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Worksheet

U3.6 An error budget

Odometry and drift · University · about 25 min

BugBotLab
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What this lesson is about

Predicting how far out you will be before you drive, which is what covariance is for.

Questions 6 marks in all

  1. [1 mark]This adds up the lesson's error budget for a 2 m run with a calibrated gyro, then again with the noise term removed. What does it print?

    import math
pieces = {"heading": 0.4, "scale": 6.0, "noise": 0.7, "slip": 2.0}
total = math.sqrt(sum(v * v for v in pieces.values()))
print("total:", round(total, 1), "cm")
print("without noise:", round(math.sqrt(total ** 2 - 0.7 ** 2), 1), "cm")

  2. [1 mark]Two independent errors of 3 cm each. What is the total, in cm to one decimal place?

  3. [1 mark]An uncalibrated gyro bias of 0.19 deg/s acts for 10 s while the robot drives 200 cm at a steady speed, so the heading error grows steadily from 0 to 1.9 degrees. Using d × e with the average heading error, how far to the side does it end up, to the nearest cm?

  4. [1 mark]Flow noise contributes 0.7 cm over a run of 100 steps. Following the random walk, what does it contribute over 400 steps, in cm?

  5. [1 mark]With the gyro calibrated, the budget reads heading 0.4 cm, scale 6 cm, noise 0.7 cm and slip 2 cm. What should be worked on next?

    1. AThe flow scale error
    2. BThe noise, by averaging more readings
    3. CThe slip
    4. DThe gyro bias again

  6. [1 mark]For that calibrated budget after a long straight run, what shape is the region the robot is likely to end up in?

    1. AAn ellipse, longest along the direction of travel, because the scale error dominates
    2. BA circle, because the errors are added in quadrature
    3. CAn ellipse, longest across the direction of travel, because heading error dominates
    4. DA line along the direction of travel, because heading error is zero after calibration

The task: an error budget

Print what you expect the dead reckoning error to be over your run, as predicted error:, before you drive. Then drive at least 90 cm and print actual error:, the real gap between odometry() and position().

from bugbot import *
import math
connect()

DISTANCE = 100.0

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

QR code
Do it on the robot
www.bugbotlab.com/learn/u3-6-an-error-budget/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

  1. Run the same thing at set_noise(3) and see which line of the budget you should have tripled.
  2. Budget a run with four corners in it. What changes?
  3. Repeat the run ten times and compare the spread of the actual errors with your predicted number.