wyh rotation matrix convert to eular angle is not same with original eular?

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xingxingcui
xingxingcui 2022-5-10
编辑： Sam Chak 2022-10-29
Ran in:
At the beginning,i use eul2rotm function to convert eular degree to rotation matrix,then use rotm2eul function convert to back ,but it not same as before,why it occur like this result,i don't it understand. Thanks in advance！
eular1 = [pi/2,pi,-pi/2] % ZYX default order
eular1 = 1×3
1.5708 3.1416 -1.5708
r = eul2rotm(eular1,'ZYX');
eular2 = rotm2eul(r,'ZYX')
eular2 = 1×3
-1.5708 0.0000 1.5708
eular2 is not same eular1?

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Matt J
Matt J 2022-5-10
编辑：Matt J 2022-5-10
Ran in:
It is the same, because eul2rotm is not a 1-1 function.
eular1 = [pi/2,pi,-pi/2]; % ZYX default order
r = eul2rotm(eular1,'ZYX')
r = 3×3
-0.0000 -0.0000 -1.0000 -1.0000 -0.0000 0.0000 -0.0000 1.0000 -0.0000
eular2 = rotm2eul(r,'ZYX');
r2=eul2rotm(eular2,'ZYX')
r2 = 3×3
-0.0000 -0.0000 -1.0000 -1.0000 -0.0000 0.0000 -0.0000 1.0000 -0.0000
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Gokul
Gokul 2022-10-28
@Sam Chak Thank you for the explanation. It helps understand it better.
With this in mind, is there a way to minimize the two representations (eular1 and eular2) to come to a common minimum rotation?
Sam Chak
Sam Chak 2022-10-29
编辑：Sam Chak 2022-10-29
You must apply the torque to rotate from one orientation to another. To achieve the minimum rotation, this implies that you need to apply the minimum torque.
You can derive a formula to compute the optimal torque needed, through the rigorous mathematics route.
Or you can take the AI/ML route to automatically find just the right torque, with a click of a button without knowing the math of the system and the torque actuator. You need to define the Cost/Objective Function though.

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