Transcript Class notes 2 (powerpoint)

Causal-link planning 2
Jim Blythe
Useful bells and whistles

Last class: state-space and plan-space planning, the
POP algorithm, principle of least commitment.
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This class: improving the action representation.
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Variablised actions
Disjunctive preconditions
Conditional effects
Universal quantifiers
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Reminder: blocks world (Sussman anomaly)
Initial:
Goal:
C
A
A
B
B
C
State I: (on-table A) (on C A) (on-table B) (clear B) (clear C)
Goal: (on A B) (on B C)
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STRIPS representation for actions:
Move-C-from-A-to-Table:
precondition: (and (on C A) (clear C))
effects:
(and (on C Table)
(not (on C A))
(clear A))
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The explicit effects are the only changes to the state.
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POP algorithm
POP((A, O, L), agenda, PossibleActions):
1. If agenda is empty, return (A, O, L)
2. Pick (Q, An) from agenda
3. Ad = choose an action that adds Q.
a.
b.
c.
4.
5.
Remove (Q, An) from agenda. If Ad is new, for each
of its preconditions P add (P, Ad) to agenda.
Q Ac
Ap
For every action At that threatens any link
1.
2.
6.
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If no such action exists, fail.
Add the link Ad Q Ac to L and the ordering Ad < Ac to O
If Ad is new, add it to A.
Choose to add At < Ap or Ac < At to O.
If neither choice is consistent, fail.
POP((A, O, L), agenda, PossibleActions)
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1. ‘Operators’ --- action schemata
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Move ?b from ?x to ?y
parameters: ?b, ?x, ?y
preconds: (and (on ?b ?x) (clear ?b) (clear ?y)
(≠ ?b ?x) (≠ ?b ?y) (≠ ?x ?y)
(≠ ?y Table))
effects:
(and (on ?b ?y)
(not (on ?b ?x))
(clear ?x)
(not (clear ?y)))
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Modifications to POP
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Keep a list of bindings with a partial plan (A, O, L, B)
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Choose action Ad adding E, with MGU(Q, E, B) defined.
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When adding an action, add bindings preconditions to B.
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Delay threat checks until ground values are known for
variables.
(why do we know they eventually will be?)
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Spot the threat!
Work on open precondition (on B C)
A0
(on C A)
(on-table A)
(on-table B)
(clear C)
(clear B)
(clear ?b2) (clear ?y2) (on ?b2 Table)
(clear ?b1) (clear ?y1) (on ?b1 Table)
A2: move ?b2 from Table to ?y2
-(on ?b2 Table) -(clear ?y2) (on ?b2 ?y2)
[[?b2 A] [?y2 B]]
A1: move ?b1 from Table to ?y1
-(on ?b1 Table) -(clear ?y1) (on ?b1 ?y1)
[[?b1 B] [?y1 C]]
(on A B)
(on B C)
Ainf
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2. Disjunctive preconditions
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Preconditions: (and (on ?x ?y)
(or (clear ?x) (big-and-flat ?x)))
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Put (or Q1 Q2) on the agenda when the action is selected.
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When it’s picked from the agenda, choose either Q1 or
Q2 to work on. (Must try all choices for completeness).
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3. Conditional effects
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Move ?b from ?x to ?y
parameters: ?b, ?x, ?y
preconds: (and (on ?b ?x) (clear ?b) (clear ?y)
(≠ ?b ?x) (≠ ?b ?y) (≠ ?x ?y)
effects:
(and (on ?b ?y)
(not (on ?b ?x))
(clear ?x)
(when (≠ ?y Table) (not (clear ?y))))
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Modifications to planning algorithm
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Allow conditional effects to be used for causal links.
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Add the condition to the agenda.
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Allow threat resolution by “confrontation”: if the threat
is from a conditional effect, add its negation to the
agenda.
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4. Universal quantification
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Move-briefcase:
preconds: (and (briefcase ?b) (at ?b ?loc)
(forall ((padlock ?p)) (not (locked ?b ?p)))
(≠ ?dest ?loc))
effects: (and (at ?b ?dest)
(not (at ?b ?loc))
(forall ((object ?x))
(when (in ?x ?b)
(and (at ?x ?dest) (not (at ?x ?loc))))
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Assume a finite, static set of typed objects.
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Approach: replace with ground literals
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Replace “forall” goals with the conjunction of all the
implied ground goals.
“Universal base”  x (x)  ( )  ..  ( )
1
n
 t1

where the instances of t1 are (C1, .., Cn) and
i  (x) \ [x  Ci ]
so (forall ((padlock ?x)) (not (locked ?x ?b)))
 (and (not (locked p1 ?b)) (not (locked p2 ?b)) …)
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Modifications to planner
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Replace a universally quantified goal with its
universal base.
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Only use ground literals from the universal base of a
quantified effect as they are needed for causal links.
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Consider threats when their bindings refer to
universally quantified variables.
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Briefcase example
A0
(briefcase B)
(briefcase B)
(at B home)
(at B ?l)
(in P B)
(at P home)
(in ?o1 B)
move B ?l office
(at B off) (not (at B ?l)) (at ?o1 off) (not (at ?o1 ?l))
(at B off)
(at P home)
Ainf
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Briefcase 2
A0
(briefcase B)
(briefcase B)
(at B home)
(at B home)
(in P B)
(at P home)
(in ?o1 B)
move B ?l office
(at B off)
(not (at B home))(at ?o1 off) (not (at ?o1 home))
(at B off)
(at P home)
Ainf
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Briefcase 3
A0
(briefcase B)
(at B home)
(briefcase B)
(at B home)
(in P B)
(in ?o1 B)
(at P home)
(not (in P B))
move B ?l office
(at B off)
(not (at B home))(at ?o1 off) (not (at ?o1 home))
(at B off)
(at P home)
Ainf
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Briefcase 4
A0
(briefcase B)
(at B home)
(in P B)
(at P home)
take-out P B
(briefcase B)
(at B home)
(in ?o1 B)
(not (in P B))
move B ?l office
(at B off)
(not (at B home))(at ?o1 off) (not (at ?o1 home))
(at B off)
(at P home)
Ainf
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