A Path Tracking Algorithm Using Future Prediction Control with Spike Detection for an Autonomous Vehicle Robot

Transcription

1 Intrnational Journal o Avanc Robotic Systms ARTICLE A Path Tracking Algorithm Using Futur Priction Control with Spik Dtction or an Autonomous Vhicl Robot Rgular Papr Muhamma Aizzat Zakaria, Hairi Zamzuri,*, Rosbi Mamat 2 an Saiul Amri Mazlan 3 UTM-PROTON Activ Saty Laboratory, Univrsiti Tknologi, Malaysia 2 Dpartmnt o Control an Mchatronic Enginring, Faculty o Elctrical Enginring, Univrsiti Tknologi Malaysia 3 Vhicl Systm Enginring Rsarch Laboratory, Malaysia-Japan Intrnational Institut o Tchnology, Univrsiti Tknologi, Malaysia * Corrsponing author hairi@ic.utm.my Rciv 8 Dc 202; Accpt 20 May 203 DOI: / Zakaria t al.; licns InTch. This is an opn accss articl istribut unr th trms o th Crativ Commons Attribution Licns ( which prmits unrstrict us, istribution, an rprouction in any mium, provi th original work is proprly cit. Abstract Trajctory tracking is an important aspct o autonomous vhicls. Th ia bhin trajctory tracking is th ability o th vhicl to ollow a prin path with zro stay stat rror. Th iiculty ariss u to th nonlinarity o vhicl ynamics. Thror, this papr proposs a stabl tracking control or an autonomous vhicl. An approach that consists o string whl control an latral control is introuc. This control algorithm is us or a non-holonomic navigation problm, namly tracking a rrnc trajctory in a clos loop orm. A propos utur priction point control algorithm is us to calculat th vhicl s latral rror in orr to improv th prormanc o th trajctory tracking. A back snsor signal rom th string whl angl an yaw rat snsor is us as back inormation or th controllr. Th controllr consists o a rlationship btwn th utur point latral rror, th linar vlocity, th haing rror an th rrnc yaw rat. This papr also introucs a spik tction algorithm to track th spik rror that occurs uring GPS raing. Th propos ia is to tak th avantag o th rivativ o th string rat. This papr aims to tackl th latral rror problm by applying th string control law to th vhicl, an proposs a nw path tracking control mtho by consiring th utur coorinat o th vhicl an th utur stimat latral rror. Th ctivnss o th propos controllr is monstrat by a simulation an a GPS xprimnt with noisy ata. Th approach us in this papr is not limit to autonomous vhicls alon sinc th concpt o autonomous vhicl tracking can b us in mobil robot platorms, as th kinmatic mol o ths two platorms is similar. Kywors Trajctory Tracking, Mobil Robot, Autonomous Vhicl, Yaw Rat Control, Path Following, String Control, Spik Control. Introuction Autonomous vhicls ar a rapily vloping il. Th application o autonomous vhicls is xpct to b wily us in urban aras, inustry an airport Muhamma Aizzat Zakaria, Hairi Zamzuri, Rosbi Mamat an Int. Saiul j. av. Amri robot. Mazlan: syst., A 203, Path Tracking Vol. 0, Algorithm 309:203 Using Futur Priction Control with Spik Dtction or an Autonomous Vhicl Robot

2 trminals, tc. An autonomous vhicl is capabl o snsing its nvironmnt, cision-making an navigating by its sl. By using autonomous vhicls, humans can in th stination or path an th rst o th navigation will b takn car o by th systm. An avanc control stratgy will us th appropriat inormation to control th vhicl's navigation. Th control systm must b abl to hanl th roa charactristics - i.., straight, curvy, rough an varying trrain typs. In trajctory tracking, th control stratgy is us to track th path an achiv zro stay stat rror. Th concpt o an autonomous vhicl can asily b implmnt on a mobil robot platorm sinc th kinmatic mol o a mobil robot is similar to that o an autonomous vhicl. Th trm autonomous vhicl us in this papr coul asily b intrprt as mobil robot, although thr is slight irnt btwn thm. Th autonomous vhicl itsl contains a robotics systm, such as snsor inputs, signals procssing an cisionmaking by th control o th actuators. Trajctory tracking has bn a ocus o rsarchrs' attntion or yars. Th main objctiv is to achiv a ully autonomous vhicl in orr to ollow a prin path. On o th popular, pionring mthos was propos by Kanayama t al. [], whr authors propos a stabl tracking control by controlling th linar vlocity an th yaw rat. Kanayama's approach us simplii vhicl kinmatics to tackl th trajctory problm. Th authors us th Lyapunov mtho to analys th stability o th controllr. Anothr control approach was introuc by Firro t al. [2] an L t al. [3], whr th backstpping control stratgy was us to improv th prormanc o th trajctory tracking problm. Ths tracking stratgis ignor th ynamics o th vhicl sinc th ocus was on th mobil robot platorm. In [4], a uzzy logic tchniqu was us or vhicl tracking, whr th authors introuc two sts o uzzy logic controls, namly a positioning controllr an a ollowing controllr. For th autonomous vhicl, th ynamics o th vhicl shoul b takn into account. This is bcaus th consiration o a ynamic mol is mor suitabl to th actual vhicl systm whn tst in a ral worl application. Most rsarchrs sign th controllr bas upon a kinmatic or ynamic mol [5], [6], [7],[8]. In orr to acilitat th vhicl motion an ynamic charactristic o th vhicl, th controllr shoul b abl to tackl th bhaviour o both mos. Thror, in this papr, th mol is vlop by combining th ynamic an kinmatic motion o th vhicl. Th ynamic mol is us to stimat th latral acclration an yaw rat rspons o th vhicl, whil th kinmatic mol is us to calculat th latral an haing irction rror whn applying th string whl. Manwhil, th kinmatic mol is us or our rrnc path gnration or vhicl to track th path. This papr aims to tackl th latral rror problm by applying th string control law to th vhicl an proposs a nw path tracking control mtho by consiring th utur coorinat o th vhicl an th utur stimat latral rror. In ral applications o trajctory tracking, svral mthos can b us to track th position o th vhicl. Bas on [9],[0],[],[2] th most common snsors us ar GPS, lctronic compass, inrtial masurmnt unit (IMU), vio camra, lasr raar, oomtr an sonar. Howvr, or outoor position tracking, most rsarchrs us GPS u to its low cost. In rcnt vlopmnts in th il o autonomous vhicl navigation, th authors in [3] rais a problm rlat to GPS whrby at last our satllits ar rquir or a lss than 20-mtr prcision rror. Thror, th propos controllr shoul b robust nough to cop with GPS s uncrtaintis. This papr is an xtn vrsion o a prvious work in [4] whr th nonlinar controllr or vhicl path tracking was stablish. In this papr, a spik tction algorithm is introuc to stimat an ruc th ovrshoot o th vhicl rspons. Th xprimnt is carri out by capturing GPS ata to obsrv th nois rom th GPS raing. This ata is us as input or th controllr or monitoring purposs. Th papr is organiz as ollows: in sction 2, th concpt o th vhicl mol is introuc; in sction 3, th propos controllr is introuc; an in sction 4 th simulation an xprimntal rsults o th propos controllr ar givn. 2. Vhicl Mol In this rsarch, th vlopmnt o th vhicl mol is bas on th two gr o rom bicycl mol, which consists o both th yaw an latral acclration [5], [6], [7]. Th longituinal vlocity is assum as constant. Th initial acclration is nglct an th stat spac o th vhicl mol is rprsnt as Equation : x = Ax + Bu y = Cx + Du whr A, B, C an D ar in as: 2 2 l c + lr cr lrcr l c A = Izv Iz lrcr l ct c + cr + mv mv () (2) 2 Int. j. av. robot. syst., 203, Vol. 0, 309:203

3 l c I B = z c mv (3) 3. Futur Priction String Control 3. String Control 0 C = l c + lrcr ( c + cr ) mv m (4) D = c m Symbol Unit Rmarks m kg vhicl mass I 2 z kg. m vhicl yaw inrtia c N / ra cornring stinss o ront tir c r N / ra cornring stinss o rar tir l m istanc COG ront axl l r m istanc COG rar axl v km / h Tabl. Vhicl Paramtrs vhicl vlocity intrval whr A nxm, B nxm, C pxn, D pxm an n, m an p rprsnt th numbr o stats, control inputs an output rspctivly. Th stat o th vhicl mol is rprsnt by x = [ ψ, β] T, whr ψ is th yaw rat, β is th boy slip angl, an y = [ ψ, y] T whr y is th latral acclration Th input to th vhicl mol is th whl string angl, δ. Consir a vhicl locat at point x, y in a global coorinat ram with a haing orintation θ. From x, y, θ, which is th rrnc point, th postur rror can b obtain. Th latral rror, y, th haing rror, θ, an th longituinal rror, x, can b obtain by matrix transormation rom th global coorinat to th vhicl s local coorinat: x cosθc sinθc 0 x xc y sinθc cosθc 0 x x = c θ 0 0 θ θ c Th vhicl's motion pns upon th vlocity an th yaw rat vlocity. Th vhicl kinmatic is in as: x cosθc 0 v y sinθc 0 = ψ θ 0 (5) (6) (7) Figur. Futur Priction String Control Block Diagram Figur shows th ovrall control systm. A rrnc gnrator is us to gnrat th sir path, which consists o x an y coorinats an a vhicl haing irction, θ. An rror btwn th rrnc path an th priction vhicl position is calculat bor back to th nonlinar controllr. Th nonlinar controllr calculats th sir string whl angl in orr to achiv zro path rror. Th output rom th string control is tch as th input o th spik tction algorithm or string whl angl ajustmnts. Th propos controllr is sign bas upon th yaw rat tracking, whrby th string controllr will gnrat a larg string angl whn th latral rror is incras in orr to turn th vhicl towars th sir path. During cornring, th raius o th arc ns to b maintain in orr to navigat proprly. This coul b scrib by th vlocity an angular rat s rlationship to th raius. Thus, th string whl angl controllr is pnnt upon th longituinal vlocity an th angular rat, whr v is th vhicl vlocity an ψ is th vhicl yaw rat, as givn by r = v / ψ. Figur 2 shows th currnt vhicl position an th utur vhicl position. Th latral rror,, is calculat bas upon th irnc btwn th sir position, ( X, Y ), an th prict location, ( X, Y ), as stat in Equation 8 an Equation 9: X = Lcosθc + X c (8) Y = Lsinθc + Yc (9) y = sin θc( X X ) + cos θc( Y Y ) (0) θ = θ θc () an th nonlinar control law or whl string is in as: whr δ K y v y = sinθ + (2) X an Y ar th utur priction point, y is th utur latral rror, δ is th string whl angl, K is th gain an θ is th vhicl irction rror. Muhamma Aizzat Zakaria, Hairi Zamzuri, Rosbi Mamat an Saiul Amri Mazlan: A Path Tracking Algorithm Using Futur Priction Control with Spik Dtction or an Autonomous Vhicl Robot 3

4 an k =.4, k =.4, k =. For this papr, th longituinal x y z vlocity is assum as constant, which givs th valu o 2 2 k a = 0. Furthrmor, sinc th motion is on th x y x wx 2 2 plan, it causs k a = 0. z wz Figur 2. Currnt Position an Futur Position o th Vhicl Th controllr is us to th gnrat yaw rat that is rquir or th vhicl to navigat its position rom th prictvhicl location to th rrnc path. Th irst trm o Equation 2 acts as a limitr with a rang o [ 0, ]. Th scon trm acts as th string whl ratio bas upon th latral rror an th vhicl vlocity. Th trms nsur that th string whl ratio is proportional to th vhicl latral rror in orr that it can ollow th path with zro stay stat rror. Vhicl vlocity plays an important rol in ajusting th ratio o th string whl angl. Whn th vlocity incrass, th scon trm ratio o Equation 2 crass, causing th string whl angl output to cras. Th rspons o th controllr is in by gain K proportional to th latral rror convrgnc, whrby th gain has a signiicant impact on th vhicl yaw rat. An aitional saturat unction is introuc to control th maximum string whl angl. From Equation 2 it has bn shown that th latral rror, y, is proportionat to th string angl, δ, an may xc th maximum vhicl string whl angl. Thror, th π π string whl angl is limit btwn δ. Th 4 4 nw saturat valu is th rvis valu rom th prvious rsarch, whr th valu is obtain by xprimnt. Th ISO 263- stanar was us as th bnchmark to trmin th comort lvl o th vhicl, as shown in Tabl. Th ovrall acclration in by th ISO 263- stanar is as in [8], whrby: a = k a + k a + k a (3) w x wx y wy z wz whr awx, awy, awz ar th acclrations on th x, y, z irctions rspctivly, kx, k y, k z ar multiplying actors Ovrall Acclration Consqunc a w < 0.35 Comortabl 0.35 < a w < 0.63 A littl uncomortabl 0.5 < a w < Fairly comortabl 0.8 < a w <.6 Uncomortabl.25 < a w < 2.5 Vry uncomortabl a w > 2.5 Extrmly uncomortabl Tabl 2. Comort Lvl Bas on th ISO 263- Stanar 3.2 Spik Dtction Algorithm Whil a lot o control sign vlopmnt isrgars th ct o wrong ata inputs into th controllr, this papr introucs a simpl algorithm to chck an inaccurat input into th controllr by monitoring th output rspons o th controllr. It is otn th cas uring rror raing that th spik occurs u to th valu o th raing sunly changing to a non-rlat valu. This can b illustrat whn navigating th vhicl using GPS. Th GPS raing can sunly chang or b lost or many rasons, such as an inconsistnt numbr o satllits or multipath ata rrors bing rciv. Th ata rciv in this conition is normally inaccurat ata an th irnc rom th prvious ata is obvious. Bcaus o this, th string control will gnrat a larg string angl u to th luctuation o th GPS ata raing, which will caus th incorrct navigation o th vhicl. To ovrcom this problm, th authors propos a solution by consiring th cas whr tracking th controllr sun changs an by monitoring th bhaviour o th string control angl rivativ gnrat rom th controllr. This rivativ valu can b us as an inicator i th spik occurs by chcking th ost o th rivat: δ > δost (4) t Th spik tction algorithm is in as: δk = δk K2 δk (5) Whr δk- is th prvious string angl valu at on tim stp, K2 is th string tuning gain an δost is th rivat ost limit or spik tction. Th simpl algorithm can b scrib by analysing th trm us in th algorithm. In Equation 4, th string rat ost is 4 Int. j. av. robot. syst., 203, Vol. 0, 309:203

5 st in th program to monitor th string controllr output bhaviour in a crtain rgion that is allow to oprat. Th valu o th string rat ost can asily b achiv by tuning th string rat uring th xprimntal tsting. Th allowabl maximum string rat is th string ost in Equation 4. Ovr this ost valu, th program will inicat that th spik is occurr in th string output o th controllr. This mans that th currnt ata rciv by th controllr input is incorrct. Thror, to ruc th ct o an rronous controllr rspons, Equation 5 will b us to provi th ix or th string control output. Equation 5 will b us to ruc th string controllr output by th actor o K2. Th valu o th string whl angl rquir, δ, is always positiv, which is th magnitu valu sinc th ngativ sign inicats th irction o th string turning rspons. Th propr valu o K2 can b obtain through th tuning procss uring th xprimnt so as to gt th bst string angl corrction rquir. convrg on zro. Th simulation rsults show that th latral rror stay stat or K = 0 is At K =.00, th rspons o th vhicl is astr in achiving th sir stat. Howvr, rom Figur 4, it is obsrv that chattring os xist in th initial trajctory bor th vhicl bcoms stabl at K =.00. This is bcaus th yaw rat gnrat rom th controllr is highr at K =.00 in achiving a ast rspons as shown in Figur 3.2. From Figur 3., on th latral rror rspons, th variation o K impacts upon th rspons tim o th controllr in convrging on zro. Hnc, th K charactristic is a tim-varying gain. 4. Simulation an Exprimntal Rsults 4. String Control Rspons This sction iscusss th rspons o th whl string controllr to th latral rror an th sir yaw rat. Th latral acclration o th vhicl associat with controllr gain is prsnt. Th chosn o K is pnnt upon th initial haing rror, th vhicl latral acclration an th rspons o th controllr to th path. An appropriat optimiz valu o gain K is slct: Figur 3. Latral Rspons or Multipl Gain K K a w Tabl 3. K Tuning Rspons or θ0 = 0, v = 7ms - (25kmh - ) Tabl 3 shows th variation o K with th ovrall acclration rspons. Bas upon analysis in Tabl 3, th controllr alls unr th lvl a littl uncomortabl or a low gain o K bas upon th comort lvl as in Tabl. Unr high K, th rspons o th vhicl bgan to all unr uncomortabl. From Tabl 3, it has bn shown that th incrass o gain K will rsult in th lvl uncomortabl or th rivr. Th latral rror rspons o K = 0 can b sn in Figur 3.. Th graph shows that at K = 0 th rror has not Figur 3.2 Yaw Rat Rspons or Multipl Gain K From Figur 4, with an initial haing rror an whr θ is qual to zro, it can b sn that at K = 0 th vhicl was unabl to rach th sir path in a stay stat sinc th latral rror was not stabiliz at zro. This is u to th scon trm o th control law in Equation 8 bing cancll by th coicint zro. Thus, whn th vhicl haing irction is th sam as th sir haing irction, th irst trm o th control law will bcom zro. Th scon trm in th latral rror controllr, y, os not giv any back to th string whl. As a rsult, th vhicl ollows th sir path in paralll u to thr bing no rror corrction. Muhamma Aizzat Zakaria, Hairi Zamzuri, Rosbi Mamat an Saiul Amri Mazlan: A Path Tracking Algorithm Using Futur Priction Control with Spik Dtction or an Autonomous Vhicl Robot 5

6 It can b conclu that at a high valu o K, th vhicl approachs th sir path astr u to th high yaw rat gnrat rom th string whl input. Howvr, this caus th latral acclration incrass as a rsult o th ast turning rat to th sir path. 4.2 Exprimnt with GPS ata (a) In orr to valiat th prormanc o th nonlinar controllr sign, a ral GPS coorinat was us. A low cost GPS snsor moul was us. Th raing was takn only whn at last six satllits ar oun by GPS moul. Th raw GPS ata is convrt into th Cartsian coorinat ormat whrby a local North-East-Down (NED) ram is us an th vhicl starting location was at (0,0) an moving along th path by manual control an capturing th GPS coorinat. Th coorinat transormation rom a Earth-Cntr Earth-Fix (ECEF) coorinat to a local NED ram is in as in [9], whrby: (b) R P = R ( P P )) (6) n n/ c, r sinϕr cosλr sinϕr sin λr cosϕ r = sin λ cosλ 0 cosϕr cosλr cosϕr sin λr sinϕ r n/ r r (7) whr P n is a point in th NED coorinat ram, R n/ is th transormation matrix, P is th position vctor in th ECEF ram, P c, r th is th location o th origin o th local NED ram, λ r is th gotic longitu o P c, r an ϕ r is th gotic latitu o P c, r. (c) Figur 5. an Figur 5.2 show th longitu an latitu movmnt, which ar rprsnt by th X an Y coorinats. Th vhicl is moving towars a northwar location, such that in th ial cas th longituinal movmnt shoul b zro. Capturing a straight lin path is th bst an asist way to gt an inconsistnt ata raing. Th inconsistnt ata raing can asily b compar with th ial valu. From th igur, it can b sn that th GPS raing is a combination o th GPS position an th nois causing an inconsistnt raing rom th actual valu. This is u to such rrors occurring as satllit clock rrors, phmris rrors, ionosphr rrors, troposphr rrors, rcivr rrors an multipath rrors [20]. Ths rrors contribut to th noisy raing o th snsors. () Figur 4. Actual an Rrnc Vhicl Trajctory Figur 6 shows th trajctory rspons o th vhicl. It can b sn that th rspons is not as smooth as in th 6 Int. j. av. robot. syst., 203, Vol. 0, 309:203

7 ial cas u to th nois rror in th position raing. From th rspons, it is obsrv that th vhicl is still abl to track th rrnc path with minimal rror. Th controllr is abl to avoi sharp turning, although th rrnc rror is larg. This is important sinc sharp turning is caus by th incras o th latral acclration o th vhicl, which is not ial or vhicl navigation. Figur 7. Latral Error Rspons with Nois Data 4.3 Analysis o Spik Dtction Algorithm Th string angl rat is obsrv whn th spik occurs. From Figur 8, it can b sn that th spik causs a rspons o a high string valu. Thror, it is obsrv that th spik is corrlat with th string rat rspons o th controllr. Figur 5. Latitu GPS Data in XY Coorinat Figur 5.2 Longitu GPS Data in XY Coorinat Figur 9 shows th string control rspons both with an without th spik tction algorithm. Th spik signal in th simulation is introuc to simulat uncrtaintis in th position o th coorinat. Th spik is introuc with signiicant or abrupt changs rom th currnt position raing. This is to simulat th potntial rrors rom th GPS raing, which will act th controllr s rspons. From th rsults, it can b sn that th rspons o th string control without th spik tction algorithm tns to manouvr away rom th pr-in track compar with th string control with th spik tction algorithm. Thror, it rucs th latral acclration gnrat rom th vhicl, which will rsult in a smooth rspons o th vhicl bing achiv Dsir an Actual Trajctory at K = 0.25 Actual Rrnc 0 Y X Figur 6. Trajctory Rspons at K=0.25 with Nois Data Figur 8. String Rat Rspons whn Spik Occurs Figur 7 shows th crosstrack rror o th vhicl with its rrnc path. It is xpct that th rror at K = 0 is not convrg on zro bcaus thr is no crosstrack rror corrction. Th rror or K is qual to 0.25, 0.5 an.0, which ar rlativly small. Muhamma Aizzat Zakaria, Hairi Zamzuri, Rosbi Mamat an Saiul Amri Mazlan: A Path Tracking Algorithm Using Futur Priction Control with Spik Dtction or an Autonomous Vhicl Robot 7

8 Y Figur 9. Vhicl Trajctory Rspons or Spik Control 5. Conclusion Bas upon th simulation carri out, it can b conclu that th propos nonlinar controllr was abl to ollow th rrnc path. Th vhicl latral acclration an path rspons wr obsrv in orr to trmin th optimum paramtr valu o th controllr gain. Th multipl valus o gain ar illustrat to prsnt th ct o th gain on th vhicl. Th appropriat K hav bn chosn by obsrving th charactristics o th controllr. By slcting a small valu o K, a slow rspons o th controllr is obtain; howvr, th small valu o th latral acclration gnrat caus th comort lvl to incras. I th ast rspons controllr is slct, th comort lvl o th vhicl is thror ruc. Furthrmor, th spik tction algorithm is introuc. Th simulation rsults show that th algorithm is abl to ruc th unwant coorinats o th vhicl an achiv a smoothr rspons. Th xprimnt is carri out to monitor th nois charactristics o th GPS snsor. From that, th actual GPS ata is tch to th controllr to monitor th controllr rspons i th input ata is noisy. Th propos controllr is provn to b stabl by simulation an xprimnt rom th actual GPS ata. Howvr, noisy ata will act th prormanc o th controllr as wll. For utur rsarch, an Extn Kalman Filtr will b invstigat in orr to stimat th GPS coorinat an ruc th nois in th position raing. 6. Acknowlgmnts This rsarch is ully support by th Ministry o Highr Eucation Malaysia an th Univrsiti Tknologi Malaysia unr ERGS (vot no: 4L033) rsarch grant. Th work is also support by PROTON Holings Bh. 7. Rrncs without spik algorithm with spik algorithm rrnc path X [] Y. Kanayama an Y. Kimura, A stabl tracking control mtho or an autonomous mobil robot, Robotics an Automation, 990, vol., pp , 990. [2] R. Firro an F. L. Lwis, Control o a Nonholonomic Mobil Robot: Backstpping Kinmatics into Dynamics, vol. 4, no. 3, pp , 997. [3] S. L, Virtual trajctory in tracking control o mobil robots, Procings 2003 IEEE/ASME Intrnational Conrnc on Avanc Intllignt Mchatronics (AIM 2003), no. Aim, pp , [4] N. Ouaah, L. Ourak, an F. Boujma, Car-lik mobil robot orint positioning by uzzy controllrs, Intrnational Journal o Avanc Robotic Systms, vol. 5, no. 3, pp , [5] P. Falcon an F. Borrlli, Prictiv activ string control or autonomous vhicl systms, in IEEE Transactions on Control Systms Tchnology, Vol. 5, No. 3, May 2007, 2007, vol. 5, no. 3, pp [6] S. Hima, B. Lustti, an B. Vanholm, Trajctory tracking or highly automat passngr vhicls, in 8th IFAC Worl Congrss, 20, pp [7] J. Wang, J. Stibr, an B. Surampui, Autonomous groun vhicl control systm or high-sp an sa opration, Intrnational Journal o Vhicl Autonomous Systms, vol. 7, no., pp. 8 35, [8] G. Rao an G. Goms, A prictiv controllr or autonomous vhicl path tracking, Intllignt Transportation Systms, IEEE Transactions, vol. 0, no., pp , [9] V. Subramanian, T. Burks, an W. Dixon, Snsor usion using uzzy logic nhanc kalman iltr or autonomous vhicl guianc in citrus grovs, Transactions o th ASAE, vol. 52, no. 5, pp , [0] S. Limsoonthrakul, M. N. Daily, M. Parnichkunl, C. Scinc, I. Managmnt, an K. Luang, Intllignt Vhicl Localization Using GPS, Compass, an Machin Vision, pp , [] S. Sukkarih, E. M. Nbot, an H. F. Durrant-whyt, A High Intgrity IMU/GPS Navigation Loop or Autonomous Lan Vhicl Applications, vol. 5, no. 3, pp , [2] E. Abbott an D. Powll, Lan-Vhicl Navigation Using GPS, vol. 87, no., 999. [3] V. Milanés, J. E. Naranjo, C. Gonzálz, J. Alonso, an T. Pro, Autonomous vhicl bas in cooprativ GPS an inrtial systms, Robotica, vol. 26, no. 05, Mar [4] M. A. Zakaria, H. Zamzuri, S. A. Mazlan, an S. M. H. F. Zainal, Vhicl Path Tracking Using Futur Priction String Control, Procia Enginring, vol. 4, pp , Jan [5] R. Isrmann, Diagnosis Mthos or Elctronic Controll Vhicls, Intrnational Journal o Vhicl Mchanics an Mobility, no. April 202, pp. 37 4, 200. [6] M. Doumiati, O. Snam, L. Dugar, J. Martinz, P. Gaspar, an Z. Szabo, Intgrat vhicl ynamics control via coorination o activ ront string an rar braking, pp. 32, Int. j. av. robot. syst., 203, Vol. 0, 309:203

9 [7] D. Thomas, Funamntals o vhicl ynamics, Socity o Automotiv Enginring Inc., 992. [8] R. Sola an U. Nuns, Trajctory Planning with Vlocity Plannr or Fully-Automat Passngr Vhicls, 2006 IEEE Intllignt Transportation Systms Conrnc, pp , [9] G. Cai, B. M. Chn, an T. H. L, Unmann Rotorcrat Systms, pp , 20. [20] E. Nbot an S. Sching, Navigation systm sign, Muhamma Aizzat Zakaria, Hairi Zamzuri, Rosbi Mamat an Saiul Amri Mazlan: A Path Tracking Algorithm Using Futur Priction Control with Spik Dtction or an Autonomous Vhicl Robot 9