1 / 20

Automated Planning

Automated Planning. Dr. H é ctor Mu ñ oz-Avila. Domain-configurable Planning Domain independent planning algorithm Add domain-specific search control Examples: SHOP TLPlan. What is Planning? Classical Definition. Planning: finding a sequence of actions to achieve a goal.

vargase
Télécharger la présentation

Automated Planning

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Automated Planning Dr. Héctor Muñoz-Avila

  2. Domain-configurable Planning • Domain independent planning algorithm • Add domain-specific search control • Examples: • SHOP • TLPlan What is Planning? Classical Definition • Planning: finding a sequence of actions to achieve a goal • Domain Independent: symbolic descriptions of the problems and the domain. The plan generation algorithm remains the same • Domain Specific: The plan generation algorithm depends on the particular domain Advantage: - opportunity to have clear semantics Disadvantage: - symbolic description requirement Advantage: - can be very efficient Disadvantage: - lack of clear semantics - knowledge-engineering for adaptation

  3. Plan adaptation Classical Assumptions (I) • A0: Finite system • finitely many states,actions, and events • A1: Fully observable • the controller alwaysknows what state  is in • A2: Deterministic • each action or event hasonly one possible outcome • A3: Static • No exogenous events: no changes except those performed by the controller

  4. Plan space planning TLPlan HTN planning Classical Assumptions (II) A4: Attainment goals • a set of goal states Sg A5: Sequential plans • a plan is a linearlyordered sequence of actions (a1, a2, … an) A6 :Implicit time • no time durations • linear sequence of instantaneous states A7: Off-line planning • planner doesn’t know the execution status Dana Nau: Lecture slides for Automated PlanningLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/

  5. Plan Representation • Classical representation • Predicates, variables, constants • Most of our systems used it • Set-theoretic representation • Predicates and constants (no variables!) • Useful in algorithms that manipulate ground atoms directly • Used in internal representations: planning graphs (Chapter 6), satisfiability (Chapters 7) • State-variable representation • Keeps track of the value of each variable: loc(truck) = l1

  6. Expressive Power • Any problem that can be represented in one representation can also be represented in the other two • Can convert in linear time and space, except when converting to set-theoretic (where we get an exponential blowup) P(x1,…,xn) becomes fP(x1,…,xn)=1 trivial Set-theoretic representation Classical representation State-variable representation write all of the groundinstances f(x1,…,xn)=y becomes Pf(x1,…,xn,y) Dana Nau: Lecture slides for Automated PlanningLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/

  7. Classical Planning

  8. State space • V: set of states • E: set of transitions (s, (s,a)) • But: computed graph is a subset of state space • Search modes: • Forward • Backward • Sussman Anomaly • Generally thought to be slow • But: Fastforward, TLPlan, SHOP are state-space planners • How come? State-Space Planning C A B C A B C B A B A C B C B A B C C A B A C A A B C A A B C B C C B A A B C

  9. Plan space • V: set of plans • E: plan refinement transitions • As before: computed graph is a subset of plan space • Least commitment: • Does not commit on action ordering • Threats • Open conditions • Solves the Sussman anomaly • Also thought to be slow • But: VHPOP Plan-Space Planning Initial plan complete plan for goals

  10. Plan Adaptation • Transformational analogy: transforms an input plan • Derivational analogy: reuses the derivational trace that led to a plan • Therefore requires more knowledge to be provided • Both forms of adaptation have been developed for state-space, plan-space, hierarchical (HTN) planning • All can be subsumed in the Universal Classical Planning framework • Interesting: some authors have proposed using planning graphs during adaptation (is this derivational? Transformational?)

  11. Neo-Classical Planning

  12. P0 A1 P1 Planning Graphs • Planning graphs encode an inclusive disjunction of actions • Since some actions in a disjunction may interfere with one another (mutex), it keeps track of incompatible propositions • Solution extracted via backward chaining in the planning graph • Must consider mutex • Can improve performance • More crucially: used for defining heuristics (FF,…) B A B C C A Clear(C) On(B, table) On(B, C) On(A, B) On(A,table) Clear(B) On(B, A) Clear(A) On(C,table) Move(B,C,table) A Clear(B) On(B, C) Clear(A) On(A, table) On(C,table) B C Move(A,table,B) Move(B,C,A) B C A

  13. Planning as Satisfiability • Encodes the planning problem as a logical formula • For example: • The initial state is represented as: • Applicability of Actions as: • Davis-Putnam procedure: finds truth assignments that make the formula true • Blackbox: encodes the planning graph rather than the planning problem • Trial and error process

  14. State space • V: set of states • E: set of transitions (s, (s,a)) • (s,G): estimates how far is s from achieving G • This estimate is made by constructing the goal graph… • …on a relaxation of the problem: domain with no negative effects • A greedy strategy is selected (pick the one with highest value) after performing breadth-first search Heuristics in Planning C A B C A B C B A B A C B C B A B C C A B A C A A B C A A B C B C C B A A B C

  15. Domain-configurable Planning

  16. State space • V: set of states • E: set of transitions (s, (s,a)) • Uses temporal logic to prune potential actions / states • υ (until), □ (always), ◊ (eventually), ○ (next), GOAL • Example rule: “Don’t move container if position is consistent with goal” • Formula progress(Φ,si) is true in si+1 iff Φ is true in si. Search Control Rules in Planning C A B C A B C B A B A C B C B A B C C A B A C A A B C A A B C B C C B A A B C

  17. Reasoning with Time in Planning • Extends search control rules representation as in TLPlan • After all this representation is based on temporal logics • Example: (def-adl-operator (drive ?t ?l ?l’) (pre (?t) (truck ?t) (?l) (loc ?l) (?l’) (loc ?l’) (at ?t ?l)) (del (at ?t ?l)) (delayed-effect (/ (dist ?l ?l’) (speed ?t) (add (at ?t ?l’)))) • It associates a time stamp with every state • Transformations between states with same time stamp are instantaneous • Crucial: each state has an associated event queue (future updates)

  18. Distinguishes between primitive and non-primitive tasks • Primitive tasks: concrete actions (instances of operators) • Compound task: high-level goals (decomposed by methods) • Operators: standard STRIPS knowledge • Methods: domain-configurable constructs Hierarchical Planning Order in which subtasks are fulfilled Non-primitive task method instance precond Non-primitive task primitive task primitive task operator instance operator instance precond effects precond effects s0 s1 s2

  19. Final Summary • Classical Planning • State-space • Plan-Space • Plan adaptation • Neo Classical planning • Planning graphs • Planning as Satisfiability • Heuristics in Planning • Domain-configurable planners • Search control rules • Reasoning with time • Hierarchical Planning • Complexity of Planning

More Related