march2003 planning lecture

8/2/2019 March2003 Planning Lecture

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Lectures on Planning

Chris Handy

Centre for Knowledge Management

March 2004


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PLANNING

Definition

Planning is an important topic in

artificial intelligence, cognitivepsychology, neurobiology,

business management,

manufacturing science andengineering, satellite control,and a host of other subjects.


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PLANNING

Definition

In AI, planning involves the

generation of an action sequence

or action program for an agent,

such as a robot or a software

system or a living artefact, that can

alter its surroundings.


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PLANNING

Definition

For instance, the purpose of a plan

may be to guide and enable a robot

to fetch an object, say A, and place

on top of another object, say B.


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PLANNING

Definition

For instance, the purpose of a plan may be to guide

and enable a robot to fetch an object, say A, andplace on top of another object, say B.

Note that in the above example:

the action -- fetching -- has been definedexplicitly, the initial state is clearly described -- an object

A and an object B, such that A can be placed on top

of B,

the goal for the robot or the software system isclearly outlined.


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PLANNING

Definition

Planning has also been described

as one of the reliable method for

controlling the behaviour of living

and artificial agents, which may not

be the fastest of the methods and,

perhaps, not the only one.


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PLANNING

Definition

Planning implies thenotion of synthesis:

synthesis of actions,goals, initial states.


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PLANNING

Definition

Planning is sometimes contrasted with the

retrieval and application of stored behaviourprograms.

The later includes a number of 'routine'

activities performed by humans: for example,

handling hot surfaces and utensils; opening andclosing doors and windows etc. In familiar situations

little or no overt planning is in evidence, however the

predominance of stored behaviour is quite

noticeable.


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PLANNING

It is in the handling ofnovel

situations or critical situationsthat we see the a substantial

planning-related activities:

examination of initial states, acollection of actions for

transforming the initial states and a

set of goals.


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Definitions of aplan, aplanning

system, and an operator in a

planning context

Definition a: Aplan is a defined as a

prescription for a sequence of actions that, iffollowed, will change the relations among

objects so as to achieve a desired goal.

PLANNING


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PLANNING

Definition b A planning system performs the following functions:

1. Choice The system can choose the best

rule to apply next based on the

best available heuristic information

2. Application The system can apply the chosen

rule to compute the new problem

state that arises from its

application.3. Detection The system can detectwhen a

solution has been found

4.

Abandonment

The system can abandon dead-

ends and can direct its efforts to

more fruitful avenues.


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PLANNING

Definition c An operator in planning is

essentially a if-then-delete rule; the ifconditions of each operator are called pre-

requisites. The operator can, for example, used

to describe an action moving a block, clearing

some space and so on.


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THE BLOCKS WORLD

The 'blocks world' was amongst the favourite topics in AI:

there were Ph D theses, there were learned papers,

conferences and so on during the late sixties and the early

seventies.

The 'blocks world' is an imaginary two-dimensional world

comprising:

A number of (usually distinctly labelled) square blocks;

The square blocks can be arranged to form stacks;

A table of unbounded size.


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THE BLOCKS WORLD

The BLOCKSworld states can be described by three kinds ofliterals

CLEAR (x) There is no block on top ofx

ON (x, y) Block x rests directly on block y

HOLDING

(x)

A hand of an agent holding

block x

The initial state description for a completely

known world consists of a conjunction of these


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THE BLOCKS WORLD - EXAMPLE 1

Consider the following initial and final states of a 'world'

that comprises a table and three blocks: A, B, C:

C

A B

A

A

B

C

Initial State Goal State


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The initial state of the above 'world'can be described in terms of the

literals as follows:CLEAR (C)ON (C, A)

ON (A, Table)CLEAR (B)ON (B, Table)


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Consider blocks A, B, C, and D which

are on a table.

The initial situation is as follows: Block A is onblock C, and block D on block B. The goal

situation is: Block A is on top of block B, B is on

C, and Cis on the table; block D is also on the

table.

In the following generic operators the mapping

to the above is: A x, C y and D z


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Three operators: The operators are made up of the literals

explained above and are shown below:

Operator

1:

/* Move block x from block y to block z */

IF

ON (x, y)CLEAR (x)

CLEAR (z)

ADD LIST ON (x, z)

CLEAR (y)

DELETE LIST On (x, y)

CLEAR (z)


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Operator 2: /* Move block x from block y to Table*/

IF ON (x, y)

ADD LIST ON (x, Table)

CLEAR (y)

DELETE LIST ON (x, y)


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Operator 3: /* Move block x from Table to block z */

IF ON (x, Table)

CLEAR (x)CLEAR (z)

ADD LIST ON (x, z)

CLEAR (y)

DELETE LIST ON (x, Table)

CLEAR (z).


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A simple breadth-first search will mean

that every operator will have to be triedand instantiated in every possible way,

as long as the operators' pre-requisites

are satisfied. This approach will leadto an exponential tree growth in the

search space.

Search strategy not breadth first

but backward chaining


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Search strategy not breadth

first but backward chaining

In order to conduct a more intelligent search for

the final situation in that the sequencing of the

operators has to be more carefully organised the

breadth-first search. The goal is described here

by only a few assertions that must hold for the

problem to be solved, whereas any full

description of a situation involves many more

assertions. Backward chaining search is,

therefore, more appropriate than a forward

chaining search.


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Initial Situation

On (A, C)

Clear (A)

On (D, B)

Clear (D)

On (C, Table)

On (B, Table)

Initial Situation

On (A, C)

Clear (A)

On (D, B)

Clear (D)

ON (C, Table)

ON (B, Table)

Initial Situation

On (A, C)

Clear (A)

On (D, B)

Clear (D)

On (C, Table)

On (B, Table)

Operator 2

If On (D, B)

Clear (D)

Add On (D, Table)

Clear (B)

Delete On (D, B)

Operator 2

If On (D, B)

Clear (D)

Add On (D, Table)

Clear (B)

Delete On (D, B)

Operator 1

If On (A, C)

Clear (A)

Clear (B)

Add On (A, B)

Clear (C)

Delete On (A, C)

Clear (B)

Operator 1

If On (A, C)

Clear (A)

Clear (B)

Add On (A, B)

Clear (C)

Delete On (A, C)

Clear (B)

Operator 1

If On (A, C)

Clear (A)

Clear (B)

Add On (A, B)

Clear (C)

Delete On (A, C)

Clear (B)

Goals

On (A, B)

Goals

On (A, B)

Goals

On (A, B)

Three steps toward constructing a plan for achieving a simple goal using backward chaining. All links shown are Establishes

links. Most of them tie an addition in one instantiated operator to a prerequisite .in another instantiated operator, thus

creating an ordering constraint between the tow operators. Other Establishes links are connected to initial-situationassertions or goal assertions.

Search strategy not breadth first but backward chaining


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Initial Situation

On (A, C)

Clear (A)

On (D, B)Clear (D)

On (C, Table)

On (B, Table)

Initial Situation

On (A, C)

Clear (A)

On (D, B)

Clear (D)

On (C, Table)

On (B, Table)

Operator 2

If On (D, B)

Clear (D)

Add On (D, Table)

Clear (B)

Delete On (D, B)

Operator 2

If On (D, B)

Clear (D)

Add On (D, Table)

Clear (B)

Delete On (D, B)

Operator 1

If On (A, C)

Clear (A)

Clear (B)

Add On (A, B)

Clear (C)

Delete On (A, C)

Clear (B)

Operator 3

If On (B, Table)

Clear (B)

Clear (C)

Add On (B, C)

Delete On (B, Table)

Clear (C)

Operator 1

If On (A, C)

Clear (A)

Clear (B)

Add On (A, B)

Clear (C)

Delete On (A, C)

Clear (B)

Goals

On (A, B

On (B, C))

Goals

On (A, B)

On (B, C)

Construction of a plan for achieving tow goal assertions using backward chaining. All links shown are Establishes links. The

top portion deals with moving blockA onto blockB; the bottom portion adds an operation intended to move blockB onto block

C. The plan is flawed because operator 1 interferes with an Establishes link between operator 2 and operator 3.



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CONDITIONALPLANNING

Conditional planning, also known as contingencyplanning,

deals with incomplete information by constructing a

conditional pllan that accounts for each possible situation or

co

ntingencythat may arise.Conditional planning differs from the ideal planning and

execution discussed in the beginning of this lecture. We

dealt with cases where we were dealing worlds that are

accessible, static and deterministic and the action

descriptions must be correct and complete describing all the

consequences exactly.

Contingencies are dealt on a one by one basis and the

planning program finds out which part of the plan to execute

by including sensing actions in the plan to test for the


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CONDITIONALPLANNINGA worked example

Consider the problem of repairing the flat tyre of a car. The

following literals describe the location and the state of the

malfunctioning tyre:On (x) Tyre x is on (the car)

Off(x) Tyre x is off (the car)

Intact (x) Tyre x is intact

Inflated (x) Tyre x is inflated

Flat(x) Tyre X is Flat

ClearHub (x) Tyre x is not on the hub


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CONDITIONALPLANNINGThe following operators will help in fixing the tyre:

Table 1

Operator1:

/*Remove Tyre x*/

IF On (x)

Add list Off (x)

ClearHub (x)

Delete list On (x)


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Table 2

Operator

2:

/* Put Tyre x On */

IF Off (x)

ClearHub(x)

Add list On (x)

Delete list ClearHub(x)

Off(x)

CONDITIONALPLANNING


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CONDITIONALPLANNING

Table 3

Operator

3:

/* Inflate Tyre x*/

IF Intact (x)

Flat(x)

Add list Inflated (x)

Delete list Flat(x)


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The typical goal can be described as:

On(x) ^ Inflated (x),

with the initial conditions:

Inflated (Spare) ^ Intact (Spare) ^ Off(Spare) ^ On(Tyre1)

^ Flat (Tyre1)

The standard plan to repair the car will be as follows:

[Remove (Tyre1), PutOn(Spare)]

CONDITIONALPLANNING


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Dealing with incomplete

informationIn the above example we have assumed

that the tyre was not intact: the description

of the initial conditions does not use the

operatorintact. It is quite possible that when

the tyre of a car is flat it may be due to the

fact tyres need to be pumped at regularintervals in that they always leak air, albeit

very slowly.


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STAGESOF THE PLANNING

PROCESSThe planning process can be described through six

stages:

Stage1 : The plan has the typical Startand Finish states.The initial condition suggests that Tyre1 is a Flattyre and

that we have an Inflatedspare tyre to replace the Flat

tyre.

Start Finish

On(Tyre1)

Flat (Tyre1)Inflated

(Spare)

On(x)Inflated (x)


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STAGESOF THE PLANNINGPROCESS

Stage2 : There are two open conditions to be

resolved: On(x) and Inflated(x). The first is

satisfied by unifying the literal On in both the initial

and final state by the variable Tyre1 . The secondis satisfied by adding the step Inflate(Tyre1). Recall

that the Inflate operator has antecedent conditions

Flatand Intact. The first antecedent literal (Flat) is

satisfied by linking it with the same literal in theStartstate. However, we have a problem with the

Intactliteral. There is no action schema with the

effect Intact, that is in the statement of the problem

there are no actions that can make the tire intact.


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Inflate(Tyre1)

Start FinishOn(Tyre1)

Flat (Tyre1)

Inflated

(Spare)

On(x)

Inflated (x)

Flat (Tyre1)

Intact ((Tyre1)


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Stage3 : In the conditional planning systems, as opposed to

conventional planning systems which will abandon Stage2now and

pursue other goals if they can, one can add an action Check(x) :

Operator4:

/* Check Tyre x*/

IF Tyre (x)

Add list KnowsWhether(Intact(x))

This operator helps in determining the truth value of the propositionthat unifies with Intact(x). The check tyre operation helps in

conditional planningthrough the addition of a conditional linkto

the Inflate(Tyre1) operation. Such a step is called a conditional step

because it will become a branch point in the final plan.


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Intact (Tyre1)

Start Finish

Inflate(Tyre1)

On(Tyre1)

Flat (Tyre1)

Inflated (Spare)

On(Tyre1)

Inflated (Tyre1)

Flat (Tyre1)

Intact

((Tyre1)Check(Tyre1

)

(Intact (Tyre1))

(Intact (Tyre1))


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Stage4 : This involves planning for the eventuality that Tyre1 may not

be Intact. Therefore, the tyre cannot be Inflatedand has to be

replaced by the Spare tyre. There are now two alternative Finish

states depending upon whether or not Tyre1 was intact or not

Intact (Tyre1)

Start

Inflate(Tyre1)

On(Tyre1)Flat (Tyre1)

Inflated

(Spare)

On(Tyre1)

Inflated (Tyre1)

Flat (Tyre1)

Intact((Tyre1)Check(Tyre1)

(Intact (Tyre1))

Finish

(Intact (Tyre1))

Finish

( Intact (Tyre1))

On(x)

Inflated (x)


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Stage5: The Inflated (Spare) literal in the Startstate can be unified

with the alternative Finish states literal of the same name but

comprising a variablex.

Intact (Tyre1)

Start

Inflate(Tyre1)

On(Tyre1)

Flat (Tyre1)

Inflated (Spare)

On(Tyre1)

Inflated (Tyre1)

Flat (Tyre1)

Intact ((Tyre1)

Check(Tyre1)(Intact (Tyre1))

Finish

(Intact (Tyre1))

Finish

( Intact (Tyre1))

On(Spare)

Inflated

(Spare)


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Stage6: The final stage of planning now involves the addition of theoperators Remove(Tyre1) and PutOn(Tyre1). The PutOn operator has

the consequent (literal) On and this can be unified by its counterpart in

the second of the two Finish states. Our plan to fix the Tyre is now

complete.

Intact (Tyre1)

Start

Inflate(Tyre1)

On(Tyre1)

Flat (Tyre1)Inflated (Spare)

On(Tyre1)

Inflated (Tyre1)

Flat (Tyre1)

Intact ((Tyre1)Check(Tyre1)

(Intact (Tyre1))

Finish

(Intact (Tyre1))

Finish

( Intact (Tyre1))

On(Spare)

Inflated(Spare)

Remove(Tyre1) PutOn(Tyre1)( Intact (Tyre1))( Intact (Tyre1))

Intact (Tyre1)


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Such an algorithm is called Conditional

Partial-Order Planner or CPOP for short.

STAGESOF THE PLANNING

PROCESS

march2003 planning lecture

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