Why do matlab and python convert Euler angles to quaternions with different results?

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cui,xingxing
cui,xingxing 2022-5-25
评论： cui,xingxing 2023-3-3
Ran in:
I converted the following Euler angles/radians into quaternions using matlab's built-in function eul2quat, the external order is: first around the x-axis, then around the y-axis, and finally around the z-axis.
eulars = [-1.78E-15 -0.09548759 -3.141592;
-1.78E-15 -0.09548759 -3.141592;
0 -0.1113647 -3.136936;
-0.000419181 -0.1113141 -3.132684;
-0.000802144 -0.1113117 -3.128802;
-0.001152084 -0.1113079 -3.12526;
-0.001180313 -0.1101197 -3.122032;
-0.001413606 -0.1086281 -3.119092;
-0.001928661 -0.1062565 -3.116415];
matlab_q = eul2quat(eulars,"ZYX")% first x, then y,final z
matlab_q = 9×4
0.0000 -0.9989 -0.0000 -0.0477 0.0000 -0.9989 -0.0000 -0.0477 0.0023 -0.9984 -0.0001 -0.0557 0.0044 -0.9984 -0.0000 -0.0556 0.0064 -0.9984 0.0000 -0.0556 0.0081 -0.9984 0.0001 -0.0556 0.0097 -0.9984 0.0001 -0.0550 0.0112 -0.9985 0.0001 -0.0543 0.0125 -0.9985 0.0003 -0.0531
Then I also used python to convert the above data to quaternions as follows：
from scipy.spatial.transform import Rotation as R
import numpy as np
myeulars = np.array([[-1.78E-15, -0.09548759, -3.141592],
[-1.784486e-15, -0.09548759, -3.141592],
[0, -0.1113647 , -3.136936],
[-0.000419181 , -0.1113141, -3.132684],
[-0.000802144, -0.1113117, -3.128802],
[-0.001152084 , -0.1113079, -3.12526],
[-0.001180313 , -0.1101197, -3.122032],
[-0.001413606 , -0.1086281, -3.119092],
[-0.001928661 , -0.1062565, -3.116415]])
python_q = R.from_euler('xyz', myeulars, degrees=False).as_quat() # first x, then y,final z
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print(python_q)
[[-4.77256586e-02 -1.55965008e-08 -9.98860482e-01 3.26422508e-07]
[-4.77256586e-02 -1.55965008e-08 -9.98860482e-01 3.26422508e-07]
[-5.56534295e-02 -1.29579605e-04 -9.98447432e-01 2.32471611e-03]
[-5.56286986e-02 -3.85220084e-05 -9.98441671e-01 4.43575562e-03]
[-5.56285404e-02 4.46916188e-05 -9.98431257e-01 6.36307029e-03]
[-5.56280572e-02 1.20882279e-04 -9.98418522e-01 8.12154965e-03]
[-5.50351559e-02 5.10113472e-05 -9.98436979e-01 9.73287224e-03]
[-5.42918402e-02 9.49786087e-05 -9.98462346e-01 1.11951287e-02]
[-5.31111500e-02 2.94403626e-04 -9.98510080e-01 1.25195214e-02]]
The above data result is left-right symmetric, according to the documentation, matlab uses quaternions of the form w+x*i+y*j+z*k output; while python uses quaternions of the form x*i+y*j+z*k+w.
It can be inferred that the matlab calculation result (a,b,c,d) should correspond to the python order (w,x,y,z), why the above result corresponds to the python is (w,z,y,x)?
b = quaternion(eulars,'euler','XYZ','point') % However, this result is consistent with Python
9×1 quaternion array
3.2642e-07 - 0.047726i - 1.5597e-08j - 0.99886k
3.2642e-07 - 0.047726i - 1.5597e-08j - 0.99886k
0.0023247 - 0.055653i - 0.00012958j - 0.99845k
0.0044358 - 0.055629i - 3.8522e-05j - 0.99844k
0.0063631 - 0.055629i + 4.4692e-05j - 0.99843k
0.0081215 - 0.055628i + 0.00012088j - 0.99842k
0.0097329 - 0.055035i + 5.1011e-05j - 0.99844k
0.011195 - 0.054292i + 9.4979e-05j - 0.99846k
0.01252 - 0.053111i + 0.0002944j - 0.99851k

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采纳的回答

Brian Fanous
Brian Fanous 2023-3-2
@cui I believe you saw my post on other thread already. But in case someone else comes along this question, the way the MATLAB quaternion class handles euler angle conversions is detailed here:

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