1 / 9

GraphPlan

GraphPlan. (you don't have to know anything about this, but I put it here to point out that there are many clever approaches to try to find plans more efficiently; another would be OBDD, ordered binary decision diagrams). SatPlan. Encode as propositional Sat Add time index

adonica
Download Presentation

GraphPlan

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. GraphPlan • (you don't have to know anything about this, but I put it here to point out that there are many clever approaches to try to find plans more efficiently; another would be OBDD, ordered binary decision diagrams)

  2. SatPlan • Encode as propositional Sat • Add time index • At(p1,SFO)0&At(p2,JFK)0 • Axioms: one for each plane X city X time • Actions: Fly(p1,SFO,JFK)1, Fly(p1,JFK,SFO)1, Fly(p1,JFK)2... • Guess a time and assert goal • at(p1,JFK)t&at(p2,SFO)t • Try for t=0..Tmax • Use DPLL to find a model • Look at truth values for actions Pre-cond axioms: Effect/successor-state axioms: Exclusion axioms: -Fly(p1,JFK,SFO)0 v -Fly(p1,JFK,LAX)0 one destination at a time -Fly(p1,a,b)0 v -Fly(p2,c,d)0 one at a time? Is satisfiable if...

  3. Scheduling • Find plan that minimizes total time • Assume each operator has a known duration • Strategy • Construct partial-order plan first • Then find an optimal linearization • CPM – critical path method • identify max-duration sub-sequence; schedule actions without any delay/slack • More difficult with resource constraints • e.g. 1 drill press in shop, 1 inspector, 1 data-bus

  4. CPM • ES: earliest start time, LS: latest start time, slack = LS-ES • Forward pass: ES(B)=max(A<B) ES(A)+duration(A) • Backward pass: LS(A)=min(A<B) LS(B)-duration(A)

  5. Hierarchical Task Networks • Plan libraries • Make pizza={roll dough,apply sauce,add toppings,put in oven} • Standard operation procedures, alternative methods • Abstraction (leave out pre-conditions) • Example: fly to destination city, take “transport” to hotel, expand it later • Opportunities for interleaving/sharing? • Example: building a house • Can use POP to expand nodes in graph with sub-graphs

  6. Conditional Planning • non-determinism – actions that could fail; external events could change state of world • uncertainty, partial observability • can’t see in rooms not yet visited (e.g. Wumpus) • don’t know what resources will be available, or used • approaches • build “robust” plans that will work regardless • use sensors and conditional/contingent actions • keep chopping tree “until it falls” • effect of sensing action is to change “belief state” • use probabilities to find plan most likely to succeed • Markov Decision Problems (MDP’s) • maximize reward accumulated over time, subject to probability distribution over successor states

  7. Plan Monitoring and Repair • Non-determinism: what if actions fail, or unanticipated external events happen? • Check pre-conds of each step • If not sat, re-plan from new current state to goal? • Make plan to get back to nearest state in original plan? • Serenditiy – check pre-conds of every step • Futility – re-executing same action might not help (e.g. Prometheus)

  8. Additional topics • Plan optimization - Goal is not only to find any plan, but to find one that minimizes cost, probability of success... • Dealing with uncertainty • Probability, Markov Decision Problems, reward • Partial observability – keep track of belief states • Multi-agent planning – e.g. 2 cooperating agents in BlocksWorld • Reactive planning – build a state/action table (quick rules to eval) to handle all situations and lead to goal

More Related