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Jurusan Teknik Informatika – Universitas Widyatama

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Planning

Pertemuan : 11

Dosen Pembina :

Sriyani Violina

Danang Junaedi

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• Deskripsi

• Introduction

• Hierarchical Planning

• Sensorless Planning

• Conditional Planning

• Execution Monitoring and Replanning

• Continous Planner

• State of the world (STRIPS language)

• The Block World– Goal stack Planning (GSP)

Overview

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• Pertemuan ini mempelajari bagaimana

memecahkan suatu masalah dengan teknik

planning.

• Metode planning yang dibahas pada

pertemuan ini adalah Goal Stack Planning

(GSP)

Deskripsi Introduction

• We studied how to take actions in the world

(search)

• We studied how to represent objects, relations,

etc. (logic)

• Now we will combine the two!

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Introduction

• Problem-solving is a search through a state space.

• Planning is the process of computing several steps

of a problem-solving procedure before executing

them.

• Planning = problem sloving in advance.

• Planning is important if solutions cannot be undone.

• If the universe is not predictable, then a plan can fail

⇒⇒⇒⇒ dynamic plan revision.

Hierarchical Planning

• Hierarchical Task Network(HTN)

– At each “level,” only a small number of

individual planning actions, then descend to

lower levels to “solve these” for real.

– At higher levels, the planner ignores “internal

effects” of decompositions. But these have to be

resolved at some level…

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HTN Sample

• Construction Domain:

– Actions:

• Buy Land: Money � Land

• Get Load: Good Credit � Money

• Get Permit: Land � Permit

• Hire Builder: � Contract

• Construction: Permit ∧ Contract � House Built

• Pay Builder: Money ∧ House Built � House

• …

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HTN Sample (cont)

• Macro Action in Library:

– Build House:

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HTN Sample (cont)

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HTN Sample (cont)

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HTN Cons and Pros

• What’s Bad?

– Recursion?

– Sub Task Sharing:

• Enjoy honey moon in Hawaii and raise a family.

• Library:

– Enjoy Honey moon in Hawaaii: Get Married , Go to Hawaii.

– Raise Family: Get Married, Have two children.

• What’s Good:

– Almost all real applications are HTN + some thing else.

– It’s a heuristic to decrease the branching factor by a great

level.

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NonDeterministic Domains

• What if we don’t know all about situations

and effects.

• E.g.

– Init: A table and a chair of unknown colors.

– Goal: A table and a chair of the same colors.

– Condition: Painting may have flaws.

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Sensorless Planning

• We don’t know all beforehand and we can’t

find it out, even when it is done.

– Plan so that to reach the goal state, regardless of

everything. (Coercion)

– Not always possible.

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Conditional Planning

• We can check the state ahead, then perform

the pre-planned program.

– Sense Actions

– Conditional Branches

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Conditional Planning in

Fully Observable Domains

• Vacuum World:

– Left: AtRight � AtLeft ∧ ¬AtRight

– Left: AtRight �

(AtLeft ∧ ¬AtRight)∨ (¬AtLeft ∧ AtRight)

– Suck: when AtLeft�CleanLeft

when AtRight�CleanRight

– Left: when AtLeft� ¬CleanLeft

when AtRight�AtLeft ¬AtRight

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Notation Expantion:

• Expanding Plan Notation:

– If (state) Then (…) else (…)

– If (AtLeft∧CleanLeft ∧CleanRight) Then {}

else Suck.

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State Space:

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Conditional Planner:

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Unavoidable Loops in Conditional

Planner

• New Notation:

– Instead of just Left : while (AtRight) Left

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Partially Observable Domains

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Partially Observable Domains

• Easiest Approach:

– Assume set of current states and the next state

sets are created, quite similar to non-

deterministic actions case.

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Execution Monitoring and Replanning

• Check if the plan is going on is pre-decided?

If not, replan based on current situation.

• Action Monitoring:

• See if current state is as it was supposed, if not, find a

solution to return it to what it was (repair).

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Execution Monitoring & Replanning

• Plan Monitoring:

– See if the previous plan is still wise?

– Serendipity!

– A precondition of future actions has failed and

can not be recovered.

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Execution Monitoring in Partially

Observable Domains

• Things may fail and we don’t know.

• Sensing actions may be required

– And they may need extra-planning.

• We may stuck in futile attempts:

– The electronic key is incorrect, but we think it

might be due to incorrect pushing in.

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Continues Planner

• Keep planning, sensing and executing…

– Which is not unlikely, such as maintenance

planning, auto-pilot, plant control, …

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Continuous Planner

• POP + …

– Missing Goal:

• A new goal has erupted. Just add it.

– Open precondition:

• An action has lost its support links. Add a new causal

link.

– Causal Conflicts:

• A causal link is suddenly threatened. Choose an

appropriate ordering.

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Continuous Planner

• POP + …

– Unsupported Link:

• A link from start to something has suddenly last its

true value. Remove it.

– Redundant Action:

• An action no more produces something needed.

Remove it.

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State of the world (STRIPS language)

• State of the world = conjunction of positive, ground,

function-free literals

• At(Home) AND IsAt(Umbrella, Home) AND

CanBeCarried(Umbrella) AND IsUmbrella(Umbrella) AND

HandEmpty AND Dry

• Not OK as part of the state:

– NOT(At(Home)) (negative)

– At(x) (not ground)

– At(Bedroom(Home)) (uses the function Bedroom)

• Any literal not mentioned is assumed false

– Other languages make different assumptions, e.g., negative literals

part of state, unmentioned literals unknown

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An action: TakeObject

• TakeObject(location, x)

• Preconditions:

– HandEmpty

– CanBeCarried(x)

– At(location)

– IsAt(x, location)

• Effects (“NOT something” means that that

something should be removed from state):

– Holding(x)

– NOT(HandEmpty)

– NOT(IsAt(x, location))

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Another action

• WalkWithUmbrella(location1, location2,

umbr)

• Preconditions:

– At(location1)

– Holding(umbr)

– IsUmbrella(umbr)

• Effects:

– At(location2)

– NOT(At(location1))

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Yet another action

• WalkWithoutUmbrella(location1,

location2)

• Preconditions:

– At(location1)

• Effects:

– At(location2)

– NOT(At(location1))

– NOT(Dry)

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A goal and a plan

• Goal: At(Work) AND Dry

• Recall initial state:

– At(Home) AND IsAt(Umbrella, Home) AND

CanBeCarried(Umbrella) AND IsUmbrella(Umbrella) AND

HandEmpty AND Dry

• TakeObject(Home, Umbrella)

– At(Home) AND CanBeCarried(Umbrella) AND

IsUmbrella(Umbrella) AND Dry AND Holding(Umbrella)

• WalkWithUmbrella(Home, Work, Umbrella)

– At(Work) AND CanBeCarried(Umbrella) AND

IsUmbrella(Umbrella) AND Dry AND Holding(Umbrella)

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Planning to write a paper• Suppose your goal is to be a co-author on an AI paper with both

theorems and experiments, within a year

LearnAbout(x,y)

Preconditions: HasTimeForStudy(x)

Effects: Knows(x,y),

NOT(HasTimeForStudy(x))

HaveNewIdea(x)

Preconditions: Knows(x,AI),

Creative(x)

Effects: Idea, Contributed(x)

ProveTheorems(x)

Preconditions: Knows(x,AI),

Knows(x,Math), Idea

Effect: Theorems, Contributed(x)

PerformExperiments(x)

Preconditions: Knows(x,AI),

Knows(x,Coding), Idea

Effect: Experiments, Contributed(x)

WritePaper(x)

Preconditions: Knows(x,AI),

Knows(x,Writing), Idea,

Theorems, Experiments

Effect: Paper, Contributed(x)

Goal: Paper AND Contributed(You)

FindExistingOpenProblem(x)

Preconditions: Knows(x,AI)

Effects: Idea

Name a few things that are

missing/unrealistic… 33IF-UTAMA

Some start states

• Start1: HasTimeForStudy(You) AND Knows(You,Math) AND

Knows(You,Coding) AND Knows(You,Writing)

• Start2: HasTimeForStudy(You) AND Creative(You) AND

Knows(Advisor,AI) AND Knows(Advisor,Math) AND

Knows(Advisor,Coding) AND Knows(Advisor,Writing)

(Good luck with that plan…)

• Start3: Knows(You,AI) AND Knows(You,Coding) AND

Knows(OfficeMate,Math) AND HasTimeForStudy(OfficeMate) AND

Knows(Advisor,AI) AND Knows(Advisor,Writing)

• Start4: HasTimeForStudy(You) AND Knows(Advisor,AI) AND

Knows(Advisor,Math) AND Knows(Advisor,Coding) AND

Knows(Advisor,Writing)

We’ll use these as examples…

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Forward state-space search (progression

planning)• Successors: all states that can be reached with an action

whose preconditions are satisfied in current state

At(Home)

IsAt(Umbrella, Home)

CanBeCarried(Umbrella)

IsUmbrella(Umbrella)

HandEmpty

Dry

At(Home)

Holding(Umbrella)

CanBeCarried(Umbrella)

IsUmbrella(Umbrella)

Dry

TakeObject(Home, Umbrella)

At(Work)

IsAt(Umbrella, Home)

CanBeCarried(Umbrella)

IsUmbrella(Umbrella)

HandEmpty

WalkWithoutUm

brella(Home,

Work)

WalkWithUmbrella(

Home, Work,

Umbrella)

At(Work)

Holding(Umbrella)

CanBeCarried(Umbrella)

IsUmbrella(Umbrella)

Dry

WalkWithout

Umbrella(Wor

k, Home)

At(Home)

IsAt(Umbrella, Home)

CanBeCarried(Umbrella)

IsUmbrella(Umbrella)

HandEmpty

GOAL!

WalkWithoutUmbrella(

Home, Umbrella) (!)

WalkWithoutUm

brella(Home,

Work)

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Backward state-space search (regression

planning)

• Predecessors: for every action that accomplishes one of the

literals (and does not undo another literal), remove that

literal and add all the preconditions

At(location1)

At(location2)

IsAt(umbr, location2)

CanBeCarried(umbr)

IsUmbrella(umbr)

HandEmpty

Dry

At(location1)

Holding(umbr)

IsUmbrella(umbr)

Dry

TakeObject(location2, umbr)

This is accomplished in the

start state, by substituting

location1=location2=Home,

umbr=Umbrella

WalkWithUmbrella(

location1, Work,

umbr)At(Work)

Dry

GOAL

WalkWithUmbrella(location2, location1)

WalkWithoutUmbrella can never be used, because it undoes Dry

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Heuristics for state-space search

• Cost of a plan: (usually) number of actions

• Heuristic 1: plan for each subgoal (literal) separately, sum

costs of plans

– Does this ever underestimate? Overestimate?

• Heuristic 2: solve a relaxed planning problem in which

actions never delete literals (empty-delete-list heuristic)

– Does this ever underestimate? Overestimate?

– Very effective, even though requires solution to (easy) planning

problem

• Progression planners with empty-delete-list heuristic

perform well

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The Blocks World

AB C Dstart AC DBgoalPlanning = generating a sequence of

actions to achieve the goal from the start

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The Blocks World

Actions:

• UNSTACK(A, B) : angkat balok A yang menempel

di atas balok B

• STACK(A, B) : simpan balok A di atas balok B

• PICKUP(A) : angkat balok A dari atas meja

• PUTDOWN(A) : simpan balok A di permukaan

meja

• MOVE(A,B,C): simpan balok A di atas balok C

• MOVETOTABLE(A,B) : simpan balok A yang

menempel di atas balok B ke atas permukaan meja

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The Blocks World

Conditions and results:

• ON(A, B) : balok a menempel di atas balok B

• ONTABLE(A) : balok A berada di permukaan meja

• CLEAR(A) : tidak ada balok yang menempel di atas

balok A

• HOLDING(A) : lengan robot sedang memegang

balok A

• ARMEMPTY: lengan robot tidak sedang memegan

balok

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The Blocks World

Specification of actions:

• PRECONDITION (P): list of predicates that must be true for an operator to be applied.

• ADD (A): list of new predicates that an operator causes to become true.

• DELETE(D): list of old predicates that an operator causes to become false.

• Predicates not in ADD nor DELETE are unaffacted.

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The Blocks World

Specification of actions:

STACK(x, y):

P: CLEAR(y) ∧∧∧∧ HOLDING(x)

D: CLEAR(y) ∧∧∧∧ HOLDING(x)

A: ARMEMPTY ∧∧∧∧ ON(x, y)

UNSTACK(x, y):

P: ON(x, y) ∧∧∧∧ CLEAR(x) ∧∧∧∧ ARMEMPTY

D: ON(x, y) ∧∧∧∧ ARMEMPTY

A: HOLDING(x) ∧∧∧∧ CLEAR(y)

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The Blocks World

Specification of actions:

PICKUP(x):

P: CLEAR(x) ∧∧∧∧ ONTABLE(x) ∧∧∧∧ ARMEMPTY

D: ONTABLE(x) ∧∧∧∧ ARMEMPTY

A: HOLDING(x)

PUTDOWN(x):

P: HOLDING(x)

D: HOLDING(x)

A: ONTABLE(x) ∧∧∧∧ ARMEMPTY

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The Blocks World

Specification of actions:

MOVE(x,y,z):

P: ON(x,y), CLEAR(x), CLEAR(z)

D: ON(x,y) ∧∧∧∧ CLEAR(Z)

A: ON(x,z), CLEAR(y), NOT(ON(x,y)), NOT(CLEAR(z))

MOVETOTABLE(x,y):

P: ON(x,y), CLEAR(x)

D: ON(x,y)

A: ONTABLE(x) ∧∧∧∧ ONTABLE(y) ∧∧∧∧CLEAR(y) ∧∧∧∧NOT(ON(x,y))

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The Blocks World

AB ON(B, A) ∧∧∧∧ONTABLE(A) ∧∧∧∧ONTABLE(C) ∧∧∧∧ONTABLE(D) ∧∧∧∧ARMEMPTY C Dstart: AC ON(C, A) ∧∧∧∧ON(B, D) ∧∧∧∧ONTABLE(A) ∧∧∧∧ONTABLE(D) ∧∧∧∧DBgoal:

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Goal Stack Planning

GoalsOperators to satisfy the Goals Current situationSpecification of Operators/ActionsStack Database

+

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Goal Stack Planning

Push the original goal to the stack. Repeat until the

stack is empty:

– If stack top is a compound goal, push its unsatisfied

subgoals to the stack.

– If stack top is a single unsatisfied goal, replace it by an

operator that makes it satisfied and push the operator’s

precondition to the stack.

– If stack top is an operator, pop it from the stack, execute

it and change the database by the operation’s affects.

– If stack top is a satisfied goal, pop it from the stack.

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Goal Stack Planning

AB ON(B, A) ∧∧∧∧ONTABLE(A) ∧∧∧∧ONTABLE(C) ∧∧∧∧ONTABLE(D) ∧∧∧∧ARMEMPTY C Dstart: AC ON(C, A) ∧∧∧∧ON(B, D) ∧∧∧∧ONTABLE(A) ∧∧∧∧ONTABLE(D) ∧∧∧∧DBgoal:

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Goal Stack PlanningON(C, A) ON(B, D) ON(C, A) ∧∧∧∧ ON(B, D) ∧∧∧∧ OTADCLEAR(A)HOLDING(C)CLEAR(A) ∧∧∧∧ HOLDING(C)STACK(C, A)ON(B, D)ON(C, A) ∧∧∧∧ ON(B, D) ∧∧∧∧ OTADON(B, A) OTACDARMEMPTY ON(B, A) OTACDARMEMPTY

Stack DatabaseIF-UTAMA

Note:

OTAD = ONTABLE(A)∧∧∧∧

ONTABLE(D)

1

2

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Goal Stack PlanningON(B,A)CLEAR(B)ARMEMPTYON(B,A) ∧∧∧∧CLEAR(B) ∧∧∧∧ARMEMPTYUNSTACK(B,A)HOLDING(C)CLEAR(A) ∧∧∧∧ HOLDING(C)STACK(C, A)ON(B, D)ON(C, A) ∧∧∧∧ ON(B, D) ∧∧∧∧ OTADOTACDHOLDING(B)Stack Database

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3 1.UNSTACK(B,A)Planning :

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Goal Stack PlanningHOLDING(C)CLEAR(A) ∧∧∧∧ HOLDING(C)STACK(C, A)ON(B, D)ON(C, A) ∧∧∧∧ ON(B, D) ∧∧∧∧ OTAD OTACDHOLDING(B)Stack Database

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OTCCLEAR(C)ARMEMPTYOTC ∧∧∧∧ CLEAR(C) ∧∧∧∧ ARMEMPTYPICKUP(C)HOLDING(C)CLEAR(A) ∧∧∧∧ HOLDING(C)STACK(C, A)ON(B, D)ON(C, A) ∧∧∧∧ ON(B, D) ∧∧∧∧ OTADOTACDHOLDING(B)5

1.UNSTACK(B,A)Planning :1.UNSTACK(B,A)Planning :

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Goal Stack PlanningCLEAR(D)HOLDING(B)CLEAR(D)∧∧∧∧ HOLDING(B)STACK(B,D)OTC ∧∧∧∧ CLEAR(C) ∧∧∧∧ ARMEMPTYPICKUP(C)HOLDING(C)CLEAR(A) ∧∧∧∧ HOLDING(C)STACK(C, A)ON(B, D)ON(C, A) ∧∧∧∧ ON(B, D) ∧∧∧∧ OTADOTACDON(B,D)ARMEMPTYStack Database

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6 1.UNSTACK(B,A)2.STACK(B,D)Planning:

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Goal Stack PlanningOTC ∧∧∧∧ CLEAR(C) ∧∧∧∧ ARMEMPTYPICKUP(C)HOLDING(C)CLEAR(A) ∧∧∧∧ HOLDING(C)STACK(C, A)ON(B, D)ON(C, A) ∧∧∧∧ ON(B, D) ∧∧∧∧ OTADOTADON(B,D)HOLDING(C)Stack Database

IF-UTAMA

7 1.UNSTACK(B,A)2.STACK(B,D)3.PICKUP(C)Planning :HOLDING(C)CLEAR(A) ∧∧∧∧ HOLDING(C)STACK(C, A)ON(B, D)ON(C, A) ∧∧∧∧ ON(B, D) ∧∧∧∧ OTAD OTADON(B,D)ON(C,A)ARMEMPTY8 1.UNSTACK(B,A)2.STACK(B,D)3.PICKUP(C)4.STACK(C,A)Planning :54

Goal Stack Planning

ACON(C, A) ∧∧∧∧ONTABLE(A) ∧∧∧∧ONTABLE(B) ∧∧∧∧ARMEMPTY Bstart: AON(A, B) ∧∧∧∧ON(B, C) CBgoal:Sussman Anomaly (1975)IF-UTAMA

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Goal Stack Planning1. UNSTACK(C, A) 2. PUTDOWN(C) 3. PICKUP(A)4. STACK(A, B)5. UNSTACK(A, B)6. PUTDOWN(A)7. PICKUP(B)8. STACK(B, C)9. PICKUP(A)10. STACK(A, B)Plan

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Goal Stack Planning1. UNSTACK(C, A) 2. PUTDOWN(C) 3. PICKUP(A)4. STACK(A, B)5. UNSTACK(A, B)6. PUTDOWN(A)7. PICKUP(B)8. STACK(B, C)9. PICKUP(A)10. STACK(A, B)Plan

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IF-UTAMA 57

Studi Kasus/Tugas

1. Jabarkan proses GSP untuk slide 54 sehingga

menghasilkan planning pada slide 55

2. Jelaskan secara singkata. Teknik planning prinsipnya hapir sama dengan searching, apa

perbedaanya?Untuk kasus-kasus tertentu kenapa planning

cenderung lebih baik dibanding searching?

b. Kapan dan kenapa sebaiknya kita memilih planning dibanding

searching?

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Referensi

1. Suyanto.2007.”Artificial Intelligence” .Informatika. Bandung

2. Ramin Halavati.-. “An Introduction to Artificial Intelligence Chapter 12 – Planning and Acting in Real World[online]”.url : -. Tanggal Akses : 11 April 2011

3. -.-.” Planning[online]” url:-.Tanggal Akses: 11 April 2011

4. Vincent Conitzer.-.” CPS 270: Artificial IntelligencePlanning[online]” url:http://www.cs.duke.edu/courses/fall08/cps270/.Tanggal Akses: 11 April 2011

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