Document 10553751
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mi t co m p u t e r sc i e n ce a n d a r t i f ic ia l i n t e l l ig e n ce l a b o ra t o r y
Generative Temporal Planning with
Complex Processes
Jonathan Kennell
AI Technical Report 2004-002
© 2004
May 2004
m a s s a c h u s e t t s i n s t i t u t e o f t e c h n o l o g y, c a m b r i d g e , m a 0 2 1 3 9 u s a — w w w . c s a i l . m i t . e d u
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Reactive Model-based
Programming Language
Titan Model-based Executive
Control
Program
Control Sequencer
State
estimates
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Model
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Goals
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Mode
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Programming Language
Control
Program
Kirk Model-based Executive
Optimal Strategy Selection
Mission
Status
Vehicle
Dynamics/
Terrain Map
Mission
Goals
text
Deductive Controller
Localization
Spock
Environment/
Hardware
Observations
Commands
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bAa
forest fire 2
forest fire 1
Forest
stranded
family
UFFAV 2
Rescue
Helicopter
UFFAV 1
:SWK6J?>LbK & :=J?>->Al?TU69>5TU>AM9IVJ?:=C
Rescue-Mission( )
{
{
if (UFFAV1 = ok AND UFFAV2 = ok)
{
UFFAV1.extinguish(forest-fire-1),
UFFAV2.extinguish(forest-fire-2)
}
else if ( UFFAV1 = ok )
{
UFFAV1.extinguish(forest-fire-1);
UFFAV1.extinguish(forest-fire-2)
}
else if ( UFFAV2 = ok )
Rescue-Mission( )
{
{
forest-fire-1 = extinguished,
forest-fire-2 = extinguished
};
family = rescued
}
{
UFFAV2.extinguish(forest-fire-1);
UFFAV2.extinguish(forest-fire-2)
}
};
Rescue-Helicopter.rescue(family)
}
RMPL Control Program
Specifies Actions
RMPL Control Program
Elevated to Intended States
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Group-Enroute()[l,u] = {
choose {
do {
Group-Fly-Path(PATH1_1,PATH1_2,PATH1_3,TAI_POS)[l*90%,u*90%];
} maintaining PATH1_OK,
do {
Group-Fly-Path(PATH2_1,PATH2_2,PATH2_3,TAI_POS)[l*90%,u*90%];
} maintaining PATH2_OK
};
{
Group-Transmit(FAC,ARRIVED_TAI)[0,2],
do {
Group-Wait(TAI_HOLD1,TAI_HOLD2)[0,u*10%]
} watching ENGAGE_OK
}
}
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Goal
graph-based
planner solution
• In this domain, the vehicle
• The optimal plan traces the
• Graph-based planners
optimal
solution
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Rescue-Helicopter.Retrieve(group g) // activity 1
{ // activity / method body
do pickup(g) maintaining { threat = low } [300,+INF];
g = safe
}
Fire-Helicopter.Extinguish-Fire(location loc) // activity 2
{ // activity / method body
do {
if (retardant = present) then
drop-retardant()
else
call-for-assistance()
} watching { fire = controlled };
threat = low
}
Rescue-Family() // control program
{ // method body
{ // thread 1
Rescue-Helicopter.fly-to(rescue-point);
Rescue-Helicopter.Retrieve(family)[400,500];
Rescue-Helicopter.fly-to(hospital);
},
{ // thread 2
Fire-Helicopter.fly-to(forest-fire);
Fire-Helicopter.Extinguish-Fire(forest-fire)[300,400];
Fire-Helicopter.fly-to(base);
},
[0,1200]
}
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Start preconditions A
Start effects B
Invariant conditions C
Invariant effects D
End preconditions E
End effects F
Duration G
PDDL-Operator {
if A then {
B,
{
do D maintaining C;
achieve E;
F
}
} [G,G]
}
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PDDL+ Operator
Corresponding RMPL Operator
a
1
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An episode comprised of state assertions (Tells), state queries (Asks), and primitive actions
Tell ( location = unknown )
Decision node – only one out-arc
needs to be selected
Ask ( battery = charged )
drive-path ( )
2
[400,500]
3
Simple temporal constraints
400 d (time(3) – time(2)) d 500
Nodes represent events in time
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a<"
Rescue-Helicopter
Retrieve
Ask ( threat = low )
pickup ( family )
7
Macro 1
3
4
[400,500]
[0,+INF]
9
[0,+INF]
Rescue-Helicopter
Retrieve ( family )
Rescue-Helicopter
fly-to ( rescue-point )
Top-Level
Tell ( family = safe )
8
[300,+INF]
Rescue-Helicopter
fly-to ( hospital )
[0,+INF]
[0,1200]
1
START
2
[0,+INF]
5
Fire-Helicopter
fly-to ( forest-fire )
Fire-Helicopter
Extinguish-Fire
[300,400]
Fire-Helicopter
Extinguish-Fire ( forest-fire )
Fire-Helicopter
fly-to ( base )
11
[0,+INF]
Ask ( retardant = present )
[0,0]
[0,+INF]
6
Ask ( not ( fire = controlled ) )
10
Macro 2
END
[0,+INF]
[0,+INF]
14
12
[0,0]
Ask ( not ( retardant = present ) )
drop-retardant ( )
[0,+INF]
13
[0,+INF]
15
call-for-assistance ( )
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:SMOh>AIXl :S7QS>8L:glDlD:=CXM^GQgIVM<DE9IV<):gl<DE>AJD>HOhCKJ?>MCK<)>H0>kTU6<mIV7QS>K CKJ)>UIV8LGQS>Kc
:SM :SWK69JD> & %c
<\C^IK>HJ?:SIKQRvK>AE:STHQ=>klIKJD>BTHCK8L8xIVM9@>A@<DCJD>AM9@> AvKCX69loI|<;I
nIw1G`CK:SM1<AR]M>CKO+<DE>vK>HE9:STHQ=>klR:glRO IKJ\InIwIVMY@L-:=QSQ9<mIVX>I|<NQ=>kIKl < & ECX6Jml
&
d
Sequential Composition:
[l1,u1]
[l2,u2]
A
A[l1,u1]; B[l2,u2]
[0,0]
B
[l1,u1]
Parallel Composition:
[0,0]
[0,0]
A
A[l1,u1], B[l2,u2]
[0,0]
[l2,u2]
[0,0]
B
[l1,u1]
A
Ask(c)
[0,0]
Conditional Execution:
Ask(not(c))
if c then A[l1,u1]
[0,0]
else B[l1,u1]
[l2,u2]
B
Reactive Execution:
[0,f]
[0,0]
[l,u]
A
Ask(c)
when c then A[l,u]
A
Condition Maintenance:
[l,u]
do A[l,u] maintaining c
Ask(c)
Preemption:
A
[l,u]
do A[l,u] watching c
Ask(Not(c))
Choice:
[l1,u1]
[0,0]
[0,0]
A
choose{ A[l1,u1],
B[l2,u2] }
[0,0]
[l2,u2]
[0,0]
B
:SWK6J?> & & p^\Z\CX87:SM9IV<DCKJml\<DCx- 567y M>U<NCKJ?l
Table 4-2 RMPL Combinators to TPN Sub-networks
&
a
[0,0]
3
UAV1.fly-to ( waypoint )
[240,+INF]
4
[0,0]
1
2
[0,0]
5
UAV2.fly-to ( waypoint )
[0,180]
6
[0,0]
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TUCX8LGQ=>H<D><DE>nJ?>HM9@> HvXCK69l:=M;I|<8LC1l<aECX6JmlH
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l?IwL<DE9IV<-<DE>GQgIVM}:glN<D>A8;G`CKJmIVQSQSw~:=MYTUCKMYl :gl<?>HM1<A
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>A8y
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u ll E9C|-M70wF>kTmEX<?>HJ;IVM9@p
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5 lRIVM9@L- lRTAIVML7Y>-J?>UOhCXJD86QgI|<D>k@:SM1<DCoIKM;>kj16:=v|IKQ=>AMX<RWXJ?IKGEcKTAIVQSQ=>k@LI
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IVMY@ Q=C|N>HJo7`CK69M9@:SMI^WKJmIVG9E-:=<DE#l :S8LGQ=>~<D>H8LG`CKJmIVQNTUCKMYl<?J?IK:=M1<?lAZ\CKMy
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lDGYCXM9@l
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S b U u WKJmIVGE^-:=<DE lD:=8LGQS><?>H8LG`CKJmIVQTUCXM9l<?J?IK:=M1<mlTAIVM>kIKlD:=QSw
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<DE9>:SMG6<
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IKl<DE9>[lD:=8LGQS>f<D>H8LG`CKJmIVQnTUCXM9l<?J?IK:=M1<k :SM9IVQSQ=wXcR>AIXTmEQSC|\>AJ7`CK6M9@ :=M <DE>
:SMG6<xWKJmIVG9E:SlLTUCXM0vK>HJD<D>k@:SMX<?CI'@:SJD>kT_<D>k@ IKJ?TB-:{<?E <?E>fM9>HWXIV<D:SvK>fvIKQ=69>
IVMY@BCXGGYC1l :=<D>@:SJ?>AT_<?:=CXM
IKlN<DE9>lD:S8;G9Q=><?>H8LGYCXJ?IKQTUCXM9l<?J?IK:=M1<k
u l8L>HM1<?:=CXM>A@IV7`C|vK>XcY<?>H8LG`CKJmIVQTUCXM9l :gl <D>HMYTUw
:SMI}- CKJo5 THCKJDy
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S !c+b U ]M9TU>)<DE9>@:Sl <?IKM9TU>)WKJmIVGE~OhCKJIWK:SvK>HM[- E9IKlN7`>H>AM[THCKM9l <DJ?69T_<?>A@+c
CKM9>\THIKM>kIKlD:=QSw@>U<?>HJ?8;:SM>\<D>A8;G`CKJmIVQ0TUCXM9lD:Sl <D>AM9TUw70w69lD:=MW)IM>AWXIV<D:SvK>\THwTUQS>
@>H<D>ATU<D:SCKM~IKQ=WXCKJ?:{<?E8}cXlD69TmEBIKlR<DE> QSC|w@0y IKJ?lDE9IVQSQ9IKQ=Q=yGYIV:SJ?lRlDECXJ <?>Al <G9I|<?E
IVQSWKCXJD:=<DE98 S #2UCKJn<DE9> ]QgIV7`>HQ=y THCKJ?JD>kT_<?:=MWLIVQSWKCXJD:=<DE98 S d U
&&
TPN
3
[0,0]
UAV1.fly-to ( waypoint )
[240,+INF]
4
[0,0]
1
2
[0,0]
5
UAV2.fly-to ( waypoint )
Distance Graph
0
[0,180]
[0,0]
6
+INF
3
0
4
-240
0
1
0
0
2
0
0
5
180
6
0
0
:SWK69JD> & z M9THCKM9lD:gl<?>HM1<- -:{<?EZ\CKJ?JD>kl G`CKM9@:=MWLF:Sl <?IKM9TU> ) JmIVGE
make-distance-graph (TPN input)
returns distance graph
1. Let d = distance graph
2. For each event, i, in input
3.
add node i to d
4. For each episode from i to j in input
5.
add arc (i,j) to d with episode upperbound as weight
6.
add arc (j,i) to d with negative episode lowerbound as weight
7. return d
:=WX6J?> & #- <DC~F:Sl <?IKM9TU> ) JmIVGE}lD>H6Y@CBZ\C0@>
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IVQglDCo>HM9lD6J?>-<DEYI|<\:=<?lNIKl?lD:=WXM8L>HM1<?lq<?Cl <?IV<D>v|IKJD:gIV7QS>Al@CMCK<NTHCKM9:gT_<knE:Sl
:glN<DCL>HM9lD6J?>)<DE9IV<>AIKTmE}l <?I|<?>vIKJD:gIV79Q=>):SlIKl?l :SWKM>k@BI;6M:gj16>v|IVQS6>I|<>kIKTmE
G`CK:SMX<:=M}<?:=8L>KNE>AM
<\C~>HQSQglTUCXMX<mIV:SM}:=M9THCKM9lD:gl<?>HM1<l <?I|<?>oIKl?l :SWKM98;>AM1<?lAc
N>RlDIw<DE9IV<<DE>Aw)<DEJ?>AIV<D>HM>kIKTmECV<?E>HJknE069lAcH<?E>G9JDCTU>klDl.CKO>HM9lD6J?:=MW<DE9IV<
MC:SM9TUCXM9l :gl <D>HM1<R>HQSQSlRTHCVy CTHTU69J
:SM<D:S8;>-:glJ?>UOh>AJDJ?>A@o<DCoIKl
<?EJ?>AI|<J?>AlDCKQS6<D:SCKM
Tell ( X )
This ordering arc ensures
that the two conflicting
episodes do not co-occur
Tell ( not ( X ) )
:SWK6J?> & !- nEJ?>AIV<->AlDCKQS6<D:SCKM
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GJ?CKE:S7:=<?ln<?E><NC~>AQ=QglnOhJ?CK8 THCVy CTHTU69JDJ?:=M9W9 :=M9IKQ=QSwKcY\>ol?Iwx<?E9I|<Ix-
:gl)THCKM9lD:gl<?>HM1<-E>AM:=<?l<D>A8LGYCXJ?IKQqTHCKM9l <DJmIV:SM1<?lIVJ?>TUCXM9lD:Sl <D>AMX<IVMY@^:=<?l>AQ=Q
TUCXM9l <DJmIV:SMX<mlnIVJ?>THCKM9lD:gl<?>HM1< CKJ-M9CV<n<DEJ?>AIV<D>AM:=M9$W _
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GJ?CKWXJ?IK8 - 7Y>A:=MWl 6YTHTU>klDl Oh6QSQ=w TUCX87:SM>k@-:{<?E I^- >HM0v0:SJDCXM8L>HM1<
8LC@>HQIKM9@}Ixl >H<CVOIKTU<D:Sv1:=<wf- lnOhJ?CK8 <DE>oIXT_<?:=v0:=<wBQS:=7JmIVJ?w~:SM}CKJm@>HJn<?C
IKTmE9:=>AvK><DE>8L:glDlD:=CXM[@>AlD:=WXM>HJ lNGQgIVM9M:=M9WxWKCXIKQSlA
zMxI>A8;G`CKJmIVQQSIKM >U<NCKJ?.c u lDTUCXM9l <DJmIV:SMX<mlqJD>AGJ?>AlD>HM1<
CXGY>AMxTUCKMY@:{y
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Il?TU>HMYIVJ?:=C lRTHCKM1<DJ?CKQG9JDCXWKJmIV8 IKM9@xIKTU<D:Sv1:=<D:S>Al\IVQSNIwl
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->ATAIVQSQ9<?E9I|<N-E>HJ?>AIXl u l xTUCXM9l <DJmIV:SMX<mlJ?>Aj16>Al <Nl <?IV<D>IXlDlD:SWKM8L>HM1<mlHc0>AQ=Q
TUCXM9l <DJmIV:SMX<mlIKl?l >AJ <l <?IV<D>IXlDlD:=WXM8L>HM1<?lAqnE16YlqOhCKJ<?E>CXGY>AMxTUCKMY@:{<?:=CXMx:=M~IKM
u lDoTUCXM9l <DJmIV:SMX<<DC7`>nTHQ=C1l >k@+cVI)- 869l <WK69IKJ?IKMX<?>H><?E9I|<q<?E> u lD lql<mI|<?>
IKl?lD:=WXM8L>HM1<:gl>AMX<mIV:SQ=>k@x70wxl CX8;>)>AQ=Q+THCKM9l <DJmIV:SM1<:=MB<DE>M>U<NCKJ?. u QSlDC9c0IKl
u lDIVM9@>AQ=QTHCKM9l <DJmIV:SM1<?lIKJD>NIKl?l :SWKM9>A@<?>H8LGYCXJ?IKQX>AG:gl C@>klHcVI>AQ=QTHIKMoCKM9Q=w
&
TUQSCXlD>oIVM u l f:{O:=<?l-<?:=8L>Hy7`CK6MY@llD679lD68L> CXJTUCXMX<mIV:SM N<?E><D:S8L>Uy 7YCX6M9@l
CVO<DE> u l [TUCXM9l<?J?IK:=M1<k
E>HMIKQ=QqCVO\<DE> u l ^THCKM9l <DJmIV:SM1<?l):=M I[- IVJ?>;THQ=C1l >k@^70w>HQSQRTUCKMy
l <DJmIV:SMX<mlIKM9@IVM0w TUCXM9:gT_<D:SMW>HQSQnTUCKMYl<?J?IK:=M1<?lIVJ?>~CKJm@>AJD>k@lDC'IXl<?CMCK<
TUCKyCTATU6Jkc0\>l?IwL<DE9IV<-<DE>o- :Sl-THCK8LGQS>U<D>X
Ask ( lights = on )
1
2
[13,16]
[0,+INF]
[0,+INF]
Tell ( lights = on )
3
4
[0,20]
:=WX6J?> & "9PIV8LGQS>CVOZ\CX8LGQ=>H<D>o-
Z\CKM9lD:g@>HJn<?E>>UIV8LGQS>:SM :SWK6J?> & "zM[<DE:gl->HIK8LGQ=>Xc<DE9>o- E9IKl
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nE>>HQSQTUCXM9l<?J?IK:=M1<IKl?lD>HJD<?l\<DE9IV<-<DE>QS:=WXE1<?lIKJD>)CKM[OhCKJ-69GB<?CBdVeLl >kTUCXM9@lA
NwxTUCKM9M>ATU<D:SMWo<?E> u l ~IKM9@B>HQSQ.TUCKMYl<?J?IK:=M1<?l\-:=<DEfTAIV69l?IVQYQ=:SMl >AG:SlDC@>Al
-:=<DE S ec \ U.<D:S8L>Uy 7YCX6M9@l _c<DE>- >HM9lD6J?>Al\<DEYI|<N<DE>>HQSQ.THCKM9l <DJmIV:SM1<
TUCXM1<?IV:SM9l\<DE9> u lDfTUCXM9l <DJmIV:SMX<kc1<DE069lTHQ=C1l :SMW;<DE>CXGY>AM[THCKM9@:{<?:=CXM
0
0 '(+ z
"1
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>Al <?IK7QS:SlDE>A@o<DE>
RQgIVM9M:=M9W^FCX8LIK:=MF>Al?TUJ?:=G<D:SCKMIKMWK6YIVWK> F)F \IKloIl<mIVM9@IKJ?@: A>A@
OhCKJ?8xI|<OhCKJ>HM9THC0@:=MW
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<D:SvK>LIKTU<D:SCKM9lAc+l<mIVJD<GJ?>UyzTUCXM9@:=<D:SCKM9l)IVMY@^> .>ATU<?lAc+:=M0v|IVJ?:gIVM1<TUCXM9@:=<D:SCKM9lIKM9@
> .>ATU<?lAc9IVMY@B>AM9@[GJD>Hy THCKM9@:{<?:=CXM9lnIVM9@[> .>ATU<?lA
u M':=8LG`CKJD<?IVM1<THQSIK:=8 OhCXJ<DE9:Sl<DE>kl :gl:Sl<DE9IV<50G`CTm lGQSIKMM:SMW~CXGY>AJ?IVy
<DCXJ?lAc>H8LGYCXJ?IKQRQgIVM >U<NCKJ?lHc+IVQSQSC| <DE>xlDGY>kTU:=iYTHIV<D:SCKM'CVO\J?:gTmE'IKTU<D:Sv0:{<w
8LC@>HQglHnE:gl)TUQgIV:S8:Sl)l 69GGYCXJ <?>A@
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lD68L>oF)F \ CXGY>AJ?IV<DCXJ?lA :=WX6JD> & =bkeL@>H8LCKMYl<?J?IV<D>AlnE9C|IKM1w[IVJ?7:=<DJmIVJ?w
F)F) \CXGY>AJ?IV<DCXJnTAIVM[7Y>>HGJD>klDlD>A@[IKl-IL- IXT_<?:=v0:=<wK
&#
Kirk Activity:
PDDL+:
Start preconditions A
Start effects B
Invariant conditions C
Invariant effects D
End preconditions E
End effects F
Duration G
Ask A
Tell B
F]
[0,+IN
Ask C
[0,0]
Tell D
[G,G]
Ask E
[0,0]
Te
[0,+ ll F
INF
]
:SWK6J?> & S bAe9
p^IKGG:SMW;OhJDCX8 \FF)\]GY>AJ?IV<DCKJml\<DCx- u T_<?:=v0:=<D:S>Al
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RMPL
Control
Program
RMPL
Activity
Specifications
Initial Candidate Generator
Initial Candidate
Cost
Update
Candidate
Priority Queue
No
Child
Candidates
Child
Expansion
Least-cost
Candidate
Candidate
Consistent?
Activity
Data
Activity Library
No
Yes
Candidate
Complete?
Yes
:SWK6J?> % SbKR50G`C0Tm[NQ=CTmBF:SIKWKJmIV8
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%b
Spock ( control program, activity library )
returns complete, consistent plan that achieves the control program
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
let C = initial candidate based on control program
let priority queue = {C}
while priority queue is non-empty
let C = least cost candidate from priority queue
if C is consistent,
if C is complete, return C
let children = child-expansion ( C, activity library )
for each D in children
update-cost(D)
insert D into priority queue
endfor
endif
endwhile
:=WX6JD> % d5GYCTmfCKGyQS>HvX>HQ+lD>H69@CVyzTUC@>
Forest Fire 2
Residential Area
Forest Fire 1
UAV
Base
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%Kd
Note:
Fire-Suppression ( )
{
[0,60];
fire1 = suppressed [0,0];
[0,90];
fire2 = suppressed [0,0]
}
• Deadline for fire1 suppression
is 60 time units after mission
start
• Deadline for fire2 suppression
is 90 time units after fire1 is
suppressed
Control Program RMPL Code
Ask ( fire1 = suppressed )
[0,60]
Ask ( fire2 = suppressed )
[0,90]
[0,0]
Control Program TPN
[0,0]
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% U
%Va
Move (origin, destination)
{
fly-to(destination),
location UAV = unknown,
[dist(origin,destination),+INF];
location UAV = destination [0,+INF]
}
Fly-to ( destination )
Tell ( location UAV = unknown )
Tell ( location UAV = destination )
[0,+INF]
[dist(origin,destination),+INF]
Move Activity TPN
Move Activity RMPL Code
Drop-water (waypoint)
{
do {
open-doors() [1,1];
drop-water() [15,15];
close-doors() [1,1]
} maintaining location UAV = waypoint;
waypoint = suppressed [0,+INF]
}
drop-water ( )
open-doors ( )
[15,15]
close-doors ( )
[1,1]
[1,1]
Tell ( waypoint = suppressed )
[0,+INF]
Ask ( location UAV = waypoint )
Drop Water Activity RMPL Code
Drop Water Activity TPN
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Move ( Base, fire1 )
Move ( fire1, fire2 )
Fly-to ( dest )
Fly-to ( dest )
Tell ( location UAV = unknown )
Tell ( loc UAV = dest )
[dist(origin,dest),+INF]
[0,+INF]
Tell ( location UAV = unknown )
Tell ( loc UAV = dest )
[dist(origin,dest),+INF]
[0,+INF]
[0,+INF]
[0,+INF]
[0,+INF]
[0,+INF]
[0,+INF]
Drop-Water ( fire1 )
Drop-Water ( fire2 )
drop-water ( )
open-doors ( )
drop-water ( )
[15,15]
open-doors ( )
close-doors ( )
[1,1]
[1,1]
[15,15]
close-doors ( )
[1,1]
[1,1]
Tell ( wpt = spprsd )
Ask ( location UAV = waypoint )
[0,+INF]
Tell ( wpt = spprsd )
[0,+INF]
Ask ( location UAV = waypoint )
[0,+INF]
[0,+INF]
[0,+INF]
[0,+INF]
Control Program
Ask ( fire1 = suppressed )
[0,60]
[0,0]
Ask ( fire2 = suppressed )
[0,90]
[0,0]
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Move ( Base, fire1 )
Fly-to ( fire1 )
Tell ( location UAV = unknown )
Tell ( location UAV = fire1 )
[dist(Base,fire1),+INF]
[0,+INF]
[0,+INF]
[0,+INF]
Drop-Water ( fire1 )
drop-water ( )
close-doors ( )
open-doors ( )
[15,15]
[1,1]
[1,1]
Tell ( fire1 = suppressed )
[0,+INF]
Ask ( location UAV = fire1 )
Control Program
Ask ( fire1 = suppressed )
[0,60]
[0,0]
[0,90]
Ask ( fire2 = suppressed )
[0,0]
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%
Activity A - Enabled
Activity B – Not Enabled
Ask (Y)
Ask (X)
Activity Library
Plan Candidate
Inserted Episodes
Tell (X)
Inactive
Episodes
Pending Event
Active Tell
Inserted Event
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Enabled Pending Event
Inserted Events
Un-enabled Pending Events
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Enabled Pending Event
%#
Inactive
Tell ( battery = charged )
Active
Tell ( light = on )
Enablement for Episodes
- Start event inserted
- Ask constraints supported by
candidate active Tells
- Tell constraints consistent
with candidate active Tells
Ask ( light = on )
Ask (battery = charged )
Enabled
Not Enabled
Ask ( light = on )
Tell ( light = off )
Inserted Event
Inserted Episode
Pending Event
Pending Episode
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%!
Child-Expansion (candidate, activity-library)
returns child candidate
1.
let c = copy of candidate
2.
choose between lines 3, 7, 11:
3.
4.
5.
6.
find enabled activities
let a = choose an enabled activity
instantiate(c,a)
return c
7.
8.
9.
10.
find enabled episodes
let e = choose an enabled episode
insert(c,e)
return c
11.
12.
13.
14.
find enabled events
let e = choose an enabled event
insert(c,e)
return c
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"
%
Find-Enabled-Activities (candidate C, activity library L)
1.
let S = empty set of activities
2.
for each activity, A, in L
3.
let OK = true
4.
for each Ask, K, following the start event of A
5.
if K is not closed by the active Tells in C
6.
OK = false
7.
end-for
8.
if OK = true
9.
add A to S
10.
end-if
11. end-for
12. return S
:=WX6J?> % =bd :=MY@[PM9IV79Q=>k@ u T_<D:Sv0:{<?:=>kllD>H6Y@CBZ\C0@>
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Activity A - Enabled
Activity B – Not Enabled
Ask (Y)
Ask (X)
Activity A - Enabled
Activity B – Not Enabled
Ask (Y)
Ask (X)
Activity Library
Activity Library
Plan Candidate
Plan Candidate
Tell (X)
Before Activity Instantiation
Tell (X)
Ask (X)
After Activity Instantiation
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Find-Enabled-Episodes (candidate C)
1.
let S = empty set of Episodes
2.
for each pending episode, T, in C
3.
let OK = true
4.
for each Ask, A, in T
5.
if A is not closed by the active Tells in C
6.
OK = false
7.
end if
8.
end-for
9.
for each Tell, L, in T
10.
if L is inconsistent with the active Tells in C
11.
OK = false
12.
end-if
13.
end-for
14.
if OK = true
15.
add T to S
16.
end-if
17. end-for
18. return S
:=WX6JD> %=b & :=M9@}PM9IV7QS>A@[PRG9:SlDC@>Al-\l >A69@C~Z\C0@>
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b
Tell ( light = on )
Before Episode Insertion
Ask ( light = on )
Tell ( temperature = hot )
Episode to be Inserted
Tell ( temperature = cold )
Tell ( light = on )
After Episode Insertion
Ask-Support Causal Links
[0,+INF]
[0,+INF]
Ask ( light = on )
Tell ( temperature = hot )
Conflict-Avoidance
Causal Link
[0,+INF]
Newly Inserted Episode
Tell ( temperature = cold )
Inserted Event
Pending Event
Inserted Episode
Pending Episode
:SWK69JD> % Sb %
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d
Causal Link
[0,+INF]
:SWK6J?> % Sb u ZNIK69lDIKQ+:SM
Find-Conflicting-Tells (candidate C, Tell A)
1.
let S = empty set of Tells
2.
for each inactive Tell, T, in C
3.
if T conflicts with A, add T to S
4.
end-for
5.
return S
:=WX6JD> % =b #0 :SM9@^Z\CKM9:STU<D:SMW~>HQSQSl-\l >A69@CBZ\C@>
a
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CVO<DE>M9>H>AQ=QTHCKM9l <DJmIV:SM1< l >A> :=WX6JD> %=b !_
Insert (candidate, episode)
1.
for each Ask, A, in episode
2.
let S = choose supporting active Tell in candidate
3.
add causal link to candidate from S.start to A.start
4.
add causal link to candidate from A.end to S.end
5.
end-for
6.
for each Tell, T, in episode
7.
for each Tell, C, in candidate that conflicts with T
8.
add causal link to candidate from C.end to T.start
9.
end-for
10. end-for
:SWK6J?> % Sb !9zMYl >AJ <PRG9:SlDC@>lD>H69@CKyZ\C@>
/1D! qs /
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7`>ATUCX8L>Alo:SM9THCKM9lD:Sl <D>AM1<-E>HMITUCK87:SM9I|<?:=CXMCKOn<DE>B<D:S8;>Hy7`CK69M9@loCXM <DE>
&
Not Enabled
Tell ( light = on )
[0,+INF]
[0,+INF]
Ask ( light = on )
Enabled
Tell ( temperature = hot )
[0,+INF]
Before Event Insertion
Tell ( temperature = cold )
Tell ( light = on )
[0,+INF]
[0,+INF]
Ask ( light = on )
Tell ( temperature = hot )
After Event Insertion
[0,+INF]
Tell ( temperature = cold )
Inserted Event
:=WX6J?> % =b#"PRvX>HM1< z M9l >AJ <?:=CXM
Pending Event
Inserted Episode
Pending Episode
Find-Enabled-Events (candidate C)
1.
let S = empty set of Events
2.
for each pending event, E, in C
3.
let OK = true
4.
for each preceding episode, P, of E
5.
if P is not inserted
6.
OK = false
7.
end-if
8.
end-for
9.
if OK = true
10.
add E to S
11.
end-if
12. end-for
13. return S
:SWK6J?> % dVe :SM9@}PRM9IK7Q=>k@fPvK>AMX<ml-lD>H69@CxZ\C@>
Insert (candidate, event)
1.
mark event inserted (not pending)
:=WX6JD> % dbKzM9lD>HJD<-PvK>AMX<\l >A69@CVy Z\C@>
%
>HG9:SlDC@>AlfCVO<DE> - TUCXM9:gT_<A 50:=MYTU>>HG:gl C@>'<D:S8L>Uy 7YCX6M9@l
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QgI|<D:SMWxI|<-QS>AIXl<CXM>CVO<?E><D>A8LGYCXJ?IKQTUCKMYl<?J?IK:=M1<?lA
Temporally Inconsistent Candidate
This candidate is inconsistent
Problem: Single
Activate Battery 1
battery cannot
Tell ( radio bus = powered )
power radio for
1
[0,10]
duration of data
[0,+INF]
transmission.
Transmit Data
Ask ( radio bus = powered )
3
[15,15]
2
[0,+INF]
4
10
Corresponding
Distance Graph
1
2
0
+INF
0
3
+INF
15
4
-15
consistency
violated due to
presence
of negative cycle
0
:SWK6J?> % dKdqPRIV8LGQS>)CKO zM9THCKM9lD:gl<?>HM1<ZNIVM9@:g@IV<D>
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> ~TH:=>AM9TUwx70wxvK>AJD:=Ohw0:=M9W<?>H8LGYCXJ?IKQ+TUCKMYl :gl<?>HM9THw~I|O <?>HJn>AIXTmEBTHIKM9@:g@I|<?>):gln@>Uy
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OhCKJN<?E> ]QgIV7`>HQ=y THCKJ?JD>kT_<D:SMWIKQ=WXCKJ?:{<?E8:glNlDEC|-Mf:=MBi9WK6J?> :SWK69JD> % dVa9
u l\<DE9>TmEYIVMWX>Al<DCLITHIKM9@:g@I|<?>)- IKJD>)l 8xIKQ=Q`OhJ?CK8CKM9>:=<D>HJmI|<?:=CXM~<?C
<DE9>M>U0<Ac9:{<8xIVX>AlnlD>HM9lD><DCxTmE>kTmx<D>A8;G`CKJmIVQTHCKM9lD:gl<?>HM9THw~69lD:=MWxIKM[:SM9THJD>Hy
8L>HM1<?IKQIVQSWKCXJD:=<DE8 <DE9IV<JD>A69l >kln\CXJD~OhJDCX8 G9IKl <:=<D>HJmI|<?:=CXM9lA u M
IVQSWKCXJD:=<DE8
OhCKJBGY>AJ OhCXJD8L:SMW:=MYTUJ?>H8L>HM1<?IKQ-<D>A8LGYCXJ?IKQTUCXM9l :gl <D>HMYTUw TmE>kTm0:=MWYc ZcRE9IKl
J?>ATU>AM1<DQSw;7`>H>AMf:SM1<DJ?C@69TU>k@~70w y E9l :gIVM9W;50E06 S d ##UE:SQS>MCK<N:SM1<D>AWKJmI|<D>k@~:SM
<DE9>;TH6JDJ?>HM1<:S8LGQS>H8L>HM1<?IV<D:SCKM'CVON50G`CTm.c`6Yl :SMW Z<DCBG`>HJDOhCKJ?8 <D>A8;G`CKJmIVQ
TUCXM9lD:Sl <D>AM9TUwBTmE9>ATm0:=M9W:gl-@:glDTH69lDlD>A@[:SMBOh6<D6J?>\CXJD[50>ATU<D:SCKM &
FIFO-label-correcting (N,s)
1.
For i = 1 to |nodes of N|
2.
d(i) = +INF
3.
examined_count(i) = 0;
4.
End-For
5.
d(source) = 0;
6.
list = {source};
7.
while (list is non-empty)
8.
i = pop head of list;
9.
examined_count(i)++;
10.
if examined_count(i) > n
11.
return “Negative Cycle”
12.
End-If
13.
For each arc (i,j) in N
14.
If d(j) > d(i) + c(i,j)
15.
d(j) = d(i) + c(i,j);
16.
If j is not in list
17.
push j to end of list;
18.
End-If
19.
End-If
20.
End-For
21. End-While
22. return “No Negative Cycles”
=: WX6J?>% dKa ]IK7Y>AQZ\CKJ?JD>kT_<?:=MW u QSWKCKJ?:=<DE8OhCXJ-F>H<D>ATU<D:SMW >AWXI|<?:=vX>
Z\wTUQS>Aln:SM
I;F:gl<mIVM9TH> )JmIVG9E
#
&% ( % N
% 0_0
(D
zM
<?E>;@CK8xIV:SM^CVO<?>H8LG`CKJmIVQ
GQSIKMM:SMW9c.:=<):gl:=8LG`CKJD<?IVM1<<DC}TUCKMYl :g@>HJ)THIXl >kl
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<D>A8LGYCXJ?IKQ=QSw~QSCKMWxIKTU<D:Sv0:{<w l >A> :SWK69JD> % d & _ zM
50G`C0Tm.c<?E:gl-CTHTU69J?ln-E>AM
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lDCK8L> u lDTUCKMYl<?J?IK:=M1<AE>HMo<DE:glEYIVGG`>HM9lAc86Q=<D:SGQS>\>HQSQ1THCKM9l <DJmIV:SM1<?l8LIw
7`>TmE9IK:=M>k@f<DCKWX>U<?E>HJ<DCBTHQ=C1l ><?E> u l }TUCXM9l <DJmIV:SMX<k-nE:Sl:Sl)IKTATUCX8;G9Q=:gl E9>A@
70w#IX@@:SMW IVM>AG:gl C@>}OhJ?CK8 <DE>'l<mIVJD<BCVO>AIXTmE>AQ=Q<DC<?E>^>HMY@tCVO<DE>
CKG9GYC1l :=<D>>HQSQ cYJD>kjX69:=J?:=M9W<?E9I|<-<?E>i9Jml<>HQSQMCK<>HM9@[6M1<D:SQ<?E>olD>ATUCXM9@ CKJ
TUCXM1<D:SM169:=MW N>AQ=QEYIKln7`>HWK69M
Continuation: Problem and Solution
Problem: Single
Activate Battery 1
battery cannot
Tell ( radio bus = powered )
power radio for
[0,10]
duration of data
[0,+INF]
transmission.
Transmit Data
Ask ( radio bus = powered )
[0,+INF]
[15,15]
Solution: Use
multiple batteries
to power radio.
Activate Battery 1
Tell ( radio bus = powered )
[0,
+IN
F]
[0,+INF]
Activate
Battery 2
[0,10]
[0,+INF]
Tell ( radio bus = powered )
Tell ( radio bus = powered )
[0,10]
Transmit Data
[0,+INF]
Ask ( radio bus = powered )
[15,15]
:=WX6J?> % d & Z\CKM1<?:=M069IV<D:SCKMRJ?CK79Q=>A8 IVM9@
50CXQ=6<?:=CXM
u M
>HIK8LGQ=>CKOqTHCKM1<D:SM069I|<?:=CXMf:gllDEC|-Mf:SM :=WX6JD> % d & zM[<DE:gl>HIK8;y
GQS>KcI DJ?IKM9l 8L:=<)F)I|<mI BIXT_<?:=v0:=<w
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79IV< <D>AJDwTHIKMCXMQSwG`C|\>AJ<DE>~7969lOhCKJI|<o8LCXl <~bAe[<?:=8L>~6M9:{<mlH[nE16Yl<DE>
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76Ylo:glGYC|ny
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IK@9@l\THCKM9l <DJmIV:SMx<?E>)<\C u TU<D:Sv|I|<D>nI|<D<D>HJ?w IXT_<D:Sv0:{<?:=>klR<?CC|vX>HJ?QSIKGc1>HM9lD6JDy
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J?CK6<?:=M> lD>H> :SWK69JD> % d %UE>AM
<DE>;>HG9:SlDC@>:SM9lD>HJD<D:SCKM
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!
@ QS>Al\IVML>HG:glDC0@> l>HQSQSlAcX:=<\TmE>kTmlq<DClD>H>-:=O+<DE9CXlD>>AQ=QglR8xI|<mTmExCV<?E>HJNIKT_<?:=vX>
>HQSQSl-:{<?E:=M<DE>fGQSIKMTHIKM9@:g@I|<?>B- E>AM:{<i9M9@lI
8xI|<mTmEcR50GYCTm
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CK8L:=<?lN<?E>oTUCXMX<?:=M069IV<D:SCKM
Insert (candidate, episode)
1.
for each Ask, A, in episode
2.
let S = choose supporting active Tell in candidate
3.
add causal link to candidate from S.start to A.start
4.
add causal link to candidate from A.end to S.end
5.
end-for
6.
for each Tell, T, in episode
7.
for each Tell, C, in candidate that conflicts with T
8.
add causal link to candidate from C.end to T.start
9.
end-for
10.
if candidate contains matching active Tell, C
11.
optionally:
12.
add episode to candidate from C.start to T.end
13.
add episode to candidate from T.start to C.end
14.
add Tell to candidate from C.start to T.end
15.
add Tell to candidate from T.start to C.end
16.
end-option
17.
end-if
18. end-for
:=WX6J?> % d% zM9lD>HJD<PG:SlDC@>\l >A69@CKyZ\C@>-:{<?E506G9GYCXJ <OhCKJoZ\CKM1<?:=M069IVy
<D:SCKM
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MC@>\CVO>AIXTmE>HQSQK<?C<DE9>\>AM9@oMC@>\CVO<?E>\CXGG`CXlD:{<?>\>HQSQ c|J?>Aj16:SJD:SMW-<?E9I|<<DE>
<NC>HQSQglqC|vK>HJ?QgIVG:SM;<D:S8L> lD>H> :=WX6JD> % d _qPIXTmEM>A#>AG:gl C@>n:glQSIK7Y>AQ=>k@
-:=<DE~Io>HQSQ`THCKM9l <DJmIV:SM1<<DE9IV<J?>HGJ?>AlD>HM1<?l<DE>THCK87:=M9>A@x>HQSQ`THCKM9l <DJmIV:SM1<?l
OhCKJ
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7`>69lD>A@L:SMLOh6<D6J?>:=<D>AJ?IV<D:SCKM9lR<DCoTUQSCXlD> u lDl<?E9I|<J?>Aj16:SJ?>l 6G9GYCXJ <ROhJ?CK8 <DE>
TmE9IK:=M[CVOq>AQ=QTHCKM9l <DJmIV:SM1<?lA
0 N q02 -1#
50G`CTmBNCK6Qg@}7Y>869TmE
QS>Al?l-> ~TH:=>AMX<:{OR:=<N>HJ?><DC~J?>Hv0:gl :=<GJ?>Hv0:=CX69lDQ=w[TUCKMy
Dl :S@>AJD>k@LGQgIVMM:SMW;l<mI|<D>klHqnE:gl:glNIK@@J?>Al?lD>A@L:SMf50G`C0TmL70w;8;>A8LCK: H:SMW>kIKTmE
:SM9l >AJ <?:=CXMBIKlN:=<-:SlnTUCXM9lD:S@>AJD>k@+c0IVM9@[@:glDIKQ=QSC|-:=M9WIVM0wxGJ?>Hv0:SCK69lDQ=wxTHCKM9lD:S@>HJ?>A@
THIKM9@:g@I|<?>~>UG9IKM9lD:=CXM :SWK6J?>% d#}8;CK<D:Sv|I|<D>klo<?E>BM9>H>A@OhCKJLIVM> xTH:=>AM1<
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ITHIKM9@:g@I|<?>GQgIVMx>H0GYIVM9lD:=CXMcK-E9:=QS>Ixb-J?>HGJ?>AlD>HM1<mlq<DE>:=M9THQ=6Yl :SCKMxCKO+ITHIVMy
@:g@I|<?>LGQSIKM'>HG9IVM9lD:SCKMx50G`C0Tm ll wl <D>H8 CVOn8;>A8LCK: H:SMW[IKM9@'GJDCXE:S7:{<?:=M9W
GJ?>Hv0:SCK69lDQ=w^THCKM9lD:g@>HJ?>A@GQSIKM'>HG9IVM9lD:SCKM9l):glIVM9IKQ=CXWKCK6Yl<?Cf<?E>xl >kIVJmTmE^<?JD>A>
lDEC|-MfCXMB<?E>J?:=WXEX<lD:S@>)CKO<?E>i9WX6JD>X
"
Before Continuation
After Continuation
Newly Inserted
Episode
Enabled Episode
Tell (X)
Tell (X)
X
ll (
Te
Continuation
Arcs
)
Te
ll (
X)
Tell (X)
Tell (X)
Active Inserted Episode
Active Inserted Episode
:=WX6J?> % d Z\CKM1<?:=M069IV<D:SCKMfPRIV8LGQS>
Inefficient Systematic Search
000
100
110
Efficient Systematic Search
Duplicate
State
001
101
101
???
??0
??1
011
?00
?10
?01
?11
010
110
Duplicate
State
001
011
Duplicate
State
101
011
No Duplicate States
:SWK69JD> % d#p
CV<?:=v|I|<?:=CXMBOhCXJ50wl<?>H8xI|<?:STH:{<w
#|e
111
C IKTmE9:=>AvK>BlDwl<?>H8xI|<?:STH:{<wXc\50G`C0Tm lTmE9:=Qg@>H0GYIVM9lD:=CXMOh6M9TU<D:SCKM#WK>HM9>HJDy
|I <?>Al<NC
TmE:SQS@ THIKM9@:g@I|<?>AloIXl:{<;TUCKMYl :g@>HJml>AIXTmE >UG9IVMYl :SCKMf]M9>~THIVMY@:{y
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MCK<LIKGGQSw <DE>}l >AQ=>kT_<?>A@>HG9IVM9lD:SCKM zM7YCK<DE#TmE9:=Qg@J?>HMc<?E>}l >AQ=>kT_<D>k@>H1y
G9IKM9l :SCKMx:glN8L>H8LCK: H>k@~IVM9@~GJDCXE:S7:{<?>A@~OhJDCX8Oh6<D6J?>)THCKM9lD:g@>HJmI|<?:=CXM N>THIKQ=Q
<DE9:Slq7QSCTm0:=MWIVM;>UG9IKM9lD:=CXM _
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TU>klDl
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TUCX8LGQ=>H<D>AM>Al?lHnnE>TmE9:=Qg@0y >UG9IVMYl :SCKM[Oh6M9TU<D:SCKM
-:=<DE
7QSCTm0:=MWB:SllDEC|-M
:SM
:=WX6J?> % d !
Child-Expansion (candidate, activity-library)
returns two child candidates
1.
let c1, c2 = copy of candidate
2.
if ( candidate has enabled episodes )
3.
let e = choose unblocked enabled episode
4.
insert(c1,e)
5.
block(c1,e)
6.
block(c2,e)
7.
return c1, c2
8.
else if ( candidate has enabled event )
9.
let e = unblocked enabled event
10.
insert(c1,e)
11.
block(c1,e)
12.
block(c2,e)
13.
return c1, c2
14. else if ( activity-library has enabled activity )
15.
let a = unblocked enabled activity from activity library
16.
instantiate(c1,a)
17.
block(c1,a)
18.
block(c2,a)
19.
return c1, c2
20. end-if
:=WX6JD> % d!R50G`C0Tm}Z\E:=Qg@}PG9IKM9l :SCKM[lD>H69@CVy Z\C0@>-:=<DE^NQSC0Tm0:SMW
10B q1C-;$ %&*210B0
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<DE9>HwfIKJD>oTHCKM9lD:g@>HJ?>A@+\\>kTHIK69l >79Q=CTmK>k@B>HG9IVM9lD:SCKM9l-TAIVM}M>HvX>HJ7`>THCKM9lD:S@y
>HJ?>A@IKWXIK:=Mc
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v0:SlD:=<D>A@oJD>AWXIVJm@QS>Al?lCKO<DE>NCKJm@>HJ
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50GYCTm
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CXJ
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#0b
>UG9IKM9lD:=CXM9lIv|IK:=QgIV7QS>\<DCo50G`C0TmoIKJD>n@>AGY>AM9@>HM1<kcXIVMY@o:SM9l >AJ <?:=M9W)CXM>N>HM9IK7Q=>k@
>HvX>HM1<RCKJ\>HG:glDC0@>-8LIwLTHIK69lD>-CV<DE9>HJ>AM9IV79Q=>k@L>HvK>AM1<?lCXJR>HG:glDC0@>Al<?Co7`>ATUCX8L>
6My >HMYIV7QS>A@+
Argument of Search Completeness – Case 1
2
1
Process Event 2 First…
3
Process Event 3 First…
Original Candidate
2
2
1
3
2
2
1
3
Insert
Event 3
2
1
3
Block
Event 3
3
1
3
3
Block Event 3
Insert Event 3
2
2
1
Insert
Event 3
2
1
3
Block Event 2
Insert Event 2
1
2
1
1
3
3
Insert
Event 2
Block
Event 3
2
1
2
1
3
Block
Event 2
2
1
3
Insert
Event 2
3
Block
Event 2
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#Vd
Enabled Episode
Inserting this enabled
event will cause Ask(X)
to be un-enabled, because
the Tell(X) that closes
Ask(X) will be deactivated
Ask (X)
Tell (X)
Enabled Event
Enabled Episode
Inserting either of these
enabled episodes will
cause the other episode
to be un-enabled,
because the Tell(not(Y))
constraint conflicts with
Tell(Y)
Tell (not(Y))
Tell(Y)
Enabled Episode
:=WX6JD> % aXen\C~ZNIKlD>AlnCKO My >HM9IK7Q=>A8L>HM1<
Ask (X)
Enabled
episode
If enabled event
is inserted,
enabled episode
is un-enabled
Tell (X)
Initial Candidate
Ask (X)
Ask no
longer
enabled
Consider
enabled
event
Tell (X)
(represents alternate
insertion)
Ask (X)
Tell (X)
Insert Event
Event is enabled
again, due to
addition of
causal link
Enabled
event
Block Event
Ask (X)
Consider
enabled
episode
Tell (X)
Ask (X)
Tell (X)
Block Episode
Insert Episode
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#&
Enabled Episode
Tell (not(Y))
Enabled Episode
Tell(Y)
Initial Candidate
Tell (not(Y))
Tell(Y)
Tell(not(Y)) is
re-enabled
when the
conflicting
Tell(Y)
constraint is
deactivated
Tell (not(Y))
Consider
enabled
Tell(Y)
episode
Tell(Y)
Insert Tell(Y) Episode
Block Tell(Y) Episode
Tell (not(Y))
Tell (not(Y))
Tell(Y) is
enabled again
when an
Consider
additional
enabled
conflictTell(Y)
Tell(Y)
Tell(not(Y))
avoidance
causal link is
episode
Insert Tell(Y) Episode
Insert Tell(not(Y)) Episode required
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Problem
Events in
Solution
Episodes in
Solution
1
2
3
4
5
6
7
6
10
9
11
16
20
16
5
13
11
13
32
44
30
Number of
Candidates
Generated
8
11
14
17
68
299
892
Time to Solve
0.04s
0.14s
0.14s
0.11s
0.67s
2.35s
15.21s
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"
#
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execute extinguish-fire activity
Ask (at $start)
forest fire
[0,0]
Tell (at $end)
[5,10]
[0,+INF]
UFFAV Move Activity
return
to base
fly to
forest fire
Ask (have retardant)
Forest
[0,0]
[10,20]
Tell (fire extinguished)
Ask (at forest fire)
[0,+INF]
UFFAV 1
UFFAV Extinguish-Fire Activity
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u M>UIK8;G9Q=>[TUCK8LGQS>U<?>}JD>AQSIV0>k@WKJmIVG9E79IKlD>A@ CKM <DE:glLGQgIVM#TAIVM9@:S@IV<D>[:Sl
!Ka
Plan Candidate
f-value = 10
Ask ( X = v )
3
1
2
0 [10,25] 10
Ask ( Y = k )
5
4
6
Activity Library
Tell ( X = v )
Activity A
A1
A2
Activity B
A3
[20,20]
Tell ( Y = z )
[5,5]
B4
Tell ( Y = k )
B1
B2
B3
[15,30]
[7,10]
B5
:=WX6J?> a9PIK8;G9Q=>~ZNIVM9@:S@IV<D> ) J?IKGE7`>UOhCXJD> 4 >H6J?:Sl <D:gTxZ\CXl <P\l<?:=8xIVy
<D:SCKM
Relaxed Candidate Graph
conflicting Tells
are ignored
Original Candidate
1
[10,25]
0
Tell ( X = v )
A1
A2
A3
[20,20]
Tell ( Y = z )
0
Ask ( X = v )
3
4
10
10
2
10
(f + g)-value = 15
Ask ( Y = k )
5
15
6
15
[5,5]
B4
Tell ( Y = k )
B1
0
B2
[15,30]
B3
15
[7,10]
B5
The Ax and Bx nodes do not need to be inserted, as they were
only instantiated as part of the relaxed candidate graph
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This TPN structure can be generated with RMPL
This arc cannot
currently be
represented using
RMPL
This TPN structure motivates additional RMPL constructs
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