UAV 3D FORMATION FLIGHT USING THE RELATIVE STATE SPACE METHOD

Transcription

1 VOL. NO. NOVEMBER 07 ISSN ARPN Joual of Egg ad Appld Sccs Asa Rsach Publshg Ntwok (ARPN). All ghts svd. UAV 3D FORMAION FLIGH USING HE RELAIVE SAE SPACE MEHOD ag Z. Muslmov Rustm A. Muasypov h Isttut fo Aospac chology Ufa Stat Avato chcal Uvsty Russa Fdato E-Mal: tag.muslmov@gmal.com ABSRAC I ths pap th poblm of fxd-wg umad aal vhcls (UAVs) 3D fomato flght was solvd usg th latv stat spac mthod. Usg ths mthod th UAVs fomato bcoms a autoomous dctalzd mult-agt systm sc th systm fuctoal od s gatd by th tacto of ts agts. h soluto was tstd MALAB/Smulk usg full dyamc modls of th vhcls. Kywods: UAV cotol fomato flght goup cotol UAV fomato mult-agt systm dctalzd cotol bo-spd algothm dctalzd systm. INRODUCION O of th pomsg dctos fo th dvlopmt of autoomous umad aal vhcls (UAVs) applcatos s a goup cotol. Flyg fomato.е. pcs holdg of cta spcfd latv postos dug th flght of a goup both mpovs th ffccy of cta typs of mssos ad fo a umb of tasks bcoms a pqust fo th soluto. h xampls clud th localzato of ada [] th ovcomg of my a dfs wth th fals tagts hlp th costucto of ata aays fom UAV [ 3] th wd pofls masumt fo mtoologcal studs [4] automatc fulg th a [5] th cas of usful load o ag by ducg th lft-ducd dag th cas of flght tght fomatos [6] tc. h a sval appoachs to solvg th UAVs fomato flght poblm. h most commo a th followg: Lad-Wgma mthod [7 8] ad a appoach basd o vtual stuctus [9]. h dsadvatags of Lad-Wgma mthod a th absc of fdback fom Wgma vhcls ad ctalzato of th systm whch mas th Lad UAV falu lads to th fomato loss. h appoach basd o th vtual stuctus th ogal vso also dos ot volv fdback fom th cotol objcts ad ado s lagly sstv to xtal dstubacs (fo xampl wd dstubacs) thby losg th accuacy of matag th fomato. I ou atcl th s usd th latv stat spac mthod fo th th-dmsoal fomato UAVs cotol whch s dctalzd cotol of th mult-agt systm fault-tolat th ss that th falu of dvdual agts dos ot lad th to th falu of th t systm o to th ablty to futh buld ad mata th fomato. Each agt has autoomy.. th ablty to cotol pat of th systm s global stat. hs mthod s a bo-spd algothm basd o th modl of lvg ogasms moto uos twok. I compaso wth th Lad-Wgma mthod th latv stat spac appoach volvs th costucto of a cotol hyp sufac th latv stat spac stad of just followg Lad s commads. UAV MODEL Fo th UAVs dyamc modl th a usd two coodat fams: th tal "oth-ast-dow" (NED) wth th dx ad th body fam wth th dx b. UAV coodats a spcfd as follows: p p p p d wh p s th oth coodat of th UAV posto th tal coodat fam; p s th ast UAV posto th tal coodat fam; pd s th UAV coodat alog th axs dctd to th ct of th Eath th tal coodat fam. h otato of th UAV s spcfd usg Eul agls: wh oll agl ptch agl - yaw agl. UAV spd s compots th body fam: v b u v w wh u s th vlocty compot alog th axs dctd to th vhcl s os v s th vlocty compot alog th axs dctd alog th ght vhcl wg w s th vlocty compot alog th axs dctd fom th vhcl bottom top. h agula vlocts b p q otat aoud th body fam axs. h cotol sgals put vcto u a t wh s th lvato dflcto a s th alo dflcto s th udd dflcto t s th thottl dflcto. 638

2 VOL. NO. NOVEMBER 07 ISSN ARPN Joual of Egg ad Appld Sccs Asa Rsach Publshg Ntwok (ARPN). All ghts svd. Lazd quatos of UAVs latal moto th stat spac [0]: a p L L a N N N a N N a 0 cos ta cos ta s ta cos sc p cos sc s sc * * v v p gcos cos 0 v Lv Lp L 0 0 p v p 0 0 * * * * * * * * q * * * * * * * * Lazd quatos of UAVs logtudal moto th stat spac: u * Xu Xw Xq gcos 0 u X X t w * Z s 0 0 u Zw Zq g w Z q M 0 0 q 0 u Mw M q M t * * * * * h s cos 0 u cos ws 0 h 0 0 abl- shows lazd paamts calculatd MALAB fo th Zag UAV. abl-. Lazd paamts fo latal moto v s p m s m s L v m s L p s L s.708 N v m s N p s N s m s a 0 m s s L a 8.64 L s 4.0 N s a N s Lazd paamts fo logtudal moto Xu Xw s s X q ms Z u s Z w s Z q ms.967 M u m s 0.33 M w m s M q s m s X X kg t 8.53 Z ms M s h autoplot of th logtudal ad latal moto of a sgl UAV basd o th succssv loop closu mthod was sythszd. 639

3 VOL. NO. NOVEMBER 07 ISSN ARPN Joual of Egg ad Appld Sccs Asa Rsach Publshg Ntwok (ARPN). All ghts svd. ALGORIHM OF UAVS GROUP CONROL BASED ON HE RELAIVE SAE SPACE MEHOD I th atcls [ ] accodac wth th cocpts of oscllatoy ual twoks of lvg ogasms that gat moto sgals of locomoto th modl of a dctalzd autoomous systm of tactg agts was poposd. Basd o ths appoach w df a goup of autoomous UAVs as a systm of ths typ. W cosd a mult-agt autoomous systm as a gaph wh ach agt s a vtx th gaph ad th tacto s a dg. Lt b th umb of UAVs N s th umb of tactos btw thm - th vcto of cut stats N - vcto of latv stats A s th cdc matx of th gaph. I ths cas th latoshp s dfd as follows: A Lt th dyamc quato of th -th UAV: d f wh s th latv stats of -th -th agts whch dctly tact wth -th f dfftabl fucto. hfo th quato of latv stats dyamcs ca b pstd as follows: d A f. wh f f f h accodac wth [] th followg thom holds: hom. I th latv stat spac th s a pottal fucto f ad oly f th vcto-fucto fs dfd as follows: f f f wh k k f s dyamcs commo to all agts. h th pottal fucto th latv stat spac: f V d. hus th tacto btw subsystms (agts) gats th systm od tslf makg t a ga systm. I ths cas th fal qulbum s th global mmum of th pottal fucto V th latv stat spac. I th vt of a chag th goal o th suoudg stuato ths pottal fucto wll chag ad tactos btw agts wll chag accodgly flctg th w fuctoal od costucto. I ado t should b otd th systm s dctalzd bcaus a supvso s ot qud to mak a fomato sc ach agt ms ts ow bhavo to achv th fal goal dpdg o th agts bhavo tactg wth t. If o of th agts xpcs xtal ptubatos th th oths adjust to t kpg th shap. h cotol statgy fo -th UAV latv to th coodat fam ast axs s as follows: dp p p u j j () jj wh p s th oth coodat of th -th UAV th tal fam j - coffct of tacto btw th -th ad j- th agt J - th st of UAVs tactg wth th -th agt u - cotol acto xpcd by th -th UAV. Smlaly cotol statgs a dfd fo th oth axs of coodats ad alttud: dp dh p p u j j () jj h h u j j h (3) jj wh h pd s th hght of th -th UAV abov sa lvl. h kmatc quatos of th UAV a as follows: p cos cos p vg s cos h s wh v g s th vlocty of th UAV th tal fam s th cous agl btw th vlocty vcto th tal fam ad th oth axs of th sam coodat fam s th flght path agl btw th hozotal pla ad th vlocty vcto th tal fam. hus accodac wth quatos ()-(4) th commad fo th cous agl th aspd v a ad th flght path agl ca b xpssd as follows: (4) 640

4 VOL. NO. NOVEMBER 07 ISSN ARPN Joual of Egg ad Appld Sccs Asa Rsach Publshg Ntwok (ARPN). All ghts svd. u actg u a h v u u u actg uh u u. Cotol vcto U u u fo th ast axs of th tal fam ca b foud fom th followg quato: U B P D wh ˆ d P D B H P cotol vcto of th systm th latv stat spac H s a matx dfd as follows: q q H q q q wh H q P d s th vcto of th dsd latv postos alog th ast axs of th tal fam Pˆ p s th sum of th cut UAV k k coodats th tal fam B m a j j matx obtad fom th tacto matx M whch tu ca b pstd vaous ways dpdg o th typ of tacto btw th agts. Fo xampl fo fou UAVs th cas of "achwth-ach" tacto: 3 3 M. 3 3 I th cas of th tacto "ghbo wth ghbo": M Cotol vctos U ad Uh ca b foud smlaly. HE SIMULAION RESULS Fgu- shows UAVs fomato buldg ad matag. Fgu-. 64

5 VOL. NO. NOVEMBER 07 ISSN ARPN Joual of Egg ad Appld Sccs Asa Rsach Publshg Ntwok (ARPN). All ghts svd. Fgu- shows gaphs of th UAVs latv postos os. fomato flght. IEEE Itatoal cofc o obotcs ad automato (ICRA). pp [6] Btt P. Ayu K.B. Kstc M. Bll F Fomato flght optmzato usg xtmum skg fdback. Joual of gudac cotol ad dyamcs. 6(): 3-4. [7] Paul. Kogstad.R. Gavdahl J Modllg of UAV fomato flght usg 3D pottal fld // Smulato Modllg Pactc ad hoy. 6(9): [8] Pak C. Cho N. L K. Km. 05. Fomato flght of multpl UAVs usg oboad fomato shag. Ssos. 5: Fgu-. CONCLUSIONS hs atcl dscbs th succssful applcato of th latv stat spac mthod fo th costuctg ad matag th UAV fomato. Futh sach wll focus o th algothm optmzato ad mpovmt. REFERENCES [] Sudaam B. Palaswam M. Rddy S. Sckas M Rada localzato wth multpl umad aal vhcls usg suppot vcto gsso. Itllgt ssg ad fomato pocssg. pp [] Chada R.S. Bhy S.H. D Ada R Ata aay sythss wth clusts of umad aal vhcls. Automatca. 44: [9] Bad R.W. Lawto J. Hadagh F A coodato achtctu fo fomato cotol. IEEE tasactos o cotol systms tchology. 9(6): [0] Bad R.W. McLa.W. 0. Small umad acaft: thoy ad pactc. Pcto ad Oxfod: Pcto Uvsty Pss. [] uasa H. Ito M Coodato of may oscllatos ad gato of locomotoy patts. Bologcal Cybtcs. 63(3): [] amaguch H. Aa Dstbutd ad autoomous cotol mthod fo gatg shap of multpl mobl obot goup. IEEE/RSJ/GI Itatoal cofc o tllgt obots ad systms IROS'94. : [3] Gaza J. Paduo M.A. Rya A. Romo G. dl Ro C. 06. Dsg of UAVs-basd 3D ata aays fo a maxmum pfomac tms of dctvty ad SLL. Itatoal Joual of Atas ad Popagato. [4] Coopmas C. Stak B. Js A. Ch.Q. McK M. 05. Cyb-physcal systms abld by small umad aal vhcls. I: K.P. Valavas G.J. Vachtsvaos (Eds.) Hadbook of umad aal vhcls. Dodcht; Hdlbg; Nw ok; Lodo: Spg.pp [5] Wlso D.B. Göktoga A.H. Sukkah S. 05. A vso basd latv avgato famwok fo 64