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Causal-link planning 2

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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Causal-link planning 2

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  1. Causal-link planning 2 Jim Blythe

  2. 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

  3. 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

  4. 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.

  5. 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

  6. 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)))

  7. 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?)

  8. 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

  9. 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).

  10. 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))))

  11. 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.

  12. 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.

  13. 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)) …)

  14. 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.

  15. 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

  16. 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

  17. 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

  18. 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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