1. Euler angle
is the attitude angle yaw, pitch, roll
2. Euler angle method
The orientation relationship of one Cartesian coordinate system relative to another Cartesian coordinate system can be described by three successive rotations. Each rotation revolves around The coordinate axis is orthogonal to the front and rear rotation axes. Euler angles are a classic method used to describe the relative attitude between two coordinate systems, especially for describing the motion of the carrier coordinate system relative to the local navigation coordinate system. 3.
Attitude Matrix
uses Euler angles to represent the attitude matrix
4. Attitude angle differential equation
5. Disadvantages:
When the pitch angle is ± 90 ◦ , there are singular values in the Euler angle transformation, and the roll angle and heading angle cannot be distinguished at this time. Therefore, the Euler angle method cannot be used in full-attitude navigation applications.
6. Python implementation of Euler angle conversion attitude matrix
from scipy.spatial.transform import Rotation as R
r=R.from_euler('zyx',[0.7854,0.1,0]) #Euler angle->Rotation matrix
m4=r.as_matrix() #Attitude matrix=m3.dot (m2).dot(m1)
print(m4) #Output rotation matrix
7. Know the direction cosine matrix and find the Euler angle