http://helios.hud.ac.uk/planform

Object Transition Sequences: A New Form of Abstraction for HTN

Planners

Lee McCluskey

Computing Science Dept,

The University of Huddersfield, UK

Contents

• Research Aims

• Background: the domain modelling language OCLh

• The HTN Planning Algorithm EMS

Problems

• In applications involving non-toy domain models, traditional htn/Strips domain modelling languages seem to lead to – trouble in building and reasoning with models and planners– models which are hard to validate

• There have been various recent advances in planning (e.g. advance in expression by UCPOP, in efficiency by Graphplan) but not much effort in harnessing domain STRUCTURE.

General Aims

Our general work on “object-centred planning” is aimed at:

• Making domain model building easier• making domain models clearer• making the algorithms simpler to understand

At the heart is a simple, tool-supported hierarchical language called OCLh which can be used in conjunction with a design method.

Specific Aims

• Introduce a new HTN algorithm called EMS (Expand - Make - Sound)

• EMS based on the use of “transition sequences”

• Transition sequences based on OCLh

OCLh: States and Objects

Truck; t-1; at(city-1), moveable, busy(pk-2)

S-2 ; j-2 ; ss-2

S-3 ; j-3 ; ss-3

......................

STATE = list of object descriptions

SORT; OB-ID; SUBSTATE

objectdescriptions

OCLh: Sort Hierarchy

truck ; t-1; at(t-1,city1-cl1) & moveable(t-1) & busy(t-1,pk-2)

Truck; T; moveable(T) & busy(T,package) or moveable(T) or out-of-service(T)

vehicle; V; at(V,location)

OBJECT and CLASS Expressions

truck ; t-1; at(t-1,city1-cl1) & moveable(t-1) & busy(t-1,pk-2)

vehicle ; V; at(V,C) & busy(V,P) &

in-city(C,city1)

truck ; T; at(T,C) & moveable(T) & busy(T,P)

Objectdescription

Class expression:must include fullhierarchicalcomponents

Object expression:satisfied by at least one substate

OCLh: ACTIONS and TRANSITIONS

Train ; t-1; at(city1-ts1), in-service, attached(c-2) Car ; c-2; at(city1-ts1), attached(t-1), busy, ..

......................

State-1

Train ; t-1; at(city2-ts1), in-service, attached(c-2)

Car ; c-2; at(city2-ts1), attached(t-1), busy, ..

State-2

......................

GUARDED TRANSITION SEQUENCES

• TRANSITION:

OBJECT EXPRESSION => CLASS EXPRESSION

• GUARDED TRANSITION SEQUENCE:

(SORT,OBJ-PARAM,PRE,[oe-1 => ce-1, ... ,oe-N => ce-N], POST)

• SOUND GUARDED TRANSITION SEQUENCE:

For any object description that satisfies the precondition, the transition sequence will result in an object that satisfies the post-condition.

Example

(truck,T,

[at(T,C),movable(T),available(T)] [

[movable(T),available(T)] =>

[movable(T),busy(T,pk-2)],

[at(T,C),movable(T)] => [at(T,city3-cl1)],

[at(T,city3-cl1),movable(T)] =>

[at(T,city3-cl1), movable(T),busy(T,pk-2)],

[at(T,city3-cl1),movable(T)] =>

[at(T,city1-cl1)],

[at(T,city1-cl1), movable(T),busy(T,pk-2)] =>

[at(T,city1-cl1), movable(T),available(T)]

], [at(T,city1-cl1), movable(T),available(T)] )

Hierarchical OperatorsGENERAL FORM

(ID, PRE, TRANSITIONS, STATICS, TEMPS, DECOMPOSITION)

EXAMPLE:

(carry-direct(P,O,D),

[ ],

[ (package, P,

[at(P,O), waiting(P), certified(P)] =>

[at(P,D), waiting(P), certified(P)] )]

[is-of-sort(P,package), is-of-sort(V,truck),

in-city(O,CY), in-city(D,CY) ],

[before(1,3), before(2,3), before(3,4), before(4,5)],

[commission(V,P), achieve((truck,V,[at(V,O)])),

load-package(P,V,O), move(V,O,D,R1),

unload-package(P,V,D) ]

)

Summary: an OCLh Domain Model

DOMAIN MODEL = OBJECTS; SORT HIERARCHY;CLASS EXPRESSIONS;ATOMIC INVARIANTS;GENERAL INVARIANTS;PRIMITIVE OPERATORS;HIERARCHICAL OPERATORS

The EMS Algorithm: Input and Output

( [ achieve(ss(traincar,traincar1,[at(traincar1,city1-ts1)])), transport(pk-5-z,city3-cl1-z,city2-cl1), achieve(ss(package,pk-5,[at(pk-5,X),delivered(pk-5)] )) ], [before(1,3)], [serves(X,city3-x)])

- INPUT TASK: ( BODY, TEMPS, STATICS)

- EXAMPLE TASK:

OUTPUT: a solution - a partially ordered/instantiated set of primitive ops

EMS: Search Space

PARTIAL PLAN = (NETWORKS, STATICS)

NETWORKS is TREE STRUCTURED:

ROOT NETWORK

NODE NETWORK NODE NETWORK

LEAF NETWORKLEAF NETWORK

LEAF NETWORK

EMS: Operation

• Network = (Id, Pre, Post, Steps, Temps)

• Each non-root Network comes from a Step in its parent Network

• A Network is SOUND if all its guarded transition sequences are sound, where – Pre and Post contain the guards– all sequences are those that satisfy Temps

EMS: Operation

• Outline Algorithm:– 1. Construct and store an initial partial plan using initial state

and task as usual– 2. Choose a partial plan P; If all networks in P are sound and

contain primitive operators, go to 6.– 3. If all networks in P are sound, expand leaf networks by

replacing hierarchical ops with their expansions– 4. If some networks in P are not sound, make them sound by

manipulating their pre- and post-conditions; if this introduces new objects into the guards, these must be ‘passed-up’

– 5. Go to 2– 6. Extract a solution from P’s network leaves

EMS: Example Network

A0P0B0

B5P1

N2 P2

A5P3

A1B1

N3 A2 A3 N4 A4

EXPANSION OF STEP N3:

A1B1

A6V1B2

N5A7V2B3

V3 N6V4 A2

SOUND NETWORK:

EMS: Network Made Sound

A0P0B0V7

B5P1

N2 P2

A5P3B6V6

A1B1V0

N3 A2B4V5

A3 N4 A4

NETWORK MADE SOUND:

A1B1V0

A6V1B2

N5A7V2B3

V3 N6V4 A2

B4V5

EMS uses another form of abstraction..

• The EMS Algorithm draws on the LINK between:

Operator Structure,

Substate Class Structure, and

Transition Sequences

EMS: EVALUATION

• Theoretical– current algorithm proved sound– current algorithm not complete

• Empirical– tried out on Translog-derived domains of varying complexity

(results in paper)

Conclusions• The main innovation in the EMS algorithm -

– sound algorithm with the potential of application to complex applications

– object transitions correspond, in general, to the sequential parts of a plan. This allows the pre and post-conditions of transitions in a network to be efficiently computed, and these conditions can be used as guards in reasoning within higher-level networks.

– the sort-abstraction technique means that we only consider transitions of a related sort when reasoning about soundness.

– reasoning about the soundness of transition sequences is essential done locally - at no time does EMS have to consider the soundness of the whole plan at a global level.

Future Work

• EMS is new and requires a great deal of development. One development would be to make it very generic so that it could be (automatically) configured to various domains.

• Through the PLANFORM project we will be applying EMS to some complex ‘real’ applications