Artificial%20Intelligence%20II

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Artificial Intelligence II
S. Russell and P. Norvig Artificial
Intelligence A Modern Approach Chapter 11
Planning
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Planning

• Planning versus problem solving
• Situation calculus
• Plan-space planning

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Planning as Problem Solving

• Planning
• Start state (S)
• Goal state (G)
• Set of actions
• Find sequence of actions that get you from start
  to goal

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What is Planning (more generally)?

• Generate sequences of actions to perform tasks
  and achieve objectives.
• Search for solution over abstract space of plans.
• Assists humans in practical applications
• design and manufacturing
• military operations
• games
• space exploration

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Planning versus Problem Solving

• Problem solving is basically state-space search,
  i.e., primarily an algorithmnot a
  representation.
• initial state, goal-test, successor function
• Planning is a combination of an algorithm
  (search) and a set of representations, usually
  situational calculus.
• provides a way to open up the representation of
  initial state, goal-test, and successor function
• planner free to add actions to plan wherever
  needed
• most parts of world independent from other parts,
  i.e. nearly decomposable

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Assumptions

• Atomic time
• No concurrent actions
• Deterministic actions
• Agent is sole cause of change
• Agent is omniscient
• Closed World Assumption

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Simple Planning Agent Algorithm

• Generate a goal to achieve
• Construct a plan to achieve goal from current
  state
• Execute plan until finished
• Begin again with new goal

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Planning Emphasizes whats inside the goal and
operators

• Open up the representation of state, goals and
  operators
• State/Situation Representation A conjunction of
  facts
• Ex pyramid(C), on(A,B), on(B,Table), clear(A),
  handempty
• Goal Description a conjunction of positive
  literals.
• Ex on(A,B), on(B,C)
• Operators given as STRIPS-type if-then rules.
  STRIPS is the STanford Research Institute Problem
  Solver.
• Action name Description of action
• Preconditions Conjunction of positive literals
  representing what must be true beforehand.
• Effects Conjunction of positive or negative
  literals

Name pickup(x) Preconditions ontable(x),
clear(x), handempty Add holding(x) Del
ontable(x), clear(x), handempty
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Representing States of the World
C
A
B
on(c,a),ontable(a),clear(c),ontable(b),clear(b),ha
ndempty()
Goal on(b,c)
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Strips Example

• Action
• Buy(x, store)
• Pre At(store), Sells(store, x)
• Eff Have(x)
• Go(x, y)
• Pre At(x)
• Eff At(y), not At(x)
• Goal
• Have(Milk) and Have(Banana) and Have(Drill)
• Start
• At(Home) and Sells(SM, Milk) and Sells(SM,
  Banana) and Sells(HW, Drill)

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Planning as Search

• Situation-Space Search
• Plan-Space Search

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Situation-Space Search

• Search space All possible world states or
  situations.
• Initial state defines one node.
• Goal node is a state where all goals in goal
  state are satisfied.
• Solution Sequence of actions in path from start
  to goal.

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Plan-Space Search

• Search space All possible (partial) plans
• Partial plan defines a node an initial plan is
  one node
• Goal node contains a plan which is complete,
  satisfying all goals in goal state
• The node itself contains all of the information
  for determining a solution plan

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Planning Algorithms

• Progression planners (forward chaining) consider
  the effect of all possible actions in a given
  state.

• Regression planners (backword chaining)to
  achieve a goal, what must have been true in
  previous state.

Have(M) and Have(B) and Have(D) Buy(M,store) At(st
ore) and Sells(store,M) and Have(B) and Have(D)

• Both have problem of lack of direction what
  action or goal to pursue next.

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Forward and Backward State-Space Search
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Algorithm for Progression-Based Planner

• 1. Start from initial state
• 2. Find all operators whose preconditions are
  true in the initial state
• 3. Compute effects of operators to generate
  successor states
• 4. Repeat 2 and 3 until new state satisfies goal
  conditions

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Progression Planning Example

• Initial State S clear(A), clear(B), clear(C),
  ontable(A), ontable(B), ontable(C), handempty
• Operator pickup(x) with ? x/A
• Successor state T clear(B), clear(C),
  ontable(B), ontable(C), holding(A)
• Operator instance associated with the action from
  S to T is pickup(A).

Name pickup(x) Preconditions ontable(x),
clear(x), handempty Add holding(x) Del
ontable(x), clear(x), handempty
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Algorithm for Regression-Based Planner

• 1. Start with goal node corresponding to goal to
  be achieved
• 2. Choose an operator that will add one of the
  goals
• 3. Replace the goal with the operators
  preconditions
• 4. Repeat 2 and 3 until you have reached the
  initial state

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STRIPS Algorithm

• A Goal-Stack Based Regression Planner uses goal
  stack to maintain set of conjunctive goals yet to
  be achieved
• Maintains a description of the current state,
  which is initially the given initial state
• Approach
• Pick an order for achieving each of the goals
• When each goal is popped from stack, if it is not
  already true in current state, push onto the
  stack an operator that adds that goal.
• Push onto the stack each precondition of that
  operator in some order, and solve each of these
  sub-goals in the same fashion.
• When all preconditions are solved (popped from
  stack), re-verify that all of the preconditions
  are still true and apply the operator to create a
  new successor state description.

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STRIPS Example
Pickup(x) P ontable(x), clear(x), handempty
E holding(x), not ontable(x), not clear(x), not
handempty Putdown(x) P holding(x) E
ontable(x), clear(x), handempty, not
holding(x) Stack(x,y) P holding(x), clear(y)
E on(x,y), clear(x), handempty, not
holding(x), not clear(y) Unstack(x,y) P
clear(x), on(x,y), handempty E holding(x),
clear(y), not clear(x), not on(x,y), not handempty
B
Goal on(a,c), on(c,b)
Initial State clear(b), clear(c), on(c,a),
ontable(a), ontable(b), handempty
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STRIPS Example
Goal Stack achieve(on(C,B), on(A,C)) State
clear(B), clear(C), on(C,A), ontable(A),
ontable(B), handempty
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STRIPS Example
Goal Stack achieve(on(C,B)), achieve(on(A,C)),
achieve(on(C,B), on(A,C)) State clear(B),
clear(C), on(C,A), ontable(A), ontable(B),
handempty
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STRIPS Example
Goal Stack achieve(clear(B),holding(C)),
apply(Stack(C,B), achieve(on(A,C)),
achieve(on(C,B), on(A,C)) State clear(B),
clear(C), on(C,A), ontable(A), ontable(B),
handempty
Stack(x,y) P holding(x), clear(y) E
on(x,y), clear(x), handempty, not holding(x), not
clear(y)
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STRIPS Example
Goal Stack achieve(holding(C)),
achieve(clear(B)), achieve(clear(B),holding(C)),
apply(Stack(C,B), achieve(on(A,C)),
achieve(on(C,B), on(A,C)) State clear(B),
clear(C), on(C,A), ontable(A), ontable(B),
handempty
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STRIPS Example
Goal Stack achieve(handempty, clear(C),
on(C,y)), apply(Unstack(C,y)), achieve(clear(B)),
achieve(clear(B),holding(C)), apply(Stack(C,B),
achieve(on(A,C)), achieve(on(C,B),
on(A,C)) State clear(B), clear(C), on(C,A),
ontable(A), ontable(B), handempty
Unstack(x,y) P clear(x), on(x,y), handempty
E holding(x), clear(y), not clear(x), not
on(x,y), not handempty
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STRIPS Example
Goal Stack achieve(clear(B)),
achieve(clear(B),holding(C)), apply(Stack(C,B),
achieve(on(A,C)), achieve(on(C,B),
on(A,C)) State clear(B), ontable(A),
ontable(B), holding(C), clear(A) Plan so far
Unstack(C,A)
Unstack(x,y) P clear(x), on(x,y), handempty
E holding(x), clear(y), not clear(x), not
on(x,y), not handempty
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STRIPS Example
Goal Stack achieve(on(A,C)), achieve(on(C,B),
on(A,C)) State ontable(A), ontable(B),
clear(A), on(C,B), clear(C), handempty Plan so
far Unstack(C,A), Stack(C,B)
Stack(x,y) P holding(x), clear(y) E
on(x,y), clear(x), handempty, not holding(x), not
clear(y)
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STRIPS Example
Goal Stack achieve(clear(C), holding(A)),
apply(Stack(A,C)), achieve(on(C,B),
on(A,C)) State ontable(A), ontable(B),
clear(A), on(C,B), clear(C), handempty Plan so
far Unstack(C,A), Stack(C,B)
Stack(x,y) P holding(x), clear(y) E
on(x,y), clear(x), handempty, not holding(x), not
clear(y)
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STRIPS Example
Goal Stack achieve(holding(A)),
achieve(clear(C)), achieve(clear(C), holding(A)),
apply(Stack(A,C)), achieve(on(C,B),
on(A,C)) State ontable(A), ontable(B),
clear(A), on(C,B), clear(C), handempty Plan so
far Unstack(C,A), Stack(C,B)
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STRIPS Example
Goal Stack achieve(ontable(A), clear(A),
handempty), apply(Pickup(A)), achieve(clear(C)),
achieve(clear(C), holding(A)), apply(Stack(A,C)),
achieve(on(C,B), on(A,C)) State ontable(A),
ontable(B), clear(A), on(C,B), clear(C),
handempty Plan so far Unstack(C,A),
Stack(C,B)
Pickup(x) P ontable(x), clear(x), handempty
E holding(x), not ontable(x), not clear(x), not
handempty
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STRIPS Example
Goal Stack achieve(clear(C)),
achieve(clear(C), holding(A)), apply(Stack(A,C)),
achieve(on(C,B), on(A,C)) State ontable(B),
on(C,B), clear(C), holding(A) Plan so far
Unstack(C,A), Stack(C,B), Pickup(A)
Pickup(x) P ontable(x), clear(x), handempty
E holding(x), not ontable(x), not clear(x), not
handempty
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STRIPS Example
Goal Stack achieve(on(C,B), on(A,C)) State
ontable(B), on(C,B), on(A,C), clear(A),
handempty Plan so far Unstack(C,A),
Stack(C,B), Pickup(A), Stack(A,C)
Stack(x,y) P holding(x), clear(y) E
on(x,y), clear(x), handempty, not holding(x), not
clear(y)
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STRIPS Example
Goal Stack State ontable(B), on(C,B),
on(A,C), clear(A), handempty Plan so far
Unstack(C,A), Stack(C,B), Pickup(A), Stack(A,C)