Outline. Single-Player Games = Planning. Planning under incomplete information. Planning. COMP s1. Michael Thielscher, Michael Genesereth 2011

Transcription

1 Plannin Outline 1 Sinle-Player Gaes = Plannin Plannin uner incoplete inforation

2 Plannin Sinle-Player Gaes 2

3 Plannin 3 A (Very) Siple Plannin Proble Pressin button a toles p. Pressin button b interchanes p an q. Initially, p an q are off. Goal: p an q are on.

4 Plannin 4 Proble Specification role(robot) Leality leal(robot,a) leal(robot,b) Upate next(p) <= oes(robot,a) true(p) oes(robot,b) true(q) next(q) <= oes(robot,a) true(q) Terination an Goal oes(robot,b) true(p) terinal <= true(p) true(q) oal(robot,100) <= true(p) true(q)

5 Plannin State Transition Syste 5 Features: Actions: p, q a, b b p, q p, q b a a a a p, q b b p, q

6 Plannin 6 Solvin Sinle-Player Gaes = Plannin Initial state {} Actions a b Goal p q Preconitions: none Effects: toles truth-value of p Preconitions: none Effects: interchanes truth-values of p an q Solution (= Plan): a, b, a

7 Plannin 7 Sinle-Player Gaes with Coplete Inforation Many sinle-player aes can be solve usin stanar search techniques introuce earlier in this course Iterative eepenin Biirectional search Special techniques Constraint solvin (suitable for Suoku, Gene Sequencin an the like) Answer set prorain (suitable for Pe Jupin, 15-Puzzle an the like) Infore search uses heuristic functions. In eneral ae playin, the rules are not known in avance an heuristics ust be constructe autoatically. More on this a little later.

8 Plannin 8 Plannin Uner Incoplete Inforation: Maze Worl a? b c Initial State: ac (robot in a, ol in c)

9 Plannin Environent Moel 9 ca a cb b ba aa ab ai i ci i = "in han" c cc c b a ac

10 Plannin Aent Actions 10,, ca a,, ba c b aa a ai i,, cb b ci cc ab c ac,,,,,, = "ove clockwise" = "rab" = "rop"

11 Plannin Aent Percepts 11,, ca a,, ba c b aa a ai i,, cb b ci cc ab c ac,,,,,, sees ol oesn't see ol

12 Plannin Initial State an Goal 12,, ca a,, ba c b aa a ai i,, cb b ci cc ab c ac,,,,,,

13 Plannin Plannin 13 Plannin is the process of finin a transition iara for our aent that causes its environent to o fro any initial state to a oal state. s1 s2 s3 s4 s5 s6 s7 Plannin can be one offline an the resultin plan/prora installe in the aent or the plannin can be one online followe by execution.

14 Plannin 14,, ca a,, ba c b State Space Plannin aa a ai i,, cb b ci cc ab c ac,,,,,,

15 Plannin 15 Incopleteness Possible sources of incopleteness: Partial knowlee of Initial state Transition iara for environent Goal Coplete Plannin Techniques uner incoplete inforation Coercion (e.. o the rab action at all locations) Conitional plan (e.. if see the ol rab it; else ove) Postponeent Techniques Delaye plannin

16 Plannin 16 Initial State Uncertainty,, ca a,, ba c b aa a ai i,, cb b ci cc ab c ac,,,,,,

17 Plannin 17 Sequential State Set Proression b rab ove b rop b ci cb cc c

18 Plannin 18 Sequential State Set Plan aa ab ac a ove ba b rab ba b ove ca ci cc c rab ca ci c ove a i rab a i ove aa ai rop aa

19 Plannin 19,, ca a,, ba c b Plan Execution aa a ai i,, cb b ci cc ab c ac,,,,,,

20 Plannin 20 Conitional State Set Proression 1 b ci cb 0 b cc c

21 Plannin 21 Conitional State Set Plan 0/ 1/ 1/ 0/ 0/

22 Plannin 22 Coparison Sequential plan possible that no plan exists plan ay contain reunant oves Conitional plan lare search space Delaye plannin irreversility probleatic As we can see fro this analysis, it is soeties esirable for an aent to o only a portion of its plannin up front, secure in the knowlee that it can o ore later as necessary. Plannin can be one offline an the resultin plan/prora execute urin play or the plannin can be one online an interleave with execution.