Planners and Planning Languages

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Planners and Planning Languages

• April 4th, 2000
• Ryan Wagner

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• Introduction
• Simple Planning Agent
• Planning vs. Problem Solving
• Planning Using Situation Calculus
• Basic Representation for Planning
• Planning Examples
• Summary

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Introduction

• Origins
• Problem solving using state-space searching
• Theorem proving
• Robotics
• Planners are like problem solving agents
• states
• goals
• actions

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Introduction (2)

• Differences
• use logic to represent goals, states, and actions
• searches are executed differently
• use of partial plans and planning algorithms to
  achieve a solution
• in some ways more intelligent than a problem
  solving agent

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• Introduction
• Simple Planning Agent
• Planning vs. Problem Solving
• Planning Using Situation Calculus
• Basic Representation for Planning
• Planning Examples
• Summary

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Simple Planning Agent

• The planning agent uses its percepts of the world
  state to form a model of the world.
• The agent then takes the goal and formulates a
  plan to achieve it.
• Planners must be able to distinguish two special
  cases
• infeasible goals
• goals that are already achieved

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Plans

• Sets of executable steps ordered to achieve the
  goal given.
• Can be formed progressively or regressively
• i.e. from the initial state (progressive), or
  from the goal state backwards (regressive)
• Partial plans are basically frameworks for the
  plan that will achieve the goal.

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Plans A simple example

• Suppose we are at home and we want to go to
  school, and we must take the bus to do so.
• A simple plan would likely be
• Start state We are at home.
• Actions required to get to school
• Go to the bus stop
• Get on the bus
• Ride the bus to school
• Get off of the bus
• Walk from the bus stop to the school
• Goal State We are at school.

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• Introduction
• Simple Planning Agent
• Planning vs. Problem Solving
• Planning Using Situation Calculus
• Basic Representation for Planning
• Planning Examples
• Summary

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Planning vs. Problem Solving

• Planning tries to create a representation of
  goals, states, and actions that are a bit more
  flexible.
• These elements are described using a formal
  language, like first-order logic.
• States and goals correspond to logical sentences
  and actions are pairings of preconditions and the
  resulting effects.

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Planning vs. Problem Solving (2)

• In creating a plan, actions are added in a
  non-linear manner - whenever and wherever they
  are needed.
• Planners try to make important decisions first to
  avoid having to backtrack.
• Planners assume the world is mostly independent,
  so multiple conjunctive goals can be achieved.

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Conjunctive Goals

• The planner will attempt to solve a conjunctive
  goal by splitting it into sub-goals and creating
  individual plans to deal with each piece.
• Often, however, we require a complex planning
  algorithm to achieve a solution as there may be a
  particular order in which the sub-plans must be
  executed.

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Video Rental - Search
Goal Rent a video, buy some bread, and come home
Start
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Video Rental - Planning

• A simple regressive plan might be
• Start state At Home without Video and Bread
• Actions
• Go to Store
• Buy Bread
• Go to Rogers
• Rent Video
• Go Home
• Goal state At Home with Video and Bread

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• Introduction
• Simple Planning Agent
• Planning vs. Problem Solving
• Planning Using Situation Calculus
• Basic Representation for Planning
• Planning Examples
• Summary

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Planning Using Situation Calculus

• Situation Calculus can often aid us in creating a
  planner, using a theorem-prover to decide on a
  plan.
• Situation Calculus planners represent the initial
  state as a sentence, the goal state as a query,
  and the actions are such that they transform the
  state.
• A solution is a plan that achieves the goal state.

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Planning Using Situation Calculus (2)

• The major drawback of using a theorem-prover for
  a planner is that a theoretical solution and a
  practical solution are often not one and the
  same.
• In fact, the only guarantee we have for the
  solution is that we have reached the goal state,
  but no information on the means.
• (DoNothing, DoNothing, , Plan)
• (DoSomething, Plan, UndoSomething)

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Planning Using Situation Calculus (3)

• Remember that the method of logical inference is
  semidecidable. This affects planning if the
  method of inference is unguided by making it
  extremely inefficient.
• The solution to the problem of semidecidability
  is to restrict the language understood by the
  prover - i.e. create a planner rather than a
  general purpose theorem prover.
• The planner will have an algorithm to handle its
  language efficiently.

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• Introduction
• Simple Planning Agent
• Planning vs. Problem Solving
• Planning Using Situation Calculus
• Basic Representation for Planning
• Planning Examples
• Summary

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Basic Representation for Planning

• The most basic representation used for creating
  planners was developed in 1970 - a language known
  as STRIPS
• STanford Research Institute Problem Solver
• Extensions of the STRIPS language are often used
  in planners today.
• STRIPS blends efficient planning with the
  expressive situation calculus representation.

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Basic Representation for Planning (2)

• States are represented as conjunctions of
  literals, though planners will often not store
  entire sets of literals describing the current
  state.
• In fact, incomplete states often assume that
  the literals not indicated are to be treated as
  false.
• Goals are conjunctions of literals and (often
  existentially) qualified variables.

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Planner vs. Theorem Prover

• The fundamental difference between a planner and
  a theorem prover is that the planner requests a
  sequence of steps that, if executed, will result
  in the goal state being true. The theorem prover
  evaluates the sentences for validity.

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STRIPS Operators

• Action, Preconditions, and Effects
• An operator is applicable to a given state just
  in case the variables for the operator can be
  instantiated so all preconditions are satisfied.
• The result contains all items introduced by the
  effect, plus the old status. However, any effect
  that negates something in the old status will not
  be true in the new state.

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Situation and Plan Spaces

• Situations are nodes of the search tree between
  the initial and goal states.
• Planners can search through the situation space
  progressively or regressively.
• Regressive searches are possible because the
  operators have enough knowledge about the
  resulting state and the preconditions to decide
  if an operator is actually applicable.
• Regressive searching is desirable as goals are
  not as complex as initial states (fewer
  conjuncts), but it is very complicated in
  application, and inefficient to do attempt to
  overcome this.

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Situation and Plan Spaces (2)

• Plan spaces are made up of partial plans -
  basically frameworks for plans
• Plan modification involves inserting, removing,
  and ordering steps, instantiating variables, etc.
• The solution is the final plan
• The steps taken to achieve this are irrelevant

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Situation and Plan Spaces (3)

• Two operators are generally used on plans
• Refinement constrain or eliminate plans from the
  space
• Modification any other type of plan modification
• Plan frameworks will all contain a start state
  and a goal descriptor. The start state sets the
  preconditions for the first action, and the goal
  state matches the results of the last action.

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Plan Spaces

• Least Commitment - dont make a decision until
  you have to.
• If a decision is not important at a given stage,
  leaving it undecided allows for greater
  flexibility later on and results in less
  backtracking
• This leads to a partial order within the plan.
  Any given plan will be a linearization of this
  partial ordering.

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Causal Links

• Causal links are formed based on precondition
  fulfilling. A causal link is created when a
  given state s1 contains a precondition c for
  state s2.
• s1 c s2
• Causal links are protected. Threats that may
  delete a precondition are ordered either before
  the first state (demoted) or after the second
  (promoted) when linearizing the plan. This
  prevents removing the link.

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Causal Links (2)
promote
demote
s1
s3
c
c
s2
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Plans

• Are a set of steps (starting with a start state
  and ending with a goal), that involve
• ordering restraints (s1 comes before s2)
• variable binding (v is set to X)
• causal links (if it is possible to reach a state
  s2 from s1, any preconditions to reach s2 created
  by s1 are stored)

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Solutions

• Solutions are executable plans
• Complete Solutions
• if then s1 lt s2 and there is no s3 such that
  c results from it where s1 lt s3 lt s2
• Consistent Solutions
• there are no orderings such that s1 lt s2 and s2 lt
  s1, or where a variable v A and v B (or v x
  B)
• Note the transitivity of the lt and operators

s1 c s2
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Possible Threats

• When a state threatens to remove a precondition
  necessary to reach another state, it is called a
  threat.
• Often when variables are not yet instantiated,
  they pose possible threats, depending on what
  they are later assigned.
• There are 3 methods of dealing with the possible
  threat.

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Possible Threat Solutions

• Resolving with an equality constraint
• Immediately instantiate the variable to something
  that is non-threatening
• Resolving with an inequality constraint
• Immediately mark the variable as not equal to the
  threatening value. This has lower commitment.
• Resolve the threat later
• This has the lowest commitment, but may not
  result in an actual solution plan.

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• Introduction
• Simple Planning Agent
• Planning vs. Problem Solving
• Planning Using Situation Calculus
• Basic Representation for Planning
• Planning Examples
• Summary

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Planning Examples

• Partial-order Planner (POP) algorithm - p356
• Blocks World - p359
• Shakeys World - p360
• Video Rental Problem - revisited

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Partial Order Planner

• Uses regressive planning to create a solution.
• Starts with a minimal partial plan and extends
  the plan at each step by achieving the
  precondition of a state S.
• operators are chosen from any steps currently in
  the plan or the operator pool
• It then sets up causal links and eliminates
  threats
• If it cannot find an operator at a given point,
  it backtracks to the previous choice point.
• The POP algorithm is sound and complete - it
  always finds a solution if one is possible.

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Blocks World

• Builds stacks of blocks on a table top
• Uses two state descriptors and an operator
• On(x, y) indicates x is on top of y
• Clear(x) indicates x has nothing on top of it
• Move(x, y, z)
• Preconditions Clear(x) /\ Clear(z) /\ On(x, y)
• Effect On(x, z) /\ Clear(y) /\ On(x, y) /\
  Clear(z)
• Note Move(x, y, Table) and Move(x, Table, z)
  have some concerns with Clear(Table). In the
  former, the table must be clear to move the block
  and in the later, the table is then marked as
  clear.

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Blocks World (2)

• Solution
• Change the meaning of Clear(x) to mean there is
  room on x for a block
• Add a new rule MoveToTable(x, y)
• Preconditions On(x, y) /\ Clear(x) /\ Table(y)
• Effect On(x, Table) /\ Clear(y) /\ On(x, y)
• Modify the Move(x, y, z) rule
• Preconditions On(x,y) /\ Clear(x) /\ Clear(z)
  /\ Table(z)
• Effect On(x, z) /\ Clear(y) /\ On(x, y) /\
  Clear(z)

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Blocks World Example

• Start State On(A, Table) /\ On(C, A) /\
  Clear(C) /\ On(B, Table) /\ Clear(B)

• Goal State On(C, Table) /\ On(B, C) /\ On(A,
  B) /\ Clear(A)

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Shakeys World

• A planner designed to allow a robot to move
  between rooms and perform some restricted
  actions.
• Uses actions such as
• Go(loc),
• Push(obj, loc1, loc2),
• Climb(box) and Down(box)
• TurnOn(light_switch) and TurnOff(light_switch)
• Predicates such as
• Pushable(object), On(Shakey, level), At(Shakey,
  loc), Climbable(box), In(obj, loc)
• Constant - Floor

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Video Rental - Search
Goal Rent a video, buy some bread, and come home
Start
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Video Rental - Planning
Start
At(Home) Rents(Rogers, Video) Sells(Store, Bread)
At(Home) Have(Video) Have(Bread)
Finish
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Video Rental - Planning
Start
At(Home) Rents(Rogers, Video) Sells(Store, Bread)
At(Home) Have(Video) Have(Bread)
Finish
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Video Rental - Planning
Start
At(Home) Rents(Rogers, Video) Sells(Store, Bread)
At(Home) Have(Video) Have(Bread)
Finish
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Video Rental - Planning
Start
At(Home) Rents(Rogers, Video) Sells(Store, Bread)
At(x)
At(x)
Go(Rogers)
Go(Store)
At(Rogers) Rents(Rogers, Video)
At(Store) Sells(Store, Bread)
Buy(Bread)
Rent(Video)
At(Home) Have(Video) Have(Bread)
Finish
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Video Rental - Planning
Start
At(Home) Rents(Rogers, Video) Sells(Store, Bread)
At(Home)
Go(Rogers)
Go(Store)
At(Rogers) Rents(Rogers, Video)
At(Store) Sells(Store, Bread)
Buy(Bread)
Rent(Video)
At(Home) Have(Video) Have(Bread)
Finish
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Video Rental - Planning
Start
At(Home) Rents(Rogers, Video) Sells(Store, Bread)
At(Home)
Go(Rogers)
Go(Store)
At(Rogers) Rents(Rogers, Video)
At(Store) Sells(Store, Bread)
Buy(Bread)
Rent(Video)
At(Home) Have(Video) Have(Bread)
Finish
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Video Rental - Planning
Start
49

• Introduction
• Simple Planning Agent
• Planning vs. Problem Solving
• Planning Using Situation Calculus
• Basic Representation for Planning
• Planning Examples
• Summary

50
Summary

• Planners use formal representations of states,
  goals, and actions to allow greater flexibility
  in determining paths from the start state to the
  finish.
• Planners often take one of two approaches to
  solving a problem - progressive or regressive
  plan building.
• Least Commitment is making decisions only when it
  is necessary, thus reducing backtracking.
• Partial Plans are often a better solution
  mechanism than searching as they reduce the
  complexity of the method.
• Causal links are used to determine and resolve
  conflicts when working with partial-order plans.