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Worksheet

U10.4 Pure pursuit

Following a trajectory · University · about 35 min

BugBotLab
NameClassDate

What this lesson is about

Chase a point a fixed distance ahead on the path, and choose the one number that decides everything.

Questions 8 marks in all

  1. [1 mark]A car chases a look-ahead point 18 cm ahead that is 3 cm to the side in the body frame. What radius of arc does pure pursuit command, in cm?

  2. [1 mark]What does a longer look-ahead distance cost?

    1. ACorners are cut, and on a tight bend the robot can take the chord straight across the inside
    2. BThe robot weaves down straight lines
    3. CThe controller needs a higher gain to stay on the path
    4. DThe look-ahead point can move backwards along the path

  3. [1 mark]The BugBot follows a circle of radius 40 cm with pure pursuit, pointing its velocity at a look-ahead point L = 18 cm further along. By roughly how much does it track inside the circle, in cm to 1 decimal place?

  4. [1 mark]A robot that steers like a car, turning to face the look-ahead point and driving forwards, weaves down a straight line with a period of about 2 s. What is the fix?

    1. ARaise the look-ahead distance
    2. BRaise the gain
    3. CLower the look-ahead distance
    4. DLower the cruise speed to zero on straights

  5. [1 mark]At L = 3 and 14 cm/s a follower that steers like a car weaves up to 4.1 cm either side of the tape, but the task's follower, which points its velocity at the look-ahead point, stays within 0.5 cm. Why?

    1. APointing the velocity moves the robot sideways directly, so there is no heading to swing past the line while the lag catches up
    2. BThe task's follower has no drive lag
    3. CPointing the velocity uses a longer effective look-ahead
    4. DThe car-like follower drives faster on the straights

  6. [1 mark]Why is projecting onto the path and adding L better than intersecting a circle of radius L with the path?

    1. AIt is defined even when the robot is more than L from the path, and it cannot send the robot backwards
    2. BIt gives a shorter look-ahead distance on corners
    3. CThe circle intersection needs the path to be curved
    4. DIt avoids having to compute arc length

  7. [1 mark]The lesson's path is built from a straight, a quarter circle as 8 chords, and a straight. What does this print?

    import math
arc = [(80 + 40 * math.cos(math.radians(180 - k * 11.25)),
        120 + 40 * math.sin(math.radians(180 - k * 11.25))) for k in range(9)]
PATH = [(40.0, 40.0)] + arc + [(150.0, 160.0)]
cum = [0.0]
for (ax, ay), (bx, by) in zip(PATH, PATH[1:]):
    cum.append(cum[-1] + math.hypot(bx - ax, by - ay))
print(round(cum[-1], 1), round(80 + 20 * math.pi + 70, 1))

  8. [1 mark]Why is the look-ahead usually made to grow with speed, L = L0 + k v?

    1. AWhat the controller needs is a roughly constant preview time, and the lag costs a fixed number of seconds
    2. BA faster robot is further from the path, so it needs a longer reach
    3. CIt keeps the curvature command constant at all speeds
    4. DIt stops the look-ahead point running off the end of the path

The task: chase the look-ahead point

The tape runs straight from (40, 40) to (40, 120), round a quarter circle of radius 40 centred on (80, 120), then straight to (150, 160). Follow it with pure pursuit, plot off path and speed, print path: (the length of the path) and drove: (how far the robot actually travelled), and stop at the far end.

from bugbot import *
import math
connect()

DT = 0.1
START = (40.0, 40.0)
CRUISE, LOOK = 11.0, 18.0

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

QR code
Do it on the robot
www.bugbotlab.com/learn/u10-4-pure-pursuit/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

  1. Run it at LOOK = 6 and at LOOK = 45. Which one cuts the corner, and by how much? Does the short one weave at all?
  2. Steer it like a car instead: drive forwards only, and turn at v * 2 * sin(alpha) / L radians a second, where alpha is the angle of the look-ahead point from the way the robot faces. Run L = 3 at 14 cm/s and watch the first straight, then try L = 5.
  3. Make the look-ahead grow with speed and see whether you can keep both the straights and the corner.
  4. Measure the largest off path value in the corner and compare it with L * L / (2 * 40).