Temporal Graphplan

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Temporal Graphplan

• Smith Weld
• Presentation by Jafar Muhammadi
• Muhammadi _at_ ce.sharif.edu

2
Outline

• Standard Graphplan
• Action Models in Time Reasoning
• From SGP to TGP
• TGP Graph Expansion
• TGP Solution Extraction
• Experiments

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Graphplan
Expand plan graph Derive mutex relationships If
goals are present consistent search for a
solution
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Observation 1
p q r
p q q r
p q q r r
p q q r r
A
A
A
B
B
Propositions monotonically increase (always
carried forward by no-ops)
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Observation 2
p q r
p q q r
p q q r r
p q q r r
A
A
A
B
B
Actions monotonically increase
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Observation 3
p q r
p q r
p q r
A
Proposition mutex relationships monotonically
decrease
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Observation 4
A
A
A
p q r s
p q
p q r s
p q r s
B
B
B
C
C
C
Action mutex relationships monotonically decrease
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Doing Time
Actions Start time (s) Real duration
(d) Parallel Propositions must hold at
(s) Effects occur at end (sd) Preconditions hold
throughout
pre
A
eff1
cond1
eff2
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Some Notations

• Action A
• Duration of A A
• Earliest possible start time of A A
• Earliest possible end time of A A
• Start time of an execution of A A
• Completion time of an execution of A A

A A A A A A A
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An Example
Actions
Planning Graph
A0
P1
B0
Q2
C2
R5
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Generalizing of Mutex Reasoning

• Introducing action/proposition mutexes
• Distinguishing between eternal/conditional
  mutexes

• Action/proposition mutex

A B can never be executed in the same time
(emutex because of X,X ) ,then A B must
execute in series.
The Mutex between P Q should end at time 3 (
SGP mutex propagation is insufficient for
deducing this fact ).
It is impossible to have proposition P true and
have action B under execution at same time.
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More on emutexes

• Def1 Propositions P Q are emutex iff P is the
  negation of Q. (e.g. X X)
• Def2 Action A is emutex with Preposition P if
  P is a proposition of A or P is an effect of A
• Def3 Actions A B are emutex iff at least one
  of the following holding
• A or B delete the proposition(s) of the other
• A and B have emutex perconditions

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More on cmutexes

• Def4 Propositions P Q are cmutex when
• P is cmutex with all of the actions supporting Q
  and
• Q is cmutex with all of the actions supporting P.
• Example

P Q are cmutex when P is cmutex with B Q
is cmutex with A (B (B
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More on cmutexes

• Def5 Action A is cmutex with Propositions P
  when
• P is cmutex with any precondition of A or
• A is cmutex with all of the actions supporting P.

• Def6 Actions A B are cmutex when
• A is cmutex with any precondition of B or
• B is cmutex with any Precondition of A.

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Graph Expansion

• Keeping track of what has changed in the graph
  and only examine those propositions, actions, and
  mutex relationships that can be affected by the
  changes.

By Def. 5
Between A effe ct of B
Those with the PP as PC
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Expansion Algorithm
Temporal planning problem Set of initial
condition List of conjunctive goals Set of ground
actions

• Expand
• Add no-ops for new props
• Add new actions (new props terminate
  p-mutex)
• Add new effects
• Add mutex for new actions
• t t1
• Recheck propositions for new support
• Recheck possibly terminating mutexes
• Add mutex for new props
• If all goals are present call solution
  extractor
• if solution extractor fails then loop

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An Example
Actions
Initial state
p
Goal
q,r
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Example
t 0
p
p
A
q
B
r
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Add Prop Mutex
t A
p
p
A
q
B
r
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Add New Actions
t A
p
p
A
q
B
r
C
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New prop mutex
t B
p
p
A
q
B
r
C
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New Support
t AC
p
p
A
q
B
r
C
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New Actions from term. mutex
t AC
p
p
A
q
B
r
C
D
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Solution extraction
Status Graph extended to time tG All goals are
present Pairwise of goals are non-mutex

• Solution extractor Data structures
• Agenda
• Queue
• which the goal must be true
• Initial for all top level goals
• Queue is sorted in decreasing temporal order
• Plan
• Si is start time of Ai
• initial empty

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Solution Extraction Algorithm
Algorithm While Agenda is not empty
do dequeue from Agenda. if ( t 0 )
( G initially true ) then fail
(backtrack) else if ( t 0 ) then suppose that
S is set of actions that each Ai has G as an
effect and ( Ai not mutex with any action in plan Add
to plan for each precondition P of A add t-A to Agenda if no such A exist then
backtrack
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Experiments
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Any Question?

• ?

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Refrence

• Temporal Planning with Mutual Exclusion Reasoning
• David E. Smith, Daniel S. Weld
• IJCAI-99

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