eul2rotm missmatch why?

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?

[xingxingcui]

see this answer comment in details:

why point correspondence to rotation matrix calculation is not my expected?

document is not clear!

Answer 1

[David Goodmanson]

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.

Answer 2

[Roger Rouse]

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