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In the name of God. An Application of Planning JSHOP BY: M. Eftekhari and G. Yaghoobi. SHOP (Simple Hierarchical Ordered Planner). SHOP and its successors are domain-independent implementations of Ordered Task Decomposition

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In the name of God

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In the name of God

An Application of Planning

JSHOP

BY: M. Eftekhari and G. Yaghoobi


SHOP (Simple Hierarchical Ordered Planner)

  • SHOP and its successors are domain-independent implementations of Ordered Task Decomposition

  • An AI planning technique that has been useful in several application domains (University of Maryland)


JSHOPA Java implementation of SHOP

  • As part of their HICAP for Noncombatant Evacuation Operations (NEOs).

  • (HICAP) Hierarchical Interactive Case-based Architecture for Planning (An applet)


HTNHierarchical Task Network

  • Objective is to create a plan to perform a set of tasks (abstract representations of things that need to be done).

  • HTN planning is done by problem reduction: the planner recursively decomposes tasks into subtasks, stopping when it reaches primitive tasks that can be performed directly by planning operators


Continue

  • In order to tell the planner how to decompose nonprimitive tasks into subtasks. it needs to have a set of methods .

  • where each method is a schema for decomposing a particular kind of task into a set of subtasks (provided that some set of preconditions is satisfied).


ContinueWhat is Expressivity?

  • Expressivity of languages

    • A language L is as expressive as another language M iff any expression in L can be translated into an expression with the same meaning in M

  • HTN planning is more expressive than state-based planning

  • STRIPS-style planning is a special case of HTN planning


Continue

  • No transformations, because HTN models have richer structure (because HTNs can represent harder problems than the STRIPS language)

  • Solutions to STRIPS problems are regular sets

  • Solutions to HTN problems can be arbitrary context-free sets

  • Thus HTN’s are more expressive than STRIPS


Ordered Task Decomposition

  • Is a special case of HTN planning in which the planning algorithm always builds plans forward from the initial state of the world

  • ordered-task-decomposition: planner plans for tasks in the same order that the tasks will later be performed.

  • the planner has already planned every action that will occur beforehand


continue

  • the preconditions of its methods and operators can include logical inferences, complex numeric computations, and calls to external programs.


subtask 1

subtask 2

subtask 3

subtask 4

Search Strategy

task

method

  • Ordered task decomposition

    • Require the subtasks of each method to be totally ordered

    • Decompose these tasks left-to-right

      • The same order that they’ll later be executed

      • Analogous to PROLOG’s search strategy


Theory:

Symbolic computations (STRIPS operators)

Single agent (the planner)

Perfect information

AI Planning Is Different in PracticeThan it Was in Theory

Unstack(x,y)

Pre:on(x,y), clear(x), handempty

Del:on(x,y), clear(x), handempty

Add:holding(x), clear(y)

  • Practice:

    • Complex numeric computations(geometry, images, probabilities)

    • Multiple agents

    • Imperfect information, external information sources


Theory

Applications

Goal

  • Develop synergy between theory and applications


SHOP (Simple Hierarchical Ordered Planner)

  • Domain-independent algorithm forOrdered Task Decomposition

  • Implementation

    • Common-Lisp implementation available at

      • http://www.cs.umd.edu/projects/shop

    • Developing a Java implementation


Input and Output

  • Input:

    • State: a set of ground atoms

    • Task List: a linear list of tasks

    • Domain: methods, operators, axioms

  • Output: one or more plans

    • depending on what we tell SHOP to look for, it can return

      • the first plan it finds

      • all possible plans

      • a least-cost plan

      • all least-cost plans

      • etc.


Elements of the Input

  • Initial State: collection of ground atoms (in Lisp notation)

    • ((at home) (have-cash 50.43) (distance home downtown 10))

  • Task list: linear list of tasks to perform

    • ((travel home downtown) (buy book))

  • Each method: task, preconditions and decomposition

    • Preconditions to be established using logical inference

    • Decomposition is a task list

  • Each axiom: Horn clause

  • Each primitive operator: task,precondition, delete list, add list

    • Performs a primitive task


  • Review of the SHOP Algorithm

    state S; task list T=( t1 ,t2,…)

    operator instance o

    procedure SHOP (state S, task-list T, domain D) 1.if T = nil thenreturn nil2.t1= the first task in T3.U = the remaining tasks in T4.ift is primitive & an operator instance o matches t1then5.P = SHOP (o(S), U, D)6.ifP = FAIL then return FAIL7.return cons(o,P)8.else ift is non-primitive & a method instance m matches t1 in S & m’s preconditions can be inferred from S then9.return SHOP (S, append (m(t1), U), D)10.else11.return FAIL12. endifend SHOP

    state o(S) ; task list T=(t2, …)

    nondeterministic choice among all methods m whose preconditions can be inferred from S

    task list T=( t1 ,t2,…)

    method instance m

    task list T=( u1,…,uk ,t2,…)


    Simple Example

    • Initial task list:((travel home park))

    • Initial state:((at home) (cash 20) (distance home park 8))

    • Methods (task, preconditions, subtasks):

      • (:method (travel ?x ?y)((at x) (walking-distance ?x ?y)) ((!walk ?x ?y)) 1)

      • (:method (travel ?x ?y)((at ?x) (have-taxi-fare ?x ?y)) ((!call-taxi ?x) (!ride ?x ?y) (!pay-driver ?x ?y)) 1)

    • Axioms:

      • (:- (walking-dist ?x ?y) ((distance ?x ?y ?d) (call (<= ?d 5))))

      • (:- (have-taxi-fare ?x ?y)((have-cash ?c) (distance ?x ?y ?d) (call (>= ?c (+ 1.50 ?d))))

    • Primitive operators (task, precondition, delete list, add list)

      • (:operator (!walk ?x ?y) () ((at ?x)) ((at ?y)))

    Optional cost;default is 1


    Simple Example (continued)

    Initial state:

    (at home)(cash 20)

    (distance home park 8)

    (travel home park)

    Precond:

    Precond:

    (at home)

    (walking-distance

    Home park)

    (at home)

    (have-taxi-fare home park)

    Succeed

    Succeed (we have $20,and the fare is only $9.50)

    Succeed

    Fail (distance > 5)

    (!pay-driver home park)

    (!call-taxi home)

    (!ride home park)

    (at park)(cash 10.50)

    (distance home park 8)

    (!walk home park)

    Final state:


    Block worlds

    Final State

    Using Methods

    4

    5

    1

    2

    3

    1

    Initial state

    Task1

    Task2

    Task3

    Task4

    Task5

    How to do?

    5

    Only achieving goals

    3

    4

    1

    2

    1

    Final state

    Book keeping Planning

    Classical Planning


    What Activities Should a Planning System Plan?

    • In AI planning, researchers traditionally have only allowed the planner to plan activities that will have a direct physical effect

    • Examples:

      • picking up a block

      • moving a truck

    • In human planning, we also plan lots of other activities

    • Example 2:

      • Planning bookkeeping operations

    travel by air

    store some infoabout the ticket

    airport(x,a)

    airport(y,b)

    ticket (a,b)

    travel (x,a)

    fly(a,b)

    travel(b,y)


    Encoding the Blocks World Algorithm into SHOP

    loop

    if there is a clear block x such that

    x or a block beneath x is in a location inconsistent with the goal

    and

    x can be moved to a location such thatx and all blocks beneath x will be in locations consistent with the goal

    then move x to that location

    else if there is a clear block x such that

    x or a block beneath x is in a location inconsistent with the goal

    then move x to the table

    else exit

    endif

    repeat


    Operators for Moving Blocks

    • (:operator (!pickup ?x)

    • ((clear ?x) (on-table ?x))

    • ((holding ?x)))

    • (:operator (!putdown ?x)

    • ((holding ?x))

    • ((on-table ?x) (clear ?x)))

    • (:operator (!stack ?x ?y)

    • ((holding ?x) (clear ?y))

    • ((on ?x ?y) (clear ?x)))

    • (:operator (!unstack ?x ?y)

    • ((clear ?x) (on ?x ?y))

    • ((holding ?x) (clear ?y)))


    Bookkeeping Operator and Methods

    • (:operator (!assert ?atoms); ?atoms is a list of atoms to assert

    • (); no preconditions

    • ?atoms; put the list of atoms into the current state

    • 0); this operator has no cost

    • (:method (assert-goals (?first . ?rest) ?atoms) ; recursively build a list

    • () ; of atoms to assert into

    • ((assert-goals ?rest ((goal ?first) . ?atoms)))) ; the current state

    • (:method (assert-goals nil ?atoms); we’ve built the entire list, so assert it

    • ()

    • '((!assert ?atoms)))

    • (:method (achieve-goals ?goals) ; assert all the goals into the current state,

    • (); then call move-block to achieve them

    • ((assert-goals ?goals nil) (move-block nil)))


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