PartialOrder Planning POP

1
Partial-Order Planning (POP)
Alan Fern
Based in part on slides by Daniel Weld, José
Luis Ambite, and Malcolm Ryan.
2
Total-Order vs. Partial-Order Planning (POP)
?
A
D
C
B
B
D
A
C
There are many possible plans

• move(A, B, TABLE) move(B, TABLE, A) move(C,
  D, TABLE) move(D, TABLE, C)
• move(A, B, TABLE) move(C, D, TABLE) move(D,
  TABLE, C) move(B, TABLE, A)
• move(C, D, TABLE) move(D, TABLE, C) move(A,
  B, TABLE) move(B, TABLE, A)
• ect . . .

• State-space planning techniques produce
  totally-ordered plans, i.e. plans consisting of a
  strict sequence of actions.
• Often, however, there are many possible orderings
  of actions than have equivalent effects.
• However, often many orderings of the actions have
  equivalent effects.

3
Total-Order vs. Partial-Order Planning (POP)
?
A
D
C
B
B
D
A
C
There are many possible plans

• move(A, B, TABLE) move(B, TABLE, A) move(C,
  D, TABLE) move(D, TABLE, C)
• move(A, B, TABLE) move(C, D, TABLE) move(D,
  TABLE, C) move(B, TABLE, A)
• move(C, D, TABLE) move(D, TABLE, C) move(A,
  B, TABLE) move(B, TABLE, A)
• ect . . .

• These plans share some common structure. They are
  all different interleavings of two separate
  plans
• 1) move(A, B, TABLE) move(B, TABLE,
  A)
• 2) move(C, D, TABLE) move(D, TABLE,
  C)
• A partial-order plan is one which specifies only
  the necessary ordering information. One
  partial-order plan may have many total-orderings

4
Total-Order vs. Partial-Order Planning (POP)
5
(Partial-Order) Plan-Space Search

• Search nodes are partial plans
• some plan steps may be missing
• some orderings of actions may not be finalized
• Search arcs are plan refinements
• Solution is a node (not a path) giving the a
  partial order on actions.
• Any linearization of the plan is a total-order
  solution to the problem

It follows the least-commitment principle Do
not add constraints (e.g. action ordering) to a
plan until it becomes necessary to ensure the
correctness of the plan.
6
Representing Partial-Order Plans

• Plan (A, O, L, P), where
• A set of actions in the plan
• O temporal orderings between actions (a lt b)
• L causal links linking actions via a literal
  (used for book keeping)
• P open preconditions that need to be satisfied
• Causal Link
• Action A2 has precondition Q that is
  established in the plan by action A1.

clear(b)
Unstack(C,B)
Putdown(A,B)
7
Threats to a Causal Link

• A causal link (A1, Q, A2) represents the
  assertion that the role of A1 is to establish
  proposition Q for A2
• This tells future search steps to protect Q in
  the interval between A1 and A2

Action B threatens causal link (A1, Q, A2) if 1.
B has Q as a delete effect, and 2. B could come
between A1 and A2, i.e. O ? (A1 lt B lt A2)
is consistent
PutDown(C,B)
What is a threat to the following causal link?
clear(B)
Unstack(C,B) PutDown(A,B)
8
Consistent Plans
A plan (A, O, L, P) is consistent iff1) O
contains no cycles2) No causal link in L is
threatened

• For simplicity we introduce two actions to
  represent the intitial state and goal of a
  problem
• START
• no preconditions
• ADD effects are the initial state
• only consider plans where START is the first step
• FINISH
• no effects
• preconditions are the goal
• only consider plans where FINISH is the last step

Any consistent plan with no open preconditions is
a solution.
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POP example Blocks World
Initial plan includes only START and FINISH
actions.The open preconditions correspond to the
goal.
START
on(C, A)
ontable(A)
ontable(B)
clear(C)
clear(B)
C
B
A
on(A, B)
on(B, C)
A
FINISH
B
C
10
Work on open precondition on(B, C)
and clear(B)
START
on(C, A)
ontable(A)
ontable(B)
clear(C)
clear(B)
C
B
A
preconditions
effects
on(A, B)
on(B, C)
A
FINISH
B
C
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Work on open precondition on(A, B)
START
on(C, A)
ontable(A)
ontable(B)
clear(C)
clear(B)
C
B
A
clear(A)
clear(B)
ontable(A)
A2 move(A, TABLE, B)
on(A, B)
ontable(A)
clear(B)
on(A, B)
on(B, C)
A
FINISH
B
C
12
Protect causal links
START
on(C, A)
ontable(A)
ontable(B)
clear(C)
clear(B)
C
B
A
clear(A)
clear(B)
ontable(A)
A2 move(A, TABLE, B)
on(A, B)
ontable(A)
clear(B)
on(A, B)
on(B, C)
A
FINISH
B
C
13
Work on open precondition clear(A)
START
on(C, A)
ontable(A)
ontable(B)
clear(C)
clear(B)
C
B
A
clear(A)
clear(B)
ontable(A)
A2 move(A, TABLE, B)
on(A, B)
ontable(A)
clear(B)
on(A, B)
on(B, C)
A
FINISH
B
C
14
Final Plan
All preconditions are supported and plan is
consistent.So this partial-order plan is a
solution.
START
on(C, A)
ontable(A)
ontable(B)
clear(C)
clear(B)
C
B
A
clear(C)
on(C, A)
A3 move(C, A, Table)
on(C, A)
ontable(C)
clear(A)
clear(B)
clear(C)
ontable(B)
A1 move(B, TABLE, C)
clear(A)
clear(B)
ontable(A)
on(B, C)
ontable(B)
clear(C)
A2 move(A, TABLE, B)
on(A, B)
ontable(A)
clear(B)
on(A, B)
on(B, C)
A
FINISH
B
C
15
POP In Practice

• The book discusses some basic heuristics for
  controlling plan-space search.
• Plan-space search was observed to be better than
  state-space search.
• This led to much POP research through the 80s
  and early 90s
• But POP dropped out of favor as it was
  substantially outperformed by new ideas
• However, recent work on planning heuristics is
  effectively combining the new ideas with POP
• Nevertheless POP is an appealing and flexible
  framework.
• Often it can be generalized more easily than
  newer types of planners