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Chap.12 Practical Planning. CS570 Artificial Intelligence Kwang-hyung Lee. 12.1 Practical Planners. 12.1 Practical Planners. Spacecraft assembly, integration, and verification 1. Hierarchical plans 2. Complex conditions 3. Time 4. Resources Job Shop Scheduling

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Chap 12 practical planning l.jpg

Chap.12 Practical Planning

CS570 Artificial Intelligence

Kwang-hyung Lee

12 1 practical planners l.jpg

12.1 Practical Planners

12.1 Practical Planners

  • Spacecraft assembly, integration, and verification

    1. Hierarchical plans

    2. Complex conditions

    3. Time

    4. Resources

  • Job Shop Scheduling

  • Scheduling for space missions

  • Buildings, aircraft carriers and beer factories

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12.2 Hierarchical Decomposition

12.2 Hierarchical Decomposition

  • Solution at a high level abstraction


    It is a long way from instruction fed to the agent’s effectors

  • A low level plan

    [Forward(1 cm),Turn(1 deg),Forward(1 cm), ……]

  • Hierarchical decomposition : an abstract operator can be decomposed into a group of steps

    ex) Abstract operator: Build(House)

    decomposed operators : obtain Permit,Hire Builder,Construction, Pay Builder

  • Primitive operator:executed by the agent

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12.2 Hierarchical Decomposition

  • Hierarchical planning work

    (1) provide an extension to the STRIPS for nonprimitive operator

    (2) modify the planning algorithm to allow the replacement of a nonprimitive operator with its decomposition

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12.2 Hierarchical Decomposition

*Extending STRIPS

(1) partition operators into primitive and nonprimitive operators

nonprimitive : Install(FloorBoards)

primitive : Hammer(Nail)

(2) decomposition method

Decompose(o,p) : An operator o is decomposed into a plan p

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12.2 Hierarchical Decomposition

  • Decomposition of o into p

    The decomposed plan p correctly implements an operator if it is complete and consistent :

    1. p must be consistent (no contradiction)

    2. Every effect of o must be asserted by at least one step of p

    3. Every precondition of the steps in p must be achieved by a step in p or be one of the preconditions of o

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12.2 Hierarchical Decomposition

*Modifying the planner

  • Modification of planner POP into HD-POP

    (1) a way to decompose nonprimitive operators

    (2) the algorithm takes a plan as input, rather than just a goal

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12.2 Hierarchical Decomposition

  • SELECT-NONPRIMITIVE:selects a nonprimitive

  • CHOOSE-DECOMPOSITION:picks a decomposition method

  • The fields of the plan are altered :

    • STEPS :Add steps, remove Snonprimitive

    • BINDINGS :Add variable binding constants

    • Ordering:Call RESOLVE-THREATS

    • Links: Sic Snonprim Sic Sm : a step of method

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12.3 Analysis of Hierarchical Decomposition

12.3 Analysis of Hierarchical Decomposition

  • Abstract solution : a plan containing abstract operators, but consistent and complete

    • downward solution:if p is an abstract solution and there is a primitive solution

    • upward solution:if an abstract plan is inconsistent then no primitive sol.

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12.3 Analysis of Hierarchical Decomposition

  • if a planner(nonhierarchical) has to generate n-step plan(where b is branching factor), it takes time O(bn)

  • Hierarchical planning,

    sb steps at d=1

    bs2 at d=2

    ibs2 = O(bsd) (from i=1 to d)

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12.3 Analysis of Hierarchical Decomposition

  • The Gift of the Magic

    • A poor couple:he has a gold watch, she has long hair.

  • Plan b is inconsistent , but it can be into a consistent plan

  • The upward solution property does not hold

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12.3 Analysis of Hierarchical Decomposition

*Decomposition and Sharing

  • Merge each step of the decomposition into existing plan

  • Divide-and-conquer approach:solve each subproblem and then combine it into the rest

  • Sharing steps while merging

  • Ex) enjoy a honeymoon and raise a baby

    (1) decomposition

    • get married and go on honeymoon

    • get married and have a baby

      (2) merge

    • share the step “get married”

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12.3 Analysis of Hierarchical Decomposition

*Decomposition and approximation

  • Hierarchical decomposition

    nonprimitive operator => primitives

  • Hierarchical planning(approximation hierarchy, abstraction hierarchy)

    • It takes an operator and partitions its precondition according to their criticality levelOp(ACTION:Buy(x), EFFECT : Have(x)  Have(Money), PRECOND:1:Sells(store,x)  2:At(store)  3:Have(Money))

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12.4 More Expressive Operator Description

12.4 More Expressive Operator Description

*Conditional effects

  • ex) block world in section 11.8

    Two operators were needed

    Op(ACTION:Move(b,x,y),PRECOND : On(b,x)  Clear(b)  Clear(y), EFFECT:On(b,y)  Clear(x)  On(b,x)  Clear(y))

    Op(ACTION:MoveToTable(b,x),PRECOND : On(b,x)  Clear(b), EFFECT:On(b,Table)  Clear(x)  On(b,x))

    • initial situation:On(A,B)goal :clear(B)

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12.4 More Expressive Operator Description

  • Move A to the table or to somewhere else? : premature commitment in Move(b,x,y)

  • To eliminate it, we include conditional effect“effect when condition” : Q when POp(ACTION:Move(b,x,y),PRECOND : On(b,x)  Clear(b)  Clear(y), EFFECT:On(b,y)  Clear(x)  On(b,x)  Clear(y) when yTable)

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12.4 More Expressive Operator Description

*Universal quantification

  • ex) block world

    clear(b)x Block(x)  On(x,b)

  • ex) shopping problem

    Carry(bag, x, y) : (effect) all objects that are in the bag are at y and are no longer at x.Op(ACTION:Carry(bag,x,y),PRECOND:Bag(bag)  At(bag,x), EFFECT:At(bag,y)  At(bag,x)  I Item(i)  (At(i,y)  At(y) when In(I,bag))