Answers

U1.3 Truth and belief

The robot as a system · University · about 25 min

What this lesson is about

position() is the lab's overhead camera. odometry() is what the robot has, and it drifts.

• Watch belief come apart from truth
• Why dead reckoning drifts
• Turning the noise off

Questions 6 marks in all

1. [1 mark]Why is using position() as the input to a controller treated as cheating?

   1. AIt is the lab's overhead measurement of the robot, which a real robot does not have once it leaves the room
   2. BIt is less accurate than odometry()
   3. CIt reports the position in the body frame, not the world frame
   4. DIt updates too slowly to be used inside a control loop
   Answer: A. position() and heading() are the equivalent of motion capture: there to mark your work. The robot itself only carries flow() and imu().

2. [1 mark]A gyro reads 0.4 degrees per second too high. Integrated for 90 seconds, how many degrees of heading error does that bias alone produce?

   Answer: 36. Bias adds up linearly: 0.4 × 90 = 36 degrees, in the same direction every run.

3. [1 mark]How do the two kinds of sensor error grow when dead reckoning integrates them?

   1. AZero-mean noise grows with the square root of time; bias grows linearly with time
   2. BNoise grows linearly with time; bias grows with the square root of time
   3. CBoth grow linearly with time
   4. DNoise averages away completely; only bias grows
   Answer: A. Noise is a random walk, so its errors partly cancel and grow as the square root of time. A bias never cancels, so it marches on linearly, and linear soon overtakes square root.

4. [1 mark]Driving a square, the heading error gets a little bigger at every corner. Why does that matter more than a position error of the same size?

   1. AA heading error rotates every step taken after it, so a small error at a corner becomes a large position error down the next straight
   2. BThe gyro bias only acts while the robot is turning
   3. CThe flow sensor is noisier while turning than while driving straight
   4. Dodometry() restarts its count at each corner
   Answer: A. Heading error is the expensive one in dead reckoning. The gyro bias acts all the time; it is the travel after the corner that turns heading error into distance.

5. [1 mark]Driving the same square with set_noise(0), odometry() and position() agree exactly, yet the robot still has not come back to where it started. What does that show?

   1. Aset_noise() changes the sensors, not the drive: the drive still curves, and the robot now measures the curve exactly
   2. Bset_noise(0) also turns off the drive's coupling, so the square is perfect
   3. Codometry() stops working when the noise is off
   4. DThe gyro bias is still switched on
   Answer: A. With perfect sensors, every centimetre of dead reckoning error disappears: the error in the normal run came from the sensors. The drive is still the same imperfect drive, which is why a controller still has work to do.

6. [1 mark]At the end of a run, odometry() gives (12.0, 118.5) and position() gives (15.0, 114.5). What does this print?

   import math
   ox, oy = 12.0, 118.5
   tx, ty = 15.0, 114.5
   print("error:", round(math.hypot(ox - tx, oy - ty), 1))

   Answer:

   error: 5.0

   The gaps are 3 cm in x and 4 cm in y, and the distance is the square root of 3² + 4², which is 5.0 cm.

The task: how far out is it?

from bugbot import *
connect()

forward(70, distance=50)

from bugbot import *
connect()

for leg in range(3):
    forward(70, distance=50)
    turn_right(40, angle=90)
stop()
ox, oy, oh = odometry()
tx, ty = position()
gap = ((ox - tx) ** 2 + (oy - ty) ** 2) ** 0.5
print("odometry", ox, oy, "truth", tx, ty)
print("error:", round(gap, 1))