Answers

6.2 Following a line

Seeing more · Robot club · about 20 min

What this lesson is about

cx to rotation, the angle as a look-ahead, speed on the straights.

• One step
• The whole line
• Using the angle
• Speed on the straights

Questions 7 marks in all

1. [1 mark]follow_step uses rotation (cx - 160) * 0.4. What rotation does a line at cx = 100 give?

   Answer: -24. 100 minus 160 is -60, and -60 times 0.4 is -24.

2. [1 mark]The rotation for a line at cx = 100 is negative. What does the robot do?

   1. ATurns anticlockwise, towards the line on its left
   2. BTurns clockwise, away from the line
   3. CSlides left without turning
   4. DStops, because the error is negative
   Answer: A. Negative rotation is anticlockwise, and the line is on the left, so the robot turns towards it.

3. [1 mark]A student writes drive(60, 0, (160 - cx) * 0.4). What happens?

   1. AThe robot steers away from the line and loses it
   2. BIt follows the line more smoothly
   3. CIt follows the line backwards
   4. DNothing changes, the order does not matter
   Answer: A. Swapping the subtraction flips the sign, so every correction pushes the line further off-centre.

4. [1 mark]What does this program print?

   def rotation(cx, angle):
       return (cx - 160) * 0.3 + angle * 1.5
   
   print(rotation(160, 10))
   print(rotation(200, -8))

   Answer:

   15.0
   0.0

   The first line is centred but bending right, so the angle term starts the turn early. In the second, the two terms cancel out.

5. [1 mark]Adding angle * 1.5 to the rotation is the beginning of which kind of control?

   1. ADerivative: it reacts to where the error is heading
   2. BBang-bang: full on or full off
   3. CIntegral: it adds up past errors
   4. DOpen loop: it ignores the sensor
   Answer: A. cx says where the line is, angle says where it is going, so the robot starts turning before it drifts off-centre.

6. [1 mark]At each bend the line swings well off-centre, up to 85 pixels, before the robot has turned. What does that mean?

   1. ANothing is wrong: a P controller only turns once there is an error, and the line is still in view
   2. BThe camera is badly aligned
   3. CThe gain is negative
   4. DThe robot has lost the line
   Answer: A. To turn at all, a proportional controller needs some error, so it always lags a bend a little. That is fine as long as the line stays in view.

7. [1 mark]What does this program print?

   for angle in [0, 5, 20, -25]:
       speed = 80 if abs(angle) < 10 else 40
       print(angle, speed)

   Answer:

   0 80
   5 80
   20 40
   -25 40

   A small angle means a straight, so go fast. abs makes a bend to the left count the same as one to the right.

The task: follow the line

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

# drive forward at 60 for 90 cm, then stop
forward(60, distance=90)

from bugbot import *
connect()
def follow_step(speed=60, gain=0.4):
    # one tick of line following: steer from where the line crosses the picture
    seen = line()
    if not seen:
        return False
    cx, angle = seen
    error = cx - 160                       # pixels left (-) or right (+) of centre
    drive(speed, 0, error * gain)
    return True
set_cv('line')
while position()[1] < 85:
    if not follow_step(60, 0.4):
        forward(30)
    wait(0.1)
stop()