COMP3702 Artificial Intelligence (Semester 2, 2022)
Assignment 2: HexBot MDP
Key information:
Due: 4pm, Friday 30 September
This assignment will assess your skills in developing algorithms for solving MDPs.
Assignment 2 contributes 20% to your final grade.
This assignment consists of two parts: (1) programming and (2) a report.
This is an individual assignment.
Both code and report are to be submitted via Gradescope (https://www.gradescope.com/). You
can find instructions on how to register for the COMP3702 Gradescope site on Blackboard.
Your program (Part 1, 60/100) will be graded using the Gradescope code autograder, using testcases
similar to those in the support code provided at https://gitlab.com/3702-2022/a2-support.
Your report (Part 2, 40/100) should fit the template provided, be in .pdf format and named according
to the format a2-COMP3702-[SID].pdf, where SID is your student ID. Reports will be graded by the
teaching team.
The HexBot Robot AI Environment
You have been tasked with developing a planning algorithm for automatically controlling HexBot, a multi-
purpose robot which operates in a hexagonal environment, and has the capability to push, pull and rotate
‘Widgets’ in order to reposition them to target locations. To aid you in this task, we have provided support
code for the HexBot robot environment which you will interface with to develop your solution. To optimally
solve a level, your AI agent must efficiently find a sequence of actions so that every Target cell is occupied
by part of a Widget, while incurring the minimum possible action cost.
For A2, the HexGrid environment has been extended to model non-deterministic outcomes of actions. Cost
and action validity are now replaced by a reward function where action costs are represented by negative
received rewards, with additional penalties (i.e. negative rewards) being incurred when a collision occurs
(between the robot or a widget and an obstacle, or between widgets). Updates to the game environment are
indicated in pink font.
Levels inHexBot are composed of a Hexagonal grid of cells, where each cell contains a character representing
the cell type. An example game level is shown in Figure 1.
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COMP3702 Assignment 2: HexBot MDP
Figure 1: Example game level of HexBot
Environment representation
Hexagonal Grid
The environment is represented by a hexagonal grid. Each cell of the hex grid is indexed by (row, column)
coordinates. The hex grid is indexed top to bottom, left to right. That is, the top left corner has coordinates
(0, 0) and the bottom right corner has coordinates (nrows ? 1, ncols ? 1). Even numbered columns (starting
from zero) are in the top half of the row, and odd numbered columns are in the bottom half of the row. An
example is shown in Figure 2.
Figure 2: Example hexagonal grid showing the order that rows and columns are indexed
Two cells in the hex grid are considered adjacent if they share an edge. For each non-border cell, there are 6
adjacent cells.
Robot and its Actions
The HexBot robot occupies a single cell in the hex grid. In the visualisation, the robot is represented by the
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COMP3702 Assignment 2: HexBot MDP
cell marked with the character ‘R’. The side of the cell marked with ‘*’ represents the front of the robot. The
state of the robot is defined by its (row, column) coordinates and its orientation (i.e. the direction its front
side is pointing towards).
At each time step, the agent is prompted to select an action. The robot has 4 nominal actions:
Forward → move to the adjacent cell in the direction of the front of the robot (keeping the same
orientation)
Reverse → move to the adjacent cell in the opposite direction to the front of the robot (keeping the
same orientation)
Spin Left → rotate left (relative to the robot’s front, i.e. counterclockwise) by 60 degrees (staying in
the same cell)
Spin Right → rotate right (i.e. clockwise) by 60 degrees (staying in the same cell)
Each time the robot selects an action, there is a fixed probability (given as a parameter of each testcase)
for the robot to ‘drift’ by 60 degrees in a clockwise or counterclockwise direction (separate probabilities for
each drift direction) before the selected nominal action is performed. The probability of drift occurring de-
pends on which nominal action is selected, with some actions more likely to result in drift. Drifting CW
and CCW are mutually exclusive events. Drift occurring does not cause any additional cost/reward penalty
to be incurred except in the case where the movement direction resulting from drift causes a collision to occur.
Additionally, there is a fixed probability (also given as a parameter of each testcase) for the robot to ‘double
move’, i.e. perform the nominal selected action twice. The probability of a double move occurring depends
on which action is selected. Double movement may occur simultaneously with drift (CW or CCW). Double
movement does not cause additional cost/reward penalty to be incurred (i.e. the movement is ‘two for the
price of one’) except where the double movement results in a collision occurring.
The robot is equipped with a gripper on its front side which allows it to manipulate Widgets. When the robot
is positioned with its front side adjacent to a widget, performing the ‘Forward’ action will result in the Widget
being pushed, while performing the ‘Reverse’ action will result in the Widget being pulled.
Action Costs
Each action has an associated cost, representing the amount of energy used by performing that action.
If the robot moves without pushing or pulling a widget, the cost of the action is given by a base action cost,
ACTION_BASE_COST[a] where ‘a’ is the action that was performed.
If the robot pushes or pulls a widget, an additional cost of ACTION_PUSH_COST[a] is added on top, so the
total cost is ACTION_BASE_COST[a] + ACTION_PUSH_COST[a].
The costs are detailed in the constants.py file of the support code:
ACTION_BASE_COST = {FORWARD: 1.0, REVERSE: 1.0, SPIN_LEFT: 0.1, SPIN_RIGHT: 0.1}
ACTION_PUSH_COST = {FORWARD: 0.8, REVERSE: 0.5, SPIN_LEFT: 0.0, SPIN_RIGHT: 0.0}
Obstacles
Some cells in the hex grid are obstacles. In the visualisation, these cells are filled with the character ‘X’. Any
action which causes the robot or any part of a Widget to enter an obstacle cell results in collision, causing a
penalty value (given as a parameter of each testcase) to be subtracted from the received reward. The outside
boundary of the hex grid behaves in the same way as an obstacle.
Additionally, the environment now contains an additional obstacle type, called ‘hazards’. Hazards behave
in the same way as obstacles, but when collision occurs, a different (larger) penalty is subtracted from the
reward. As a result, avoiding collisions with hazards has greater importance than avoiding collisions with
obstacles. Hazards are represented by ‘!!!’ in the visualisation.
Widgets
Widgets are objects which occupy multiple cells of the hexagonal grid, and can be rotated and translated by
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COMP3702 Assignment 2: HexBot MDP
the HexBot robot. The state of each widget is defined by its centre position (row, column) coordinates
and its orientation. Widgets have rotational symmetries - orientations which are rotationally symmetric are
considered to be the same.
In the visualisation, each Widget in the environment is assigned a unique letter ‘a’, ‘b’, ‘c’, etc. Cells which are
occupied by a widget are marked with the letter assigned to that widget (surrounded by round brackets). The
centre position of the widget is marked by the uppercase version of the letter, while all other cells occupied
by the widget are marked with the lowercase.
Three widget types are possible, called Widget3, Widget4 and Widget5, where the trailing number denotes
the number of cells occupied by the widget. The shapes of these three Widget types and each of their possible
orientations are shown in Figures 3 to 5 below.
VERTICAL
Figure 5: Widget5
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COMP3702 Assignment 2: HexBot MDP
Two types of widget movement are possible - translation (change in centre position) and rotation (change in
orientation).
Translation occurs when the robot is positioned with its front side adjacent to one of the widgets cells such that
the robot’s orientation is in line with the widget’s centre position. Translation results in the centre position of
the widget moving in the same direction as the robot. The orientation of the widget does not change when
translation occurs. Translation can occur when either ‘Forward’ or ‘Reverse’ actions are performed. For an
action which results in translation to be valid, the new position of all cells of the moved widget must not
intersect with the environment boundary, obstacles, the cells of any other widgets or the robot’s new position.
Rotation occurs when the robot’s new position intersects one of the cells of a widget but the robot’s orientation
does not point towards the centre of that widget. Rotation results in the widget spinning around its centre
point, causing the widget to change orientation. The position of the centre point does not change when
rotation occurs. Rotation can only occur for the ‘Forward’ action - performing ‘Reverse’ in a situation where
‘Forward’ would result in a widget rotation is considered invalid.
The following diagrams show which moves result in translation or rotation for each widget type, with the
arrows indicating directions from which the robot can push or pull a widget in order to cause a translation or
rotation of the widget. Pushing in a direction which is not marked with an arrow is considered invalid.
Figure 6: Widget3 translations and rotations
Figure 7: Widget4 translations and rotations
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COMP3702 Assignment 2: HexBot MDP
Figure 8: Widget5 translations and rotations
Targets
The hex grid contains a number of ‘target’ cells. In the visualisation, these cells are marked with ‘tgt’. For a
HexBot environment to be considered solved, each target cell must be occupied by part of a Widget. The
number of targets in an environment is always less than or equal to the total number of cells occupied by all
Widgets.
Interactive mode
A good way to gain an understanding of the game is to play it. You can play the game to get a feel for how
it works by launching an interactive game session from the terminal with the following command:
$ python play.py .txt
where .txt is a valid testcase file (from the support code, with path relative to the current
directory), e.g. testcases/ex1.txt.
Depending on your python installation, you should run the code using python, python3 or py.
In interactive mode, type the symbol for your chosen action and press enter to perform the action: press ’W’
to move the robot forward, ’S’ to move the robot in reverse, ’A’ to turn the robot left (counterclockwise) and
’D’ to turn the robot right (clockwise). Use ’[’ to exit the simulation, and ’]’ to reset the environment to the
initial configuration.
HexBot as an MDP
In this assignment, you will write the components of a program to play HexBot, with the objective of
finding a high-quality solution to the problem using various sequential decision-making algorithms based on
the Markov decision process (MDP) framework. This assignment will test your skills in defining a MDP for a
practical problem and developing effective exact algorithms for MDPs.
What is provided to you
We will provide supporting code in Python, in the form of:
1. A class representing HexBot game map and a number of helper functions
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COMP3702 Assignment 2: HexBot MDP
2. A parser method to take an input file (testcase) and convert it into a HexBot map
3. A tester
4. Testcases to test and evaluate your solution
5. A script to allow you to play HexBot interactively
6. A solution file template
The support code can be found at: https://gitlab.com/3702-2022/a2-support. Autograding of code
will be done through Gradescope, so that you can test your submission and continue to improve it based on
this feedback — you are strongly encouraged to make use of this feedback.
Your assignment task
Your task is to develop algorithms for computing policies, and to write a report on your algorithms’ perfor-
mance. You will be graded on both your submitted program (Part 1, 60%) and the report (Part 2, 40%).
These percentages will be scaled to the 20% course weighting for this assessment item.
The provided support code formulates HexBot as an MDP, and your task is to submit code implementing
the following MDP algorithms:
1. Value Iteration (VI)
2. Policy Iteration (PI)
Individual testcases specify which strategy (value iteration/policy iteration) will be applied, but you may
modify the strategy specified in your local copy of the test cases for the purpose of comparing the perfor-
mance of your two algorithms. Note that any local changes you make to the test cases will not modify
the test cases on Gradescope (against which your programming component will be graded). The difficulty of
higher level testcases will be designed to require a more advanced solution (e.g. linear algebra policy iteration).
Once you have implemented and tested the algorithms above, you are to complete the questions listed in the
section “Part 2 - The Report” and submit the report to Gradescope.
More detail of what is required for the programming and report parts are given below.
Part 1 — The programming task
Your program will be graded using the Gradescope autograder, using testcases similar to those in the support
code provided at https://gitlab.com/3702-2022/a2-support.
Interaction with the testcases and autograder
We now provide you with some details explaining how your code will interact with the testcases and the
autograder (with special thanks to Nick Collins for his efforts making this work seamlessly).
Implement your solution using the supplied solution.py Template file. You are required to fill in the following
method stubs:
init (game env)
vi initialise()
vi is converged()
vi iteration()
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COMP3702 Assignment 2: HexBot MDP
vi plan offline()
vi get state value()
vi select action()
pi initialise()
pi is converged()
pi iteration()
pi plan offline()
pi select action()
You can add additional helper methods and classes (either in solution.py or in files you create) if you wish.
To ensure your code is handled correctly by the autograder, you should avoid using any try-except blocks in
your implementation of the above methods (as this can interfere with our time-out handling). Refer to the
documentation in solution.py for more details.
Grading rubric for the programming component (total marks: 60/100)
For marking, we will use 6 test cases to evaluate your solution. Each test case uses the algorithm specified
as the solver type. Each test case is scored out of 10.0 marks, in the following four categories:
Agent successfully reaches the goal
Total reward
Time elapsed
Iterations performed
The 10 marks for each test case are evenly divided amongst the four categories (i.e. 2.5 marks are allocated
for each category in each test case).
Each test case has targets for total reward, time elapsed, and iterations performed.
Maximum score is achieved when your program matches or beats the target in each category
Partial marks are available for up to 1.3 x total reward, 2 x time elapsed and 1.3 x number of iterations
Total mark for the test case is a weighted sum of the scores for each category
Total code mark is the sum of the marks for each test case
Part 2 — The report
The report tests your understanding of MDP algorithms and the methods you have used in your code, and
contributes 40/100 of your assignment mark.
Question 1. MDP problem definition (15 marks)
a) Define the State space, Action space, Transition function, and Reward function components of the
HexBox MDP as well as where these are represented in your code. (10 marks)
b) Describe the purpose of a discount factor in MDPs. (2.5 marks)
c) State what the following dimensions of complexity are of your agent in the HexBot MDP. (See
https://artint.info/html/ArtInt_12.html for definitions) (2.5 marks)
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COMP3702 Assignment 2: HexBot MDP
Planning Horizon
Sensing Uncertainty
Effect Uncertainty
Computational Limits
Learning
Question 2. Comparison of algorithms and optimisations (15 marks)
This question requires a comparison of your implementation of value iteration (VI) and policy iteration (PI).
If you did not implement PI, you may receive partial marks for this question by providing insightful relevant
comments on your implementation of VI. For example, if you tried standard VI and asynchronous VI, you may
compare these two approaches for partial marks.
a) Describe your implementations of value iteration and policy iteration in one sentence each. Include
details such as whether you used asynchronous updates, and how you handled policy evaluation in PI.
(2 marks)
b) Pick three representative testcases and compare the performance of Value Iteration (VI) and Policy Iter-
ation (PI) according to the following measures. Please include the numerical values of your experiments
in your comparisons.
Time to converge to the solution. (3 marks)
Number of iterations to converge to the solution. (3 marks)
In order to do this, you’ll need to modify the # solver type in your local copy of the test cases (the
text files in the testcases directory).
c) Comment on the difference between the numbers you found for VI and PI. List any reasons why the
differences either make sense, or do not make sense. (7 marks)
Question 3. “Risky Business”: Optimal policy variation based on probabilities & costs (10 marks)
One consideration in the solution of a Markov Decision Process (i.e. the optimal policy) is the trade off between
a risky higher reward vs a lower risk lower reward, which depends on the probabilities of non-deterministic
dynamics of the environment and the rewards associated with certain states and actions.
Consider testcase ex6.txt, which includes a risky (but lower cost) path through the top half of the grid, and
a less risky (but higher cost) path through the bottom half of the grid. Explore how the policy of the agent
changes with hazard penalty and transition probabilities.
If you did not implement PI, you may change the solver type to VI in order to answer this question.
a) How do you expect the optimal path to change as the hazard penalty and transition probabilities change?
Use facts about the algorithms to justify why you expect these changes to have such effects.(5 marks)
b) Picking three values for hazard penalty, and three sets of values for the transition probabilities, explore
how the optimal policy changes over the 9 combinations of these factors. Do the experimental results
align with what you thought should happen? If not, why? (5 marks)
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COMP3702 Assignment 2: HexBot MDP
Academic Misconduct
The University defines Academic Misconduct as involving “a range of unethical behaviours that are designed
to give a student an unfair and unearned advantage over their peers.” UQ takes Academic Misconduct very
seriously and any suspected cases will be investigated through the University’s standard policy (https://
ppl.app.uq.edu.au/content/3.60.04-student-integrity-and-misconduct). If you are found guilty,
you may be expelled from the University with no award.
It is the responsibility of the student to ensure that you understand what constitutes Academic Misconduct
and to ensure that you do not break the rules. If you are unclear about what is required, please ask.
It is also the responsibility of the student to take reasonable precautions to guard against unauthorised access
by others to his/her work, however stored in whatever format, both before and after assessment.
In the coding part of COMP3702 assignments, you are allowed to draw on publicly-accessible resources and
provided tutorial solutions, but you must make reference or attribution to its source, by doing the following:
All blocks of code that you take from public sources must be referenced in adjacent comments in your
code.
Please also include a list of references indicating code you have drawn on in your solution.py docstring.
However, you must not show your code to, or share your code with, any other student under any
circumstances. You must not post your code to public discussion forums (including Ed Discussion)
or save your code in publicly accessible repositories (check your security settings). You must not
look at or copy code from any other student.
All submitted files (code and report) will be subject to electronic plagiarism detection and misconduct proceed-
ings will be instituted against students where plagiarism or collusion is suspected. The electronic plagiarism
detection can detect similarities in code structure even if comments, variable names, formatting etc. are
modified. If you collude to develop your code or answer your report questions, you will be caught.
For more information, please consult the following University web pages:
Information regarding Academic Integrity and Misconduct:
– https://my.uq.edu.au/information-and-services/manage-my-program/student-integrity-and-
conduct/academic-integrity-and-student-conduct
– http://ppl.app.uq.edu.au/content/3.60.04-student-integrity-and-misconduct
Information on Student Services:
– https://www.uq.edu.au/student-services/
Late submission
Students should not leave assignment preparation until the last minute and must plan their workloads to meet
advertised or notified deadlines. It is your responsibility to manage your time effectively.
Late Penalties: Where an assessment item is submitted after the original deadline without an approved
extension, a late penalty will apply, as detailed in the COMP3702 Electronic Course Profile (ECP). The late
penalty shall be
10% of the maximum possible mark for the assessment item will be deducted per calendar day (or part
thereof) late, up to a maximum of seven (7) days. After seven days, no marks will be awarded for the
item. A day is considered to be a 24 hour block from the assessment item due time. Negative marks
will not be awarded.
In the event of exceptional circumstances, you may submit a request for an extension. You can find guide-
lines on acceptable reasons for an extension here https://my.uq.edu.au/information-and-services/manage-my-
program/exams-and-assessment/applying-extension All requests for extension must be submitted on the UQ
Application for Extension of Progressive Assessment form at least 48 hours prior to the submission deadline.