SAPA: A Domain-independent Heuristic Temporal Planner

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3/25 Leaving STRIPS Planning and going
to Sapa
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Administrivia 3/25

• Homework 4 due next class
• Midterm soon after that
• Will be take home
• Will have a Shock and Awe flavor
• You can be an embedded exam taker by
  suggesting problems
• Today
• Metric/Temporal planning (MTP)
• Representation issues
• Modeling MTP in Progression and Regression
• And Graphplan and PO planning etc. etc.

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Metric Temporal Planning

• Time Durative actions Temporal constraints on
  goals (deadlines inter-goal constraints eg.
  Make sure to be in airport 2 hours before you are
  in the plane) Exogenous events
• Durations may be static or dynamic
• duration depends on the contexteg. Time to fill
  your gas tank depends on how empty the tank is to
  begin with
• Advanced issues Uncertain durations
• Modeling issues When are preconditions needed?
  How long will they persist? When are effects
  given?
• A default assumption is to say that all
  preconditions are needed at the beginning and
  must hold during the entire actions duration.
  And that all effects will be available at the end
  of the action
• E.g Consider Grading homeworks actionwhen are
  the homeworks needed? When are the grades
  available? What does your teacher tell you?
• Planning issues How to support concurrency?(see
  next slide) How to support multi-objective
  (cost/make-span/robustness) optimization
• Resources Actions may consume/produce
  (continuous quantity) resources
• Modeling issues How to model resource
  availability (especially over the duration of an
  action)
• Planning issues How to efficiently reason with
  continuous quantities during planning

Special cases TP Temporal planning RP
Resource Planning
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Concurrency

• Suppose I tell you that a plan P contains actions
  A1 A10, each with duration d1d10, then what is
  the makespan (execution duration) of P?
• Makespan(P) gt max(d1d10)
• If Makespan(P) Sum(d1d10), then it is a
  strictly serial plan
• If Makespan(P) gt Sum(d1..d10), then there is
  idle-time in the plan
• Actions dont need to start right after the
  preceding action
• Think of the bank teller gossiping with his
  colleague in between servicing each customer
• Planned idle/slack time may not always be a bad
  thingit can sometimes improve the robustness of
  the plan
• Think of three travel plans involving connections
  in Minneapolis
• Plan 1 schedules 5 min for connection time
  plan 2 schedules 1 hour plan 3 schedules 2 days.
  Which one is better (all else being equal).

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Some Brand Names

• Planners that can handle similar types of
  temporal and resource constraints
• TLPlan, HSTS, IxTexT, Zeno, SAPA
• TlPlan, SAPA are progression-based planners
• HSTS,IxTET,Zeno are partial-order-based planners
• TlPlan,HSTS are domain-customized planners the
  rest are domain independent
• Planners that can handle a subset of constraints
• Only temporal TGP, TPG, LPGP
• Only resources LPSAT, GRT-R, Kautz-Walser
• Subset of temporal and resource constraints TP4,
  Resource-IPP
• LPGP and LPSAT are loosely-coupled systems.
  LPSAT connects SAT and LP solvers LPGP connects
  Graphplan and LPsolver
• Issues of how tight is the loose-connection.
• TGP,TPG,LPGP are Graphplan-based
• LPSAT is based on SAT encodings being sent to LP
  solvers
• Kautz-Walser is based solely on LP encodings

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Approaches for MTP

• In theory, pretty much every one of the
  approaches we saw for classical planning can be
  (and have been) extended to MTP (with varying
  degrees of scalability)
• There are some interesting tradeoffs
• PO planners are easiest to extend to support the
  concurrency needed for durative actions
• Have harder time handling resources (because
  resource consumption depends on exactly what
  actions occurred before this time point)
• Progression planners easiest to extend to support
  resource consuming actions
• But harder time handling concurrency (need to
  consider advancing clock as a separate option
  in addition to applying one of the actions)

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3/27 Our Road Map

• Will focus on conjunctive planning
  approacheswith special attention to Sapa
• action models
• Using PDDL2.1 standard
• how to model the search
• Progression Regression PO planning
• how to extract good heuristics

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Action Representation

• Durative with EA SA DA
• Instantaneous effects e at time
• te SA d, 0 ? d ? DA
• Preconditions need to be true at the starting
  point, and protected during a period of time d, 0
  ? d ? DA
• Action can consume or produce continuous amount
  of some resource

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PDDL 2.1 (Level 2)Pure Durative Actions
(durative-action burn_match parameters
() duration ( ?duration 15) condition (and
(at start have_match) (at start
have_strikepad)) effect (and (at start
have_light) (at end (not
have_light)) ) )
(durative-action cross_cellar parameters
() duration ( ?duration 10) condition (and (at
start have_light) (over all
have_light) (at start at_steps)) effect
(and (at start (not at_steps)) (at
start crossing)(at end at_fuse_box) )
have_match, have strikepad
(dur 15)
have_light
have_light
have_light, at_steps
have_light
(dur 10)
at_steps, crossing
at_fuse_box
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PDDL 2.1 Level 3Durative actions and numeric
quantities(but discrete effects)
The entire energy to be consumed is encumbered
at the very beginning (even though it gets
consumed Slowly over the full duration.
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PDDL 2.1 Level 4Durative actions and numeric
quantities(with continuous effects )
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Issues in modeling continuous change by discrete
vs. continuous effects

• Consider the action of boiling a pan of water
• The quantity temperature of water changes
  continuously over the duration of the action
• We can ignore continuous effects by specifying
  that temperature is 1000 C at the end
• Easy to handle can only access the temperature
  at the end of the action Reduces concurrency
  (what if we also put a blow torch to the pan to
  hasten the process?)
• Or we can specify that the temperature of the
  water raises at a linear rate until it becomes
  100
• Harder to handle but allows more concurrency
  (the total rate of increase is summation of all
  the individual rates of increase)

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PDDL 2.1 StandardSummary

• Durations
• Static and dynamic durations allowed
• Also allows duration inequalities
• Preconditions
• Can be at start or over all (throughout the
  duration)
• Doesnt model preconditions being needed for
  arbitrary durations in the middle
• Effects
• Can be at start or at end
• This makes effects discrete
• Numeric quantities
• Can be present in the preconditions or effects
• Presence in the effects can be discrete (at
  start/at end) or continuous
• Continuous change specified by giving a rate
  at which the quantity changes
• Non-linear rate harder

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State of the Art (as of IPC2002)

• At IPC 2002 PDDL 2.1 standard had three levels
• Level 1 STRIPS/ADL
• Level 2 Durative Actions
• FF, LPG, SAPA.
• Level 3 Numeric quantities
• discrete change
• Sapa, LPG
• Level 4 Continuous change
• None at IPC
• Some planners can handle it in theory but none
  are scalable

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Problem Representation

• Achievement Goals are specified as a list ltpi,tigt
  where pi needs to hold by time ti
• ti is the deadline by which G must hold. It can
  be metric time (e.g. make clear(b) true by 2pm.)
• If ti is omitted we will assume that G is a
  non-deadline goal (must be true by the time the
  plan is done.
• Persist Goals are specified as a condition and
  an interval over which it must hold
• A persist goal may be supported by different
  actions for the different parts of the duration (
  goal reduction a la ZENO)
• E.g. striking multiple matches to have light over
  a duration

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Plan representation
An executable plan must provide -- the actions
that need to be executed -- the start times
for each of the actions ? Or a set of
simple temporal constraints on the
set of actions (S.T.C. are generalization of
partial orders) E.g.
A14,5?A2 (means 4 lt
ST(A2) ST(A1) lt 5 )
Plan views Pert and Gantt charts GANTT Chart
is what is shown on the right PERT shows the
Causal links
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Plan Quality Measures

• Makespan Clock time for the execution of the
  plan (more concurrency ? lower makespan)
• Slack The difference between the deadline for a
  goal and the time by which the plan achieves it
• Tardiness is negative slack
• Optimize max/min/average slack/tardiness measures
• Cost Sum of costs of all the actions
• Can be split into multiple dimensions, one
  corresponding to each resource

Can two plans with same make-span have different
slack measures?