Planning

1
Planning

• Search vs. planning
• STRIPS operators
• Partial-order planning
• A Planning

2
Basic Idea of Planning

• To find a sequence of actions that leads to some
  goal from some start state.
• A goal and start state are some recognizable
  collection of propositional or instantiated FOL.
• In most planning formalisms an action is modeled
  by a parameter list, pre-conditions and effects
  (post-conditions). For example
• Fly(p, from, to)
• Preconditions At(p, from) Plane(p)
  Airport(from) Airport(to)
• Effects At(p,from) At(p, to)
• A start condition might be
• At(p21, SFO)Plane(p21)Airport(SFO)Airport(LAX)
  
• A goal might be At(p21, LAX)
• Of course, if the goal was At(Prof.Wilczynski,
  LAX) and he was At(Prof.Wilczynski, SFO) then you
  need BuyTicket(), BoardPlane(), etc.

3
Weve done this already

• Most of the things we have done are really types
  of planning problems.
• A logic proof is plan where the actions are
  inference rules.
• For example
• Start start is A
• Goal is C
• Rule are Actions
• (action mp1) AgtB A is precondition, B is
  effect
• (action mp2) BgtC B is precondition, C is effect
• Proof that you can start with A and wind up at C,
  is two applications of modus ponens.
• So, with the proof, the plan is (mp1, mp2)

4
Route Searching

• was really a planning problem.
• Go (from, to)
• Preconditions At(from) Link(from,to)
• Effect At(to) At(from)
• So, the plan was just a sequence of Go(A,S),
  Go(S,Y), etc.
• But, we compiled all this information away to
  make it a simple state space search.

5
Search vs. planning
6
Basic representation for planning

• Most widely used approach uses STRIPS language
  (very restricted)
• states conjunctions of function-free ground
  literals (i.e., predicates applied to constant
  symbols, possibly negated) e.g.,
• At(Home) ? ?Have(Milk) ? ?Have(Bananas) ?
  ?Have(Drill)
• goals also conjunctions of literals e.g.,
• At(Home) ? Have(Milk) ? Have(Bananas) ?
  Have(Drill)
• Book also talks about ADL language (much more
  like FOL)
• For example, in ADL quantified variables allowed
  in goals
• ?x At(P1,x) At(P2,x) Goal has P1 and P2 at
  same place
• Wont fuss over the difference as long as what we
  write is recognizable

7
STRIPS operators
Graphical notation
8
And there are more complications

• Remember these
• Qualification Real world preconditions
• Ramification Implicit effects of real world
  actions. (Joe wears watch. Joe goes to class. So
  does his watch.)
• Frame Problem We said what changes, what about
  what doesnt?
• In our simple fly action
• Fly(p, from, to)
• Preconditions At(p, from) Plane(p)
  Airport(from) Airport(to)
• Effects At(p,from) At(p, to)
• What about fuel and weight constraints?
  (qualification)
• What about scheduling, the weather, ? (more
  qualification)
• What about pilots and other crew? (ramification)
• The airport itself (frame problem)

9
The reality about planning

• To really get it right is almost impossible, but
  real-world planning is fundamental (think about
  Federal Express)
• Short plans are effective (even if not optimal)
• Long-range plans are not (need midcourse
  corrections recompute)
• MRP (manufacturing resource planning) and ERP
  (enterprise resource planning)
• Try to plan for factories and companies
• This is GIANT software from companies like SAP,
  PeopleSoft
• But, machines go down and up, operators get sick,
  unscheduled maintenance
• My guess is that most long-term planning is
  wasted.
• The real world is a nasty place.
• Need dynamic tools to repair a plan.
• Plan is just data to these tools.

10
State space vs. plan space
Search space of plans rather than of states.
11
A Full Example
12
Operations on plans

• We normally think of search as simply state-space
  search.
• But, once there are actions in the result, we
  can manipulate the so-called result.
• This leads to categories of planner
• Partial order planner some steps are ordered,
  some are not.
• Total order planner all steps ordered (plan is a
  simple list of steps)
• Linearization process of deriving a totally
  ordered plan from a partially ordered plan.

13
Types of planners

• Situation space planner search through possible
  situations (see p. 329)
• Progression planner start with initial state,
  apply operators until goal is reached
• Problem high branching factor! Need good
  heuristics.
• Regression planner start from goal state and
  apply operators until start state reached
• Why desirable? Usually many more operators are
  applicable to
• initial state than to goal state.
• Difficulty when want to achieve a conjunction
  of goals. (Achieving one subgoal may undo
  another)
• Graphplan (backward planning with fancy graph
  manipulation)
• SATplan (turns the problem into prop. logic)
• Later we will look at HSP, an A planner.
• Initial STRIPS algorithm situation-space
  regression planner

14
Partially ordered plans
15
Plan

• Set of actions that make up the steps of the
  plan. Start is an action with no
  preconditions. Finish is an action with no
  effects.
• Set of step ordering constraints
• e.g., A ? B means A before B
• Set of variable binding constraints
• e.g., v x where v variable and x constant
  or other variable
• Set of causal links
• e.g., A B means A achieves C for B
• Set of open preconditions. Initially, these are
  preconditions of Finish.

c
16
POP algorithm sketch
17
POP algorithm (cont.)
18
Clobbering and promotion/demotion
19
Example block world
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Example (cont.)
21
Example (cont.)
22
Example (cont.)
23
Example (cont.)
24
Partially ordered plans