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 Scheduling for space missions Buildings, aircraft carriers and beer factories

12.2 Hierarchical Decomposition Solution at a high level abstraction [Go(Supermarket),Buy(Milk),Buy(Bananas),Go(Home)] 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 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

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

Decomposition of o into p 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

*Modifying the planner 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

SELECT-NONPRIMITIVE:selects a nonprimitive 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: Si c Snonprim Si c 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.

Hierarchical planning, 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)

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

*Decomposition and Sharing 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”

*Decomposition and approximation 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 level Op(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)

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 P 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) when yTable)

*Universal quantification 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))