Visibility Path-finding in relation to Hybrid Strategy-based Models in Distributed Interactive Applications

Visibili y Pa h- inding in ela ion o Hyb id S a egy-based Models in Dis ibu ed In e ac i e Applica ions De mo Madden, Declan Delaney Depa men o Compu e Science, Na ional Uni e si y o I eland, Maynoo h, Co. Kilda e. [email p o ec ed] Séamus McLoone, Tomás Wa d Depa men o Elec onic Enginee ing, Na ional Uni e si y o I eland, Maynoo h, Co. Kilda e. { omas.wa d, seamus.mcloone}@eeng.may.ie Abs ac The hyb id s a egy-based modeling app oach is a me hod o educing he numbe o ne wo k packe s ha need o be ansmi ed o main ain global consis ency in Dis ibu ed In e ac i e Applica ions. I combines a sho - e m model such as dead eckoning wi h a long- e m s a egy model. A key aspec o his app oach is o de e mine s a egies ha use s adop in na iga ing he simula ed en i onmen o sa is y some objec i e o goal. Compu e -gene a ed a i icial en i ies called BOTS, na iga e by employing an A i icial In elligence echnique called pa h inding. This pape p oposes using he A* pa h inding algo i hm o au oma ically compu e s a egies ha human use s migh ake h ough he simula ed en i onmen . Since he A* algo i hm ope a es on a g aph ep esen a ion o he en i onmen and because o he eal- ime cons ain s imposed on Dis ibu ed In e ac i e Applica ions, he pape also ca ies ou a compa a i e analysis o wo ex eme g aph ep esen a ions o he en i onmen – a s anda d egula g id and a minimal g id ep esen a ion. The compa ison shows ha he minimal g id leads o an o de o magni ude educ ion in eal- ime compu a ion compa ed o he egula g id. In addi ion he pa hs compu ed using he minimal g id and he A* algo i hm a e used o de e mine s a egy models as pa o he hyb id s a egy-based modeling app oach. I is shown ha his educes he ne wo k a ic equi ed o main ain global consis ency o en i y dynamics in wo simula ed en i onmen s. 1. In oduc ion Ne wo ked compu e p og ams ha allow use s o in e ac in eal- ime in a simula ed en i onmen a e known as Dis ibu ed In e ac i e Applica ions (DIAs). One o he majo challenges acing he de elopmen and deploymen o DIAs is he main enance o a consis en wo ld iew o all pa icipan s in he ace o ne wo k la ency. Se e al echniques o comba ing la ency ha e been documen ed and implemen ed. Among hese, he hyb id s a egy-based modeling echnique has shown a educ ion in he numbe o packe s ha needs o be ansmi ed ac oss he ne wo k o main ain global consis ency [1]. This echnique ope a es by iden i ying long- e m s a egies ha use s may adop in he pu sui o goals and only communica ing he cu en use s a egy o o he pa icipan s. I is a hyb id app oach in ha i combines a sho - e m dead eckoning model wi h one o se e al possible long- e m s a egy models. One key di icul y wi h his app oach is he au oma ic de e mina ion o possible s a egies use s may adop o achie e a gi en goal. In exis ing DIAs such as compu e games, compu e -gene a ed a i icial en i ies called BOTS, ace he same di icul y – gi en an ini ial loca ion and an objec i e, wha is he bes me hod o adop o each he objec i e while minimizing some cos unc ion? This p oblem is e e ed o as pa h inding [2]. Pa h inding is an essen ial componen o he a i icial in elligence (AI) ha makes BOTs appea mo e like human use s. In DIAs such as ne wo ked games, up o 30% o compu a ional ime is spen on AI compu a ions, p edominan ly pa h inding [3]. Pa h- inding algo i hms consis o wo pa s: 1. he gene a ion o a sea ch g aph ha ep esen s he unde lining en i onmen and 2. an algo i hm ha sea ches he g aph ep esen a ion o ind a pa h connec ing gi en ini ial and a ge loca ions. The g aph ep esen a ion o a simula ed en i onmen ep esen s he en i onmen by a se ies o nodes, wi h pa hs h ough he en i onmen being cons ained o pass om one node o ano he . A minimal se o nodes can be achie ed by using a poin s o isibili y g aph o minimal g id. O he possible ep esen a ions o he en i onmen exis . P obabilis ic oadmaps andomly place nodes on a map, connec ing newly placed nodes o nea by nodes [4]. Na iga ional Meshes spli he simula ed en i onmen in o egions ha a e ee om obs acles, only allowing na iga ion be ween hese egions [5]. Po en ial Field me hods gi e he a ge loca ion an a ac i e o ce and obs acles epulsi e o ces; en i ies hen ollow he po en ial ield o he a ge [6]. O en nodes a e manually placed wi hin he en i onmen o he compu ed nodes a e weaked manually o imp o e he pe o mance o BOTs, as in Un eal Tou namen [7]. Pa h inding algo i hms compu e he pa h h ough he en i onmen unde some cons ain using he node ep esen a ion o he en i onmen . The mos widely used and a guably he bes pa h inding algo i hm used in DIAs is he A* (A s a ) heu is ic sea ch [8], al hough o he s exis such as B ead h- i s sea ch, Dep h- i s sea ch and Dijks a’s algo i hm [9]. The g aph ep esen a ion o he en i onmen used in pa h inding can ake many o ms. Examples include a egula g id, a isibili y g id o a na iga ional mesh. Howe e he e is a dea h o compa a i e esul s be ween a ious g id ep esen a ions and pa h inding algo i hms. The i s pa o his pape p o ides an ini ial con ibu ion o his a ea by compa ing an implemen a ion o he A* pa h inding algo i hm on bo h a isibili y g aph and egula g aph ep esen a ion o a simula ed en i onmen . I is shown ha he isibili y g aph p o ides an o de o magni ude sa ing in compu a ional ime compa ed o he same en i onmen ep esen ed by a egula g id. The pape also p oposes a no el echnique based on he isibili y g aph and A* algo i hm o au oma ically de e mine s a egies use s may adop in na iga ing a simula ed en i onmen . Two sample en i onmen s a e used o illus a e how s a egies can be au oma ically compu ed and da a will be p esen ed o show ha hese s a egies lead o a educ ion in ne wo k packe s compa ed o pu e dead eckoning when used as pa o he hyb id s a egy-based modeling echnique. In he ollowing sec ion we desc ibe he egula -g id and isibili y g aph ep esen a ions o he unde lying en i onmen . Sec ion 3 p esen s a compa a i e analysis o he A* algo i hm using a egula -g aph and a poin s o isibili y o minimal g aph. The applica ion o he A* algo i hm and he minimal g id o he p oblem o compu ing s a egy models in a gi en simula ed en i onmen is desc ibed in sec ion 4 and he esul s o simula ing ne wo k a ic using such a s a egy model is gi en in sec ion 5. The pape hen ends wi h some concluding ema ks and an indica ion o u u e wo k in sec ion 6. 2. G aph Rep esen a ions o he En i onmen In his sec ion wo possible ep esen a ions o he simula ed en i onmen will be desc ibed: a egula sea ch g aph [10] and a minimal g id o isibili y g aph [11]. In gene al hese ep esen a ions a e a opposi e ends o he node spec um, in ha he minimal g id ep esen s he en i onmen by associa ing nodes wi h each obs acle, whe eas he egula g id co e s all a eas o he en i onmen ha a e ee om obs acles wi h nodes. The e o e, he ac ual numbe o nodes in each case is a unc ion o he numbe and size o obs acles wi hin he en i onmen . 2.1 Regula G aph A he simples le el simula ed en i onmen s consis o obs acles ha mus be a oided and obs acle- ee o g ound a eas ha can be eely na iga ed. Figu e 1a shows an en i onmen wi h a single ec angula obs acle. A egula sea ch g aph is o med by o e laying a egula g id o nodes on he g ound a ea. Each node is connec ed o adjacen nodes and an en i y can mo e om he node i cu en ly inds i sel o any node connec ed o ha node. Such a egula g id is illus a ed in Figu e 1b. The absolu e g id spacing o g id spa ial esolu ion is dic a ed by he uni s o measu e wi hin he simula ed en i onmen , each node on he g id being one uni om o he nodes in bo h a ho izon al and e ical di ec ion [10, 12]. Gi en such a g id oge he wi h bo h s a and a ge loca ions, we can hen sea ch o a se o possible pa hs connec ing he s a and a ge nodes. Figu e 1c shows he connec ed g id, while Figu e 1d shows he sho es pa h solu ion linking he s a and a ge nodes. (a) (b) (c) (d) S a a ge obs acle (a) (b) (c) (d) S a a ge obs acle Figu e 1: (a) G ound a ea wi h obs acle; (b) Regula g id; (c) Connec ed egula g id wi h ini ial and a ge nodes; (d) Connec ed g id wi h pa h solu ion. 2.2 Visibili y G aph In he nex sec ion he egula and isibili y g aph ep esen a ion o he en i onmen will be used by he A* pa h inding algo i hm o disco e he sho es pa h h ough an en i onmen . This will p o ide a compa a i e analysis and g ea e unde s anding o he wo ep esen a ions. In con as o a egula g aph, a isibili y g aph loca es he nodes a he e ices o obs acles, o a loca ions ha will accu a ely delimi he obs acle. Each node is hen connec ed o all o he nodes ha a e isible o i . This equi es checking whe he nodes a e in line o sigh o each o he . Figu e 2a shows he en i onmen wi h a squa e obs acle. In Figu e 2b nodes ep esen ing he e ices o he obs acle oge he wi h bo h s a and a ge nodes a e shown. Figu e 2c demons a es some o he pa hs ha migh be aken by an en i y mo ing om he s a o a ge node wi hou going h ough he obs acle. The sho es pa h is indica ed in Figu e 2d. 3. An Analysis o A* using Two g id Types A es pla o m was de eloped o compa e he pe o mance o he A* algo i hm using wo g aph ep esen a ions. This phase o he wo k aimed o unde s and he A* algo i hm and he isibili y g aph ep esen a ion o he en i onmen in mo e de ail and p o ide expe imen al e idence o he cos sa ing achie ed by using he isibili y g aph wi h he A* algo i hm. This p o ided mo i a ion o conside ing pa h inding as a means o au oma ically de e mining possible s a egies wi hin a Dis ibu ed In e ac i e Applica ion. (a) (b) (c) (d) S a a ge (a) (b) (c) (d) S a a ge The A* sea ch algo i hm e alua es each node using he sum o wo cos unc ions. The i s one calcula es he cos o he pa h om he ini ial loca ion o he loca ion being e alua ed. The second unc ion p o ides a heu is ic es ima e o he emaining cos o each he a ge loca ion. The sum o hese p o ides an es ima e o he o al pa h cos h ough he e alua ed node. Du ing each i e a ion o he sea ch, A* e alua es he nodes connec ed o he node wi h he lowes es ima ed pa h cos , expanding he bes node i s [8]. In his example he ini ial and a ge nodes a e connec ed o all o he isible nodes. O he connec ion c i e ia can be used; he ini ial and a ge nodes may be connec ed o he nea es isibili y g aph node, o o he k nea es nodes, o o all isible nodes wi hin a se dis ance. Ob iously he possibili y o a di ec connec ion be ween he ini ial and a ge nodes should be es ed o . Visibili y g aphs hemsel es a e gene a ed o line and i has been shown ha isibili y g aphs can be gene a ed in O(nlogn + E) ime [13], whe e n is he numbe o nodes and E is he numbe o edges in he g aphs. Figu e 2: (a) G ound a ea and obs acle; (b) Visibili y g aph wi h s a and a ge nodes; (c) Connec ed isibili y g aph; (d) Connec ed g aph wi h pa h solu ion. Figu e 3: A sample map wi h andomly gene a ed obs acles and he pa h compu ed using A* o a egula g aph (le ) and a isibili y g aph ( igh ). The de eloped es pla o m gene a es a andom map and c ea es a isibili y g aph and egula g id; he A* algo i hm is applied o hese g id ep esen a ions and he esul s a e displayed oge he o ease o compa ison. In he expe imen s pe o med he e en i onmen s we e andomly gene a ed using a ying numbe s o obs acles; each obs acle measu ed 5 by 5 uni s. An example o such an en i onmen is gi en in Figu e 3. A egula g id and isibili y g aph we e hen c ea ed o each en i onmen and he es s we e ca ied ou . The pe o mance o he A* algo i hm using each g id was compu ed by exploi ing he high esolu ion ha dwa e coun e , which is suppo ed by Mic oso Visual C++ 2003. This coun e had a equency o 3,579,545 coun s pe second on he es pla o m employed (AMD A hlon XP 2600+ wi h 512MB RAM). The ac ual coun s we e no ans o med in o absolu e ime alues as again we a e only in e es ed in a ela i e compa ison. A se ies o expe imen s was pe o med o de e mine he compu a ion ime using bo h g aphs as he numbe o obs acles in he en i onmen was inc eased om 0 o 140 on a map size o 50 by 50 uni s. In each case, 1000 andom maps wi h andom obs acles and andom s a / a ge posi ions we e gene a ed and he a e age ime coun o A* o inish i s sea ch was measu ed. Figu e 4 illus a es he compu a ion ime as a unc ion o he numbe o obs acles. When he e a e 100 obs acles in he en i onmen a sea ch using he isibili y g id is calcula ed in 10% o he ime equi ed by he egula g id, demons a ing ha he isibili y g aph is as e by 90%. Howe e as he numbe o obs acles inc eases wo e ec s a e no iced: (1) he e is an inc ease in he sea ch imes o bo h ep esen a ions and (2) he isibili y g id ge s p og essi ely slowe in compa ison o he egula g id. These wo e ec s may be explained as ollows. Fo he egula g id, an inc ease in he numbe o obs acles means a educ ion in he numbe o nodes and connec ions as mo e g ound space is aken up wi h obs acles. Howe e , he e is also mo e ime was ed in compu ing dead end pa hs. Fo he isibili y g aph, an inc ease in obs acles esul s in an inc ease in he numbe o nodes and connec ions wi h he numbe o connec ions being O(m2), whe e m is he numbe o nodes. Despi e his, e en wi h 140 obs acles, he isibili y g aph is 80% as e . The expe imen s pe o med indica e ha he A* pa h inding algo i hm pe o ms signi ican ly be e using a isibili y g aph han a egula g aph. Cu en ly pa h inding is only used by compu e -gene a ed cha ac e s na iga ing in he en i onmen . We use pa h inding o au oma ically gene a e s a egies ha human use s may adop in na iga ing he en i onmen . These s a egies can be used in he hyb id s a egy-based model echnique. These issues a e de eloped in he ollowing sec ion. 4. S a egy Models using Visibili y g aphs Mo i a ed by he e iciency o he pa h inding algo i hm using a isibili y g aph ep esen a ion and he ac ha pa h inding is used by compu e gene a ed cha ac e s, i was decided o use pa h inding o compu e possible s a egies ha human use s migh choose when na iga ing an en i onmen . Regula G id Visibili y G aph Regula G id Visibili y G aph The hyb id s a egy-based modeling app oach educes he numbe o upda e packe s ha need o be communica ed be ween pa icipan s o a DIA o main ain global consis ency wi hin a easonable e o h eshold. The hyb id model consis s o a sho - e m dead eckoning model and a leas one long- e m s a egy model. To educe he numbe o packe s ha need o be ansmi ed, he local use ansmi s in o ma ion o in o m o he use s o he model ha bes ep esen s hei cu en ac i i y. Remo e use s main ain his model un il he local use decides a change is needed based on some h eshold c i e ia, in his case an e o ole ance alue. Because he long- e m s a egy model may ep esen a pa h o any o m, i can be communica ed using a single packe in con as o a dead eckoning ep esen a ion o he same pa h, which may equi e se e al packe s. In p e ious wo k s a egies we e chosen by isually selec ing he mos ep esen a i e use s eady-s a e ajec o y [1, 14]. He e he s a egies a e compu ed au oma ically using he A* algo i hm and isibili y g aphs. Two es en i onmen s we e cons uc ed and s a egies o he goal o na iga ing om a s a o an end loca ion in he sho es ime possible we e compu ed using A* and isibili y g aphs; en i onmen s 1 and 2 a e shown in Figu es 5 and 6 espec i ely. Figu e 4: The ime spen by A* o ind a pa h using he isibili y g aph and he egula g id, as he numbe o obs acles was inc eased on 50 by 50 maps wi h andom obs acle posi ions. By smoo hing he pa hs he s a egies can be made o ma ch ac ual use mo emen mo e ealis ically. Figu e 7 shows he smoo hed pa hs o bo h en i onmen s a e applying a s anda d smoo hing algo i hm ha akes en i y dynamics in o accoun [2]. These smoo hed pa hs became he s a egies ha we e used o simula e he gene a ion o ne wo k packe s as pa o he hyb id s a egy model. This simula ion is desc ibed in he ollowing sec ion. Figu e 5: (a) Use en i onmen 1 (b) pa h gene a ed au oma ically by A* algo i hm. s a End (a) (b) s a End s a End (a) (b) En i onmen 1 X coo dina e Y coo dina e En i onmen 2 X coo dina e Y coo dina e (a) (b) En i onmen 1 X coo dina e Y coo dina e En i onmen 1 X coo dina e Y coo dina e En i onmen 2 X coo dina e Y coo dina e En i onmen 2 X coo dina e Y coo dina e (a) (b) Figu e 6: (a) Use en i onmen 2 (b) pa h gene a ed au oma ically by A* algo i hm. s a End (a) (b) s a End s a End (a) (b) Figu e 7: A ealis ic u ns ou ine was added o c ea e mo e ealis ic s a egies, indica ed by he solid line. The dashed line shows he s a egy ound b y pa h inding o (a) en i onmen 1 and (b) en i onmen 2. 5. Simula ion Resul s Use da a was ga he ed om ou een dis inc use s. Each o hese use s maneu e ed an en i y h ough a maze om a gi en s a posi ion o a gi en a ge loca ion. Use s had no p io knowledge o he maze and we e es ic ed o iewing a ci cula a ea o he maze cen e ed on hei cu en loca ion a any poin in ime. Use s epea ed he ask o a eling om he s a o he a ge node in he sho es ime possible. Wi h each a emp hei knowledge o he maze inc eased un il hey con e ged on a s eady-s a e ajec o y. To de e mine he numbe o packe s ha would ha e o be sen o e he ne wo k o ep esen a use ajec o y a simula ion was pe o med which ook he ajec o y as inpu and hen simula ed he numbe o packe s gene a ed in h ee cases: 1. using a pu e dead eckoning model only; 2. using a hyb id s a egy model wi h he s a egy chosen by isual analysis o he use s eady-s a e ajec o ies; 3. using a hyb id s a egy model wi h he s a egy compu ed au oma ically using he A* pa h inding algo i hm and he isibili y g aph as desc ibed ea lie . Use 1 Use 2 Hyb id Hyb id Seq DR Visual Pa h inding DR Visual Pa h inding 1 31 32 33 16 13 17 2 26 27 27 22 16 19 3 18 15 11 28 28 29 4 8 3 4 15 1 5 5 10 7 5 18 9 17 6 14 4 7 13 8 8 7 13 13 9 13 5 12 8 8 4 7 10 4 1 Use 1 Use 2 Hyb id Hyb id Seq DR Visual Pa h inding DR Visual Pa h inding 1 35 42 36 52 44 51 2 38 32 34 25 23 24 3 22 6 9 34 23 26 4 18 3 3 21 4 10 5 16 6 3 24 20 21 6 20 3 3 18 7 11 The esul s o he simula ions a e p esen ed in Tables 1 and 2 o en i onmen 1 and en i onmen 2 espec i ely. Examina ion o hese esul s shows ha he e is a educ ion in he numbe o packe s ha need o be ansmi ed using he hyb id s a egy-based model app oach. In addi ion, he e is e y li le disc epancy be ween he numbe o packe s ansmi ed using a s a egy cons uc ed om isual analysis o eco ded use ajec o ies and a s a egy cons uc ed au oma ically using pa h inding. Two sample ajec o ies a e illus a ed in Figu e 8 o use 1 na iga ing h ough en i onmen 2. As hei expe ience wi hin he maze inc eases hei ajec o y con e ges o he s eady-s a e s a egy iden i ied using pa h inding. I mus be no ed ha he esul s p esen ed a e o a h eshold o 25 uni s. This choice was based on he a iance o he eco ded use s eady-s a e ajec o ies. Resul s o a lowe h eshold alue ha e been p esen ed elsewhe e [1, 2]. (a) (b) (a) (b) Table 1: En i onmen 1: packe s ansmi ed o pu e dead eckoning and he hyb id me hod; s a eg y model chosen by isual analysis and pa h inding. T ial 1 is he ini ial ial. Th eshold alue: 25. Table 2: En i onmen 2: packe s ansmi ed o bo h pu e dead eckoning and he hyb id me hod; s a eg y model chosen by isual analysis and pa h inding. T ial 1 is he ini ial ial. Th eshold alue: 25. Figu e 8: Use 1 na iga ing in en i onmen 2 – (a) i s ajec o y - explo a o y; (b) inal ajec o y - s eady-s a e. The s a egy model (solid line), pa h inding model (dashed) line and use ajec o y (wide line o ci cles) a e shown. I all ials o he wo use s in bo h en i onmen s a e conside ed, dead eckoning gene a es 596 packe s. In compa ison he hyb id echnique (employing a isual model) gene a es 402 packe s and he hyb id model (employing a pa h inding model) gene a es 438 packe s. This co esponds o educ ions o 33% o he isual heu is ic Hyb id model, and 25% o he pa h inding Hyb id model. The esul s show ha he educ ion in he numbe o gene a ed packe s compa ed o dead eckoning is simila o s a egies cons uc ed ei he isually o using pa h inding. The key di e ence be ween he wo is ha he pa h inding s a egy is gene a ed au oma ically. 6. Conclusions and Fu u e Wo k I has been shown ha isibili y g aphs educe pa h inding compu a ion ime by be ween 80 and 90%, depending on he numbe and he densi y o obs acles in he simula ed en i onmen . The isibili y g aph is also insensi i e o map size, unlike he egula g id, which makes i sui able o la ge i ual en i onmen s wi h ew obs acles. The A* pa h inding algo i hm was implemen ed on a isibili y g aph and used o au oma ically gene a e s a egy models. These we e used in he hyb id s a egy-based modeling app oach and showed a educ ion in he numbe o packe s needed o main ain global DIA consis ency. The educ ion was commensu a e wi h p e ious wo k using heu is ic echniques o de ining s a egies. The ad an age o au oma ic iden i ica ion o s a egies using A* and isibili y g aphs is wo old: 1. by educing he numbe o packe s ha need o be ansmi ed ne wo k la ency is educed, as packe s only need o be sen when he s a egy changes; i communica ion is los o a longe pe iod o ime, emo e use s can be ende ed locally as con inuing on he s a egy hey we e on be o e ne wo k connec ion was los ; 2. in he case o dynamic goals, i is p oposed ha s a egies o sa is y he goal can be ecompu ed in eal ime. Fu u e wo k will ocus on using pa h inding echniques o de e mine s a egies on he ly o dynamic goals. This will wo k by p e-compu ing he isibili y g id o all use s and hen employing he A* algo i hm o sea ch in eal ime o a pa h be ween a cu en posi ion and a dynamic a ge posi ion. The pa h inding implemen a ion will be modi ied o use He shbe ge and Su i's me hods, which p o ides a sho es pa h in O(nlogn) ime [15]. Acknowledgemen This ma e ial is based upon wo ks suppo ed by En e p ise I eland unde g an no. SC/2002/129/. Re e ences [1] Delaney, D., T. Wa d, and S. Mc Loone. On Reducing En i y S a e Upda e Packe s in Dis ibu ed In e ac i e Simula ions using a Hyb id Model. in P oceeding o he 21s IASTED In e na ional Mul i-con e ence on Applied In o ma ics, Feb ua y 10-13. 2003. Innsb uck, Aus ia. [2] Pin e , M., Towa d mo e ealis ic Pa h inding. Game De elope , 2001: p. 54-64. [3] Woodcock, S., Game AI: The S a e o he Indus y 2000-2001: I ’s No Jus A , I ’s Enginee ing. Game De elope , Augus 2001. [4] Ka aki, L.E., e al., P obabilis ic Roadmaps o Pa h inding in High-Dimensional Space. 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