AI Lecture 17 Planning

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AI Lecture 17Planning

• Noémie Elhadad
• (substituting for Prof. McKeown)

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Problem solving so far

• Need to solve a problem
• Choose a representation
• Choose a heuristic
• Choose a search algorithm
• Can this scale up to more complex problems?
• Many irrelevant actions
• Human must provide the heuristic
• No knowledge on how to decompose or
  nearly-decompose the problem

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Planning

• Combine logic and search
• General language to represent the problem
• General algorithm

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Planning components

• Expressive Formal Language describes
• Initial state of world
• Agents goal
• Possible actions that can be performed
• Solver generates a sequence of actions which
  achieve the goal
• Planning algorithm

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An example Blocks world

• Blocks on a table
• Can be stacked, but only one block on top of
  another
• A robot arm can pick up a block and movie to
  another position
• On the table
• On another block
• Arm can pick up only one block at a time
• Cannot pick up a block that has another one on it

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Representation language

• STRIPS (Fikes Nilsson, 1971)
• One of the first planning systems
• Robotics
• See it in action at http//www.ai.sri.com/movies/S
  hakey.ram
• Main contribution is its language description
  formalism
• Many variants/extensions

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STRIPS

• State is a conjunction of positive ground
  literals
• On(B, Table) ? Clear (A)
• Goal is a conjunction of positive ground literals
• Clear(A) ? On(A,B) ? On(B, Table)
• Action schema
• Conjunction of positive literals as preconditions
• Conjunction of positive and negative literals as
  effects

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More on action schema

• Example Move (b, x, y)
• Precondition Block(b) ? Clear(b) ? Clear(y) ?
  On(b,x) ? (b ? x) ? (b ? y) ? (y ? x)
• Effect Clear(y) ? On(b,x) ? Clear(x) ?
  On(b,y)
• An action is applicable in any state that
  satisfies its precondition

Add list
Delete list
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STRIPS assumptions

• Closed World assumption
• Unmentioned literals are false (no need to
  explicitly list out)
• w/an open world assumption unmentioned literals
  are unknown
• STRIPS assumption
• Every literal not mentioned in the effect of an
  action schema remains unchanged

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STRIPS expressiveness

• Literals are function free Move (Block(x), y, z)
• Any action scheme can be propositionalized
• Move(b,x,y) and 3 blocks and table can be
  expressed as 48 purely propositional actions
• No disjunctive goals On(B, Table) V On(B, C)
• No conditional effects On(B, Table) if On(A,
  Table)
• In original STRIPS, no equality x ? y
• Ramification esp. in more complex domain

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Planning components

• Expressive Formal Language describes
• Initial state of world
• Agents goal
• Possible actions that can be performed
• Solver generates a sequence of actions which
  achieve the goal
• Planning algorithm

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Planning algorithms

• Planning algorithms are search procedures
• Which state to search?
• State-space search
• Each node is a state of the KB
• Plan path through the states
• Plan-space search
• Each node is a set of partially-instantiated
  operators and set of constraints
• Plan node

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State search

• Search the space of situations, which is
  connected by operator instances
• The sequence of operators instances the plan
• Since we have both preconditions and effects
  available for each action schema, we can try
  different searches Forward vs. Backward

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Forward state-space search (1)

• Progression
• Initial state initial state of the problem
• Actions
• Applied to a state if all the preconditions are
  satisfied
• Succesor state is built by updating KB with add
  and delete lists
• Goal test state satisfies the goal of the problem

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Forward search in the Blocks world


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Forward state-space search (2)

• Advantages
• No functions in the declarations of goals ?
  search state is finite
• Sound
• Complete (if algorithm used to do the search is
  complete)
• Limitations
• Irrelevant actions ? not efficient
• Need heuristic or prunning procedure

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Backward state-space search (1)

• Regression
• Initial state goal state of the problem
• Actions
• Choose an action that
• Is relevant has one of the goal literals in its
  effect set
• Is consistent does not negate another literal
• Construct new search state
• Remove all positive effects of A that appear in
  goal
• Add all preconditions, unless already appears
• Goal test state is the initial world state

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Backward state-space search (2)

• Possible because of STRIPS-like language
• Goals are listed
• Predecessors are listed for each action/state
• Advantages
• Consider only relevant actions ? much smaller
  branching factor
• Ways to reduce even more the branching factors
• Limitations
• Still need heuristic to be more efficient

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Heuristics for state-space search (1)

• Valid both for forward and backward searches
• Valid for many planning problems
• Possible approaches
• Divide and conquer
• Derive a relaxed problem
• Combine both

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Heuristics for state-space search (2)

• Divide and conquer
• Subgoal independence assumption
• What if there are negative interactions between
  the subgoals of the problems?
• What if there are redundant actions in the
  subgoals?
• Derive a relaxed problem
• Remove all preconditions from the actions
• Remove all negative effects from the actions
  (empty delete list)

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Limitation of state-space search

• Linear planning or Total order planning
• Example
• Initial state all the blocks are clear and on
  the table
• Goal On(A,B) ? On(B,C)
• If search achieves On(A,B) first, then needs to
  undo it in order to achieve On(B,C)
• Have to go through all the possible permutations
  of the subgoals

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Partial order planning (1)

• Approaches that are not constrained to consider
  only totally ordered sequences of actions.
• Strategy
• Decompose goal into subgoals
• Solve subgoals independently with subplans
• Combine subplans into plan
• Flexibility in order of plan construction
• Least commitment
• Delay choice during search so can work on
  important subplans before working on less
  important ones

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Partial order planning (2)

• Search in Plan space not State space
• Focus search on the constrained parts of the plan
  first
• More flexible
• Graph of actions, not a sequence
• Strategy
• Start with empty plan (Start-Finish)
• Refine the plan until get a complete plan that
  solves the problem
• Actions are on the plan (not on the world/KB)
• add step to the plan
• Impose an ordering constraint between two steps
• Every linearization of a partial-order solution
  is a total-order solution.

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Partial order plan example
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Partial plan

• A set of steps/actions
• Start, Finish, A, B
• A set of ordering constraints
• A lt B A must be carried out before B, not
  necessarily right before
• A set of causal links
• A?pB A achieves p for B
• p is an effect of A and a precondition of B
• p must remain true between from A to B
• Set of open preconditions
• Preconditions not achieved in the plan
• A consistent plan has no cycles in the ordering
  constraints and no conflicts in the causal links
• Solution consistent plan with no open
  preconditions

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Maintaining consistency

• Given causal link A?pB
• C that has an effect p
• Causes a conflict if there is a possible ordering
  for which C comes after A and before B
• Say that C is a threat to causal link
• Take an action to resolve threats by introducing
  additional ordering constraints

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POP Search

• Initial plan Start and Finish
• Start lt Finish
• no causal links
• and all preconditions in Finish as open
  preconditions.
• Successor pick an open precondition p (on action
  B), and look for an action A that achieves p
• If new, then introduce A to plan, along with
  Start lt A and A lt Finish
• Add causal link add ordering constraint A lt B
• Check for conflicts
• between new causal link and all existing actions
  
• between action and all existing causal links
• Add B lt C or C lt A if necessary to resolve
  threat if no cycles then generate a successor
  state
• Goal check there are no open preconditions

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POP in the Blocks world
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POP in the Blocks world
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POP in the Blocks world
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POP in the Blocks world
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POP

• Advantages
• Causal links help prunning since avoids
  irresolvable conflicts
• Limitations
• In some cases duplication of efforts
• Since deal with plans (rather than states of the
  world), it is difficult to estimate how far we
  are from solution

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Other planning algorithms

• Planning graph allows for better heuristics
• SAT translates the planning problem into
  propositional axioms and applies a satisfiability
  algorithm to find the model that corresponds to a
  valid plan.
• Very active field of AI research!
• Not one clear winner. Each approach is better
  adapted to a type of problem.

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One more assumption

• So far, we looked only at classical planning
  environments.
• Lots of research on planning in non-classical
  environments
• Environments where time plays an important role
  (scheduling jobs)
• Partially observable or stochastic environments