Edit: Description of Conventional Euler Angles
First, we need to define two Cartesian frames with their origins located at the centre of mass of the quadrotor. The body frame is fixed to the vehicle, with its $x$-axis parallel to the plane of the rotors pointing "forward", its $y$-axis is parallel to the plane of the rotors and perpendicular to the $x$-axis pointing to the right, and its $z$-axis perpendicular to the $xy$-plane pointing down. The origin of the local-level local north (LLLN) frame translates with the body frame, but always remain level with its $N$-axis pointing north, its $E$-axis pointing east, and its $D$-axis pointing down. The orientation of the quadrotor relative to the Earth is then described by the orientation of the body frame relative to the LLLN frame. Euler angles are a set of three rotations taken about a single axis at a time in a specified order to generate the orientation of the body frame relative to the LLLN frame. The so-called "conventional" Euler angles used in the aerospace industry are yaw ($\psi$), pitch ($\theta$), and roll ($\phi$) obtained from a particular sequence of rotations.
With the body frame initially aligned with the LLLN frame so that the $x,y,z$ axes are aligned with the $N,E,D$ axes and $\psi=\theta=\phi=0$, or stated differently, that the plane of the rotors is horizontal and the quadrotor's nose is pointing north, perform the following three rotations:
- First, the body frame is rotated through the yaw angle in a positive sense around its $z$-axis.
- Then the displaced body frame is rotated through the pitch angle in a positive sense around the displaced $y$-axis.
- Finally, the displaced body frame is rotated through the roll angle in a positive sense around the displaced $x$-axis to obtain its final arbitrary orientation relative to the LLLN frame.
(Use a little model to visualize these three rotations.)
Note that these three rotations are not commutative (angle are not vectors) so that a different sequence of rotations will result in a different final orientation.