Planning III Introduction to Artificial Intelligence CS440/ECE448 Lecture 16.

Planning IIIPlanning III

Introduction to Artificial Intelligence

CS440/ECE448

Lecture 16

Mid-TermMid-Term

Mean: 71%

Median:70%

Max: 96%

Min: 41%

Last lectureLast lecture• STRIPS planningSTRIPS planning• Partial order planningPartial order planning

This lectureThis lecture• More partial order planning• Planning in the real world• Extensions• Reasoning in the presence of uncertainty

ReadingReading• Chapters 11, 12, 13

The Initial PlanThe Initial Plan• A plan with two steps (STRIPS operators):• Start Step:

– Preconditions: None– Effect: Add all propositions that are initially true

• Finish Step: – Precondition: Goal state– Effects: None

• Steps: { Start, Finish}• Orderings: { Start < Finish }• Bindings: { }• Links: { }

A Partial Order Planning AlgorithmA Partial Order Planning AlgorithmA partial order regression planner that

searches through plan space.

POP Algorithm ContinuedPOP Algorithm Continued

Example: Blocks WorldExample: Blocks World

Operators

•Symbols: Table, A, B, C

•Predicates: On (x, y), Cl(x)

A

B C

Example: Simple Blocks WorldExample: Simple Blocks World

Symbols: A, B, C, Table

Predicates:

ON(x,y) – Object x is on top of object y

CL(x) – x doesn’t have anything on top

Start State

On(A, Table)

On(B, Table)

ON(C,Table)

Cl(A)

Cl(B)

Cl(C)

Goal State

ON(B, A)

On(C, B)

A B C A

B

C


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

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

A B C

A

B

C

Start

Finish

Steps: { Start, Finish,}

Orderings: { Start < Finish }

Links: {}



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

A B C

A

B

C

Start

Finish

Steps: { Start, Finish, S1}

Orderings: { Start < Finish, Start < S1, S1 < Finish}

Links: {S1-c0->Finish}

S1: PutOn(B,A)

~On(B,Table) ~Cl (A)Cl (Table), On(B,A)

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



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

A B C

A

B

C

Start

Finish



Links: {S1-c0->FinishStart –c1->S1}

S1: PutOn(B,A)





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

A B C

A

B

C

Start

Finish



Links: {S1-c0->FinishStart –c1->S1Start –c2->S1 }

S1: PutOn(B,A)





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

A B C

A

B

C

Start

Finish



Links: {S1-c0->FinishStart –c1->S1Start –c2->S1 Start –c3->S1}

S1: PutOn(B,A)





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

A B C

A

B

C

Start

Finish

Steps: { Start, Finish, S1, S2 }

Orderings: { Start < Finish, Start < S1, S1 < Finish, Start < S2,S2 < Finish}

Links: {S1-c0->FinishStart –c1->S1Start –c2->S1 Start –c3->S1S2 –c2->FinishStart –c1->S2 …}

S1: PutOn(B,A)



S2: PutOn(C,B)

~On(C,Table) ~Cl (B)Cl (Table), On(C,B)

On(C,Table) Cl(C) Cl(B)



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

A B C

A

B

C

Start

Finish

Steps: { Start, Finish, S1, S2 }

Orderings: { Start < Finish, Start < S1, S1 < Finish, Start < S2,S2 < Finish, S1 < S2}

Links: {S1-c0->FinishStart –c1->S1Start –c2->S1 Start – c3->S1S2 –c2->FinishStart –c1->S2 …}

S1: PutOn(B,A)



S2: PutOn(C,B)

~On(C,Table) ~Cl (B)Cl (Table), On(C,B)

On(C,Table) Cl(C) Cl(B)

A Partial Order Planning AlgorithmA Partial Order Planning AlgorithmA partial order regression planner that

searches through plan space.

Clobbering and promotion/demotionClobbering and promotion/demotionA clobberer is a potentially intervening step that destroys the

condition achieved by a causal link.

Consider two steps of plan with goal:

Go(HWS)

Buy(Drill)

At(HWS)

At(HWS)

Finish

At(Home)

Go(Home)

At(Home)

• To meet precondition of goal, add step Go(Home).• But, this threatens (clobbers) precondition of Buy(Drill).

Options to protect Buy(Drill):1. Demotion: put before Go(HWS).

2. Promotion: put after Buy(Drill).

POP Algorithm ContinuedPOP Algorithm Continued


Symbols: A, B, C, Table

Predicates:

ON(x,y) – Object x is on top of object y

CL(x) – x doesn’t have anything on top

Start State

ON(C,A)

On(A, Table)

On(B, Table)

Cl(B)

Cl(C)

Goal State

ON(A,B)

On(B, C)


Operators

Initial and Final conditionsInitial and Final conditions





Insert operation to achieve goal preconditionInsert operation to achieve goal precondition

Steps: { Start, Finish,S1}

Orderings: { Start < Finish,Start<S1,S1< Finish}

Steps: { Start, Finish,S1}

Orderings: { Start < Finish,Start<S1,S1< Finish}

S1

Solid lines denote causal links

PutOn(A,B) is a threat to PutOn(B,C)PutOn(A,B) is a threat to PutOn(B,C)

Solid lines denote causal links

Steps: { Start, Finish,S1, S2 }

Orderings: { Start < Finish,Start<S1,S1< Finish, Start<S2, S2<Finish,S1<S2}

Steps: { Start, Finish,S1, S2 }

Orderings: { Start < Finish,Start<S1,S1< Finish, Start<S2, S2<Finish,S1<S2}

S1S2

PutOnTable(C)PutOnTable(C) meets precondition but must meets precondition but must be in right orderbe in right order

Steps: { Start, Finish,S1, S2, S3}

Orderings: { Start < Finish,Start<S1,S1< Finish, Start<S2, S2<Finish,S1<S2, Start<S3, S3<Finish, S3<S2, S3<S1}

Steps: { Start, Finish,S1, S2, S3}

Orderings: { Start < Finish,Start<S1,S1< Finish, Start<S2, S2<Finish,S1<S2, Start<S3, S3<Finish, S3<S2, S3<S1}

S1S2

S3

Why is called the Sussman Anomaly?Why is called the Sussman Anomaly?

Goal

Cond1 Cond2

Subplan ASubplan B

Sub-subplan AA Sub-subplan AB

In older planners, each subplan would be completely executed before the other subplan would be executed, for example:

Subplan B, [Sub-subplan AA, Sub-subplan AB, Subplan A]

“Sussman Anomaly” cannot be solved using this type of plan – must be interleaved.

POP SummaryPOP Summary

POP is: – Sound,– Complete (assuming breadth first or iterative

deepening search).

The real world: Things go wrongThe real world: Things go wrong

• Incomplete information– Unknown preconditions, e.g., Is the spare actually intact?– Disjunctive effects, e.g., Inflating a tire with a pump may cause

the tire to inflate or a slow hiss or the tire may burst or …

• Incorrect information– Current state incorrect, e.g., spare NOT intact.– Missing/incorrect postconditions (effects) in operators.

• Qualification problem:– can never finish listing all the required preconditions and

possible conditional outcomes of actions.

Consider a plan for changing a tire after getting a flat using operators of RemoveTire(x), PutOnTire(x), InflateTire(x)

SolutionsSolutions• Conditional planning

– Plan to obtain information (observation actions).– Subplan for each contingency, e.g.,

[Check(Tire1), [IF Intact(Tire1)

THEN [Inflate(Tire1)]ELSE [CallAAA] ]

– Expensive because it plans for many unlikely cases.

• Monitoring/Replanning– Assume normal states, outcomes.– Check progress during execution, replan if necessary.– Unanticipated outcomes may lead to failure (e.g., no AAA card).

• In general, some monitoring is unavoidable.

Preconditions for Remaining PlanPreconditions for Remaining Plan

ReplanningReplanning

• Simplest: on failure, replan from scratch.

• Better: plan to get back on track by reconnecting to best continuation.

• Generates ``loop until done'' behavior with no explicit loop.

Some Extensions to POPSome Extensions to POP(Chapter 12 Lite)(Chapter 12 Lite)

• More expressive representation:

– Disjunctive and negated goals (and subgoals/preconditions).

– Conditional effects reduce number of operators.

• More general temporal constraints:

– In POP/STRIPS actions take one time unit.

– Operators can take varying time periods.

• Resources, costs, value, etc.

• Hierarchical planning for efficiency:

– ABSTRIPS.

– Decompose abstract operator into multiple simple operators.

Hierarchical Decomposition into a Hierarchical Decomposition into a Partial-Order PlanPartial-Order Plan

UncertaintyUncertainty• Let action At = leave for airport t minutes before flight from O’hare• Will At get me there on time?

Problems:1. Partial observability (road state, other drivers' plans, etc.).2. Noisy sensors (traffic reports).3. Uncertainty in action outcomes (flat tire, etc.).4. Immense complexity of modelling and predicting traffic.

Hence a purely logical approach either:

1) risks falsehood: “A135 will get me there on time,” or 2) leads to conclusions that are too weak for decision making:

“A135 will get me there on time if there's no accident on I-57and it doesn't rain and my tires remain intact, etc., etc.”

(A1440 might reasonably be said to get me there on time but I'd have to stay overnight in the airport …)

Methods for handling uncertaintyMethods for handling uncertaintyDefault or nonmonotonic logic:

Assume my car does not have a flat tire.

Assume A125 works unless contradicted by evidence.

Issues: What assumptions are reasonable? How to handle contradiction?

Rules with fudge factors:

A135 0 .3 get there on time.

Sprinkler 0.99 WetGrass.

WetGrass 0.7 Rain.

Issues: Problems with combination, e.g., Sprinkler causes Rain??

Probability theory

Given the available evidence,

A135 will get me there on time with probability 0.04.

(Fuzzy logic handles degree of truth NOT uncertainty

e.g., WetGrass is true to degree 0.2)

Fuzzy Logic in Real WorldFuzzy Logic in Real World

ProbabilityProbabilityProbabilistic assertions summarize effects of

Ignorance: lack of relevant facts, initial conditions, etc.

Laziness: failure to enumerate exceptions, qualifications, etc.

Subjective or Bayesian probability:

Probabilities relate propositions to one's own state of knowledge

e.g., P(A135 | no reported accidents) = 0.06

These are NOT assertions about the world, but represent belief about the whether the assertion is true.

Probabilities of propositions change with new evidence:

e.g., P(A135 | no reported accidents, 5 a.m.) = 0.15

(Analogous to logical entailment status; i.e., does KB |= )

Making decisions under uncertaintyMaking decisions under uncertainty• Suppose I believe the following:

P(A 135 gets me there on time | ...) = 0.04




• Which action to choose?

• Depends on my preferences for missing flight vs. airport cuisine, etc.

• Utility theory is used to represent and infer preferences

• Decision theory = utility theory + probability theory

Unconditional ProbabilityUnconditional Probability• Let A be a proposition, P(A) denotes the unconditional

probability that A is true.

• Example: if Male denotes the proposition that a particular person is male, then P(Male)=0.5 means that without any other information, the probability of that person being male is 0.5 (a 50% chance).

• Alternatively, if a population is sampled, then 50% of the people will be male.

• Of course, with additional information (e.g. that the person is a CS440 student), the “posterior probability” will likely be different.

Planning III Introduction to Artificial Intelligence CS440/ECE448 Lecture 16.

Documents

Transcript of Planning III Introduction to Artificial Intelligence CS440/ECE448 Lecture 16.