Worksheet

U12.7 Capstone: the whole robot

Learning, and the capstone · University · about 90 min

What this lesson is about

Calibrate, estimate, localise, plan, follow, arrive, and report. One run, everything in it.

• What it takes
• The structure
• The fix
• What a good submission looks like
• How it would be assessed
• Where to go next

Questions 6 marks in all

1. [1 mark]Tag 21 is at (100, 195) and tag 22 at (40, 195). The robot measures r1 = 46.1 cm to tag 21 and r2 = 67.3 cm to tag 22. What does this print?

   import math
   x1, x2, wall = 100.0, 40.0, 195.0
   r1, r2 = 46.1, 67.3
   x = (x1 ** 2 - x2 ** 2 - r1 ** 2 + r2 ** 2) / (2 * (x1 - x2))
   y = wall - math.sqrt(r1 ** 2 - (x - x1) ** 2)
   print(round(x, 1), round(y, 1))

2. [1 mark]In the two tag fix, why take the negative square root for y?

   1. AThe robot is below the wall the tags are on, so it is at 195 minus the distance, not plus
   2. BSquare roots in Python are negative by default
   3. CHeading 0 points down the mat
   4. DThe tags face away from the robot

3. [1 mark]After calibration a gyro bias of 0.2 degrees per second is left uncorrected. How many degrees of heading error does that build up over 30 s of driving?

4. [1 mark]A tag fix puts the robot 40 cm from where its estimate says it is. What should the program do?

   1. ATreat it as a probable misread and gate it out, and print the disagreement
   2. BJump the estimate to the fix, since the tags are ground truth
   3. CAverage the fix and the estimate equally
   4. DStop the run, because the estimator has failed

5. [1 mark]Only one of the two tags is in view for a frame. How should that frame be used for the fix?

   1. AAs no fix at all
   2. BAs half a fix, weighted by 0.5
   3. CBy assuming the missing range equals the one seen
   4. DBy using the last range of the missing tag

6. [1 mark]Which belong in a submission that would earn a good mark?

   Tick every answer that is true.

   1. AAn estimator that runs every tick, not dead reckoning with a jump at the end
   2. BA stated frame, with every reported number in it
   3. CThe run repeated a few times with the spread reported
   4. DThe final estimate with how far out you believe it is
   5. EThe single best run, with the others left out

The task: the capstone

Reach the green target through the gap, without touching anything, and print gyro bias:, my x: and my y: from your own estimate. Plot x and y as you go. No position().

from bugbot import *
import math
connect()

DT = 0.1
V_MAX, V_LAT = 20.0, 15.0
START = (30.0, 25.0)
TAGS = {21: (100.0, 195.0), 22: (40.0, 195.0)}

Plan your program here, then type it in and press Run.

Do it on the robot
www.bugbotlab.com/learn/u12-7-capstone/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. Add a gate on the fix: reject one that disagrees with the estimate by more than three times your uncertainty, and count the rejections.
2. Run it ten times and report the mean and worst final error. Which stage contributes most of it?
3. Remove the tag fix and see how far dead reckoning alone gets. Then work out what heading accuracy would have been needed to make up the difference.