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Chapter 11

Hierarchical Task Network Planning

Lecture slides for

Automated Planning: Theory and Practice

Motivation

• We may already have an idea how to go about

solving problems in a planning domain

• Example: travel to a destination that’s far away:

– Domain-independent planner:

• many combinations of vehicles and routes

– Experienced human: small number of “recipes”

e.g., flying:

1. buy ticket from local airport to remote airport

2. travel to local airport

3. fly to remote airport

4. travel to final destination

• How to enable planning systems to make use of

such recipes?

HTN Planning

• Problem reduction
  • Tasks (activities) rather than goals
  • Methods to decompose tasks into subtasks
  • Enforce constraints
    • E.g., taxi not good for long distances
  • Backtrack if necessary

travel(UMD, LAAS)

get-ticket(IAD, TLS)

travel(UMD, IAD)

fly(BWI, Toulouse) travel(TLS, LAAS) get-taxi ride(TLS,Toulouse) pay-driver

go-to-travel-web-site find-flights(IAD,TLS) buy-ticket(IAD,TLS)

get-taxi ride(UMD, IAD) pay-driver

Task:

Method: taxi-travel( x,y )

get-taxi ride( x , y ) pay-driver

get-ticket(BWI, TLS) go-to-travel-web-site find-flights(BWI,TLS) BACKTRACK

travel( x,y )

Method: air-travel( x,y )

travel(a( y ), y )

get-ticket(a( x ),a( y ))

travel( x ,a( x ))

fly(a( x ),a( y ))

HTN Planning

• HTN planners may be domain-specific

– e.g., see Chapters 20 (robotics) and 23 (bridge)

• Or they may be domain-configurable

– Domain-independent planning engine

– Domain description that defines not only the

operators, but also the methods

– Problem description

• domain description, initial state, initial task network

Task:

Method: taxi-travel( x,y )

get-taxi ride( x , y ) pay-driver

travel( x,y )

Method: air-travel( x,y )

travel(a( y ), y )

get-ticket(a( x ),a( y ))

travel( x ,a( x ))

fly(a( x ),a( y ))

Methods

• Totally ordered method: a 4-tuple

m = (name( m ), task( m ), precond( m ), subtasks( m ))

• name( m ): an expression of the form n ( x 1 ,…, xn )
  • x 1 ,…, xn are parameters - variable symbols
• task( m ): a nonprimitive task
• precond( m ): preconditions (literals)
• subtasks( m ): a sequence

of tasks 〈 t 1 , …, t k 〉

air-travel( x,y )

task: travel( x,y )

precond : long-distance( x,y )

subtasks : 〈buy-ticket( a ( x ) , a ( y )), travel( x,a ( x )), fly( a ( x ) , a ( y )),

travel( a ( y ) ,y )〉

travel( x,y )

buy-ticket (a( x ), a( y )) travel ( x , a( x )) fly (a( x ), a( y )) travel (a( y ), y )

long-distance( x,y )

air-travel( x,y )

Methods (Continued)

• Partially ordered method: a 4-tuple

m = (name( m ), task( m ), precond( m ), subtasks( m ))

• name( m ): an expression of the form n ( x 1 ,…, xn )
  • x 1 ,…, xn are parameters - variable symbols
• task( m ): a nonprimitive task
• precond( m ): preconditions (literals)
• subtasks( m ): a partially ordered

set of tasks { t 1 , …, t k }

air-travel( x,y )

task: travel( x,y )

precond : long-distance( x,y )

network : u 1 =buy-ticket( a ( x ) ,a ( y )), u 2 = travel( x,a ( x )), u 3 = fly( a ( x ) , a ( y ))

u 4 = travel( a ( y ) ,y ), {( u 1 , u 3 ), ( u 2 , u 3 ), ( u 3 , u 4 )}

travel( x,y )

buy-ticket (a( x ), a( y )) travel ( x , a( x )) fly (a( x ), a( y )) travel (a( y ), y )

long-distance( x,y )

air-travel( x,y )

Example

• Suppose we want to move three stacks of containers

in a way that preserves the order of the containers

Example (continued)

• A way to move each stack:

– first move the

containers

from p to an

intermediate

pile r

– then move

them from

r to q

Partial-Order

Formulation

Solving Total-Order STN Planning

Problems

state s ; task list T=( t 1 ,t 2 ,…) action a

state γ( s,a ) ; task list T=(t 2 , …)

task list T=( u 1 ,…,u (^) k ,t 2 ,…)

task list T=( t 1 ,t 2 ,…) method instance m

Comparison to

Forward and Backward Search

• Like a backward search,

TFD is goal-directed

– Goals

correspond

to tasks

• Like a forward search, it generates actions

in the same order in which they’ll be executed

• Whenever we want to plan the next task

– we’ve already planned everything that comes

s 0 s 1 s 2 …

task t m …

…

task t (^) n

op 1 op 2 Si–1 op (^) i

task t (^0)

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Limitation of Ordered-Task Planning

• TFD requires totally ordered

methods

• Can’t interleave subtasks of

different tasks

• Sometimes this makes things

awkward

– Need to write methods that

reason globally instead of locally

get(p) get(q)

get-both(p,q)

goto(b)

pickup(p) pickup(q)

get-both(p,q)

pickup-both(p,q)

walk(a,b)

goto(a)

walk(b,a)

walk(a,b) pickup(p) walk(b,a) walk(a,b) pickup(p) walk(b,a)

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π={ a 1 …, a (^) k , a }; w' ={t 2 , t 3 , …}

w ={ t 1 ,t 2 ,…} method instance m

w' ={ t 11 ,…,t (^) 1k ,t 2 ,…}

π={ a 1 ,…, a (^) k }; w ={ t 1 ,t 2 , t 3 …} operator instance a

Algorithm for Partial-Order STNs

π={ a 1 …, a (^) k , a }; w' ={t 2 , t 3 , …}

π={ a 1 ,…, a (^) k }; w ={ t 1 ,t 2 , t 3 …} operator instance a

Algorithm for Partial-Order STNs

• Intuitively, w is a partially ordered set of tasks { t 1 , t 2 , …}
  • But w may contain a task more than once
    • e.g., travel from UMD to LAAS twice
  • The mathematical definition of a set doesn’t allow this
• Define w as a partially ordered set of task nodes { u 1 , u 2 , …}
  • Each task node u corresponds to a task t (^) u
• In my explanations, I’ll talk about t and ignore u

w ={ t 1 ,t 2 ,…} method instance m

w' ={ t 11 ,…,t (^) 1k ,t 2 ,…}