Partial-Order Planning
Jane Hsu
“Sussman Anomaly”
p
Solving on(A,B) first will be undone when
solving the second goal on(B,C) and vice
versa.
B
C
A
INITIAL STATE
A
B
C
GOAL STATE
1
Total-Order Plans
p
Problem: to paint the ceiling
Start
Get ladder
Get brush
Paint ceiling
Finish
Start
Get brush
Get ladder
Paint ceiling
Finish
Partial-Order Plan
p
The actions “Get brush” and “Get ladder”
may be performed in any order.
Get brush
Paint ceiling
Start
Finish
Get ladder
2
The Planning Problem: Revisited
To find an executable partially-ordered
set of actions that achieves a given goal
when performed starting in a given state.
PLAN
START
Initial
State
Operator
Instances
Get brush
Paint ceiling
Start
Goal
Finish
State
Get ladder
FINISH
State-space vs Plan-space search
3
Partial Order Planning (POP)
p
Search in the space of partial plans
n
n
p
Operators transform plans to other plans by:
n
n
n
p
Least commitment planning
Nonlinear planning
Adding steps
Reordering
Grounding variables
Earlier Planners
n
n
n
SNLP: Systematic Nonlinear Planning (McAllester and
Rosenblitt 1991)
NONLIN (Tate 1977)
NOAH (Sacerdoti 1975)
Plan-Transforming Operators
4
Partially Ordered Plans
Plan
We formally define a plan as a data structure consisting of:
p
Set of plan steps (each is an operator for the problem)
p
Set of step ordering constraints
e.g., A ` B
means “A before B”
p
Set of variable binding constraints
e.g., v = x
where v variable and x constant or other variable
p
Set of causal links
e.g., A c B means “A achieves c for B”
5
POP Algorithm
POP Algorithm (cont.)
6
Clobbering: Promotion/Demotion
Solving Sussman Anomaly w/ POP
7
Initial Step
Add Action
8
Add Action & De-clobbering
More Action & De-clobbering
9