Download Planning Representation Actions

Planning
15-381: Artificial Intelligence
●
Behrang Mohit and Davide Fossati
Planning
●
Process of organizing a sequence of actions to
achieve a goal
Approaches that combine search and logic
Some figures and tables are from Russell and Norvig
2
Representation
●
Actions
States: conjunction of facts (ground predicates)
●
at(Plane1, DOH) ∧ at(Plane2, PGH)
●
Actions: composed of precondition and effect
●
action fly(p, from, to):
precond: at(p, from) ∧ plane(p) ∧
airport(from) ∧
airport(to)
effect: ~at(p, from) ∧ at(p, to)
●
3
An action is applicable in a state if the
preconditions are satisfied
The result of an action is a state with the addition
of the positive predicates listed in the effect
section, and deletion of the negative predicates
A plan is a sequence of actions that transform an
initial state to a goal state
4
Example: Air cargo transport
Example: The blocks world
5
Blocks world
6
Example: Monkey and bananas
P1 P2 P3 P4 P5 P6
7
8
Monkey and bananas
Planning as search
(operator GOTO (params (<x>) (<y>))
(preconds (on­floor) (at monkey <y>))
(effect (del at monkey <y>) (at monkey <x>)))
(operator CLIMB (params (<x>))
(preconds (at box <x>) (at monkey <x>))
(effects (onbox <x>) (del on­floor)))
●
(operator PUSH­BOX (params (<x>) (<y>))
(preconds (at box <y>) (at monkey <y>) (on­floor))
(effects (at monkey <x>) (at box <x>) (del at monkey <y>) (del at box <y>)))
actions
(operator GET­KNIFE (params (<y>))
(preconds (at knife <y>) (at monkey <y>))
(effects (hasknife) (del at knife <y>)))
●
(operator GRAB­BANANAS (params (<y>))
(preconds (hasknife) (at bananas <y>) (onbox <y>))
(effects (hasbananas)))
(operator PICKGLASS (params (<y>))
(preconds (at glass <y>) (at monkey <y>))
(effects (hasglass) (del at glass <y>)))
(operator GETWATER (params (<y>))
(preconds (hasglass) (at waterfountain <y>) (at monkey <y>) (onbox <y>))
(effects (haswater)))
initial
state
(preconds (at monkey p1)(on­floor)(at box p2)(at bananas p3)
(at knife p4)(at waterfountain p3)(at glass p6))
goal
(effects (hasbananas) (haswater))
●
Forward chaining search
–
Start from the initial state
–
Search using all applicable actions
Backward chaining search
–
Start from the goal state
–
Search backwards using all relevant actions
State space explosion: we need good heuristics!
9
10
Forward and backward search
Planning graphs
●
Data structure that help provide good heuristics and pruning of
the planning search space
●
Can be built in polynomial time
●
Nodes: atomic facts and actions, arranged into alternate levels
–
●
●
11
First level: true facts in the initial state of the problem
Edges of two types:
–
From a fact to the actions for which it is a condition
–
From an action to the new facts that is makes true or false
Store also mutually exclusive (mutex) facts and actions
–
Facts that can't be true at the same time
–
Actions that can't be executed together
12
Planning graph example
Mutually exclusive actions
●
●
●
persistence node
mutex link
Interference: one of the effects of one action is the
negation of the precondition of the other. Example:
eat(Cake) negates the precondition of
persistence(have(Cake))
Competing needs: one of the preconditions of one action
is mutually exclusive with the precondition of the other.
Example: bake(Cake) and eat(Cake) compete on the value
of the have(Cake) precondition
13
14
Graphplan algorithm
Mutually exclusive facts
●
Inconsistent effects: one action negates an effect of the
other. Example: eat(Cake) and persistence(have(Cake))
disagree on the effect have(Cake)
(A. Blum and M. Furst)
Two facts at the same level are mutex if
–
one is the negation of the other, or
–
each possible pair of actions that could achieve the
two facts is mutex
15
16
Graphplan demo
●
System available here:
http://www.cs.cmu.edu/~avrim/graphplan.html
●
Let's play with monkeys and bananas
17