A Cell Decomposition Approach to Online Evasive Path Planning and the Video Game Ms. Pac-Man

Transcription

1 Cell Decomoson roach o Onlne Evasve Pah Plannng and he Vdeo ame Ms. Pac-Man reg Foderaro Vram Raju Slva Ferrar Laboraory for Inellgen Sysems and Conrols LISC Dearmen of Mechancal Engneerng and Maerals Scence Due Unversy MSC 2 Denver Colorado 9/28/

2 Inroducon and Movaon Ms. Pac-Man s a challengng benchmar roblem n he ursuevason famly of games. lgorhms are relevan o real-world alcaons such as roboc ah lannng moble sensor newors and ah eosure. The bes aroaches for solvng hs ye of roblem onlne erform oorly comared o a human. 2

3 Bacground The layer s man goal n Ms. Pac-Man s o acheve he hghes ossble score by earnng ons for eang ravelng over dos and oher objecs. Pac-man mus navgae hrough a maze o reach all dos whle evadng four ursung ghos adversares. level s cleared when all dos have been eaen. The game connues n a new more dffcul maze wh faser ghoss. When a ghos s able o cach Pac-man he layer loses one of hree lves. The game ends when he layer runs ou of lves. The focus of hs research so far has been o develo an arfcal layer ha s caable of lannng omal rajecores for Pac-man o evade he ghoss and ea dos. 3

4 Summary of Mehodology Consruc accurae model of game Decomose worsace no cells Use cell ma o consruc connecvy grah Ulze connecvy grah as decson ree Evaluae values assocaed wh branches Choose he decson corresondng o he branch wh hghes value 4

5 ame Model Pac-Man s sae and conrol are reresened by he 2 vecors [ ] T [ ] u u u T y where and y are Pac-Man s and y coordnaes n els. Pac-Man s conrols u and u y sgnfy he aemed movemen n he and y drecons resecvely. The ghoss saes and conrols I and u I are defned dencally where I I I r b o denoe he ghoss nde se. { } Pac-Man and he ghoss are lmed o bdreconal movemen along sragh ahs so a se of admssble acons U[ ] U s defned where U [ a a2 a3 a4] u lef down rgh y 5

6 6 hos Behavor Models any me durng he game each ghos has a arge oson: Red ghos arges Pac-man Pn ghos arges n fron of Pac-man reen ghos arges reflecon of red ghos across Pac-man Orange ghos arges Pac-man when far away boom lef corner when close T r T a u for d + [ ] 2 r R T b [ ] T d c for c for o o B T o > e R + [ ] T e 6 6

7 hos Behavor Models Red ghos arges Pac-man r T 7 *Images couresy of: Jamey Pman

8 8 hos Behavor Models Pn ghos arges n fron of Pac-man T a u for d [ ] T d where *Images couresy of: Jamey Pman

9 9 hos Behavor Models Lgh blue ghos arges reflecon of red ghos across Pac-man [ ] 2 r R T b e R + [ ] T e where *Images couresy of: Jamey Pman

10 hos Behavor Models Targes Pac-man when Eucldean dsance o Pac-man s above a hreshold and arges boom-lef corner of maze oherwse c for c for o o B T o > Orange ghos *Images couresy of: Jamey Pman

11 hos Behavor Models ll ghoss use he same algorhm o move o her arge locaons: Loos a horzonal and vercal dsances from he ghos o s arge. Tres o choose acon ha wll reduce he larger of he wo. If no ossble res o reduce he smaller dsance. If ha s no ossble chooses frs ossble acon from an ordered ls of admssble acons.

12 2 P I Py I y Py I y P I B Py I y P I P I Py I y C I y Py I P D ] [ ] [ {} ] [ ] [ } sgn{ } { ] [ } sgn{ } { j j j U a U a for U a U a U a for D C H a U a for D B H a u ll ghoss use he same algorhm o move o her arge locaons: Where hos Behavor Models

13 Model Verfcaon Comarson of Trajecores of Smulaed ghoss and ghoss from real game 3

14 Cell Decomoson The worsace was decomosed no cells such ha a se of admssble acons s assocaed wh each cell. 4

15 Connecvy rah and Decson Tree The cells are maed o creae a connecvy grah whch s hen used o generae a decson ree wh Pac-man s curren cell as he roo. 5

16 Conrol Law: Objecve Funcon and Conrol Law each mese choose he acon corresondng o branch wh he hghes value Where F F [ ] α J L[ u ] L [ u ] wv V[ u ] + wrr[ u ] [ ] R[ u ] ρ I 2 V: number of dos n corresondng cell when Pac-man wll vs w V w R : weghng consans α: dscoun facor : Manhaan norm 6

17 Smulaons aral reroducon of he game was consruced n C# usng he maze ma from he frs level derved ghos models and nown game mechancs. Some feaures such as ower lls and fru were omed o focus on he objecves of evadng he ghoss and eang dos. The ghos seeds were se as ercenages of Pac-man s seed rangng from 9% o 5%. Each run begns wh 22 dos o be eaen and ends when eher Pac-man has been caugh by he ghoss or all of he dos are eaen. The erformance was comared o ha of wo novce human layers usng a eyboard nu o he modfed game. 7

18 Resuls The smulaon was run 2 mes for each ghos seed confguraon. In he real game he ghos seeds on he s and 5 h maze are aromaely 93% and 96% of Pac-man s seed resecvely. 8

19 Resuls 9

20 Conclusons and Fuure Wor Develoed an aroach for omzng ahs onlne for he ursu-evason roblem seen n he game Ms. Pac-man. Consruced accurae model of game and adversary behavor. Decomosed worsace no cells and consruced decson ree. Evaluae values assocaed wh branches and choose omal decsons corresondng o he branches wh he hghes values. The resened mehod ouerformed human layers n a smlfed reroducon of he game. Fuure Wor Comlee nerface wh real game. Incororae ursu of ghoss. 2

21 Quesons? 2