Ari J. Tuononen Vehicle lateral state estimation based on measured tyre forces. Sensors, volume 9, number 11, pages

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1 Ai J. Tuononen. 29. Vehicle lateal state estimation based on measued te oces. Sensos volume 9 numbe pages b autho

2 Sensos ; doi:.339/s9876 OPEN ACCESS sensos ISSN Aticle Vehicle Lateal State Estimation Based on Measued Te oces Ai J. Tuononen Laboato o Automotive Engineeing Helsini Univesit o Technolog P.O. Box TKK inland; ai.tuononen@t.i; Tel.: ; ax: Received: 6 Septembe 29; in evised om: 4 Octobe 29 / Accepted: 2 Octobe 29 / Published: 3 Octobe 29 Abstact: utue active saet sstems need moe accuate inomation about the state o vehicles. This aticle poposes a method to evaluate the lateal state o a vehicle based on measued te oces. The te oces o two tes ae estimated om opticall measued te cacass delections and tansmitted wielessl to the vehicle bod. The two emaining tes ae so-called vitual te sensos the oces o which ae calculated om the eal te senso estimates. The Kalman ilte estimato o lateal vehicle state based on measued te oces is pesented togethe with a simple method to deine adaptive measuement eo covaiance depending on the diving condition o the vehicle. The estimated aw ate and lateal velocit ae compaed with the validation senso measuements. Kewods: optical position detection; intelligent te; te senso; vehicle state estimation. Intoduction The vehicle state estimation has been a subject o numeous papes especiall because o the lage scale maet penetation o Electonic Stabilit Contol ESC) sstems. Even then moe accuate and eliable vehicle state inomation is needed o upcoming active contol applications such as active steeing ont and ea) lane eeping and toque vectoing. The main disadvantage o most o the vehicle state estimation appoaches is the equiement o pio nowledge o te paametes such as coneing stiness and iction coeicient [-4]. Howeve model based estimation is ve accuate when these paametes ae nown. A esh vehicle sideslip estimato appoach is pesented in [5] whee a inematic appoach is implemented using a 6-degee-o-eedom Inetial Measuement Unit IMU). The estimato is independent o an toublesome paametes and an

3 Sensos diting o the estimate duing low lateal excitation is avoided b implementing a Kalman ilte with an adaptive covaiance matix. The estimate based on inematic omulae can also be suppoted b a vehicle state obseve b weighting estimates depending on the diving state [6]. A simila estimation stateg is implemented hee but instead o measuing acceleations and otational velocities o a vehicle bod the oigin o those quantities the te oces ae measued diectl. The advantage o te oce measuement can be seen in igue whee a vehicle is coneing unde oad inclination λ side wind wind and oll angle θ. The te lateal te oces ae paallel to lateal velocit v. I the state estimation is based on lateal acceleation the ollowing eos exist: oll angle θ and oad inclination λ intoduce oset o lateal acceleation a senso due to gavit component 57 oll angle esults.g eo o lateal acceleation) a measued g sin a global cos Inluence o side wind is not popel captued om the measued acceleation but has to be caied b the tes and inluence o v is missing) v a global vx dt is not even paallel to compensated lateal acceleation v cos The oll angle and oad inclination inluence the aw ate measuement as well but conta to the lateal acceleation gavit does not paticipate and thus the oveall impact is mino the same applies o pitch angle). igue. Lateal oces acting on one axle o coneing vehicle. bod coodinate v z CoG a v θ-λ V 2 / 9 m I a z wind mg Roll angle θ z z2 Road inclination λ

4 Sensos Consequentl the diect measuement o te oces seems beneicial in contast to bod acceleations and otational velocities. Possible technologies o the te oce measuement could be: stain measuement o suspension components [7] o im [8] measuement o te cacass displacement [9] acceleation [e.g.] o stain [] te tead displacement [2] oce sensing beaing [3] Even though thee have been man attempts to measue te oces to aid contol sstems thee ae ve ew aticles which stud how to exploit them [845]. This pape poposes a Kalman ilte estimation o vehicle aw ate and lateal velocit v based on measued te oces. 2. Optical Te Senso OTS) Concept The optical te senso was developed o the ist time in the EC-unded APOLLO-poject [6] which studied seveal dieent te senso concepts including the optical te senso OTS). The APOLLO was ollowed b the RICTI@N-poject whee the optical te senso was selected o uthe development. Duing RICTI@N te senso hadwae was eeshed and algoithms wee made moe obust and towads eal-time opeation. A tuc senso was also intoduced [7]. The senso was also tested unde aquaplaning conditions whee the tansition point om the hdodnamic aquaplaning zone to the viscous aquaplaning was measued [8]. In addition the seveit o aquaplaning was estimated in eal-time [9]. The OTS measuing pinciple is shown in igue 2. A Light Emitting Diode LED) is glued into the inne line o the te. A lens ocuses inaed light emitted b the LED to the suace o Position Sensitive Detecto PSD). The position o the light spot is elative to the cuent at the cones o the PSD. The aw data is analsed in the te and sent wielessl b adio at 433MHz to a eceive unit. A moe detailed explanation about OTS can be ound in [7]. The algoithms o the te oce estimation can be ound in [7]. igue 2. Optical te senso measuement pinciple [].

5 Sensos igue 3 shows the calibation ccle o vetical oce and te senso measuement compaed with the test ig esults. Thee dieent wheel loads ae vaied at dieent speeds. Similal igue 4 shows the calibation ccle o the lateal oce at thee dieent loads. The te oce estimation model paametes ae itted to test ig esults b the least squaes method. igue 3. Te senso calibation ccle o vetical oce and compaison with test ig measuement. 6 5 Vetical oce [N] m/h 6m/h 3m/h Te test ig Te senso Time [s] igue 4. Te senso calibation ccle o lateal oce and compaison with test ig measuement vetical oce and lateal oces duing ccle 6 m/h). 5 Vetical oce [N] Te test ig Te senso Lateal oce [N] Time [s]

6 Sensos Vehicle State Estimato A test ca setup can be seen in igue 5. The optical te sensos ae mounted at the let ont wheel and ea ight wheel position. In addition the steeing wheel angle and vehicle velocit om the CANbus) ae used in the estimation. All the othe sensos such as lateal acceleation aw ate and Coevit-senso ae o validation puposes onl. These sensos ae mounted close to the cente o gavit to avoid compensations. igue 5. Measuement ca setup. l l l Vitual te senso 2 3 Optical te senso Yaw ate & lateal acc. v x v 9 V v Optical te senso Lateal velocit senso validation onl) 4 Vitual te senso The poblem is to estimate lateal velocit and aw ate at the cente o gavit o the vehicle with a minimal set o paametes. The estimato consists o vitual te sensos a diving state estimato lineait) and a Kalman ilte. The oveall stuctue o the estimato is shown in igue 6. The opeation o the submodels is explained in the ollowing. igue 6. Bloc diagam o the estimato. Steeing wheel angle v Vehicle velocit dω/dt Single tac model ont let te senso Rea ight te senso ont ight vitual te senso Rea let vitual te senso Σ Σ ont axle Lateal oces Rea axle Lateal oces Diving state lineait detection Measuement vecto Z Kalman ilte Measuement eo covaiance R Estimates v dω/dt

7 Sensos Kalman ilte The Kalman ilte is an eective and ecusive solution o the discete data ilteing poblem om nois measuements [2]. The state tansition eads: x Ax w ) and with measuement z : z Hx v 2) whee A is state tansition matix H is measuement matix and w and v epesent pocess and measuement noise. The a pioi xˆ based on pocess nowledge) estimate eo is: e x xˆ 3) and a posteioi based on given measuement z ) estimate eo is: e x xˆ The a pioi estimate eo covaiance is: P E e e T 4) 5) and the a posteioi estimate eo covaiance is: P E e e T 6) and Kalman gain: K T HP H R T P H 7) which minimizes the a posteioi estimate eo covaiance [2]. The Kalman gain weights the a pioi estimate and esidual z Hxˆ : xˆ xˆ K z Hxˆ 8) The Kalman ilte expects the pocess and measuements noise to be with nomal pobabilit distibution: w ~ N Q) p 9) v ~ N R) p ) whee Q is pocess noise covaiance and R is measuement noise covaiance matix. In this pape this equiement o nomal pobabilit distibution is not ulilled all the time o all measuements; this it is discussed in moe detail in section Vitual te sensos The test ca was equipped with two optical te sensos. The senso positions wee at the let ont and ight ea wheels. Howeve the vehicle state estimato developed hee equies individual te oces o all tes o axle oces. Thus the lateal te oces o ight ont wheel and let ea wheel

8 Sensos have to be estimated. The natual wa to estimate is to exploit the inomation om the te senso at the same axle onl lateal dnamics consideed hee). Hence the similait method [e.g. 22] is assumed in ode to estimate the missing te oces. Thee ae seveal methods to do this two o which ae pesented hee Invese magic omula The obvious stating point is to solve slip angle α o the te om te senso oces and z. The simple ou paamete Magic omula eads [22]: Dsin C a tan B E B a tan B ) whee paametes BC and E ae assumed to be nown. The D is available om the measued wheel load and the slip angle α can be solved numeicall. Anothe equied vaiable o a vitual te senso is vetical load. The wheel load deviation o a te senso wheel is available: z z z static 2) whee static wheel load can be calculated om the long time aveage o measued z o b ecoding z values as a static wheel load when ~. The vetical load o the vitual te senso neglecting longitudinal load tanse and mass o vehicle is constant): 3) z 2 z2 static z The lateal oce o the vitual te senso can be then calculated with the same Equation as when the slip angle was solved. It should be noted that the method is not sensitive o paametes BC o E i the do not depend on wheel load and i D is linea to wheel load. This is in act an expession o a similait method Nomalised lateal oce When consideing the invese magic omula method to solve the lateal oce o the second te it is clea that thee has to be simple method to obtain it. The nomalized lateal oce eads: and the lateal oce o the second te at the same axle: 4) z 5) 2 z2 The vetical load z2 o the vitual te senso is calculated as in Equation 3. The lateal oce o the let ea te is calculated similal to that at the ont axle. The nomalised lateal oce method esults in the same behaviou as the invese magic omula. Howeve neithe o the methods in this om taes into account nomalised te oce non-lineait o high wheel loads.

9 Sensos Vehicle model o the estimato The Kalman ilte equies a state tansition matix without lineait assumption o te behaviou) which is hee based on the lateal and aw equations o motion: ma 6) z l l I 7) whee m is vehicle mass I z is aw moment o inetia l and l ae cente o gavit distances om the ont and ea axles. The lateal equation can be witten: x v m v 8) whee and ae the ont and ea axle oces. The acceleation o lateal motion can be solved: x v m v 9) Lateal te oces ae assumed to act on the cente o the contact patch neglecting pneumatic tail) thus the aw acceleation can be expessed: z z I l I l 2) The Equations 9 and 2 ae discetized and witten as the state space equation: ) ) ) ) ) ) ) ) v T I l T I l m T m T T v v s z s z s s x s 2) whee the onl vaiable is owad velocit v x which is assumed to be slowl changing. T s is time step. The te oce state tansition is modelled as an identit unction. The measuement matix eads: ) ) ) ) v 22) 3.4. Single tac model o the linea opeation egion A simple vehicle model is needed to povide vehicle aw ate lateal velocit and te oces o the othe subsstems o the estimato. The single tac o biccle model) [e.g. 23] is based on lateal and aw equations o motion:

10 Sensos v vx m 23) I l 24) l22 The axle oces and ae assumed to be linea to the slip angle: C 25) 26) C whee C and C ae the ont and ea axle coneing stiness. The slip angles o the ont and ea axle ead: v l 27) v x l v v x 28) whee δ is steeing angle at wheel Covaiance matixes o Kalman ilte Pocess noise covaiance matix The pocess noise vaiance matix Q is assumed to be constant with ve high pocess vaiance o te oces because a new measuement o te oces is alwas moe accuate than a pioi estimate due to identit state tansition in Equation 2. The suitable pocess vaiance o the lateal motion v and is not o impotance as long it has a ealistic scale compaed to the coesponding measuement noise vaiance to allow a te oce based estimation duing non-linea opeation Measuement noise covaiance matix The measuement noise covaiance matix R has to be modiied continuousl. A paticulal noticeable bias is intoduced to lateal velocit and aw ate measuements om the single tac model etc. duing had coneing. Consequentl duing non-linea vehicle behaviou the measuement vaiances o the single ccle model should have ve high values compaed with the pocess noise values. This allows Kalman gain to weight moe diect te oce integation instead o obviousl biased v and measuements. A method to deine measuement noise vaiance o single tac model measuements is explained in the ollowing Evaluation o lineait o vehicle opeating state One wa to evaluate whethe the vehicle behaves as a linea sstem is to compae nominal aw ate and actual aw ate which has been exploited in ESC-sstems [] and to estimate the iction

11 Sensos coeicient [2]. Howeve i the te oces ae available b measuement it is natual to compae measued te oces with the single tac model nominal) te oces in ode to evaluate whethe the sstem is in a linea opeating egion: onetac measued onetac measued 29) Depending on diving conditions the coesponding measuement noise vaiance o single tac v and ) is selected based on Δ whee a ela with hsteesis is implemented igue 7). The tuning o the ela is essential to achieve a ast and stable esponse o the estimate. The low vaiance value can be tuned in staight ahead diving whee the vaiance can be adjusted to as geat a value as the estimate v without diting due to the integation o te oces. On the othe hand duing coneing the vaiance should switch to a noticeabl highe level beoe the vehicle exhibits a non-linea opeating egion. The hsteesis is needed in ode to avoid unnecessa ela switch os o example duing lane changes whee single tac model te oces and te senso measuements can be almost equal tempoail. igue 7. A ela with hsteesis to select pope measuement noise vaiance. Measuement noise vaiance o single tac model 5 25N Switch o.5 8N Switch on Δ Anothe method to judge vehicle non-lineait would be to evaluate the elation o lateal and vetical oces Equation 4). Howeve the theshold value is diicult to detemine because the coneing stiness lineait egion depends on oad conditions. 4. Results A test manoeuve was sequential and aggessive lane changes on d and hoizontall even tamac oad. The lateal and vetical te oces o the test manoeuve ae shown in igue 8. The inluence o load tanse can be seen in the vetical oces. The vetical oces va between N to 7 N. o the lateal oces pea values o the let ont te senso ae actuall oveestimated due to senso-lens setup non-lineaities which wee ound at the edge o the opeating aea duing high vetical oce. This esults in an oveestimation o the nomalised lateal oce o the ont axle; hence the ight ont te lateal oce might be oveestimated as well.

12 Sensos igue 8. Lateal and vetical te oces o a diving manoeuve v x ~6 m/h d tamac). Steeing wheel angle [] Lateal acc. [ g ] Vetical te oces [N] Lateal te oces [N] ont let senso) ont ight vitual) Rea let vitual) Rea ight senso) Time [s] igue 9 shows the lateal axle oce deviation om the single tac model as calculated in Equation 29 the same test un as in igue 8). This deviation is uthe on exploited to evaluate the validit o a single-tac model state estimate. When the measued te oces deviate om the single tac model estimate the measuement noise vaiance o a single tac model measuement is high. Note that the measuement noise vaiance o the te sensos is constant. This is ealistic because the accuac o the te senso does not depend on diving conditions. The lowest plot shows how the ela with hsteesis opeates accoding to the diving state. Duing lane change shot switch-os ae detected. Othewise the ela can ecognise the staight ahead diving and coneing. igue 9. Lateal oce deviation om single tac model and measuement eo vaiance duing test un. Steeing wheel angle [] Lateal acc. [ g ] Lateal oce deviation om single tac-model ont axle Rea axle R single tac R te oces Time [s]

13 Sensos igue shows the lateal acceleation compaison with the measued nomalised) te oces. The coelation is athe good and slightl highe pea values o the lateal acceleation senso might be inluenced b oll angle gavit component). The aw ate compaison seems to poduce slightl geate values o the estimate in geneal. The let ont te estimate was obseved to oveestimate lateal oce duing high vetical oces; this can explain wh the values wee highe than expected duing positive aw ate ight tun). The undeestimation o aw ate o negative values is moe diicult to explain but the easons ma lie in the inaccuac o the vitual te sensos o in toe-in and oll-stee induced osets in lateal oces. The inluence o ont let te lateal oce oveestimation is then stonge o than a due to the integation step needed o ). Even i aw ate estimate sues om the explained inaccuac in te oce estimate the oveal peomance o the lateal velocit estimate v emains toleable. The aw ate oveestimation esults in cumulation o eo to the negative diection o v. igue. Lateal state estimate based Kalman ilte estimato and o senso measuement. Lateal acceleation [ g ] te sensos ESC-senso Yaw ate [ad/s] estimate ESC-senso Lateal velocit [m/s] estimate Coevit-senso Time [s] 5. Discussion This pape pesented one application o te sensos. The poposed vehicle lateal state estimato can similal be used with othe te oce measuements than te sensos such as suspension pat o wheel hub stain measuements. 5.. Can a te oce senso eplace an o the existing vehicle sensos? The main advantage o te oce sensing is deinitel the inomation given about the opeating state o each te. In addition it is possible to calculate the lateal acceleation o a vehicle om the sum o

14 Sensos te oces without an bias om bod oll angle and oad inclination. Also the inluence o side wind is ealisticall captued. The esults show that lateal acceleation was accuatel calculated om the te oces when measued b an optical te senso. The aw ate senso howeve is much moe complex to eplace than the acceleation senso. The equied integation step maes the estimate extemel sensitive to eos in paametes l and l which ma aise o example om the pneumatic tail in addition to the mechanical movement o the wheel hub. Thus the aw ate is a valuable measue o the dieences in ont and ea axle oces acting on a vehicle. Howeve i the te senso can poduce an accuate and eliable estimate o the vetical oce the vehicle cente o gavit position can be calculated in a stead state condition Requied vehicle paametes b the estimato One o the objectives o the estimato was to minimize the numbe o paametes. Table pesents equied vehicle paametes b the estimato and poposes some possible souces o them. Table. Requied estimato paametes. Paamete Deinition Souce Value m Vehicle mass available om vetical te oces 63 g l axle length vehicle paamete 2575 m l l Cente o gavit distance om ont axle Cente o gavit distance om ea axle available om vetical te oces in stead state condition available om vetical te oces in stead state condition.5m.525m I z Vehicle aw moment o inetia oughl m l l [24] o adapted 356 g m 2 Q Pocess noise covaiance constant diag[.. e4 e4]) R Measuement noise covaiance deived in section 3.5 vaiable C & C Coneing stiness o the linea model o chaacteistic velocit ESC-sstem nominal behaviou o a vehicle) 7664 N/ad & 8287N/ad The vehicle mass is natuall available om the vetical te oces but it equies eal oce measuements instead o the vitual te sensos implemented in this pape. Howeve easonable accuac would also be possible with two te sensos uthe eseach Impovement o the optical te senso opeation egion would enable accuate estimation o lateal oce duing high vetical oce and high slip angle. The single tac model could be extended to adapt the paametes to ensue accuate opeation duing low lateal excitation. The main beneits o this poposed Kalman ilte appoach could be seen on slippe oad conditions on side wind and on inclined oads whee the poblems o the model based estimation based on non-linea vehicle model ae seen. In addition the te oce based estimato can be itted to totall new tpes o vehicles without an majo paamete modiications as long as the axle length is nown.

15 Sensos The vitual te senso concept might be easible togethe with a moe poduction oiented te senso o othe tpe o te oce measuement. The vitual te senso concept would also lowe the theshold o poduction te sensos as hal o the senso costs would be saved i onl two tes o a ca needed be equipped with te sensos. It is possible to do this eseach and development mainl with simulation models with no signiicant investments needed o the te senso pototpes. The main poblems ae the combined slip case and the slightl non-linea inluence o the wheel load on te oces. Reeences. van Zanten A.T.; Ehadt R.; Pa G.; Kost.; Hatmann U.; Ehet T. Contol aspects o the Bosch-VDC. In Poceedings o AVEC96 Aachen Geman Septembe uada Y. Slip-angle estimation o vehicle stabilit contol. Veh. Sst. Dn Best M.C.; Godon T.J. Combined state and paamete estimation o vehicle handling dnamics. In Poceeding o AVEC 2 5th Intenational Smposium on Advanced Vehicle Contol Ann Abo MI USA August Abe M.; Kato A.; Suzui K.; Kano Y. Estimation o vehicle side-slip angle o DYC b using On-Boad-Tie-Model. In Poceedings o 4th Intenational Smposium on Advanced Vehicle Contol Nagoa Japan Septembe ; pp Klie W.; Reim A. Stapel D. Robust Estimation o Vehicle Sideslip Angle An Appoach w/o Vehicle and Tie Models; SAE Wold Congess & Exhibition: Detoit MI USA Apil Cheli.; Sabbioni E.; Pesce M.; Melzi S. A methodolog o vehicle sideslip angle identiication: compaison with expeimental data. Veh. Sst. Dn Pasteamp W.R. The Te as Senso to Estimate iction; Delt Univesit: Delt The Nethelands 997; p Gobbi M.; Boteo J.C.; Mastinu G. Impoving the active saet o oad vehicles b sensing oces and moments at the wheels. Veh. Sst. Dn Bechee T. The Sidewall Tosion Senso Sstem 2. Damstädte Reienolloquium; VDI-Velag: Düsseldo Geman 998; pp Tuononen A.J. Optical position detection to measue te cacass delections. Veh. Sst. Dn Moinaga H. The possibilit o intelligent tie technolog o contact aea inomation sensing). In Poceedings o 3st isita Wold Automotive Congess Yoohama Japan Octobe Beue B.; Eichhon U. Measuement o te/oad-iction ahead o the ca and inside the te. In Poceedings o AVEC'92 Yoohama Japan van Leeuwen B.; Pepe. SK Load Sensing HBU ATA Advanced chassis Contol Sstems Obassano Ital Kantz W.; Neubec J.; Wiedemann J. Estimation o Side Slip Angle Using Measued Tie oces; SAE: Waendale PA USA Mach 22; pp

16 Sensos Kamada T.; uudome H.; ujita T.; Muase M. Stud on ABS contol b measuing oces between oad suace and ties. In Poceedings o the Intenational Smposium on Advanced Vehicle Contol Anhem The Nethelands August 24; pp Holtschulze J. Analse de Reienveomungen ü eine Identiiation des Reibwets und weitee Betiebsgößen zu Untestützung von ahdnamiegelsstemen; PhD thesis. RWTH Aachen Univesit: Aachen Geman Apil Tuononen A.J. On-boad estimation o dnamic te oces om opticall measued te cacass delections. Int. J. Heav Veh. Sst Tuononen A.J.; Hatiainen L. Optical position detection senso to measue te cacass delections in aquaplaning. Int. J. Veh. Sst. Model. Test Tuononen A.J; Matilainen M.J. Real-time estimation o aquaplaning with an optical te senso. J. Automobile Eng Kalman R.E. A new appoach to linea ilteing and pediction poblems. Tans. ASME J. Basic Eng Welch G.; Bishop G. An intoduction to the Kalman ilte; Technical Repot TR 95-4; Depatment o Compute Science Univesit o Noth Caolina: Chapel Hill NC USA Paceja H.B. Te and Vehicle Dnamics; Elsevie: Bulington UK Gillespie T.D. undamentals o Vehicle Dnamics; SAE: Waendale PA USA Pauwelussen J. Plane Vehicle Behaviou lectue mateial; HAN-Univesit: Anhem The Nethelands b the authos; licensee Molecula Divesit Pesevation Intenational Basel Switzeland. This aticle is an open-access aticle distibuted unde the tems and conditions o the Ceative Commons Attibution license