9.4.5 PartialOrder Planning
TotalOrder vs. PartialOrder Planners
Any planner that maintains a partial solution as a totally ordered list of steps found so far
is called a
totalorder planner
, or a
linear planner
. Alternatively, if we only represent
partialorder constraints on steps, then we have a
partialorder planner
, which is also
called a
nonlinear planner
. In this case, we specify a set of temporal constraints
between pairs of steps of the form
S1 < S2
meaning that step S1 comes before, but not
necessarily immediately before, step S2. We also show this temporal constraint in graph
form as
S1 +++++++++> S2
STRIPS is a totalorder planner, as are situationspace progression and regression
planners
Partialorder planners exhibit the property of least commitment because constraints
ordering steps will only be inserted when necessary. On the other hand, situationspace
progression planners make commitments about the order of steps as they try to find a
solution and therefore may make mistakes from poor guesses about the right order of
steps.
Representing a PartialOrder Plan
A partialorder plan will be represented as a graph that describes the temporal constraints
between plan steps selected so far. That is, each node will represent a single step in the
plan (i.e., an instance of one of the operators), and an arc will designate a temporal
constraint between the two steps connected by the arc. For example,
•
S1 ++++++++> S2 ++++++++++> S5
•
\
^
•
 \++++++++++++++++

•

v

++++++> S3 ++++++> S4 ++++++
graphically represents the temporal constraints S1 < S2, S1 < S3, S1 < S4, S2 < S5, S3 <
S4, and S4 < S5. This partialorder plan implicitly represents the following three total
order plans, each of which is consistent with all of the given constraints:
[S1,S2,S3,S4,S5], [S1,S3,S2,S4,S5], and [S1,S3,S4,S2,S5].
9.5 PlanSpace Planning Algorithms
An alternative is to search through the space of
plans
rather than a space of
situations
.
That is, we start with a simple, incomplete plan, which we call a
partial plan
.
Then we
consider ways of expanding the partial plan until we come up with a complete plan that
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