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QUIZ 2: Sensors, Sensor Mappings, State Spaces

Due date: 2026-01-24 23:59.
Recommended Resources:

Sensor Characteristics

Question 1

A linear sensor is calibrated using a linear model and least squares.
Which sensor property is directly improved by calibration?
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Question 2

A linear sensor is modeled as:
r=as+b. \\\
What is the sensitivity of this sensor?
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Question 3

TODO:
  • Add assumption that only humidity is the variable that affects the temperature readings, and it is an established fact.
  • Also add references to definitions of reliability, bias and ...
  • Add another question with ground truth for humidity, and calibration results.
A digital thermometer reports temperature in discrete steps of 0.1°C. Because of humidity variations, the thermometer’s readings vary from day to day. The true temperature and the reported value on each day are:
Day 1 (low humidity): true temperature 22.0°C, reported 21.9°C
Day 2 (medium humidity): true temperature 22.5°C, reported 22.1°C
Day 3 (high humidity): true temperature 22.6°C, reported 22.3°C
Day 4 (medium humidity): true temperature 22.0°C, reported 22.0°C
Day 5 (low humidity): true temperature 22.5°C, reported 21.8°C
Which of the following statements are DEFINITELY correct?
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State Spaces

Question 4

A point-sized mobile robot moves in an environment:
E \subset \mathbb{R}^2. \\\
The robot position is given by coordinates (𝑥,𝑦) ∈ 𝐸 and it has no other degrees of freedom.
Let the state space be denoted by 𝑋. Which of the following statements correctly describe the state space 𝑋?
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Question 5

A point-sized mobile robot moves in an environment:
E \subset \mathbb{R}^2. \\\
The robot position is (𝑥,𝑦) ∈ 𝐸 and the robot heading is 𝜃 ∈ 𝑆¹.
Let the state space be denoted by 𝑋. Which of the following statements correctly describe the state space 𝑋?
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Question 6

Consider 10 point-sized mobile robots moving in a planar square environment
E = [-1,1]^2 \subset \mathbb{R}^2. \\\
Each robot has no heading and no additional degrees of freedom. Let the state space of the system be denoted by 𝑋, and the state of the robot 𝑖 is its position:
p_i = (x_i,y_i) \in E, \quad i = 1,\dots,10. \\\
Let the detection region be a fixed set 𝑉 ⊂ 𝐸.
Which of the following statements are TRUE?
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Sensor Mappings

Question 7

Consider a point-sized mobile robot with a heading that moves within a planar square environment:
E = [-1,1]^2 \subset \mathbb{R}^2. \\\
The robot state is (𝑥,𝑦,𝜃), in which (𝑥,𝑦) ∈ 𝐸 and 𝜃 ∈ 𝑆¹. Let the observation space be 𝑌 ⊂ ℝ.
A sensor is modeled as a virtual sensor mapping:
h : X \to Y, \\\
which maps each physical state to a sensor observation.
Which of the following are TRUE statements about a sensor mapping ℎ that measures the distance from the robot’s position to the closest wall?
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Question 8

Consider a point-sized mobile robot with a heading that moves within a planar disc environment:
E = \{(x,y) \in \mathbb{R}^2 \mid x^2 + y^2 \le 1\} \subset \mathbb{R}^2. \\\
The robot state is (𝑥,𝑦,𝜃), where (𝑥,𝑦) ∈ 𝐸 and 𝜃 ∈ 𝑆¹. Let the observation space be 𝑌 ⊂ ℝ.
A sensor is modeled as a virtual sensor mapping:
h : X \to Y. \\\
Which of the following are TRUE statements about a sensor mapping ℎ that measures the distance from the robot’s position to the closest wall of the environment?
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Question 9

Consider a point-sized mobile robot with a heading that moves within a planar square environment:
E = [-1,1]^2 \subset \mathbb{R}^2. \\\
The robot state is (𝑥,𝑦,𝜃), where (𝑥,𝑦) ∈ 𝐸 and 𝜃 ∈ 𝑆¹. Let the observation space be 𝑌 ⊂ ℝ.
A sensor is modeled as a virtual sensor mapping:
h : X \to Y. \\\
Which of the following are TRUE statements about a sensor mapping ℎ that measures the distance to the wall along the robot’s heading?
Varoitus: Et ole kirjautunut sisään. Et voi vastata.

Question 10

Consider a point-sized mobile robot with a heading that moves within a planar circular environment:
E = \{(x,y) \in \mathbb{R}^2 \mid x^2 + y^2 \le 1\}. \\\
The robot state is (𝑥,𝑦,𝜃), where (𝑥,𝑦) ∈ 𝐸 and 𝜃 ∈ 𝑆¹. Let the observation space be 𝑌 ⊂ ℝ.
A sensor is modeled as a virtual sensor mapping:
h : X \to Y. \\\
Which of the following are TRUE statements about a sensor mapping ℎ that measures the distance to the wall along the robot’s heading?
Varoitus: Et ole kirjautunut sisään. Et voi vastata.

Authors

Anna LaValle, Steven M. LaValle
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