How to find (calculate) transformation matrix in a 6-DOF robot assembly?

Question

Alireza Babaei 2022-9-27

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1813290-how-to-find-calculate-transformation-matrix-in-a-6-dof-robot-assembly

回答： Eljan 2022-12-28

在 MATLAB Online 中打开

Dear all,

Suppose, I have a column vector of location (position) and orientation of a robot:

[x ; y ; z ; Rx ; Ry ; Rz]

the first three rows are the location and the last three pertain to the orientation.

Now, suppose I want rotate the assembly in Rz with -90 degrees.

I was wondering how to calculate such a matrix transformation?

We know the formula for matrix transformation is 4 by 4 (T = [Rot , Transpose(P) ; 0 , 1]). But my location and orientation matrix is 6 by 1.

Any hints?

I see Jacobian matrix is 6 by 6, but not sure if that works as Jacobian matrix for velocities.

theta = -90*(pi/180) % in radians 
TMrow1 = [1,0,0,0,0,0]
TMrow2 = [0,1,0,0,0,0]
TMrow3 = [0,0,1,0,0,0]
 %TMrow4dummy = [1,0,0,cos(theta),-sin(theta),0]
TMrow4 = [0,0,0,cos(theta),-sin(theta),0]
 %TMrow5dummy = [0,1,0,sin(theta),cos(theta),0]
TMrow5 = [0,0,0,sin(theta),cos(theta),0]
 %TMrow6dummy = [0,0,1,0,0,1]
TMrow6 = [0,0,0,0,0,1]
TM = [TMrow1 ; TMrow2 ; TMrow3 ; TMrow4 ; TMrow5 ; TMrow6] % I am not sure if this 
% matrix is the correct transformation matrix???!!!
% TeM is the matrix to be transformed and updated by -90 degrees around Rz
% and the order of elements (location and orientation) is shown in column vector AA:
%AA = [x ; y ; z ; Rx ; Ry ; Rz] 