From: AAAI Technical Report SS-93-03. Compilation copyright © 1993, AAAI (www.aaai.org). All rights reserved.
Classical
Honeywell
Nonlinear
Planning
in
Complex
Mark
Boddy
boddy@src.honeywell.com
Systems & Research
Center,
:]660 Technology Drive
Minneapolis,
MN 55418
Abstract
Classical nonlinear planning has been studied in
the abstract since the early 1970’s. More recently,
interest has grown in applying these techniques to
real problems, or at the least to simplified versions
of real problems. In this paper, we explore someof
the implications and results of those applications,
with an eye to addressing the question of where
the main problems lie. What successes have been
achieved? What remains to be done? In particular,
what fundamental representational or algorithmic
issues, if any, need to be addressed before classical
planning becomesa useful tool for large, complex,
real-world problems?
Introduction
This paper is primarily a discussion of classical nonlinear planning in complex domains. Our concern is
with how the planning problem is changed when we
attempt to model more of the characteristics
encountered in these domains. Abstraction has both benefits
(refining away details to reveal the essential nature of
a problem) and disadvantages (some of those details
have a profound impact on the nature of the problem).
For example, the Blocksworld has proved to be a useful
abstraction in which to isolate and examine certain issues in planning. However, as the limitations of the
Blocksworld have became apparent, more recent abstract domains (e.g., Tileworld [Philips and Bresina,
1991]) added such complexities as duration and deadlines, events not under the planner’s control, and uncertain action outcomes.
Section provides somedefinitions and historical perspective. Wethen investigate the problems caused for
planners by the introduction of partially-ordered plans,
action durations and deadlines, simultaneous actions,
and events not under the agents control. This is not
a list of arguments for abandoning classical planning.
Quite the contrary: for every difficulty raised here,
there is at least a partial solution to the problem. We
close with a summary and some recommendations for
future work.
Domains
MN65-2100
Definitions
Webegin by defining some terms and providing a limited historical background. A plan is an internal representation of actions an agent may perform to bring
about changes in the environment. Representing a plan
requires operators: abstract representations of the actions available. Predicting the effects of executing a
plan (i.e., performing the corresponding actions) requires some representation of the environment’s state
and how that state is modified by the performance
of the actions corresponding to the various operators.
This prediction is commonly called projection. The
effects of actions are frequently modelled as operator
poatconditioa8, sometimes specified as add and delete
lists of propositions modified by performance of the action. Operator preco~clitions encode the states in which
a given action maybe taken and howthe effects of that
action depend on the state in which the action is performed. 1
The plannin9 problem starts with an initial state description, and a 9o~1 to be achieved. The goal consists
of a set of conditions to be achieved at the end of the
plan’s execution. 2 Workon replanning or generative
planning adds a pc~rtigl plar~ to be modified so that the
goal is achieved. For this paper, I take "classical planning" to be the study of generative methods for solving the planning problem. Included in this definition
are specializations such as hierarchical or constraintposting planning.
The planner cannot make perfect predictions about
the effects of a given plan. This true is independent
of any consideration of dynamic domains (e.g., malicious infants knocking over towers of blocks). The issue
is purely one of abstraction: any practical model of a
physical process omits some details. In order to plan
in the classical sense of the term, the planner needs to
manipulate models of both the environment and the
1For the moment,we finesse the frame problem and related issues by assuminga STKIPS-rulesemantics on a linear sequenceof completelyspecified operators.
aThis definition of a god can be extendedin a straightforward wayto include descriptions of states to be avoided
or maintained throughout the plan’s execution.
agent’sactions.
The moredetails
omittedfrom these
no possible
intervening
defeater,
thegoalis declared
to
be satisfied.
Thisis notprojection,
because
wearemakmodels,
themoreerrors
willoccurin theplanner’s
preing onlya localdetermination.
No attempthas been
dictions.
As planners
areapplied
to morecomplex
dowhetherthe preconditions
forthe
mains,thedomainandactionmodelsrequired
to main- madeto determine
operator
satisfying
the goalaretrue.Thisapproach
taina reasonable
degreeof fidelity
becomemorecomsuffices
foran environment
in whichtheplannerhas
plexaswell.
complete
control
overwhathappens:
goalscanbe satIn STRIPS[Fikesand Nilsson,1971],statesare
represented
as listsof predicates
andactions
aredeisfiedby addinga newoperator
or movingexisting
operators
around.
If thereareevents
notundertheagent’s
scribed
by operators
including
preconditions,
addand
control,
it maynotbe possible
to addoperators
where
deletelists.Theseoperators
makeno provision
for
desired
or to forcethenecessary
orderings.
Thisputs
context
dependent
effects,
simultaneous
actions,
or acbackin theposition
of needing
projection
tion durations.More recently,STRIPSoperators ourplanner
in themorecomplete
sense.
have beenextendedto modelcontext-dependent
effects[Pednault,
1988]andadditional
inference
mechThisresultalsoimplies
thatnonlinear
planners
doanismshavebeenaddedto derivecontext-dependent ingprojection
(i.e.,
thosenotusingsomelocalcriterion
effects,
e.g.[Wilkins,
1984,AllenandKoomen,
1983]. liketheMTC)areeither
solving
a hardproblem
in some
cases,or computing
incorrect
results
in somecases.If
Someworkhas beendoneto add duration
[Vere,1983,
computationally
expensive
problem
instances
aresuffiDeand al., 1989, Tats et al., 1992].
The advent of nonlinear planning [Sacerdoti, 1977,
ciently
rare,thismaybc acceptable.
Thepossibility
of
Tats, 1977] introduced new complications to the probincorrect
results
is moretroubling.
lem of determining the effects of a given plan. WefolIn previouswork[Deanand Boddy,1988],we have
low [Minton et al., 1991] in defining nonlinear classical
demonstrated
thatit is possible
to compute
an approxplanning to be generative planning that manipulates
imation
to projection
fornonlinear
plansin polynomial
partially-ordered sets of operators, whether or not the
time.Thealgorithm
is sound,meaning
thatif it says
final plan produced is required to be completely orthata factisnecessarily
trueata point,
thatdetermidered.
nationis correct.
Theapproximation
involved
is that
thealgorithm
is notcomplete:
itmayfailto detect
the
factthatsomefactis necessarily
true.s SincethealProjection
and Partial
Orders
gorithm
handles
negated
propositions,
it is possible
to
The original intuition behind nonlinear planning was
compute
projections
involving
a
fact
and
its
negation
the happy thought that we could plan by a process of
so as to determine
whether
a proposition
is necessarily
adding orderings only as required to ensure that our
true
at
a
point,
necessarily
false
at
that
point,
or indeplan has the right effects. This "least commitment"
terminately
one
or
the
other.
Thus,
even
for
planning
approach was entended to other forms of constraints
problems
involving
events
beyondtheplanner’s
control,
as the notion of constraint-posting planning was genprojection
canbe regarded
as a solvedproblem,
though
eralized to include other aspects of a developing plan
onethatrequires
a little
carein implementation.
4
(e.g., [Stefik, 1981]. Constraint-posting planning can be
viewedas an incremental process of eliminating possible
Duration
and Deadlines
plans from a set defined by the current set of constraints
by adding additional constraints. For this process to be
The fact that actions take time was abstracted out in
effective, it must be the case that the planner can dethe earliest domain models. Planners using these modtermine whether
or notthereis a planin thecurrent els will be of limited use in domains where synchronizasetofpossibilities
thatwillachieve
thegoal,or that
tion with other events or processes is important. This
canbe augmented
so thatit willachieve
thegoal.If
may include such domains as manufacturing planning
theplanner
cannotconstruct
a nontrivial
description and scheduling, spacecraft operations, robot planning
of theremaining
possible
plansandhowthatsetwould in any but the most simplified domains, and scheduling
be changed
by additional
constraints,
it is essentially distributed problem-solving or other processing.
adding
constraints
arbitrarily
soas toobtain
a plansufAs mentioned in Section , several planners include
ficiently
constrained
thatit canbe analyzed.
Making representations
for metric timeandactiondurations.
sucharbitrary
choices
is exactly
thekindof behavior In addition,
variouspeoplehaveimplemented
"temthatthe leastcommitment
approachwas intendedto
poralreasoning
systems"
in an attempt
to isolate
and
circumvent.
optimize
reasoning
abouttherelations
amongactions,
Generating
a correct
andnon-trivial
description
of
or betweenactionsandotherprocesses
[Allen,
1983,
theeffects
ofa nonlinear
planis computationally
expensive[Chapman,
1987,DeanandBoddy,1987].One way
SThecircumstances
underwhich
thisalgorithm
is incomaround
thisdifficulty
is to treatplanning
as a purely plete
aredescribed
in[Schrag
etal.,
1992].
constructive
activity.
For example,
Chapman’s
Modal
4Assuming
nonlinear
plansconsisting
of STRIPS
operTruthCriterion
focuses
onlyontheeffects
of operators: ators.
Itiscertainly
possible
tocomplicate
projection
by
ifthereis a preceding
operator
establishing
a goal,and
adding
other
features
totherepresentation.
chical Interval Constraints (HIC). Each HICtype has
..................
1.2................. function defined for calculating bounds on its duration.
0.70
0.70
FigureI: A simpleproblemwithduration
andpartial
orders
For the example in Figure ??, the two activities would
be contained in an HIC whose duration was calculated
by summingthe duration of the included operators.
The problem with this approach is the requirement
of a rigid hierarchy. If actions must be ordered for reasons that are not locally determinable (e.g. because of
resource conflicts, not because they are sequential steps
in some task reduction), this representation will break
down. It may be possible to augment Williamson and
Hanks’ representation to cope with a limited number of
special structures representing such nonlocal information.
Simultaneous
Actions
The general problem of reasoning about the effects of
actions, when those effects may depend on what other
Dean and McDermott,1987, Arthurand Stillman, actionsoccurred at thesametime,is a computational
1992].Oplan-2contains
a separate
reasoning
module nightmare.
Potentially,
youneedto construct
a descrip(thetimepointnetwork
manager)
withsimilar function- tionofsimultaneous
effects
forthepowersetoftheset
ality.Thiskindof reasoning
tendsto be computation- of operators
available
to theplanner.
Therearea couallyexpensive.
Forbin,
Deviser,
andSipeallsuffer
from pleofpossible
approaches
to representing
andreasoning
performance
problems
limiting
thesizeof theproblems aboutsimultaneous
effects
moreefficiently:
to whichtheycan be applied.
Oplan-2appearsto be
¯ Replaceprojection
witha moregeneral
representaableto handlelargerproblems
thantheotherplanners
tionof causality
and theevolution
of a domainin
mentioned
here.
termsof statevariables
[Muscettola,
1990].
Implementing
an efficient
temporal
reasoning
system
¯
Restrict
the
kinds
of
operator
interaction
modelled,
is not thesolehurdle,however.
Addingduration
to
considering
onlyresource
usage[Wilkins,
nonlinear
plansincreases
thedifficulty
of determining forexample
whether
or notthecurrent
partial
plancanbe refined
1988].
intoa planthatwillhavethedesired
effects.
In fact, Reasoning about resource usage is simpler than the genit becomes
difficult
to determine
simplywhetherthe
eral problem of simultaneous effects because the interactions
described
in thecurrent
partial
plancaneven
actions compose. In other words, it doesn’t matter why
be executed.
the present current demandis 5 amps. If your task reConsider
thesimpleplanfragment
in Figure1. There
quires 3 amps, the resulting demandis 8 amps. Wecan
arctwounordered
tasks,eachannotated
withan esticertainly construct resource modelsfor which this propmatedduration.
If actionscan onlybe takenin seerty does not hold, but from an applications viewpoint,
quence,
thetwotasksdepicted
musteventually
be orthe aim is to expand the set of domain characteristics
dered.Whentheplannertriesto orderthem,it will
we can model, not to prove that the general problem is
discover
thatneither
ordering
willwork,because
there hard.
simply
isn’troomforthemto be performed
in sequence.
In general, determining whether there is an ordering for
Summary
a set of actions constrained in this way is a hard probIn this paper, we briefly explore some of the modelling
lem.
and computational problems introduced by augmenting
There are two proposed techniques for addressing this
problem. The first is 8imulatiom the planner mainour domain models to include additional characteristics
of complex domains. The particular characteristics we
tains a partial order, and after every modification expends some effort exploring the corresponding set of
consider include unordered and simultaneous actions,
and duration and deadlines. Webriefly survey some
total orders to ensure that there is some feasible toproposed methods for dealing with these issues. It is
tal order [Miller, 1985, Muscettola, 1990]. As generally
employed, this is a heuristic method: the planner gives
not accidental that in doing so we stray in the direcup before exploring the complete set of consistent total
tion of scheduling terminology and techniques. It has
been clear for some time (certainly the earliest papers
orders.
Another
possible
approach
is
proposed
on Forbin in 1985 madethis point) that effective "planning" for real-world domains will require techniques
by Williamson and Hanks in [1988]. In this approach,
drawn from both the planning and scheduling commuthe partially ordered set of operators is organized into a
nities. More people than we have room to cite here
hierarchy of abstract operator types, knownas Hierar-