DOC PREVIEW
Pitt CS 2710 - Foundations of AI

This preview shows page 1-2-20-21 out of 21 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

1CS 2710 Foundations of AICS 2710 Foundations of AILecture 13Milos [email protected] Sennott SquarePlanning CS 2710 Foundations of AIAdministration• PS-6:– Due on Thursday, October 28, 2004• Midterm: – Back on Tuesday, next week2CS 2710 Foundations of AIPlanningPlanning problem:• find a sequence of actions that achieves some goal • An instance of a search problemMethods for modeling and solving a planning problem:• State space search • Situation calculus based on FOL– Inference rules– Resolution refutationCS 2710 Foundations of AIPlanning problemsProperties of many (real-world) planning problems:• The description of the state of the world is very complex• Many possible actions to apply in any step• Actions are typically local – - they affect only a small portion of a state description• Goals are defined as conditions referring only to a small portion of state• Plans consists of a large number of actionsThe state space search and situation calculus frameworks may be– too cumbersome and inefficient to represent and solve the planning problems3CS 2710 Foundations of AISituation calculus: problemsFrame problem refers to: • The need to represent a large number of frame axiomsSolution: combine positive and negative effects in one ruleInferential frame problem:– We still need to derive properties that remain unchangedOther problems:• Qualification problem – enumeration of all possibilities under which an action holds• Ramification problem – enumeration of all inferences that follow from some facts∨∧=∧=¬⇔)),,())()((())),,,((,,( svuOnyvxuszyxMOVEDOvuOn)),(),(),,())()((( szClearsxClearsyxOnzvxu∧∧∧=∧=∨CS 2710 Foundations of AISolutions• Complex state description and local action effects:– avoid the enumeration and inference of every state component, focus on changes only• Many possible actions:– Apply actions that make progress towards the goal– Understand what the effect of actions is and reason with the consequences• Sequences of actions in the plan can be too long:– Many goals consists of independent or nearly independent sub-goals– Allow goal decomposition & divide and conquer strategies4CS 2710 Foundations of AISTRIPS planner• Defines a restricted representation language as compared to the situation calculusAdvantage: leads to more efficient planning algorithms.– State-space search with structured representations of states, actions and goals– Action representation avoids the frame problemSTRIPS planning problem:• much like a standard search (planning) problem;CS 2710 Foundations of AISTRIPS planner• States:– conjunction of literals, e.g. On(A,B), On(B,Table), Clear(A)– represent facts that are true at a specific point in time• Actions (operators):– Action: Move (x,y,z)– Preconditions: conjunctions of literals with variablesOn(x,y), Clear(x), Clear(z)– Effects. Two lists:• Add list: On(x,z), Clear(y)• Delete list: On(x,y), Clear(z)• Everything else remains untouched (is preserved)5CS 2710 Foundations of AISTRIPS planningOperator: Move (x,y,z)• Preconditions: On(x,y), Clear(x), Clear(z)• Add list: On(x,z), Clear(y)• Delete list: On(x,y), Clear(z)),( CBOn),( TableAOn),( TableCOn)( AClear)(BClear)(CClear)(TableClear),( TableBOn),( TableAOn),( TableCOn)( AClear)(BClear)(TableClearunchangeddeleteadd),,( CTableBMoveABCA B CCS 2710 Foundations of AISTRIPS planningInitial state:• Conjunction of literals that are trueGoals in STRIPS:• A goal is a partially specified state• Is defined by a conjunction of ground literals– No variables allowed in the description of the goalExample:On(A,B) On(B,C)∧6CS 2710 Foundations of AISearch in STRIPSObjective:Find a sequence of operators (a plan) from the initial state to the state satisfying the goalTwo approaches to build a plan:• Forward state space search (goal progression)– Start from what is known in the initial state and apply operators in the order they are applied• Backward state space search (goal regression)– Start from the description of the goal and identify actions that help to reach the goalCS 2710 Foundations of AIForward search (goal progression)• Idea: Given a state s– Unify the preconditions of some operator a with s– Add and delete sentences from the add and delete list of an operator a from s to get a new state (can be repeated)),( CBOn),( TableAOn),( TableCOn)( AClear)(BClear)(CClear)(TableClear),( TableBOn),( TableAOn),( TableCOn)( AClear)(BClear)(TableClearunchangeddeleteadd),,( CTableBMoveABCA B C7CS 2710 Foundations of AIForward search (goal progression)• Use operators to generate new states to search• Check new states whether they satisfy the goalSearch tree:Initial stateA B C),,( CTableBMove),,( CTableAMove),,( BTableAMove),,( BTableAMoveCBAgoalABCCS 2710 Foundations of AIBackward search (goal regression)Idea: Given a goal G• Unify the add list of some operator a with a subset of G• If the delete list of a does not remove elements of G, then the goal regresses to a new goal G’ that is obtained from G by:– deleting add list of a– adding preconditions of a),( CBOn)( AClear)(BClear),( TableAOn),( BAOn),( TableCOnpreconditionadd),,( BTableAMove),( CBOn),( TableCOnGoal (G)New goal (G’)Mapped from GCBAABC8CS 2710 Foundations of AIBackward search (goal regression)• Use operators to generate new goals• Check whether the initial state satisfies the goalSearch tree:Initial stateA B C),,( CTableBMove ),,( BTableAMoveCBAgoal),,( TableBAMoveABCCS 2710 Foundations of AIState-space search • Forward and backward state-space planning approaches:– Work with strictly linear sequences of actions• Disadvantages:– They cannot take advantage of the problem decompositions in which the goal we want to reach consists of a set of independent or nearly independent sub-goals– Action sequences cannot be built from the middle– No mechanism to represent least commitment in terms of the action ordering9CS 2710 Foundations of AIDivide and conquer • Divide and conquer strategy:– divide the problem to a set of smaller sub-problems, – solve each sub-problem independently– combine the results to form the solution In planning we would like to satisfy a set of goals• Divide and conquer in planning:– Divide the planning goals along individual goals– Solve (find a plan for) each of them independently– Combine the plan solutions in the resulting plan• Is it


View Full Document

Pitt CS 2710 - Foundations of AI

Documents in this Course
Learning

Learning

24 pages

Planning

Planning

25 pages

Lecture

Lecture

12 pages

Load more
Download Foundations of AI
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Foundations of AI and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Foundations of AI 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?