1. Outline
Artificial Intelligence
Planning
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Definition of AI planning
Key ideas: representation and search
STRIPS representation
partial-order planning and other techniques
for reducing complexity of plan search
• limiting assumptions of classical planning
• Recent trends on planning research
Blocks world example
A planning problem is specified by:
• an initial state
• a goal
• a model of the actions that can be performed
A solution to a planning problem is a sequence of
actions (a plan) that transforms the initial state
into a state that satisfies the goal description,
and possibly optimizes some measure of
performance.
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initial state
goal state
Plan: Move C from A to table
Move B from table to C
Move A from table to B
Distinctions
• Planning is closely-related to problemsolving and search, but there are important
differences
• Planning is also related to, but different
from, scheduling, theorem-proving,
automatic programming, and work in
control theory, decision theory and
operations research, etc.
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Applications
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Robot navigation and control
Spacecraft control (Deep Space One)
factory and manufacturing operations
intelligent tutoring
natural language generation and
understanding (plan recognition)
• many others
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2. Beginnings of planning research
Key issues: Representation and search
• A domain-independent planner consists of a
language for expressing planning problems and
an associated search algorithm for finding plans
• Examples:
Situation calculus (1959-)
QA3 (1969)
frame problem
Resolution theorem-proving (1965)
STRIPS (1972)
GPS (1969)
Epistemological and heuristic adequacy
The two key issues in planning research are:
– modeling actions and change
– organizing the search for plans
“There is a spectrum of more and more expressive languages
for representing the world, an agent’s goals, and possible actions.
The task of writing a planning algorithm is harder for more
expressive representation languages, and the speed of the resulting
algorithm decreases as well.” (Dan Weld)
– situation calculus and resolution theorem-proving
– STRIPS language and planning algorithm
– many others
STRIPS Language (1)
• States and goals described by conjunctions of
predicates applied to constant symbols
• Example:
– constants: blocks A, B, C, table
– predicates:
• (clear A) = “block A has nothing on it”
• (on A, B) = “block A is on block B”
• (on B, table) = “block B is on the table”
– state: (clear A) ∧ (on A B) ∧ (on B table)
STRIPS Language (2)
• Actions represented as follows:
– name:
– precondition list:
– delete list:
– add list:
(move x from y to z)
(on x y) ∧ (clear x) ∧ (clear z)
(on x y) ∧ (clear z)
(on x z)
• An action (operator) with variables is called
an action (operator) schema
Partial descriptions
• Only relevant aspects of the world need to be
included in state description
• STRIPS Assumption: Everything about the
world that is not mentioned by the action
schema remains unchanged by action – this is
“solution” to frame problem
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3. Influence
• The STRIPS planning algorithm had many
deficiencies and was never used again.
Many improved planning algorithms have
been developed since.
• The STRIPS language, and variations of it,
continues to be used by most planners
Search in situation space
Searching for a plan
• Besides modeling actions and change, the
second important issue in planning is how
to make the search for a plan efficient
• Distinction between searching in situation
space and plan space
Situation space for the blocks world
• States represent situations
• Edges represent actions that transform a
situation into a new situation
• Search strategies:
– forward from initial state (progression) or
backward from goal (regression or backward
chaining)
– total-order planning = plan is build action-byaction in forward or backward direction
Search in plan space
Plan space for the blocks world
• First used by planner called NOAH [1975].
• States represent partially specified plans.
• Edges represent plan-refinement operations (e.g.
adding actions or ordering constraints).
• Search strategies
– least-commitment = planner avoids making decisions
until a good reason to make a choice
– partial-order planning = decide what actions to
perform before deciding ordering of actions
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4. Example of nonlinear plan
(move A from table to B)
Finish
Start
(move B from table to C)
Example of partial-order planning
Advantages of partial-order planning
• By postponing choice about how to order actions,
can avoid search of exponential possible orderings
• It may take only a few steps to construct a plan that
would take thousands of steps using a standard
total-order approach
• The least-commitment approach means the planner
only needs to search in places where subplans
interact with each other
The null plan for the Sussman anomaly contains two actions:
*start* specifies the initial state and *end* specifies the goal.
• The following simple blocks-world planning
problem is called the “Sussman anomaly”
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B
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B
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• The next few slides show some of the steps involved
in finding a plan using a partial-order planner
The plan after adding a causal link to support (on b c)
The agenda contains [(clear b) (clear c) (on b table) (on a b)]
The plan after adding a causal link to support (clear b)
The agenda is set to [(clear c) (on b table) (on a b)]
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