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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. This class: improving the action representation. Variablised actions Disjunctive preconditions Conditional effects

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useful bells and whistles
Useful bells and whistles
  • Last class: state-space and plan-space planning, the POP algorithm, principle of least commitment.
  • This class: improving the action representation.
    • Variablised actions
    • Disjunctive preconditions
    • Conditional effects
    • Universal quantifiers
reminder blocks world sussman anomaly
Reminder: blocks world (Sussman anomaly)

State I: (on-table A) (on C A) (on-table B) (clear B) (clear C)

Goal: (on A B) (on B C)

Initial:

Goal:

A

C

B

A

B

C

strips representation for actions
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))

  • The explicit effects are the only changes to the state.
pop algorithm

Q

Ac

Ap

POP algorithm

POP((A, O, L), agenda, PossibleActions):

  • If agenda is empty, return (A, O, L)
  • Pick (Q, An) from agenda
  • Ad = choose an action that adds Q.
    • If no such action exists, fail.
    • Add the link Ad Ac to L and the ordering Ad < Ac to O
    • If Ad is new, add it to A.
  • Remove (Q, An) from agenda. If Ad is new, for each of its preconditions P add (P, Ad) to agenda.
  • For every action At that threatens any link
    • Choose to add At < Ap or Ac < At to O.
    • If neither choice is consistent, fail.
  • POP((A, O, L), agenda, PossibleActions)

Q

1 operators action schemata
1. ‘Operators’ --- action schemata
  • 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)))

modifications to pop
Modifications to POP
  • Keep a list of bindings with a partial plan (A, O, L, B)
  • Choose action Ad adding E, with MGU(Q, E, B) defined.
  • When adding an action, add bindings preconditions to B.
  • Delay threat checks until ground values are known for variables.

(why do we know they eventually will be?)

work on open precondition on b c
Work on open precondition (on B C)

Spot the threat!

A0

(on C A)

(on-table A)

(on-table B)

(clear C)

(clear B)

(clear ?b2)

(clear ?y2)

(on ?b2 Table)

A2: move ?b2 from Table to ?y2

(clear ?b1)

(clear ?y1)

(on ?b1 Table)

-(on ?b2 Table)

-(clear ?y2)

(on ?b2 ?y2)

A1: move ?b1 from Table to ?y1

[[?b2 A] [?y2 B]]

-(on ?b1 Table)

-(clear ?y1)

(on ?b1 ?y1)

[[?b1 B] [?y1 C]]

(on A B)

(on B C)

Ainf

2 disjunctive preconditions
2. Disjunctive preconditions
  • Preconditions: (and (on ?x ?y)

(or (clear ?x) (big-and-flat ?x)))

  • Put (or Q1 Q2) on the agenda when the action is selected.
  • When it’s picked from the agenda, choose either Q1 or Q2 to work on. (Must try all choices for completeness).
3 conditional effects
3. Conditional effects
  • 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))))

modifications to planning algorithm
Modifications to planning algorithm
  • Allow conditional effects to be used for causal links.
  • Add the condition to the agenda.
  • Allow threat resolution by “confrontation”: if the threat is from a conditional effect, add its negation to the agenda.
4 universal quantification
4. Universal quantification
  • 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))))

  • Assume a finite, static set of typed objects.
approach replace with ground literals
Approach: replace with ground literals
  • Replace “forall” goals with the conjunction of all the implied ground goals.
  • “Universal base”

where the instances of t1 are (C1, .., Cn) and

so (forall ((padlock ?x)) (not (locked ?x ?b)))

 (and (not (locked p1 ?b)) (not (locked p2 ?b)) …)

modifications to planner
Modifications to planner
  • Replace a universally quantified goal with its universal base.
  • Only use ground literals from the universal base of a quantified effect as they are needed for causal links.
  • Consider threats when their bindings refer to universally quantified variables.
briefcase example
Briefcase example

A0

(briefcase B)

(at B home)

(in P B)

(at P home)

(briefcase B)

(at B ?l)

(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

briefcase 2
Briefcase 2

A0

(briefcase B)

(at B home)

(in P B)

(at P home)

(briefcase B)

(at B 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

briefcase 3
Briefcase 3

A0

(briefcase B)

(at B home)

(in P B)

(at P home)

(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

briefcase 4
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