Denavit Hartenberg parameters - 3DOF articulated manipulator

Question

I am trying to solve a forward kynematics problem for a 3DOF manipulator.

I am working with the Robotics Toolbox for MatLab created by Peter Corke and after calculte the DH parameters and introduce them into MatLab to compute the fordward kynematics the plotted robot is not what it should be.

I guess I made some mistakes calculating the DH parameters.

Attached is the file where you can see what are the DH frames calculated for each joint and the DH parameters for each frame.

Anyone could give me a clue whether this is the correct answer?

Here is the image with the frames calculated by me.

And here the robot I get from Matlab (using the Robotics Toolbox by P.Corke)

Answer 1

I defined the robot using your (assumed standard) DH parameters:

>> robot = SerialLink([pi/2 1 0 pi/2; pi/2 1 0 -pi/2; pi/2 1 1 0])
robot = 
noname:: 3 axis, RRR, stdDH, fastRNE                             
+---+-----------+-----------+-----------+-----------+-----------+
| j |     theta |         d |         a |     alpha |    offset |
+---+-----------+-----------+-----------+-----------+-----------+
|  1|         q1|          1|          0|     1.5708|          0|
|  2|         q2|          1|          0|    -1.5708|          0|
|  3|         q3|          1|          1|          0|          0|
+---+-----------+-----------+-----------+-----------+-----------+

Note that for revolute joints the value of theta is ignored, not it is replaced with the values q1 to q3 in the printed table above.

To plot the robot at this configuration:

>> robot.plot([pi/2 pi/2 pi/2])

shows a robot somewhat different to your diagram. I think your DH parameters are not correct.

I really don't like DH parameters. Looking at your diagram I can write the forward kinematics as a string of simple transformations expressed in the world coordinate frame

>> DHFactor('Rz(q1)Tz(L0)Rz(q2)Ty(L1)Tx(L2)Ry(q3)Tx(L3)')
  .
  .
  .
DH(q1, 0, 0, 0).DH(q2, L0, L2, -90).DH(q3, L1, L3, 90)

where the parameters of the DH() functions are theta, d, a, alpha.

Answer 2

Try these:

Theta = [pi/2, -pi/2, -pi/2];
D     = [L0,    L2,    L1  ];
A     = [0,     0,     L3  ];
Alfa  = [pi/2, -pi/2,  0   ];

with

 T = [cos(theta) -sin(theta)*cos(alpha) sin(theta)*sin(alpha) a*cos(theta); 
      sin(theta) cos(theta)*cos(alpha) -cos(theta)*sin(alpha) a*sin(theta);
      0          sin(alpha)             cos(alpha)            d;
      0          0                      0                     1];

i added the matrix to make sure the differences do not come from the differences in the DH and modified DH paramters.