(Classical)AI Planning

General-Purpose Planning: State & Goals

• 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)

A

C

B C

B

AInitial state Goals

(Ke Xu)

General-Purpose Planning: Operators (I)

?y

?x

No block on top of ?x

transformation

?y

?x…

…

No block on top of ?y nor ?x

Operator: (Unstack ?x ?y)• Preconditions: (on ?x ?y) (clear ?x) • Effects:

– Add: (on ?x table) (clear ?y)– Delete: (on ?x ?y)

On table

General-Purpose Planning: Operators (II)

?y

?x

No block on top of ?x

transformation

?y

……

No block on top of ?y nor ?x

Operator: (Stack ?x ?y ?z)• Preconditions: (on ?x ?z) (clear ?y) (clear ?x)• Effects:

– Add: (on ?x ?y) (clear ?z)– Delete: (on ?x ?z) (clear ?y)

?z

?x?z

So what is the solution plan for this problem?

• 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)• Operators: (Stack ?x ?y), (Unstack ?x ?y ?z)

A

C

B C

B

AInitial state Goals

(Ke Xu)

Planning: Search Space

AC

B A B C A CB

CBA

BA

C

BAC

B CA

CAB

ACB

BCA

A BC

AB

C

ABC

(Michael Moll)

Some Examples

• 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.

Which of the following problems can be modeled as AI planning problems?

Answer: ALL!

FSM vs AI Planning

Plan

ning

Ope

rato

rs

• PatrolPreconditions:

No MonsterEffects:

patrolled• Fight

Preconditions: Monster in sight

Effects: No Monster

Patrol Fight

Monster In Sight

No Monster

FSM:

A resulting plan:

Patrolpatrolled

Fight

No MonsterMonster in sightNeither is more powerful than the other one

But Planning Gives More Flexibility• “Separates implementation from data” --- Orkin

reasoning knowledge

Plan

ning

Ope

rato

rs

• PatrolPreconditions:

No MonsterEffects:

patrolled• Fight

Preconditions: Monster in sight

Effects: No Monster…

Many potential plans:

PatrolFightPatrolFightPatrolFightPatrolFight

PatrolFight

…

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

General purpose: symbolic descriptions of the problems and the domain. The plan generation algorithm the same

Domain Specific: The plan generation algorithm depends on the particular domain

Advantage: - opportunity to have clear semanticsDisadvantage: - symbolic description requirement

Advantage: - can be very efficientDisadvantage: - lack of clear semantics - knowledge-engineering for plan generation

Planning: find a sequence of actions to achieve a goal

Classes of General-Purpose Planners

General purpose planners can be classified according to the space where the search is performed:

• SAT

• Hierarchical

• Disjunctive plans

• state

• plan 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)

BA

C

C

B

A

Why Plan-Space Planning?

• Problem of state-space search:– Try (on A B) first:

• put C on the Table, then put A on B

• 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

A BC C BA

CBA

Hierarchical (HTN) Planning

Travel(UMD, Lehigh)

Fly(National, L.V. International)Travel(L.V. Int’nal,Lehigh)

Travel(UMD,National)

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.

alternativemethods

Travel from UMD to Lehigh University

Travel by car

Enough money for gasoline

Roads are passable Seats available

Travel by plane

Enough money for air fare available

Taxi(UMD,UMD-Metro)Metro(UMD-Metro,National)

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 increasesthe number of nodes exponentially– worst case: about 6x1044 leaf nodes– average case: about 1024 leaf nodesNot enough time to search the game tree

(Dana S. Nau)

How to Reduce the Sizeof 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)

• Loop:– If the current partial plan is a solution, then exit– Nondeterministically choose a way to refine the plan

• Some of the possible refinements– Forward & backward state-space refinement– Plan-space refinement– Hierarchical refinements

Universal Classical Planning (UCP) (Khambampati, 1997)

Plan-space

partially instantiated steps, plus constraints

add steps & constraints

State-space

Abstract Example

Initialstate

finalstate

Initial plan:

Plan-spacerefinement

State-spacerefinement

Plan-spacerefinement

State-spacerefinement

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