In eg a ed Compu e -Aided Enginee ing 22 (2015) 343–360 343
DOI 10.3233/ICA-150493
IOS P ess
Reac i e execu ion o sol ing plan ailu es in
planning con ol applica ions
Cesa Guzmana, Pablo Cas ejona, E a Onaindiaa,∗and Je emy F ankb
aUni e si a Poli ècnica de València, Valencia, Spain
bNASA Ames Resea ch Cen e , Mo e Field, CA, USA
Abs ac . We p esen a no el eac i e execu ion model o planning con ol applica ions which epai s plan ailu es a un ime.
Ou p oposal is a domain-independen eg ession planning model which p o ides good-quali y esponses in a imely ashion.
The use o a eg essed model allows us o wo k exclusi ely wi h he su icien and necessa y in o ma ion o deal wi h he plan
ailu e. The model pe o ms a ime-bounded p ocess ha con inuously ope a e on he plan o eco e om incoming ailu es.
This p ocess gua an ees he e always exis s a plan epai o a plan ailu e a any ime. The model is es ed on a simula ion o a
eal-wo ld plane a y space mission and on a well-known ehicle ou ing p oblem.
Keywo ds: Reac i e planning, dynamic execu ion, moni o ing plan execu ion, eac i e execu ion agen , unp edic able en i on-
men
1. In oduc ion
The applica ion o A i icial In elligence AI plan-
ning echniques is helping indus ies o imp o e hei
e iciency and pe o mance in a g ea a ie y o ap-
plica ions: manu ac u ing and elecommunica ion ne -
wo ks [31,37], educa ion [20], ou e planning [10,41],
mili a y and ci ilian coali ion ope a ions [36], space
explo a ion [9], e c.
In gene al, e en hough much o he esea ch on AI
planning is aimed a gene a ing domain-independen
planning echnology, he applica ion o planning o in-
dus y gi es ise o special-pu pose sys ems, which a e
expensi e o ex end o o he cases. On he o he hand,
he e exis ew sys ems ha in eg a e au oma ed plan-
ning and plan execu ion and his is, pe haps, one o he
main causes o he ela i ely low deploymen o au o-
ma ed planning applica ions [22]. While he p ima y
ocus o planning is on delibe a i e ools o calcula e
plans ha achie e ope a ion goals, he ocus o execu-
∗Co esponding au ho : E a Onaindia, Depa men de Sis emas
In o má icos y Compu ación, Uni e si a Poli ècnica de València,
Spain. Tel.: +34 963 877 755; Fax: +34 963 877 359; E-mail:
[email p o ec ed].es.
ion is on de eloping con ol me hods o e ela i ely
sho ime spans o ensu e he plan ac ions a e execu ed
s ably [3].
Mos planning and execu ion (P&E) sys ems ollow
an in eg a ed app oach in which he execu ion moni o -
ing sys em is in eg a ed wi h he planne o ice e sa.
Sys ems like IXTET-EXEC [29] o TPOPEXEC [46]
wo k unde a con inual planning app oach [6], in e -
lea ing planning and execu ion in a wo ld unde con-
inual change. Ano he example can be ound in [9],
whe e he planne o a spacec a con inuously ope -
a es on he plan execu ion o epai ailu es. IDEA (In-
elligen Dis ibu ed Execu ion A chi ec u e) [1] is a
eal- ime a chi ec u e ha p oposes a uni ied iew o
delibe a ion and execu ion whe e he planne is em-
bedded wi hin he execu o ; and T-REX [32](Teleo-
Reac i e EXecu i e) is a delibe a i e P&E sys em o
AUV con ol inspi ed om IDEA. This ype o uni ied
app oaches allows only o a s ic and con olled in e -
lea ing o P&E, making i di icul o ha e a gene al-
pu pose planne o di e en ypes o execu o sys-
ems.
Some o he a o emen ioned P&E sys ems [29,46],
deal wi h empo al plans and ocus on a uni ied ap-
p oach ha accommoda es lexible plan execu ions, bu
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344 C. Guzman e al. / Reac i e execu ion o sol ing plan ailu es in planning con ol applica ions
hey a e no conce ned wi h p o iding esponses in a
imely ashion. In con as , he wo ks in [1,32], besides
gene a ing plans o e ela i ely long ime pe iods, hey
also in oduce a eac i e planne o allow obus pe -
o mance in dynamic en i onmen s. The e m eac i e
planning has been app oached om di e en pe spec-
i es [8]:
–Responding e y quickly o changes in he en i-
onmen h ough a eac i e plan lib a y ha s o es
he bes cou se o ac ion o each possible con in-
gency.
–Choosing he immedia e nex ac ion on he basis
o he cu en con ex ; in his case, a delibe a i e
p ocedu e can be used o speci y he nex ac .
–Using mo e complex cons uc s in o de o handle
execu ion ailu es o en i onmen al changes.
The i s app oach, used by ea ly P&E sys ems, im-
plies s o ing a plan o each possible s a e o he wo ld,
an op ion which is no a o dable in highly dynamic
en i onmen s. Hie a chical con ol s uc u es p o ide a
mechanism o choose he immedia e nex ac ion when
a quick esponse is equi ed in unp edic able en i-
onmen s [7]. This is he app oach ollowed by he
models ha emphasize eac i eness, compu ing jus
one nex ac ion in e e y ins an , based on he cu -
en con ex [32]. The use o mo e complex s uc-
u es allow o conside mo e delibe a i e (long ho i-
zon) esponses a he han sho - e m eac i eness bu ,
in p ac ice, none o hese eac i e amewo ks ha e
e e exploi ed he idea o p o iding quick delibe a i e
esponses. They eac o a change o ailu e bu hey do
no gua an ee a esponse wi hin a limi ed ime.
A key aspec o eac i e planning is ha i is no only
abou p o iding quick esponses o changes bu also
p ese ing he plan s abili y [18] and gua an ee ha he
ope a ion goals achie ed by he plan a e s ill eachable
a e he plan epai . In con as o con ol applica ions
ha use condi ion moni o ing o an icipa ing and e-
ac ing o aul s [4,40], eac i e planning is abou e-
pai ing a aul when is de ec ed while ying o main-
ain he execu abili y o he es o he plan.
The ocus o his wo k is on he de elopmen o a
eac i e P&E sys em capable o p o ide as delibe -
a i e esponses o epai a ailed ac ion wi hou ex-
plici ly ep esen ing con ingency b anches and eligible
plans o each possible s a e o he wo ld. Ou sys em
does no simply e u n he immedia e nex execu able
ac ion bu i ope a es o e a planning ho izon ha is
longe han he minimum la ency in e al s a ing a he
cu en execu ion ime. This idea was exposed, hough
ne e exploi ed,in IDEA [13], which in p ac ice wo ks
wi h he minimal planning ho izon in o de o educe
he eac i e planne ’s sea ch space; ha is, he sho e
he planning ho izon, he mo e eac i i y, bu also he
less con ex ual in o ma ion o epai he ailu e. The
idea o planning ho izon has been also exploi ed in
non- eac i e dynamic planning applica ions [47].
In his wo k, we p opose a no el eac i e P&E
model ha keeps ack o he execu ion o a plan and
epai s he incoming ailu es. The execu o - epai ing
sys em inco po a es a eac i e planning p ocedu e
which is exclusi ely used o plan epai and i is inde-
penden o he delibe a i e planne ha compu es he
solu ion plan o he p oblem. Unlike he in eg a ed
P&E app oaches men ioned be o e, ou s is a highly
modula and econ igu able P&E a chi ec u e. The e-
ac i e planne is specialized in small plan epai s ha
mus be accomplished p omp ly. Addi ionally, i p e-
compu es an ini ial sea ch space which encodes solu-
ion plans o po en ial ailu es in a agmen o he
plan named plan window (we use his e m equi a-
len ly o he concep o planning ho izon in IDEA [1]).
The cons uc ion o he sea ch space is a ime-bounded
p ocess subjec o he agen ’s execu ion la ency and he
numbe o execu ion cycles in he plan window, whose
objec i e is o ha e a solu ion plan a ailable when a
ailu e a ises. Once he sea ch space is buil , he agen
p oceeds wi h he plan execu ion, and simul aneously
he eac i e planne compu es he sea ch space o he
nex plan window. The eac i e model is hus capable
o deduce s ic limi s o he leng h o he plan win-
dow and compu e he la ges sea ch space wi hin he
ime limi . Then, i a ailu e occu s, he co esponding
sea ch space is used o ind a eco e y plan. This gi es
ou eac i e model an any ime-like beha iou .
Ou model con ibu es wi h se e al no el ies: (a) i
is a domain-independen P&E model ha can be ex-
ploi ed in any applica ion con ex ; (b) i is indepen-
den o he delibe a i e planne ; (c) i ades o de-
libe a i e and eac i e mechanisms o p o ide good-
quali y esponses in a imely ashion; (d) i a oids deal-
ing wi h unnecessa y in o ma ion om he wo ld, han-
dling speci ically he in o ma ion ele an o he ail-
u e; and (e) i pe o ms a ime-bounded delibe a i e
p ocess ha pe mi s o con inuously ope a e on he
plan o epai p oblems du ing execu ion.
This pape is o ganized as ollows. Sec ion 2 p e-
sen s some ela ed wo k and Sec ion 3 ou lines he
gene al P&E a chi ec u e whe e he eac i e model is
in eg a ed. The wo ollowing sec ions p esen some
o mal concep s and in oduce he eac i e planning
model o eco e om plan ailu es. Sec ion 6 p esen s
C. Guzman e al. / Reac i e execu ion o sol ing plan ailu es in planning con ol applica ions 345
a mo i a ion example on he Ma s space mission. Sec-
ion 7 p esen s he model e alua ion, Sec ion 8 dis-
cusses some limi a ion o he model and, inally, he
las sec ion concludes and ou lines u u e esea ch
lines.
2. Rela ed wo k
Classical planning e e s gene ically o planning o
s a e- ansi ion sys ems ha adop a se ies o assump-
ions like ha he sys em is de e minis ic and s a ic,
ha ac ions a e ins an aneous ansi ions and ha he
planne is no conce ned wi h any change ha may oc-
cu in he sys em while i is planning [21]. In con as ,
eac i e planning ope a es in a imely ashion wi h
highly dynamic, non-de e minis ic and unp edic able
en i onmen s, assuming unce ain y in he wo ld and
he exis ence o mul iple ou comes due o ac ion ail-
u es o exogenous e en s [34]. Ou eac i e planne
is no a empo al planne bu i is designed o e u n
imely esponses in highly dynamic en i onmen s.
Rega ding non-de e minis ic planning, he s udy o
inding he sequence o ac ions o e en s ha explain
he cu en obse ed s a e o he wo ld is called diagno-
sis. Mos o he esea ch on diagnosis pu he emphasis
in mal unc ioning componen s and ob aining a plan o
eco e om he componen ailu e a he han mon-
i o ing a plan execu ion [5,43]. Pa icula ly, he wo k
in [43] p o ides a o mal cha ac e iza ion o diagno-
sis and i s ela ion o planning and, in [5], au ho s p o-
pose an e olu iona y s a egy ha success ully diag-
noses se e al ypes o componen ailu es, such as he
sepa a ion o a body pa o he comple e ailu e o a
senso o mo o .
Planning in non-de e minis ic en i onmen s has also
been add essed om a p obabilis ic pe spec i e, ep-
esen ing p obabili ies o e he expec ed ac ion ou -
comes o belie s a e space. Planning based on Ma ko
Decision P ocesses is a well-known app oach o deal
wi h non-de e minism when an accu a e p obabili y
dis ibu ion on each s a e ansi ion is a ailable [27,33].
In highly dynamic en i onmen s whe e exogenous
e en s equen ly occu , i is no possible o ha e a
model o he unce ain y in he wo ld. Likewise, a Fi-
ni e S a e Machine (FSM) can also be used o imple-
men a eac i e beha iou [39] bu FSM equi es an ex-
plici modeling o a ini e se o plans (s a es and an-
si ions) and i is pa icula ly aimed a choosing only
he immedia e nex ac ion. When a plan is o be exe-
cu ed in an unp edic able en i onmen , i is imp ac i-
cal o ha e all po en ial epai plans explici ly ep e-
sen ed and he emphasis is no only on sho - e m eac-
i i y bu also on p ese ing he achie abili y o he op-
e a ion goals. Fo his eason, a ime-bounded eac i e
planne ha calcula es p omp ly eco e y plans o e a
planning ho izon is he mo e sui able solu ion.
3. An a chi ec u e o planning and execu ion
Ou wo k akes place in he con ex o PELEA [24], a
single-agen a chi ec u e in which an agen is endowed
wi h capabili ies o gene a ing a plan, execu ing, plan
moni o ing and, op ionally, lea ning. Ou ul ima e goal
o ex ending his model o a mul i-agen con ex is dis-
cussed in Sec ion 8. Be o e add essing his issue, ou
pu pose is o ha e an agen equipped wi h a eac i e
execu ion mechanism ha enables he agen o epai
a plan a un ime, hus a oiding he need o eso o
he delibe a i e planne each ime a ailu e occu s. In
he ollowing, we will e e o he concep o agen ,
speci ically o execu ion agen , as an au onomous en-
i y capable o pe o ming easoning and communica -
ing wi h o he en i ies o he sys em like he delibe a-
i e planne , which o e s a planning se ice.
In ou app oach, a planning se ice p o ides execu-
ion agen s wi h independen plans o be execu ed. An
agen , which is an ex ension o a PELEA1agen [24],
execu es and moni o s one ac ion a a ime and calls
i s epai ing mechanism o a eco e y plan whene e
a ailu e a ises. In case he agen is unable o sol e he
ailu e by i s own, i will eques he planning se ice
anewplan.
The ocus o his pape is on he epai ing mecha-
nism o he execu ion agen . The planning module em-
bedded in o he execu ion agen is a eac i e planne ,
which is used o eco e om ailu es a un ime. The
componen s o an execu ion agen (see Fig. 1) a e:
–Execu ion module (EX). The EX is ini ialized
wi h a planning ask, which cu en s a e is ead
om he en i onmen h ough he senso s. The
EX is esponsible o eading and communica ing
he cu en s a e o he es o modules as well as
execu ing he ac ions o he plan in he en i on-
men .
–Moni o ing module (MO). The main ask o he
MO is o e i y ha he ac ions a e execu able in
1A mo e de ailed desc ip ion may be ound a h p://se e g ps.
dsic.up .es/pelea/.
346 C. Guzman e al. / Reac i e execu ion o sol ing plan ailu es in planning con ol applica ions
Fig. 1. Flow o he eac i e execu ion model.
he cu en s a e be o e sending hem o he EX.
When he EX epo s he MO he s a e esul ing
om he execu ion o some ac ion o he plan, he
MO checks whe he he nex ac ion o he plan is
execu able in he esul ing s a e. This p ocess is
called plan moni o ing, e i ying whe he he al-
ues o he a iables o he ecei ed s a e ma ch he
expec ed alues o no . O he wise, he MO will
de e mine he exis ence o a plan ailu e.
–Reac i e Planne module (RP). The RP is used
when a plan ailu e is de ec ed by he MO
and a eco e y is equi ed. The RP uses a p e-
compu ed sea ch space, called epai ing s uc-
u e, o p omp ly ind a plan ha b ings he cu -
en s a e o one om which he plan execu ion
can be esumed (see Sec ion 5). In case he RP is
no able o ind a plan wi h i s epai ing s uc u e,
he MO eques s he planning se ice a new plan.
The EX, MO, and RP modules o an execu ion
agen ope a e he Reac i e Execu ion Model. The con-
ol low o he eac i e execu ion model is shown in
Fig. 1. An ac ion plan Π o sol ing a planning ask is
calcula ed by he planning se ice. Πconsis s o a se-
ies o ac ions o be execu ed a gi en ime s eps, each
o which makes a de e minis ic change o he cu en
wo ld s a e. The elapsed ime om one ime s ep o
he nex one de ines an execu ion cycle; i.e., he mon-
i o /ac ing/sensing cycle o an ac ion execu ion. The
model ollows se e al execu ion cycles, pe o ming he
scheduled ac ion in each cycle un il he plan execu ion
is comple ed.
Ini ially, he MO ecei es he plan Π om he plan-
ning se ice and, be o e sending Π o execu ion, i pe -
o ms wo ope a ions:
1. I sends Π o he RP, which c ea es a epai ing
s uc u e o a agmen o Πo leng h lcalled
plan window,whe elis he numbe o ac ions
o execu ion cycles in he plan window. The e-
pai ing s uc u e associa ed o he plan window
con ains in o ma ion, in he o m o al e na i e
plans, o epai a ailu e ha a ec s any o he l
ac ions included in he plan window.
2. When he ime o he RP expi es, and a epai -
ing s uc u e has been calcula ed o a pa icula
plan window, he MO moni o s he a iables o
he i s ac ion o he window. I he sensed al-
ues o he ac ion a iables ma ch he equi ed al-
ues o he ac ion o be execu ed, he MO sends
he scheduled ac ion o he EX o i s execu ion
(see Fig. 1). O he wise, a ailu e is de ec ed and
he MO calls he RP, which will make use o he
epai ing s uc u e o ix he ailing ac ion. No-
ice ha a ailu e ha occu s in he i s ac ion
o a window is due o an exogenous e en (e.g.
o he agen s change he wo ld s a e) and no due
o an e oneous execu ion o he p eceding ac ion
in he plan.
The MO ecei es he esul o he sensing ask om
he EX a e execu ing he ac ion, i upda es he plan
window acco dingly by elimina ing he al eady exe-
cu ed ac ion and p oceeds wi h he nex ac ion o he
plan window. Fo ins ance, assuming a plan o i e ac-
ions and a epai ing s uc u e o a plan window o
l=3([a1,a
2,a
3]), he plan window will be upda ed
o [a2,a
3]a e success ully execu ing a1,and heRP
will use he same epai ing s uc u e o ix a po en ial
ailu e in he emaining ac ions o he plan window,
ha is, a2o a3. Subsequen ly, he RP will c ea e a new
epai ing s uc u e, o example, o he plan window
[a4,a
5]. The low goes on as long as no plan ailu es
a e encoun e ed. In case ha a non-execu able ac ion is
ound, he MO epo s he ailu e o he RP. Then, he
RP uses he epai ing s uc u e associa ed o he plan
window o he non-execu ableac ion and ob ains a new
plan Π ha sol es he ailu e and eplaces he old plan
Π, a aining likewise he goals o he planning ask.
The RP is cons an ly wo king while he EX is ex-
ecu ing he ac ions o he plan. Hence, besides ha -
ing a epai ing s uc u e eady o a end a ailu e in
an ac ion o he cu en plan window, he RP is also
gene a ing he subsequen s uc u e o he nex plan
window. Typically, he ime o he RP o compu e
he epai ing s uc u e o he subsequen plan window
is he ime ha he EX will ake o execu e he ac-
ions included in he cu en window. The e o e, he
C. Guzman e al. / Reac i e execu ion o sol ing plan ailu es in planning con ol applica ions 347
mo e ac ions in he cu en plan window, he mo e ime
he RP will ha e o c ea e he nex epai ing s uc u e
and, consequen ly, he longe he window associa ed
o his epai ing s uc u e. This wo king scheme gi es
ou model an any ime beha iou , hus gua an eeing he
RP can be in e up ed a any ime and will always ha e
a epai ing s uc u e a ailable o a end an immedia e
plan ailu e.
On he o he hand, some simila i ies be ween ou
model and he li e cycle o a scien i ic wo k low can
be ound. Following [23], we can do his analogy: he
modeling phase is equi alen o he planning ask mod-
eling; he deploymen phase amoun s o he plan Πcal-
cula ed by he planning se ice; and he execu ion and
moni o ing phase would be he same in ou model. Un-
like scien i ic wo k low, ou model does no include an
analysis phase; howe e , successi ely epe i ions o he
deploymen ( epai plan) and execu ion phases happen
when a plan ailu e a ises.
4. Fo mal model
In his sec ion, we o malize he concep o planning
ask, pa ial s a e and a solu ion plan o a ask as a se-
quence o pa ial s a es [21]. Ou planning o malism
is based on a mul i- alued s a e- a iable ep esen a ion
whe e each a iable is assigned a alue om a mul-
iple alue domain ( ini e domain o a a iable). Fo
modeling planning p oblems, we used PDDL3.1,2 he
mos ecen e sion o he Planning Domain De ini ion
Language [17] (PDDL).
De ini ion 1. Planning ask A planning ask is gi en
by he 4- uple P=V,I,G,A:
–Vis a ini e se o s a e a iables, each associa ed
o a ini e domain, D , o mu ually exclusi e al-
ues ha e e o objec s in he wo ld. ∈Vmaps
a uple o objec s o an objec po he planning
ask, which ep esen s he alue o .Fo exam-
ple, in a plane a y Ma s o e s domain,3a o e
(B) can be placed a any o he waypoin s w1,w2o
w3. Hence, he a iable loc-B ep esen s he loca-
ion o o e B,andDloc-B={w1,w2,w3}.
A a iable assignmen o luen is a unc ion on
a a iable such ha ( )∈D
,whe e e ( )
2PDDL syn ax de ini ion in oduced in 2008 by M. Helme (h p:
//ipc.in o ma ik.uni- eibu g.de/PddlEx ension/).
3Ou PDDL speci ica ion o his domain can be ound a h p://
se e g ps.dsic.up .es/planin e ac ion/ esou ces/.
Fig. 2. Plan as a sequence o pa ial s a es. Va iables a e loc-B:lo-
ca ion o o e B;link-w1-w2: map o a el om w1 o w2;com- :
communica ion o he esul s o analyzing he ock . Unde lined
a iables a e he p econdi ions o he ac ion Na iga e.
is de ined. A luen is ep esen ed as a uple  ,p,
meaning ha he a iable akes he alue p.
A o al a iable assignmen o s a e applies he
unc ion o all a iables in V. A s a e is always
in e p e ed as a wo ld s a e. A pa ial a iable as-
signmen o pa ial s a e o e Vapplies he unc-
ion o some subse o V.
–Iis a s a e ha ep esen s he ini ial s a e o he
planning ask.
–Gis a pa ial s a e o e Vcalled he p oblem goal
s a e.
–Ais a ini e se o ac ions o e V. An ac ion a
is de ined as a pa ial a iable assignmen pai
a=p e,e o e Vcalled p econdi ions and e -
ec s, espec i ely. I an ac ion is execu able in a
s a e, i.e. i s p econdi ions hold in such a s a e,
he alues o he s a e a iables ( luen s) change
as speci ied in he e ec s.
An ac ion plan, ΠA, ha sol es a planning ask Pis
a sequence o ac ions ΠA=a1,...,a
n ha applied
in he ini ial s a e Isa is ies he goal s a e G. An ac-
ion ai∈ΠAis execu able in a wo ld s a e Si he lu-
en s con ained in Ssa is y he p econdi ions o ai;i.e.
p e(ai)⊆S. The esul o execu ing aiin a s a e Sis
anews a eS ha con ains he luen s o Swhich a e
no modi ied by e (ai)plus he luen s as speci ied in
e (ai). Then, execu ing ΠAin he ini ial s a e I esul s
in a sequence o s a es S1,...,S
nsuch ha S1is he
esul o applying a1in I,S2is he esul o applying
a2in S1,..., and Snis he esul o applying anin
Sn−1.AplanΠAis a solu ion plan i G⊆Sn[21].
A plan can also be iewed om he poin o iew
o he wo ld condi ions ( luen s) ha a e necessa y o
he plan o be execu ed. Tha is, ins ead o iewing a
plan as he esul o i s execu ion, we can iew a plan
as he necessa y condi ions o i s execu ion. Thus, a
plan can also be de ined as a sequence o pa ial s a es,
a he han wo ld s a es, con aining he minimal se o

348 C. Guzman e al. / Reac i e execu ion o sol ing plan ailu es in planning con ol applica ions
Fig. 3. Plan as a sequence o pa ial s a es o he plan ΠA. Va iables a e loc-B: loca ion o o e B;loc-L: loca ion o lande L;loc- -w3:
loca ion o he ock ;ha e-B: indica es i Bhas he ock ;link-wi-wj: map o a el om wi o wj; is-w3-w2: loca ion w2is isible om w3.
com- : esul s o analyzing he ock a e communica ed.
luen s ha mus holdin hewo ld o heplan obe
execu ableinsuchawo lds a e.
In he example depic ed in Fig. 2, he pa ial s a e
Gis he goal s a e Go a planning ask P,andi
con ains wo luen s. Le ’s conside he las ac ion o
aplanis(Na iga e Bw
1w2), which achie es he e -
ec loc-B,w2. Then, he necessa y luen s o be able
o execu e he ac ion and achie e he luen s in Ga e
ep esen ed in s a e G. We can obse e ha Gdoes
no only con ain he luen s ha ma ch he p econ-
di ions o he ac ion Na iga e (i.e., loc-B,w1and
link-w1-w2, ue, which ep esen ha he loca ion
o o e Bmus be he waypoin w1and a link be ween
w1and w2mus exis , espec i ely) bu also he luen
com- , ue. This is because his luen (communi-
ca ing he esul s o analyzing he ocks ) is a goal
o G ha is no achie ed by he e ec s o he ac ion
Na iga e. The eby, com- , ueis achie ed ea lie
in he plan and i mus hold in Gin o de o gua an ee
ha i is sa is ied in G.
The s a e Gin Fig. 2 is called a eg essed pa ial
s a e because i is calcula ed by eg essing he goals in
G h ough he ac ion Na iga e. Likewise, he same e-
g ession can be applied o he es o ac ions o a gi en
plan ΠA.Le aibe an ac ion and Ga goal s a e such
ha P=p e(ai),E=e (ai)and E⊆G.Thepa -
ial s a e Gin which aican be applied is calcula ed by
he eg essed ansi ion unc ion Γ(G, ai),de inedas:
G:= Γ(G, ai):=G E∪P(1)
Gis a pa ial s a e ha ep esen s he minimal se o
luen s ha mus hold in he wo ld s a e in o de o
achie e Gby means o he execu ion o ai. No ice ha
Gincludes P, he p econdi ions o ai, plus he luen s
which a e in Gbu a e no p oduced by E(G E); i.e.,
he luen s ha a e achie ed be o e Gin he plan and
mus keep hei alues un il G.
The eg essed pa ial s a e app oach was i s used
by PLANEX [11] o supe ise he execu ion o a se-
Fig. 4. Plan ΠA o a plane a y Ma s o e domain.
quence o ac ions. Plans a e ep esen ed by means o
a iangle able ( his s uc u e p o ides suppo o
plan moni o ing) and he p oblem goals a e eg essed
om he las column o he able, including ac ion
p econdi ions, h ough he emaining ac ions o he
plan. Roughly, he eg ession o a luen o e an ac ion
( h ough he eg essed ansi ion unc ion Γ)isasu i-
cien and necessa y condi ion o he sa is ac ion o he
luen ollowing he execu ion o he ac ion. The wo k
in [19] o malizes his concep in he si ua ion calculus
language whe eas we apply he same o maliza ion in
PDDL.
De ini ion 2. Solu ion plan as a sequence o pa ial
s a es Gi en a solu ion plan ΠA=a1,...,a
n o
a planning ask P, he eg essed plan o ΠAis de ined
as a ch onologically o de ed sequence o pa ial s a es
G0,G
1,...G
n,whe e:
Gn:= G
G0⊆I
Gi−1:= Γ(Gi,a
i)
A eg essed plan is deno ed by ΠG0−Gn,whe eG0
is he ini ial pa ial s a e and Gnis he inal pa ial
s a e o he plan ΠA. De ini ion 2 speci ies he ele-
an luen s a each ime s ep o he success ul execu-
ion o ΠA, whe e each ai∈ΠAis he ele an ac ion
o achie ing Gi om Gi−1. Hence, a eg essed plan
ΠG0−Gnde i ed om ΠAdeno es he luen s ha mus
hold in he en i onmen a each ime s ep o success-
ully execu e he ac ions in ΠA. In o he wo ds, his
de ini ion allows us o disce n be ween he luen s ha
a e ele an o he execu ion o a plan and hose ones
ha a e no . I exploi s he idea o anno a ing plans
C. Guzman e al. / Reac i e execu ion o sol ing plan ailu es in planning con ol applica ions 349
Fig. 5. Repai ing s uc u es o a o e Bin a Plane a y Ma s Domain. a: eg essed plan ΠG0−G5 o a1,a
2,a
3,a
4,a
5,b1: he epai ing
s uc u e o he plan window [a1,a2,a3], and b2: he epai ing s uc u e o he plan window [a4,a5].
wi h condi ions ha can be checked a execu ion ime
o con i m he alidi y o a plan [11]. Tha is, i he
luen s o a pa ial s a e Gihold in a wo ld s a e S
(Gi⊆S) hen he ac ions comp ised in he plan ag-
men ΠGi−Gna e execu able in S, hus gua an eeing
he goals o he planning ask a e achie ed.
Figu e 3 shows he eg essed plan ΠG0−G5de i ed
om he solu ion plan shown in Fig. 4, and calcula ed
h ough he successi e applica ion o he eg essed
ansi ion unc ion Γ. The plan in Fig. 4 shows he ac-
ions o a o e o ga he a ock sample, communi-
ca e he esul s o analyzing he ock and na iga e back
o he ini ial posi ion. Ac ion a2, o ins ance, c ea es
he luen ha e-B, in G2; and he pa ial s a e G1
is he esul om applying Γ(G2,a
2), which includes
p e(a2)( he luen s which a e unde lined in node G1
o Fig. 3) plus he luen s ha a e in G2bu a e no
p oduced by e (a2). The e o e, i he senso eading
e u ns a wo ld s a e in which all o he luen s in G1
hold, hen ac ion a2is execu able in such a wo ld s a e;
i he luen s in G2occu in he subsequen wo ld s a e
hen a3is execu able and so on. The las pa ial s a e,
G5, comp ises G, he goals o he planning ask. In
e ms o plan moni o ing, G5 ep esen s he luen s ha
sa is y he p econdi ions o a ic i ious inal ac ion, a ,
whe e p e(a )=Gand e (a )=∅,i.e.Gis moni-
o ed by checking he p econdi ions o a .
As a inal ema k, we no e ha he eac i e execu ion
model is de ined a he same g anula i y le el han he
planning model, and bo h use PDDL as he speci ica-
ion language. This eases he communica ion be ween
he planning se ice and execu ion agen s and a oids
he o e head o ansla ing a high-le el planning spec-
i ica ion in o a low-le el desc ip ion as i happens in
o he models [14].
5. Reac i e execu ion model
The key concep o ou eac i e execu ion model is
he epai ing s uc u e. Gene ally speaking, gi en a so-
lu ion plan ΠA, a epai ing s uc u e Tis a pa ial-s a e
sea ch ee ha encodes eco e y plans o a plan win-
dow o ΠA. Since nodes in Ta e pa ial s a es, he e-
ac i e execu ion model only handles he minimal da a
se ha is necessa y o ca y ou a epai ing ask.
Figu e 5 shows wo epai ing s uc u es, T1and T2,
o he eg essed plan in Fig. 3 ( o simplici y, we do
350 C. Guzman e al. / Reac i e execu ion o sol ing plan ailu es in planning con ol applica ions
no show all he pa ial s a es ha would be gene a ed).
T1is he sea ch ee associa ed o he plan window
[a1,a
2,a
3], o , equi alen ly, o he eg essed subplan
ΠG0−G3. The leng h o he window is h ee (l=3),
because i comp ises h ee ac ions, and he pa ial s a e
G3is called he oo node (G )o T1. A pa h in T1
ep esen s a ( eg essed) plan o each he oo node
G3. Speci ically, a pa h in a epai ing s uc u e is in e -
p e ed as a eco e y plan ha leads he cu en wo ld
s a e o ano he s a e om which he execu ion o he
plan ΠAcan be esumed. All eco e y plans in T1
ha e one hing in common: hey e en ually guide he
execu ion o he plan owa ds G3, he oo node o
T1. Fo ins ance, suppose ha Sis he se o luen s
ha ep esen s he s a e o he wo ld s a e such ha
G
16 ⊆S(see Fig. 5 b1). The applica ion o he plan
Π=a1,a
4,a
8,a
6 o Swill each he pa ial s a e
G3, om which he es o he plan ΠA,a4,a
5, can
be execu ed.
The ee T2(see Fig. 5 b2) is associa ed o he plan
window [a4,a
5], o o he eg essed plan ΠG3−G5.The
numbe o epai ing s uc u es necessa y o keep ack
o he execu ion o a plan ΠAdepends on he ime limi
o c ea e he sea ch ees, which, in u n, delimi s he
size o he ee. Two pa ame e s de e mine he size o a
sea ch space T, he leng h o he plan window associ-
a ed o T(l), and he dep h o he ee (d). In gene al,
he la ge he alue o l, he mo e al e na i es o ind
a eco e y plan; and he deepe he ee, he longe he
eco e y plans comp ised in T. The minimum alue o
dmus be l+1in o de o ensu e ha he ee com-
p ises a leas one ac ion ha epai s he i s ac ion o
he plan window associa ed o T. On he o he hand,
he maximum alue o dis de e mined by he a ailable
ime o build T. Pa icula ly, in T1,d=6,which e-
sul s om l=3and he ime limi o build T1(Sec ion
5.3 explains in de ail how o es ima e he maximum
size o a epai ing s uc u e).
In he ollowing, we explain (1) he p ocess o build
a epai ing s uc u e, (2) how o ind a plan in a sea ch
ee o epai a ailu e and (3) he analysis o es ima e
he size o he sea ch ee.
5.1. Building a epai ing s uc u e T
The cons uc ion o he epai ing s uc u e Ts a s
a e es ima ing he size o T; i.e., when he alues o l
and da e known. The gene a ion p ocess, shown in Al-
go i hm 1, consis s in expanding T om he oo node
G ia he applica ion o he eg essed ansi ion unc-
ion Γ(G, a) ollowing Eq. (1) (line 6 o Algo i hm 1).
The algo i hm is a classical backwa d cons uc ion o
a planning sea ch space [21], whe e a node Gis ex-
panded un il dep h(G)=d;i.e.,G eaches he max-
imum dep h ee (line 4), o Gis supe seded by an-
o he node ha exis s in he ee (lines 7 o 13 de ine a
mechanism o he con ol o epea ed s a es which is
de ailed below).
Inpu : G ,d
Ou pu : T
1: Q←{G },T←{G }
2: while Q =∅do
3: G← emo e i s node om Q
4: i dep h(G)<d hen
5: o all {a|a∈Ais a ele an ac ion o G}do
6: G←Γ(G, a)
7: i G/∈T hen
8: i ∃G∈T |G⊂G hen
9: ma k Gas supe se o G
10: else
11: Q←Q∪G
12: se ansi ion (labeled a) om G o G
13: T←T∪G
14: else
15: Q←∅
16: e u n T
Algo i hm 1: Gene a ing he epai ing s uc u e T.
The pu pose o Algo i hm 1 is o gene a e mul i-
ple eg essed plans om G . Unlike he applica ion o
Γ(G, a)in De ini ion 2, which depa s om a gi en so-
lu ion plan ΠA, such a plan does no exis when build-
ing a ee T. Ac ually, he aim o Algo i hm 1 is p e-
cisely o ind he ele an ac ions o a node G(line 5),
and e en ually c ea e a plan ΠA ha links wo pa icu-
la pa ial s a es.
The ope a ion o eg essing a luen in a node G
o e an ac ion achecks whe he ais a ele an ac ion
o achie e o no . An ac ion ais ele an o ,and
o igina es an a c (G,G)in T, i i does no cause any
con lic wi h he luen s in Gand G. The cons uc ion
o Thas hen o check wo consis ency es ic ions: (1)
ha e (a)does no con lic wi h he luen s in G,and
(2) ha p e(a)does no con lic wi h he luen s in G.
We de ine Φ(G,G)as he unc ion ha e u ns
whe he o no a con lic be ween wo se s o luen s
Gand Gexis s. Φ(G,G)holds i ∃ ,p∈Gand
∃ ,p∈Gand p=p.
De ini ion 3. Rele an ac ion Gi en a luen ∈G,
ais a ele an ac ion o i he ollowing condi ions
hold:
1) ∈e (a)and
C. Guzman e al. / Reac i e execu ion o sol ing plan ailu es in planning con ol applica ions 351
2) ¬Φ(e (a),G)and
3) G=Γ(G, a)∧¬Φ(p e(a),G
)
The cons uc ion o T ollows he applica ion o
De ini ion 3 o each luen o a pa ial s a e Gwhich
has no eached dep h(G)=d(lines4and5o Algo-
i hm 1), and he expansion con inues un il no new pa -
ial s a es a e added o he ee. The sea ch space Tis
ac ually a g aph due o he exis ence o mul iple pa hs
ha each he same pa ial s a e om he oo node du -
ing he cons uc ion o T. Mul iple pa hs a e o igina ed
because o ac ions like (Communica e ock B L w3w2)
and (Communica e soil B L w3w2), which can be ex-
ecu ed in ei he o de , o he exis ence o e e sible ac-
ions like (Na iga e Bw
1w2)and(Na iga e Bw
2w1).
Consequen ly, Tmay con ain many edundan pa hs.
A se o s a e a iables induce a s a e space ha has
a size ha is exponen ial in he se , and, o his ea-
son, planning, as well as many sea ch p oblems, su -
e om a combina o ial explosion. E en hough nodes
in Ta e pa ial s a es ha con ain a less luen s han
wo ld s a es, he la ge size o he epai ing s uc u es
a e some imes una o dable o a eac i e sys em. Wi h
he aim o educing he size o T, we only conside
o expansion he luen s o G ha a e ela ed o he
ele an a iables, ha is, he a iables in ol ed in he
p econdi ions o he ac ions o he plan window. Thus,
gi en a plan window [a1,a
2,a
3], we app oxima e Tby
expanding only he luen s ela ed o he ele an a i-
ables in ol ed in he se p e(a1)∪p e(a2)∪p e(a3),
which is ac ually he se o luen s ha migh need o
be epai ed. The ime complexi y o Algo i hm 1 e-
sponds o he classical complexi y o he gene a ion o
a ee, ha is O(ˆ
bd),whe eˆ
bis he es ima ed b anching
ac o o T ha is de ailed in Sec ion 5.3.
The gene a ion p ocess makes wo nodes in Tbe
connec ed by a unique simple pa h. Since we a e in e -
es ed in keeping only he sho es (op imal) pa hs, he
cons uc ion o Tp unes epea ed s a es (line 7 in Al-
go i hm 1) and a oids he expansion o supe se nodes
(lines 8 and 9). Le ’s assume ha Tcon ains a pa h
om a node G o he oo node G o T. A node G
such ha G⊂Gis said o be a supe se o node G.In
his case:
–Gs ands o he minimal se o luen s ha mus
hold in Sin o de o execu e he ac ions o he
pa h ha eaches G .
–The bes eco e y plan om Gis also he bes
pa h om Gbecause he RP e u ns he sho es
plan o G .
All in all, a epai ing s uc u e encodes he op imal
pa h be ween each pai o nodes o which a eco e y
plan can be ound. Once he RP has c ea ed T,i com-
munica es he MO all he a iables in ol ed in T.
5.2. Repai ing a ailu e
When an ac ion o he plan window associa ed o a
epai ing s uc u e T ails, he RP inds a way o keep
he plan going, ei he by eaching a pa ial s a e in T
om which o execu e he aul y ac ion again o a he
ano he s a e om which o execu e a la e ac ion o
he plan window.
Le Tbe a epai ing s uc u e o a eg essed plan
ΠG0−G associa ed o he plan window [a1,...,a
]o
aplanΠA.Whenanac ionin[a1,...,a
] ails, a e-
pai ing ask de ined as R=S, G is ac i a ed, whe e
S4is he se o luen s o he cu en wo ld s a e and G
is he a ge s a e we wan o each in T. The node G
a ies depending on he ailed ac ion and he pa icula
epai ing ask o such ac ion. Since se e al eco e y
plans can be ound o ix a aul y ac ion, he RP will
successi ely execu e a epai ing ask un il one o hem
is success ul o ixing he ac ion. This way, i he e -
oneous ac ion is a1, he RP will i s y he epai ing
ask R=S, G0; o he wise, i will y R=S, G1
and so on un il G =G ; i he ailu e occu s in a2,
he i s a emp will be R=S, G1and he las a -
emp will be o G =G ; in he case ha he ail-
u e a ec s a , only wo epai ing asks can be ealized,
R=S, G −1and R=S, G .
Mo e o mally, gi en R=S, G  o a aul y ac-
ion a, he RP applies a modi ied b ead h- i s sea ch
om G un il a node Gs ha sa is ies Gs⊆Sis ound
in T.Gsis a consis en s a e wi h S, a s a e ha com-
p ises all he necessa y luen s o execu e in he cu -
en wo ld s a e he plan o med wi h he ac ions om
Gs o G .I Gs⊆Sis ound, he eco e y plan om
Gs o G is conca ena ed wi h he plan om G o
G (unless G =G ), and wi h he plan om G o
Gn,whe eGnis he las s a e o he o iginal plan ΠA
which con ains G, he p oblem goal s a e. I Gs⊆S
is no ound, he RP will execu e he subsequen e-
pai ing ask R=S, G +1un il one o hem success-
ully e ie es a eco e y plan o Ris in oked wi h G
=G and a plan is no ound. In his la e case, T
does no comp ise he necessa y in o ma ion o ind a
4Technically speaking, he MO does no communica e he RP all
o he luen s in Sbu only he alues o he a iables ha appea in
T; hese a iables we e sen by he RP o he MO a e building T.
358 C. Guzman e al. / Reac i e execu ion o sol ing plan ailu es in planning con ol applica ions
Table 4
Summa y o s a is ics o RP, LPG-ADAPT and LAMA pe o -
mance
S abili y (%) ΔΠ
ATime (ms)
μσ μσ μ σ
RP 92 19 0.97 0.85 1.85 4.33
LPG-ADAPT 85 19 2.40 1.94 49.47 4.72
LAMA 51 27 1.33 1.52 62.83 36.99
alyze i , o calib a ing he o e ’s came a again (e.g.,
ailu e 2 o p oblem 4). Failu es o ype C we e ound
in wo cases, which could be epai ed because hei e-
spec i e T1included pa hs in ol ing he second o e
(e.g., ailu e 3 o p oblem 6). He e, a ha dwa e ailu e
p e en he o e om analyzing he soil in a speci ic
loca ion, ou model epai s he ailu e using he second
o e ha explo es he a ea seeking o soils, analyzes
he soil and communica es he esul s o he lande . In
he ailu es o ype D, he RP akes ad an age o he
posi i e ailu e, which achie es he e ec s o he nex
ac ion o execu e and, consequen ly, he RP p oceeds
wi h he ollowing ac ion in ΠA.
The pe o mance esul s in Table 3 and he sum-
ma y o s a is ics in Table 4 show ha ou RP pe -
o ms admi ably well in all he measu ed dimensions.
Rega ding s abili y, RP ou pe om s LPG-ADAPT and
LAMA. LAMA is he app oach wi h he wo s a e
o s abili y (51%), which is easonable since he plan-
ne does no epai a plan bu i compu es a new plan.
In Table 3 we can see ha he plan quali y o numbe
o ac ions o Π
Ais sligh ly highe wi h he RP han
wi h LAMA in some cases (e.g., ailu e 1 o p ob-
lem 12 o ailu e 3 o p oblem 7), and lowe in some
o he cases (e.g. ailu e 2 o p oblem 12 o ailu es 1
and 2 o p oblem 10). LAMA is able o ind sho e
plans in a ew cases because i compu es a plan o he
new si ua ion wi hou being subjec o keep he ac ions
in ΠA. Ne e heless, all in all, he RP e u ns plans
o be e quali y han LAMA as Table 4 shows ( he
mean alue in he inc ease o he numbe o ac ions
is 0.97 in RP agains 1.33 in LAMA). The compa i-
son be ween RP and LPG-ADAPT clea ly bene i s RP
in bo h s abili y and quali y o he eco e y plan, pa -
icula ly in he mos complex p oblems (10 o 12). As
o he compu a ion ime, inding a eco e y pa h o
he oo node is mo e cos ly since he epai ing mech-
anism explo es he en i e sea ch space. Howe e , RP
shows ou s anding esul s compa ed o LPG-ADAPT
and LAMA, which p o es he bene i o using he RP
o epai plan ailu es in eac i e en i onmen s besides
a oiding he o e head o communica ing wi h a de-
libe a i e planne . In conclusion, we can a i m ha
ou model is a obus eco e y mechanism o eac i e
planning ha also p o ides good-quali y solu ions.
8. Limi a ions and ex ensions o he model
The esul s in Sec ion 7 show ha ou eac i e ex-
ecu ion model mee s he pe o mance needs o a e-
ac i e plan epai and ha i also ou pe o ms o he
epai ing mechanisms. Howe e , he model p esen s
some limi a ions ha we in end o o e come in he u-
u e. One limi a ion is he machine dependency o he
es ima ion model explained in Sec ion 5.3. In o de o
ep oduce he expe imen s, o o expo hem o o he
sys ems, he aining o he es ima ion model mus be
epea ed o adjus he alue o ¯
Γ o a pa icula p o-
cesso .
Assuming se e al agen s execu ing hei plans in
a common en i onmen , a epai ing ask o an agen
migh cause con lic s in he plan o he o he s. Addi-
ionally, he occu ence o ailu es could es ic he ca-
pabili ies o he agen s, p e en ing hem om achie -
ing some goal. The e o e, a mul i-agen app oach
whe e execu ion agen s ac , coo dina e and join ly e-
pai a ailu e is desi able [2,16,35]. A communica-
ion p o ocol ha helps agen s eques , p o ide and
ag ee on a pa icula eco e y plan is a desi able ap-
p oach o a mul i-agen epai sys em [25]. Pa icu-
la ly, he p esen wo k ep esen s a i s s ep owa ds
a mul i-agen P&E sys em capable o coo dina ing
agen s plans while minimizing c owd-e ec s [44].
Ou model can be easily ex ended o pa allel and
empo al planning. The pa allel execu ion o se e al
ac ions o an agen is achie able by g ouping oge he
he p econdi ions and e ec s o he pa allel ac ions in o
a new ac ion. The exis ence o g ouped ac ions would
a oid he duplica ed s a es ha a ise om he mul iple
se ializa ion o he ac ions in he g oup. On he o he
hand, handling du a i e ac ions in empo al planning
would in ol e c ea ing a eg essed pa ial s a e a each
ele an ime poin o an ac ion and adding luen s o
ep esen he ongoing execu ing ac ions a each execu-
ion cycle.
9. Conclusions and u u e wo ks
This pape p esen s a eac i e execu ion model,
which comp ises a RP, o eco e om ailu es in plan-
ning con ol applica ions. The model is embedded in o
a P&E sys em whe e an execu ion agen ecei es a
plan om a delibe a i e planne and i s mission is o
moni o , execu e and epai he gi en plan.
P o iding ime-bounded esponses in eac i e en i-
onmen s is a di icul and some imes un easible ask

C. Guzman e al. / Reac i e execu ion o sol ing plan ailu es in planning con ol applica ions 359
due o he unp edic abili y o he en i onmen and he
impossibili y o gua an ee a esponse wi hin a gi en
ime. An al e na i e solu ion o o e come his di icul y
is wo king wi h ime-bounded da a s uc u es a he
han designing ime-bounded easoning p ocesses. By
ollowing his app oach, ou model ensu es he a ail-
abili y o a epai ing s uc u e, o sea ch ee, wi hin a
gi en ime, which is la e used o ix he ac ion ailu es
du ing he plan execu ion.
Se e al ea u es ha e been conside ed in o de o
ha e a sea ch ee gene a ed in due ime: (1) he ee is
o med o pa ial s a es which con ain a less luen s
han wo ld s a es; (2) he ee is limi ed o a pa icula
agmen o he plan and ee dep h ha a e calcula ed
by an es ima ion model; and (3) he expansion o he
ee only conside s he ele an a iables ha migh po-
en ially ail du ing he plan execu ion.Unde hese c i-
e ia, we show he esul s ob ained o wo di e en do-
mains, a simula ion o a eal NASA space p oblem, and
a ehicle ou ing domain. The esul s co obo a e ha
he e is a 95% likelihood o ob ain a epai ing s uc-
u e in ime. Addi ionally, he exhaus i e expe imen-
a ion on he epai ing asks con i m ha he epai ing
s uc u e oge he wi h he sea ch eco e y p ocess is
a e y sui able mechanism o ix ailu es ha ep esen
sligh de ia ions om he main cou se o ac ion in a
planning con ol applica ion. The esul s suppo se -
e al conclusions: he accu acy o he model o gene -
a e epai ing s uc u es in ime, he use ulness o a sin-
gle epai ing s uc u e o epai mo e han one ac ion
in a plan agmen while eusing he o iginal plan as
much as possible, and he eliabili y and pe o mance
o ou eco e y sea ch p ocedu e in compa ison wi h
o he well-known classical planning mechanisms.
The cu en RP can be ex ended in se e al di e en
di ec ions as, o ins ance, by including he necessa y
machine y o deal wi h empo al plans. Ou nex u u e
wo k is o exploi his model o a mul i-agen eco e y
mechanism in which agen s dynamically o m a eam-
wo k a execu ion ime and wo k oge he in he epai
o a plan ailu e.
Acknowledgmen s
This wo k has been pa ly suppo ed by he Spanish
MICINN unde he p ojec s TIN2014-55637-C2-2-R,
and he Valencian p ojec PROMETEOII/2013/019.
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