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eul2rotm missmatch why?

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Wouter Boessenkool
评论： cui,xingxing 2022-5-11
Hello why do the following don't match:
ax=90;
ay=0;
az=90;
Cx = [1 0 0; 0 cosd(ax) -sind(ax); 0 sind(ax) cosd(ax)];
Cy = [cosd(ay) 0 sind(ay); 0 1 0; -sind(ay) 0 cosd(ay)];
Cz = [cosd(az) -sind(az) 0; sind(az) cosd(az) 0; 0 0 1];
C1 = Cz*Cy*Cx; % 'XYZ'
C2 = eul2rotm(deg2rad([ax ay az]),'XYZ');
C3 = eul2rotm(deg2rad([az ay ax]),'ZYX');
Why is `C1` not the same as `C2`? But `C1` is equal to `C3`...
In the documentation it says for example for 'XYZ':
'XYZ' – The order of rotation angles is x-axis, y-axis, z-axis.
Implying that when 'XYZ' is used you first rotate about X, then Y and finally Z. Same as C1 = Cz*Cy*Cx, right?

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回答（2 个）

David Goodmanson
David Goodmanson 2018-5-9
编辑：David Goodmanson 2018-5-10
Hello Wouter,
I don't have the robotics toolbox, but in the documentation for eul2rotm it says:
"When using the rotation matrix, premultiply it with the coordinates to be rotated (as opposed to postmultiplying)"
That sounds like the coordinates are a row vector in front rather than a column vector afterwards. In that case obviously the order of multiplication of the C's is not reversed.
Roger Rouse
Roger Rouse 2021-10-12
This is the command line help for eul2rotm. It does not mention whether to pre or post mulitpy the matrix. It should be stated in this help somewhere!
>> help eul2rotm
eul2rotm Convert Euler angles to rotation matrix
R = eul2rotm(EUL) converts a set of 3D Euler angles, EUL, into the
corresponding rotation matrix, R. EUL is an N-by-3 matrix of Euler rotation
angles. The output, R, is an 3-by-3-by-N matrix containing N rotation
matrices. Rotation angles are input in radians.
R = eul2rotm(EUL, SEQ) converts 3D Euler angles into a rotation matrix.
The Euler angles are specified by the body-fixed (intrinsic) axis rotation
sequence, SEQ.
The default rotation sequence is 'ZYX', where the order of rotation
angles is Z Axis Rotation, Y Axis Rotation, and X Axis Rotation.
The following rotation sequences, SEQ, are supported: 'ZYX', 'ZYZ', and
'XYZ'.
Example:
% Calculate the rotation matrix for a set of Euler angles
% By default, the ZYX axis order will be used.
angles = [0 pi/2 0];
R = eul2rotm(angles)
% Calculate the rotation matrix based on a ZYZ rotation
Rzyz = eul2rotm(angles, 'ZYZ')
See also rotm2eul

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