Automated%20Planning

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Automated Planning

• Dr. Héctor Muñoz-Avila

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What is Planning? Classical Definition

• Planning finding a sequence of actions to
  achieve a goal

• Domain Independent symbolic descriptions of the
  problems and the domain. The plan generation
  algorithm remains the same
• Domain Specific The plan generation algorithm
  depends on the particular domain

Advantage - opportunity to have clear
semantics Disadvantage - symbolic description
requirement
Advantage - can be very efficient Disadvantag
e - lack of clear semantics
- knowledge-engineering for adaptation
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Classical Assumptions (I)

• A0 Finite system
• finitely many states,actions, and events
• A1 Fully observable
• the controller alwaysknows what state ? is in
• A2 Deterministic
• each action or event hasonly one possible
  outcome
• A3 Static
• No exogenous events no changes except those
  performed by the controller

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Classical Assumptions (II)

• A4 Attainment goals
• a set of goal states Sg
• A5 Sequential plans
• a plan is a linearlyordered sequence of actions
  (a1, a2, an)
• A6 Implicit time
• no time durations
• linear sequence of instantaneous states
• A7 Off-line planning
• planner doesnt know the execution status

Dana Nau Lecture slides for Automated
PlanningLicensed under the Creative Commons
Attribution-NonCommercial-ShareAlike License
http//creativecommons.org/licenses/by-nc-sa/2.0/
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Plan Representation

• Classical representation
• Predicates, variables, constants
• Most of our systems used it
• Set-theoretic representation
• Predicates and constants (no variables!)
• Useful in algorithms that manipulate ground atoms
  directly
• Used in internal representations planning graphs
  (Chapter 6), satisfiability (Chapters 7)
• State-variable representation
• Keeps track of the value of each variable
  loc(truck) l1

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Expressive Power

• Any problem that can be represented in one
  representation can also be represented in the
  other two
• Can convert in linear time and space, except when
  converting to set-theoretic (where we get an
  exponential blowup)

P(x1,,xn) becomes fP(x1,,xn)1
trivial
Classical representation
State-variable representation
Set-theoretic representation
write all of the groundinstances
f(x1,,xn)y becomes Pf(x1,,xn,y)
Dana Nau Lecture slides for Automated
PlanningLicensed under the Creative Commons
Attribution-NonCommercial-ShareAlike License
http//creativecommons.org/licenses/by-nc-sa/2.0/
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Classical Planning
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State-Space Planning

• State space
• V set of states
• E set of transitions (s, ?(s,a))
• But computed graph is a subset of state space
• Search modes
• Forward
• Backward
• Sussman Anomaly
• Generally thought to be slow
• But Fastforward, TLPlan, SHOP are state-space
  planners
• How come?

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Plan-Space Planning

• Plan space
• V set of plans
• E plan refinement transitions
• As before computed graph is a subset of plan
  space
• Least commitment
• Does not commit on action ordering
• Threats
• Open conditions
• Solves the Sussman anomaly
• Also thought to be slow
• But VHPOP

Initial plan
complete plan for goals
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Plan Adaptation

• Transformational analogy transforms an input
  plan
• Derivational analogy reuses the derivational
  trace that led to a plan
• Therefore requires more knowledge to be provided
• Both forms of adaptation have been developed for
  state-space, plan-space, hierarchical (HTN)
  planning
• All can be subsumed in the Universal Classical
  Planning framework
• Interesting some authors have proposed using
  planning graphs during adaptation (is this
  derivational? Transformational?)

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Neo-Classical Planning
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Planning Graphs
P0
A1
P1

• Planning graphs encode an inclusive disjunction
  of actions
• Since some actions in a disjunction may interfere
  with one another (mutex), it keeps track of
  incompatible propositions
• Solution extracted via backward chaining in the
  planning graph
• Must consider mutex
• Can improve performance
• More crucially used for defining heuristics
  (FF,)

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Clear(C) On(B, table) On(B, C) On(A,
B) On(A,table) Clear(B) On(B, A) Clear(A) On(C,t
able)
Move(B,C,table)
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Clear(B) On(B, C) Clear(A) On(A,
table) On(C,table)
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Move(A,table,B)
Move(B,C,A)
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Planning as Satisfiability

• Encodes the planning problem as a logical formula
• For example
• The initial state is represented as
• Applicability of Actions as
• Davis-Putnam procedure finds truth assignments
  that make the formula true
• Blackbox encodes the planning graph rather than
  the planning problem
• Trial and error process

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Heuristics in Planning

• State space
• V set of states
• E set of transitions (s, ?(s,a))
• ?(s,G) estimates how far is s from achieving G
• This estimate is made by constructing the goal
  graph
• on a relaxation of the problem domain with no
  negative effects
• A greedy strategy is selected (pick the one with
  highest value) after performing breadth-first
  search

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Domain-configurable Planning
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Search Control Rules in Planning

• State space
• V set of states
• E set of transitions (s, ?(s,a))
• Uses temporal logic to prune potential actions /
  states
• ? (until), ? (always), ? (eventually), ?
  (next), GOAL
• Example rule Dont move container if position
  is consistent with goal
• Formula progress(F,si) is true in si1 iff F is
  true in si.

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Reasoning with Time in Planning

• Extends search control rules representation as in
  TLPlan
• After all this representation is based on
  temporal logics
• Example
• (def-adl-operator (drive ?t ?l ?l)
• (pre (?t) (truck ?t) (?l) (loc ?l) (?l) (loc
  ?l) (at ?t ?l))
• (del (at ?t ?l))
• (delayed-effect
• (/ (dist ?l ?l) (speed ?t)
• (add (at ?t ?l))))
• It associates a time stamp with every state
• Transformations between states with same time
  stamp are instantaneous
• Crucial each state has an associated event queue
  (future updates)

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Hierarchical Planning

• Distinguishes between primitive and
  non-primitive tasks
• Primitive tasks concrete actions (instances of
  operators)
• Compound task high-level goals (decomposed by
  methods)
• Operators standard STRIPS knowledge
• Methods domain-configurable constructs

Order in which subtasks are fulfilled
Non-primitive task
method instance
precond
Non-primitive task
primitive task
primitive task
operator instance
operator instance
precond
effects
precond
effects
s0
s1
s2
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Final Summary

• Classical Planning
• State-space
• Plan-Space
• Plan adaptation
• Neo Classical planning
• Planning graphs
• Planning as Satisfiability
• Heuristics in Planning

• Domain-configurable planners
• Search control rules
• Reasoning with time
• Hierarchical Planning
• Complexity of Planning