as planning - cse.iitd.ernet.insak/courses/foav/planning-as-mc-slides.pdf · planning as model chec...
TRANSCRIPT
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PlanningasModelChecking
MarcoPistore
DepartmentofInformaticsandTlc.UniversityofTrento-Italy
e-mail:[email protected]
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The“Classical”PlanningProblem
•Domain=States(blockpositions)+Actions(moves)
•InitialState(“RedonTable”,“BlueonTable”,“GreenonBlue”)
•GoalState(“BlueonGreen”,“GreenonRed”,“RedonTable”)
•Plan(“MoveGreenonRed”,then“MoveBlueonGreen”)
PlanningProblem:Givenadomain(statesandactions),aninitialandgoalstate,theplanningproblemistheproblemtofindaplanofactionsthatleadsfromtheinitialstatetothegoal
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The“Classical”PlanningProblem(cont.)
Abasicassumption...
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The“Classical”PlanningProblem(cont.)
Abasicassumption...nouncertainty...
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The“Classical”PlanningProblem(cont.)
Abasicassumption...nouncertainty...
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PlanningunderUncertainty
Whathappensif...
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PlanningunderUncertainty
Whathappensif...
The“Classical”PlanningAnswer:Planforthenominalcase!
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PlanningunderUncertainty
Whathappensif...
The“Classical”PlanningAnswer:Planforthenominalcase!
BUT...
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PlanningunderUncertainty
Whathappensif...
The“Classical”PlanningAnswer:Planforthenominalcase!
But:
•thissolutionisnotalwaysviable(planningunderuncertainty)
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PlanningunderUncertainty
Whathappensif...
The“Classical”PlanningAnswer:Planforthenominalcase!
But:
•thissolutionisnotalwaysviable(planningunderuncertainty)
•thereisamuchbetterapproach(planningasmodelchecking)
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Outline
•Whyplanningunderuncertainty?
•“Classical”planningasmodelchecking
•Planningwithtemporallyextendedgoals
•Conclusions
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Outline
•Whyplanningunderuncertainty?
•“Classical”planningasmodelchecking
•Planningwithtemporallyextendedgoals
•Conclusions
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PlanningunderUncertainty:Non-Determinism
Planforthenomicalcase?
Inmanydomains:
•actionshavenon-nominaloutcomesthatarehighlycritical.
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PlanningunderUncertainty:Non-Determinism
Planforthenomicalcase?
Inmanydomains:
•actionshavenon-nominaloutcomesthatarehighlycritical.
•thereareactionswithnonominaloutcome.
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PlanningunderUncertainty:Non-Determinism
Planforthenomicalcase?
Inmanydomains:
•actionshavenon-nominaloutcomesthatarehighlycritical.
•thereareactionswithnonominaloutcome.
Difficulties:
•aplanmayresultinmanydifferentexecutions.•theplannermustgenerateplansthathaveconditional
behaviours.•...
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PlanningunderUncertainty:PartialObservability
Theassumptionofclassicalplanning:observationsnotneeded!
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PlanningunderUncertainty:PartialObservability
Theassumptionofclassicalplanning:observationsnotneeded!
Butinseveralrealisticproblems,observationsareneeded.
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PlanningunderUncertainty:PartialObservability
Theassumptionofclassicalplanning:observationsnotneeded!
Butinseveralrealisticproblems,observationsareneeded.
Difficulties:
•thestateofthesystemisonlypartiallyvisibleatrun-time.
•differentstatesareindistinguishableforthecontroller,namelyobservationsreturnsetsofstatesratherthansinglestates.
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PlanningunderUncertainty:Extendedgoals
Theassumptionofclassicalplanning:goalsaresetsofstates!
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PlanningunderUncertainty:Extendedgoals
Theassumptionofclassicalplanning:goalsaresetsofstates!
Butinseveralrealisticproblems,goalsareconditionsontheentireexecutionpathofaplan!
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PlanningunderUncertainty:Extendedgoals
Theassumptionofclassicalplanning:goalsaresetsofstates!
Butinseveralrealisticproblems,goalsareconditionsontheentireexecutionpathofaplan!
•Goalsmayinvolvetemporalconditions(e.g.,airconditioner,safetyconditions)
•Goalsmayspecifyrequirementsofdifferentstrenghtthattakeintoaccountnondeterminismandpossiblefailures.
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PlanningunderUncertainty:Extendedgoals
Theassumptionofclassicalplanning:goalsaresetsofstates!
Butinseveralrealisticproblems,goalsareconditionsontheentireexecutionpathofaplan!
•Goalsmayinvolvetemporalconditions(e.g.,airconditioner,safetyconditions)
•Goalsmayspecifyrequirementsofdifferentstrenghtthattakeintoaccountnondeterminismandpossiblefailures.
Difficulties:
•Extendedgoalsaddafurthercomplexitytothealreadycomplicatedproblem.
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PlanningunderUncertainty:DifferentDimensions
probabilistic
non-determ.
deterministic full obs.
partial obs.
no obs.
reachability goals
extended goals
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WhyPlanningunderUncertainty?
DomainPlanner
Plan
Controller
SystemActions
Observations
Goal
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BecauseitisUseful!RealCase(I)
3456789
AAB
SDBSDBSDBSDBSDBSDBSDB
OPERATOR
. . . . . .
SCHEDULER
PROCESS i
PROCESS n
Safety Logic
PROCESS 1
COMMANDS
MANUAL
PERIPHERAL CONTROLS
PERIPHERAL STATUS
DEVICESPHERIPHERAL
Sourcesofuncertainty:
•operator,traindynamics,faults(actionswithuncertaineffects)•localsensors,neighborscontrollers(partialobservability)
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BecauseitisUseful!ARealCase(II)
Dir. Gas
Interfaccia Utente
ON/OFF
ALARM/RESET
ALTA PRESSIONE
FN
ON/OFF/RESET
REQUEST
OPERATION
TERMICA
Evapor
Condensatore
Dir. Gas
Alta
pre
ssio
ne
Con
trol
lo
Con
trol
lo V
alvo
la
Ven
tole
Tem
pera
tura
Ven
tole
Bassa Pressione
Comandi
Compressore
Termica
Compressore
Controllo led
Pressione tasti
Tem
pera
tura
term
oreg
olaz
ione
Flussostato
Condensatore
Bassa Pressione
Flussostato
Controller
Sourcesofuncertainty:
•operator,temperature,faults(actionswithuncertaineffects)•unaccessiblevariables(partialobservability)
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Outline
•Whyplanningunderuncertainty?
•“Classical”planningasmodelchecking
•Planningwithtemporallyextendedgoals
•Conclusions
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ModelChecking
ModelChecking:atechniquetovalidateaformalmodelofasystemagainstalogicalspecification.
temporal formula
finite−state model
p
q
G(p −> Fq)
ModelChecker
p
yes!
no!
counterexample
q
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PlanningbyModelChecking
PlanningbyModelChecking:atechniquetosynthesizeaplanfromaformalmodelofadomainandalogicalspecificationofagoal.
planning domain
goal
α
β
no plan!
yes!
Planner
reach r
p
q rα
βχ
plan
α
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ModelCheckingandPlanning(informal)
•Themodelcheckingproblem:givenamodelMofasystemandapropertyϕ,where...
–ModelMisrepresentedasaFSM.
–Propertyϕisatemporallogicformula.
checkwhetherthepropertyissatisfiedinthemodel:M|=ϕ
•Theplanningproblem:givenamodelMofasystemandagoalϕ,findaplanπthatachievesthegoal:Mπ|=ϕ
•Theplanningvalidationproblemisamodelcheckingproblem
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PlanningunderUncertaintybyModelChecking
Keyingredients:
2Planningdomainsasnon-deterministicstate-transitionsystems
2Goalsasformulasintemporallogic
2Plangenerationby(BDD-based,symbolic)modelcheckingtechniques
Results:
2Well-founded:formalframework,completeandcorrectalgorithms
2General:planninginnondeterministicdomains,underpartialobservability,andfor(temporally)extendedgoals,...
2Practical:implementationintheModelBasedPlanner(MBP)-automaticplanningforproblemsoflargesize
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TheFirstResults:PlanningforReachabilityGoals
•Domains:nondeterministicautomata
•Goal:setofdesiredfinalstates
•Plans:memory-lesspoliciesthatmapstatestoactions
•Solutions:
1.Weaksolutions:“optimisticplans”[ECP97]
2.Strongsolutions:“safeplans”[AIPS98]
3.Strongcyclicsolutions:“iterativetrial-and-errorstrategies”[AAAI98]
A.Cimatti,M.Pistore,M.Roveri,P.Traverso.
Weak,Strong,andStrongCyclicPlanningviaSymbolicModelChecking.ArtificialIntelligence,147(1–2),2003
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AnExample
DoorUncontrollable
Sensorsare not perfect
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AnExample
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Reachabilitygoals
Strongsolutions:Plansthatareguaranteedtoreachthegoal•allexecutiontracesreachthegoal
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Reachabilitygoals
Weaksolutions:Plansthatmayachievethegoal•atleastoneexecutiontracereachesthegoal
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Reachabilitygoals
StrongCyclicsolutions:trial-and-errorstrategies
•goalisreachablefromallthestatesofexecutiontraces•solutionsthatareguaranteedtoreachthegoalunderthe
fairnessassumptionof“noinfinitebadluck”
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Implementation:TheMBPplanner
•MBP:AModelBasedPlanner(http://sra.itc.it/tools/mbp/)
•MBPbuiltontopofastate-of-the-artsymbolicBDD-basedmodelchecker,NUSMV(http://sra.itc.it/tools/nusmv/)
•MBPhastheplanningalgorithmsforweak,strong,andstrongcyclic(localandglobal)planning
•MBPhasalgorithmsforconformantplanning,forplanningunderpartialobservability,andforplanningfortemporallyextendedgoals
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BDD-basedSymbolicModelChecking:Intuitions
SymbolicModelChecking[McMillan’93]basedonBDDs[Bryant’86]:
2Exploresetsofstatesrepresentedsymbolicallyasbooleanformulas
2BooleanformulasasOrderedBinaryDecisionDiagrams(BDDs)
2OBDDsrepresentstheassignmentssatisfying(andfalsifying)abooleanformula
2Operationsoversetsofstates(e.g.union,intersection)asbooleanoperations(e.g.conjunction,disjunction)implementedastransformationsoverBDDs
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PlannigasSymbolicModelChecking:Intuitions
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MoreResultsonPlanningforReachabilityGoals
•StrongSolutionswithPartialObservability:uncertaintyinobservations[Bertoli&Cimatti&Roveri&TraversoIJCAI01]
•PlanningforTemporallyExtendedGoals[Pistore&TraversoIJCAI01-AAAI02]
•Optimistic,Pessimistic&StrongCyclicplanninginUMOP[Jensen&VelosoJAIR00]
•Adversarialweak,strong,andstrongcyclicsolutions:environmentevents[Jensen,Veloso,BowlingECP01]
•SetBranchBDDbasedsearchenvironmentevents[Jensen&VelosoAIPS03]
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Outline
•Whyplanningunderuncertainty?
•“Classical”planningasmodelchecking
•Planningwithtemporallyextendedgoals
•Conclusions
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MotivationsforExtendedGoals
Themainmotivationsforintroducingextendedgoalsare:
•safeplanning:
–safetyconditions(“avoiddangerousstates”)complementthemaingoal.
•planningforreactivesystems:
–infiniteplanthatreactstoeventsintheenvironment(maildelivery,elevatorsystem,...).
•non-determinism:
–needtoexpress(reachability/maintainability)goalsofdifferentstrength(preferences).
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Anexample
storelab
dep
Goal“reachdepandavoidlab”:
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Anexample
storelab
dep
Goal“reachdepandavoidlab”:
•“Doreachdepanddoavoidlab”isunsatisfiable
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Anexample
storelab
dep
Goal“reachdepandavoidlab”:
•“Doreachdepanddoavoidlab”isunsatisfiable•“Doreachdepandtrytoavoidlab”issatisfiablebyplan→
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Anexample
storelab
dep
Goal“reachdepandavoidlab”:
•“Doreachdepanddoavoidlab”isunsatisfiable•“Doreachdepandtrytoavoidlab”issatisfiablebyplan→
•“Trytoreachdepanddoavoidlab”issatisfiablebyplan→
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Planningforextendedgoals
Objectives:
•Planninginnon-deterministicdomainsforextendedgoals
•Dealinginpracticewithnon-determinismandcomplexgoalsindomainsoflargesize
Problems:
•Howcanweexpressextendedgoals?
•Whichkindofplansmustbegenerated?
•Planningalgorithm?
•Howcantheplanningalgorithmdealinpracticewithdomainsoflargesize?
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The“PlanningbyModelChecking”approach
2ExtendedgoalsasformulasintheCTLtemporallogic:temporalconditionson“allpossiblestates”andon“somestates”resultingfromactionexecutions.
2Plansencodingconditional,iterative,andhistorydependentbehaviours,strictlymoreexpressivethanmemory-lesspolicies
2PlanningalgorithmsbasedonBDD-basedSymbolicModelCheckingtechniques,designedtodealwithlargestatespaces
2ImplementationintheModelBasedPlanner(MBP),aplannerbasedonthestate-of-theartsymbolicmodelcheckerNuSMV
2Experimentalresultsshowthattheplanningalgorithmworksinpractice
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ExtendedGoalsareCTLformulas
CTL:g::=b|g∧g|g∨g|AFg|EFg|AGg|EGg|
A(gUg)|E(gUg)|A(gWg)|E(gWg)
Intuition:CTLcombines
•temporaloperators:F(eventually),G(always),U(until)...
FGU
•pathquantifiers:A(forallevolutions),E(forsomeevolution)
AE
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ReachabilityGoalsinCTL
GivenaplaningdomainΣ(astatetransitionsystem),andagoalφ(aCTLformula),findaplanπsuchthatΣπ|=φ
1.WeakSolutions:φisEFp-plansthatmayreachthegoal
2.StrongSolutions:φisAFp-plansguaranteedtoreachthegoal
3.StrongCyclicsolutions:φisA(EFpWp)-iterativetrial-and-errorstrategieswhoseexecutionsalwayshaveapossibilityofterminatingand,whentheydo,theyareguaranteedtoreachthegoal.
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MaintainabilityGoalsinCTL
GivenaplaningdomainΣ(astatetransitionsystem),andagoalφ(aCTLformula),findaplanπsuchthatΣπ|=φ
1.WeakMaintain:φisEGp-plansthatmaymaintainthegoal
2.StrongMaintain:φisAGp-plansguaranteedtomaintainthegoal
3.StrongCyclicMaintain:φisAGEFp-“maintainthepossibilityofreachingp”
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ExamplesofCTLgoals
DoreachdepanddoavoidlabAFdep∧AG¬lab
DoreachdepandtrytoavoidlabAFdep∧EG¬lab
TrytoreachdepanddoavoidlabEFdep∧AG¬lab
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Plansforextendedgoals:anexample
lab store
dep
•Thelabisadangerousroom—itmayharmtherobot
•Thegoalis“Continuously,trytoreachdepanddoreachstore”
•CTLgoal:AG(EFdep∧AFstore)
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Plansforextendedgoals:anexample
store
dep
lab
Goal“Continuously,tryreachdepanddoreachstore”
•Satisfying“tryreachdep”(EFdep),...
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Plansforextendedgoals:anexample
storelab
dep
Goal“Continuously,tryreachdepanddoreachstore”
•Satisfying“doreachstore”(AFstore),......
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Plansforextendedgoals:anexample
store
dep
labstorelab
dep
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Plansforextendedgoals:anexample
lab
dep
store
Goal“Continuously,tryreachdepanddoreachstore”
•Satisfying“tryreachdep”...
•Satisfying“doreachstore”...
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Plansforextendedgoals:anexample
Context 1Context 2
ExecutionContextsarenecessaryforthedifferentintentionsoftheexecutor:
•Context1:“tryreachdep”
•Context2:“doreachstore”
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Plans
Aplanisdefinedintermsofanactionfunctionact:S×C⇀A,andacontextfunctionsense:S×C×S⇀C
statecontextactionnextstatenextcontext
swcontext1go-rightswcontext2
swcontext1go-rightdepcontext1/2
swcontext2go-upstorecontext1
...............
Context 1Context 2
store
storestore lablab
depdep sw
ne
sw
ne
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Plans
APlanforadomainDisatuple〈C,c0,act,sense〉,where:
•Cisasetofexecutioncontexts,•c0istheinitialexecutioncontext,•act:S×C⇀Aistheactingfunction,•sense:S×C×S⇀Cisthesensingfunction.
Theidea:
•act(s,c)returnstheactiontobeexecutedbytheplan,•sense(s,c,s
′)associatestoeachreachedstates
′thenew
executioncontexts.
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PlanExecution
•AtransitionofplanπinDisatuple(s,c)a
→(s′,c
′)suchthat:
–sa
→s′,
–a=act(s,c),and
–c′=sense(s,c,s
′).
•Arunofplanπfromstates0isaninfinitesequence(s0,c0)
a0
→(s1,c1)a1
→(s2,c2)a2
→(s3,c3)···
•TheexecutionstructureΣpofplanπhas:
–states(s,c)
–transitions(s,c)→(s′,c
′)
•Planthatsatisfiesagoal:Planπsatisfiesgoalgfrominitialstates0,writtenπ,s0|=g,if(s0,c0)|=ΣπgaccordingtothestandardsemanticsofCTL.
⇒planvalidationasmodelchecking:Σπ|=g
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PlanningAlgorithm
functionsymbolic-plan(g):Plan
aut:=build-aut(g)
assoc:=build-assoc(aut)
plan:=extract-plan(aut,assoc)
returnplan
1.build-autconstructsanautomatonthatcontrolsthesymbolicsearch(statesarecontexts)
2.build-assocassociatesasetofstatesintheplanningdomaintoeachstateinthecontrolautomaton.
3.extract-planconstructsaplanfromthestatesassociatedtothecontexts.
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Phase1:buildthecontrolautomaton
Whenwebuildthecontrolautomatonforthegivengoal:
•thecontrolstatesarethecontextsoftheplanthatisbeingbuilt
•thetransitionsrepresentthepossibleevolutionsofthecontextswhenactionsareexecuted.
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Phase1:buildthecontrolautomaton
TwocontextsareneededforgoalAG(EFdep∧AFstore):
•onecorrespondingEFdep
•onecorrespondingAFstore
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Phase1:buildthecontrolautomaton
store
store
InordertosatisfycontextAFstore,findanactionsuchthat:
•ifstoreholds,then:
–contextEFdepissatisfiableforALLtheoutcomes
•ifstoredoesnotholdthen:
–contextAFstoreissatisfiableforALLtheoutcomes
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Phase1:buildthecontrolautomaton
dep
SOMEALL−OTHER
dep
InordertosatisfycontextEFdep,findanactionsuchthat:
•ifdepholds,then:
–contextAFstoreissatisfiableforALLtheoutcomes
•ifdepdoesnotholdthen:
–contextEFdepissatisfiableforSOMEoftheoutcomes–contextAFstoreissatisfiableforALLtheotheroutcomes
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Phase1:buildthecontrolautomaton
dep
store
SOMEALL−OTHER
store dep
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Phase2:search
Inthesearchphasethealgorithmassociatestoeachcontextthesetofstatesthatadmitaplanforthecontext.
•Initially,allthedomainstatesareassociatedtoeachcontext
•Theassociationisiterativelyrefined:
–Acontextischosen
–Thecorrespondingstatesarecomputed,basedonthecurrentassociation
–Theassociationforthecontextisupdated
•Thesearchterminateswhenafixpointisreached
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Phase2:search
~dep
dep
~store
store
SOMEALL−OTHER
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Phase2:search
~dep
dep
SOMEALL−OTHER
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Phase2:search
~store
store
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Phase2:search
~dep
dep
SOMEALL−OTHER
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Step3:planextraction
•Findsuitableactionsforthestatesassociatedtothecontexts.
•Alltheinformationnecessarytoextracttheplanhasbeenalreadycomputedinthesearchphase.
•Reachabilityanalysisallowsforsimplerplans.
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Step3:planextraction
~dep
dep
~store
store
SOMEALL−OTHER
go−south go−south
go−eastgo−northgo−north
go−west
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Propertiesofthealgorithm
•Thealgorithmalwaysterminates.
•Thealgorithmiscorrectandcomplete:
–wheneverplansexist,thealgorithmfindsone;
–wheneverthereisnoplan,thealgorithmreturnsfail.
•Thecriticalstepforperformanceis“symbolicsearch”.
•ThealgorithmforextendedgoalsisimplementedinMBP
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PlanningforCTLgoals:ExperimentalEvaluation
Aims:
•Testthescalabilityoftheapproach(domainsize,nondeterminism,goalcomplexity)
•ComparisonwithSimplan[Kabanzaet.al.](LTLgoals,explicitstate,handcodedstrategies)
•Comparisonwithspecialpurposestrong(cyclic)MBP
Results:
•Deterministiccase:SimPlanhandcodedstrategieswin•Nondeterministiccase:
–MBPperformancesdonotdegradewithnondeterminism–MBPoutperformsSimPlanevenwithhandcodedstrategies–Planningforextendedgoalscomparablewithspecialpurpose
strong(cyclic)algorithms
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PlanningforCTLgoals:conclusions
•Goalswithtemporalconditionsonthewholeexecutionpath
•Goalsthattakeintoaccountnondeterminism(“forall”,“forsome”actionoutcomes)
•ImplementationintheMBPplanner(http://sra.itc.it/tools/mbp/)
•Experimentalevaluationshowsthattheapproachispractical
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PlanningforCTLgoals:Conclusions
•Goalswithtemporalconditionsonthewholeexecutionpath
•Goalsthattakeintoaccountnondeterminism(“forall”,“forsome”actionoutcomes)
•ImplementationintheMBPplanner(http://sra.itc.it/tools/mbp/)
•Experimentalevaluationshowsthattheapproachispractical
...BUT...
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LimitsofCTLgoals
RD
U A
S
Alarm!
Alarm!
SwitchToD
TrytoreachtheDirectposition,and...ifyouFail,DoreachtheAlarmposition
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LimitsofCTLgoals
RD
U A
S
Alarm!
Alarm!
SwitchToD
TrytoreachtheDirectposition,and...ifyouFail,DoreachtheAlarmposition
Problem(1)...EFD–doesnotcaptureintentionality!!
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LimitsofCTLgoals
RD
U A
S
Alarm!
Alarm!
SwitchToD
TrytoreachtheDirectposition,and...ifyouFail,DoreachtheAlarmposition
Problem(2)...CTLformulasdonotcapturepreferencesandfailurehandling!!
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EaGLe:anExtendedGoalLanguage
EaGLeisanewExtendedGoalLanguagethat:
•canexpresstheintentionalaspectsnotcapturedinCTLandLTL(e.g.,“doeverythingpossibletoreachp”);
•candealwithfailureofgoalsandwithfailurerecovery(e.g.,“trytoachieveagoaland,ifyoufail,tryadifferentgoal”).
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SyntaxofEaGLe
•reachability(basic)goals:DoReachp,TryReachp
•maintenance(basic)goals:DoMaintainp,TryMaintainp
•conjunction:gAndg′
•failure:gFailg′
•controloperators:gTheng′,Repeatg
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DoReach
Goal“DoReachp”:
•requiresaplanthatguaranteestoreachpdespitenondeterminism
•failsifnosuchplanexists.
p
p
p
p
p
p
p
p
p
pp
success
failure
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TryReach
Goal“TryReachp”:
•requiresaplanthatdoesitsbesttoreachp;
•failswhenthereisnopossibilitytoreachp.
p
pp
p
p
p
pp
p
p
p
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Fail
Goal“g1Failg2”:
•dealswithfailure/recoveryandwithpreferencesamonggoals.
•Theplantriestosatisfygoalg1;wheneverafailureoccurs,goalg2isconsideredinstead.
•Example:DoReachpFailDoReachqvsTryReachpFailDoReachq
p
pq
q
q
q q qqq
p
p
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TheRailwaysSwitchExample
RD
U A
S
Alarm!
Alarm!
SwitchToD
TryReachDFailDoReachA
R DUA
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And/Then/Repeat
Goal“g1Andg2”:
•requirestosatisfyg1andg2inparallel.
Goal“g1Theng2”:
•requirestosatisfyg1andthentosatisfyg2.
Goal“Repeatg”:
•requirestosatisfyginacyclicway.
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Asimpleexample
lab
store dep
office
Sensors arenot perfect
Uncontrollabledoor
Continuously,pickanobjectfromthestoreandtrytodeliverittotheoffice;ifyoufail,deliverittothedep.Donotenterthelab.
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Apossibleplan
lab
store dep
office
Sensors arenot perfect
Uncontrollabledoor
init:/*inthestore*/
pickobject
/*trytoreachtheoffice*/
goeast;gosouth
if(room=office)then
dropobject
/*gobacktothestore*/
gowest;gonorth;gotoinit
else
/*reachthedep*/
gowest;gowest;dropobject
/*gobacktothestore*/
goeast;gotoinit
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TheEaGleGoal
lab
store dep
office
Sensors arenot perfect
Uncontrollabledoor
Repeat(DoReach(store∧objpicked)
And(TryReach(office∧objdelivered)
FailDoReach(dep∧objdelivered)))
AndDoMaintain¬lab
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TheEaGleControlAutomaton
dep
office
store lab
lab
lab
lab
dep
office
store
DoMaintainDoReach
TryReach
DoReach
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PlanningwithEaGle
•Oncethecontrolautomatonhasbeenbuilt,thesamealgorithmusedforCTLgoalscanbeapplied.
•Thealgorithmisterminating,correct,andcomplete.
•ThealgorithmhasbeenimplementedinMBP.
•TheperformanceissimilartotheoneforCTLgoals...
•...butthequalityofthegeneratedplansismuchhigher.
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Outline
•Whyplanningunderuncertainty?
•“Classical”planningasmodelchecking
•Planningwithtemporallyextendedgoals
•Conclusions
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PlanningasModelChecking
goal
planning domain
q
r
α
βPMC
rαq
βα
χp
plan
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Relatedwork
•TheMDP-planningapproach(e.g.,GPT[Bonet&Geffner])(includingMDP-planningbasedonADDs[Hoeyetal.])
•TheSAT-planningapproach([Rintanen],[Giunchiglia])
•Interleavingplanningandexecution([Koenig&Simmons])
•UMOP[Jensen&Veloso],basedonSymbolicModelChecking
•Plannersbasedonothermodelcheckingtechniques:
–Simplan[Kabanza]–ModelCheckingwithtimedautomata[Goldmanetal.]
•Automatatheoreticapproachtosynthesis
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DirectionsforFutureResearch
null
reachability
GOALS
full partial
OBSERVABILITY
maintainability
.....................
MDP + MBP
TIME & RESOURCESEXECUTION
CONTROLLER SYNTHESIS
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ThankstomanypeopleatTrento,butespeciallyto...
•PiergiorgioBertoli
•AlessandroCimatti
•MarcoRoveri
•PaoloTraverso
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