High-speed autonomous navigation system for heavy vehicles

1 High-speed au onomous na iga ion sys em o hea y ehicles A. Rod iguez-Cas año, G. He edia and A. Olle o Robo ics, Vision and Con ol G oup, h p://g c.us.es Enginee ing School, Uni e si y o Se ille Camino de los Descub imien os s/n, 41092 Se illa (Spain). Co esponding au ho : G. He edia , [email p o ec ed] Camino de los Descub imien os s/n, 41092, Se illa, Spain Tel: +34-954486035 Fax: +34-954487340 Abs ac : This pape p esen s echniques o GPS based au onomous na iga ion o hea y ehicles a high speed. The con ol sys em has wo main unc ions: ehicle posi ion es ima ion and gene a ion o he s ee ing commands o he ehicle o ollow a gi en pa h au onomously. Posi ion es ima ion is based on usion o measu emen s om a ca ie -phase di e en ial GPS sys em and odome ic senso s using uzzy logic. A Takagi-Sugeno uzzy con olle is used o s ee ing commands gene a ion, o cope wi h di e en oad geome y and ehicle eloci y. The p esen ed sys em has been implemen ed in a 13 ons uck, and ully es ed in e y demanding condi ions, i.e. high eloci y and la ge cu a u e a ia ions in pa ed and unpa ed oads. Keywo ds: au onomous ehicles; na iga ion; hea y ehicles; uzzy con ol; Di e en ial GPS; senso da a usion. 1. In oduc ion Au onomous guidance o g ound ehicles has been an ac i e esea ch and de elopmen opic in he las 30 yea s. Fo example, se e al sys ems ha e been implemen ed in expe imen al ou doo au onomous ehicles such as he Na lab amily a Ca negie Mellon Uni e si y [1], he ARGO au onomous ehicle [2], he ROMEO ehicles [3]. The in e es in au onomous ehicles’ echnologies has g own specially in he US, whe e DARPA has o ganized he G and Challenges and he U ban Challenge om 2004 o 2007 [4][5], which ema kably p omo ed he echnologies o in elligen ehicles a ound he wo ld. Re e ence [6] p esen s he main au onomous ehicles de eloped in he las yea s in he US. O he ema kable examples in he las yea s a e he VisLab au onomous ehicles [7][8]. Mos o hese ehicles a e he esul o he adap a ion o con en ional ca s o ans. Howe e , he numbe o e e ences p esen ing expe imen al esul s wi h au onomous hea y ehicles, such as ucks, is lowe . In e es in hea y ehicle au onomous guidance has g own om he nine ies in he amewo k o he ini ia i es on in elligen anspo a ion sys ems (ITS) and au oma ed highway sys ems (AHS). Published esul s on au onomous hea y ehicles come mainly om he Cali o nia PATH p og am [9][10][11] and Uni e si y o Minneso a’s SAFETRUCK [12][13][14]. O he P ep in e sion, he inal publica ion is a ailable a h p://dx.doi.o g/10.1016/j.asoc.2016.02.026 Rod iguez-Cas año A, He edia G and Olle o A (2016), High-speed au onomous na iga ion sys em o hea y ehicles, Applied So Compu ing, jun 2016, Vol. 43, pp. 572-582. 2 wo k on au onomous hea y ehicles has been done wi h TERRAMAX [15][16], designed o o - oad na iga ion, and by Isuzu Mo o s in Japan [17]. Recen ly, special a en ion has been de o ed o ehicle pla ooning o semi-au onomous “ oad ains” [18], composed by a leade ehicle wi h a human d i e wi h one o se e al au onomous ehicles ollowing i closely, o i s po en ial in uel and emissions sa ings and inc ease o oad capaci y. The SARTRE Eu opean P ojec has made a oad demons a ion o a pla oon wi h a leade uck and se e al ehicles ollowing i [19][20]. Tes s wi h a h ee uck pla oon ha e been pe o med wi hin he Ene gy ITS P ojec in Japan [21][22]. O he examples include he Ge man KONVOI p ojec which analyzes he implica ions o uck pla oons in au obahns [23] and he Swedish esea ch p og am on In elligen Vehicles [24]. Many o hese au onomous ehicle esea ches ha e been done a medium o low speeds. High speed na iga ion o au onomous ehicles is s ill a challenging applica ion due o he equi emen s on eliabili y and sa e y. The choice o he senso s used o posi ion es ima ion in au onomous na iga ion may ha e impo an p ac ical equi emen s. Some senso s equi e auxilia y guidance mechanisms in o a ound he ield o in e es [25], as is he case wi h mos o PATH p og am wo k [13], which uses magne ic ma ke s bu ied in he oad. The wo k in [17] also uses magne ic ma ke s, bu i s o es a “map” o he ma ke s o p e iew con ol. This pape deals wi h GPS based au onomous na iga ion by implemen ing a senso da a usion and pa h ollowing echniques. Wi h he ad en o mode n GPS ecei e s, kinema ic cen ime e -le el absolu e posi ion es ima ion and a i ude measu emen s o he ehicle a e a ailable using ca ie -phase Di e en ial Global Posi ioning Sys em (DGPS) wi h posi ion accu acy up o ew cen ime e s. Ca ie -phase DGPS echniques a e being used o s aigh line acking and heading con ol o gol ca s and a m ehicles a low eloci ies [25], and adap ed o con en ional ca s [26]. The Te aMax au onomous hea y ehicle [15] uses 3 di e en DGPS ecei e s o imp o ed eliabili y. Howe e , he use o GPS ecei e s equi es ope a ion en i onmen s wi h good sky isibili y. Fu he mo e, in p ac ical implemen a ions, also a ise o he sou ces o e o s like communica ion loss o di e en ial co ec ion messages, ou pu a iable la ency and ecei e e o s [13]. Some o hem can be de ec ed aking in o accoun he ehicle dynamics, using model-based aul de ec ion and iden i ica ion echniques, as is desc ibed in [14], and in [27] o an ae ial ehicle. I has been also ecognized ha senso da a usion can imp o e signi ican ly he eliabili y o posi ion es ima ion. Senso da a usion o ehicle posi ion es ima ion can be sol ed by means o s a is ical app oaches, such as Kalman il e ing (see, o example, [28]). These echniques equi e a s ochas ic s a e-space ep esen a ion o he ehicle model and o he measu emen p ocess. A kinema ic model o he ehicle and knowledge o measu ing equipmen a e ypically used o de i e he s a e-space ep esen a ion, al hough o nonlinea sys ems an Ex ended Kalman Fil e o mula ion is needed. Howe e , a main d awback o Kalman il e ing is ha senso noise is modelled as whi e noise. Al hough his can be accu a e o se e al senso s, i is clea ly no ue o DGPS. Mo eo e , he implemen a ion o Kalman Fil e ing equi es es ima ions o he measu emen co a iance ma ix, which can be ob ained om he echnical cha ac e is ics o he senso equipmen , and 3 he p ocess co a iance ma ix, ha ep esen s he model inaccu acies, which is much mo e di icul o ob ain. I has been also shown ha a poo es ima ion o inpu noise s a is ics may se iously deg ade Kalman il e pe o mance and e en cause il e di e gence [29]. In his pape uzzy logic is applied o posi ion es ima ion wi hou he need o p ecise in o ma ion, which can be di icul o expensi e o ob ain. The pa h ollowing componen o a ehicle con olle has he mission o gene a ing he ehicle’s s ee ing o ack a p e iously de ined pa h, by aking in o accoun he ehicle’s ac ual posi ion and o ien a ion and he cons ain s imposed by he ehicle and i s low-le el mo ion con olle . Pa h ollowing, which is some imes e e ed o as “la e al con ol“ o “pa h acking”, is di ec ly ela ed o he la e al ehicle mo ion and s ee ing con ol. Vehicle con ol also in ol es speed con ol. Bo h a e coupled p oblems. Howe e , pa h ollowing has been usually s udied o cons an eloci y. Thus, he pa h ollowing algo i hm implemen s a s ee ing con ol law by using he e o be ween he cu en es ima ed ehicle posi ion/ o ien a ion and he pa h o ollow. The inpu s o he pa h acke a e a iables de ining he s a e o he ehicle wi h espec o he pa h, and he ou pu is he s ee ing command o be execu ed by he low-le el mo ion con olle . Linea con ol me hods ha e been success ully applied o ehicle au oma ed s ee ing [30][31]. Howe e , i he linea iza ion condi ions a e iola ed o nonlinea i ies in he s ee ing mechanism o in he mo ion senso s exis , he acking de e io a es. Nonlinea pa h ollowing echniques, as Takagi-Sugeno (TS) uzzy con ol, ha e shown good pe o mance [26]. TS uzzy sys ems a e a special ype o uzzy sys ems in which he consequen pa o he ules is no de ined by a uzzy membe ship unc ion bu by a ine linea dynamic sys ems. A TS uzzy model will app oxima e a nonlinea sys em by smoo hly in e pola ing hese a ine local models. Fuzzy con ol can also be used o in eg a e he d i ing knowledge acqui ed in he o m o i - hen ules om an expe ienced d i e , and TS d i ing con ol laws di ec ly ex ac ed om senso da a eco ded while he ehicle is ope a ed by a human d i e [32]. Fu he mo e, design echniques ha gua an ee s abili y based on Lyapuno unc ions and o he me hods can be also applied [33-37]. Mos pa h ollowing me hods ha e pa ame e s ela ed o he selec ion o a goal poin , o a pa icula segmen o he pa h o ollow, which a e equi ed o compu e he signal e o in he pa h ollowing loop. This has been in eg a ed wi h pa h acking h ough he concep o p e iew con ol. TS uzzy logic also p o ides an e icien amewo k o in eg a ing his pa ame e adap a ion in he s ee ing con olle [38] and could be also implemen ed o une au oma ically he pa ame e s acco ding o he cu en na iga ion condi ions. This pape p esen s a Takagi-Sugeno uzzy pa h ollowing con olle o hea y ehicles a high speeds, including uzzy senso da a usion o ehicle posi ion es ima ion. The emaining o he pape is o ganized as ollows. Sec ion 2 in oduces he main cha ac e is ics o GPS-based pa h ollowing. In sec ion 3 he Takagi-Sugeno uzzy pa h ollowing s a egy is p esen ed. Sec ion 4 desc ibes he expe imen s ca ied ou wi h a 13 Tons uck. Finally sec ion 5 p esen s he Conclusions. 4 2. GPS based pa h ollowing 2.1. Posi ion es ima ion GPS ecei e s p o ide low- equency posi ion in o ma ion which is clea ly insu icien o con ol a ehicle a high eloci ies. I is necessa y o use addi ional high- equency senso s o imp o e he pe o mance and in eg i y o GPS na iga ion sys ems. A posi ion es ima ion algo i hm should use low- equency senso in o ma ion o co ec ing low- equency d i e o in high equency senso s and should use high equency senso in o ma ion o deco ela e he e o s in low- equency senso s. Kalman il e ing is one o he mos widely used senso da a usion echnique in au onomous na iga ion. This pape p oposes he applica ion o uzzy senso da a usion o conside he heu is ic knowledge in ol ed in he es ima ion p oblem. This echnique is based on he use o a uzzy sys em o he on-line usion o he measu emen s om a achome e , a gy oscope and a ca ie -phase DGPS ecei e . The p oposed uzzy posi ion es ima ion sys em ini ially showed simila pe o mance o he Ex ended Kalman il e in expe imen al es s, bu he uzzy posi ion es ima ion was much mo e lexible and easily uned han he Kalman il e . This lexibili y comes om he ac ha a human designe can easily unde s and wha each ule does and i is much easie o une hem o ma ch expe imen al esul s. The uzzy posi ion es ima ion sys em uses he da a om he a ailable senso s o ob ain an es ima ion o he posi ion and o ien a ion o he uck in eal ime. The DGPS ecei e p o ides da a on la i ude and longi ude o he ecei e an enna, which is hen con e ed o UTM (Uni e sal T ans e se Me ca o ) coo dina es. On he o he hand, he gy oscope p o ides an es ima ion o he angula eloci y o he ehicle, and he achome e senso eadings a e con e ed o linea eloci y o he ehicle. Wi h hese measu emen s i is possible o ob ain an inc emen al es ima ion o he posi ion and o ien a ion o he ehicle using he kinema ic model. A a i s app oxima ion and o sho dis ances, he uck can be conside ed o mo e on a plane, and a simpli ied 2D model can be used. Fo na iga ion in 2D, he posi ion and o ien a ion o he ehicle is gi en by (x, y, ) (see Figu e 1), whe e x and y a e he ehicle’s ca esian coo dina es, is he o ien a ion angle, and ( , ) a e he linea and angula eloci ies o he uck, espec i ely.  5 Figu e 1 Vehicle kinema ics Then, he kinema ic model is gi en by he ollowing di e en ial equa ions [3]: (1) I he di e en ial equa ions (1) a e disc e ized using he Eule me hod, he ollowing exp essions a e ob ained o he posi ion and heading a ins an k+1: (2) whe e x(k) and y(k) a e he absolu e ehicle posi ion in UTM coo dina es, (k) is he o ien a ion a ime k, (k) is he ehicle eloci y, is he yaw a e, and T is he sampling pe iod. This me hod is usually known as dead eckoning (DR) o odome y. I has a high pe o mance o sho dis ances and can be compu ed e y quickly, bu he g ow h o posi ion unce ain y is unbounded since i is an inc emen al me hod. A las he e a e wo independen es ima ions. The GPS es ima ion is a e y accu a e, absolu e posi ion es ima ion, bu he sampling equency is low, 5-10 Hz a mos . Fu he mo e, in some si ua ions he es ima ions can be deg aded due o sa elli e loss o o he ac o s (i.e. in u ban canyons). Luckily mos ecei e s p o ide an indica o o he accu acy o he es ima ion (i.e. me e , subme e , cen ime e ), which can be used in he posi ion es ima ion algo i hms. In some cases he GPS ecei e may p o ide one o a g oup o ew ou lie poin s ha a e a om he p e ious es ima ions. These ou lie poin s a e no compa ible wi h he ehicle kinema ics, and can be de ec ed compa ing hem wi h he DR es ima ions. On he o he hand, he DR es ima ion is ela i e, i is e y as (up o 200 Hz o mo e) and i is e y accu a e o sho dis ances. Howe e , o la ge pe iods he e o s accumula e and g ow unboundly, and hen a good indica o o i s accu acy is he dis ance om he las absolu e co ec ion. The uzzy posi ion es ima ion uses he complemen a y cha ac e is ics o bo h o ob ain an y X Y x  x · –sin= y · cos=  ·= xk 1+()xk() –kTksin= yk 1+yk() kTkcos+= k1+()k() k()T+= k() 6 es ima ion. The uzzy sys em can be spli up in o wo subsys ems [40], a posi ion uzzy sys em and an o ien a ion uzzy sys em (see Figu e 2). Figu e 2 Senso da a usion block diag am Then, he posi ion is compu ed by means o : Posi ion = pos_GPS_ ac o * GPS_posi ion + (1 - pos_GPS_ ac o ) * DR_posi ion whe e DR_posi ion is he ehicle posi ion compu ed using dead eckoning, and pos_GPS_ ac o is he posi ion uzzy sys em ou pu , which gi es he con idence in he senso s. This ac o should be e y close o 1.0 mos o he ime, as shown om s a is ics ob ained in es s (GPS ecei e posi ion e o less han 2 cm wi h 95% p obabili y), and i should be close o 0.0 when he GPS measu emen is oo a om he DR es ima ion, assuming DR es ima ion unce ain y is low o sho in e als. Al hough his assump ion is ue mos o he ime, i could ail due o loss o GPS measu emen s. The uzzy senso da a usion me hod akes i in o accoun . The posi ion uzzy sys em inpu s a e he le el o accu acy (me e , subme e , cen ime e ) p o ided by he DGPS ecei e , he dis ance a elled by he ehicle in he DR es ima ion since las GPS upda e, and he posi ion e o be ween he DR es ima ion and he GPS posi ion. The ules a e as: IF accu acy IS high AND pos_e o IS low THEN pos_GPS_ ac o IS high whe e he membe ship unc ions o he inpu s and he ou pu a e de ined in Figu e 3. A simila scheme is used in he o ien a ion uzzy sys em. Figu e 3 Membe ship unc ions This uzzy posi ion and heading es ima ion sys em has been implemen ed and es ed in a es hea y ehicle (which is desc ibed in Sec ion 4), wi h good pe o mance: i is able o achie e ack la e al e o s o less han 7 cm in cu ed pa hs, and less han 3 cm in s aigh pa hs. I is able o wo k a high ou pu equencies (i has been es ed a up o 200 Hz). The posi ion and heading uzzy es ima ion sys em was uned in he ollowing way. Se e al expe imen s we e done in one o he acks desc ibed in sec ion 4 ( ack A). The “ ue” Gy oscope GPS Tachome e P ocessing and DR es ima ion O ien a ion Fuzzy Sys em Posi ion Fuzzy Sys em yaw a e accu acy posi ion e o heading e o dis _ a elled o _GPS_ ac o pos_GPS_ ac o LM H 30 60 90 10 25 40 H L 100 40 70 1 0 0.5 M dis _ a elled (m) HLM LMH 0 00 pos_e o (cm) accu acy (cm) pos_GPS_ ac o 0 11 0 1 0 1 0 7 posi ion and heading we e ob ained wi h a human d i ing he es uck along ack A. The ehicle posi ion and heading we e eco ded by he onboa d compu e , and hey we e pos p ocessed i s o emo e ou lie s. Then he pa h was ob ained om he da a using p incipal cu es [39], which a e cu es ha pass h ough he “middle” o he da a dis ibu ion, and a e sel -consis en (i.e., a poin on he cu e is he a e age o all da a poin s ha p ojec on o i ). Then, he ou pu o he uzzy posi ion and heading es ima ion sys em was compa ed o he “ ue” solu ion; he ules we e uned in he ack sec ions wi h la ge e o s. Al hough he e may be a conside able numbe o ules, only e y ew o hem a e ac i e a a gi en ins an . The e o e, he candida e ules can be easily selec ed and, as he ules a e sel -explana o y, hey can be easily modi ied o educe he e o . This p ocess is epea ed i e a i ely un il he posi ion and heading e o is educed o a speci ied le el. 2.2. Pa h ollowing con ol loops The pa h ollowing con olle gene a es he ehicle´s s ee ing o ack a p e iously de ined pa h, based on he es ima ed e o s be ween he cu en ehicle posi ion and he pa h o ollow. As shown in Figu e 4, he pa h ollowing ehicle con olle has wo componen s, a mo ion low le el con olle and a pa h ollowing s a egy. In his Figu e RP is he e e ence pa h, e is he e o be ween ac ual ehicle posi ion and he pa h o ollow, is he desi ed cu a u e and p is he ac ual ehicle posi ion. Figu e 4 Pa h ollowing con olle a chi ec u e The low le el con olle commands he s ee ing wheel mo o o he ehicle o ge he cu a u e gi en by he high le el con olle . PID mo ion con olle s a e usually applied in his low mo ion con ol le el, which equi es a cu a u e o s ee ing wheel angle mapping. PID con olle s p o ides good esul s in mos cases i a sa is ac o y eedback signal is a ailable. The objec i e o he pa h ollowing high le el con olle (o simply pa h ollowing con olle , as is usually e e ed o) is o gene a e con ol commands o he ehicle o ollow a p e iously de ined pa h by aking in o accoun he ac ual posi ion and he cons ain s imposed by he ehicle and i s low le el con olle . Pa h ollowing is a nonlinea con ol p oblem. The e a e many algo i hms ha ha e been used bu he e is no gene al solu ion ha can gua an ee obus ness when he cu a u e o he pa h a ies. Fuzzy logic is a sui able echnique o apply o pa h ollowing s a egies de ined by means o ules. The esul ing con olle s a e known as di ec uzzy con olle s. The con olle inpu s a e he a iables de ining he s a e o he ehicle wi h espec o he pa h. The ou pu o  e o compu a ion high le el con ol low le el con ol ehicle posi ion es ima ion  e RP p 8 he uzzy con olle is he s ee ing command o be execu ed by he low le el mo ion con olle . Se e al me hods ha e pa ame e s ela ed o he selec ion o a goal poin on he pa h o ollow. This goal poin is equi ed o compu e he signal e o in he pa h ollowing loop. These pa ame e s a e ela ed o he gain o he closed loop sys em and ha e a signi ican e ec on he acking pe o mance. Thus, oscilla ions o e en ins abili y can a ise o some alues o he con olle pa ame e s. These ins abili y condi ions a e ela ed o bo h he ehicle´s cha ac e is ics and na iga ion condi ions including speed, pa h o ollow and e ain. Usually hese algo i hms selec a goal poin P on he pa h a a ixed dis ance om he ehicle ha is called he lookahead dis ance L, as shown in Figu e 5. Using his goal poin h ee alues can be ob ained ha a e he inpu s o he pa h acke . These inpu s a e he la e al posi ion e o in ehicle coo dina es , he o ien a ion e o wi h espec o he goal poin and he cu a u e e o wi h espec o he goal poin . The exp essions o and a e: (3) whe e and a e he o ien a ion and cu a u e o he pa h a he goal poin . Figu e 5 Pa h ollowing. These algo i hms a e usually e icien , bu a common p oblem is ha he esul s a e c i ically dependen on he app op ia e uning o he lookahead dis ance o he cu en na iga ion condi ions. Fo example, a a gi en eloci y i he lookahead is oo long he ehicle may cu co ne s and i oo sho oscilla ions may a ise. 3. TS Fuzzy pa h ollowing o high speed na iga ion In his sec ion, a Takagi-Sugeno (TS) uzzy pa h ollowing sys em o hea y au onomous ehicles a high speeds is p esen ed. TS uzzy sys ems a e a special ype o uzzy sys ems in which he consequen pa o he ules is no de ined by a uzzy membe ship unc ion bu by a ine linea dynamic sys ems [41]. A TS uzzy model will app oxima e a nonlinea sys em by smoo hly in e pola ing hese a ine local models. Each local model con ibu es o he global model in a uzzy subse o he inpu space. The TS uzzy model has ecen ly ound wide applicabili y in uzzy model based con ol. F om a con ol enginee ing pe spec i e he use o local a ine (o local linea ) models b idges he gap be ween uzzy con ol and con en ional con ol. Many exis ing ools and heo ies in linea  e e e e e pa h –= e pa h –= pa h pa h X Y  Pa h  L pa h P x y 9 sys ems heo y can be pa ially applied o TS uzzy models and con olle s. Fu he mo e, gene al TS uzzy sys ems ha e been shown o be uni e sal app oxima o s, and hey can be used o e ec i ely model a wide class o nonlinea sys ems. S abili y analysis o TS sys ems also bene i om i s in e nal s uc u e. Su icien s abili y condi ions o his class o sys ems ely on he exis ence o a common quad a ic Lyapuno unc ion [33] o a piecewise-quad a ic (PWQ) Lyapuno unc ion o less conse a i e s abili y condi ions [34]. The sea ch o he Lyapuno unc ion can be s a ed as a con ex op imiza ion p oblem in e ms o linea ma ix inequali ies (LMI) o which e icien sol ing me hods and so wa e exis . S abili y condi ions o unce ain sys ems ha e also been de eloped [35]. O he app oaches seek o educe he conse a i eness o he s abili y condi ions ob aining local domains o a ac ion wi h uzzy Lyapuno unc ions [36]. Al e na i e s abili y analysis based on LaSalle heo em has also been p oposed [37]. The pa h ollowing con olle o hea y ehicles should ul ill he condi ions explained in he p e ious sec ion: (i) i should be able o d i e he ehicle a a la ge ange o eloci ies, ollowing he pa h wi hou cu ing co ne s and wi hou oscilla ions; (ii) i should d i e he ehicle h ough pa h sec ions wi h di e en cu a u es and cu a u e a ia ions; (iii) he con olle should be able o manage he di e en dynamic egimes ha appea in hea y ehicle guidance; and (i ), in hea y ehicle au onomous guidance con ol signals mus be smoo h, specially a high eloci ies; con ol signals wi h as a ia ions can cause oscilla ions. A sa is ac o y pa h- acking needs a as esponse o he s ee ing sys em when he ehicle has o change i s cu a u e o manage a u n. This as esponse is necessa y because he ehicle’s cu a u e se poin is con inuously upda ed. I he s ee ing esponse is slow, he c oss ack e o will inc ease in hese si ua ions, and hen con ol signals should be s ong. The p oposed TS uzzy con olle is an ideal candida e o deal wi h all hese condi ions. The TS uzzy con olle is composed o wo se s o ules. One o hem make an es ima ion o he lookahead dis ance o each d i ing condi ions, and i is de i ed om heu is ic knowledge om expe ienced d i e s and ehicle expe imen s. The second se p o ide he con ol inpu o he low le el con olle , and i is de i ed om inpu /ou pu da a ob ained in pa h ollowing expe imen s wi h a human d i e . Lookahead dis ance selec ion depends on pa h cha ac e is ics (cu a u e and cu a u e change), as ha e been de i ed om human d i e and p io expe imen heu is ics. In gene al, d i e s epo ed ha hey used a close e e ence poin on he pa h and applied a igh con ol when he cu a u e was changing be ween s aigh and cu ed pa h segmen s. Fu he mo e, e e ence poin s used by d i e s whe e close in cu es han in s aigh segmen s. F om ha , he idea ha has been implemen ed in he lookahead selec o uzzy se o ules is o inc ease he con olle gain (dec ease lookahead dis ance, since gain is in e sely p opo ional o he lookahead dis ance) when he cu a u e o he pa h is changing ( ypically en e ing o lea ing a u n) and ha e a lowe gain (highe lookahead dis ance) when he ehicle mus ollow a cons an cu a u e segmen (s aigh o u n). Also, lookahead dis ance will be la ge in s aigh segmen s han in cu ed segmen s. A ypical lookahead a ia ion can be seen in Figu e 6, o a oad composed o a s aigh sec ion, a cu ed sec ion and ano he s aigh sec ion. The ehicle mo es along a s aigh pa h wi h a lookahead L1; when a goal poin is 16 (). The  R con olle has as addi ional inpu he la e al de ia ion om he pa h ( ). . In Poin 1 he uck is app oaching he 30 m u ning adius cu e in ack A (see Figu e 10). The ehicle is mo ing a 35.8 km/h speed, i is in a s aigh segmen (NTR=1000, =0.0) and he goal poin is inside a ansi ion a ea (GTR=142, =0.8). In his case, he ou pu o he lookahead con olle L is dec eased o 15.8 m, and he la e al e o is low (-0.12 m). In his si ua ion he con ol ou pu gene a ed by he cu a u e uzzy con olle is -0.0112 m-1, co esponding o app oxima ely 3 deg ees in he s ee ing wheels. In Poin 2 he es uck is al eady inside he u n (NTR = 30, = 0.0, GTR = 30 and = 0.0). This case co esponds o a poin inside he u n and i will con inue in he same u n in he nea u u e, as GTR and a e he same han NTR and espec i ely. The ou pu o he lookahead con olle L is inc eased o 18.2 m and he cu a u e con ol command is inc eased o 0.0504 (co esponding o 14 deg ees in he s ee ing column), due o he lowe eloci y (26.2 km/h) and la ge la e al e o ( = 0.41 m). Ano he example is Poin 3, which co esponds o he middle poin o he s aigh segmen ma ked as “C” in Figu e 10 (NTR = 1000, = 0.0, GTR = 1000 and = 0.0, he uck is in a s aigh segmen and i will con inue in a s aigh segmen in he nea u u e). In his case, o a 48.1 km/h speed an ou pu lookahead L = 27.2 is ob ained. E en hough he speed is no a om he case shown o Poin 1, he lookahead alue is nea ly doubled. This is due o he ac ha in Poin 1 he ehicle is app oaching a u n, while in his case he uck is on a comple ely s aigh segmen . The cu a u e command ou pu is lowe (-0.0112 s 0.0074 m-1) due o he ac ha he con olle is smoo he as speed inc eases. I his example is compa ed wi h Poin 2, he lookahead L is lowe (18.2 s. 27.2 m) o lowe speed (26.1 s. 48.1 km/h) and lowe u ning adius (30 s. 1000 m). S aigh line- acking es s a high speed (80-100 km/h) ha e been made in ack B, which is a unpa ed oad composed o s aigh sec ions and sec ions o la ge u ning adius (be ween 600 and 750 m), which can be conside ed as a long s aigh oad. Figu e 13 shows he speed eco d o one o hese es s in a 2 km long sec ion o ack B. The maximum c oss- ack e o on he s aigh segmen s was 28 cm. and he s anda d de ia ion was 10 cm (see Figu e 13). The maximum c oss- ack e o on he s aigh segmen s was 28 cm. and he s anda d de ia ion was 10 cm (see Figu e 13). Se e al es s o e i y he pe o mance o he p oposed con ol sys em ha e been done also in acks C and D, shown in Figu e 14. T acks C and D a e unpa ed oads, and hey a e composed o sec ions o di e en u ning adius connec ed wi h s aigh sec ions. Minimum u ning adius is 40 m. in bo h acks. V (km/h) NTR (m) GTR (m) (m) L (m)  R (1/m) Poin 1 35.8 1000 0.0 142 0.8 -0.12 15.8 -0.0112 Poin 2 26.2 30 0.0 30 0.0 0.41 18.2 0.0504 Poin 3 48.1 1000 0.0 1000 0.0 0.10 27.2 0.0074 Table 2: Nume ic alues o inpu s and ou pu s o he uzzy con olle s a selec ed poin s in ack A G  N G  N G N G G N  N G 17 The esul s o a 45 minu es es un in ack C a e shown in Table 3. The ehicle mo es clock wise o 7 laps a a cons an eloci y o 45 km/h. The s anda d de ia ion ob ained is simila o he es s in ack A, while he maximum c oss ack e o has inc eased om 50 o 70 cm. This is due o he g ea e speed in u ns o se e e cu a u e and he di e en oad su ace; ack A is made o asphal while ack C is unpa ed di so he ehicle slips much mo e en e ing and lea ing he u ns. Figu e 13 S aigh line acking speed eco d and c oss- ack e o ( ack B). In ack D, one es was done a a cons an speed o 30 km/h, wi h a c oss- ack e o s anda d de ia ion o 14 cm and a maximum alue o 46 cm. Ano he es was done a a cons an speed o 45 km/h. In his case, he s anda d de ia ion was 16 cm, and he maximum c oss- ack e o 010 20 30 40 50 60 70 80 75 80 85 90 95 100 im e (se c) Speed (Km/h) 010 20 30 40 50 60 70 80 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 im e (se c) C oss ack e o (m ) S d: 0.18 m ime (s) V (km/h) e (m) ime (s) 18 was 71 cm. The esul s a e also shown in Table 3. Figu e 14 T acks C (le ) and D ( igh ). Numbe s close o cu es indica e u ning adius (m) I 4.1. Compa ison o esul s I is impo an o men ion ha he compa ison wi h he esul s o o he me hods published in he li e a u e is quali a i e, since he e a e many ac o s as he cha ac e is ics o he ehicles, he condi ions o he expe imen al es s and he implemen a ion o he con olle s ha can a ec he pe o mance o he expe imen s and a e no epo ed in he pape s o a e no easily compa able. Mos o he au onomous na iga ion expe imen al esul s ha can be ound in he li e a u e ha e been done wi h small ehicles o ca s, and a low speeds. Then, i is di icul o compa e he p oposed na iga ion sys em o hea y ehicles. The mos ele an published expe imen al esul s wi h hea y ehicles ha e been done in he amewo k o Cali o nia PATH and Uni e si y o Michigan's SAFETRUCK p og ams. In [10] esul s o he au onomous na iga ion o a hea y uck using a obus linea con olle a e p esen ed. The es s ha e been done on an asphal oad composed o s aigh segmen s and cu ed segmen s wi h a adius o 800 m. The maximum eloci y is be ween 65 and 75 km/h. T ack C Max. e o (cm) S d. de . (cm) T ack D Max. e o (cm) S d. de . (cm) Full es 71.2 16.17 Tes 1 (30 km/h) 46.4 14.10 Lap 1 63.7 15.21 Tes 2 (45 km/h) 71.1 16.56 Lap 2 69.1 14.19 Tes 2-Lap 1 70.6 16.68 Lap 3 70.3 14.88 Tes 2-Lap 2 71.1 16.35 Lap 4 69.7 16.43 Lap 5 71.2 16.29 Lap 6 71.0 16.02 Lap 7 70.7 16.37 Table 3: Resul s o es uns on acks C and D 19 The la e al e o is less han 0.15 m in s aigh segmen s and 0.35 m in he cu ed segmen s, bu a e g ea e han 0.5 m in ansi ions be ween segmen s. These esul s ha e o be compa ed o he au onomous uck es s in ack B, since we ha e conside ed as oads wi h adius la ge han 600 m as s aigh oads (in ac , ack B combines s aigh segmen s wi h cu ed segmen s o adius be ween 600 and 750 m). These es s we e done a speeds o be ween 80 and 100 km/h on an unpa ed oad, and he maximum e o was less han 0.28 m, wi h s d. de . less han 0.1 m, which gi es be e esul s han [10], especially in ansi ion segmen s. Bo h con olle s show simila pe o mance in s aigh and cons an cu a u e segmen s, bu he uzzy con olle p oposed in his pape pe o ms ema kably be e in ansi ions be ween segmen s since i adap s smoo hly o oads o changing cu a u e. In [12], a modi ied pu sui me hod is used o d i e a hea y ehicle on an asphal oad. In a s aigh segmen he maximum e o is a ound 0.25 m a a speed o up o 65 km/h. This con olle ob ains sligh ly be e maximum la e al e o han he p oposed uzzy na iga ion sys em (0.28 m a speeds o up o 100 km/h), bu a conside ably lowe speeds. In an S-shaped oad segmen wi h adius 85 m, he con olle in [12] ge s a maximum la e al e o o abou 0.45 m a a speed o 35 km/h. A compa able oad es o he es uck is he oad segmen on ack A a ound he "C" poin ( adius o 83 m), whe e he uzzy na iga ion sys em achie es a maximum la e al e o o 0.32 m a a ound 45 km/h, which gi es a be e pe o mance. In [22] a 11 on. au onomous uck is con olled a speeds be ween 60 and 80 km/h in a 3 km es ack wi h 700 m. s aigh sec ions and 800 m o al sec ions. The la e al e o is wi hin 0.35 m a 60 km/h (in o al sec ions) and 0.5 m a 80 km/h (in s aigh sec ions). Wi h he uzzy con olle p oposed in his pape he maximum la e al e o is smalle o speeds om 80 o 98 km/h in s aigh pa hs (0.30 m in ack B) and la ge in cu ed sec ions (0.50 m in ack A), bu i is di icul o compa e because he minimum u ning adius o he o al sec ions a e unknown. Mo eo e , he con olle in [22] is unable o co ec he la e al e o du ing hal o each cu ed sec ion (400 m), keeping a s eady la e al e o wi hin 0.20 o 0.30 m. O e all, he uzzy con olle shows be e acking pe o mance in s aigh and cu ed oads compa ed o [12] and [22]. The con olle de eloped in [43] o he guidance o an elec ic powe an is es ed in a 2 km oad inside he campus wi h a ypical squa e shape. The ehicle is guided a an a e age speed o 26 km/h and a maximum speed o 46 km/h using a pa ially speed-dependen lookahead anging be ween 8 o 14 m. They achie e a mean la e al e o o 0.13 m, a s anda d de ia ion o 0.15 m and a maximum la e al e o abou 0.90 m in a 6 laps expe imen . E en hough he e a e no de ails abou he u ning adius o he co ne s and he su aces o he acks a e di e en (pa ed s unpa ed) his expe imen could be compa ed o he esul s p esen ed in his pape o acks C and D (see able 2) gi en he simila ange o speeds and shape o he ack. As can be seen he esul s a e simila in e ms o s anda d de ia ion (0.14 m o 30 km/h and 0.17 m o 45 km/h) bu he maximum la e al e o is la ge in [43] (0.90 m s 0.71 m). Compa ing he esul s, he uzzy con olle has simila pe o mance o [43] in s aigh pa hs, and be e pe o mance in he cu ed sec ions. This beha io can be due o he uzzy con olle add essing be e oad cu a u e changes, since he con olle in [43], al hough adap ing he lookahead o he ehicle eloci y seems no o add ess well changes in oad cu a u e. 20 In he SARTRE Eu opean p ojec [20], expe imen al es s wi h a mixed pla oon o ucks and ca s ha e been pe o med. Un o una ely, only he da a o one o he ca s is p esen ed in [20]. The expe imen s show a sedan ca a eling a 90 km/h in s aigh pa hs. The la e al e o is wi hin 0.35 m, ha is qui e simila o he 0.30 m ob ained wi h he uzzy con olle p esen ed in his pape , and he s anda d de ia ion is 0.10 m, be e han he 0.18 m ob ained in ack B. The same ehicle in a ligh ly cu ed oad (470 m u ning adius) keeps an a e age e o o - 0.01 m wi h a s anda d de ia ion o 0.09 m and he maximum e o wi hin 0.25 m. In [20] he ehicle ends o go sligh ly sepa a ed om he pa h in he s aigh sec ions wi h an a e age e o o 0.09 m, bu he pe o mance is be e in he sligh ly cu ed sec ions. The e a e no de ails abou he con ol me hod o explain he di e ence in pe o mance be ween he cu ed and s aigh sec ions. Fu he mo e, he e a e main di e ences in he expe imen s, he su ace o he acks (pa ed s unpa ed) and he weigh o he ehicles (14 on uck s a sedan ca ), wha makes di icul he compa ison. One common e ec ha can be obse ed in some sec ions o he expe imen s in [20] and [22] is ha he a e age la e al e o is la ge han ze o wha indica es a lack o in eg al ac ion in he con olle s, wha is p ope ly add essed in he uzzy con olle in his pape . As a conclusion, and keeping in mind ha all he compa isons in his sec ion ha e o be conside ed as quali a i e since he e a e no su icien de ails in he li e a u e on he ehicles, he oads and he con olle implemen a ion o make a di ec quan i a i e compa ison, he p oposed uzzy con olle has simila o sligh ly be e pe o mance acking s aigh and cons an cu a u e pa hs. The main ad an age o he uzzy con olle is ha i adap s much be e o oad segmen s wi h changes in cu a u e, and hus i is mo e lexible and can be used in a wide se o oads in eal condi ions. 5. Conclusions This pape p oposes a pa h ollowing sys em designed and implemen ed o hea y unmanned ehicles. A TS uzzy con ol sys em can be used o con ol hea y ehicles a di e en d i ing condi ions. A good pe o mance is achie ed ollowing pa hs wi h e y di e en cu a u es and eloci ies wi h his single con olle . The con olle is able o d i e he uck a high speed (up o 100 km/h) on unpa ed oads, and i can also con ol he ehicle on cu ed oads wi h a u ning adius o 30-40 m. The condi ions in which he d i ing es s ha e been done a e e y demanding, because in mos o hem legal speed limi s ha e been exceeded. Mo eo e , mos o he es s ha e been done on unpa ed g a el oads. The main ad an age o he p esen ed con olle is i s capabili y o adap a ion o oad segmen s o di e en cu a u es and he ansi ions be ween hem. 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