Buoyancy effect control in multi legged robot locomotion on seabed using integrated impedance-fuzzy logic approach

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1 Idia Joual of Go-Mai Scic Vol. 44(), Dcm 5, pp Buoyacy ffct cotol i multi lggd oot locomotio o ad uig itgatd impdac-fuzzy logic appoach Md. Moktadi Alam, Addi Iawa* & Ta Y Yi ootic ad Umad Sytm (US) ach goup, Faculty of Elctical & Elctoic Egiig, Uiviti Malayia Pahag, Pka, Pahag, 66 Malayia [ moktadi.alam@hotmail.com, addiiawa@ump.du.my*, yyi8@gmail.com] civd 3 Octo 5; vid 5 Dcm 5 Buoyac foc a pat of th fudamtal phyical itac that act o movig o wimmig ojct i th oca viomt. Fo th ca of multi-lggd oot, uch a hxapod walkig o th ad, uoyac affct th hoizotal taility if th motio of th oot foot do ot hav ufficit foc to tp o th ottom of th ad. Thfo, thi tudy i caid out y itgatig a divd Ct of Ma (CoM)-ad impdac cotol with fuzzy logic cotol to cat fo th dyamic tat that ldd with udwat uoyac foc o th motio of th hxapod foot. Thi itgatd cotol tatgy i digd, modld ad vifid o th al-tim ad 4-dg of fdom (DoF) lg cofiguatio of a hxapod oot modl with uoyacy foc modl a foc dituac. Th cop of aalyi i focud o vifyig th tiff of uda ottom oil with th tipod walkig patt, th vtical foot motio of th lg, ad th ody ma coodiatio movmt duig locomotio piod. [Kywod: CoM-ad impdac modl; fuzzy logic cotol, foc toatio; foot motio] Itoductio Th ach hav widly tudid th ad o tidal cut udwat viomt that div though th complx ytm ad cotol tatgi i mai vhicl ytm. Thfo, it i tial to dig a appopiat imulatio modl that i al to pfom lik th havio of a al-wold autoomou udwat vhicl (AUV). Hydodyamic chaactitic a vy igificat facto i ach i th fild of udwat ootic ytm. Th fficicy ad taility of th cotol algoithm ad th mot optimum tuctu of th oot a dpdt o pop hydodyamic aaly. Fo th oca viomt, val motio cotol algoithm hav dvlopd ic th pat two dcad ud a ag of hypoth. By adoptig a liaizd modl, vaiou lia cotol tchiqu, uch a popotioal-itgal-divativ (PID) cotoll ad Lia Quadatic gulato (LQ) algoithm, hav itoducd with accptal pfomac i oly uuual kid of maipulatio 3. Howv, uch mthod igo th itactio tw u-cotoll ad implify th dg of fdom (DoF) modl ito val uytm 4. Coidig qua itgal oudd dituac ito accout, lia cotoll hav futh impovd i th ac of paamt vaiatio 5. Numou mod ivtigatio coc with modl uctaiti ad cut olia-ad mthod, uch a lidig mod cotol i which th upp oud of uctaiti ad dituac i kow i advac, itlligt cotol algoithm ad o ual twok ad fuzzy logic hav alo applid to th UV 6.7. Adaptiv motio cotol of a gal cla of AUV i th pc of modl uctaiti ad viomtal dituac ha tudid, a potd i 8. Icopoatd ito th mathmatical modl a th paamtic ad amophou dituac du to th vaiatio i hydodyamic ad dampig cofficit. A adaptiv ad cotol algoithm i fit dvlopd to udtak th paamtic modl dituac, ad th a out cotol law i implmtd i od to u th out of th mthod with pct to utuctud uctaiti ad xtal dituac. I th oca viomt, oca wav hav vayig wav piod ad hight dtmid y wid ad th ditac tavd. Accodig to th D Allmt paadox, i a tady flow th i o foc o a ody ud o-vicou fluid. Fo tidal cut i a utady ituatio with addd ma, dag foc, uoyacy ad cut, pcially i th xitc of f ufac wav, it i quid to

2 938 INDIAN J. MA. SCI., VOL. 44, NO., DECEMBE 5 coid tim-dpdt motio of oth th wat ad th oot ody; th ytm ital a wll a xtal foc addig to th total foc o th ytm 9. Thu, fo vhicl o tity that mov o th ad uch a multi-lggd oot, it i cucial that foc cotol i tak ito accout. Commo ootic foc cotol fo aticulatd cofiguatio am ad lggd ytm ha pacticd i two tatgi; foc-ad ad poitio-ad foc cotol. I thi tudy, a itgatio cotol tchiqu tw itlligt cotol ad dyamic cotol fo hxapod oot foot motio duig walkig o ad i popod. Th fuzzy logic cotol (FLC) i applid uig two dyamic tat of ct of ma (CoM) ad impdac modl (poitio ad vlocity) a cip iput to cat th ufficit dyamic motio of ach hxapod oot foot placmt duig locomotio o ad. Hypothtically, th itgatd gai-ad FLC uch a PD-FLC ytm i lial o pdictio ad coctig th lag ovhoot ut th divativ pat affct th tady-tat o of a ytm ut thi tudy tady-tat i ot th iu. Th appoach a imulatd ad vifid i thi tudy: Hxapod oot walkig with CoM-Impdac-FLC, th oot walkig with CoM-Impdac oly ad th oot walkig without impdac cotol. Th platfom ud fo th vificatio i th ytm idtificatio modl of a 4-dg of fdom (4-DoF) lg of hydaulically div hxapod oot amd COMET- IV. I ctio : th hxapod oot i aumd to poply dowd o ad aft tuig th ody ma of th oot to coqu th uoyat facto, I ctio 3: aft tuig th dampig cofficit ad tiff cofficit of th ootic foot a CoM- Impdac-FLC cotol modl i popod i 4-DoF lg cofiguatio of Hxapod oot it i ady to walk o th ad viomt. I ctio 4: th popod cotol achitctu i imulatd ad vifid with difft tuig facto. Th aalyi of th ult i focud o th foot motio ad th total foc o th foot compad to th uoyac foc of th oca. Eviomt Modl Coidig th Buoyat Foc Bouyacy facto via uoyac foc, id th ad gavity ad it uv tai, will affct th locomotio of multi-lggd oot. Th diffc tw gavitatioal ad uoyacy foc a calld toig foc ad thi foc i compaal to th pig foc i a ma-pig damp ytm3. With fc to th Achimd' picipl, th uoyat foc o a umgd igid ody will a upwad foc qual to th wight of th fluid diplacd y th ody that it th wight of a immd ojct. Th uoyat foc i activatd though th ct of gavity of th ojct that it to pull up th ojct out of th wat ufac. Fig. how th dfiitio of uoyat foc picipl fo a multi-lggd oot ytm. I thi tudy ca Ekma lay of th ad i coidd that coit a foc alac tw pu gadit foc, Coioli foc ad tuult dag; ad th oca wat tmpatu at o C. M Oca Sufac D F B W K Sad m E k m a L a y Fig. Udwat uoyat foc actig o a multi-lggd oot fo Ekma Lay of ad Th uoyat foc ( F B ) i qual to th wight of wat diplacd y th umgd oot ( W ) ad ca calculatd uig Eq.. Coid th atio of th whol oot ody to wat dity (d w ) to a follow: d d w W W

3 ALAM t al.: BUOYANCY EFFECT CONTOL IN MULTI LEGGED OBOT LOCOMOTION 939 Thu th wight of wat diplacd y th umgd oot: W W F d () B w d wh, d M i th dity of th oot; V ad V a pctivly ma (i kg) ad volum (i m 3 ) of th oot. Th wight of th oot, W M g ; wh g 9.8m i th gavity of ath, thu uoyat foc ca xpd a follow: F M g W () B S w V 3 Wh, wat dity, w 4.83kgm fo oca with fc to Itatioal Aociatio fo th Popti of Wat ad Stam (IAPWS) at C. I od to dtmi whth o ot th oot float o th ufac o dow to th ottom of th ad, toig foc ( F ), th diffc tw th oot ma ad uoyat foc, i calculatd a follow: F W FB (3) wh, F mut poitiv ough to u that th oot lg i al to tad o th ottom of th ad. I th ca of multi-lggd oot, thi i oly tu fo tatic o tadig poitio (igid ody). I th ca of a oot that mov, th total foc o ach foot that tp d to coidd; with fc to Fig., th foc o ach foot i calculatd a follow: F F M z( t) D z( t) K z( t) (4) f wh...6 i th um of lg of th oot; D ad K a pctivly th damp ad tiff of th oil/goud coutd y th lg o vtical motio, z-axi ( z ) (f to Fig.3 fo dtail of hxapod oot lg ad ody ax) Bad o th viatio thoy fo pig-ma damp, y tatig M M a a f ody (aumd ( ) Ff M z t ) ad applyig Nwto cod law, D i dtmid a follow y aagig Eq.4 a follow: D K z z z M M Thu, th (uddampd) atual fqucy ad dampig atio fo th impdac modl ca witt a follow; K D (5), M M K I od to cotol th ocillatio i th iput, citical dampig (f viatio with dampig) i cho, wh. Th damp of th oil/goud coutd y th lg D ca xpd a follow; D K (6) wh, th ma of th oil (M ) i aumd to ukow, whil z( t) i th chag i th motio i th vtical axi of th lg i al-tim. Thu, th toig foc duig th difft pha i th locomotio ca calculatd a i Eq. 7: walkig pha with l um of lg o th goud/oil ad tait pha with -lg a follow; F l k k F F walkig _ pha k F F tait _ pha B B (7) Itgatio of divd CoM-ad Impdac Cotol with FLC fo Hxapod oot Lg Vtical Poitio Cotol i Sad Eviomt

4 94 INDIAN J. MA. SCI., VOL. 44, NO., DECEMBE 5 Oth tha uoyac, th ad that cotaid oft oil ad coal f qui th hxapod oot to hav lg with adaptal tiff. O th oth had, ovpuhd ituatio alo d to avoidd y ach lg duig locomotio o oft oil ad uv tai to u th oot walk i a hoizotally tal coditio. A dicud i Sctio, th total uoyacy foc F f d to ufficitly poitiv uch that F. Thfo, to achiv thi pupo ad to u that oot locomotio i o th ottom ufac of th a, impdac quiliium i divd, a how i Fig., y coidig th toig foc, F that ca xpd i Eq.8 a follow: F M h D h K h (8) wh, dtmid a D i th total dampig cofficit, imilaly D dicud i Sctio, ad h i th tat of oot vtical motio chag with tim (t ). Moov with th wight of th oot tak ito accout, ad th cofficit ca xpd a follow: D K M (9) wh K i th total tiff of th oot ody fom th hould to th goud (total tiff of uppotd lg), a how i Fig., which i a poitiv tuig paamt. F i th total vtical foc actig o th lg that touch th goud, i which FB i coidd a th a uoyacy facto. Th total foc covy th ifomatio o th ct of ma (CoM) fo th oot duig tait ad walkig pha. A pviouly tatd, 4-DoF lg cofiguatio of hxapod oot modl with tipod walkig patt i ud i thi tudy. Th tald CoM fo tatic taility cofiguatio oot 4, uch a hxapod oot, d to hav total of foc fo th foot placmt at lat a to th actual total wight of th oot. Thu, th calculatio of F ad o tipod walkig patt i how i Tal, with fc to th otificatio giv i Fig. 3. I itgatig th FLC, th h (t) tat a ud a iput vaial. Th cotiuou fuzzy modl popod y 5 i ud via fuzzy if-th ul to optimiz th iput vaial. th Th fuzzy ul a cotaiig i ul fo a multiiput igl-output (MISO) fuzzy ytm with th followig fom 6 i coidd a follow: i i i k if h i M ad... if hk i M th H () k i M k wh hk a th ytm tat vaial, i a th fuzzy t, ad H a th output chaactizd i liguitic tm, that i, SMALL (S), MEDIUM (M), ad BIG (B) fo oth poitiv (P) ad gativ (N) coodiatio. Th fial output, o cip output, of th fuzzy ytm ( ) fo dyamic vtical poitio i ifd a follow (uig a iglto fuzzifi with a miimum opato a th atcdt pat of th ul ( ) ad th ct of ma mthod fo dfuzzificatio): I i I i i a a a H [ ( ) ] i a a a H ( ) () wh, I i th um of ul lctd fom th th total of i ul that a pt i th ul a fo a t of iput, a i th fdack compato that claimd with K ad D valu, i thi ca a how i Fig. 4. Alo, h i a iput vaial (which mut atify H ( t) ), i th calig facto fo ach dfid mmhip fuctio, that i, NB, NM, NS, PS, PM, PB, wh.8 followig th cotait of th oot ytm with fc to th pot i. I additio, ( v a ) i th mmhip fuctio valu fo th H iput vaial, wh it pt difft valu fo difft. Thi popod CoM-Impdac-FLC achitctu ca illutatd a i Fig.. oot (tadig up poitio) F, F, F 4 6 SOIL/GOUND F, F, F 3 5 D Spig-ma-damp (latic modl) D Fig. Equivalt latic modl of th oot M K K M F

5 ALAM t al.: BUOYANCY EFFECT CONTOL IN MULTI LEGGED OBOT LOCOMOTION 94 Th cotol iput u( t) ca ptd with th diviio a follow: q ;,3,4,6 3 u( tq) q q ;,5 3 () With fc to th hxapod oot cofiguatio a lald i Fig. 3, foc dlivy o ach foot (placmt piod) at tim ( t q ) i taulatd i Tal. X Tal Calculatio of th total vtical foc ad o th tipod walkig patt Total foc Statu Suppotd Lg (foot placmt) Walk,3,5 Walk,4,6 Tait All (Fo hxapod oot) F F F 3 5 F F F Thu, th impdac cotol output ca xpd a follow: z z u (3) I q q q F y Lg Lg Y Lg 3 x z Z Lg 4 Lg 5 Lg 6 Th popod CoM-Impdac-FLC with coidatio of uoyacy facto ad viomt taild tajctoy (ETT) 7 i dcid y th diagam of ovall hxapod modl cotol tuctu how i Fig 4. Fig.3 Coodiat ytm ad lg otificatio fo hxapod oot modl Impdac Modl (h) Fom tajctoy modul (tipod quc ad lg aic motio) K h( t) FLC z q x ( t), y ( t), z ( t) Divid z I q Iv Kimatic T 3 4 ( t) [ ] Poitio Cotol (PID) oot Plat F D h( t) z o q Dict Kimatic T ( ) [ 3 4 ] o t F ( t) To tajctoy modul (tipod quc) Eviomt Modl Fig. 4 Ovall viw of th popod CoM-Impdac-FLC cotol i 4-DoF lg cofiguatio of Hxapod oot modl

6 94 INDIAN J. MA. SCI., VOL. 44, NO., DECEMBE 5 ult ad Dicuio Th popod itgatio of impdac-flc cotol i implmtd ad vifid with val imulatio o hxapod oot cotol tuctu. Th aalyi i do y compaig pviou tipod walkig with CoM-ad impdac cotol (CoMI) 8 with th popod CoM-Impdac-FLC impdac cotol (CIFLC), icludig tipod walkig without impdac cotol (No Imp). Th imulatio ad aalyi a do i two ituatio: oot walkig with cotat K (Situatio ) ad oot walkig with vaial K (Situatio ); oth ituatio a aumd to hav o hoizotal cut tidal ut with uifom adom oi a igal dituac. Th oot i u ud th omidictioal flow that ivolvd cuv tuig ad zig-zag a how i Fig. 5. Tal Popod impdac cotoll ad viomt modl paamt t ad o th dowig o ad coditio Paamt Valu Situatio Situatio K 4kN/m 4N/m ~ 4kN/m K M 8kN/m ~ kn/m 3 kg V.355 m 3 Th total ma ( M ) which i th optimal valu to achiv th hxapod oot tatically ikig ito th a ad tadig o th ottom of th a to i od to u F. A how i Tal, th viomt tiff ( K ) i t i uifom adom valu that pt th oft tai of th ad oil (K > K ) fo th ca of oft oil/tai imulatio). Fo Situatio, a how i Fig. 5, o tad-up poitio, th oot walk o th ad with CoMI, CIFLC ad No Imp whil pfomig th am vtical foot motio fo aout 34 cod util it tak th fit tp. Aft th fit foot wig-pha, th oot with CoMI ad CIFLC how xta puh dow (xta foc) to th oil compad to th oot walkig without th impdac cotol. A ovd i Fig. 6, F FB fo th oot with impdac cotol ha complid with th coditio fo hxapod oot to walk o th ottom of th a a compad to th oot without impdac cotol. Howv, th hight of th oot ody m to ica fom th fit tadig poitio, a ca i th ody hight pfomac ptd y th ct of pu (CoP) o foot a how i Fig. 7. Moov, itgatig th FLC affct th CoMad Impdac cotoll output y ducig xta puh at th am tiff valu a how i th imulatio ult fom Fig. 5 to Fig. 7. Nvthl, oth CoMI ad CIFLC pfomd tal walkig o tup omidictioal locomotio path fom th ody ma coodiatio (BMC) 9 a how i Fig.8. z-axi [m] Stad-up Swig Pha No Imp Suppot/Foot placig Pha Fig. 5 Sampl of foot poit motio o th z-axi viw (ampl: Lg 3) Foc [kn] Stad-up Swig Pha Suppot/Foot placig Pha F B F No Imp Fig. 6 Sampl of total vtical foc o foot of hxapod oot

7 ALAM t al.: BUOYANCY EFFECT CONTOL IN MULTI LEGGED OBOT LOCOMOTION 943 Foot CoP (m) Z Coodiatio [m] oot Stadig oot Walkig Iitial No Imp Y Coodiatio [m] Fig. 7 Sampl of oot foot CoP - -5 Locomotio flow X Coodiatio [m] Stad-up 5 f Fig. 8 Sampl of BMC fo omidictioal walkig mod i Situatio z-axi [m] Fig. 9 Sampl of foot poit motio o th z-axi viw fo vaial K (ampl: Lg ) Th imulatio i xtdd with Situatio, i which th locomotio of th hxapod oot with th popod impdac cotoll CIFLC ad CoMI a t with th ag of tiff ( K ) valu a taulatd i Tal. Difft locomotio pfomac a otaid i thi ituatio a ca i Fig.9, i which th foot motio fo th hxapod oot walkig with CoMI ad vaial K i utal. Th utal ituatio of th foot motio fo th hxapod oot walkig with CoMI tatd fom th fit tp of th lg movmt (aout 34 cod) ad th output ult how foot motio timig a affctd y thi vaiac of tiff. O th cotay, th hxapod oot walkig with th popod IFLC i tal, a how i Fig.9; i which FLC m al to compat with th foot motio timig ad taaliz th locomotio although K i chagd y tim, a how i Fig.. O th oth had, a how i Fig., th total foc o foot actd xtmly high fo th hxapod oot walkig with CoMI: tatd with appoximatly 4kN fo aout 53 cod ad dcad to appoximatly kn aft 85 cod, ad th mai cotat. Thi i cau mot of th oot lg a tiffd ad ot movig, uch a Lg a how i Fig.9. Thfo, thi affct th oot locomotio a a whol a how i Fig., i which th hxapod oot walkig with CoMI o ttd with vaial K i ual to mov a plad compad to that of th oot with th popod CIFLC. K B [N/m] x Fig. Th vaiatio of K duig hxapod oot locomotio fo Situatio

8 944 INDIAN J. MA. SCI., VOL. 44, NO., DECEMBE 5 Foc [kn] F B viomt, hoizotal cut tidal i alo pat of th foc that affct th ytm that i movig o th ad. Thfo, thi iu hould tudid ad ivtigatd i th futu, which ca impovd y icludig th hydodyamic cut tidal foc i th viomt modl ad y impovig o digig a w compliat cotol fo th hxapod oot Fig. Sampl of total vtical foc o foot of hxapod oot Z Coodiatio [m] Y Coodiatio [m] Locomotio flow Stad-up X Coodiatio [m] f Fig. Sampl of BMC fo omidictioal walkig mod i Situatio Cocluio Th imulatio ult how th popod adaptiv appoach of impdac cotol with FLC itgatio, amly CoM-Impdac-FLC impdac cotol (CIFLC), that wa implmtd i 4-DoF lg hxapod oot ha uccfully compatd ad tod th ultat foc that act vtically o th oot duig locomotio o th ad. I Situatio, th popod CIFLC m to pfom th am actio a i pviou appoach uig CoMI 8. Howv, i Situatio, y vayig K i adom uifom valu, th aalyi how th popod CIFLC ult i mo tal walkig compad to that uig CoMI; i th lat ca, th lg uddly toppd o th tp of movmt a how i Fig.. Fom thi imulatio, it i how that CIFLC i al to cop with th dyamic cotoll output i od to uit with th cotait motio of th hxapod ytm, which ha t a th calig facto i FLC tuctu. I th al ituatio of uda Ackowldgmt Th ach wok i uppotd y th Miity of Educatio Malayia ud th ach Accultuatio Collaoatio Effot (ACE) i collaoatio with Udwat oot ach Goup (UG), Uiviti Sai Malayia (USM). Thi ach i alo patially uppotd ud th Uiviti Malayia Pahag (UMP) ach Gat. fc K. M. Ta, T.-F. Lu, ad A. Ava, "Dag Cofficit Etimatio Modl to Simulat Dyami Cotol of Autoomou Udwat Vhicl (AUV) Motio " i th Itatioal Cog o Modllig ad Simulatio, Adlaid, Autalia, 3 pp. 6. C. Yu, S. Guo, ad L. Shi, "Hydodyamic aalyi of th phical udwat oot SU-II " Itatioal Joual of Advacd ootic Sytm 3. 3 A. I. Fild, D. Chcha, ad S. Calial, "Optimal cotol of a autoomou udwat vhicl," i Wold Automatic Cog, Hawaii, USA,. 4 J. Ptich ad D. J. Stilwll, "Modl implificatio fo AUV pitch-axi cotol dig," Oca Egiig, vol. 37, pp ,. 5 L. Lapi, "out divig cotol of a AUV," Oca Egiig, vol. 36, pp. 9-4, 9. 6 S. S. You, T. W. Lim, ad S. K. Jog, "Gal pathfollowig maouv fo a udwat vhicl uig out cotol ythi," ptd at th Poc. IMchE, Pat I: J. Sytm ad Cotol Egiig,. 7 J. S. Wag ad C. S. G. L, "Slf-adaptiv cut uo-fuzzy cotol of a autoomou udwat vhicl," ptd at th IEEE Ta. ootic ad Automatio, 3. 8 H.. Koofiga, "Adaptiv Cotol of Udwat Vhicl with Ukow Modl Paamt ad Utuctud Uctaiti," ptd at th SICE Aual Cofc Akita, Japa,. 9 L. Lapi, P. Fai, ad P. Dauchz, "Poitio/Foc Cotol of a Udwat Moil Maipulato," Joual of ootic Sytm, vol., pp. 77-7, 3. A. Iawa ad K. Noami, "Optimal impdac cotol ad o ody itia fo a hydaulically div hxapod oot walkig o uv ad xtmly oft tai," Joual of Fild ootic, vol. 8, pp ,. N. Siddiqu, Itlligt Cotol: A Hyid Appoach Bad o Fuzzy Logic, Nual Ntwok ad Gtic Algoithm: Spig Itatioal Pulihig, 3.

9 ALAM t al.: BUOYANCY EFFECT CONTOL IN MULTI LEGGED OBOT LOCOMOTION 945 K. Noami,. K. Baai, A. Iawa, ad M.. Daud, "Hydaulically Actuatd Hxapod oot," 4. 3 L. Liol, "Udwat oot Pat II:Exitig Solutio ad Op Iu," i Moil oot: towad Nw Applicatio, A. Laziica, Ed., d Gmay: ITchOp, 6, pp Sigwat, I..Nouakhh Itoductio to autoomou moil oot: MIT P, 4. 5 T. Takagi, M.Sugo, "Fuzzy Idtificatio of Sytm ad It Applicatio to Modlig ad Cotol," IEEE Taactio O Sytm, Ma ad Cyatic, vol. 5, pp. 6-3, A. Vaickaiova, M.Bakaova, "Locally Optimal Fuzzy Cotol of a Hat Exchag," WSEAS Taactio o Sytm, vol. 9, pp ,. 7 K. Noami,. K. Baai, A. Iawa, ad M.. Daud, "Kimatic, Navigatio, ad Path Plaig of Hxapod oot," i Hydaulically Actuatd Hxapod oot, d: Spig Japa, 4, pp M. M. Alam ad A. Iawa, "Adaptiv impdac cotol ad o CoM fo hxapod oot walkig o th ottom of oca," i Th 5th Itatioal Cofc o Udwat Sytm Tchology: Thoy ad Applicatio 4 (USYS'4), Mlaka, Malayia, 4, pp H. Ohoku, A. Iawa, ad K. Noami, "A 3D modlig fo hydaulic-div hxapod walkig oot uig 3D gomtic tchiqu with ditiutd umical modl," It J Autom oot Auto Syt, vol. 9, pp. 36, 9.