Answers

U3.5 A fix from a landmark

Odometry and drift · University · about 30 min

What this lesson is about

Dead reckoning between landmarks, and a reset whenever something known comes into view.

• The oldest idea in navigation
• A fix from a tag
• Replacing and blending
• When not to trust a fix

Questions 6 marks in all

1. [1 mark]Tag 7 is 165 cm up the mat from the start, and the robot, facing it, reads it at 40 cm. What y does the fix give, in cm?

   Answer: 125. fixed = TAG_Y - distance to the tag = 165 - 40 = 125 cm.

2. [1 mark]The estimate is y = 120 and three fixes in a row all say 130. The estimate is blended as in the lesson. What does this print?

   y = 120.0
   for fixed in (130.0, 130.0, 130.0):
       y = 0.8 * y + 0.2 * fixed
       print(round(y, 2))

   Answer:

   122.0
   123.6
   124.88

   Each blend moves y a fifth of the way to the fix: 120 to 122, then 123.6, then 124.88. The gap shrinks by a factor of 0.8 each time instead of vanishing at once.

3. [1 mark]Dead reckoning with a fix every so often. What does a plot of the position error against time look like?

   1. AA sawtooth: growing between fixes and dropping to nearly nothing at each one
   2. BA straight line that grows all run, only more slowly
   3. CA square root curve that levels off without any fixes
   4. DFlat at zero, because each fix removes the error for good
   Answer: A. Between fixes the error grows as before, and each fix throws the accumulated error away. Only information from outside stops it growing without limit.

4. [1 mark]When is replacing the estimate with the fix, rather than blending, the right choice?

   1. AWhen the fix is far better than the estimate
   2. BAlways, because a fix comes from outside the robot
   3. CWhen the fix is noisy, so that its noise is removed at once
   4. DWhen the tag is far away, since a distant tag covers more of the mat
   Answer: A. Replacing throws away the dead reckoning. That is right for a much better fix and wrong for a noisy one, which makes the estimate jump about. The Kalman filter in U6 sets the weight from the uncertainties.

5. [1 mark]Which of these are reasons in the lesson to distrust a fix?

   Tick every answer that is true.

   1. AThe tag is far away
   2. BThe tag is seen at a sharp angle
   3. CIt is a single detection
   4. DThe id does not match the landmark you think it is
   5. EThe same id has been detected on two ticks in a row
   Answer: A, B, C, D. Range error grows roughly with the square of distance, edge-on tags give worse fixes, and one reading can be a mistake. Two detections in a row from the right id is the cheap safeguard, not a warning sign.

6. [1 mark]Watching the printout, each fix makes a bigger jump in the estimate than the last. What does that tell you?

   1. AThe dead reckoning error between fixes is growing, which points to a bias such as an uncalibrated gyro
   2. BThe tag is moving
   3. CThe fixes are getting noisier as the robot gets closer
   4. DThe blend weight is too high
   Answer: A. The jump is the error accumulated since the last fix. If it grows run after run, something one-sided is driving it.

The task: a fix from a tag

from bugbot import *
connect()

set_cv("apriltag")
TAG_Y = 165.0

from bugbot import *
connect()

DT = 0.1
TAG_Y = 165.0          # how far up the mat the tag is, from where the robot starts

set_cv("apriltag")
y = 0.0
forward(75)
for i in range(85):
    y += flow()[1] * DT
    seen = [t for t in apriltags() if t[0] == 7]
    if seen and seen[0][3] < 120:
        y = TAG_Y - seen[0][3]        # a fix: replace the estimate, do not add to it
    wait(DT)
stop()
print("my y:", round(y, 1))
print("truth", position())