Adaptive track-keeping control of underwater robotic vehicle

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1 Aapiv ack-kping conol o unwa oboic vhicl Jzy Gau Abac Th pap cib a ho o conol o h unwa oboic vhicl o h pobl o acking o a nc ajcoy. A uliinional non-lina ol xp h obo ynaic. oan ignal a gna by an auopilo coniing o ou inpnn conoll wih a paa aapaion law ipln. A qualiy o conol i concn wihou an in pnc o nvionnal iubanc. Slc ul o copu iulaion illuaing civn an obun o h popo conol y a in. ou cion. Bi cipion o quaion o oion o h URV an h aapiv conol law a pn in Scion. Th nx cion povi o ul o h iulaion uy. oncluion i givn in Scion 4. II. OLIEAR AAPTIVE OTROL LAW Th gnal oion o ain vl o ix OF cib h ollowing vco [3] [5] Kywo Unwa obo, auopilo, non-lina conol, acking. U I. ITROUTIO nwa oboic ha known an incaing in in h la ya. Th ain bni o uag o Unwa Roboic Vhicl (URV can b oving a an o h ang o h una nvionn an ucion in co o xploaion o p a. unly, i i coon o u h URV o accoplih uch iion a h inpcion o coaal an o-ho ucu, cabl ainnanc, a wll a hyogaphical an biological uvy. In h iliay il i i ploy in uch ak a uvillanc, inllignc gahing, opo covy an in coun au. Th URV i coni bing a loaing plao caying ool qui o poing vaiou uncion. Thy inclu anipulao a wih inchangabl n-co, caa, cann, ona, c. An auoaic conol o uch objc i a iicul pobl cau by i nonlina ynaic [1], [], [4] [6]. Moov, h ynaic can chang accoing o h alaion o coniguaion o b ui o h iion. In o o cop wih ho iiculi, h conol y houl b lxibl. Th convnional URV opa in cab-wi ann in ou g o o (OF wih all oll an pich angl ha can b nglc uing noal opaion. Tho i baic oion i ovn in hoizonal plan wih o vaiaion u o iving. An objciv o h pap i o pn a uing o a ol nc aapiv algoih o iving h obo along a i ajcoy in paial oion. Th pap coni o Manucip civ May 17, 7 Rvi Augu 1, 7 J. Gau i wih h Polih aval Acay, Gynia, Polan (phon: ax: ail: j.gau@ aw.gynia.pl. Iu 4, Volu 1, 7 17 η v τ T [ x, y, z, φ, θ, ψ ] T [ u, v, w, p, q, ] [, Y, Z, K, M, ] T η poiion an oinaion vco in h inial a x, y, z cooina o poiion φ, θ, ψ cooina o oinaion (Eul angl v lina an angula vlociy vco wih cooina in h boy-ix a u, v, w lina vlocii along longiuinal, anval an vical ax p, q, angula vlocii abou longiuinal, anval an vical ax τ vco o oc an on acing on h obo in h boy-ix a, Y, Z oc along longiuinal, anval an vical ax K, M, on abou longiuinal, anval an vical ax. onlina ynaical an kinaical quaion o oion in boy-ix a can b xp a [4], [5] M (v (1 M v + ( v v + ( v v + g( η τ ( inia aix (incluing a a aix o oioli an cnipal (incluing a a (v hyoynaic aping an li aix g (η vco o gaviaional oc an on.

2 III. SIMULATIO STUY Fo h URV h a o paaic uncaini in h ynaic ol (, an cain paa a gnally unknown. Hnc, paa iaion i ncay in ca o ol-ba conol. Fo hi pupo i i au ha h quaion o oion ( a lina accoing o a paa vco p, i.. [8]: wh Y( η v, v (, v v p τ M v + ( v v + ( v v + g( η Y η, (3, i a known aix uncion o au ignal, uually a h go aix (inion n, an p i a vco o uncain o unknown paa. L ia o h aic M, ( v, ( v an h v v ĝ η. I vco ( η g b cib a Mˆ, Ĉ (, ˆ ( an ( ol paa a known wih o accuacy h ollowing nonlina conol law can b appli [5], [8]: τ Mu ˆ + ˆ ( v u + ˆ ( v u + gˆ( η K (4 Y ( η, v, u, u pˆ K M inia aix (incluing a a K poiiv ini iagonal aix + Λ 1 1 η η v v u v Λ 1 Λ poiiv ini wighing aix. hooing h paa upa law a [4], [8]: p T ˆ ΓY ( η, v, u, u (5 wh Γ i a poiiv ini yic aix, abiliy o h conol y an convgnc o zo i guaan. A block iaga o h conol y wih paa aapaion law how Fig. 1. A ain ak o h ign acking conol y i o iniiz ianc o aiu o h obo cn o gaviy o h i ajcoy un aupion: 1. h obo can ov wih vaying lina vlocii u, v, w an angula vlociy. i vlocii u, v, w, an cooina o poiion x, y, z an haing ψ a auabl 3. h i ajcoy i givn by an o o waypoin {( x i, yi, zi } 4. gn o h nc ajcoy bwn wo ucciv way-poin a in a ooh an boun cuv 5. h coan ignal τ coni o ou coponn: τ τ 1, τ τ Y Y, τ τ 3 Z Z an τ τ 4 calcula o h conol law (4. A ucu o h popo conol y i pic in Fig.. To valia h poanc o h vlop nonlina conol law, iulaion ul uing h MATLAB/Siulink nvionn a pn blow. Th ol o h vhicl bai on a al conucion o an unwa obo call oal ign an buil o h Polih avy. Th URV i an opn a obo conollabl in ou g o o, bing 1.5 long an having a populion y coniing o ix hu. iplacn in hoizonal plan i on by an o ou on which gna oc up o ±75 auing p up o ±1. / an ±.6 / in x an y icion, conqunly. All paa o h obo ynaic a pn in h Appnix. Fig. Main pa o h conol y Fig. 1 iaga howing h paa aapaion law uical iulaion hav bn a o coni qualiy o h popo conol algoih o h ollowing aupion: 1. h obo ha o ollow h i ajcoy bginning o (1, 1,, paing ag way-poin: (1, 1, -5, (1, 9, -5, (3, 9, Iu 4, Volu 1, 7 18

3 -5, (3, 1, -5, (6, 1, -5, (6, 9,-5, (6, 9, -15, (6, 1,-15, (3, 1, -15, (3, 9,-15, (1, 9, -15 an ning in (1, 1, -15. a uning poin i ach i h obo i ini o a hal cicl o accpanc 3. h a cun inac h obo wih axiu vlociy.3 / an icion ynaic quaion o h obo oion a inga wih high quncy (18 Hz han h o oul (6 Hz. I ha bn au ha h i-vaying nc ajcoi a h way-poin i o h nx way-poin i+1 a gna uing i p poil [7], [8]. Such appoach allow u o kp conan p along cain pa o h pah. Fo h aupion an h ollowing iniial coniion: ( b, η ( b η (, 1 η ( η1 η η η η ax η η ( ax (6 wh k 1, 4, h i h gn o h ajcoy in a pio o i b, ha bn oll accoing o h xpion [8]: η wh ( η ax η η + η1 + η ηax + ηax ( η ax η1 η1 η η 1. ηax ( ( + b < < Th algoih o conol wok ou bai on h iplii URV ol popo in [4], [9]: (7 in h paa vco p in a o p [ ] T Y Y Z Z h xpion (8 can b win a: Y ( v, v u ( v v p τ Y, (1 u u v v v w w w. Th gulaion pobl ha bn xain un inacion o nvionnal iubanc, i.. a cun. To iula uch inlunc on obo oion h cun vlociy V c wa au o b lowly vaying an having a ix icion. Fo copu iulaion i wa calcula by uing h 1 o Gau-Makov poc [5]: V μ V ω (11 c + c wh ω i a Gauian whi noi, μ i a conan an Vc ( V. c ax Rul o ack-kping in h pnc o xnal iubanc an h cou o coan ignal a pn in Fig. 3. I can b n ha h popo auopilo nhanc goo acking conol o h i ajcoy in h paial oion. Th ain avanag o h appoach i uing h ipl nonlina law o ign h auopilo an i high poanc o laiv lag a cun iubanc (copaabl wih ulan p o h obo. uing iulaion i wa au ha h u valu o coponn o h vco p a unknown. An valuaion poc a o h lvl o hal o noinal valu o a an aping coicin. Ti hioi o ia paa uing acking a pn in Fig. 4. ( v v τ M v + (8 wh all kinaic an ynaic co-coupling a nglc. H M an (v a iagonal aic wih h iagonal ln o h inia an aping aic, conqunly. Uncaini in h abov ol a copna in h ign conol y. Th ol (8 o oion o ou OF ak a o: u + Y v + Y Z w + + Z u u τ v v τ Y w w τ Z τ (9 IV. OLUSIO In h pap h nonlina conol y o h unwa obo ha bn cib. Th obain ul o iulaion uy allow o a ha h popo algoih wih paa aapaion law au a high accuacy o acking conol along a pin ajcoy an how i nuical ipliciy an uuln o pacical applicaion. iubanc o h a cun w a o viy h poanc an coni cocn an obun o h appoach. Fuh wok a vo o h pobl o uning o h auopilo paa in laion o h obo ynaic. Iu 4, Volu 1, 7 19

4 - poiion z [] poiion z [] poiion y [] poiion x [] 1 o z [] i [] poiion x [] cou pi [g] o x [] 1 o pi [g] - poiion y [] o y [] i [] i [] [] i [] 1 oc an on Y [] Z [] [] i [] Fig. 3 Tack-kping conol un inacion o a cun iubanc (axiu vlociy.3 / an icion 135 : i ( an al ( ajcoi (l upp plo, x-, y-, z-poiion an hi o ( n 4 h plo, cou an i o (5 h plo, coan (igh low plo Iu 4, Volu 1, 7

5 6 ia o oion along x axi 5 ia o oaion abou z axi [kg] 4 [kg ] [kg/] [kg ] i [] 6 ia o oion along y axi i [] Fig. 4 Eia o a an aping coicin: valu ( an ia valu ( [kg] [kg/] [kg] [kg/] i [] ia o oion along z axi i [] APPEI Th o paa u in copu iulaion: 1. h URV ol: M iag { } ( v + ( v iag 1. ( v 1 11 { } 7. u iag 11 1 ( v 1 6w v q 6w 18u 5 p 6q p 45.4 v 3. p 8v 18u 478. w 14. q 1.9 Iu 4, Volu 1, 7 1

6 ( η g 17 in( θ 17 co( θ in( φ 17 co( θ co( φ 79 co( θ in( φ 79. nonlina conol law: K iag Γ iag ( in( θ + co( θ co( φ { 1 5 1} { 1 } { 5 1 } Λ iag. REFEREES [1] G. Anonlli, F. accaval, S. Saka, M. W, Aapiv onol o an Auonoou Unwa Vhicl: Expinal Rul on OI, IEEE Tan. onol Sy Tchnology, vol. 9, no. 5, pp , Sp. 1. [] R. Bhaachayya, ynaic o Main Vhicl. hich: John Wily an Son, 1978, ch. 3. [3] J. avn, R. Suon, R. S. Bun, onol Sagi o Unann Unwa Vhicl, J. avigaion, no.51, pp , Aug [4] T.I. Fon, Guianc an onol o Ocan Vhicl. hich: John Wily an Son, [5] T.I. Fon, Main onol Sy. Tonhi: Main ybnic AS,. [6] J. Gau, Z. Kiowki, on-lina onol o Moion o Unwa Roboic Vhicl in Vical Plan, in Rcn Avanc in Inllign Sy an Signal Pocing,. Maoaki, V. Mlanov, E. WSEAS P, 3 pp [7] J. Gau, Z. Kiowki, Tajcoy Tacking onol o Unwa Vhicl in Hoizonal Moion, WSEAS Tan. Sy, vol.3, no.5, July 4, pp [8] M. W. Spong, M. Viyaaga, Robo ynaic an onol, hich: John Wily an Son, 1989, ch. 8. [9] J. K. Yuh, Molling an onol o Unwa Roboic Vhicl, IEEE Tan. Sy Man ybnic, vol. 15, no., pp , Ap Iu 4, Volu 1, 7