CSE 683: Lab 5
Due Wednesday, Oct. 27

LAB 5: Implement inverse kinematics

• Modify the control for the linkage from Lab #4 (i.e., 3-joint; 5-DoF; 3-1-1 DoF/joint) to implement one of the IK approaches covered in class - either the Jacobian Transpose or Cyclic Coordinate Descent is suggested.

• Procedurally generate a new randomly positioned goal every time the end effector gets within some epsilon of the goal. Move the end effector from one goal to the next.

• Here is a pseudo-code snippet to keep track of joint positions and orientations in global coordinates:

    set_identity_matrix();
  
    set_material("redPlasticMaterial");
    for (i=0; i<NUMDOFS; i++) {  
      record_transformed_joint(i); 
      glRotatef(angle[i],axis[i][0],axis[i][1],axis[i][2]);
      append_rotation(angle[i],axis[i][0],axis[i][1],axis[i][2]); 
      if (linkLen[i] != 0.0) {
        append_translation(0.0,linkLen[i],0.0);
        draw_linkage(linkLen[i]);
        glTranslatef(0.0,linkLen[i],0.0);
      }
    }
    record_endEffector();
    glPopMatrix();
  

  The append routines (rotation and translation) form the corresponding matrix and post multiplies the transformation matrix.

  The routine that records the transformed joint gets the position and axis of rotation in global coordinates. It extracts the position from the 4th column of the transformation matrix and computes the axis of rotation by multiplying the rotation axis by the transformation matrix.

• After forming the Jacobian and taking the transpose, mutlipling by the desired motion vector, V, will produce a vector of delta-thetas. If the maximum value of the delta-thetas is above some threshold, then scale the vector down to get the largest delta-theta equal to the threshold. If the maximum is already smaller than the threshold, then leave it alone.

• Display updates to the armature to show the intermediate positions as they are computed. However, you don't need to display every update - it's ok to display every nth armature update where n is chosen so the armature makes fast enough progress toward the goal with out looking like it's skipping intermediate positions.

Extra Credit:

• implement one of the IK methods requiring a linear-solver
  • basic pseudo-inverse of the Jacobian
  • above with control term
  • above with damped least squares term
  • using alternative Jacobian
• compare CCD method to using the transpose of the Jacobian
• modify the outside-in ordering of joints in the CCD method and compare results
• implement joint limits with the CCD method and analyze results
• use the curvilinear code from lab2 to trace out frame-by-frame goals for the end-effector
• show gimbal lock at the 3DoF joint when interpolating Euler angles.