OntologiesReasoningComponentsAgentsSimulations

Homework Assignment 1: Homework Assignment 1: Modeling the Tangram PuzzleModeling the Tangram Puzzle

in UML and OCLin UML and OCL

Jacques Robin& Franklin Ramalho

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The Tangram Puzzle SpecificationThe Tangram Puzzle Specification

A set Ii of polygon instances from a set of polygon sub-classes Pi lay on a table in an initial random configuration

Ii is partitioned into: Atomic polygon instances that are made of a single piece Compound polygon instances that result from joining several

polygons by laying them on the table in positions such that their sides are aligned in contact which each other

A compound polygon instance generally belongs to a different class than its atomic (or recursively compound) components

A configuration is defined solely by: The number of instances of each polygon class laying on the table Which sides of this instance set are in contact (i.e., joined) to form

compound polygons The puzzle consists in disjoining and joining some of these

polygons to assemble on the table another goal set of polygons instances Ig taken from a possible distinct goal set of polygon sub-classes Pg

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The Tangram Puzzle SpecificationThe Tangram Puzzle Specification

The puzzle is executed by an robotic agent: Which sensors provide full information on about:

How many instances of each polygon class lay on the table, Which of these instances are atomic and compound, and For compound polygons what is their recursive decomposition in sub-

components, sub-sub-components etc. until the bottom embedding level of atomic components.

Which actuators allow moving one atomic polygon either: From a position where it is joined with another polygon (atomic or

compound) to form a third compound polygon to a position where it is alone, disjoint from any other polygon

From such an isolated position, to a position where it is joined with another polygon (atomic or compound) to form a third compound polygon

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Revision of Polygonal GeometryRevision of Polygonal Geometry

http://www.mathleague.com/help/geometry/polygons.htm#polygon

http://www.math.com/tables/geometry/polygons.htm

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Example of Tangram Puzzle Input:Example of Tangram Puzzle Input:Initial and Goal ConfigurationsInitial and Goal Configurations

Initial configuration: Two convex quadrilaterals Each one assembled from one

equilateral triangle joint with a right triangle on the opposite side of the right angle triangle

Goal configuration: One convex hexagon, assembled

from two equilateral triangles and one square

where the square is itself recursively assembled from two right triangles

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Example of Tangram Puzzle Output:Example of Tangram Puzzle Output:Sequence of ActionsSequence of Actions

ET1RT1

ET2RT2

ET1RT1

ET2RT2

ET1RT1

ET2RT2

Move ET2 from RT2 to Table

ET1RT1

ET2RT2

Move RT2from Table to RT1

Move ET2from Table to RT2

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Topic Variations and AllocationTopic Variations and Allocation

Roster divided in teams of at most 5 students Each team chooses one of the following topic variations:

Topic 1: Atomic sub-classes: only triangles Input sub-classes: any convex polygon of at most 8 sides Goal sub-classes: any convex polygon of at most 8 sides

Topic 2: Atomic sub-classes: any convex polygon of at most 6 sides Input sub-classes: any convex polygon of at most 6 sides Goal sub-classes: any convex polygon of at most 6 sides

Topic 3: Atomic sub-classes: any regular convex polygon of at most 10 sides Input sub-classes: any regular convex polygon of at most 10 sides Goal sub-classes: any regular convex polygon of at most 10 sides

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Topic Variations and AllocationTopic Variations and Allocation

Topic 4: Atomic sub-classes: only right triangles Input sub-classes: any right convex polygon of at most 8 sides Goal sub-classes: any right convex polygon of at most 8 sides

Topic 5: Atomic sub-classes: only triangles Input sub-classes: any concave polygon of at most 12 sides Goal sub-classes: any concave polygon of at most 12 sides

Topic 6: Atomic sub-classes: any regular concave polygon of at most 8 sides Input sub-classes: any regular concave polygon of at most 8 sides Goal sub-classes: any regular concave polygon of at most 8 sides

Topic 7: Atomic sub-classes: only triangles Input sub-classes: any regular convex polygon of at most 6 sides Goal sub-classes: any regular concave polygon of at most 8 sides

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Artifacts to ConstructsArtifacts to Constructs

Ontology of the relevant polygon classes as an UML class diagram associated with OCL invariants and defaults

Test set of input pair configurations (initial configuration and corresponding goal configuration) as a set of UML object diagram pairs

Robotic agent’s structural model as an UML class diagram with OCL invariants and defaults

Robotic agent’s behavioral model as OCL bodies, derivation rules and method pre and post conditions