Programming & Written Assignment - Planning

Max points:
The assignment should be submitted via Canvas.

Instructions

Task 1 (CSE 4308: 60 Points; CSE 5360: 60 points)

The task in this programming assignment is to design appropriate descriptions of facts, actions, and goals, using the PDDL language, for two planning problems: the Tower of Hanoi problem, and the 7-puzzle problem (a variation of the 8-puzzle problem where two squares are clear instead of one). You will use your descriptions as inputs to a Graphplan implementation. If your descriptions are correct, Graphplan will produce appropriate plans.

Compiling and Running the Software

The Graphplan software can be downloaded from graphplan.zip. See the README file in that package for additional information. To compile the software on omega, unzip the directory, and, from that directory, type 
make graphplan
Once the program compiles, it can be invoked from the commandline as follows: 
graphplan -o [operators_file] -f [facts_file]
For example: 
graphplan -o block_ops.txt -f block_facts3.txt
Once you start running the software, it will ask you three questions. Just hit enter for each question, so as to use the default settings. If your descriptions of actions and facts are correct, the program will print out a plan achieving the stated goal.

Note that the preconds in each fact file will contain both statements that are always true in that domain (i.e., in the Tower of Hanoi domain or the 7-puzzle domain), and statements that simply describe the initial state for that specific planning problem. In addition to the facts files for the specific planning problems you are given, you will have to create a separate text file that includes all the statements that must be present in ANY facts file for that domain.

Tower of Hanoi Description

A description of the Tower of Hanoi domain can be found at Wikipedia. In all problems that your program will be tested with there will be five discs (called disk1, disk2, disk3, disk4, disk5) and three pegs (called A, B, C). In all your facts files you will have to include both a common part (defining objects and relations among objects) and a plan-specific part (describing the initial state and goal for each plan). Note that some of the five disks may not appear in some of the planning problems.

The two planning problems you have to solve are:

Problem 1 

initial state:
(on disk1 disk2)
(on disk2 A) 
(clear disk1)
(clear B)
(clear C) 

goal:
(on disk1 B)
(on disk2 C)
Problem 2 
initial state:
(on disk1 disk2) 
(on disk2 disk3)
(on disk3 disk4)
(on disk4 disk5)
(on disk5 C) 
(clear disk1) 
(clear A) 
(clear B)

goal:
(on disk1 disk2) 
(on disk2 disk3)
(on disk3 disk4)
(on disk4 disk5)
(on disk5 A)

7-puzzle Description

7-puzzle is like 8-puzzle, except that there are only pieces numbered from 1 to 7 (not from 1 to 8), and there are two clear squares on the board. At any move, we can move a numbered piece to an adjacent clear square.

The two planning problems you have to solve are (X indicates a clear square):

Problem 1 

initial state:
123
456
7XX

goal:
123
X56
4X7
Problem 2 
initial state:
XX7
654
321

goal:
123
456
7XX

Grading

This task will be graded for 60 points. Half the points will correspond to your solutions for the Tower of Hanoi world, and the rest will correspond to your solutions for the 7-puzzle problem. Specifically, the point allocation is:

Task 2 (CSE 4308: 15 Points (+10 Points EC); CSE 5360: 15 points (+10 Points EC))

Consider the following scenario:

Planning Task

Your task is to get all the blue marbles in P1 and red marbles in P2

The actions available are as follows:
Give the PDDL description to represent the above as a Planning Problem. Do not forget to also define and describe the predicates and constants that your are going to use.

Extra Credit (10 pts): Also, give a complete plan (using the actions described) for getting from the start to the goal state

Task 3 (CSE 4308: 10 Points (EC); CSE 5360: 10 points)

Consider the problem in Task 2. Let us say that, when you move the marbles, it is possible to sometimes end up moving only one of them (You try to move 2 Red marbles from P2 to P1 but only end up moving one). How would you modify the actions you described in Task 2 to account for this if you were going to try and handle this scenario by
In both cases, show what the modifications are (If no modification is necessary, explain why).

Task 4 (CSE 4308: 15 Points; CSE 5360: 15 points)

Suppose that we are using PDDL to describe facts and actions in a certain world called JUNGLE. In the JUNGLE world there are 4 predicates, each predicate takes at most 3 arguments, and there are 5 constants. Give a reasonably tight bound on the number of unique states in the JUNGLE world. Justify your answer.