Ai Principles Planning[1]

8/8/2019 Ai Principles Planning[1]

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AI Principles, Lecture on Planning

Planning

Jeremy Wyatt


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Plan

Situation calculus

The frame problem

The STRIPS representation for planning

State space planning:

Forward chaining search (progression planning)

Backward chaining search (regression planning)

Reading: Russell and Norvig pp.375-387


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Situation Calculus

The situation calculus is a general system for allowing you

to reason automatically about the effects of actions, and to

search for plans that achieve goals.

However, it has some flaws that took a long time to iron

out

The situation calculus is composed of

Situations: S0 is the initial situation Result(a,S0) is the situation that

results from applying action a in situation S0

Fluents: functions and predicates that may be true of some situation

e.g. Holding(G1,S0) says that the agent is not holding G1 in

situation S0


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Situation Calculus

Actions are described in the situation calculus using two kinds ofaxioms:

Possibility Axioms: say when you can apply an action Effect Axioms: that say what happens when you apply them

The essential problem with situation calculus however, is that

EffectA

xioms only say what changes, not what stays the same, butreasoning in the situation calculus requires the explicit representation of allthe things that dont change. These are handled by Frame Axioms, andhence this is called the Representational Frame Problem.

Reasoning about all the effects and non-effects of a sequence of actions isthus very inefficient. This is known as the Inferential Frame Problem.

Eventually solutions to both the Frame Problems were found. But in themeantime researchers began to look for representations to support moreefficient planning.


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The STRIPS representation

The Grandad of planning representations

Avoids the difficulties of more general representations (e.g.situation calculus) for reasoning about action effects andchange

Devised for, and used in the Shakey project

The key contribution ofthe representation of action effects isto assume that anything that isnt said to change as theresult of an action, doesnt change

It is this assumption (sometimes called the STRIPSassumption) that avoids the representational frame problem


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STRIPS operators

All effects are modelled, anything that isnt

in the effects list stays the same

The effect P^Q adds P to the worlddescription and removes Q

Variables in the operator(e.g. x) must bebound (unified) with entities in thedescription of the world to apply theoperator, so Move(C,A,B) requires{b/C,x/A,y/B}, i.e. b is substituted by C etc.

BA

C

BA

C

Action(Move(b,x,y))-

Preconditions: On(b,x) ^ Clear(b) ^ Clear(y)

Effects: On(b,y) ^ Clear(x) ^ On(b,x) ^ Clear(y)


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STRIPS operators

STRIPS doesnt allow us to use full first orderlogic

So we have to create a Clear(b) predicate,rather than use to indicate thatthere is no block x on block b

Also we actions like Move(C,A,A) createinconsistent effects

And we may need additional special operatorse.g. Move_to_table(b,x,Table) whenever theeffects are slightly different

BA

C

BA

C




),( bxOnx


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The STRIPS state and goal descriptions

In the state description anything that isnt stated is assumed to be false(Closed World Assumption)

So only +ve literals are allowed in the state description

Only ground literals are allowed in the goals. So not

On(Next_Alpha(x),C) or On(x,C)

The goal description specifies a set of states

BA

C

On(A,Table) On(B,Table)

On(C,A) Clear(C)Clear(B)

B

A

C

On(A,B)

On(B,C)

State Goal


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Application of an action

Apply Move(C,A,B)

BA

C



BA

State State






Action(Move(C,x,y))-

Preconditions: On(C,x) ^ Clear(C) ^ Clear(y)

Effects: On(C,y) ^ Clear(x) ^ On(C,x) ^ Clear(y)

Action(Move(C,A,y))-

Preconditions: On(C,A) ^ Clear(C) ^ Clear(y)

Effects: On(C,y) ^ Clear(A) ^ On(C,A) ^ Clear(y)

Action(Move(C,A,B))-

Preconditions: On(C,A) ^ Clear(C) ^ Clear(B)

Effects: On(C,B) ^ Clear(A) ^ On(C,A) ^ Clear(B)



Action(Move(C,A,B))-

Preconditions: On(C,A) ^ Clear(C) ^ Clear(B)

Effects: On(C,B) ^ Clear(A) ^ On(C,A) ^ Clear(B)


Clear(C)


On(C,B) Clear(C)Clear(A)

C


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Forward Chaining Search

On(A,Table)

On(B,Table)On(C,A)

Clear(C) Clear(B)

On(A,Table)

On(B,Table)

On(C,Table)

Clear(A)

Clear(C) Clear(B)

On(A,Table)

On(B,Table)

On(C,B)

Clear(C) Clear(A)

Move(C,A,

Table)

Move(C,A,B)


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Forward Chaining Search

Because of the restrictions on STRIPS representation there

can only be a finite number of states

You need a graph search algorithm (e.g. A*)

You need a decent heuristic to control search behaviour

Forward search is inefficient in the number of irrelevant

actions there are.

BA

C

F ED


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Backward Chaining Search

On(B,C) On(A,B)

Move(A,x,B)




{x/Table}

Initial State: On(A,Table)

On(B,Table) On(C,A)

Clear(C) Clear(B)

C

BA

A

C

B


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On(B,C) On(A,B)

On(A,Table)

Clear(A)

Clear(B)

On(B,C)Move(A,x,B)




{x/Table}


On(B,Table) On(C,A)

Clear(C) Clear(B)

C

BA

B

AC

A

C

B


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On(B,C) On(A,B)

On(A,Table)

Clear(A)

Clear(B)

On(B,C)Move(A,x,B)




{x/Table}


On(B,Table) On(C,A)

Clear(C) Clear(B)

C

BA

Move(b,A,x)

On(A,Table)

Clear(B)

On(B,A)

Clear(C)

B

AC

A

C

B

{x/C, b/B}

B

AC


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On(B,C) On(A,B)

On(A,Table)

Clear(A)

Clear(B)

On(B,C)Move(A,x,B)




{x/Table}

Move(B,x,C)


On(B,Table) On(C,A)

Clear(C) Clear(B)

C

BA

Move(b,A,x)

On(A,Table)

Clear(B)

On(B,A)

Clear(C)

{x/Table}

B

AC

A

C

B

{x/C, b/B}

B

AC

BAC

On(A,Table)

On(B,Table)

Clear(B)

Clear(C)

Clear(A)


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An operator is chosen that achieves one of the unachievedparts of the goal state

Variables in the action are bound to entities in the world

When an operator is applied

Its positive effects are deleted to create the predecessor

Each precondition is added to the list of sub-goals

A sub-goal that is not true in the initial state is then chosen

to be achieved


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Linear vs non-linear planning

In early planners it was assumed that sub-goals could be solved completely

independently

And the plans produced for these sub-goals could then be sequenced

This approach is called Linear Planning (Sacerdoti, 1975), but it is incomplete

(not guaranteed to find solutions when they exist) because it doesnt interleave

the solutions.

Non-interleaved planners cant solve some problems (e.g. the Sussman

Anomaly)

Non-linear planners attempt to solve this problem

BA

C

C

BA


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Conclusion

Planning is an important area ofAI. State of the art planners are nowbeyond human level performance.

Specialist representations of action effects have been used to overcomeissues of representational and inferential inefficiency

The STRIPS representation has been influential, succeeded by ADL andthe overarching framework of PDDL

State space planning still requires search, either forward or backwardchaining

This is the ancient history of planning, later on came partial order

planning (1975-1995), satisfiability planners (1992 on), graph planning(1995 on), and then the resurgence of state space planning (1996 on),and also planning under uncertainty (decision theoretic planning) (1997on).

Ai Principles Planning[1]

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