# 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 May 25, 2017 at 8:39
• Yes, you can. However, take into account that rotation matrix R changes, as Wikipedia explains May 25, 2017 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.

Yes, it has an effect on the controller if you are going to take advantage of the simple model and small angles assumption. What matter most is that the yaw should go first in the order. because the yaw angle unlike the other two is not going to be held close to zero. Imagine we are at a pitch angle of 10deg and then a 180deg of yaw is commanded, if a rotation order of YZX (for example) is defined, things become upside down and a 10deg of pitch would be in the wrong direction making the quad title toward the wrong direction if not going unstable. I was suffering from inability to control the quad in simulation every time I set the yaw to far from zero angle until I figured out I was setting the wrong rotation order.