Answers

3.1 What a controller is

Control · Robot club · about 15 min

What this lesson is about

The error and its sign, wrapping headings, bang-bang control, overshoot.

• The error
• The simplest controller: bang-bang
• Overshoot
• Fixing it the crude way

Questions 7 marks in all

1. [1 mark]What does this program print?

   def wrapped(h):
       return (h + 180) % 360 - 180
   
   print(wrapped(200))
   print(wrapped(350))

   Answer:

   -160
   -10

   Headings wrap round. 200 degrees is the same as 160 the other way, and 350 is the same as 10 to the left, so they become -160 and -10.

2. [1 mark]A controller uses error = target - measured. The target heading is 90 and the robot faces 60. What is the error? Give a whole number.

   Answer: 30. 90 minus 60 is 30. It is positive, so the robot is short of the target and should turn clockwise.

3. [1 mark]What is bang-bang control?

   1. ALooking at the sign of the error and going that way at a fixed speed
   2. BPushing harder the bigger the error is
   3. CDriving into a wall and backing off
   4. DTurning on and off at random
   Answer: A. It is how a thermostat works: fully on one way or the other, with nothing in between.

4. [1 mark]The bang-bang loop calls stop() when the error is under 2 degrees, but the robot ends further off. Why?

   1. AThe robot keeps turning for a moment after stop()
   2. BThe heading sensor is wrong
   3. Cwrapped() gives the wrong answer
   4. Dabs() removes the sign
   Answer: A. It coasts in rotation just as it does driving forward. The faster the spin, the bigger the overshoot.

5. [1 mark]What does this program print?

   for error in [30, -10]:
       speed = 60 if abs(error) > 25 else 20
       print(error, speed)

   Answer:

   30 60
   -10 20

   abs() ignores the sign. 30 is more than 25 so it gets 60, while -10 is only 10 away so it gets the slow speed of 20.

6. [1 mark]What does break do inside while True:?

   1. ALeaves the loop
   2. BStops the robot's motors
   3. CPauses the loop for a moment
   4. DStarts the loop again from the top
   Answer: A. while True would repeat for ever. break is how you get out once the error is small enough.

7. [1 mark]What is the problem with the crude fix: fast when far, then short slow bursts with a pause?

   1. AIt works, but it is slow at the end
   2. BIt never gets within 2 degrees
   3. CIt spins the wrong way
   4. DIt only works for heading 0
   Answer: A. Stopping and settling between bursts takes time. Proportional control, in lesson 3.2, does better.

The task: face north

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

print("heading:", heading())

from bugbot import *
connect()
def wrapped(h):
    return (h + 180) % 360 - 180
while True:
    error = wrapped(heading())
    print('error:', round(error, 1))
    if abs(error) <= 2:
        break
    speed = 60 if abs(error) > 25 else 20      # fast when far, careful when close
    if error > 0:
        turn_left(speed)
    else:
        turn_right(speed)
    wait(0.1)
    if abs(error) <= 25:
        stop()
        wait(0.3)     # let it settle before looking again