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S I C E - I C A SE k h n a o t i n a l J o i n t C onfence 2006O c t . 1 8 - 2 1 , 2006 i n B exo, Busan, K oiea

D ynam rsof a F ih-L ke R obotand I t ' s C o n t r o l D esgnn A u i y a n t , T a e s a m K a n g 2 , Y oung J a e L ee

D e p a x t n e n t o f M e c h a n i c a l a n d A ermsace E n g i n e e 2 i n g , K onkuk U n i v e m i t y , S e o u l , S o u U h K onea( T e l : + 8 2 - 2 - 4 5 7 - 3 5 4 4 ; E - m a i l : genirin@ y a h o o com )2 D e p a x t n entofM e c h a n i c a l a n d A e r m s a c e E n g i n e e 2 i n g , K onkuk U n i v e m i t i y , S e o u l , S o u U h K o n e aT e l : + 8 2 - 2 - 4 5 0 - 3 5 4 4 ; E - m a i l : t k a n g @ konkuk a c k r )3 D e p a x t n e n t o f M e c h a n i c a l a n d A ermsace E n g i n e e 6 n g , K onkuk U n i v e m i t y , S e o u l , S o u U h K o n e a( T e l : + 8 2 - 2 - 4 5 0 - 3 3 5 8 ; E - m a i l : y o u n g l e e @ konkuk a c k r )

A b s t r a c t : A f i s h - l k e i o b o t b o a t h a s b e e n b u i W t t s i m u l a t f i s h s w m m i n g dynam i c s . T h i s i o b o t b o a t u s e s o s c i l 1 a t n gp l a t sw 1mm i n g mode as i t uses o n l y s i n g l e o s c i l 1 a t h g t a i l f i n . S e v e i a l e x p e r n m e n t s h a s b e e n c a r d e d ou t t p i o v i d es u f i c i e n t d a t t be p i n c e s s e d fr t h e i d e n t i f r H o t i n p n c e s s . Th e e x p e 2 n m e n t d a t a r L e c o l l e c t E by u s i n g an I n e r t i a lM easun e n t U n i t ( 1 M U ) w h i c h c o n s i s t s o f t - m e e g y m n s c o p e s a n d t - n e accelem e t a l . A m a t h e m a t i c a l m o d e l , at U a n s e H r f L m c b D n b e t w e e n t h e s w imm i n g d i L c t o n a n d t h e f i n ' s m e a n a n g l e o f o s c i l a t o n , i s o b t a i n e d frm t h e d a ta n d i d e n t i f r A d t i o n a l g o r i t h m . The i d e n t U 5 e m o d e l a p p i o x 1 m a ts t h e e a l sysEm quie w e l l . T h i s m o d e l h a s b e e n u s e d td e s i g n P I D d i c d o n a lcontlerfDr the f i s h - l M k e i o b o t .K ey w o r d s : f i s h - ] j k e i o b o t , f i s h - ] k e boa, m o d e l i d a e n - 5 f i c . a n , dieLcnaltUansrfLmcon, P ] D c o n b m ] l e r d e s i g n .

1 . I[NTRO DUCT I O ND e v e b p i n g u n d e n w atr o b o t s c a n be a b i g a d v a n t a g ei n i h e f i e l d s o f o c e a n devebpm e n t , o c e a n i n v e s t i g a t i o n ,a n d m arne e n v i i o n m e n t a l p m t - c d o n . To pivide h i g he f c i c i n c y a n d p i p u l s i v e p e r f r n a n c e , f i s h - l i k ep e r n x n a n c e i s entida1y s q u h i - d i n d e v e b p i n gu n d e n w a t e r i b o t s . H e n c e , t h e f i s h - l j k e i o b o t i s a u s e f u la n d i n t m e s L t n g one t devebp [ 2 ] .A f i s h - l j k e b o a t h a s b e e n b u i l t t s t u d y f i s h

s w m m i n g d y n a m i c s , p a r c u l a r l y o s c i l O a t h g p l a ts w m m i n g m o d e w ih s i n g l e t a i l f i n . T h i s f i s h - l j k e b o a ti s e q u p p e d w i t h an ] M U ( I n e r b a l M eaan e n t U n i t )s n s c r w h i c h c x n s i s t s o f i m e a c c e l e o m els a n d i m eg y i o s c m o p e s . U s i n g f h e ] M U, d a t w ee c o lc t e d Umugha e v e r m l e x p e n i m e n t s o f t h e f i s h - l k e b o a t , t h e n t h e d a tw e m e p i o c e s e i n m o d e l i d e n t i f r A d t o n p i c e d u i e .

M o d e l i d e n t i f i r a d n n p i c e d u m e o f t h e f i s h - l i k e b o a th a s p r i d u c e d am a i h e m a t i ca l m o d e l ( a t U a n L r T m c U D n )w h i c h m l a t E s s w 1 m m i n g d i m e c t i o n a s i h e o u t p u t v a n i a b l ea n d t h e m ea n o f i h e f i n o s c i l 1 a t o n a n g l e a s f h e i n p u t .Th e t U a n i r m n c t o n h a s a ] s c b e e n s h o w n t des=bet h e e a l systm q u i e w e l l .

By u s i n g t h e t Lanar m n c t b n , w e h a v e d e s i g n e d ac o n t o ] l e r t 1 m p i o v e t h e f i s h - l i k e b o a t ' s t=ingprfrn a n c e . Th e c o n t D l d e s i 3 n u s e s P D d e s i g n tm e e t secifc r m q u m e n t s . I t i s a sc d e s i g n e d tsuppess e x t l n a l d i s t i n b a n c e s .

2.THE FISH -LIKE BOATTh e f i s h - l k e b o a t u s e d t s i m u l a t s w m m i n g f i s h h a s

o n l y one o s c i l 1 a t h g ( t a i l ) f n . Th e s h a p e o f t h e f i n i sf l e x i b l e p i k e - t p e f i n w h i c h , t h e o r e c t i c a y , g i v e s g o o dp efm a n c e a t b w f i a u e n c y o s c i l a t i D o n [ 2 , 4 ] . F i g . 1s h o w s i h e p i c b u i e o f t h e boatand T a b l e 1 sm e d e t a i l o ft h e f i a h - l k e b o a t .

F i g . 1 P i c t i m o f t h e f i s h - l j k e b o a t .T a b l e 1 M an i n f r n atdn o f i h e f i s h - l k e b o a t .T o t a l l r i g t h ( a n ) 3 5 . 0Totlw i d t h ( a c n ) 1 4 . 5T o t a l h e i g h t ( a n m ) 1 9 . 0T o t a l m a s s ( g r ) 421Servo H i e c H S=55M i i c o n t b o l l e r A t i n e l1 28Pow e r s u p p ] y T h m e 9V b a t t p B i e sI M U snsor M i c o s b a i n I n c .D a t connecin B l u e t D o t h

Th e p i p u l s i o n o f a s w mm i n g f i s h i s g e n e i a t E d byvorExes a i o u n d i t ' s t a i l f i n which a i e c e a t E d by f i no s c i l 1 a t i n . The e q u a t D n o f t i l f i n m otDn i s g i v e n byE q . ( 1 ) [ 1 ] ,0 ( t ) 0 = a + 0 0 c o s ( 2 7 T t ) . ( 1 )w h e r m 0 ( t ) i s t h e a n g l e b e t w e e n i h e t a i l a n d i h e] o n g A u L d i u a l a x i s o f t h e v e h i c l e , O a i s t h e m ea n o f 0d u n n g on e p e r i o d i n ea n a n g l e o f o s c i a a t o n ) a n d f i st h e o s c i l 1 a t i n f r e q u e n c y . B a ed on o b s e r v a t d n o f f i s hs w 1 m m i n g k i n e m a t i c s , L e a s n a b l e e s t i m aton o f i h ea m p l i t u d e ( 0 0 ) i s a b o u t 1 5 0 [ 1 ] . V a l y i n g O a p r D v i d e sc o n t i l o f s w mm i n g dicdn w h i 1 e c h a n g i n g f r i e s u t ss w mm i n g seed c h a n g e s .

8 9 - 9 5 0 0 3 8 - 5 - 5 9 8 5 6 0 / 0 6 / $ 1 0 C 2 0 0 6 ICASE 4 2 9 7

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i n t h i s L e s a I c h , w e a e i n t m e s t d t o b s e r z e f i s hs w i m m i n g diecton i n t e l a t d o n w A i h i n p u tO w h e r e t h eo s c i l a t d o n f i u r u e n c y i s f i x e d a t 8 r a d / s . T h i so b s e r z v a t i D n i s u s e f u l t a n a l y z e t=mng p e r f f n a n c e o fa s i m i l a r f i s h - l i k e i n b o t V a n a b l e s mpesentng f h es w i m m i n g d i 2 E c b D n a i e p a t h a n g l e , q f p , a n d p a t h a n g l ei a t , c o - p ( s e e F i g 2 ) .

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p a t h a n g l e a t E frm yaw a n g l e d a t a .31 I d e n t i f i c a t i n Procedure

F nm a v e z a l t h e o n e t c a l L e v i e w s a n d s t e p i n p u t ( s t pV a ) mteonse o b s e r v a t i D n s , w e h a v e bund ou t u s e f u li n f r n a t i W n g a r d i n g U h e f i s h - ] j e b o a t t=ingd y n a m i c s [ 3 ] . F u i s t one i s U h a t t h e d i l e c d o n a l tUanFrh m c t h n n i s t h e m o s t ] - e l y t be i n s ec o n d o r d e r s y s t mfDn . S e c o n d , t h e vale o f O a w h i c h m a k e s z e i o stady- st ming 2 a t O p = 0 ) i s a b o u t 6 . 8 d e g . H e n c e , w eh a v e s e t t h i s a n g l e a s reknce o f t h e m icontbolerc o d e ( i n s t a d of O a = 0 d e g ) .

Th e m a i n i d en t if ir . ad n e x p e n i m e n t h a s b e e n donea n d t h e e s u l t ( i n p u t - o u t p u t d a t a ) i s s h o w n F i i g . 4 . N ott h a t i n t h e a l l f i s h - l k e b o a t e x p e 2 i m e n t s , t h e f i no s c i l 1 a t o n f r t 1 u e n c y i s 8 r a d / s .

F i g . 2 Th e s w i m m i n g f i sh - lk e b o a t i l l u s b a t i n .By d o i n g systm i d e n t u i f l a t i n p r c e d u i e , w e c a no b t a m i a m a t h e m a t i c a l m o d e l b e t w e e n p a t h a n g l e L a t E( o u t p u t ) a n d m ea n a n g l e o f o s c i l l a t i n ( i n p u t ) .3.SYSTEM MODEL IDENTIFICATION

Th e g o a l of t h e m o d e l i d e n d 5 f r a t i o n p i o c e d i u - e i s to b t a i n a m a i h e m a t d c a l model f i a t m a i r h e s q u i e we l lwithe a c t i a l e x p e n i m en t d a t a . For t h i s f i h - l j k e boatp r 4 e c t , i t i s a tUansr Thncdon e l a t n g mean a n g l e ofo s c i l 1 a t o n ( i n p u t ) and p a t h a n g l e a t E ( o u t p u t ) . W e c a l li t t h e diecdnaltran r Tnctdn.

P r a c t r a l l y , it is dif5cult t ma s w i e f h e a c t u a l p a f hand p a t h a n g l e i a t E . H ow ever, we can s t i l l a p p i o x i m a tt h e m f r o m yaw a n g l e d a t a by a p p l y i n g a bw pass f i E l rs y s t . I n f i s emse a c h , t o b t i i n t h e p a f h a n g l e i a t EO p ) frm yaw d a t a , h e filr shown in F i g . 3 i sempbyed. Not f l a t t h i s f i l l E r i s t f i l l r ou t f h eo s c i l l a t o n freuency component of 8 r a d / s f r o m t h ea n g l e L a t E of t h e f i s h -] k e b o a t .

F i g . 3 Th e f i l l rdiagam u s e d t obain p a t h a n g l e and

F i g . 4 Th e i n p u t - o u t p u t p b t .To be picessed in t h e m o d e l i d e n d f r a d O n i I t a a d c n , f h ed a t a ( i n p u t o u t p u t d a t a ) s h o u l d be p i e - p i c e s s e d f i s tFor t h i s c a s e , i t i s done by mm o v i n g m e a n o r f f s e t of t h ed a t a .

Next s t E p of s y s t E m i d e n t f r c a d n n p i o c e d u l i e i s m o d e li t I r d t o n . T h i s i tR I t iO n i n v o lv e s of com p u t n g someARX m o d e l s and a n a l y z i n g t h e i r q u a i l y i n tEn of esrt s i g n a l a t i D [ 6 ] . By t h i s i J I r t i n , we can g e t t h e m o s ts i i I c b l e modelwt h t h e best q u a E l y Cbw est ernr ts i g n a l 2 a t o ) . T h i s ts k i s e a s i l y done u s i n g S y s t EI d e n t i f a t i c a n Toolbox of M a t L a b [ 7 ] .3 2 I d e n t i f e a t i o n r e s u l t a nd a n a l y s i sA frdoing te i3tron and sm e t b a l and e i r r, we

have obtined t h e f D l b T w i n g m odelas in Eq . ( 2 ) .Wp(Z) 0.02083z-0.01041 2u ( z ) z2- 1 982z+ 0 9825

N o t E fa t t h e sam p l i n g t i n e i s 0 . 0 2 s e c and t h ee c L u l a l e n t c o n t n u o u s fDn i s gi ven a sCOp(S) 0.7874s+26 28u ( s ) s 2 + O.8 83 6 s + 2A75

I n Eq . ( 2 ) and Eq . ( 3 ) , t h e i p u t u ( t ) i s s i n ( O ( t ) ) . Th eeort s i g n a l o a t i D d e f i n e d asin Eq. ( 4 ) i s aboutlO %

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w h i c h m e a n s i t i s a c c e p t b l e t be ourm o d e l .e r i r / s i # g a l ( % ) = 2W V pmodel 0Wpdata2

cV p d a t

F i g . 5 show s t h e pbtof t h e m o d e l com p a i d t D t h ed a t a .I r

F i g . 7 Two-diees-of feedom contlsystm .

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- 6 E r o t o s i g n a l r a t i o ' 0 60 5 1 0 1 5 2 0 2 5 3 5 4 4 5

F i g . 5 Th e modelcompaed t D t h e d a t aSt p i n p u t w e o o n s e of t h e t L a n s r T n c t i D n ( E q . ( 3 ) ) i sshown in F i g . 6 .

S t e r p s p n s F o o l t h eO v e r s h o o t ( % ! 3 9 1 S( , A l t i m e C ( s o ) 2

* -1. . . . . .

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F i g . 6 St p mponse of t h e di2ecdnalt1an rfnctdn.W e can se in F i g . 6 t h a t b o t h ovemshoot and s t l e h n gt d m e of s h e dimctbnal tUanar f h n c c o n ai e e l a t d v e l ybng. I n e f c t . tni-ng m o t i D n of t h e f i s h - ] i k e boatis no tw e l l perfrned. T h i s means we need contller tim p i o v e t h e e q p o n s e caiactic of s h e p a t h a n g l elat.

4.CONTROLLER DESIGNI n t h i s s c d b n , a PI D ( P i o p o r d o n a l I n a g a lD evatve) c o n t b ] l e r d e s i g n e d fr t h e f i s h - l k e boat in

order t a d h i e v e we l l t u m i n g moton w i l be des=edand a n a l y z e d . i n t h i s c o n t l l l e r d e s i g n ,t w o - d e g m e s - o f - f r e e d o m PI D c o n t b l d e s i g n i s used ( s eF i g . 7 ) [ 5 ] .

I n F i g . 7 , Y ( s ) i s t h e c o n t b ] l e r o u t p u t , in t h i s c a s e ,p a t h a n g l e i a t . R ( s ) i s refrbce i n p u t ( d e s i r d p a t ha n g l e a t E ) and D ( s ) i s anexta1disWuance 0 ( s ) a l s mcanbe c o n s i d e m I a s p l a n t / s y s t m u n c e r t i n t y ) . ] t c a n beshown f i a t :Y ( s ) G p G s G c lR ( s ) 1 + G p G S G C G s eY ( s ) G p ( 6 )D ( s ) 1 + G G S G C G s ewherm Gc= ( G c l + G G 2 ) n d e i J i n g Eq . ( 5 ) , wes e tD ( s ) = 0 , a n d i n d e i z i n g E q . ( 6 ) w e s e t R ( s ) = 0.

Th e g o a l s of s h e contbl d e s i g n ( d e s i g nu E q u i - m m e n t s ) :1 . t h e overshoot i s in s h e L a n g e 5 - 1 0 % and t h e t h e

s e t l i n g t i n e s h o u l d be l e s s an 1 5 seands ( a t 2 %2 . itsuppiess extanalstp d i s d d u b a n c e D ( s ) .3 . a s an a d d i i o n a l uquiam e n t , i t i s d e s i d t D maket h e systm h a v i n g z e r r stady-st eirms i n

e q p o n s e s t s t E p , = a m p and a c c e l e a t i o n i n p u t .Ra m p eonse L q u i r m e n t in p o i n t d i i e e i s q u i Ei m p o r t n t , b e c a u s e i t i s i n d i m e c l y e c u a v a l e n t w i l hc o n t ] l l T n g p a t h a n g l e . Wewl l c]eary se t h i s mtterl a t r i n t h e s i m u l a t o n m s u l L .4 . 1 Z e r o - p l a c e m entm ethodW e us e zem p l a c e m en t m e t h o d t c o r m p u t G c l andG c 2 [ 5 ] . Forthe f i s h - l k e b o a t ,

0 .7874s+26 28G ( s ) = 8)7 )P s2+0B2836s+2.475and we h a ve asam e d t h a t s h e servo a nd sensoraie fs tenough s o t h a t w e canmodelitas c o n s t a n t .G ( s ) G ( s ) 1. ( 8 )s

Forthe f i s t s t E p , we w i i t G i n E q . ( 5 ) and E q . ( 6 )in geneal P 1 D bin ass h o w n in E q . ( 9 ) .

K ( 2 + (a + g ) s+ac(s 0.7874s+ 26 28

T h u s , E q . ( 6 ) becomesEq. ( 1 0 ) .

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Y ( s ) 0 . 7 8 7 4 s 2 + 2 6 . 2 8 sD ( s ) [ s 3 + ( 0 . 8 8 3 6 + K ) )2

- + ( 2 . 4 7 5 + K ( a x + , l ) ) s + K a , 6 -( 1 0 )

T h e n , w e s e l e c t s = - a + t t D be t h e d o m i n a n tcbsed-bop p o l e s a n d s h e mm a i n i n g p o l e i s s = - c .H e nc e , t he cbsed ] D o p denom miatrw i l l b e :

s 3 + ( 0 . 8 8 3 6 + K ) s 2( 2 475+ K ( a + , 8 ) ) s + K a , 8 J

=(s+a+ t)(s+a- t ) ( s + c )= s 3 +(2a+c ) s 2 +( a2 +b 2 + 2ac) s + (a 2 +b2)c.

( 1 1 )

S i n c e t h e denom inatrofY ( s ) p ( s ) a n d Y ( s ) , ( s ) a r e s h es a m e , h o s e s e e c t B d p o l e s w i l l a l s o detEn ne t h eL e q p o n s cdaactEidc brthe refence i n p u t .To m e e t a l l d e s i g n g o a l s d e f i n ed a b o v e , e s p e c i a l y t h e

i i 1 d q u i m m e n t , w e h a v e t s e t t h e c b s e d - b D o ptransrnctiDn Y ( s ) , ( s ) a s E q s . ( 1 2 ) .Y ( s ) ( 2 a + c ) s 2 ( a 2 + b 2 + 2 a c ) s + ( a 2 + b 2 ) c ( 1 2 )R ( s ) s 3 + ( 2 a + c ) s 2 ( a 2 + b 2 + 2 a c ) s + ( a 2 + b 2 ) cH e n c e , now t h e n e x t t s k i s t s e a c h a s e t o f a , b a n d cvales w h i h m e e t t h e d e s i g n g o a l s . T h i s s e a c h c a n bee a s - i y d o n e by u s i n g M a t L a b . Th e v a h i e s a = 0 . 6 , b =0 2 a n d c = 1 6 . 6 h a v e b e e n bund t a c h i e v e t h e g o a l s .Thus,byEq. ( 1 1 ) , K = 1692, x + f l ) = 1 . 0 5 5 , a , = 0392,a n d E q . ( 1 2 ) b e c o m e s E q . ( 1 3 ) .Y ( s ) 1 7 B s 2 + 2032s+ 6 . 6 4R ( s ) s 3 + 1 7 . 8 s 2 + 2 0 32s+ 6 . 6 4

4 2 R eslts and s i n u l a t i D nW e f i n a l l y h a v e s h e com p l e t PD c o n t o l l e x d i a g = a ma s shown i n F i g . 8 . By u s i n g S i m r u l i n k , t h e contol

d i a g = a m h a s b e e n t e s t d . F i g . 9 s h o w s t h e s tp e q o n s eo f t h e c o n t r o l e c r .S e p r s p p n s d t h e o W o l l e r1 4 1

P e a k a m p i i u d e 1 . 0 5' A t t i n * ( s e q ) : 0369 S e t t l i a T se 1 3 9

0 6 LC 1

j ~-0 , 5 1 1 , 5 2 1 5 . 3 3 5T i r a I S k ]

F i g . 9 Si p e p o n s e o f f h e c o n t L l 1 r r d e s i g n .F r o m F i g . 9 , we ca n s e e ht t h e s t e p eonse o f t h ec o n t ] l e r h a s o v e r s h o o t 527% ] e s s a m n 10% ) a n ds e t l i n g d i n e a b o u t l 39 seands ] e s s a m n 1 5 s e a n d s ) .Thism e a n s sh e c o n t b o l e r d e s i g n h a s m e e t o u r f i s t g o a l .

Nex, F i g . 1 0 s h o w s t h e e s p o n s e o f s h e c o n t ] l e rw hen exinal stp d i s b u a n c e , D ( s ) , s t s i n f i l e n c i n gt h e s y s t E m fom t i n e 1 5 s e a n d s .

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r e f i p h u t - 4 d e d t s . n r o J s t u b F c L er f i p d t 4 d e K.( s ) = 0 4 s t f o r n 1 5 s4 6 8 1 0 1T c i m e [ s e c ]

F i g . 1 0 R e q p o n s e o f t h e c o n t i ] l e r d e s i g n t t h e s t e pd i s b . n b a n c e .I f h s sen f r o m F i g . 1 0 f h a t U i e stp d i s b f f b a n c e e f f c t L i ss u p p i e s e q u a i w e l l by t h i s c o n t i D ] l e r . H e n c e , t h ed e s i g n a l s f u i l l s t h e seand d e s i g n g o a l .

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= 1286, c x + f l ) = 1125, a n d a , B = 0395, E q . ( 9 )b e c o m e s E q . ( 1 4 ) .G e ( s ) 2 1 5 S s +22.67s+8.424 ( 1 4 )s ~ s + 33 3 8 ~By c o m b i n i n g E q s . ( 5 ) , ( 1 3 ) a n d ( 1 4 ) , w e g e t G c l a n dG c 1 a s shown i n E q s . ( 1 5 ) a n d ( 1 6 ) .2 2 . 6 s 2 + 2 5 Bls+ 8 . 4 3 3 1l ( s ) =5s t s + 3 3 3 8 )G c2()3-11s2 _ 3 . 1 4 s - 0.0 1( 1 )F i g . 8 s h o w s t h e com p l e t c o n t i o l d e s i g n .

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Th e ] a s t t s L i s o b s e r v a t o n s h e c o n t i ] l e r m p o n s e o ft h e = p i n p u t m e p o n s e ( a m p p a t h a n g l e i a t E ) . Ass t a t d befie t h a t = m p i n p u t e q p o n s e o f t h e c o n t i ] l e ri s m d i m e c l y ecuvalentw i l h t h e e q p o n s e o f p a t h a n g l e .R a m p i n p u t e q p o n s e s w i l h z e r sbady-st e i r m sc a u e s h e p a t h a n g l e o u t p u t bT1w s a g i v e n c i c u l a r ( o ra r c ) p a t h w e l l a n d q u i c k l y w hen a stp refence p a s ha n g l e a t E i s n p u t t e d . H e n c e , t h e f i s h - l j k e b o a t w i l lp e i f n m w e l l t n i n g a t t h e c i u l a r ( o r a r c ) p a t h . F g . 1 1s h o w s s h e p a t h a n g l e a tE e p o n s e w hen 3m p i n p u t 4t

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d e g / s i s a p p l i e d a n d F i g . 1 2 s h o w s t h e e p o n s e o f p a t ha n g l e w hen r e f e r c e i n p u t 6 p a t h a n g l e a t E ) 4 d e g / s( s t r p ) i s a p p l i e d . Both s i n u l a t i D n a i e d o n e w i t h z erd i s b i - b a n c e .

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F i g . 1 2 Th e p a t h a n g l e m e o n s e o f c o n s t a n t ( s t e p ) p a t ha n g l e L a t E iefnce ( 4 d e g / s ) .I t ' s ee n t h a t F i g . 1 1 a n d F i g . 1 2 a L e e x a c d y t h e s am e .T h e L e f L e , t h e d e s i g n h a s a s c m e t t h e Ui d r l q u i m n e n t .The m oeim portnt ing i s t h e c o n t b o l ] r d e s i g n c a n

m a k e t h e f i s h - l k e b o a t t tun w e l l f D b T w i n gc i C u l a r / , = p a t h . I n c o n c l u s i o n , t h e c o n t o l l e r d e s i g nh a s a c i e v e d a l l d e f i n e d g o a l s f i e u i i r a e n t s .

model w i i h b e t t e r ( a n d b e t t e r ) q u a h t y . A ] s c , t h ec o n t o l l e r d e s i g n i n U i f i s w o i s s b l l b a s i c a n dp m e i m i n a y d e s i g n f h a t n e e d s t be 3 m p r o v e d u s i n ganothercontlm e t h o d ( I o b u s t c o n t b l , a d a p t i v e c o n t l ,e t r ) . F i n a l l y , i m p l e m e n t a t i D n o f t h e COnt]ler d e s i g nw i l l be t h e u ] i i n a t E f u t r i e w oi o f tis f i s h - l k e L o b o tdevebpm e n t .

ACKNOW LEDGEM ENTT h i s wo0 w a s supportd by t h e K o r P e a R e s a i hF o u n d a t i D n G a n t KR F - 2 0 0 4 - 0 0 5 5 - B 0 0 0 4 7 ) .

REFERENCES[ 1 ] D. T z e = a n s , E. Papadopoubs a n d G . .T r a n t a f y l b u , O n t h e D esgn o f a n AutDnom ou sRobot F i h , " N a t i D n a l T e c h n i c a l U n i v e m i I y o fA t h e n s , G L e c e 2 0 0 3 .[ 2 ] h t t p : / / q ww a i m 1 L g o . p / e n g $ k h a t a / i h / n d e x _ e h t u n1[ 3 ] I . A i J y a n t , T . S . Kang a n d Y. J . L e e , "T d a n t f i c a i D n o f a F i s h - l T e Robot U s i n g I n e r t i a l

S e n s o r s , " Th e I n t a m a t i D o n a l C onfrice onE x p e r i m e n t a l M e d i a n i c s , K o P a , 2 0 0 6 .[ 4 ] K. H i a t a , " Devebpment o f E x p e r i m e n t a l F i s hR o b o t ' S h i p R e s a c h I n s d l t t e , T o k y o , 2 0 0 0 .[ 5 ] K. O g a t , " M o d e m n Contol E n g i n e e r i n g 4 * 1E d i t i D n , P L n t i c e H a l l 1 N ew Jeiy, 2 0 0 2 .[ 6 ] L. L j n g , " Systm I d a n t f i c a t i D n , T h e o r y b r U s e r ,2 n d E d , , ' P r n t i c e H a l a N ew e 1 9 9 9 .[ 7 ] L . L j n g , g Systm I d a n t f i c a i o n T o o l b o x , For U eW ih M ATLAB, The M a t h W ois I n c . , 1 9 9 7 .[ 8 ] M i c s b t i n , 3DM - G U s e r Ma n u a l , F i r n r w aa v .13.00,"M i l s b a i n I n c . , W i T i s t o n , U S A , 2 0 0 3 .[ 9 ] P . H a i d u c , " C o d e V i s i o n AVR User M a n u a l v1 2 4 . 0 / ' ] h D T e c h d S L R , 2 0 0 3 .

5.CONCLUSION AND FUTURE W ORKSTo d e v e b p a f i h - l J k e o b o t , w e h a v e pL gssed i ns t u d y i n g a n d s i n u l a t n g f i s h s w i m m i n g d y n a m i c s ,e s p e c i a 1 y t=ing, u s i n g a f i s h - h k e b o a t w i t h s i n g l eos i a l a t n g f i n . F i i s L i e s e a c h a n d s t u d y h a s b e e n fcused

on t h e f i s h - l k e b o a t model i d a e n d f i c a t i c a n t fnd t h ed i L e c d n a l t r a n q r T h n c t o n a s t h e g o a l . Th ei d a e n 5 t i c H A H n p r : c e d u L e h a s L e s u l t e d a m o d e l n s f e rT h n c t D n w i l h a c c e p t b l e q u a a i i y ( e n D r t s i g n a l a t d oa b o u t 1 0 % ) . W e a L s c h a v e d e s i g n e d t h e a c n t o l e r b a s e don t h e t r a n s k r T h n c t d n o b t a i n e d t i mprve t u m i n gp e r i r n a n c e of t h e f i h - l I k e b o a t . Th e d e s i g n em p by st w o - d e g i e s - o f - f r e e d o m PD a c n t z D l d e s J q n . T h e d e s i q nh a s a ] s c b e e n p L o v e d t m e e t a l l d e f i n e d L i i q m e n t s .

Th e s t s m model i d e n t i f i a t n m s e a I c h o f t h ef i h - l I k e b o a t i s s b l l g o i n g i n oder t f i n d a n o t h e r

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