frame; $\{r\}$ with axes $(X_R,Y_R)$

Main variables

Velocity variables (for a point in the body):

• $v$ – translational/linear velocity
• $\omega$ – rotation/angular velocity

Position variables:

• $x$ – horizontal position
• $y$ – vertical position
• $\theta$ – rotation angle

Different types of robot model describe relations between these variables.