Lab Partner Names: ________________________________________________

15-494/694 Cognitive Robotics: Lab 4

Note: You can do the in-lab portion (parts I through V) with a partner if you wish. The homework (parts VI through VIII) must be done individually.

I. Software Update and Initial Setup

  1. At the beginning of every lab you should update your copy of the cozmo-tools package. Do this: 
    $ cd ~/cozmo-tools
$ git pull
  2. For this lab you will need a robot, a charger, a Kindle, and some light cubes.
  3. Log in to the workstation.
  4. Make a lab4 directory.
  5. Place the robot on the desktop facing sideways (away from the edge).
  6. Hide the cubes behind the robot so he can't see them.
  7. Connect the Kindle to the robot and start simple_cli.
  8. Make sure the robot is in radio contact with the cubes even though he can't see them. Type "cube1" in simple_cli and it should show up. Make sure the robot is talking to your cubes and not someone else's.
  9. Type "show viewer" in simple_cli so you can see what the robot sees. He should not be seeing any cubes!

II. Examining Cozmo's Built-In Localization

  1. Hide the charger so the robot can't see it even if it turns. (There should be no cubes in view either.)

  2. What is cube1's initial pose? What about cube2 and cube3?

    ________________________________________

  3. Type cube1.pose.is_valid. What do you get?

    ________________________________________

  4. Write down the x/y/z poses and origin_id's:

    Robot: ________________________          Cube 1: ________________________

  5. Place cube1 (the "paperclip") in front of the robot so he can see it.

  6. What are cube1's x,y,z coordinates and origin_id now?

    ________________________________________

  7. Use your hand to block the robot's eyes and shift the cube slightly. Keep your hand there so the robot can't see it.

  8. What are cube1's x,y,z coordinates and origin_id now? Is the cube visible?

    ________________________________________

  9. Take your hand away.

  10. What are cube1's x,y,z coordinates and origin_id now? Is the cube visible?

    ________________________________________

  11. Quickly pick up the robot by grabbing and lifting him so that his camera points toward the ceiling. Wave him around a little.

  12. Put the robot down facing away from you, so that cube1 is about 6-7 inches off his right side and he can't see it. What are the robot's and cube's poses and origin_id now?

    Robot: ________________________          Cube 1: ________________________

  13. In simple_cli do Turn(-90).now() so that the robot is now facing the cube and can see it. What are the robot's and cube's poses and origin_id now?

    Robot: ________________________          Cube 1: ________________________

  14. Pick up the robot and wave him around again, then put him back facing away from you, like before. What are the robot's and cube's poses and origin_id now?

    Robot: ________________________          Cube 1: ________________________

  15. Now pick up the cube, wave it around a bit, and put it six inches behind the robot, not off its right side. What are the robot's and cube's poses and origin_id now?

    Robot: ________________________          Cube 1: ________________________

  16. Do Turn(-90).now(). The cube should be off the robot's right side and still out of sight. What are the robot's and cube's poses and origin_id now?

    Robot: ________________________          Cube 1: ________________________

  17. Do Turn(-90).now() again. The robot should now see the cube. What are the robot's and cube's poses and origin_id now?

    Robot: ________________________          Cube 1: ________________________

  18. Pick up the robot, wave him around, and put him back down in a position where he can see the cube. What are the robot's and cube's poses and origin_id now?

    Robot: ________________________          Cube 1: ________________________

  19. What you should have observed in this experiment is that sometimes the robot gets a new origin_id when picked up, and sometimes he doesn't. Furthermore, when the robot turns to bring a cube into view, sometimes that changes the cube's origin_id, but other times it changes the robot's origin_id. Explain the logic behind this:

III. Kinematics Engine: Joint Frames

For this and subsequent parts of this lab you may find it helpful to review the kinematics lecture slides. Remember the organization of the 4x4 transformation matrix using homogeneous coordinates:

  1. In simple_cli, type robot.kine.joints to see the joints.

  2. Type show kine to see the robot's kinematic tree. This is just a nicely formatted version of robot.kine.joints.

  3. With the robot off the charger, zero the lift using SetLiftHeight(0).now()

  4. Examine the source code in ~/cozmo-tools//cozmo_fsm/cozmo_kin.py. This file creates the kinematic description of the robot using the Denavit-Hartenberg conventions discussed in lecture. Study how the shoulder joint relates to the base frame, and the lift_attach joint relates to the shoulder joint.

  5. Type show kine shoulder to see the shoulder joint, which controls the lift. Also look at show kine lift_attach.

  6. Examine the results of the following expressions. Pay particular attention to the fourth column of each matrix.
    sj = robot.kine.joint_to_base('shoulder')
    tprint(sj)

    laj = robot.kine.joint_to_base('lift_attach')
    tprint(laj)
  7. What is the value of sj[0,3] - laj[0,3]? ____________ Why isn't it 66? _______________________________

  8. By experimentation, find the lift height that gives a shoulder joint angle close to 0 degrees. Note that you will not be able to use SetLiftHeight to make tiny changes in the lift height; such requests are ignored. So to change the lift height from 0.1 to 0.15 you should first do SetLiftHeight(0.6).now() and then SetLiftHeight(0.15).now().

  9. What lift height did you settle on? _______________

  10. Recompute sj and laj. Why did one change and one remain the same? (Hint: remember that the joint reference frame does not rotate with that joint.)

  11. Recompute the difference sj[0,3] - laj[0,3] with the shoulder angle now roughly 0 degrees. What value do you get?

    _____________

  12. Raise the lift by doing SetLiftHeight(1).now(). Then recompute sj and laj.

  13. Let's make a point pt_base that is 50 mm in front of the base frame by typing:
    pt_base = transform.point(50,0,0)
    Note that pt_base is in homogeneous coordinates.

  14. Find the coordinates of pt_base relative to the lift_attach frame by writing:
    pt_lift_attach = \
       robot.kine.base_to_joint('lift_attach').dot(pt_base)
    tprint(pt_lift_attach)
    What value did you get? ____________________________

IV. Kinematics Engine: Link Frames

A joint's reference frame does not rotate as the joint angle changes. The angle is actually measured relative to that reference frame. But the link reference frame does rotate with the joint.
  1. Set the lift height to 0.6. Then compare the following:
    tprint(robot.kine.joint_to_base('shoulder'))

    tprint(robot.kine.link_to_base('shoulder'))
    Why are the translation values (last column) the same?

  2. Now compare the following:
    tprint(robot.kine.base_to_joint('shoulder'))

    tprint(robot.kine.base_to_link('shoulder'))
    Why are the translation values (last column) different?

  3. The joint_to_base and base_to_joint transformation matrices are inverses of each other, as are the link_to_base and base_to_link matrices. What result does the following produce?
    ltb = robot.kine.link_to_base('shoulder')
    btl = robot.kine.base_to_link('shoulder')
    tprint(ltb.dot(btl))
    tprint(btl.dot(ltb)
    ________________________

  4. We can use np.linalg.inv() to invert a matrix. What result does the following produce?
    tprint(ltb - np.linalg.inv(btl))
    ________________________

V. Defining New Reference Frames

  1. Consider the kinematic tree between the base frame and the camera frame. The base frame coordinate system has z pointing up and x pointing forward. What is the camera frame coordinate system? _______________________________________________

  2. A single DH transformation matrix is sufficient to convert any reference frame orientation to any other orientation, but it cannot always reposition the origin of the new reference frame at the same time, since this would require six degrees of freedom but there are only four DH parameters.

  3. What trick did we have to use to get the camera reference frame set up so that both its orign and orientation are correct?

    ________________________________

This is the end of the in-lab portion. Please hand in your completed worksheet before leaving.

Homework

Note: The homework problems (parts VI through VIII) must be done individually.

VI. Extending the Kinematic Description

Make your own copy of cozmo_kin.py and modify it by adding the following reference frames:
  • left_front_wheel and right_front_wheel: the z axis for each wheel should point to the right. The x axis should point forward.

  • left_hook and right_hook: these are the hooks on the lift. The z axis should point up and the x axis should point forward. You may need to use a trick like we did for the camera frame.

VII. Kinematics Calculations

Suppose we have an object that is 100 mm in front of the camera's focal plane, and we want to know how far forward of the front axle it lies. If the head is tilted up, the object will not be as far forward of the axle as if the head is pointing straight horizontal. Write a function to calculate the answer using transformation matrices.

Then write a program to move the head through a range of head angles (-10, 0, +10, +20, +30, and +40 degrees) and print the answer for each head angle. Write down your results and include them with your hand-in.

VIII. Inverse Kinematics: Pointing the Camera

This is a simple IK problem. Given an object of height h at position (x,y) in base frame coordinates, write code to point the camera directly at the top of the object. First you should turn to the correct heading. Assume this can be done without error. Then you must set the head angle so that the center of the camera (the z axis in the camera reference frame) points directly at the top of the object. Note that the camera reference frame and head joint reference frame are different: the camera rotates around the head joint origin, not the center of the camera image. So you must be careful with your coordinate transformation. Write a program to point the camera accurately.

Take an object of known height, place it at a known position relative to the robot, and run your program. Try different distances and heights. How accurately is the top of the object centered in the camera image?

Hand In

Collect all your homework code and results in a zip file.

Hand in your work through AutoLab by next Friday.

Back to the Cognitive Robotics main page

Dave Touretzky
Last modified: Fri Feb 17 04:18:59 EST 2017