From: AIPS 1994 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved.
Quantitative Operator Selection for Planning Under Uncertaintyt
Todd Michael ~
Manseli
Departmentof ComputerScience
The University of Melbonrne
Parkville, Victoria 3052,Australi&
mansell@modmel.mrl.dsto.gov.au.
Abstract
Thispaperdescribesthe best fLrst searchstrategyused
by U-Plan(Mausell1993a), a planning systemthat
constnt~ quantitatively ranked plans given an
incompletedescription of an unce~environment.UPlanacceptsuncertainandincomplete
information
about
the environment,characterisesit using a DempsterShaferinterval, andgeneratesa set of multiplepossible
world sta~s. Plan cctmtruction takes place in an
abstractionhierarchywherestrategic decisimm
are made
beforetactical decisions.Searchthroughthis abstraction
hierarchyis guidedby a quantitativemeasure
(expected
fxdfilment) based on decision theory. This search
strategyis best first withthe provisionto Ul~_~_teexpectedfulfdmentsandreviewpreviousdecisionsin
the fight of planningdevelopments.
U-Plangenerates
multipleplans for multiplepossibleworlds,andwill
attemptto use existingplansfor newwm’ld
situatictm.A
super-planis thenconstructed,basedonmerging
the set
of plansandappropriatelytimedknowledge
acquisition
operators, whichare used to decide betweenplan
alternativesduringplanexecution.
1 Introduction
to U-Plan
Traditional planning systems describe the planning
problem as the composingof a course of action that
transforms the world from a given initial state to a
desired goal state. This description makes two
assumptions about the planning domain: complete and
accurate informationabout the ~rld is available; and the
environmentis static. Theseassumptionsensure that a
constructedplan can be successfully executedin such an
ideal world. However,such planners rarely produceplans
that workin the real world, that by its nature is dynamic
and its description is imprecise. To devise a useful plan
given uncertain and/or incomplete information about a
dynamic environment requires the removal of these
assumptions.
A major problemwhenplanning given incomplete and
uncertain informationabout the environment
is that it is
not possible to construct oneinitial state that precisely
tThis work was done under the CRCfor Intelligent Decision
Systems, while the author was employedby DSTOAustralia.
*Present address Materials Research Laboratory, PO Box 50,
Ascot Vale, 3032, Melbourne, Australia.
and nnambig~3~qly
represents the world. U-Planuses a
possibleworldsrepresentation,wherethe availableinitial
informationis used to construct every possible initial
state of theworld.Associatedwith each possible worldis
a numericalmeasureof belief specifying the degree to
whichthe evidencesupports each possible world as the
onethat representsthe true state of the world.
A hierarchical approach to planning is used as it
significantly
reduces
thesearchspacebyfirst planning
at
abstract levels, and then expandingthese abstract plans
into moredetailed plans. At the highestabstraction level
strategic decisionsare made,whileat the lowestlevels of
abstraction, ta~cal decisions about how best to
implement
the strategy, are made.U-Planutilises a set of
(predefined) goal reduction operators that encodehow
planninggoal is reducedby the operatoxasapplication.
Whatresults is a planninghierarchytree wherethe goals
are broken up into subgoals by the goal reduction
operators.This allows us to first makethe strategic
decisions, whichthen guidesall other decisions downto
the tactical implementation
of the subgoals. Ameasureof
expectedfulfilment (section 5.1) is used whenselecting
whichoperator to apply next.
In support
of hierarchical
planning,
eachpossible
worldis describedat a numberof predefinedabstraction
levels, resulting in decisions being madebased on a
descriptionof the worldat a suitablelevel of detail.
U-Planconstructs a plan for one possible world at a
time, the first plan being constructed for the possible
worldwith the greatest likelihoodof representingthe true
world. Beforea plan is constructedfor the next possible
world, the suitability of reapplyingan existing plan to
this worldis assessed. Associatedwith each plan is the
set of possible worldsit worksfor. If a plan partially
worksfor anotherpossible world(e.g. the strategy works
but someof the detail is different), then that part of the
plan is used for this possible world, and planning
continuesfromwherethe plan failed. Whena plan exists
for every possible world, the operator order of all the
plans is combinedto obtain a single planning tree that
brancheswhenthe operator executionorder differs. At
this point the ability to acquire additional knowledge
is
used. At each branch, a knowledgeacquisition operator
can be inserted to gather current informationabout the
state of the world and so determinewhichaction in the
planningtree to carry out next.
MANSELL
311
From: AIPS 1994 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved.
Central to planningusing U-Planis: the set of states
are representedat several abstractionlevels; the selection
of reduction operators is not based on the modaltruth
criterion, but dependenton a calculation of expected
fulfilment; the system will plan to acquire additional
knowledgewhenit is advantageous to do so, and an
attempt is madeto apply an existing plan to morethan
oneinitial state.
1.1
The Air Combat Domain
U-Plan has been applied to a simplified air combat
domain.The air combatdomainis dynamicand requires
agents to act given uncertainand incompleteinformation.
Generatinga plan for aircraft operating in such a domain
requires the consideration of a large numberof plan
strategies. Therole of an AI plannerin sucha domainis
to constructa planthat best fulfils the stated goalsusing
only available information, with the option to plan to
acquireadditional informationif required.
A simplified air combatdomainis introduced in this
paper that considers two agents: the defender (whose
objective is to defendhimselfand a designatedairspace)
and the aggressor (who is invading the airspace
controlled by the defender). Whilethe various actions
availableto the agents in this domainare diverse, certain
patterns in the moreabstract strategies can be identified.
For examplesomeof the actions available to the defender
are target monitoring, strategy selection, strategy
implementation,and evaluation of attack strategy. To
operate in such an environmentrequires a sophisticated
planning and reasoningsystem. Thestrategies available
to U-Planare centred around the selection of either a
Beyond-Visual-Range
Attack or a Visual-RangeAttack.
Thedifferent wayssucha strategies can be carried out are
numerous,each one involvesa uniquecourseof action.
It is intendedthat U-Plangeneratea suitable courseof
action for the defenderaircraft givenonly the information
available to the aircraft at plan time. This plan should
intend to acquire necessary information when
appropriate,havea high likelihoodto success,be suitable
to as manypossible worldsas feasible, and workfor the
worldsthat are mostlikely to be true. Theplan produced
by U-Planis intendedfor use in post missionanalysis of
the defenderaircraft, not as a real time planningaid (as
the systemis not runningin real time).
$ State
Representation
Whenan incomplete model of the world is all that is
available,a set of initial states canbe usedto describethe
alternative environments.U-Planemploysa set of initial
possiblestates (P-states) to describewhatmightbe true
the world. AP-state, ps(a), is a completedescription
one possible world using propositional statements. Each
P-state is described hierarchically with n levels of
abstraction, (ps(a)={tl(a) ... in(a)}) wheren is domain
312 POSTERS
dependentand selected during knowledgeengineering.
Thelevel ti(a ) is a completedescriptionof a worldat the
ith level. Thehighestlevel of abstraction gives a coarse
description of the state of the world. Thelowest level
gives a detailed view of the world. Intermediate levels
provide the description required to makea smooth
transition betweenboth extremes.
Associated with each P-state is a two valued
quantitative measure(an evidential interval (Shafer
1976)) that characterises the weight of evidence that
supportsthe P-state accuratelydescribesthe true state of
the world. This information is used by U-Plan in
determiningthe order in whichP-states are plannedfor,
and the final executionorder of operators. Adetailed
descriptionof howP-states are generatedandused can be
found in t~ansel11993a).
3 Reduction Operator
Planningoperators represent actions that the systemmay
performin the given domain.Therole of an action is to
changethe state of the world,the aimof an operatoris to
represent howapplying that action will change the
system’s view of the state of the world. U-Plan uses
reduction operators to give alternative methodsfor
achievingthe goal at a lowerlevel of abstraction, or at
the tactical level it describesthe direct effects of an action
on the P-state. Theseare SIPE-like operators (Wilkins
1988) where the closed world assumption is
implemented,and hierarchical planningused.
Each operator contains information about howand
whenit should be applied (Mansell 1993a). Included
this frameworkis the operator’s name,the abstraction
level it operatesin, the necessarypreconditionsthat must
be true of the P-state, andthe satisfiable preconditionsit
will attempt to maketrue. The plot of the operator
providesstep-by-step instructions on howto performthe
action represented by the operator. This includes a
description of the goal reduction operators that are
appliedat the next level of abstraction, or at the lowest
level of abstraction,howthe operatorchangesthe P-state.
A function for calculating the probability of the
reductionoperator succeedinggiventhe current P-state is
also included. The availability of such a function is
domainspecific and non-trivial to formulate. In the air
combatexamplediscussed here the function is obtained
empirically(basedon historical data). Theprobability
succcssdoesnot providesufficient informationto select a
reduction operator as it does not take into account the
goals of the system.It is for this reasonthat associated
with eachreductionoperatorlisted in the plot of a parent
reduction operator is a measure of fulfilment,
representing the degree to whichthe reduction operator
achievesthe goalof the parent.
U-Planuses a deductivecausal theozy (Wilkins1988),
to deducethe context dependenteffects of applying a
c’urca~
~ [Boo]
From: AIPS 1994 Proceedings. Copyright
© 1994, AAAI
(www.aaai.org). the
All rights
almsreserved.
of the system,andthe
[900,SO0]
SVt_ATrA~
[,~Ol
[2OOl
[SOOl
~n~ZN_c~Br~L~01~
f200l
[~o,~oJ~ol
ARD
[1000]
/
ATTA~
[
[700]--~_~9~.4D
]L~P
Figure 1: The strategic portion of the absttaction
hierarchy for the ~plified mr combatex~nple.
reduction operator to a P-state. The effects that are
deducedare considered to be side effects, wherethose
that are introduceddirectly by the reductionoperator are
the direct effects. Theuse of deducedeffects simplifies
the description of the operators by removingthe needfor
extensiveacid and delete lists. After the application of
each reduction operator a set of triggers arc used to
determineif the world has been changedin such a way
that the deductive rules need he applied. If so, the
deductivecausal theoryis usedto changethe P-state to be
consistent with all the effects of an action. Theside
effects of applyinganyreductionoperator are recordedin
the planninghierarchytree.
expansionof each layer in
the tree describesa moredetailed level of abstraction in
the plan wpresentedby the nodesin the tree.
5 Operator Selection
Manyclassical planningsystemsnsc a state-based search
strategy to solve planningproblems.To find a solution
one applies operators to a state description until an
expressiondescribingthe goal state is found. U-Planuses
a quantitative
measure,called expectedfulfilment, in an
abstractionhierarchyto guidethe selectionof operators.
A plan constitutes the successive application of
reduction operator from~ highest level of abstraction
(i.e. the goal function)downto the mosttactical detail.
the air combatexample(fig. l) the goal of defending
specifiedassets is accomplished
by first choosingwhether
to attack or turn awaythe aggressor, through specific
strategies and manoeuvres
available, downto the detailed
implementation
of a specific manoeuvre.
The following sections outline howthe reduction
operators are selected and implemented,and the process
that is continuallyreviewingthese decisions.
5.1 Calculating
Expected
Fulfilment
Goals in manydomainsdealing with uncertainty (for
instance the air combat domain) are not precise
requirements. Manygeneral goals can be fulfilled to
various degrees by acl,.ieving alternative subgoals.
However,not all subgoals are equally likely to be
4 The Abstraction
Hierarchy
achieved. We adopt an approach to planning by
determininga course, of action that is likely to maximise
U-plandoes not construct a state-based search tree, but
the expected fulfilment of our goal. Consequently,our
constructs a strategy hierarchy whichis a decision tree
plans are not exhaustive. Theydo not elaborate all the
like structure,, wherethe nodesin the hierarchyrepresent
alternative actionsrequiredin all possibleworlds.Rather,
a continuoustransition of actions fromthe strategic (at
they specify alternative actions that are likely to
the root node) to the tactical (at the leaf nodes).
maximisothe expected fulfilment of our goal in the
strategy hierarchy can be represented as an AND/OR possible worlds that are consistent with our partial
search tree, the root noderepresentingthe strategic goal
descriptionof the environment.
of the system,andthe leaf nodesrepresentingthe tactical
Expectedfulfilment is a quantitative measureused to
details of howthe goal is to be achieved. Eachnode in
rank the reduction operators whichachieve the goals of
the tree is a subgoalnoderepresenting the current goal
the active operator (i.e., the next reduction operator
and P-state, and certain pairs of nodes are cormectedby
chosen to be expanded) for selection purposes. For
arcs representingthe application of a reductionoperator
example,if Attack is the active operator who’sgoals we
that producesthis subgoalnode.
wish to achieve, the expectedfulfilment for BVRAttack
For example, figure 1 shows part of the strategy
and VRAttack(the operatorsthat achievethis subgoal)is
hierarchyfor a simplified air combatdomain.Thegoal of
calculatedandusedas a basis for the selection.
defendingdesignatedassets can he achievedby either an
Probability theory provides an effective methodfor
Attack or Turn_Away.Thestrategy hierarchy showsthat
choosing actions capable of producing consistently
there are two reduction operators that can be applied to
accurate choices. Information such as intelligence
achieve anAttack, the BVR_Attack(or BeyondVisual
reports, preferences, and raw data can be encodedand
Range attack) and the VR_Attack (or Visual Range
manipulated by a probabilistic inference engine to
attack). Thenext level presents the manoeuvresapplied
produce useful recommendations.Whereasprobabilities
to achieve these specific attacks, whichare achievedby
are usedto representthe likelihoodof events, fulfilments
the implementationof tactical actions (not shown).The
are used as a local measureof the degree to whichthe
applicationof these operatorsrepresentsa clarification of
consequentof the action achieves the intendedgoal and
MANSELL
313
From: AIPS 1994 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved.
the desirability of achievingthe goal using that action.
Thetermfulfilment is usedto captureboth the essenceof
utility scaled accordingto the desire to use a particular
approach.Theterm utility is not used in this description
to avoidconfusion,as there are subtle differencesin how
they are usedand whatthey represent.
The expected fulfilment is used as a measure of an
action’s likelihood to produce the consequent that
achievesthe agent’s goals. If weuse the measureF(c)
represent the degree of fulfilment of consequentc, then
the overall expectedfulfilmentassociatedwith action a is
givenby:
EF(a) = F(c)P(cla,e),
(1)
where, P(cla, e) is the probability of achieving
consequence¢, conditioneduponselecting action a and
observing evidence e. For example, to calculate the
expectedfulfilmentof the Attackoperator in figure I, the
probability of successfully executing an attack in the
given P-state is multiplied by the degree of fulfilment
obtainedby executingthe action (depictedin figure 1 as
the first number
in squarebracketsabovethe operator).
Theexpectedfulfilment of action a, EF(a),is regarded
as a gauge of the merit of action a. The expected
fulfilment is used as a procedure for choosing among
alternative (or competing) actions. Whengiven the
choice betweentwo action (eg, Attack and Turn-Away)
the selectionis basedon the actionthat yields the highest
expected fulfilment (ie, EF(Attack)or EF(Turn-Away)).
This result will dependon the description of the P-state
whenthe selection is made.This process can be thought
of as establishing a rank order in which one should
attemptedto apply them.
The semantics and justification of fulfilments are
identicalto thoseoutlinedfor utility theory.Utility theory
is not simplya convenientmathematicalformula, but is
basedon studies of the psychologicalattitude towardrisk,
choice, preference,and likelihood. Theessenceof utility
theory, and therefore fulfilment, is captured by the
axioms of utility Theory (Von Neumann
& Morgenstern
1947).
5.2 Applying an Operator
Oncethe reductionoperatorsthat achievethe goals of the
parent operator have been ranked using the expected
fulfilment calculation, they can be tested to determine
their suitability to the P-state. U-Planwill attempt to
applythe reductionoperatorsto the P-state in the order in
which they were ranked (by their EF), until
appropriateaction is found.If the necessarypreconditions
of a reductionoperatorare true in the active P-state, then
the reductionoperator is provisionallyselected, else the
planfail for that operatoris applied(this usuallyinvolves
backtracking). Whena reduction operator that satisfies
the necessary preconditions has been found, the
satisfiable preconditions
are tested. If anyof these are not
314 POSTERS
true, U-Plancan attempt to satisfy themusing reduction
operators of equal or lower abstraction. If these
preconditionsare not satisfied, the operator is rejected,
andit’s planfail procedureis implemented.
Onceboth sets of preconditionsof a reductionoperator
can be shownto be true in the active P-state, the operator
is accepted and its plot can be applied. The plot
represents the effects the reduction operator has on the
state of the world, andthe subgoalsthat maybe used to
achieve this subgoal. Whenapplying the plot, the next
level of the strategy hierarchyis exposed,andagain the
subgoalwith the highestexpectedfulfilmentis selectedto
be expanded next. The plot of operators ~presents
actions at the lowestlevel of abstraction specifyhowthe
P-state is physicallychangedbytheir application.
This process of applyingoperators continuesuntil the
next layer of the strategy hierarchyhas beenexposed.At
this point, the earlier selection of specific actions are
reviewedas describedbelow.
5.3 Reviewing
Selected
Operators
When
constructinga strategyhierarchyit is possiblethat,
as a plan’s detail is filled out, it becomes
less likely to
succeed. This is partially becausethe initial strategic
decisionsare basedon informationat a morecoarse level
of abstraction. Asthe plan is expandedandmoretactical
decisions aboutthe implementation
of specific strategies
are made, the expected fulfilment of specific plan
branchesmaydecreases. Also, the EFcalculation for a
higher level operator mayinclude a range of possible
useful actions. However,as the plan becomesmore
detailed, certain alternatives will be discarded,possibly
resulting less that ideal actions beingselected, reducing
the true e, xp~edfulfilmentof the plan branch.
This makesit important to review earlier decisions
while planning. After the application of a group of
reduction operators U-Plan compares the e~ected
fulfilment of the current subgoals,with those of previous
subgoals, to determinesif the current subgoal remains
favourable. U-Planuses an offset added to the current
subgoal to take into account expected lower EF as
increaseddetail is addedto the plan. Includingan offset
is an iterative deepeningstrategy includedto avoid the
problemof the system jumpingaround from branch to
branchin the strategy hierarchy. Theoffset value will
dependon the difference in abstraction level of the
subgoals. Theiterative deepeningstrategy will not be
discussionin the remainderof the paper, whichwill focus
on the moregeneris process.
To review these selections one must have a wayof
updatingthe EFvalues calculated for the nodes in the
abstraction hierarchy basedon the detail addedto that
nodesplanningbranch.A set of updaterules are used to
re-evaluate the fulfilment and probability of previously
expanded operators given the most recent planning
From: AIPS 1994 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved.
developments.The update rules used dependon whether
the nodeproducesan AND
or ORbranch in the tree.
In the case whenan operator is expandedproducingan
ORbranchin the abstraction hierarchy, the updaterules
used to determine the fulfilment and probability of a
parentnodegivena set of possiblechildren are givenby:
I MAX
F(parent) = {F(child)]childreEF(child)}
, (2)
]~I~o.o.,,
[85o,81o,7oo1
/VR
ATFACK
-
(
/ SET_~.ARn~O
/ {iooo,o.9;
[8001
VISUAL LOCK
[sso.slo.6~ts] ACQUmE
j ~ [~LOSE_D4
~r_TARGET ~ {800~ "0/
/
’
’ "
AR LOCK
pooo,
o.80~\ gaoo.s.o}
0ooo.~71
{8o~o.81)
\
I MAX
e(~nO= {e(ch~ld)[childrenF~(child)L
VntE
~ARM_WEAPON
READY,m~{IO00,1.O}
{zooo, o.9} ~mRE~N
{ZO00,O.9}
{zooo,o.o}
Wherechildren is the set of children operatorsthat have
been expandedor considered for expansionand have not
beenrejoct~ Simplystated, rules 2 and3 tell us that the
fulfilment andprobability values for the parent of an OR
nodeis equalto the fulfilmentandprobabilityof the child
nodewith the greatest expectedfulfilment that has not
beenruled inapplicableto the P-state (i.e. dueto failure
of preconditionsduring expansion).If the operator with
greatest EFis not fromthe current subgoal, a changein
the planningdirection occursand is recorded.
The updating of the parent reduction operator at an
ANDnode involves updating the probability and
fulfilmentas follows:
I MIN
F(parent) = {F(child)lchildreF(Child)}
, (4)
P(parent) = I-I P(child).
ffoo]
(5)
children
In the AND
case the rules and their justifications are
less obvious(Mansell1994). The fulfilment of a parent
operator is replaced by that of the child fromthe set of
children with the lowest fulfilment. Normally, when
confronted by an AND
node, the children are given the
samefulfilment as that of the parent. Thejustification
being, that as the parent can ouly be achievedby a single
sequence of actions, then this reduction is simply a
refinement of the parent operator 0.e., these actions
should wholly achieve the desired goal). Howeverthe
situation mayarise when, at a lower level in the
abstraction hierarchy, the fulfilment valuefor oneof the
child operators mayitself be updated(by its subsequent
descendants) to a new, lower valuer. Whensuch
circumstancearise, the child operator is not fulfilled
completely by its descendant, and consequently, the
parent operator is no longer completelyfulfilled by its
children.
In the subset of the air combatexamplegiven in figure
2, a simple scenario for a Close_Inmanoeuvre
operator is
evaluated. Theexpectedfulfilment for this operator is
calculated (the first numberin the squarebrackets above
the operator, i.e., [850]) based on the fulfilment and
probability values (shown in the braces below the
Figure 2: Anexampleof the abstraction hieraroby for a
Close In manoeuvre scenario that demon~ates the
updating of Palfilments and probabilities. Progressive
(fulfilment, probabilUy)and[EF]values are givenfor each
operator.
operator, i.e., 1000and0.85 respectively) obtainedfrom
the operator. Onexpandingthe Close In operator, the
next level of the plan is uncovered.This showsthat the
Set_Bearing, Acquire_Targetand Fire_Readyoperator
are to be applied. Thefulfilments and probabilities for
these are calculated and shownin braces below the
operators. As this is an AND
operation, update rides 4
and5 are usedto updatethe fiflfilments andprobabilities
for the parent, Close_In, operator (shownin the second
set of braces belowthe operator, (1000,0.81)). These
updatedvalues are used to calculate the updatedEFvalue
for the Close_Inoperator(i.e., [810]).
Figure 2 also includes an examplewhererules 2 and 3
are usedto updatethe fulfilmentandprobabilities for the
parent of an ORnode. In this case the Acquire_Target
can be achieved by either a I~sual_Lock or a
Radar_Lock.The Visual_Lockis chosen as it has the
higher EF of the two. However,the V~sual
Lock has a
m
lower fulfilment than its parent and this is propagated
back through the branch updating the Close_In EF to
[648]. Asa result of propagatingthese valuesbackup the
branch, the Side operator becomesfavourable over the
expandedbranch Close_In.
5.4 Sensitivity
of Expected
Fulfilments
The ~ fulfilment
value is calculated
by
multiplyingthe probability of success of an operator by
the degreeto whichthe operatorfulfils its intendedgoal.
It is therefore useful to knowthe relative sensitivity
(Karnavas,Sanchez,and Bahill 1993) of probability and
fulfilment on the expected fulfilment function. The
relative-sensitivity of a function F to the parameterct
over the normaloperatingpoints is givenby:
SF= %changein F °~’//F
~ ~nor = o~ar//a = ~[NOP FO’
MANSELL
315
From: AIPS 1994 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved.
whereNOPand the subscripts 0 meansall functions and
their parameters are evaluated over their normal
operatingpoints. Given,the expectedfulfilment function
in equation 1, the relative-sensitivities fimctions are
computedas follows:
NapEFoFo,
$~ =--~ F0 P
CO
(8)
Therelative-sensitivities of probability andfulfilment
on the expected fulfilment are independent. This
informationis used whendeterminingthe certainty with
whichprobabilities and fulfiknents mustbe knowngiven
a set of expected fulfilments. For example,given the
choice betweentwo actions with close EFvalues, one can
calculate the degreeof confidencein the fulfilmentvalues
required of the actions, given the percentagedifference
betweenthe actions probabilities.
6 Plan Reapplication
U-Plan applies plan reapplication in an attempt to
determineif a plan generatedfor one initial P-state can
be adoptedfor anotherinitial P-state. Thedesiredresult
being fewer plans than the numberof initial P-states.
This is implementedby attempting to reapply plans
generatedfor oneinitial P-stateto other initial P-state.
Aplan is reapplicableif all the reductionoperatorsin
the plan (that are not redundant)havetheir preconditions
metunderthe newinitial P-state, andwhenapplied result
in the goal state being achieved. If a plan, during
re, application,fails dueto the unsuccessful
applicationof
an operator, that plan is not entirely discarded. U-Plan
will attemptto use the part of the plan that wassuccessful
and planning continues from the point where the plan
failed. Thedesire is to construct plans with the sameor
similar strategies by reusing, at least part of, the plan at
the high level of abstraction. Whenmorethan one plan
partially worksfor a newinitial P-state the best plan
(Mansell1993a)is used.
7 Super-Plans
Onceplans exists for all the P-states, with supportand
plausibility abovesomethreshold, a single super-planis
constructed. This is achievedby mergingthe set of plans
constructedfor the set of initial P-states, that is applying
identical operator sequencesand branchingat the point
whereplans differ. At each branch in the super-plan a
knowledgeacquisition operator is added, attaining the
informationrequired to select whichaction in the superplan to apply next. Thecase mayarise whenthe required
informationto differentiate betweenalternative branches
is not available.In this case, the selectionis basedonthe
316 POSTERS
degree of evidence supporting for each branch of the
super-plan (see (Mansell1993a, Mansell1994) for more
detail). This final step of producinga super-planis an
importantpart of presentinguseful coarseof action that
couldbe applied by the system.
In most cases, U-Planproducesa super-plan in less
time than it wouldtake a traditional planner to produce
one plan for every possible world (see (Man~ll1993a,
Mansell1993b)for moredetails on these results).
9 Conclusion
U-Plan is a hierarchical planner that deals with
information represented at a level of abstraction
equivalentto the action
being investigated. Outlinedin
this paper is the quantitative best-first search method
employed by U-Plan for operator selection in an
abstraction hierarchy. As this process is a forward
propagatingpartial decision tree, a methodfor reviewing
previousdecisionsin the light moredetailed information
is included. The update rides are presented in some
detail, and an exampleof their operation presented. UPlan has provedto be a effective planningsystemin the
air combatdomain(Mansell 1993a), and the expected
fulfilment calculation a reliable formulafor operator
selection.
Acknowledgments
I would like to thank Dr. GrahameSmith and Dr.
Elizabeth Sonenbergfor their manyinsightful comments.
References
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