Inenaional Jounal o Auooive echnology, Vol.?, No.?, pp.??(yea) Copyigh 000 KSAE Seial#Given by KSAE IRE LAERAL FORCE ESIMAION USING KALMAN FILER Eun Jae Lee ), Ho Jin Jung ) and Sei Bu Choi )* ) Hanoo ie R&D cene, Daejeon 347, Koea ) Mechanical Engineeing, KAIS, Daejeon 344, Koea (Received dae ; Revised dae ; Acceped dae ) * Please leave blan ABSRAC As o he ie analysis, laeal ie oce is a undaenal aco ha descibes he sabiliy o vehicle handling. Aeps o analyze he vehicle sabiliy have been ade based on vaious objecive es ehods and soe speciic acos such as yaw, laeal acceleaion and oll angle. Howeve, he poble o ideniy which axle is lac o he ie gip a a ceain siuaion sill eains. Since indoo ie oce easueen syse canno epesen a eal oad and vehicle condiions, ie oce easueen hough a eal vehicle es is ineviable. Due o he high pice o he ie oce easueen device, ie oce esiao can be an alenaive owad cos educion and device ailue. In his pape, nonlinea plana ull ca odel cobined wih ie odel is poposed. hen, using discee-ie exended Kalan-Bucy ile (EKBF), individual ie laeal oce ae esiaed wih odiied elaxaion lengh odel. KEY WORDS : Kalan ile, Relaxaion lengh, ie oce esiaion, Plana ull ca odel, Coneing siness odel NOMENCLAURE V x V y : longiudinal velociy, /s : laeal velociy, /s : yaw ae, ad/s : vehicle ass, g : oen o ineia abou yaw axis, g : le wheel see angle, ad : igh wheel see angle, ad : hal o vehicle ac widh, : disance o on axle o he cene o gaviy, I z l l : disance o ea axle o he cene o gaviy, : densiy o ai, g/ 3 ai C d A l : dag coeicien, - : vehicle on coss secional aea, : oll angle, ad : on oll see copliance, - : ea oll see copliance, - : wheel base lengh, : heigh o gound o cene o gaviy, h cg c : on oll siness, n/ad c : ea oll siness, n/ad : disance o cg o oll axis, h * Coesponding auho. e-ail: sbchoi@ais.ac. : olling esisance, - R : eecive adius, e : oad icion coeicien, - : elaxaion lengh, : coneing siness, N/ad : laeal siness, N/ : disoion siness, N/ad R C K L K D SUBSCRIPS l,, l, : on le, on igh, ea le, ea igh. INRODUCION Evaluaing he seeing esponse and sabiliy o he vehicle have elied on a well-ained evaluao called subjecive es enginee. his have been nown o be he os eliable es ehod ha canno be eplaced in he indusy. o analyse he subjecive es esuls physically, pseudo objecive es ehods and epesenaive paaees wee deanded, heeae a huge vaiey o indices have been suggesed. Aong he, ie oce is one o he undaenal acos ha descibes he sabiliy o handling peoance. Fo delibeae peoance evaluaion o developed ie poduc, he indoo ie oce easueen syse is widely used. he syse easues he oce vesus slip angle diecly o vaious
Inenaional Jounal o Auooive echnology, Vol.?, No.?, pp.??(yea) veical loading condiions. Alhough i subsiues he ie and oad ineace chaaceisics indiecly, i canno epesen a eal paved oad and vehicle condiions. hen, ie oce easueen daa o vehicle diving expeien conduced by equipping wih wheel oce ansduce (WF) senso has been acquied addiionally. Howeve, i is ipacical due o he high cos o easueens device. heeoe, he design o ie oce esiao is highly equied o educe he cos. hee coon paaees ha have been widely used by nueous ie-anuacuing copanies o indoo ess ae coneing siness, laeal siness, and disoion siness. hese hee ie paaees copise he sandad indices o deeine he laeal oion o a ie by poviding speciic physical eanings o he ie laeal oion (Schilippe, 954; Paceja, 005). hen, hese paaees can be ipleened in a ie elaxaion lengh odel. Howeve, convenional odel which has been adoped o he laeal dynaics epesenaion includes only coneing siness and laeal siness. In he aspecs o laeal ie oce esiaion, use o advanced ie elaxaion lengh odel can help ipove he accuacy o ie laeal oce esiaion especially in ansien esponse (Higuchi and Paceja, 997; Mass, 009). o deal wih he aoeenioned issue, his pape poposes he ie oce esiaion algoih designed wih exended Kalan-Bucy ile (EKBF) based on nonlinea vehicle dynaic and ie odel by o-line pocessing. Copaed wih pevious sudies (Ray, 997; Bae, 007; Ki, 009; Douiai, 0), his pape suggess he ipoved ehod o laeal ie oce esiaion by applying odiied elaxaion lengh and odiied coneing siness in he dynaic ie odel. Based on he plana ull ca odel, eleven degee o eedo dynaic equaions conaining laeal and wheel dynaics wee used o he esiao design. he poposed esiao was validaed hough he copaison o eal laeal ie oce a each wheel easued o WF senso equipped in es vehicle. In he es vehicle, a seeing obo and dynaic oion sensos wee also equipped o pecise eeence inpu and analysis. he validaion es ode is double lane change ha epesens highly ansien aneuves. he eainde o his pape is oganized as ollows. In he ollowing secion, he vehicle odel which will be adoped o he esiao design is inoduced. he hid secion descibes he ie odel o epesen ie-oad ineacion. In his secion, odiied elaxaion odel including disoion siness is suggesed, which helps o ipove he accuacy o he laeal ie dynaic odel. he ouh secion descibes he ie oce esiaion saegy. And inally he esiaion esuls and he eal oce value easued by he vehicle ess will be copaed in he ih secion.. PLANAR FULL CAR MODEL Copyigh 000 KSAE Seial#Given by KSAE his sudy chose hee degee o eedo odel o vehicle oion saes o esiae and veiy laeal ie oce a all posiions. his odel has been widely used o descibe he vehicle laeal dynaics (Douiai, 007). Based on he saes and paaee noinaions descibed a Figue, he equaions o oion ae descibed as ollows: Vx Fxl cos( ) Fx cos( ) Fylsin( ) () Fysin( ) Fxl Fx CavVx Vy Vy Fxlsin( ) Fxsin( ) Fylcos( ) F cos( ) F F V y yl y x l Fxlsin( ) Fxsin( ) Fylcos( ) I z F cos( ) F cos( ) F cos( ) F sin( ) y xl x yl Fysin( ) Fxl Fx l Fyl F y whee Vx, Vy,,, I z,,,, l, l ae he longiudinal velociy, laeal velociy, yaw ae, vehicle ass, oen o ineia abou yaw axis, le wheel see angle, igh wheel see angle, hal o ac widh, disance o on axle o he cene o gaviy (CG), and disance o ea axle o he CG, especively. () (3) F, F ae longiudinal ie oce and laeal ie oce ollowed by subscips l,, l, epesening on le, on igh, ea le, ea igh, especively. C av is he luped paaee o epesen he dag esisance, which is expessed as ollows: Cav aicd A (4) whee ai, Cd, A ae densiy o ai, coeicien o ai dag and on coss secional aea, especively. Fon and ea slip angle a each wheel ae epesened as ollows (Ki, 009): V y l i j an, i l, ; j, (5) Vx V y l i an, i l, (6) Vx whee,, ae oll angle, on oll see copliance, and ea oll see copliance, especively... Veical load calculaion he laeal ie oce is aeced by load anse while he vehicle is coneing. he aoun o load anse is deeined by he vehicle geoey, siness o he suspension, and he sping ae o he ies. In his x y
Inenaional Jounal o Auooive echnology, Vol.?, No.?, pp.??(yea) Copyigh 000 KSAE Seial#Given by KSAE Figue. Plana ull ca odel. pape, he linea equaion o oll oion and oll siness is ipleened. Couplings beween he veical load and laeal oce ae descibed as ollows (Gillespie, 99; Douiai, 007; Ki, 009). l hcg hcgl Fzl v g v ax v ay z l l l l h cg hcgl Fz v g v ax v ay z l l l (7) l hcg hcgl Fzl vg v ax v ay z l l l l hcg hcgl Fz v g v ax v ay z l l l a (8) zi i y c i l l i i h h, i, c c gh l (9) whee l, hcg, ax, ay, g, c, c, h ae he wheel base lengh, heigh o gound o CG, longiudinal acceleaion, laeal acceleaion, gaviaional acceleaion, on oll siness, ea oll siness, and disance o CG o oll axis, especively... Wheel dynaics odel Wheel dynaics can be deived as: i di bi ReFxi ReR Fzi, i l,, l, (0) I w whee, I,,, R, F, R ae he wheel angula i w di bi e xi velociy, wheel oen o ineia, diving oque, baing oque, eecive adius, longiudinal oce, and olling esisance coeicien, especively..3. Oupu sha oque dynaics odel o conigue he wheel dynaics equaion enioned above, he inoaion o diving oque anseed o he engine is essenial. o conside dynaic odel Figue. Coneing siness vaiaion vesus veical load (a) seady coneing (b) ansien coneing. esponses such as oque conveo slip and ansission gea shiing even, oque obseve can be designed using engine oque and ohe vehicle daa o conolle aea newo (CAN) signal. Howeve, vehicle ess ae soeies conduced wihou obaining all vehicle daa o CAN signal. Fo his eason, his pape ocuses on he laeal ie oce esiaion, which allows less accuae dive oque inoaion o be accepable. heeoe, sipliied dynaics odel o oupu sha oque is applied in his pape. Hee oupu sha oque is divided ino load oque and ineia oque, and ineia oque is expessed by consideing diveain as a luped ass as delineaed below (Han, 06): l d Jv L _ od el () l () L _ od el Re R Fz ai Re Cd A whee and ae he oupu sha oque and luped oen o ineia. Hee, equaion () and () apply o on wheel dive ype. I is noewohy ha wheel angula velociy is changeable depending on onwheel-dive o ea-wheel-dive ype. he es vehicle used o conduc expeien in his pape was based he on on wheel dive ype. o J v 3. IRE DYNAMICS FOR VEHICLE MODEL INEGRAION 3.. Reeence laeal ie odel
Inenaional Jounal o Auooive echnology, Vol.?, No.?, pp.??(yea) Copyigh 000 KSAE Seial#Given by KSAE In his pape, Dugo s odel is used as he eeence ie odel. I expesses he ie oce hough concening boh o nonlinea chaaceisics and A ypical is ode dynaic odel which expesses he lagged behavio o he laeal ie oce can be epesened as ollows: cobined eec o longiudinal and laeal oce Fyi Fyi Fyi, i l,, l, geneaion. By neglecing longiudinal oce, he (8) Vx sipliied nonlinea laeal oce is given by (Dugo, whee is he elaxaion lengh discussed below. 970): Fyi Cyian( i) ( i ), i l,, l, (3) 3.3.. Modiied elaxaion lengh odel whee is he coneing siness a each ie posiion. Hee, is expessed as ollows: Heydinge (99) deived a dynaic odel ha elaes saic laeal ie oce and lagged laeal ie ( i ) i, i i ( i ) (4) oce. his odel expesses he elaxaion lengh as,, i i which is epesened as ollows: Fz i, i l,, l, C an( ) (5) (9) C yi ( ) i yi i Hee, is he oad icion coeicien. In his pape, he noinal is assued as 0.9 o epesen a noinal high u suace. Wih he sipliied Dugo s odel, he ie oce esiao suggesed in his pape ocuses on he individual laeal ie oce a each wheel. 3.. Weigh shiing eec in coneing siness Laeal ie oce is gealy aeced by veical load changes as well as slip angle duing he vehicle aneuves lie double lane change. heeoe, coneing siness is also inluenced by hese eecs. Figue shows he expeienal esul o coneing siness vaiaion vesus ie veical load, which is obained o indoo esing achine o MS Fla- ac es achine. In ode o epesen he coneing siness oe pecisely in he Dugo s odel, we have econsuced he coneing siness o he siple epiical laeal ie oce odel ha includes boh weigh shiing and side slip angle e given by: Fy C Fz, n F z C Fz, n Fz Cy (6) whee C, C ae he coneing siness elaion coeiciens and Fz, n, Fz ae he saic veical load and he dieence beween dynaic veical load ha includes vehicle acceleaion and saic veical load. o ipove he accuacy o he laeal oce, adjusen acos, and, ae applied o he coneing siness equaion. hese values can be changed accoding o he es ie chaaceisics. Fo he equaion (6), ollowing odiied coneing siness C is adoped in his sudy: y Cy C Fz, n F z C Fz, n Fz (7) 3.3. Dynaic ie odel C K whee C is exacly sae as L CF zn, and K L is laeal siness. Howeve, accoding o Lee (06), elaxaion lengh odel can be uhe elaboaed hough consideing hee ie chaaceisic paaees as ollows: 3 3 C 3CK D 3 (0) KL KL whee is disoion siness. his sudy suggess he ipoved ie oce esiaion by applying odiied elaxaion lengh odel. Expeienal esul o indoo esing achine is used as noinal values o C, K, K K D 4. ESIMAOR DESIGN L D. Based on he lieaue eviews o he ie oces esiaion ehods (Ray, 997; Bae, 007; Ki, 009; Douiai, 0), Kalan ile has been poved o be oe advanageous han ohe ypes o esiaos, because i aes he sochasic ile o ha shows obusness owad paaee unceainies. Especially, his sudy adoped exended Kalan-Bucy ile (EKBF) ha applies coninuous ie odel in he pocess o obaining esiaes, because vehicle dynaic esponse is no ha swi copaed wih easueens o sapling ie. 4.. EKBF design o saes esiaion o nonlinea odel By inegaing equaions ()-(3), (0) and (8), sae space o o he ull ca vehicle dynaic odel is obained as ollows: x( ) x ( ),u( ) w ( ) () z( ) hx ( ),u( ) v ( ) ()
Inenaional Jounal o Auooive echnology, Vol.?, No.?, pp.??(yea) Copyigh 000 KSAE Seial#Given by KSAE he sae veco,, is coposed o longiudinal x velociy, laeal velociy, yaw ae, ou wheel angula x velociies and ie oces: x8 x9 cos( u) x x3 sin( u) x () Vx, Vy,,ω [ 4],F[ 8] x, x,, x5 (3) Hee, he coponens o he wheel angula velociy x0 x Cavx and ie oce veco ae h x8 x9 sin( u) x x3 cos( u) (9) ω 4 l l [ ],,, (4) x4 x5 F 8 Fxl Fx Fxl Fx Fyl Fy Fyl F [ ],,,,,,, y (5) x3 x4 he conol inpu veco is copised o wheel see x 5 angle and each wheel oque given by: x 6 u () /, di bi, i l,, l, (6) x 7 Hee, longiudinal ie oces ae eaed as ando Hee, i was assued ha le and igh wheel see wal signal, which iplies ha i does no involve angles ae alos sae because wheel see angle is dynaic equaion a all. geneally obained o seeing wheel angle uliplied he easueen noise eo covaiance aix was by seeing gea aio. heeoe, wheel see inpu is chosen as R = diag[0.000, 0.00, 0.000, 0.000, expessed as ean value. is obained o he oupu 0.00000, 0.0, 0.0, 0.0, 0.0] based upon he acual sha oque dynaics odel explained in secion.3. es daa and equipen speciicaions. And he pocess he easueens ae: noise eo covaiance aix was chosen as Q = diag[,, 0.000, 0.0, 0.0, 0.0, 0.0,,,,, 000, 000, 000, 000]. Sae veco can be esiaed by applying disceeie EKBF as ollows (Ray, 997; Sion, 006): x() v() di z () Vx, Vy, ax, ay,,ω [ 4] (7) Hee i is assued ha pocess noise and easueens noise ae zeo ean Gaussian and hey ae uncoelaed each ohe. In equaions () and (), he paicula uncion and he obsevaion uncion h ae expessed as ollows: x8 x9 cos( u) x x3 sin( u) x0 x Cavx xx3 x8 x9 sin( u) x x3 cos( u) x4 x5 xx3 l x8 x9 sin( u) x x3 cos( u) I z x8 x9 cos( u) x x3 cos( u) x0 x l x4 x5 u Rex8 ReR Fzl Iw u3 Re x9 ReR Fz Iw u4 Rex0 ReR Fzl Iw u5 Rex ReR Fz Iw 0 [ 4 ] x x Fyl x x3 Fy x x4 F yl x x5 Fy w() (8) xˆ xˆ x ˆ( ),u( ) d P P F( ) P( ) P( ) F ( ) Q( ) d K P H HP H R xˆ xˆ K z H ˆ (x ) P I K H P (30) Hee, F and H ae Jacobian aices o pocess and easueen odel, especively, x ˆ,u ) hx ˆ,u F, H (3) xˆ xˆ Copuaion o he discee-ie EKBF gain is a suble ix o pocessing and easueen noise. Since he easueens have high accuacy, R aix was se wih sall values in his as. 5. EXPERIMENAL RESULS 5.. Expeienal seup his secion pesens he expeienal sudies caied ou o obain he eal ie oces. he equipen and poving gound wee povided by Hanoo ie R&D cene. he es vehicle is a B class hachbac wih 95/55R6 size sue ies. o inpu an accuae hand-wheel seeing angle, seeing obo was equipped wih he vehicle. Vehicle oion was ecoded by R-300 IMU/GPS senso
Inenaional Jounal o Auooive echnology, Vol.?, No.?, pp.??(yea) Copyigh 000 KSAE Seial#Given by KSAE Figue 3. Ipleenaion o daa acquisiion devices o he esiao validaion. Figue 4. Bloc diaga o esiao and validaion pocess. and ie oces was easued by SWIF. All he daa was colleced a 00Hz sapling equency. he ipleenaion o he seaing inpu and acquisiion devices is illusaed in Figue 3. Figue 4 shows he bloc diaga o he esiao and validaion pocess. Fo he vehicle oion sensos, easueen veco ha is used o poseioi esiaion o EKBF was obained. In addiion, vehicle dive oque was calculaed o he vehicle oion senso values, which was explained in secion.3. o validae he esiaion peoance ha includes consideable weigh shiing o he vehicle, an open loop es wih a highly sevee aneuveing ode was conduced. A iangula shape 40 00 60 hand-wheel seeing angle inpu duing a. second ie peiod was adoped o a eeence scenaio(see Figue 5(a)). his ode was sevee enough o cause he nonlinea behaviou o he vehicle laeal oion. And he es was conduced by an expe dive o ainain consan longiudinal speed. z() 5.. Vehicle oion validaion A is, esiaed vehicle saes wee copaed wih he expeienal daa. Figue 5 epesens he esiaion esuls o he longiudinal velociy, laeal velociy and yaw ae o he eeence seeing inpu. Alhough he es was conduced a a highly sevee ode, he esuls eveal vey accuae esiaion peoance. he oo ean squae (RMS) eos o esiaed oion saes ae 0.7/s, 0.008/s and 0.00063ad/s. 5.3. Laeal ie oce validaion F ˆ y () Fˆ yl Fy Fyl F, ˆ, ˆ, ˆ y was obained o he ie oce esiao, and hen i was copaed wih he expeienal daa. Figue 6 shows he esiaion esuls o he laeal ie oce a all wheel posiions. he RMS esiaion eos o each ie ae 34N, 0N, 93N and 6N on on le ie, on igh ie, ea le ie and ea igh ie especively. Consideing he bigge axiu laeal ie oce o on wheel han ha o ea one, i is easonable ha he RMS eo o he esiaion accuacy o ie oce a on wheel is lage han he ea one. Expeienal esuls pove ha he suggesed esiao is suicienly uncional in he es wih a axiu laeal oce ove 4000N. Howeve, he peoance o he obseve was deeioaed ove inne wheels a which ie gip oce is no geneaed uch due o he less veical load han oue wheels (see blac doed cicles o igue 6). Moe speciically, esiaion eo was wose a ea wheels han ha o on wheels duing he coune see oion. his was ainly due o he absence o suspension and vehicle osional siness odels. Wihou hose odels, he dieence o he weigh shiing eecs beween he on and ea axles canno be descibed accuaely. 6. CONCLUSION In his pape, esiaion ehod o he ie oces a all wheel posiions was suggesed. he eleven degee o eedo vehicle odel was designed wih he plana ull ca odel and he eeence ie odel. In paicula, he odiied ie elaxaion lengh was applied o he laeal ie dynaic odel and he coneing siness ha includes he weigh shiing eec was applied o
Inenaional Jounal o Auooive echnology, Vol.?, No.?, pp.??(yea) Copyigh 000 KSAE Seial#Given by KSAE Figue 5. Vehicle inpu and esiaion esuls o vehicle oion saes (a) Seeing wheel angle (b) Longiudinal velociy (c) Laeal velociy (d) Yaw ae. he laeal seady ie odel in ode o ipove esiaion accuacy o he laeal ie oces o sevee ansien aneuves. hen, he discee-ie EKBF esiaion saegy was applied o esiae he saes o vehicle oions and ie oces, which have nonlinea chaaceisics. he peoance o he suggesed esiao wee validaed by he copaison wih he expeienal daa. he expeienal esuls showed vey accuae esiaion peoance even unde he exeely ansien es ode o double lane change. he suggesed esiao is expeced o assis vehicle Figue 6. Esiaion esuls o laeal ie oces (a) Fon le (b) Fon igh (c) Rea le (d) Rea igh. and ie design enginees in esiaing he ie oce oe accuaely. Wih he accuae ie oce inoaion, peoance o vehicle chassis conol syses can be ipoved gealy. Moeove, he esiaed ie oces can be applied o he deivaion o epiical ie odel ha can suppleen he indoo es esuls. ACKNOWLEDGEMEN he auhos would lie o appeciae Hanoo ie Co. Ld. o povision o expeienal equipen and devices. his eseach was suppoed by he MSIP(Minisy o Science, IC and Fuue Planning), Koea,
Inenaional Jounal o Auooive echnology, Vol.?, No.?, pp.??(yea) Copyigh 000 KSAE Seial#Given by KSAE unde he IRC(Inoaion echnology Reseach Cene) Ki, J. (009). Nonlinea ie oce esiaion and oad suppo poga(iip-07-0-0-0068)supevised by he icion ideniicaion: siulaion and expeiens. IIP(Insiue o Inoaion & counicaions echnology Conol Engineeing Pacice. 7, 3, 357 367. Pooion). his wo was suppoed by he Naional Lee, E. e al., (06). Sing ie odel o evaluaing Reseach Foundaion o Koea(NRF) gan unded by he seeing agiliy peoance using ie coneing oce Koea govenen(msip) (No. 07RAB40046). and laeal saic chaaceisics. Veh. Sys. Dyn. 55,, APPENDIX 3 43. Maas, J. W. L. H. (009). A Copaison o Dynaic ye Models o Vehicle Shiy Sabiliy Analysis. able. Modelling paaees o he es vehicle body and ie. M.S. hesis. Eindhoven Univesiy o echnology. Eindhoven, Nehelands. Paaee Value Paceja, H. (005). ie and vehicle dynaics. Elsevie. Disance o CG o on and ea axle,.5,.7 Ray, L. R. (997). Nonlinea ie oce esiaion and Heigh o gound o CG, 0.4 oad icion ideniicaion: siulaion and Disance o he CG o he oll axis, 0.5 expeiens. Auoaica. 33, 0, 89 833. Fon and ea ac widh,.46,.46 Schilippe, B. v. (954). Shiying o a Pneuaic Wheel(English anslaion ve. o Das Flaen eines Eecive wheel adius, 0.3 bepneuen Rades), NACA M 365, pp. 5-47 Vehicle cub weigh + dive + es equipen, 50 g Sion, D. (006). Opial sae esiaion: Kalan, H Vehicle oen o ineia abou yaw axis, 3350 g ininiy, and nonlinea appoaches. John Wiley & Wheel oen o ineia, 0.6g Sons. h cg, R e Fon and ea oll see coeicien, Fon and ea oll siness, I w l, l h, c, c I z 0.07, 0.08 650N/ad, 650N/ad Coneing siness elaion coeiciens, C, C, 8. Laeal siness, Disoion siness, Adjusen acos, K L K D, 84N/ 5080N/ad 0.98, 0.99 REFERENCES Bae, G. e al., (007). An Obseve o ie-road Foces and Ficion o Acive Secuiy Vehicle Syses. IEEE/ASME ans. Mechaonics., 6, 65 66. Douiai, M. e al., (0). Onboad eal-ie esiaion o vehicle laeal ie oad oces and sideslip angle. IEEE/ASME ans. Mechaonics. 6, 4, 60 64. Dugo, H. e al., (970). An analysis o ie acion popeies and hei inluence on vehicle dynaic peoance. SAE echnical Pape 700377 Gillespie,. D. (99). Fundaenals o vehicle dynaics. SAE Inenaional. Han, K. e al., (06). Robus esiaion o axiu ie-oad icion coeicien consideing oad suace iegulaiy. In. J. Auooive echnology. 7, 3, 45 45. Heydinge, G. J. e al., (99). he ipoance o ie lag on siulaed ansien vehicle esponse. SAE echnical Pape 9035 Higuchi, A. and Paceja, H. (997). ie elaxaion lengh concep a lage wheel slip and cabe. Veh. Sys. Dyn. 7,, 50-64.