UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
FINAL EXAM, April 28, 2025
Fourth Year - Engineering Science
ROB521 - Mobile Robotics and Perception
Calculator Type: 1 (all calculators)
Exam Type: D (2-sided aid sheet permitted)
Examiner - T D. Barfoot
Name:
Student Number:
You have 2.5 hours to answer all of the below questions in the booklets provided. Marks for each
question are shown in the left margin in parentheses, totalling (100). Fill out your name on this cover
page and each booklet used.
Student Marks Max Possible
Question 1 : Multiple Choice 20
Question 2: Kinematics, Planning, and Control 20
Question 3: Transformation Matrices 20
Question 4: Localization 20
Question 5: Batch Estimation 20
Total Marks 100
Page 1 of 6 pages
, Name:
1. Multiple Choice
For each, indicate the most appropriate response (2 marks each).
(a) Which of the following robots operated on the surface of Mars?
(i) Marsokhod, (ii) Lunokhod, (Hi) Sojourner, (iv) Shakey
(b) The first commercial field robot was called
(i) Mowbot, (ii) Roomba, (Hi) Autoplow, (iv) Packbot
(c) In occupancy grid mapping, which of the following is not assumed?
(i) each real cell is occupied or free, (ii) our sensor can directly measure the probability of
a cell being occupied, (Hi) the occupancy probabilities of cells are statistically independent,
(iv) the noises affecting measurements are statistically independent
(d) The Kinect camera uses which of the following ranging principles?
(i) time of flight, (ii) frequency-modulated continuous wave, (Hi) triangulation, (iv) echo
localization
(e) The augmented state in the EKF-SLAM algorithm refers to the concatenation of
(i) translation and rotation of the robot, (ii) robot poses and landmark positions, (iii) mean
and covariance, (iv) position and velocity
(f) In batch SLAM the resulting linear system we solve at each iteration has a left-hand-side
whose sparsity pattern is referred to as
(i) hollow, (ii) block-diagonal, (iii) arrowhead, (iv) chordal
(g) The cost-to-come value function represents
( i) the lowest possible cost to arrive at the current state from the start, ( ii) the lowest possible
cost to get from the current state to the goal, ( Hi) the lowest cost to getfrom the current state
to any neighbouring state, (iv) the heuristic cost to get to the current state from the start
(h) Dijkstra’s algorithm is a special case of which of the following algorithms?
(i) RRT*, (ii) A*, (iii) Field-D*, (iv) Dubin’s algorithm
(i) If T32, Ti2 G SEflf) then the expression for T13 is
(i) t12 + T32, (ii) T32T^, (iii) T12TJ2, (iv) t12t32*
(j) If a covariance matrix is diagonal this means that
(i) the variables are orthogonal to one another, (ii) the distribution is unbiased, (iii) the
variables are uncorrelated with one another, (iv) the distribution is Gaussian
Page 2 of 6 pages
FACULTY OF APPLIED SCIENCE AND ENGINEERING
FINAL EXAM, April 28, 2025
Fourth Year - Engineering Science
ROB521 - Mobile Robotics and Perception
Calculator Type: 1 (all calculators)
Exam Type: D (2-sided aid sheet permitted)
Examiner - T D. Barfoot
Name:
Student Number:
You have 2.5 hours to answer all of the below questions in the booklets provided. Marks for each
question are shown in the left margin in parentheses, totalling (100). Fill out your name on this cover
page and each booklet used.
Student Marks Max Possible
Question 1 : Multiple Choice 20
Question 2: Kinematics, Planning, and Control 20
Question 3: Transformation Matrices 20
Question 4: Localization 20
Question 5: Batch Estimation 20
Total Marks 100
Page 1 of 6 pages
, Name:
1. Multiple Choice
For each, indicate the most appropriate response (2 marks each).
(a) Which of the following robots operated on the surface of Mars?
(i) Marsokhod, (ii) Lunokhod, (Hi) Sojourner, (iv) Shakey
(b) The first commercial field robot was called
(i) Mowbot, (ii) Roomba, (Hi) Autoplow, (iv) Packbot
(c) In occupancy grid mapping, which of the following is not assumed?
(i) each real cell is occupied or free, (ii) our sensor can directly measure the probability of
a cell being occupied, (Hi) the occupancy probabilities of cells are statistically independent,
(iv) the noises affecting measurements are statistically independent
(d) The Kinect camera uses which of the following ranging principles?
(i) time of flight, (ii) frequency-modulated continuous wave, (Hi) triangulation, (iv) echo
localization
(e) The augmented state in the EKF-SLAM algorithm refers to the concatenation of
(i) translation and rotation of the robot, (ii) robot poses and landmark positions, (iii) mean
and covariance, (iv) position and velocity
(f) In batch SLAM the resulting linear system we solve at each iteration has a left-hand-side
whose sparsity pattern is referred to as
(i) hollow, (ii) block-diagonal, (iii) arrowhead, (iv) chordal
(g) The cost-to-come value function represents
( i) the lowest possible cost to arrive at the current state from the start, ( ii) the lowest possible
cost to get from the current state to the goal, ( Hi) the lowest cost to getfrom the current state
to any neighbouring state, (iv) the heuristic cost to get to the current state from the start
(h) Dijkstra’s algorithm is a special case of which of the following algorithms?
(i) RRT*, (ii) A*, (iii) Field-D*, (iv) Dubin’s algorithm
(i) If T32, Ti2 G SEflf) then the expression for T13 is
(i) t12 + T32, (ii) T32T^, (iii) T12TJ2, (iv) t12t32*
(j) If a covariance matrix is diagonal this means that
(i) the variables are orthogonal to one another, (ii) the distribution is unbiased, (iii) the
variables are uncorrelated with one another, (iv) the distribution is Gaussian
Page 2 of 6 pages
