Planning: Representation and examples

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Planning Representation and examples Computer
Science cpsc322, Lecture 17 (Textbook Chpt 11.1 -
11.2) February, 13, 2008
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Lecture Overview

• Recap Were are we?
• Planning
• Example
• STRIPS a Feature-Based Representation
• Forward Planning

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Big Picture

• Environment

Stochastic
Deterministic
Search
Single Action
Constraint Satisfaction (CSPs)
Decision
Logics
Search
Sequence of Actions
Constraint Satisfaction (CSPs)
Planning
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Lecture Overview

• Recap We are we?
• Planning
• Example
• STRIPS a Feature-Based Representation
• Forward Planning

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Planning

• How to select and organize a sequence of actions
  to achieve a given goal
• Relying on the powerful representation of states
  as a set of features. (like CSPs)
• Relying on sophisticated actions representation
  (unlike CSPs)

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Planning vs. CSPs

• With CSPs, we looked for solutions to essentially
  atemporal problems.
• and a single variable assignment (state) that
  satisfies all of our constraints.
• Now consider a problem where we are given
• A description of an initial state
• A description of the actions
• A goal to achieve
• ...and want to find a sequence of actions that is
  possible and will result in a state satisfying
  the goal.

• Note here we want not a single state that
  satisfies our constraints, but rather a sequence
  of states that gets us to a goal

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Representation of a Planning Domain

• We solved similar planning problems when we
  considered generic search .

• state is a "black box any arbitrary data
  structure that supports three problem-specific
  routines
• successor function,
• heuristic function
• goal test

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Planning with Feature-Based Representation

• Now what we want to find is a sequence of
  variable assignments that
• begins at an initial state
• proceeds from one state to another by taking
  valid actions
• ends up at a goal

Goal v1 F
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Lecture Overview

• Recap We are we?
• Planning
• Example
• STRIPS a Feature-Based Representation
• Forward Planning

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Delivery Robot Example

• Consider a delivery robot named Rob, who must
  navigate the following environment

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Delivery Robot Example States

• The state is defined by the following features
• RLoc - Rob's location
• domain coffee shop (cs), Sam's office (off ),
  mail room (mr ),
• or laboratory (lab)
• RHC - Rob has coffee
• domain True/False. By indicate that Rob
  has coffee and
• by that Rob doesn't have coffee.
• SWC - Sam wants coffee (T/ F)
• MW - Mail is waiting (T/ F)
• RHM - Rob has mail (T/ F)
• An example state is
  .
• How many states are there?

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Delivery Robot ExampleActions

• The robots actions are
• Move - Rob's move action
• move clockwise (mc ), move anti-clockwise (mac )
  not move (nm )
• PUC - Rob picks up coffee
• must be at the coffee shop
• DelC - Rob delivers coffee
• must be at the office, and must have coffee
• PUM - Rob picks up mail
• must be in the mail room, and mail must be
  waiting
• DelM - Rob delivers mail
• must be at the office and have mail

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Lecture Overview

• Recap
• Planning
• Example
• STanford Research Institute Problem Solver
  (STRIPS) a Feature-Based Representation
• Forward Planning

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Feature-Based Representation

• How would a feature-based representation work?
• the state space is easy joint assignment to
  variables
• initial state and goal state are also easy
• the key is modeling actions

In STRIPS, an action has two parts 1.
Preconditions a set of assignments to features
that must be satisfied in order for the
action to be legal 2. Effects a set of
assignments to features that are caused by
the action
NOTE Skip feature-centric representation on
textbook
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STRIPS actions Example

• STRIPS representation of the action pick up
  coffee, PUC
• preconditions Loc cs and RHC F
• effects RHC T
• STRIPS representation of the action deliver
  coffee, DelC
• preconditions Loc and RHC
• effects RHC and SWC

Note that Sam doesn't have to want coffee for Rob
to deliver it one way or another, Sam doesn't
want coffee after delivery.
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STRIPS Actions (cont)

• The STRIPS assumption
• all variables not explicitly changed by an action
  stay unchanged

• So if the feature/variable V has value v after
  the action a has been performed, what can we
  conclude about a and/or the state of the world
  immediately preceding the execution of a?

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Another Example The Blocks World

• Infinitely wide table, finite number of
  childrens blocks
• Ignore where a block is located on the table
• A block can sit on the table or on another block
• Want to move blocks from one configuration to
  another
• e.g.,
• initial state goal

a
d
b
c
c
e
a
b
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State Representation Symbols

• For five blocks, there are 36 propositions
• Here are 5 of them
• ontable-a - block a is on the table
• on-c-a - block c is on block a
• clear-c - block c has nothing on it
• holding-d - the robot hand is holding block d
• handempty - the robot hand isnt holding anything
• .

d
c
e
a
b
Limitations become clear when we think about the
actions.
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Set-Theoretic Actions
c
a
b
Fifty different actions Here are four of them
c
a
b
c
a
b
c
b
a
c
a
b
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Lecture Overview

• Recap
• Planning
• Example
• STRIPS a Feature-Based Representation
• Forward Planning

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Forward Planning

• Idea search in the state-space graph.
• The nodes represent the states
• The arcs correspond to the actions The arcs from
  a state s represent all of the actions that are
  legal in state s. (What actions are legal?)
• A plan is a path from the state representing the
  initial state to a state that satisfies the goal.

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Example state-space graph
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Lecture Summary

• Planning How to select and organize a sequence
  of actions to achieve a given goal
• Relying on the powerful representation of states
  as a set of features/variables. (like CSPs)
• Goal?
• Relying on sophisticated actions representation
• STRIPS preconditions and effects
• STRIPS assumption
• Propositional vs. relational representation

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Next class
Finish Planning (Chp 11)