Modeling - simulation - design - Control a Robot Arm

After finishing the blog "Control a Dynamixel Motor from Matlab", I'm going to make a project : Robot Arm, My plan is:

1. Modeling a Robot base on Denavit–Hartenberg parameters

2. Solve the kinematic and invert kinematic equation.

3. Simulate the kinematic and kinematic equation

4. Design the model on Solidwork and export the model to simulink model.

5. Trajectory design, test on real robot.

1.Modeling a Robot base on Denavit–Hartenberg parameters

- I'm going to design a 4-DOF robot arm.

- Now we will put the coordinator to each link base on Denavit–Hartenberg method.

- Now we have the D-H table

2. Solve the kinematic and invert kinematic equation.

       2.1 Kinematic equation.

• Transform matrix from coordinates(n) to coordinates(n+1)          

• Transform matrix from coordinates(0) to coordinates (n).

• We will use roll-pitch-yaw angle to illustrate  the orientation of coordinates(n) to the coordinates(0)

.RPY (Φa, Φo, Φn) = Rot (a, Φa). Rot (o,Φo). Rot (n,Φn)

with:

• For clearly we have:

     2.2 Invert kinematic equation.

• Assume that we have a 2 links 2 joints robot

2 links 2 joints robot

• Coordinates of point B:

• The derivative:

=

• From above equation we have the Jacobi matrix:

• Now we can calculate the changing of joints variable from the changing of position 

• the J matrix is not always a square matrix, so we cannot calculate the invert matrix J^-1. So we use Levenberg-Marquardt method to get the invert matrix of non-square matrix.
  
• We have solved the kinematic/invert kinematic equation of the 4-DOF robot. Now let go to code and simulate on Matlab.

3. Simulate the kinematic and kinematic equation

• Simulate the kinematic of  4-DOF robot arm

• Simulate the invert kinematic of 4-DOF robot arm

4. Design the model on Solidwork and export the model to simulink model.

• I'm going to create a 3D model on solidwork and export to Matlab simulink

Design 3D model on Solidwork

• Export to *.xml file and import to matlab

3D model in Matab

5. Trajectory design, test on real robot.

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