(Classical)
AI Planning
General-Purpose Planning: State & Goals
Initial state
A
C
B
A
B
Goals
C
• Initial state: (on A Table) (on C A) (on B Table) (clear B)
(clear C)
• Goals: (on C Table) (on B C) (on A B) (clear A)
(Ke Xu)
General-Purpose Planning: Operators
No block on
top of ?x
No block on top
of ?y nor ?x
?x
?y
?y
…
transformation
Operator: (Unstack ?x)
• Preconditions: (on ?x ?y) (clear ?x)
• Effects:
– Add: (on ?x table) (clear ?y)
– Delete: (on ?x ?y)
…
On table
?x
Planning: Search Space
A
C
B
B
C
A
C
A B
C
A B
A
B C
C
A
B
C
B
A
B
A C
A B C
A
A
B
C
B
C
A
B C
B
A
C
(Michael Moll)
Some Examples
Which of the following problems can be modeled as AI planning
problems?
• Route search: Find a route between Lehigh University and the
Naval Research Laboratory
• Project management: Construct a project plan for organizing an
event (e.g., the Musikfest)
• Military operations: Develop an air campaign
• Information gathering: Find and reserve an airline ticket to
travel from Newark to Miami
• Game playing: plan the behavior of a computer controlled player
• Resources control: Plan the stops of several of elevators in a
skyscraper building.
Answer: ALL!
Planning Operators
FSM vs AI Planning
FSM:
Monster In Sight
Patrol
Fight
No Monster
•Patrol
Preconditions:
No Monster
Effects:
patrolled
•Fight
Preconditions:
Monster in sight
Effects:
No Monster
A resulting plan:
Monster in sight
Fight
No Monster
patrolled
Patrol
Neither is
more
powerful
than the
other one
But Planning Gives More Flexibility
•
“Separates implementation from data” --- Orkin
Planning Operators
reasoning
•Patrol
Preconditions:
No Monster
Effects:
patrolled
•Fight
Preconditions:
Monster in sight
Effects:
No Monster
…
knowledge
Many potential plans:
Fight
Fight
Fight
Fight
Fight
Patrol
Patrol
Patrol
Patrol
Patrol
…
If conditions in the state change making
the current plan unfeasible: replan!
But… Does Classical Planning Work for Games?
F.E.A.R. not!
General Purpose vs. Domain-Specific
Planning: find a sequence of actions to achieve a goal
General purpose: symbolic descriptions of the problems and
the domain. The plan generation algorithm the same
Advantage: - opportunity to have clear semantics
Disadvantage: - symbolic description requirement
Domain Specific: The plan generation algorithm depends on
the particular domain
Advantage: - can be very efficient
Disadvantage: - lack of clear semantics
- knowledge-engineering for plan generation
Classes of General-Purpose Planners
General purpose planners can be classified according to the space
where the search is performed:
• state
• plan
• Hierarchical
• Disjunctive plans
• SAT
We are going to discuss these forms
State- and Plan-Space Planning
• State-space planners transform the state of the world. These
planners search for a sequence of transformations linking the
starting state and a final state
State of the world
(total order)
• Plan-space planners transform the plans. These planners search
for a a plan satisfying certain conditions
(partial-order, least-commitment)
Why Plan-Space Planning?
• 1. Motivation: “Sussman Anomaly”
– Two subgoals to achieve:
(on A B) (on B C)
A
C
A
B
B
C
Why Plan-Space Planning?
• Problem of state-space search:
– Try (on A B) first:
• put C on the Table, then put A on B
A
C
A
B
C
A
B
B
C
• Accidentally wind up with A on B when B is still on the Table
• We can not get B on C without taking A off B
• Try to solve the first subgoal first appears to be mistaken
Hierarchical (HTN) Planning
Principle: Complex tasks are decomposed into simpler tasks.
The goal is to decompose all the tasks into primitive tasks,
which define actions that change the world.
Travel from UMD to Lehigh University
alternative
methods Travel by car
Travel by plane
Enough money for air
fare available
Enough money
for gasoline
Seats available
Roads are passable
Travel(UMD, Lehigh)
Travel(UMD,National)
Taxi(UMD,UMD-Metro)
Metro(UMD-Metro,National)
Fly(National, L.V. International)
Travel(L.V. Int’nal,Lehigh)
Taxi(L.V. Int’nal,Lehigh)
Application to Computer Bridge
• Chess: better than all but the best humans
• Bridge: worse than many good players
• Why bridge is difficult for computers
– It is an imperfect information game
– Don’t know what cards the others have (except the dummy)
– Many possible card distributions, so many possible moves
• If we encode the additional moves as additional branches
in the game tree, this increases
the number of nodes exponentially
– worst case: about 6x1044 leaf nodes
24 leaf nodes
– Not
average
case:
about
10
enough time to search the game tree
(Dana S. Nau)
How to Reduce the Size
of the Game Tree?
• Bridge is a game of planning
– Declarer plans how to play the hand
by combining various strategies (ruffing, finessing, etc.)
– If a move doesn’t fit into a sensible strategy,
then it probably doesn’t need to be considered
• HTN approach for declarer play
– Use HTN planning to generate a game tree in which each move
corresponds to a different strategy, not a different card
• Reduces average game-tree size to about 26,000 leaf
nodes
• Bridge Baron: implements HTN planning
– Won the 1997 World Bridge Computer Challenge
– All commercial versions of Bridge Baron since 1997 have
include an HTN planner (has sold many thousands of copies)
(Dana S. Nau)
Universal Classical Planning (UCP)
(Khambampati, 1997)
partially instantiated steps, plus constraints
• Loop:
– If the current partial plan is a solution, then exit
– Nondeterministically choose a way to refine the plan
add steps & constraints
• Some of the possible refinements
– Forward & backward state-space refinement
State-space
– Plan-space refinement
– Hierarchical refinements
Plan-space
Abstract Example
Initial plan:
Plan-space
refinement
Initial
state
final
state
State-space
refinement
Plan-space
refinement
State-space
refinement
Why “Classical”?
• Classical planning makes a number of assumptions:
– Symbolic information (i.e., non numerical)
– Actions always succeed
– The “Strips” assumption: only changes that takes place are
those indicated by the operators
• Despite these (admittedly unrealistic) assumptions some
work-around can be made (and have been made!) to apply
the principles of classical planning to games
• Neoclassical planning removes some of these assumptions