# Euler Angles Order For Quadrotor Modelling

I am modelling a quadrotor and I need to choose an order for the rotations that transfer vectors which are represented in Earth Frame to the Body Frame.

• what is the most logical order for these rotations?
• which order is likely used?
• does the order have a big effect on the control of the quadrotor?

I don't understand what you mean by order. I have always seen the quadrotor modelled like this, for instance.

For your question of how to represent the body-frame vectors into inertial frames, no quadrotor knowledge is necessary. Just Applied Mechanics, where the rotation matrix R showed in previous link is necessary.

It has no influence on the control, as the control is usually modelled with body-frame angles of the quadrotor.

• what i mean by the order that we can choose more than one way to represent the rotation from the Earth-Frame to the Body-Frame like it is possible to do the rotation around z first then about y then x or we can choose to do the rotation around x first so i am asking if there is an order that makes sense more or easier to understand – Ghadeer Elmkaiel May 25 '17 at 8:39
• Yes, you can. However, take into account that rotation matrix R changes, as Wikipedia explains – galtor May 25 '17 at 13:18

For a flying vehicle an intuitive representation of orientation is roll-pitch-yaw angles aka Tait-Bryan angles.

For a quadrotor it is common to assume a left-handed world coordinate frame with the z-axis down and the x-axis to the north (a so called NED frame). Attach a similar frame to the vehicle (the body frame) with its z-axis down and its x-axis in forward direction (choose one rotor to be the front). Now the rotation matrix from world frame to body frame is the result of a sequence of canonical rotation matrices, multiplied in this order:

1. Yaw rotation about the z-axis, which describes the vehicle's heading direction.
2. Pitch rotation about the y-axis, which describes the "angle" of attack. A positive rotation causes the nose to pitch down which is commonly considered a negative pitch angle (nose is pitched down). Since a quad rotor is under-actuated, it is pitch motion that is used to generate forward thrust for forward flight.
3. Roll rotation about the x-axis.