Consider the task get milk, bananas, and a cordless drill

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Consider the task get milk, bananas, and a
cordless drill
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Search vs. planning

• Standard search algorithms seem to fail
  miserably
• Problems with search approach
• too many irrelevant actions
• finding good heuristics is difficult
• cannot take advantage of problem decomposition

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Planning as search with logic

• Planning systems do the following
• 1. open up action and goal representation to
  allow selection
• 2. divide-and-conquer by subgoaling
• 3. relax requirement for sequential construction
  of solutions

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Planning and Intelligent Partial Ordering
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Classic Planning

• Planning devising a sequence of actions
  achieving a goal
• fully observable
• deterministic
• static
• discrete
• specific language to represent planning problems
• In Ch. 11 we will assume above
• In Ch. 12 we will handle real world situations
  where these assumptions cant be met.

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Language for planning problems

• STRIPS STanford Research Institute Problem
  Solver
• world described by logical conditions
• state as conjunction of positive literals
• propositional e.g., Happy Hungry to represent
  the state of the agent
• first-order ground and function-free terms
• e.g., At(Plane1, Verona) At(Plane2,Malpensa)
• closed-world assumption i.e., any not mentioned
  condition is false
• goal is a partially specified state
• a state satisfies a goal if contains all the
  literals of the goal
• e.g. state At(Plane1, Verona)
  At(Plane2,Malpensa) satisfies goal
  At(Plane2,Malpensa)

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STRIPS actions

• actions are described by
• preconditions when the action can be applied
• effects state changes by the action
• add-list propositions that become true
• delete-list propositions that become false
• actions contain variables
• a single action schema represents different
  actions (instantiation of variables)

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STRIPS actions (contd.)

• Tidily arranged actions descriptions, restricted
  language
• Action schema
• ACTION specifies name and parameter list
• Buy(x)
• PRECONDITION conjunction of positive literals
• At(p) Sells(p, x)
• EFFECT conjunction of literals (positive or
  negative)
• Have(x)
• Note no information on how to execute the
  action!
• A complete set of STRIPS operators can be
  translated into a set of successor-state axioms

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Semantics

• Given a state (conjunction of literals)
• precondition is satisfied if there is a variable
  assignment s.t. the literals are included in the
  state e.g.,
• state At(HW) Sell(HW,Drill)
• satisfies precondition At(p) Sells(p, x)
• with assignment p/HW and x/Drill
• actions with preconditions satisfied can be
  applied
• delete items from the delete-list
• add items from the add-list
• order does matter!
• new state At(HW) Sell(HW,Drill) Have(Drill)

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Example Shopping

• Actions
• Buy(x)
• PRE At(store), Sells(store, x)
• EFF Have(x)
• Go(x, y)
• PRE At(x)
• EFF At(y),At(x)
• Start
• At(Home) Sells(SM,Milk) Sells(SM,Banana)
  Sells(HWS,Drill)
• Goal
• Have(Milk) Have(Banana) Have(Drill)

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Example Air cargo transport

• Actions
• Load(c, p, a)
• PRE At(c, a) At(p, a) Cargo(c) Plane(p)
  Airport(a)
• EFF At(c, a) In(c, p)
• Unload(c, p, a)
• PRE In(c, p) At(p, a) Cargo(c) Plane(p)
  Airport(a)
• EFF At(c, a) In(c, p)
• Fly(p, from, to)
• PRE At(p, from) Plane(p) Airport(from)
  Airport(to)
• EFF At(p, from) At(p, to)
• actions Load, Unload, Fly
• predicates In(, ),At(, )
• type predicates Cargo(), Plane(),Airport()

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Example Air cargo transport (contd.)

• Start
• At(C1, SFO) At(C2, JFK) At(P1, SFO) At(P2,
  JFK) Cargo(C1) Cargo(C2) Plane(P1)
  Plane(P2) Airport(JFK) Airport(SFO)
• Goal
• At(C1, JFK) At(C2, SFO)
• a solution is
• Load(C1, P1, SFO), Fly(P1, SFO, JFK), Unload(C1,
  P1, JFK),Load(C2, P2, JFK), Fly(P2, JFK, SFO),
  Unload(C2, P2, SFO)

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Example Air cargo transport (contd.)

• Start
• At(C1, SFO) At(C2, JFK) At(P1, SFO) At(P2,
  JFK) Cargo(C1) Cargo(C2) Plane(P1)
  Plane(P2) Airport(JFK) Airport(SFO)
• Goal
• At(C1, JFK) At(C2, SFO)
• a solution is
• Load(C1, P1, SFO), Fly(P1, SFO, JFK), Unload(C1,
  P1, JFK),Load(C2, P2, JFK), Fly(P2, JFK, SFO),
  Unload(C2, P2, SFO)

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STRIPS Planning

• STRIPS planning problem
• find a sequence of actions that lead to a goal
• states and goals are defined by a conjunctions of
  literals
• State-space search
• Forward search (goal progression) from the
  initial state try to reach the goal
• Backward search (goal regression) from the goal
  and try to project it to the initial state
• Plan-space search
• partial-order planning (POP) search the space of
  partially build plans

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State-space search

• planning problem defines the search problem
• initial state is the start state
• goal test checks whether state satisfies the goal
• actions define the operators
• step cost is usually 1
• (a) forward or
• (b) backward search