# Coordinate Systems

There are several different coordinate systems used in the documentation and code. This page illustrates the
configuration of each, and

## The Body Frame

The body frame is centered at the center of mass of the quadcopter.

* X points 'forward'
* Y points 'right'
* Z points 'up'

See the diagram below for an illustration

<img src="_static/coordinate_system_diagram.png" alt="drawing" width="500"/>

[Diagram reference](https://link.springer.com/article/10.1007/s42452-019-0698-7)

## Euler Angles

The commonly used euler angles Roll, Pitch and Yaw describe the orientation of the body frame with respect to the
horizon plane. That is, the plane incident to the drone's center of mass and perpendicular to gravity. These are:

* Roll: The angle (in radians) of the Body Frame's X axis WRT the horizon plane
* Pitch: The angle (in radians) of the Body Frame's Y axis WRT the horizon plane
* Yaw: The angle (in radians) of the Body Frame's Z axis WRT it's starting position. This measurement isn't well
defined, as the 2D horizon plane does not have 'zero' orientation for the Z axis

## The IMU Frame

The IMU frame is simply the frame that the IMU is mounted to. It is important that the rotation matrix config parameter
`R_imu_body` is set properly so that the control loop can calculate coordinate system transformations correctly

## The Navigation Frame

The navigation frame is simply the body frame at time==0. As the drone moves around in 3D space, it's position can be
tracked by it's (X,Y,Z) position in the navigation frame