Planning 2

1
Planning 2
2
GPS

• GPS essentially does max search in operator
  space.
• Operators are vectordifference to vector
  functions.
• Want to minimize depth of path by maximizing.

3
GPS and Search

• Thus, any of the search algorithms will apply.
• General goals
• Sound any plans generated are good plans
• Complete all good plans generated are generated.
• Efficient1 minimal cost to plans.
• Efficient2 plans can be generated soon enough.
  (i.e. the computational characteristics are
  acceptable).

4
Again, reminders

• In general, well have to give up on two of the
  three.
• Hard to come up with reasonable transition
  functions partly due to the vector
  representation (comparing apples to oranges
  problem).

5
Logic to the rescue?

• Represent states, possible states, and goals in
  FOPC.
• Represent operators as possible state transition
  functions.
• Represent operator preconditions as FOPC
  statements.

6
Advantages

• Clearly a richer language of description than the
  atoms of GPS vector space.
• More transparent language for goals and states
  (meaning isnt hidden in the vector indices).
• Intermediate logical steps and causal chains can
  be described.

7
Disadvantages

• If vector space has computational problems.
• Easy to see that most planning problems will be
  NP-complete.
• Most planning will be at least as hard as the
  satisfiability problem, right?

8
Search in Planning

• Natural to consider regression as the way to
  plan.
• From a goal description, consider the operators
  that will get you there.
• (Intermediate causal chains might be a problem).
• Allows for possible bidirectional search.
• b(d/2) b(d/2)
• Typically regression only.

9
Coffee example

• Goal have-coffee
• State plugged-in
• Ops
• Add-coffee (filter-in, plugged-in/coffee in)
• Brew (water-in, filter-in, coffee-in,
  plugged-in/have-coffee)
• Install-filter (plugged-in/filter-in)
• Fill-water (plugged-in/water-in)
• Plug-in-machine (T/plugged-in)

10
Lets be careful

• Exists(c,s) Own(c,s) and Porsche(c)
• Find a Volkswagen and turn it into a Porsche?
• Unification variables
• (and (own ?c ?s) (porsche ?c t))

11
Indexing

• Natural index is the set of results
• View goals as a conjunction of (existential)
  states
• Assume independence of goal states.
• View results as the conjunction of states.
• Goal (own ?c) (porsche ?c) is an annotation on
  the goal (not a goal itself).

12
Strips algorithm (cartoon version)

• If goal is achieved, return plan else
• For each conjunct in goal
• Select an operator to achieve conjunct
• Recurse on operators preconditions as subgoals
• Simulate action (project new results)

13
What do we need?

• The action, which is the name parameters type
  info
• The add list, which is the list of things which
  will become true
• The delete list, the list of the things that will
  become no longer true (false).
• (Note negation as failure assumption)

14
For example

• (define-operator (pour ?stuff ?source ?dest ?amt)
• (pre (contains ?source ?stuff (- ?current
  ?amt))
• (add (contains ?dest ?stuff ?amt) (contains
  ?source ?stuff 0))
• (del (contains ?dest ?stuff ?old-amt) (contains
  ?source ?stuff ?amt))
• Hmm
• Fluents vs. Propositions

15
More details

• Push goal on stack
• Repeat until empty stack
• Is top a goal?
• Is it true? Pop it.
• Is it conjunctive?
• Push it again. Push conjunctions.
• Else choose operator to achieve goal.
• Instantiate it push it.
• Push its preconditions.
• Is top an operator?
• Pop it, add to partial plan.
• Apply delete list.
• Apply add list.

16
Grind/Paint example