Lab 4: Trajectory Following

Grading Sheet

Lead TAs: Soohyun Jang (soohyunj@andrew), Melvin Rayappa (mrayappa@andrew), James Wahawisan(jwahawis@andrew)

Due Date: February 14th, 2012

Part 1:

Challenge Statement:

Using feedback control, make a marker that is attached to your robot follow a trajectory of the form x_ycm, drawing a pretty shape. See Sample Trajectories for examples of shapes. Note that during the demo, the TA will specify one of the shapes from the sample trajectories file for your robot to draw. Be prepared to draw any one of them!

How to:

The following description applies only to a standard differential drive robot.

  1. Start by reusing the code from last lab and attaching a marker to the robot some distance away and to the front or back of the center. Note that the math below will not work if the marker is exactly in the center of your robot. You will see why.
  2. From here, two things can be done :

i) The position of the center of the robot can be computed just like in the previous lab and from that, the position of the marker can be found using geometry. Important equations for this method are :
pos_rel

l_x_yis the position of the marker wrt. the center of the robot in Cartesian coordinates

ii) Equations for the motion of the marker tip can be directly integrated. Important equations for this method are : 
vel_rel
  1. Armed with the knowledge of where the marker is (from the numerical integration), where the marker should be (from the given trajectory) and the relationship between linear velocity of the pen and the linear and angular velocities of the center of the robot, a control law can be made that outputs wheel velocities that brings the robot closer to its desired location.
    Let p_cbe the current position of the marker and p_dthe desired position obtained from the trajectory. Our desired planar velocity is now proportional to p_c- p_d. So, vel_rel2where κ is some positive real number. From the equations of motion for the marker tip given above, we can solve for v_w: 
    v_w_2
    Now wheel velocities (in degrees / second) can be obtained from v_wusing the equations defined in Lab 3 : 
    v_;
    v_r
  2. Now that the desired velocities for the left and right motors are known, we need a way to ensure that the motors spin at that speed. The only variable we can control is motor power which is only weakly related to motor rotational velocity. However, due to the proportional nature of our controller, if we set the motors to a slightly slower speed than desired, the disparity between current and desired position will grow larger and a higher velocity is demanded. So, set the motor velocities to the desired motor velocities (in degrees / second) * 0.1 and wait for a small time interval before proceeding to the beginning of the loop again so that the motors have some time to catch up to the velocity desired of them.

Other tips:

  1. It is essential to have a low PID update interval (2 - 10 ms).
  2. The integration loop must be small (5 - 20 ms) but no smaller than the PID update interval so as to let the motor catch up to the desired velocity.
  3. Save this lab. It will be used in the next lab.
  4. Play around with the proportional constant in order to fine tune the controller. Increasing the constant causes the marker to catch up to the trajectory faster. In the worst case this will cause the marker to overshoot its desired position or request the robot wheels to spin faster than physically possible. Decreasing the constant causes the marker to catch up to the trajectory slower. Lagging behind too far may cause the controller to again, request more power than is physically possible from the motors.
  5. The controller described above is going to lag behind the desired trajectory by some amount. This can be reduced by either fine tuning the constants or looking ahead in the trajectory.

 

Demo:

  1. Place the robot in a position (for the center of the robot) and orientation on a plane specified by a TA (in cm and degrees respectively). This is the start of your trajectory.
  2. Run one of the trajectories from the sample trajectories file. These can be preprogrammed as separate programs or as a minor change to your program, however you will not have a lot of time to select a new trajectory.
  3. Press a button on the robot so that it follows the trajectory specified in the challenge statement where t is the time in seconds after the button press.
  4. After the trajectory is completed, the robot must come to a complete halt. Your time must also be within 5 seconds of the time listed for each trajectory in the sample trajectory file.
  5. Three tries will be given in order to improve your score if needed. All tries are independent of each other. Progressively easier trajectories and initial configurations can be requested, each for a 10 point penalty and only once per try. A request cannot be made on the first try.

 

Evaluation:

1.      Error score (out of 50 points) Mean error = distance from start point to end point of trajectory (aim to get this to zero) :

a.       Mean error <= 5 cm = 50 Points

b.      Mean error > 5 cm = 40 Points

c.       Mean error > 10 cm = 30 Points

d.      Mean error > 15 cm = 20 Points

e.       Mean error > 20 cm ? 10 Points

f.       Mean error > 25 cm ? 0 Points

 

2.      Time score (out of 10):

a.       Robot stops within +- 5 seconds of listed trajectory time = 10 points

 

3.      Trajectory quality (subjective and determined by the TA) - out of 35 points

a.       Trajectory is generally free of extra squiggles (overshoot) = 15 points

b.      Trajectory is generally uniform and true to the picture = 20 points

 

Total: 95 points

 

Part 2:

For part 2, make your robot draw your team number and a creative picture on a piece of 8.5x11 inch paper. You do not have to lift up the pen between the number and the picture; however we still need to be able to recognize your team number. Team 1 must draw the base and angled top on the 1. Team 10 and above do not need to add this on their 1s.

Below is an example team 1 picture that I drew in Paint without lifting up the pen.

Your team does not have to draw the picture on demo day. You can bring in your picture, and we will trust that your robot drew it.

Evaluation:

1.      Number is recognizable: 3 points

2.      Picture is creative: 2 points

 

Bonus:

The class will get pizza if all of the team’s pictures can link together to form an awesome robot mural.

 

Lab Demo Sign up:


Last Updated : 2/13/12 by SooHyun Jang
(c) 1999-2012: Howie Choset, Carnegie Mellon University