Planning: Regression Planning

Transcription

1 Planning: CPSC 322 Lecture 16 February 8, 2006 Textbook 11.2 Planning: CPSC 322 Lecture 16, Slide 1

2 Lecture Overview Recap Planning: CPSC 322 Lecture 16, Slide 2

3 Forward Planning Idea: search in the state-space graph. The nodes represent the states The arcs correspond to the actions: The arcs from a state s represent all of the actions that are legal in state s. A plan is a path from the state representing the initial state to a state that satisfies the goal. Planning: CPSC 322 Lecture 16, Slide 3

4 Example state-space graph Actions mc: move clockwise mac: move anticlockwise cs,rhc,swc,mw,rhm nm nm: no move puc puc: pick up coffee mc mac dc: deliver coffee pum: pick up mail dm: deliver mail cs,rhc,swc,mw,rhm mc off,rhc,swc,mw,rhm mc mr,rhc,swc,mw,rhm mac off,rhc,swc,mw,rhm mac lab,rhc,swc,mw,rhm cs,rhc,swc,mw,rhm dc cs,rhc,swc,mw,rhm mc off,rhc,swc,mw,rhm mr,rhc,swc,mw,rhm mac mr,rhc,swc,mw,rhm Locations: cs: coffee shop off: office lab: laboratory mr: mail room Feature values rhc: robot has coffee swc: Sam wants coffee mw: mail waiting rhm: robot has mail Planning: CPSC 322 Lecture 16, Slide 4

5 Improving Search Efficiency Forward search can use domain-specific knowledge specified as: a heuristic function that estimates the number of steps to the goal domain-specific pruning of neighbors: don t go to the coffee shop unless Sam wants coffee is part of the goal and Rob doesn t have coffee don t pick-up coffee unless Sam wants coffee unless the goal involves time constraints, don t do the no move action. Planning: CPSC 322 Lecture 16, Slide 5

6 Lecture Overview Recap Planning: CPSC 322 Lecture 16, Slide 6

7 Idea: search backwards from the goal description: nodes correspond to subgoals, and arcs to actions. Nodes are propositions: partial assignments to state variables Start node: the goal condition Arcs correspond to actions A node that neighbours N via arc A is a variable assignment that specifies what must be true immediately before A so that N is true immediately after. The goal test is true if N is a proposition that is true of the initial state. Planning: CPSC 322 Lecture 16, Slide 7

8 Defining nodes and arcs A node N is a partial assignment of values to variables: [X 1 = v 1,..., X n = v n ] An action which can be taken to this node is one that achieves one of the X i = v i, and does not achieve any X j = v j where v j is different from v j. Any node that neighbours N via arc A must contain: The prerequisites of action A All of the elements of N that were not achieved by A N must be consistent. Planning: CPSC 322 Lecture 16, Slide 8

9 Formalizing arcs using STRIPS notation If we re currently at a node [X 1 = v 1,..., X n = v n ] then an arc labeled A exists to another node N if There exists some i for which X i = v i is on the effects list of action A For all j, X j = v j is not on the effects list for A, where v j v j N is preconditions(a) {X k = v k : X k = v k / effects(a)} and N is consistent in that it does not assign multiple values to any one variable. Planning: CPSC 322 Lecture 16, Slide 9

10 Regression example Actions mc: move clockwise mac: move anticlockwise nm: no move puc: pick up coffee dc: deliver coffee pum: pick up mail mc dm: deliver mail [cs,rhc] [mr,rhc] mc puc [cs] [swc] dc [off,rhc] mac [off,rhc] Locations: cs: coffee shop off: office Feature values lab: laboratory rhc: robot has coffee mr: mail room swc: Sam wants coffee mw: mail waiting mac rhm: robot has mail [lab,rhc] mc [off,rhc] mac [mr,rhc] Planning: CPSC 322 Lecture 16, Slide 10

11 Find the errors (none involve room locations) mc [swc,rhc,mw] pum dc puc [swc,rhc,off] [off,rhc,mw] [swc,cs,mw] mc dm puc [cs,rhc, mw] [off,rhc, rhm,mw] [swc,rhc,cs] Locations: cs: coffee shop off: office lab: laboratory mr: mail room [swc,cs,mw] Feature values rhc: robot has coffee swc: Sam wants coffee mw: mail waiting rhm: robot has mail Actions mc: move clockwise mac: move anticlockwise nm: no move puc: pick up coffee dc: deliver coffee pum: pick up mail dm: deliver mail Planning: CPSC 322 Lecture 16, Slide 11

12 Loop detection and multiple-path pruning Goal G 1 is simpler than goal G 2 if G 1 is a subset of G 2. It is easier to solve [cs] than [cs, rhc]. Loop detection: if during the search we encounter a node N, but one of its ancestors N is the same or simpler, you can prune N. Multiple path pruning: if during the search we encounter a node N, but elsewhere in the search tree (not as a descendent of N) we have encountered a node N which is the same or simpler, you can prune N. Planning: CPSC 322 Lecture 16, Slide 12

13 Improving Efficiency You can define a heuristic function that estimates how difficult it is to solve the goal from the initial state. You can use domain-specific knowledge to remove impossible goals. E.g., it may not be obvious from the action description that the agent can only hold one item at any time. Planning: CPSC 322 Lecture 16, Slide 13

14 Comparing forward and regression planners Which is more efficient depends on: The branching factor How good the heuristics are Forward planning is unconstrained by the goal (except as a source of heuristics). Regression planning is unconstrained by the initial state (except as a source of heuristics) Planning: CPSC 322 Lecture 16, Slide 14