Integrated Chassis Control Using ANFIS

Transcription

1 Procdngs of th IEEE Intrnatonal Confrnc on Automaton and Logstcs Qngdao, Chna Sptmbr 008 Intgratd Chasss Control Usng ANFIS Yumng Hou, J Zhang, Yunqng Zhang, Lpng Chn Cntr for Computr-Add Dsgn Huazhong Unvrsty of Scnc & Tchnology Wuhan, Hub Provnc, Chna zhangyq@hust.du.cn Abstract - A nonlnar control systm that ntgratd actv front strng systm and vhcl dynamcs control systm basd on a mult-body vhcl dynamc modl s ntroducd n ths papr. Th multbody vhcl dynamc modl basd on ADAMS can accuratly prdct th dynamcs prformanc of th vhcl. Th control stratgy conssts of two control objctvs (yaw vlocty and sdslp angl ). An ntgratd controllr s bult accordng to th latral acclraton to dstrbut th dsrd yaw momnt to VDC and AFS. Th VDC and AFS controllrs ar stablshd usng ANFIS (Adaptv-Ntwork-basd Fuzzy Infrnc Systm) and Fractonal-ordr PI μ control algorthm, rspctvly. Th adaptv fuzzy controllr can adjust th fuzzy control ruls and mmbrshp functons through by tranng of ANFIS, and th paramtrs of fractonal-ordr PI μ ar tund usng gntc algorthm (GA) optmzaton mthod. Th co-smulaton scnaro taks plac on an cy road at hgh spd wth a stp str nput. Th smulaton rsults show that ntgratd chasss control systm can nhanc vhcl handlng stablty and safty gratly. Indx Trms - Lst ky ndx trms hr. No mar than 5. I. INTRODUCTION Wth rfrnc to th automobl as an ndspnsabl lmnt of our prsonal moblty, th dsr for mor comfort and scurty hav placd thr mark n all aras of vhcl dsgn. Th vhcl chasss control s n gnral to control vhcl latral, vrtcal and longtudnal motons n ordr to mprov handlng prformanc, rd comfort and tracton/brakng prformanc. To nhanc such prformanc, t has bascally bn dpndng on th strng control, suspnson control and tracton/brakng control. Durng rcnt yars, som lctroncally controlld systms such as four-whl strng systm (4WS), ant-lock brakng systm (ABS), actv front strng systm (AFS), vhcl dynamcs control systm (VDC), actv suspnson systm (AS), tracton control systm and othrs, hav bn dvlopd and sgnfcant bttrmnt of vhcl prformanc hav bn dmonstratd by thm. Howvr, Th ffct of chasss control can b furthr ncrasd by th ntgraton and coordnaton of thos controls basd upon a dpr obsrvaton and study of vhcl dynamcs and tr charactrstcs. Fg. 1 shows th structur of ntgratd chasss control. In Ptr E. Rth s papr [1], ESC II (ESC wth actv strng ntrvnton) s prsntd, whch consdrs th ntgraton of braks and strng. In [], coopraton of 4WS and drct yaw momnt control (DYC) has bn consdrd, In whch a lnar 4WS controllr dsgnd ndpndntly of th DYC controllr was usd. Yu and Moskwa [3] proposd an ntgratd control systm dsgnd by usng fdback lnarzaton tchnqu and sldng mod control thory. Mauro Vlardoccha and Andra Morgando [4] prsntd a VDC-4WS-Actv Roll Control (ARC) ntgraton basd on on rfrnc body yaw rat for all actv systms. Yuqng Wang and Masao Naga [5] ntroducd an ntgratd control systm provdng hgh prformanc wthn trs strong nonlnar aras wth an adapton to th changng road and othr condtons, by optmally controllng th front and rar strng angls and th yaw momnt, basd on th nformaton of systm paramtrs dntfcaton. In Jang W and Yu Zhuopng s papr [6], a chasss control systm ntgratd AFS and DYC was prsntd usng fuzzy logc controllr to dstrbut th rqurd yaw momnt to AFS and DYC control systm proprly. Kazuya Ktajma and Hu Png [7] dsgnd two ntgraton algorthms for vhcl chasss control systms a fdforward ntgraton mthod and an H control algorthm amng to coordnat VDC, 4WS and actv suspnson functons of ground vhcl. In G. Burgo and P. Zglaar s publcaton [8], th fdback lnarzaton tchnqu was proposd for th dsgn of th ntgratd vhcl controllr, wth strng (AFS, SBW) and braks (or quvalntly tracton) actuators. E. M. Elbhry, Y. F. Zyada and M. E. Elaraby [9] suggstd th ntgraton btwn Actv Front Strng (AFS) and Actv Roll Momnt Control (ARMC) systms n ordr to nhanc th vhcl controllablty and th AFS systm adoptd a robust sldng mod controllr (SMC). In E. Ono and Y. Hattor s artcl [10], th vhcl dynamcs ntgratd control for four-whldstrbutd strng and four-whl-dstrbutd tracton/brakng systms basd on frcton crcl of ach whl was proposd. Ths papr focuss on th ntgratd chasss control of VDC and AFS, whch conssts of fv sctons. Th scond scton prsnts th multbody vhcl dynamc modl consdrng both AFS and VDC control systm. In th thrd scton, th ntgratd controllr s dsgnd to dstrbut th yaw momnt to VDC and AFS. Th VDC and AFS systm ar controlld by ANFIS and Fractonal-ordr PI μ mthod, rspctvly. Th smulaton rsults and concluson ar prsntd n th last two sctons /08/$ IEEE 165 Authorzd lcnsd us lmtd to: Rnsslar Polytchnc Insttut. Downloadd on Aprl 19,010 at 00:00:00 UTC from IEEE Xplor. Rstrctons apply.

2 Fg. 3 shows th prncpl of th actv front strng systm. Th drvr controls th vhcl va th hand strng whl (th strng whl angl s dnotd by s ) and th actuator provds an addtonal strng whl angl a accordng to th sgnal from ECU. Both angls rsult n a pnon angl down at th strng track.. Fg. 1 Intgratd chasss control II. VEHICLE SYSTEM MODEL In ths scton frst, a lnar -DOF modl s dscrbd, whch s proposd as and dal rfrnc modl and thn, a mult-body dynamc modl whch s consdrd for smulaton s prsntd. A. Lnar -DOF rfrnc modl W consdr th multbody dynamc modl as a wholvhcl modl and th -DOF modl (Fg. ) as an dal rfrnc modl. Ths -DOF modl rprsnts th drvr s dsrd vhcl prformanc and drvng trackng. If th drvr s dsrd vhcl prformanc and drvng trackng ar xprssd as lnar functons, th vhcl wll b much asr and safr to drv. In Fg., G dnots th ground rfrnc, and th vhcl has a front-whl strng systm. Th vhcl dynamc quatons for th dal -DOF rfrnc modl ar formulatd as Caf + Car acaf bcar mv ( y + ucω) = vy ω + Cafδ f uc uc (1) acaf bcar a Caf + b Car I ω = vy ω + acarδ f uc uc Fg. 3 Prncpl of th actv front strng systm C. VEHICLE DYNAMICS CONTROL SYSTEM OVERVIEW VDC can control th longtudnal and latral stablty synthtcally to unfy th ABS, TCS, and drct yaw momnt control (DYC). Dffrnt compans hav dffrnt nams for thr systms: Bosch calls t th lctronc stablty program (ESP) [11], Toyota calls t vhcl stablty control (VSC) [1], and othrs call t ntractv vhcl dynamcs (IVD). Fg. A -DOF dal vhcl modl whr m dnots th mass of th vhcl; v y s th latral spd; ω rprsnts th yaw vlocty; u c s vhcl forward vlocty; C af and C rprsnt th front- and rarwhl cornrng stffnss, rspctvly; δ ar f s th front strng angl; I s th momnt of nrta; and a and b ar th lngth from th front and rar axls, rspctvly, to th cntr of gravty of th vhcl. Th paramtrs of th dal -DOF vhcl ar gvn as follows: m =100Kg, I=549kg m, b =1.368m, C =75kN/rad and C =100.4kN/rad. af B. ACTIVE FRONT STEERING SYSTEM OVERVIEW ar a =1.56m, Fg. 4 Prncpl of th vhcl dynamc control systm Fg. 4 shows th prncpl of vhcl dynamcs control systm. Vhcl dynamcs control s ralzd manly by th dffrntal controls on th brak forcs on four whls, whch provds yaw momnt to kp th vhcl runnng accordng to th drvr s ntnt. In addton, t can prvnt sharp turnng whn th drvr oprats too havly. Vhcl dynamcs control uss brak momnt and ngn momnt to mantan stablty and mak t asy for th drvr to str th vhcl. D. MULTIBODY VEHICLE DYNAMIC MODEL Multbody smulaton has bn wdly usd to prdct vhcl handlng, safty, stablty and prformanc, and th loads calculatd from ths smulatons ar usd for subsqunt strss and durablty analyss. Th actual multbody soluton procss nvolvs numrcally ntgratng th quatons of moton. Th mathmatcal algorthm usd to drv th quatons of moton was dvlopd by Prof. Ed Haug and hs tam at th Unvrsty of Iowa n th arly 1980 s [13]. It s basd on usng a maxmal st of Cartsan gnralzd coordnats (X, Y, Z) and Eulr Paramtrs (0, 1,, 3) to form a systm of dffrntal-algbrac quatons. 166 Authorzd lcnsd us lmtd to: Rnsslar Polytchnc Insttut. Downloadd on Aprl 19,010 at 00:00:00 UTC from IEEE Xplor. Rstrctons apply.

3 In ths papr, th multbody vhcl dynamc modl s bult n th ADAMS/CAR nvronmnt. Ths modl ncluds svn subsystms: th front suspnson systm, th rar suspnson systm, th brak systm, th powrtran systm, th strng systm, th tr and th bodywork systm, as shown n Fg. 5. (sdslp angl dscrpancy and yaw vlocty dscrpancy) can b obtand by comparng th ral valus of th sdslp angl and yaw vlocty wth th dsrd valus. Thn, w can calculat th corrctv yaw momnt for both VDC and AFS. In addton, th brakng forc on ach whl, th throttl opnng and th addtonal front strng angl ( a ) can b dntfd by th corrctv yaw momnt. Fg. 5 Multbody vhcl dynamc modl E. TIRE MODEL In most tm, th ntgratd chasss systm has strong nonlnarty and w should adopt nonlnar tr modl. Thus, t ntroducs Pacjka's Magc Formular Modl [14] whch has hgh prcson for longtudnal forc of whl and sd-forc and also has bttr confdnc lvl out of rang of lmt valu. Th Pacjka's Magc Formular Tyr Modl can b dscrbd as follows: 1 1 y = Dsn( C tan { Bx E[ Bx tan ( Bx)]}) () wth Y( X) = y( x) + SV, x = X + SH Whr Y rprsnts th output varabl (longtudnal forc F x or latral-forc F y or slf-algnng torqu M z ), X s th nput varabl (sdslp angl or longtudnal slp κ ). Th coffcnts B, C, D, E ar th stffnss factor, th shap factor, th pak valu and th curvatur factor, rspctvly; SH, S V dnots th horzontal and vrtcal shft, rspctvly. Hr B, C, D, E, S H and S V ar known as prmary Magc Formular paramtrs. Fg. 6 Th structur of ntgratd VDC and AFS control Th vhcl dynamc quatons for th dal -DOF rfrnc B. ADAPTIVE FUZZY CONTROLLER FOR VDC Th ANFIS s an attractv comproms btwn th adaptablty of a nural ntwork and ntrprtablty of a fuzzy nfrnc systm. Fuzzy nfrnc systm dosn t mantan slf-larnng functon, whch lmts ts applcaton; th artfcal nural ntwork lkng a black box cannot xprss th lngustc fuzzy nformaton and nfrnc functon. Th ANFIS proposd by Jyh-Shng Rogr Jang [15] can compnsat th dfcncy of fuzzy nfrnc systm by adoptng th slf-larnng capablty of nural ntwork. For th VDC controllr, th Takag-Sugno (TS) fuzzy controllr trand by ANFIS archtctur s dsgnd. Whn 0.5 <Δ ω < 0.5, t s n a stabl stat and dffrnt whls can b controlld n th rangs Δ ω < 0.5 and Δ ω > 0.5. Two adaptv fuzzy controllrs ar bult wth two sam nput varabls (yaw vlocty dscrpancy and sdslp angl dscrpancy) and on output varabl (Brak or Throttl). Th structur of th adaptv fuzzy controllr s showd n Fg. 7 and Fg. 8. III. INTEGRATED VDC AND AFS CONTROL SYSTEM A. INTEGRATED CHASSIS CONTROL STRUCTURE Th smulaton systm s stablshd by th combnaton of ADAMS and MATLAB. Th structur of co-smulaton s showd n Fg. 6. AFS can gnrat corrctv larg yaw momnt n ach drcton whn vhcl s drvn straght; whn th str angl s larg, AFS s mor ffctv n controllng ovrstr than undrstr; whn vhcl s at th lmt of adhson, th yaw momnt gnrat by AFS s vry wak and th VDC should b th man actor. In ths papr, th yaw momnt s dstrbutd to AFS and VDC accordng to th valu of latral acclraton whch s a man factor to judg th stat of th vhcl. Th ANFIS and fractonal-ordr PI μ mthods ar appld on th control of VDC and AFS, rspctvly. Frst, th stat of VDC and AFS controllrs (on or off) ar dtrmnd by th dstrbutng controllr, and Δ β and Δω Fg. 7 Adaptv fuzzy controllr to obtan brak forc Fg. 8 Adaptv fuzzy controllr to obtan throttl opnng Fg. 9 shows th gnral structur of ANFIS. Th two nput varabls can b dvdd nto 5 lvls: ngatv bg (NB), ngatv mdan (NM), zro (Z0), postv mdan (PM), and postv bg (PB). Th output varabl (Brak or Throttl) s th lnar functon of th two nput varabls. Th rul-bas contans 5 fuzzy IF-THEN ruls of TS typ as follows: 167 Authorzd lcnsd us lmtd to: Rnsslar Polytchnc Insttut. Downloadd on Aprl 19,010 at 00:00:00 UTC from IEEE Xplor. Rstrctons apply.

4 Rul : If X s A and Y s B, thn f = aω+ bβ + c Whr X, Y and f ar lngustc varabls rprsntng two nputs varabls (sdslp angl dscrpancy and yaw vlocty dscrpancy) and on output varabl (Brak or Throttl), rspctvly. A and B ar partcular fuzzy substs dfnd by nonlnar coffcnt, namly prms paramtrs, whl a, b and c ar lnar coffcnts dtrmnng th output of ach appld fuzzy rul and usually known as consqunt paramtrs. Fg. 1 MF of sdslp angl for BrakControllr whn Δ ω > 0.5 Fg. 13 MF of yaw vlocty for ThrottlControllr whn Δ ω > 0.5 Fg. 9 Th gnral structur of ANFIS Th tranng procss of ANFIS s prsntd n Fg. 10. Th tranng data st of sdslp angl dscrpancy, yaw vlocty dscrpancy, brak forc and throttl opnng s obtand through th smulaton basd on multbody vhcl dynamc modl bult n ADAMS/CAR. Ths data ar collctd from varous xprmnts at dffrnt stuatons lk sngl lan chang tst, ISO lan chang tst, Brak n turn tst, Constant-radus cornrng tst, Powr-off cornrng tst, Fsh-hook tst, Stp str tst, Swpt sn str tst and so on. ANFIS taks th ntal fuzzy modl and tuns t by mans of a hybrd tchnqu combng gradnt dscnt back-propagaton and man last-squars optmzaton algorthms. Fg shows th mmbrshp functon aftr tranng and MF s th rprsntaton of mmbrshp functon. Fg. 10 Th procss of tranng fuzzy logc controllr by ANFIS Fg. 11 MF of yaw vlocty for BrakControllr whn Δ ω > 0.5 Fg. 14 MF of sdslp angl for ThrottlControllr whn Δ ω > 0.5 C. FRACTIONAL-ORDER PI μ CONTROLLER FOR AFS VDC can control th longtudnal and latral stablty synthtcally to unfy th ABS, TCS, and drct yaw momnt control (DYC). Dffrnt compans hav dffrnt nams for thr systms: Bosch calls t th lctronc stablty program (ESP) [11], Toyota calls t vhcl stablty control (VSC) [1], and othrs call t ntractv vhcl dynamcs (IVD). 1) Fractonal-ordr PI μ ovrvw In 1994, Podlubny [16] proposd a gnralzaton of th PID controllr, whch s calld th fractonal-ordr PI μ controllr bcaus of nvolvng an ntgrator of λ and dffrntator of ordr μ, and whch also shows bttr prformanc than th classcal PID controllr. Fractonal-ordr PI μ controllrs ar dscrbd by fractonal-ordr dffrntal quatons. Fractonal-ordr PI μ control s th gnralzaton and dvlopmnt of th ntgr-ordr PID control. It s dscrbd as follows [16]: λ μ ut () = kt p () + kd t t () + kdt d t () (3) whr t () s th systm rror, λ s th fractonal ntgral ordr, μ s th fractonal drvatv ordr. Whn λ = 1, and μ = 1, classcal ntgr ordr PID controllr s obtand. λ = 1 and μ = 0 dfn a PI controllr; λ = 0 and μ = 1 gv a PD controllr. λ = 0 and μ = 0 gv a gan. ) Fractonal-ordr PI λ controllr dsgn and optmzaton A PI λ controllr wth yaw vlocty dscrpancy as nput varabl s dsgnd to gnrat addtonal front strng whl angl. Th addtonal front strng whl angl a s dscrbd as follows: λ = K () t + K D () t (4) a pfra ω Fra t ω 168 Authorzd lcnsd us lmtd to: Rnsslar Polytchnc Insttut. Downloadd on Aprl 19,010 at 00:00:00 UTC from IEEE Xplor. Rstrctons apply.

5 whr ω () t s th yaw vlocty dscrpancy btwn th mult-body vhcl dynamc modl and th -DOF dal rfrnc modl. Paramtrs lk K pfra, K Fra, and fractonal ntgral ordr λ ar tund by GA optmzaton algorthm. W can consdr to buld th PI λ controllr from th vw of optmzaton. Th objctv functon slctd to b optmzd s: (1) sdslp angl dscrpancy; () yaw vlocty dscrpancy. To fnd: Dsgn varabls to mnmz: F t = Ψ max ω β ω ωmn Whr Ψ= ρ1 + ρ + ρ3 + ρ4 B B B B ω β ωmax ωmn max β βmn + ρ 5 + ρ 6 B B βmax βmn subjct to: N ( az ) 3 = 1 + max( az ) 1 / N ay 7 m/ s φ 3dg m s whr B ω, B β, B ω, B max ω, B mn β and B max β ar th mn maxmum valus of ω, β, ω max, ω mn, β max and β mn rspctvly. ρ1... ρ 6 ar th corrspondng wghts; β s th man valu of dffrnc btwn th ral sdslp angl and st valu; β max and β mn ar th maxmum and mnmum valus, rspctvly, of th dffrnc btwn th ral sdslp angl and st valu; ω s th man valu of dffrnc btwn th ral and dal yaw vlocty; ω max and ω mn ar th maxmum and mnmum valus, rspctvly, of th dffrnc btwn th ral and dal yaw vlocts; a z s th body acclraton; a y s th latral acclraton; and φ rprsnts th roll angl of bodywork. Th paramtrs for fractonal-ordr PI λ controllr tund by GA ar gvn as follows: K = pfra, K =3.45, λ = Fra D. INTEGRATED CHASSIS CONTROL Th dstrbutng controllr s dsgnd basd on latral acclraton n ths scton. Thr ar two man control objctvs for th ntgratd chasss control and thy ar th sdslp angl and yaw vlocty control. Th sdslp angl control stratgy rducs th latral moton and transportaton of vhcl, whl t mprovs handlng manuvrablty and rducs th dlay of rspons of th vhcl; th yaw vlocty control stratgy mnmzs th rotatonal moton of vhcl and lads th vhcl to latral sd trackng th dsrd trajctory. Accordng to th control authorty n undrstr and ovrstr corrcton and th work smulaton, som basc ruls of ntgratd chasss control ar obtand [6, 8, 9]: (1) whn latral acclraton s small, such as runnng straght, th yaw momnt dmand should b mplmntd only through AFS to nsur th rd comfort prformanc. () Whn latral acclraton s mdum, th yaw momnt should b mplmntd through both AFS and VDC. (3) Whn th latral acclraton s larg, lk th vhcl s at th lmt of adhson, th yaw momnt should b mplmntd only through VDC. IV. SIMULATION RESULTS AND DISCUSSION Stp strng xprmnt s adoptd to valdat th prformanc of ntgratd control of VDC and AFS. Th vhcl vlocty s 80km/h, and th drvr nput strng whl angl s 30 dgrs. Fgs. 15 through 18 show th smulaton rsults of ntgratd chasss control, only VDC control and wthout control wth th sam condton whr th tst s on an cy road (adhson coffcnt s 0.). W can s that th yaw vlocty and sdslp angl convrgnc rapdly, and th oscllaton of th systm rducs wth th ntgratd control of VDC and AFS. Th yaw vlocty of ntgratd control systm can also track th dof dal rfrnc modl closly. Fg. 15 Strng whl angl Fg. 16 Comparson of yaw vlocty 169 Authorzd lcnsd us lmtd to: Rnsslar Polytchnc Insttut. Downloadd on Aprl 19,010 at 00:00:00 UTC from IEEE Xplor. Rstrctons apply.

6 Fg. 17 Comparson of sdslp angl Fg. 18 Comparson of latral acclraton V. CONCLUSION A smultanous control tchnqu basd on th coopraton of ANFIS VDC controllr and fractonal-ordr PI μ AFS controllr has shown a good prformanc. Th dstrbuton of yaw momnt s basd on th control authorty n undrstr or ovrstr corrcton. Th tranng data of ANFIS s obtand from th smulaton basd on multbody vhcl dynamc modl, and ts prformanc would b bttr f th data coms from xprmnt. Th paramtrs of th fractonal-ordr PI μ ar tund usng GA optmzaton mthod, whch nsur ts good qualty. ACKNOWLEDGEMENTS Th authors gratfully acknowldg th fnancal support by th Natonal Hgh-Tch R&D Program, Chna (No. 007AA04Z131). [4] Mauro V., Andra M. and Aldo S.. Four-whl-strng Control Stratgy and ts Intgraton wth Vhcl Dynamcs Control and Actv Roll Control. SAE papr [5] Yuqng Wang and Masao Naga. Intgratd Control of Four-Whl-Str and Yaw Momnt to Improv Dynamc Stablty Margn. Procdngs of th 35 th Confrnc on Dcson and Control. Kob, Japan. 1996: [6] Jang W, Yu Zhuopng and Zhang Ljun. Intgratd Chasss Control Systm for Improvng Vhcl Stablty. IEEE ICVES , [7] Kazuya Ktajma and Hu Png. H Control for Intgratd Sdslp, Roll and Yaw Controls for Ground Vhcls. Procdngs of AEVC 000. Ann Arbor, Mchgan [8] G. Burgo and P. Zglaar. Intgratd Vhcl Control Usng Strng and Braks. Intrnatonal Journal of Control. 006, 79(5): [9] E. M. Elbhry, Y. F. Zyada and M. E. Elaraby. Handlng Capablts of Vhcls n Emrgncs Usng Coordnatd AFS and ARMC Systms. Vhcl Systm Dynamcs. 001, 35(3): [10]E. Ono, Y. Hattor, Y. Muragsh and K. Kobuch. Vhcl Dynamcs Intgratd Control for Four-whl-dstrbutd Strng and Four-whl-dstrbutd Tracton/Brakng Systms. Vhcl Systm Dynamcs. 006, 44(): [11]J. Ackrmann. Yaw dsturbanc attnuaton by robust dcouplng of car strng. In Procdngs of th IFAC World Congrss, San Francsco, CA, [1]Hraoka, T. Et al.. Stablty analyss of coopratv strng systm by usng drvr modl basd on cntr of prcusson (n Japans wth Englsh summary). Procdngs of JSAE Autumn Convnton, No (000). [13]Haug E. J. Computr-Add Knmatcs and Dynamcs of Mchancal Systms. Allyn and Bacon, Boston [14]Pacjka H B and Bsslnk. Magc Formula Tyr Modl wth Transnt Proprts. Vhcl Systm Dynamcs, 1997 (7): 34~49. [15]Jyh-Shng Rogr Jang. ANFIS: Adaptv-Ntwork-Basd Fuzzy Infrnc Systm. IEEE Trans. on Systms, Man and Cybrntcs. 1993, 3(3): [16]Podlubny I. Fractonal-Ordr Systms and PI μ - Controllrs. IEEE Transactons on automactc control. 1999, 44(1): REFERENCES [1] Ptr E. Rth and Ralf Schwarz. ESC II ESC wth Actv Strng Intrvnton. SAE papr [] Furukawa Y. and Ab M.. On-board-tyr-modl Rfrnc Control for Coopraton of 4WS and Drct Yaw Momnt Control for Improvng Actv Safty of Vhcl Handlng. Procdngs of AVEC , [3] Yu S. H. and Moskwa J. J.. A Global Approach to Vhcl Control: Coopraton of Four Whl Strng and Whl Torqu. J. Dyn. Systms Mas. Control. 1994, 116: Authorzd lcnsd us lmtd to: Rnsslar Polytchnc Insttut. Downloadd on Aprl 19,010 at 00:00:00 UTC from IEEE Xplor. Rstrctons apply.