Worksheet

U8.1 A map of cells

Mapping · University · about 25 min

What this lesson is about

What a map has to do for a robot, why a grid is the usual answer, and what a cell costs.

• What a map is for
• Two families
• Resolution
• Indexing
• The pose is assumed known here

Questions 6 marks in all

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

   CELL = 5.0
   x, y = 102.4, 187.6
   col = int(x / CELL)
   row = int(y / CELL)
   print(col, row)
   print(col * CELL + CELL / 2, row * CELL + CELL / 2)
   

2. [1 mark]What does this program print?

   CELL = 5.0
   grid = [0] * 40
   x = -7.0
   grid[int(x / CELL)] = 1
   print(grid.index(1))
   

3. [1 mark]Why do occupancy grids beat feature maps for planning, despite using far more memory?

   1. AThey represent free space explicitly, and "nothing is there" is what a planner needs most
   2. BThey store each feature with a covariance
   3. CThey need fewer sensor readings to become confident
   4. DThey suit a Kalman filter better

4. [1 mark]A 200 by 200 cm mat is mapped with 1 cm cells, each stored as a 4 byte float. How many bytes does the grid need?

5. [1 mark]Which cell size best follows the page's rule of thumb for a robot that must fit through 20 cm gaps, with a sensor whose noise is about 2 cm?

   1. A5 cm
   2. B1 cm
   3. C20 cm
   4. D40 cm

6. [1 mark]Every mapping task in U8 gives the robot its true pose from the overhead camera. Why?

   1. AMapping with known poses is a tidy, solved problem, whereas building a map while localising against it lets the two errors feed each other
   2. BThe robot's sensors cannot measure distance without the camera
   3. COccupancy grids cannot be built from odometry
   4. DThe camera is more accurate than any map could ever be

The task: which cell did that reading land in?

The robot stands at (100, 50) on the mat facing straight up it. Print cells:, how many cells a 5 cm grid needs for this mat, and hit col: and hit row:, the cell the reading ahead lands in.

from bugbot import *
connect()

CELL = 5.0
W = 40

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

Do it on the robot
www.bugbotlab.com/learn/u8-1-a-map-of-cells/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. Work out how much memory a 1 cm grid of this mat needs if each cell is a 4 byte float.
2. Print the centre of the hit cell in centimetres. How far is it from the point the reading actually gave?
3. At what cell size would a 20 cm doorway be at risk of closing up?