CSE 683: Lab 4
Due Monday, Oct. 18

LAB 4: Implement forward kinematics

updated 10/17

• Write a program to animate a linkage with 3 joints and 5 degrees of freedom. Use DoFs of 3-1-1 at the joints (or at least something this complex).

• Specify poses using Euler angles (not fixed angles) at the joints.

• In the zero position (i.e., pose vector of [0.0, 0.0, 0.0, 0.0, 0.0]) the linkage should be extended, standing straight up. The base of the linkage is has the 3 DoFs with the 2 higher joints each having 1 DoF

• For any 3 DoF joint, use the rotations in the following order: y-axis, z-axis, x-axis. This corresponds to yaw-pitch-roll (or heading-attitude-bank) angles. The other 2 joints should be around the z-axis to match my examples.

• Design the link shape however you want. As a suggestion, make the links 10, 8, and 6 units long, respectively. You can hardcode the poses to interpolate - use the list below (so I can make sure your code as the appropriate functionality).

• Use quaternions to perform the interpolation for the 3 DoF joint:
  • convert key poses to quaternions,
  • perform slerp interpolation,
  • convert back to Euler angles to perform transformation, specifying the rotations in reverse order than what you normally would if they were fixed angles.
  Use this and this for the conversions.

• The poses to use are as follows:

  static floatpose[NUMPOSES][NUMDOFS] = {
             // exercise each 3 DoF joint independently
             0.0, 0.0, 0.0, 0.0, 0.0,               // straight up
             0.0, 0.0, 0.0, -45.0, 45.0,            // kinked arm - so rotations are easier to see
             90.0, 0.0, 0.0, -45.0, 45.0,           // 1st DoF
             0.0, 0.0, 0.0, -45.0, 45.0,            // kinked arm
             0.0, 90.0, 0.0, -45.0, 45.0,           // 2nd DoF
             0.0, 0.0, 0.0, -45.0, 45.0,            // kinked arm
             0.0, 00.0, 90.0, -45.0, 45.0,          // 3rd DoF
             0.0, 0.0, 0.0, -45.0, 45.0,            // kinked arm
  
             // test Euler angle implementation
             45.0, 0.0, 0.0, -45.0, 45.0,            // 1st DoF
             45.0, 90.0, 0.0, -45.0, 45.0,           // 1st + 2nd DoF
             45.0, 0.0, 0.0, -45.0, 45.0,            // 1st DoF
  
             // exercise last two joints independently
             0.0, 0.0, 0.0, 0.0, 0.0,                // straight up
             0.0, 00.0, 0.0, 80.0, 00.0,             // 4th DoF
             0.0, 0.0, 0.0, 0.0, 0.0,                // straight up
             0.0, 00.0, 0.0, 0.0, 80.0,              // 5th DoF
  
             // put in gimbal lock configuration and test quaternion interpolation
             0.0, 0.0, 0.0, 0.0, 0.0,                // straight up
             0.0, 0.0, 0.0, -45.0, 45.0,             // kink arm
             0.0, 90.0, 0.0, -45.0, 45.0,            // 2nd DoF
             -90.0, 0.0, 90.0, -45.0, 45.0,          // 1st + 3rd DoF showing gimbal lock
             0.0, 90.0, 0.0, -45.0, 45.0,            // 2nd DoF
             0.0, 0.0, 0.0, 0.0, 0.0,                // straight up
      };
  

Kink	Euler Test
Joint Test	Gimbal Lock Configuration #1	Gimbal Lock Configuration #2

Extra Credit:

• use ease-in/ease-out interpolation
• use a more complex linkage (like 3-1-3 DoFs)
• show gimbal lock with Euler angles/fixed angles; use quaternions at the 3DoF joint and show the difference
• use quaternions with curvilinear interpolation