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Planning

Chapter 11- Part1

Author: Vali Derhami

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Outline

• Search vs. planning

• STRIPS operators

• Forward and backward search algorithms

in planning

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Search vs. Planning

• Consider the task get milk, bananas.• Standard search algorithms seem to fail miserably:

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Search vs. Planning (cont.)

Assume a problem-solving agent using search . . .

♦ Which actions are relevant?

– Our previous state-space definition does not clarify this

♦ What is a good heuristic function?

– Must be provided by a human in each individual case

♦ How to decompose the problem?

– Most real-world problems are nearly decomposable

– But the state-space definition does not reveal any structure of the problem

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What is planning?

• Planning in AI is the problem of finding a sequence of actions to achieve some goals.

• The sequence of actions is the system’s plan which then can be executed.

• Planning requires the following:

– representation of goal to achieve;

– knowledge about what actions can be performed;

– knowledge about state of the world;

to generate a plan to achieve the goal.

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Architecture of a Planner

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Planning Language

• What is a good language?– Expressive enough to describe a wide variety of

problems

– Restrictive enough to allow efficient algorithms to operate on it

Planning algorithm should be able to take advantage of the logical structure of the problem

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STRIPS Language

• STanford Research Institute Problems Solver

• The language of predicate logic to representgoal to be achieved; state of environment; actions available to agent;

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Example: Blocks world

• To represent this environment, need the following predicate names:On(x, y) obj x on top of obj yOnTable(x) obj x is on the tableClear(x) nothing is on top of obj xHolding(x) arm is holding xArmEmpty robot arm is emptyHere is a FOL representation of the blocks world described above:Clear(A)Clear(C) On(A,B) OnTable(B) OnTable(C)

ArmEmpty

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Representation of states and goal

• Representation of States = conjunction of ground and function free literals

مثبت لیترالهای از عطفی گزاره( ترکیت لیترالهای بیشتر اینجا در ای)

– e.g. At(A,B) Clear(C), . . . But not At(A, x) or At(neighbour(A),B)!

closed-world assumption is used, meaning that any conditions that are not mentioned in a state are assumed false.

• Representation of goals: A goal is a particular state– e.g. OnTable(A) OnTable(B) OnTable(C)A state s satisfies a goal g if s contains all the atoms in g (and possibly others)

Rich Famous Miserable satisfies Rich Famous

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Representation of actionsAction(Fly(p, from, to), PRECOND:At(p, from) Plane(p) Airport(from) Airport(to)

Effect: At(p, from) At(p, to)) Each action schema has:

– a name and parameter list– a pre-condition list: conjunction of function-free positive literals, list of facts which must be true for action to be executed;

Any variables in the precondition must also appear in the action's parameter list.

– an effect list: a conjunction of function-free literals describing how the state changes when the action is executed. may be contains: a delete list: list of facts that are no longer true after action is performed (negative literals); an add list: list of facts made true by executing the action. (positive literals)

Each of these may contain variables.

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Applicable actions

An action is applicable in any state satisfying its preconditions

Example: Action(Fly(p, from, to),

PRECOND:At(p, from) Plane(p) Airport(from) Airport(to)

Effect: At(p, from) At(p, to))

• Current State: At(Pi, JFK) At(P2, SFO) Plane(Pi) Plane(P2) Airport(JFK) Airport(SFO) .

={p/Pi, from/JFK, to/SFO} جایگزین تعریف• Thus, the concrete action Fly (Pi, JFK, SFO) is applicable.

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Effect of actions

• Starting in state s, the result of executing an applicable action a is a state s' that is the same as s except thatAny positive literal P in the effect of a is added to s' any negative literal P is removed from s‘ all other atoms do not change their value!

After Fly (Pi, JFK, SFO), • current state:

At(Pi, SFO) At(P2, SFO) Plane(Pi) Plane(P2) Airport(JFK) Airport(SFO) .

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Expressiveness and extensions

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Air cargo transport

In(c, p) means that cargo c is inside plane p, and At(x, a) means that object x (either plane or cargo) is at airport a.

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Air cargo transport (Cont.)

• Following plan is a solution to the problem: [Load(C1, P1, SFO), Fly(P1, SFO, JFK), Unload(C1,P1, JFK),Load(C2, P2, JFK), Fly(P2, JFK, SFO), Unload(C2, P2, SFO)] .