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2020-T-ASE/transformations/README.MD

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The following rules have been applied in order to create PDDL files from IEC 62264 production system models.

PDDL Domain Definitions

Metamodel Concepts

Metamodel concepts of IEC 62264 are being converted to a set of PDDL type specifications and predicates. Relevant elements are those that appear within a given IEC 62264 model. Unused elements are not translated in order to reduce file size and increase performance and readability.

  • IEC 62264 elements (e.g., Equipment, Equipment Class) are converted to types.
  • IEC 62264 relations (e.g., Equipment can be classified by [0..*] Equipment Classes) are converted to predicates.

For the above mentioned examples, the IEC 62264 concepts are translated from

classDiagram
	Person "0..*" --> "0..*" Personnel Class : defined by
	Equipment "0..*" --> "0..*" Equipment Class : defined by
	Material Lot "0..*" --> "1" Material Definition : defined by
	Material Definition "0..*" --> "0..*" Material Class : grouped by

to

(:types
	PersonnelClass Person
	EquipmentClass Equipment
	MaterialClass MaterialDefinition MaterialLot
)
(:predicates
	(PersonClassed ?P - Person ?C - PersonnelClass)
	(EquipmentClassed ?E - Equipment ?C - EquipmentClass)
	(MaterialClassed ?D - MaterialDefinition ?C - MaterialClass)
	(MaterialDefined ?L - MaterialLot ?D - MaterialDefinition)
	(MaterialLotClassed ?L - MaterialLot ?C - MaterialClass)
)

Where the last predicate (MaterialLotClassed ?L - MaterialLot ?C - MaterialClass) is the composition of defined by and grouped by in the material information model.

Model Concepts

IEC 62264 instance data is converted into PDDL information using the rules laid out in the following clauses. Note, that we are using class diagram visual syntax instead of object diagram syntax due to limitations in the used Markdown rendering engine.

* Class and Material Definition

* Class and Material Definition instances are converted to constants

From

classDiagram
	class MaintenanceEngineer
	<<PersonnelClass>> MaintenanceEngineer
	class PositioningUnit
	<<EquipmentClass>> PositioningUnit
	class Chassis
	<<MaterialClass>> Chassis
	class ChassisBlack
	<<MaterialDefinition>> ChassisBlack

to

(:constants
	PC_MaintenanceEngineer - PersonnelClass
	EC_PositioningUnit - EquipmentClass
	MC_Chassis - MaterialClass
	MD_Chassis-Black - MaterialDefinition
)

* Class Property and Material Definition Property

Boolean * Class Property and Material Definition Property instances are converted to predicates and actions. Non-boolean properties are not supported in the current state of implementation. The actions are only generated, if the property is not marked as of kind implicit, in which case the corresponding predicate is only triggered by other actions' effects.

From

classDiagram
	class PositioningUnit
	<<EquipmentClass>> PositioningUnit
	class Locked
	<<EquipmentClassProperty>> Locked
	PositioningUnit *-- Locked : has property

to

(:predicates
	(PositioningUnitLocked ?E - Equipment)
)

(:action LockPositioningUnit
	:parameters (?E - Equipment)
	:precondition	
		(and
			(EquipmentClassed ?E EC_PositioningUnit)
			(not (PositioningUnitLocked ?E))
		)
	:effect	
		(and
			(increase (total-cost) 1)
			(PositioningUnitLocked ?E)
		)
)

(:action UnlockPositioningUnit
	:parameters (?E - Equipment)
	:precondition	
		(and
			(EquipmentClassed ?E EC_PositioningUnit)
			(PositioningUnitLocked ?E)
		)
	:effect	
		(and
			(increase (total-cost) 1)
			(not (PositioningUnitLocked ?E))
		)
)

Please, note that we have applied hard-coded "pretty-printing" to some of the * Class Property instances. In the above case PositioningUnit's locked is translated into the terms LockPositioningUnit and UnlockPositioningUnit. The default translation for this instance would be PositioningUnitLockedTrue PositioningUnitLockedFalse. Action cost for setting a property are considered to be 1.

Resource Network Connection Type

Resource Network Connection Type instances are converted to predicates.

From

classDiagram
	class EquipmentReachTo
	<<ResourceNetworkConnectionType>> EquipmentReachTo
	class MaterialLocation
	<<ResourceNetworkConnectionType>> MaterialLocation

to

(:predicates
	(ReachesTo ?R ?E - Equipment)
	(MaterialLocation ?M - MaterialLot ?E - Equipment)
)

Please, note that we have applied hard-coded "pretty-printing" to some of the ResourceNetworkConnectionType instances. In the above case EquipmentReachTo is translated into the term ReachesTo.

Process Segment

Process Segment instances are converted to actions, with their * Segment Specification instances becoming their parameters and being used in certain pre and post condition statements. In the example below, we are not listing all elements specified in the IEC 62264 input model, as this would increase complexity a lot. Instead, we are listing the main elements of the input model, but we are listing the complete result for the PDDL domain description.

From

classDiagram
	class MoveShuttle
	<<ProcessSegment>> MoveShuttle
	class SHUTTLE
	<<EquipmentSegmentSpecification>> SHUTTLE
	class Shuttle
	<<EquipmentClass>> Shuttle
	class FROM
	<<EquipmentSegmentSpecification>> FROM
	class TO
	<<EquipmentSegmentSpecification>> TO
	class LockedFrom {
		<<EquipmentSegmentSpecificationProperty>> 
		description = "pddl:pre"
		value = false
	}
	class PositioningUnit
	<<EquipmentClass>> PositioningUnit
	class TransportationNode
	<<EquipmentClass>> TransportationNode
	class LockedTo {
		<<EquipmentSegmentSpecificationProperty>> 
		description = "pddl:pre"
		value = false
	}
	class Locked
	<<EquipmentClassProperty>> Locked
	MoveShuttle *-- SHUTTLE : contains
	MoveShuttle *-- FROM : contains
	MoveShuttle *-- TO : contains
	SHUTTLE --> Shuttle : specifies
	FROM *-- LockedFrom : has property
	FROM --> PositioningUnit : specifies
	FROM --> TransportationNode : specifies
	TO --> PositioningUnit : specifies
	TO --> TransportationNode : specifies
	TO *-- LockedTo : has property
	PositioningUnit *-- Locked : has property
	LockedFrom --> Locked : corresponds to
	LockedTo --> Locked : corresponds to

to

(:action MoveShuttle
	:parameters (?SHUTTLE ?FROM ?TO - Equipment)
	:precondition	
		(and
			(EquipmentClassed ?SHUTTLE EC_Shuttle)
			(or
				(EquipmentClassed ?FROM EC_PositioningUnit)
				(EquipmentClassed ?FROM EC_TransportationNode)
			)
			(imply (EquipmentClassed ?FROM EC_PositioningUnit) 
				(not (PositioningUnitLocked ?FROM))
			)
			(or
				(EquipmentClassed ?TO EC_PositioningUnit)
				(EquipmentClassed ?TO EC_TransportationNode)
			)
			(imply (EquipmentClassed ?TO EC_PositioningUnit) 
				(not (PositioningUnitLocked ?TO))
			)
			(TransportationNodeConnection ?FROM ?TO)
			(EquipmentLocation ?SHUTTLE ?FROM)
			(not (EquipmentLocation ?SHUTTLE ?TO))
		)
	:effect	
		(and
			(increase (total-cost) (shuttle-time ?FROM ?TO))
			(not (EquipmentLocation ?SHUTTLE ?FROM))
			(EquipmentLocation ?SHUTTLE ?TO)
		)
)

Please, note that we are adding a few pre- and post conditions hard-coded in the transformation process, based on our knowledge of the underlying production system, e.g., utilization of the EquipmentLocation and TransportationNodeConnection predicates.

Further, the action cost are encoded as a function shuttle-time that is filled with values in the PDDL problem description.

PDDL Problem Definitions

Person, Equipment, and Material Lot

Instances of Person, Equipment, and Material Lot are converted to objects. Their relations to * Class or Material Definition instances are materialized as initialization statements.

From

classDiagram
	class MaintenanceEngineer1
	<<Person>> MaintenanceEngineer1
	class MaintenanceEngineer
	<<EquipmentClass>> MaintenanceEngineer
	class Shuttle1
	<<Equipment>> Shuttle1
	class Shuttle
	<<EquipmentClass>> Shuttle
	class ChassisBlack1
	<<MaterialLot>> ChassisBlack1
	class ChassisBlack
	<<MaterialDefinition>> ChassisBlack
	class Chassis
	<<MaterialClass>> Chassis
	MaintenanceEngineer1 --> MaintenanceEngineer : defined by
	Shuttle1 --> Shuttle : defined by
	ChassisBlack1 --> ChassisBlack : defined by
	ChassisBlack --> Chassis : grouped by

to

(:objects
	P_MaintenanceEngineer-1 - Person
	E_Shuttle-1 - Equipment
	ML_Chassis-Black-1 - MaterialLot
)
(:init
	(PersonClassed P_MaintenanceEngineer-1 PC_MaintenanceEngineer)
	(EquipmentClassed E_Shuttle-1 EC_Shuttle)
	(MaterialClassed MD_Chassis-Black MC_Chassis)
	(MaterialDefined ML_Chassis-Black-1 MD_Chassis-Black)
	(MaterialLotClassed ML_Chassis-Black-1 MC_Chassis)
)

Resource Network Connection

Resource Network Connection instances are converted to init statements.

From

classDiagram
	class Robot1ReachesToTable1
	<<ResourceNetworkConnection>> Robot1ReachesToTable1
	class Robot1ReachesToPUMC1
	<<ResourceNetworkConnection>> Robot1ReachesToPUMC1
	class Robot1ReachesToPUMC2
	<<ResourceNetworkConnection>> Robot1ReachesToPUMC2
	class EquipmentReachTo
	<<ResourceNetworkConnectionType>> EquipmentReachTo
	Robot1ReachesToTable1 --> EquipmentReachTo : derived from
	Robot1ReachesToPUMC1 --> EquipmentReachTo : derived from
	Robot1ReachesToPUMC2 --> EquipmentReachTo : derived from

to

(:init
	(ReachesTo E_Robot-1 E_Table-1)
	(ReachesTo E_Robot-1 E_PositioningUnit-MachiningCenter-1)
	(ReachesTo E_Robot-1 E_PositioningUnit-MachiningCenter-2)
)

Intralogistic Routing Topology

Resource Network Connection instances of type Transport-System-Track-Connection and Transport-System-Positioning-Unit-Connection are converted in a very specific way. The former raw connections represent the physical connections of all track curves, lines, and switches. The latter represent the physical location where a positioning unit has been attached to a track. This information is read in, and a directed graph structure is generated. Here, we already show a simplified graph where only topologically important elements are kept (curves and straight lines without positioning units attached are removed). Elements starting with a J are Joins, D depicts Divides, and A represents a special item, an Arena (two inputs, two outputs). Stadium-shaped nodes depict positioning units.

graph LR
	J5 --> A1
    D4 --> J4
    D3 --> P1([PU-MC-1]) --> J3
    D2 --> P2([PU-MC-2]) --> J3 --> J2
    D1 --> P3([PU-MC-3]) --> J2 --> J1
    A1 --> J1 --> D1 --> D2 --> D3 --> D4 --> P10([PU-IO-2]) --> J4 --> D5 --> J5
    A1 --> P100([PU-IO-1]) --> A1
    D5 --> P50([PU-Buffer]) --> J5

In order to reduce computational complexity for the PDDL solver, an even more simplified topology is computed that only contains the positioning units and leaves out all intermediate elements. The edge weight of the graph corresponds to the physical track length between the positioning units and is converted into seconds based on an assumed average speed of 0.56 m/s.

graph LR
    P1 & P2 & P3 & P10 & P50 --> P100([PU-IO-1])
    P1 & P2 & P3 & P10 & P100 --> P50([PU-Buffer])
    P1 & P2 & P3 & P50 & P100 --> P10([PU-IO-2])
    P1 & P2 & P10 & P50 & P100 --> P3([PU-MC-3])
    P1 & P3 & P10 & P50 & P100 --> P2([PU-MC-2])
    P2 & P3 & P10 & P50 & P100 --> P1([PU-MC-1])

For each "positioning unit connection" two init statements are created: one that states that these two positioning units are connected with each other (TransportationNodeConnection), and another one setting the function value for the function shuttle-time, representing the estimated traveling time in seconds between these two positioning units. The resulting PDDL init statements are listed below:

(:init
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-3 E_PositioningUnit-MachiningCenter-2)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-3 E_PositioningUnit-MachiningCenter-2) 25)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-3 E_PositioningUnit-MachiningCenter-1)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-3 E_PositioningUnit-MachiningCenter-1) 30)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-3 E_PositioningUnit-Buffer)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-3 E_PositioningUnit-Buffer) 54)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-3 E_PositioningUnit-IO-1)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-3 E_PositioningUnit-IO-1) 78)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-3 E_PositioningUnit-IO-2)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-3 E_PositioningUnit-IO-2) 37)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-2 E_PositioningUnit-MachiningCenter-3)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-2 E_PositioningUnit-MachiningCenter-3) 25)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-2 E_PositioningUnit-MachiningCenter-1)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-2 E_PositioningUnit-MachiningCenter-1) 35)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-2 E_PositioningUnit-Buffer)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-2 E_PositioningUnit-Buffer) 59)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-2 E_PositioningUnit-IO-1)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-2 E_PositioningUnit-IO-1) 83)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-2 E_PositioningUnit-IO-2)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-2 E_PositioningUnit-IO-2) 42)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-1 E_PositioningUnit-MachiningCenter-3)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-1 E_PositioningUnit-MachiningCenter-3) 28)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-1 E_PositioningUnit-MachiningCenter-2)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-1 E_PositioningUnit-MachiningCenter-2) 33)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-1 E_PositioningUnit-Buffer)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-1 E_PositioningUnit-Buffer) 62)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-1 E_PositioningUnit-IO-1)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-1 E_PositioningUnit-IO-1) 86)
	(TransportationNodeConnection E_PositioningUnit-MachiningCenter-1 E_PositioningUnit-IO-2)
	(= (shuttle-time E_PositioningUnit-MachiningCenter-1 E_PositioningUnit-IO-2) 45)
	(TransportationNodeConnection E_PositioningUnit-Buffer E_PositioningUnit-MachiningCenter-3)
	(= (shuttle-time E_PositioningUnit-Buffer E_PositioningUnit-MachiningCenter-3) 30)
	(TransportationNodeConnection E_PositioningUnit-Buffer E_PositioningUnit-MachiningCenter-2)
	(= (shuttle-time E_PositioningUnit-Buffer E_PositioningUnit-MachiningCenter-2) 35)
	(TransportationNodeConnection E_PositioningUnit-Buffer E_PositioningUnit-MachiningCenter-1)
	(= (shuttle-time E_PositioningUnit-Buffer E_PositioningUnit-MachiningCenter-1) 40)
	(TransportationNodeConnection E_PositioningUnit-Buffer E_PositioningUnit-IO-1)
	(= (shuttle-time E_PositioningUnit-Buffer E_PositioningUnit-IO-1) 26)
	(TransportationNodeConnection E_PositioningUnit-Buffer E_PositioningUnit-IO-2)
	(= (shuttle-time E_PositioningUnit-Buffer E_PositioningUnit-IO-2) 47)
	(TransportationNodeConnection E_PositioningUnit-IO-1 E_PositioningUnit-MachiningCenter-3)
	(= (shuttle-time E_PositioningUnit-IO-1 E_PositioningUnit-MachiningCenter-3) 18)
	(TransportationNodeConnection E_PositioningUnit-IO-1 E_PositioningUnit-MachiningCenter-2)
	(= (shuttle-time E_PositioningUnit-IO-1 E_PositioningUnit-MachiningCenter-2) 23)
	(TransportationNodeConnection E_PositioningUnit-IO-1 E_PositioningUnit-MachiningCenter-1)
	(= (shuttle-time E_PositioningUnit-IO-1 E_PositioningUnit-MachiningCenter-1) 28)
	(TransportationNodeConnection E_PositioningUnit-IO-1 E_PositioningUnit-Buffer)
	(= (shuttle-time E_PositioningUnit-IO-1 E_PositioningUnit-Buffer) 52)
	(TransportationNodeConnection E_PositioningUnit-IO-1 E_PositioningUnit-IO-2)
	(= (shuttle-time E_PositioningUnit-IO-1 E_PositioningUnit-IO-2) 36)
	(TransportationNodeConnection E_PositioningUnit-IO-2 E_PositioningUnit-MachiningCenter-3)
	(= (shuttle-time E_PositioningUnit-IO-2 E_PositioningUnit-MachiningCenter-3) 51)
	(TransportationNodeConnection E_PositioningUnit-IO-2 E_PositioningUnit-MachiningCenter-2)
	(= (shuttle-time E_PositioningUnit-IO-2 E_PositioningUnit-MachiningCenter-2) 56)
	(TransportationNodeConnection E_PositioningUnit-IO-2 E_PositioningUnit-MachiningCenter-1)
	(= (shuttle-time E_PositioningUnit-IO-2 E_PositioningUnit-MachiningCenter-1) 61)
	(TransportationNodeConnection E_PositioningUnit-IO-2 E_PositioningUnit-Buffer)
	(= (shuttle-time E_PositioningUnit-IO-2 E_PositioningUnit-Buffer) 22)
	(TransportationNodeConnection E_PositioningUnit-IO-2 E_PositioningUnit-IO-1)
	(= (shuttle-time E_PositioningUnit-IO-2 E_PositioningUnit-IO-1) 47)
)

Material Assembly Information

Information about what material can be assembled from what other material is captured from the assembly relation in the MaterialClass and MaterialDefinition instances.

From

classDiagram
	class OpenTopBlackYellowBlue
	<<MaterialDefinition>> OpenTopBlackYellowBlue
	class ChassisBlack
	<<MaterialDefinition>> ChassisBlack
	class CabinYellow
	<<MaterialDefinition>> CabinYellow
	class BodyOpenTopBlue
	<<MaterialDefinition>> BodyOpenTopBlue
	OpenTopBlackYellowBlue --> BodyOpenTopBlue : assembled from
	OpenTopBlackYellowBlue --> CabinYellow : assembled from
	OpenTopBlackYellowBlue --> ChassisBlack : assembled from

to

(:init
	(MaterialDefinitionAssembly MD_OpenTop-Black-Yellow-Blue MD_Chassis-Black)
	(MaterialDefinitionAssembly MD_OpenTop-Black-Yellow-Blue MD_Cabin-Yellow)
	(MaterialDefinitionAssembly MD_OpenTop-Black-Yellow-Blue MD_Body-OpenTop-Blue)
)

Information about the current assembly state are expressed through the assembly relation of the MaterialLot relation. This is not only used to express the current state, but also for the formulation of goal statements, es depicted below. The from IEC 62264 model is extracted from the goal description model.

From

classDiagram
	class OpenTopBlackYellowBlue1
	<<MaterialLot>> OpenTopBlackYellowBlue1
	class ChassisBlack1
	<<MaterialLot>> ChassisBlack1
	class CabinYellow1
	<<MaterialLot>> CabinYellow1
	class BodyOpenTopBlue1
	<<MaterialLot>> BodyOpenTopBlue1
	OpenTopBlackYellowBlue1 --> BodyOpenTopBlue1 : assembled from
	OpenTopBlackYellowBlue1 --> CabinYellow1 : assembled from
	OpenTopBlackYellowBlue1 --> ChassisBlack1 : assembled from

to

(:goal
	(and
		(MaterialLotAssembly ML_OpenTop-Black-Yellow-Blue-1 ML_Body-OpenTop-Blue-1)
		(MaterialLotAssembly ML_OpenTop-Black-Yellow-Blue-1 ML_Cabin-Yellow-1)
		(MaterialLotAssembly ML_OpenTop-Black-Yellow-Blue-1 ML_Chassis-Black-1)
	)
)