## Problem specification

We'll assume that the following parameters are known:

- is the radius of the wheels
- the distance between the center of the robot and the wheels
- and are the instantaneous angular velocities of respectively the left and right wheels

Our goal is to calculate the pose of the robot according to the upper figure:

- and are the coordinates of the robot
- is the angular orientation of the robot

## Elementary displacement calculation

First, let's calculate the linear velocity of each wheel:

The average velocity of the robot is then given by:

The robot velocity can now be projected along the and axes:

The angular velocity of the robot is given by the difference of the wheels linear velocities:

Previous equation can be reformulated as:

The elementary displacement of the robot is given by the following relation:

## Absolute position

The absolute position can be calculated thanks to the following equations :

\begin{array}{r c l}

x_{i}&=&x_{i-1}+\Delta_x \\

y_{i}&=&y_{i-1}+\Delta_y \\

\Psi_{i}&=&Psi_{i-1}+\Delta_{\Psi}

\end{array}

where

- and are the coordinates of the robot at time step
- is the orientation of the robot at time step