EE 570: Programming Laboratory 3

3D Visualization and Inverse Kinematics

Due: W 03/03/2010

Write a program to compute the inverse (position) kinematics and display the resulting manipulator configuration in three dimensions. The program should take as inputs:

1. the D-H Table; and
2. Homogeneous Transformation matrix representing desired end-effector position and orientation.

The program should:

1. display desired end-effector position and orientation as a frame (with ability to turn on/off);
2. compute the values of joint variables, q, that achieve desired end-effector position;
3. display manipulator configurations (via forward kinematics) that reach desired end-effector position and orientation (with ability to turn on/off); and
4. display D-H frames attached to links and end-effector (with ability to turn on/off).

Manipulators for which inverse kinematics and visualization should work:

1. Stanford
2. SCARA
3. PUMA 260
4. Three-Link Planar RRR
5. Two-Link Planar RP
6. Elbow Manipulator with Spherical Wrist (from problem 3-8)

Test your inverse kinematics using the following desired end-effector position and orientation. Note you can check these by viewing the desired end-effector reference frame and that which results from the forward kinematics.

• Stanford: o₆ = [4; 4; 2], R₆ = [0, -1, 0; -1, 0, 0; 0, 0, -1]
• SCARA: o₄ = [500; 500; 250], R₄ = [0, -1, 0; -1, 0, 0; 0, 0, -1]
• PUMA 260: o₆ = [10; 10; 5], R₆ = [0, -1, 0; -1, 0, 0; 0, 0, -1]
• Three-Link Planar RRR: o₃ = [1; 1; 0], R₃ = [0, 1, 0; -1, 0, 0; 0, 0, 1]
• Two-Link Planar RP: o₂ = [0; 1; 0], R₂ = [-1, 0, 0; 0, 0, 1; 0, 1, 0]
• Elbow Manipulator with Spherical Wrist from problem 3-8: o₆ = [-0.75; -0.75; 0.5], R₆ = [-1, 0, 0; 0, 1, 0; 0, 0, -1] where we'll use d₁ = 1m, a₂ = 0.7m, d₄ = 0.7m, d₆ = 0.3

Turn in a clear, concise document that convinces me your calculations are correct. Include nicely drawn diagrams of robots with D-H frames, D-H tables, derivation of equations used for inverse kinematics, summary of equations used for inverse kinematics, resulting joint variables for each test case, forward kinematics for each test case, and a 3D visualization for each case that shows the end-effector is in the correct configuration.