Decomposing a Transformation Matrix

Hi!

I have been trying to look for a function that will "undo" a transformation matrix.

I saw in Matlab that there's a function "makehgtform" to create a transformation matrix. Now, I'm looking for something that is the exact opposite of this.

Example:

M = makehgtform('xrotate',30*pi/180);

It would result to a 4x4 matrix. But I want to actually extract the X, Y, Z translation and X,Y,Z rotation.

Can anyone help me or just give me an idea? I would really appreciate it! :(

Thanks in advance!

Answer 1

[Matt J]

Here's an example that makes use of the attached file for rotation matrix decomposition.

>> M = makehgtform('translate',[1,2,3],'xrotate',30*pi/180)

M =

    1.0000         0         0    1.0000
         0    0.8660   -0.5000    2.0000
         0    0.5000    0.8660    3.0000
         0         0         0    1.0000

>> translation=M(1:3,end)

translation =

     1
     2
     3

>> rotation=rot2taitbryan(M(1:3,1:3),'xyz'), %see attached file

rotation =

   30.0000         0         0

[Kash Costello]

Hi omg you are a life saver! Yes, I know that the translation is the last column and the rotation matrix is the first 3x3 but I didn't think of actually... processing them separately. -facepalm- Anyway, I saw the matlab function! Is it possible to NOT use the function you created? Like, just use any built-in commands in matlab?

I tried to use this:

M = makehgtform('translate',[1,2,3],'xrotate',30*pi/180);

M2 = M(1:3,1:3);

translation = M(1:3,end);

eul = rotm2eul(M2,'ZYX');

eul1 = eul.*(180/pi);

eul2 = fliplr(eul1);

It gave me --> 30.0000,0,0 just like what I want. But when I tried to put

'yrotate',30*pi/180

It's giving me --> 33.6901,25.6589,33.6901

Do you have any idea what happened on this one? Thanks a lot!!

[Matt J]

You can extract the lines of code from rot2taitbryan.m that are relevant to you, if you wish. I do not know what conventions rotm2eul uses and cannot play around with it, since I do not have the Robotics System Toolbox.

[Kash Costello]

Okay, that's fine. Thanks so so so much! I really appreciate your help and the code you shared. It helped me a lot!!

[Kash Costello]

Oh uh by the way... if it's not too much to ask, could you explain (perhaps with an example?) why you wrote the function that way? I'm watching videos but I'm still kind of confused. If it's not okay, I totally understand. Thanks again! Have a good day!

[Matt J]

It's not mine. I downloaded it from somewhere.

[Kash Costello]

Oh. Okay, but do you at least know why the sequence is like this?

case 'XYZ'

ang(1) = atan2d(-R(2,3),R(3,3));

ang(2) = asind(R(1,3));

ang(3) = atan2d(-R(1,2),R(1,1));

I understand why it's R(2,3), R(3,3) and such. But I am confused why it's -R(2,3) first and why not R(3,3).

[Bruno Luong]

Oh. Okay, but do you at least know why the sequence is like this?

See this document section 2.1

[Kash Costello]

Ok I'm being an idiot but I'm still confused even after reading that document. I guess I don't fully grasp what atan2 is and still, it didn't explain why the sequence is like that. My question still remains... :(

[Matt J]

I guess I don't fully grasp what atan2 is

Even after googling? https://en.wikipedia.org/wiki/Atan2

Answer 2

[Bruno Luong]

Translation vector is T(1:3,4);

Rotation matrix is T(1:3,1:3).

If you want to decompose in rotation on axis, there are many conventions (intrinsic, extrinsic, Euler's angle, Tait–Bryan angles, etc...) see https://en.wikipedia.org/wiki/Euler_angles and pick your choice.