ACS6121 - Unit 05 (Sensing and Estimation)

Question 1

What is the main goal of probabilistic robotics?

Answer 1

To model and manage uncertainty in sensing, motion, and decision-making using probabilistic methods.

Question 2

What is a belief 𝑏𝑒𝑙(𝑥_𝑡) in the context of Bayes filtering?

Answer 2

The probability distribution over the robot’s state at time 𝑡 given all measurements and controls up to that point.

Question 3

What does Bayes’ rule compute?

Answer 3

The posterior probability of a state given a measurement.

Question 4

What is the Kalman Filter best suited for?

Answer 4

Linear systems with Gaussian noise; it estimates the mean and covariance of the state distribution.

Question 5

How does the Extended Kalman Filter differ from the standard Kalman Filter?

Answer 5

It linearizes nonlinear models using Jacobians before applying Kalman filtering.

Question 6

What are the two main components of a motion model?

Answer 6

The control input and a noise model describing uncertainty in actuation.

Question 7

What is the key idea behind Particle Filters?

Answer 7

Represent the belief distribution using many samples (particles), and use resampling to focus on likely states.

Question 8

What problem does Monte Carlo Localisation solve?

Answer 8

It estimates a robot’s pose in a known map using particle filtering, even with noisy sensors and uncertain motions.

Question 9

What is occupancy grid mapping?

Answer 9

A method to represent an environment as a grid where each cell has a probability of being occupied.

Question 10

What is the main challenge in SLAM?

Answer 10

Estimating both the robot’s trajectory and the map of the environment simultaneously.

Question 11

1. Multiple Choice:
   Which method is best for nonlinear, non-Gaussian localisation problems?
   A) Kalman Filter
   B) Extended Kalman Filter
   C) Particle Filter
   D) Histogram Filter

Answer 11

→ Correct Answer: C) Particle Filter

Question 12

2. True/False:
   In the Kalman Filter, the state must be represented using particles.

Answer 12

→ False

Question 13

3. Fill in the Blank:
   The _______ model describes how the robot’s state changes due to movement commands.

Answer 13

→ Motion

Question 14

4. Short Answer:
   What does the measurement model
   𝑝(𝑧_𝑡∣𝑥_𝑡) represent?

Answer 14

→ The probability of receiving measurement 𝑧_𝑡 given the robot is in state 𝑥_𝑡.

Question 15

5. Multiple Choice:
   Which of the following is a primary reason to use probabilistic estimation in robotics?
   A) Speed
   B) Precision control
   C) Handling uncertainty
   D) Simpler math

Answer 15

→ Correct Answer: C) Handling uncertainty

Question 16

6. True/False:
   In SLAM, knowledge of one landmark can help improve the estimate of another.

Answer 16

→ True

Question 17

7. Short Answer:
   Why is the EKF suitable for SLAM applications?

Answer 17

→ It can estimate correlated uncertainties in both robot and landmark positions in nonlinear settings.