Gyroscope based control and stabilization of unmanned aerial mini vehicle (mini UAV)

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1 Ti atile a dnladed by: [ ] On: 03 Setembe 05, At: 4:9 Publie: Tayl & Fani Infma Ltd Regiteed in England and Wale Regiteed Numbe: Regiteed ffie: 5 Hik Plae, Lndn, SWP WG Aviatin Publiatin detail, inluding intutin f aut and ubitin infmatin: tt://.tandfnline.m/li/tavi0 Gye baed ntl and tabilizatin f unmanned aeial mini veile (mini UA) R. Caty a & Z. Kuba b a Kiele Univeity f Tenlgy (KUT), Al.000 leia P.P. 7, 5 34, Pland b Kiele Univeity f Tenlgy (KUT), Al.000 leia P.P. 7, 5 34, Pland Publied nline: 4 Ot 00. T ite ti atile: R. Caty & Z. Kuba (005) Gye baed ntl and tabilizatin f unmanned aeial mini veile (mini UA), Aviatin, 9:, 0-6 T link t ti atile: tt://dx.di.g/0.080/ PLEASE SCROLL DOWN FOR ARTICLE Tayl & Fani make evey efft t enue te auay f all te infmatin (te Cntent ) ntained in te ubliatin n u latfm. Heve, Tayl & Fani, u agent, and u lien make n eeentatin aantie ateve a t te auay, mletene, uitability f any ue f te Cntent. Any inin and vie exeed in ti ubliatin ae te inin and vie f te aut, and ae nt te vie f ended by Tayl & Fani. Te auay f te Cntent uld nt be elied un and uld be indeendently veified it imay ue f infmatin. Tayl and Fani all nt be liable f any le, atin, laim, eeding, demand, t, exene, damage, and te liabilitie ateve eve aued aiing dietly indietly in nnetin it, in elatin t aiing ut f te ue f te Cntent. Ti atile may be ued f eea, teaing, and ivate tudy ue. Any ubtantial ytemati edutin, editibutin, eelling, lan, ub-liening, ytemati uly, ditibutin in any fm t anyne i exely fbidden. Tem & Cnditin f ae and ue an be fund at tt://.tandfnline.m/age/tem-and-nditin

2 ISSN AIATION, l IX, N, 005 PROCEEDINGS OF THE SIXTH INTERNATIONAL SEINAR ON Reent Reea and Deign Pge in Aenautial Engineeing and it Influene n Eduatin Riga, Latvia GYROSCOPE-BASED CONTROL AND STABILIZATION OF UNANNED AERIAL INI-EHICLE (INI-UA) R. Caty, Z. Kuba Kiele Univeity f Tenlgy (KUT), Al.000-leia P.P. 7, 5-34, Pland. Reeived , aeted Dnladed by [ ] at 4:9 03 Setembe 05 Rafał CHATYS a bn in 970 in Kiele (Pland). In 989 e tated a mate-level ue at te Faulty f eanial Engineeing, te Riga Intitute f Civil Aviatin Enginee (RICAE), mleting it in 994. He a aaded a dt degee in 998 by te Cai f te Stutue and Stengt f Aeial eile, Riga Aviatin Univeity (fmely RICAE). N e k a an aitant fe at te Cai f etallgay and ateial Siene at te Kiele Univeity f Tenlgy. He i nened it te blem f meani f mite mateial and metd f feating fatigue etie f lyme mite. He i te aut -aut f ve 58 k ublied in natinal and feign feinal junal. Zbignie KORUBA a bn in 957 intzebnia (Pland). In 98, e gaduated fm te Kiev Intitute f Civil Aviatin Enginee (KICAE) it a ate f eanial Engineeing it nu. He btained i dt degee in 990 at te Cai f Teetial eani at KIILC. He a aaded te tatu f a abilitated dt in 00 at te ilitay Tenial Aademy in Waa. N e k a a fe at te Cai f eile and eanial Equiment at Kiele Univeity f Tenlgy (Pland). He deal it te blem f dynami, ntl, and ming f aeial veile. He a itten me tan 80 ae, (30 a a -aut) ublied in natinal and feign feinal junal, mnga, and bk f univeity tudent. Abtat. Ti k diue te ue f a mini gye it tee degee f feedm t ntl emte ntl an unmanned aeial mini-veile (mini-ua). Te gye detemine te efeene ytem f te navigatin f te UA. Te algitm f te gye ntl mment and te la f defletin f te UA ufae ntl ae eented. Te mini autilt lay a le f a ytem tat make te lngitudinal line inide it te gye axi. Te tutue and duability aet f te emte and gammed navigatin ae nideed. Keyd: mini-ua, mini gye, tengt, tutue f mite. Intdutin Unmanned aeial mini-veile ae bjet bigge tan a uman and tat an fly like bid, and ave te intelligene f inet. Tei field f bevatin i aximately 0 km, and te unit t uld nt exeed US$,000. In te ealy 90, bbyit nly f amuement fle u bjet. Sn, eve, militay ganizatin beame inteeted in tei ue, and, f intane, te US Defene Advaned Reea Pjet Ageny (DARPA) initiated a fu-yea jet t $35 millin t devel a mini-ua. Tday, ne f te mt ignifiant allenge faing aeae engineeing nened it mini-veile i tat f imving te dive, fligt ntl, en, mieletni, and mimeani, and, abve all, analyzing te ai lad ating n a tutue duing a ntlled fligt. Tee ae vaiu aliatin f mini-ua; tug ennaiane tak eem t be edminant, tey an al be ued f aing infmatin t aate. Te aamete equiement etablied f a mini-ua inlude: lengt u t 5 m, ma 50 g, fligt time min, flying eed 0 0 m/, and ange 3 0 km. A mini-ua uld be able t vide image at 0.5 ft elutin, ea a taget by itelf ete in en led ae, and, in etain vein, al detet emial, bilgial, and eletni agent

3 R. Caty, Z. Kuba / AIATION, l IX, N, 005, 0-6 Tee ae till a numbe f blem tat fligt yiit dealing it flying bt mini-lane ave t exlain. Aeae deigne ae tying t make te aedynami f a mini-ua eemble te aedynami f an inet a bid a mu a ible [6]. Of ignifiane i te elatively ig ugne f ing. It make a bid ufae teamlined f fligt atef. In te ae f a mini-lane, it nt nly enue gd aedynami but al imve te adeene f te miniatuized intument and en fixed n te ing. Te equatin f tanlaty mtin f te mini-ua in te elated Oxyz dinate ytem ae given a fll: du m q v Fx (a) dv m u Fy (b) Dnladed by [ ] at 4:9 03 Setembe 05. Ne mateial f a mini-ua T ineae te maneuveability f an unmanned aeial veile, e an ue mite nanmite, te latte being bund t evlutinize t entuy tenlgy [, 3]. Studying te atmi and mleula tutue f mateial el t entut te fligt f te bid an inet. A ing it a fibu ating imve aedynami lift by utilizing vtie and aifl nditining te mliated fligt f a bid. In te exeiment, e tutue made f 3 mm lng ie element ee ubjeted t inteing in adane it IS 740 tandad []. A e kn, ai ente te bdy f a bid an inet tug eial ening. Ten, it i evenly ditibuted by a ytem f taeae. Te aifl inide a mini-lane uld be fed by te inkage and tigtening f te mite nanmateial atile (mateial tain). It i eential t einfe te ing tutue, and ti an be aieved by alying lymei fibe, i ae t elae adiating leve [4]. An imtant blem in te fligt meani f mini-ua i t enue te aiate tability f mtin ile ealizing gammed tajetie. One f te lutin uggeted in u a ae eem t be te ue f a gye f te autmati fligt ntl f mini-ua.. Gye navigatin f a mini-ua Cnide a mini aeial veile it a gye fixed inide utide it. Aume initially tat a ymmetial gye t evlve und te AA axi aving ne degee f feedm in elatin t te mini-ua (Fig ). Sine te t at ae egulaly aanged aund te axi f ig-eed tatin, te ditibutin f te ma f te le mini-ua-gye ytem de nt ange duing it eatin. Tu, te mment f inetia f te ytem ill be ntant and te t mtin an be deibed in te ame ay a tat f a ingle igid bdy. Ten, aume tat te mini-ua i a igid bdy, i.e. ne tat de nt undeg a defmatin, it ntant ma. Te mtin f te mini-ua-gye ytem an be eeented by mean f t ytem f equatin deibing te mtin f te ytem ma ente and te mtin aund te ma ente. Additinally, nide te imlet ae, en te t axi, O, i al te main ental axi f inetia f te mini-ua, Ox. x 3 d m v q u Fz () ee: m mini-ua-gye ytem ma; u, v, mnent f te linea velity f te mini-ua in te elated Oxyz dinate ytem;, q, mnent f te angula velity f te mini-ua in te elated Oxyz dinate ytem; F x, Fy, Fz mnent f te main vet f extenal fe ating n te mini- UA ee: Fig. ie f te gye ntl f a mini-ua it et dinate ytem - -

4 R. Caty, Z. Kuba / AIATION, l IX, N, 005, 0-6 Dnladed by [ ] at 4:9 03 Setembe 05 F x Ax Gx Fy Ay G y Fz Az Gz On te te and, te equatin f tatin f te mini-ua in te ame dinate ytem ae deibed a fll: x d dω gx ( ) q L z y gx (a) dq y ( x z ) gxω gx (b) ( ) q N d y y x gxω gx () ee:,, main ental mment f inetia x y y f te mini-ua in elatin t te atiula axe f teoxyz ytem; gx, gy, main ental mment f inetia f te gye t in elatin t te atiula axe f te Oxyz ytem; ω gx angula velity f te ig eed tatin f te gye t; y y gy, z z ; L,, N mnent f te main vet f te mment f extenal fe, ee: L N N A A LA LG G N L A, A, N A mnent f te main vet f mment f aedynami fe; L G, G, NG mnent f te main vet f mment f te fe f gavity; b, mment f te gye ntl fe. 3. Kinemati f te uled mtin f te unmanned aeial mini-veile (mini-ua) and te beved gund taget (izntal lane) Te kinemati equatin f te mini-ua mtin duing te bevatin and taing f a gund taget mving in te izntal lane at a et altitude H an be eeented in te flling fm: G b d (3a) in in ω gn (3b) (3) ee: ditane beteen te fligt at f te mini- UA ma ente S and tat f te taget C;, fligt at velitie f te mini- UA and te taget, eetively; σ angle detemining te itin f te vet f latin f te mini-ua in elatin t te taget in te Oxy lane; χ, χ angle detemining te itin f te vet f velitie i in te Oxy lane, eetively. If (a in Fig ) σ σ κ κ ain ten Fig. Kinemati f te uled mtin f te mini-ua and a taget in te izntal lane d σ d d σ (4) ( ) ( ) Wen te ditane beteen te mini-ua and te taget i nt, ten equatin. (3a) ill ave te fm ( χ ) 0 σ (5) - -

5 R. Caty, Z. Kuba / AIATION, l IX, N, 005, 0-6 Dnladed by [ ] at 4:9 03 Setembe 05 χ Tu, σ a (6) Alying te time-deendent deivative fm equatin (6), e get: ee ( χ σ ) in in ina (7a) (7b) If te taget i mving it a unifm taigt-line mtin ( nt, χ nt ), and te velity f te mini-ua i ntant ( nt ), ten in( σ χ ) (7) ( σ χ ) In a geneal ae, taking int aunt (3), (6) and (7), te equatin f mtin f te mini-ua in te izntal lane an be given a fll d Π ( t, t ) [ ] ( t, t ) 0 Π k ( t, t ) ( t, t ) in in (8a) in in (8b) Π ( t t ) d ω gn ( t, t ) σ a k, d (8) ee: t, t, t, tk e tat time, taget detetin time, taget bevatin time and e fini time, eetively; Π funtin f a etangula ule. ten e ave d Π ( ) ( ) Π If nt i 0 ( t, t ) Π( t, t ) 0 Π k ( t, t ) Π( t, tk ) ( t t ) ω gn d π ( t, t ) σ k, Te tajety f te mini-ua mtin dx dy dz d (9a) (9b) (9) χ (0a) in χ (0b) 0 Te tajety f te taget mtin dx dy dz (0) χ (a) in χ (b) 0 () - 3 -

6 R. Caty, Z. Kuba / AIATION, l IX, N, 005, 0-6 Dnladed by [ ] at 4:9 03 Setembe Gye Cntl Tee ae tee metd f gye-baed ntl: a) autnmu, b) emte and ) mbined. Te fit metd aume tat te gye ealize a et mtin gam. Te ue f te UA i maintained by te autilt in u a ay tat te UA lngitudinal axi inide it te gye axi. Te angle detemining te itin f te gye axi, ϑ g and ψ g, uld be equal t te angle detemining te itin f te UA lngitudinal axi, ϑ and ψ : ϑ ϑ, ψ ψ. () g g Ti all te UA t ea a deied int in ae alng a et tajety. Te edue an be ued in te navigatin f unmanned aeial veile. Heve, metime te autilt de nt take int aunt te gye mtin ile ealizing a edetemined mtin. Te gye axi a te mtin gammed; it ll, f intane, t deibe an enaned aea f a iula ellitial ne, i.e. it mve alng te ial f Aimede. A n a te gye axi aume a deied itin in ae, i may inide it te mment f taget detetin, te gye tat eating in te tae-te-taget mde and te UA autilt emly te etablied algitm f ntl. A a eult, te UA iulate ve a deteted taget aae it uing te ignal abut te gye itin, a i te ae f ming miile guided bmb. Te end metd invlve ntlling te gye fm a ditane. An eat at te mmandand-ntl int beve tug a amea te aea abve, i te UA flie. Te mment te taget i deteted, te eat itin te igt tat i te gye axi. Fm n n, te UA (e.g. a guided bmb, am ieing ell, et.) ill mve tad te taget. Te tid, mbined, metd f gye-baed ntl an be ued in mbat unmanned aeial veile. Fit, te UA i gammed t ea te aea f a taget latin. Ten, te gye ite int te taget-taking mde, i invlve anning te ae by te gye axi. Finally, afte te taget i deteted, te axi mve in adane it te dilaement f te taget bevatin line, i.e. a taigt line nneting me eleted int f te UA and te taget. Wieve ntl metd i alied, te ntl mment an be eeented in te flling fm [6] k b b b (3) k In equatin (), te quantitie b and tand f gam ntl, i ae detemined fm te invee blem f dynami [6, 7]: b ϑ ψ ( t) b ϑ b ( t, t ) ( t) 0 ( t, t ) 0 ϑ in ϑ ( ψ ) in ϑ ψ ϑ ] [ ψ ϑ ϑ ϑ ] g bψ g (4a) (4b) ee: Π ( ) funtin f a etangula ule; t mmening te taking e, t taget latin time; g lateal mment f inetia f te gye t, ϑ, ψ et angle detemining te itin f te gye axi in ae. deϑ b ( t) ( t, tk ) kb eϑ k eψ g (5a) deψ ( t) ( t, tk ) kb eψ k eϑ g (5b) e ϑ ϑ, e ψ ψ ; ϑ, ψ ee: ϑ g ψ g angle detemining te itin f te taget bevatin line; t mmening te taking e; t k end f te taking e; k b, k effiient f te egulat amlifiatin; g effiient f te egulat daming. In te gammed ntl f te gye axi, it i neeay t et te flling angula velitie and aeleatin: dϑ d ϑ 0, dψ Te quantity ile 0, (6a) d ψ d σ,. (6b) i detemined fm equatin (9b), d σ i equal t d σ - 4 -

7 R. Caty, Z. Kuba / AIATION, l IX, N, 005, 0-6 Dnladed by [ ] at 4:9 03 Setembe 05 in in If ( σ χ )( ) ( σ χ )( σ χ ) ( σ χ ) ( σ χ )( σ χ ) (6) nt and nt, and te taget i being aaed ading t tinal navigatin, e get d σ [ in ] in and, ile taing and ligtening te taget, e get d σ Fig 3. Gye ntl f a mini-ua Additinally, if te taget i immvable ( 0 ), and te taget i being aaed, e ave d σ in and, ile taing te taget, it i d σ 0 (7) (8) (9) (0) Te la f ntl etablied by te autilt (i.e. te eigt and dietin udde angle, δ m and δ n eetively) f te mini-ua i a fll: δ m ( t) km ( ϑg ϑ ) m ( ϑ g ϑ ) (a) δ n ( t) kn ( ψ g ψ ) n ( ψ g ψ ) (b) ee: k, effiient f autilt amlifiatin; m k n k m, k n m n, effiient f autilt daming. Figue 3 illutate a emati diagam f te navigatin f a flying bjet uing a ntlled gye. Cnluin Advane in te deign f nanmaine and nanbt ae ible tank t te ue f nanmateial and nanmite. Knledge f te ne mateial enable u t make te fligt f a mini- UA and te fligt f a bid an inet exatly alike. Te eult f te eea n te aliatin f a gye a te exeutive element f te mini-ua autmati ntl ytem nfim tat it i ible t imve te tability and ntlability f te aaatu [7]. It uld be nted tat te aamete f te gye and te UA autilt egulat ave t be eleted in an timal ay due t te minimum time f tanient e fading, i eult fm extenal intefeene iting n te ntl ytem f te gye (ntl l ) and te flying bjet (ntl l ). Oteie, te aeial veile ill nt mve alng te edetemined tajety, and te inteeted taget may diaea fm te na viual field f te taking ytem len. Refeene. Pietua., Sibilki K. Od tzeń latająy d miniatuy tatkó ietzny // Nauka, innaje, tenika N. P. 8.. Bu W., Tiumentev Yu. Advaned infmatin tenlgie and tei aliatin in te aenauti // Peeding f te end Semina n Reent eea and deign ge in aenautial engineeing and it influene n eduatin. Waa, 996. P Caty R., Ozeki T. Te diffuin inteing f metalli mite in te ntutin f igly effiient eat exange // Cmute Aided Sytem f anufatue and eauement f aine Element. CEEPUS, 003. P Caty R. Adein Stengt Etimatin beteen Diffeent Cmite Cmnent // unal f Tant and Engineeing. Tant: Aviatin tant l 6, N. P

8 Dnladed by [ ] at 4:9 03 Setembe 05 R. Caty, Z. Kuba / AIATION, l IX, N, 005, Kuba Z. Dynami and Cntl f a Gye n te Bad f an Aeial eile // nga, Studie, Dietatin. Kiele: Kiele Univeity f Tenlgy, 00. N 5. P Kuba Z. Seletin f te timum aamete f te gye ytem n elati uenin in te ming miile ytem // unal f Tenial Pyi / Pli Aademy f Siene, Intitute f Fundamental Tenlgial Reea, Waa ilitay Univeity f Tenlgy. Waa, 999. l 40, N 3. P Kaгy Л.И. Гикпичeкиe прибы и итeмы // Cyдтeниe. Ленинград,

Recall Gibbs eqn. ds. Using h version. for ideal gas. integrate AE3450. for ideal gas. integrate s. s(t,p) behavior? AE3450. T p.

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