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# Chap.12 Practical Planning - PowerPoint PPT Presentation

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

CS570 Artificial Intelligence

Kwang-hyung Lee

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

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

• 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

*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

• 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

*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

• 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

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.

• 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)

• 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

*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”

*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))

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)

• 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)

*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))