Graphplan: Fast Planning through Planning Graph Analysis

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Graphplan Fast Planning through Planning Graph
Analysis

• Avrim Blum
• Merrick Furst
• Carnegie Mellon University

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The setting STRIPS planning

• Initial Conditions
• Block A on Block B, Light is on, Door is closed,
  
• Legal Actions
• Pick up object, Move from X to Y, Toggle light,
• Goals
• Block B on Block A, Door is open,

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Representation

• Standard representation State Graph
• Each state of world is a node. Actions move you
  from node to node.
• Goal find a path from the start to a goal node.
• Graph size may be exponential in problem
  description

S4
S2
S1
S5
S3
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Representation

• Graphplan idea Encode problem in much more
  compact (poly size) graph
• Node represents single literal in a time step
• State is a set of nodes
• Goal find a flow of truth values.

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Truth flowing through time
At x At y A on B A has cleartop C has
cleartop A on C B has cleartop
Move X-gtY
Unstack A from B put on C

• Allow multiple independent actions in the same
  time step

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Graphplan high level

• Build graph in fast forward pass
• Annotate graph with important info as you go
• Actually, dont use flow algorithms. Instead
• Perform backward-chaining search, guided by graph
  and stored constraints

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Example Rocket/Airplane Problem

• 2 Vehicles at Montreal, have fuel
• people at start. Half want to go to SF,
  half to Paris.
• Load/Unload operators
• (load ltpersongt ltvehiclegt ltlocationgt)
• Move operator deletes fuel
• (move ltfromgt lttogt)

V1, V2
N
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Example, contd.

• Example is hard for planners like prodigy
  because
• Cant just solve goals one at a time
• Also issue of resource allocation

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Graph Creation
A at M V1 at M V1 has fuel
A at M A in V1 V1 at M V1 at SF V1 has fuel
Load A into V1
Move V1 to SF
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Mutual exclusions
A at M V1 at M V1 has fuel
A at M A in V1 V1 at M V1 at SF V1 has fuel
Load A into V1
Move V1 to SF
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Next level
A at M A in V1 V1 at M V1 at SF V1 has fuel
A at M A in V1 V1 at M V1 at SF V1 has fuel
Unload A from V1 in SF Move V1 from M to SF
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Propagating mutexs
V1 at X V1 at Y V1 at Z V1 at W
V1 at X V1 at Y V1 at Z V1 at W
Move X-gtY Move Z-gtW ...
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Growing the graph

• Grow forward until all goals appear, not marked
  as exclusive.
• Rules for marking as exclusive
• Facts P,Q exclusive if all ways of making P true
  are exclusive of all ways of making Q true.
• Actions A,B marked exclusive if either
• Interference One deletes a precond or
  add-effect of the other, or
• Competing Needs some precond P of A is
  exclusive of some precond Q of B

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Basic loop

• Grow until all goals appear, not exclusive.
• Perform backward search. If fail, grow one more
  level and repeat.
• Termination step

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Backward Search

• Level by level.
• Given goal set at time t,
• For each goal, choose some action not exclusive
  of previous choices, and doesnt cut off anyone.
• This creates goal set at time t-1. Recurse on
  it.
• If fail, backtrack

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Example
A at SF B at SF C at Paris D at Paris
Unload A V1 at SF Unload B V2 at SF Unload B V1
at SF Unload C V1 Paris Unload C V2 Paris
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Run Graphplan on Rocket,Flat-tire, etc.
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Graph creation is poly time

• IF operators have a constant number of
  parameters.
• (move ltxgt from ltygt to ltzgt), (open ltxgt)
• IF operators dont create new objects.
• THEN polynomial number of ways to instantiate
  each operator. So, time is poly in operators,
  objects, and length of plan.
• Can speed up using goals to throw out irrelevants

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Terminationwhat if not solvable?
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When Graphplan does well
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When Graphplan performs badly
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Open Questions