Unscented Kalman filter for real-time vehicle lateral tire forces andsideslip angle estimation

Moustapha Doumiati, Alessandro Victorino, Ali Charara andDaniel Lechner

Abstract— Knowledge of vehicle dynamic parameters is im-portant for vehicle control systems that aim to enhance vehiclehandling and passenger safety. Unfortunately, some fundamen-tal parameters like tire-road forces and sideslip angle aredifficult to measure in a car, for both technical and economicreasons. Therefore, this study presents a dynamic modeling andobservation method to estimate these variables. The ability toaccurately estimate lateral tire forces and sideslip angle is a crit-ical determinant in the performances of many vehicle controlsystem and making vehicle’s danger indices. To address systemnonlinearities and unmodeled dynamics, an observer derivedfrom unscented Kalman filtering technique is proposed. Theestimation process method is based on the dynamic response ofa vehicle instrumented with easily-available standard sensors.Performances are tested using an experimental car in realdriving situations. Experimental results show the potentiel ofthe estimation method.

I. I NTRODUCTION

Today, automotive electronic technologies are developingfor safe and comfortable travelling of drivers and passengers.There are a lot of vehicle control system such as RolloverPrevention System, Adaptive Cruise Control System, Elec-tronic Stability Control (ESC) and so on. These controlsystems installation rate is increasing all around the world.Vehicle control algorithms have made great strides towardsimproving the handling and safety of vehicles. For example,experts estimate that ESC prevents 27% of loss-of-controlaccidents by intervening when emergency situations aredetected [1]. While nowadays vehicle control algorithms areundoubtedly a life-saving technology, they are limited by theavailable vehicle state information.Vehicle control systems currently available on productioncars rely on available inexpensive measurements such aslongitudinal velocity, accelerations and yaw rate. Sidesliprate can be evaluated using yaw rate, lateral accelerationand vehicle velocity [2]. However, calculating sideslip anglefrom sideslip rate integration is prone to uncertainty anderrors from sensor bias. Besides, these control systems useunsophisticated, inaccurate tire models to evaluate lateraltire dynamics. In fact, measuring tire forces and sideslipangles is very difficult for technical, physical and economicreasons. Therefore, these important data must be observedor estimated. If control systems were in possession of thecomplete set of lateral tire characteristics, namely lateralforces, sideslip angle and the tire-road friction coefficient,they could greatly enhance vehicle handling and increasepassenger safety.As the motion of a vehicle is governed by the forcesgenerated between the tires and the road, knowledge ofthe tire forces is crucial when predicting vehicle motion.Accurate data about tire forces and sideslip angle leads toa better evaluation of road friction and the vehicles possible

M. Doumiati, A. Victorino and A. Charara are with Heudi-asyc Laboratory, UMR CNRS 6599, Universite de Technologie deCompiegne, 60205 Compiegne, Francemdoumiat@hds.utc.fr,acorreav@hds.utc.fr and acharara@hds.utc.fr

D. Lechner is with Inrets-MA Laboratory, Departement of AccidentMechanism Analysis, Chemin de la Croix Blanche, 13300 Salon deProvence, Francedaniel.lechner@inrets.fr

trajectories, and to better vehicle control. Moreover, it makespossible the development of a diagnostic tool for evaluatingthe potential risks of accidents related to poor adherence ordangerous maneuvers.Vehicle dynamic estimation has been widely discussed inthe literature. Several studies have been conducted regardingthe estimation of tire-road forces, sideslip angle and thefriction coefficient. For example, in [9], the authors esti-mate longitudinal and lateral vehicle velocities and evaluatesideslip angle and lateral forces. In [13] and [5], sideslipangle estimation is discussed in detail. More recently, thesum of front and rear lateral forces have been estimated in[4] and [6]. However, lateral forces at each tire/road levelwere not estimated. Other studies present valid tire/road forceobservers, but these involve wheel-torque measurements re-quiring expensive sensors [15].The goal of this study is to develop an estimation method thatuses a simple vehicle model and a certain number of validmeasurements in order to estimate in real-time the lateralforce at each tire-road contact point and the sideslip angle.The observation system is highly nonlinear and presentsunmodeled dynamics. For this reason, an observer based onUKF (the Unscented Kalman Filter) is proposed.In order to show the effectiveness of the estimation method,some validation tests were carried out on an instrumentedvehicle in realistic driving situations.The remainder of the paper is organized as follows. Section 2describes briefly the estimation process algorithm. Section 3presents and discusses the vehicle model and the tire-roadinteraction phenomenon. Section 4 describes the observerand presents the observability analysis. In section 5 theresults are discussed and compared to real experimental data,and then in the final section we make some concludingremarks regarding our study and future perspectives.

II. ESTIMATION PROCESS DESCRIPTION

The estimation process is shown in its entirety by the blockdiagram in figure 1, whereax andaym are respectively thelongitudinal and lateral accelerations,ψ is the yaw rate,θ isthe roll rate,∆ij (i represents the front(1) or the rear(2) andj represents the left(1) or the right (2)) is the suspensiondeflection,wij is the wheel velocity,Fzij and Fyij arerespectively the normal and lateral tire-road forces,β is thesideslip angle at the center of gravity (cog). The estimationprocess consists of two blocks, and its role is to estimatesideslip angle, normal and lateral forces at each tire/roadcontact point, and consequently evaluate the used lateralfriction coefficient. The following measurements are needed:

• yaw and roll rates measured by gyrometers,• longitudinal and lateral accelerations measured by ac-

celerometers,• suspension deflections using suspension deflections sen-

sors,• steering angle measured by an optical sensor,• rotational velocity for each wheel given by magnetic

sensors.

901978-1-4244-3504-3/09/$25.00 ©2009 IEEE

Suspension

deflection

sensors

Inertial

sensors

Magnetic

sensor

Optical

sensor

Block 1

Block 2

Roll plane model +

coupling

longitudinal/lateral

dynamics

Four wheel vehicle

model + Dugoff tire

modelδ

ψ

β

∆

.

Fzij

ax, aym

ax, ay

Fyij

ij

wij

ij

θ.

Fig. 1. Process estimation diagram

The first block aims to provide the vehicle’s weight, lateralload transfer, normal tire forces and the corrected lateralaccelerationay (by canceling the gravitational accelerationcomponent that distorts the accelerometer signalaym). Wehave looked in detail at the first block in a previous study[11]. This article focuses only on the second block, whosemain role is to estimate lateral tire forces and sideslip angle.The second block makes use of the estimations provided bythe first block. In fact, it is of major importance to includethe impact of accurate normal forces in the calculation oflateral forces.One specificity of this estimation process is the use of blocksin series. By using cascaded observers, the observabilityproblems entailed by an inappropriate use of the completemodeling equations are avoided, enabling the estimationprocess to be carried out in a simple and practical way.

III. V EHICLE-ROAD MODEL

This section presents the vehicle model and tire-roadinteraction dynamics, especially the lateral tire forces.Sincethe quality of the observer largely depends on the accuracy ofthe vehicle and tire models, the underlying models must beprecise. Taking real-time calculation requirement, the modelsshould also be simple.

A. Four-wheel vehicle model

The Four-Wheel Vehicle model (FWVM) is chosen forthis study because it is simple and corresponds sufficientlyto our objectives. The FWVM is widely used to describetransversal vehicle dynamic behavior [4], [9], [5].Figure 2 shows a simple diagram of the FWVM modelin the longitudinal-lateral plane. In order to simplify thelateral and longitudinal dynamics, drive force and rollingresistance were neglected. Additionally, the front and reartrack widths (E) are assumed to be equal.L1 and L2represent the distance from the vehicle’s center of gravityto the front and rear axles respectively. The sideslip at thevehicle center of gravity (β) is the difference between thevelocity heading (Vg) and the true heading of the vehicle(ψ). The yaw rate (ψ) is the angular velocity of the vehicleabout the center of gravity. The longitudinal and lateralforces (Fx,y,i,j) are shown for front and rear tires of the

vehicle. Assuming front-wheel drive, rear longitudinal forcesare neglected relative to the front longitudinal forces; weassume thatFx1 = Fx11 + Fx12.The lateral dynamics of the vehicle can be obtained bysumming the forces and moments about the vehicle’s centerof gravity. Consequently, the simplified FWVM is formulatedas the following dynamic relationship:

Vg = 1m

[

Fx1 cos(β − δ) + Fy11 sin(β − δ)+Fy12 sin(β − δ) + (Fy21 + Fy22) sinβ

]

,

ψ = 1Iz

[

L1[Fy11 cos δ + Fy12 cos δ + Fx1 sin δ]−L2[Fy21 + Fy22]+E2 [Fy11 sin δ − Fy12 sin δ]

]

,

β = 1mVg

[

−Fx1 sin(β − δ) + Fy11 cos(β − δ)+Fy12 cos(β − δ) + (Fy21 + Fy22) cosβ

]

− ψ,

ay = 1m [Fy11 cos δ + Fy12 cos δ + (Fy21 + Fy22) + Fx1sinδ],

ax = 1m [−Fy11 sin δ − Fy12 sin δ + Fx1 cos δ],

(1)wherem is the vehicle mass, andIz the yaw moment ofinertia.The tire slip angle (αij), as shown in figure 2, is thedifference between the tire’s longitudinal axis and the tire’svelocity vector. The tire velocity vector can be obtainedfrom the vehicle’s velocity (at the cog) and the yaw rate.Assuming that rear steering angles are approximately null,the direction or heading of the rear tires is the same as thatof the vehicle. The heading of the front tires includes thesteering angle (δ). The front steering angles are assumed tobe equal(δ11 = δ12 = δ). The vehicle velocityVg, steeringangleδ, yaw rateψ and the vehicle body slip angleβ arethen used to calculate the tire slip anglesαij , where:

α11 = δ − arctan[

Vgβ+L1ψ

Vg−Eψ/2

]

,

α12 = δ − arctan[

Vgβ+L1ψ

Vg+Eψ/2

]

,

α21 = − arctan[

Vgβ−L2ψ

Vg−Eψ/2

]

,

α22 = − arctan[

Vgβ−L2ψ

Vg+Eψ/2

]

.

(2)

B. lateral tire-force modelThe model of tire-road contact forces is complex because a

wide variety of parameters including environmental factorsand pneumatic properties (load, tire pressure, etc.) impactthe tire-road contact interface. Many different tire modelsare to be found in the literature, based on the physicalnature of the tire and/or on empirical formulations derivingfrom experimental data, such as the Pacejka, Dugoff andBurckhardt models [8], [7], [5]. Dugoff’s model was selectedfor this study because of the small number of parameters thatare sufficient to evaluate the tire-road forces. The nonlinearlateral tire forces are given by:

Fyij = −Cαitanαij .f(λ) (3)

whereCαi is the lateral stiffness,αij is the slip angle andf(λ) is given by:

f(λ) =

{

(2 − λ)λ, if λ < 11, if λ ≥ 1

(4)

902

ψ

Vgβ

E

Fy21

Fy22

δ12

Fy11

δ11

L2

L1

Fx11

Fy11

Fx21

Fx22

α11

α12

α21

α22

Fy11

Fx12

Fy12

Fig. 2. Four-wheel vehicle model.

−0.04−0.02 0 0.02 0.04−4000

−2000

0

2000

α11

(rad)

Fy 11

(N

)

−0.04−0.02 0 0.02 0.04−2000

−1000

0

1000

2000

3000

α12

(rad)

Fy 12

(N

)

−0.02 0 0.02 0.04−3000

−2000

−1000

0

1000

α21

(rad)

Fy 21

(N

)

−0.02 0 0.02 0.04

−1000

0

1000

2000

α22

(rad)

Fy 22

(N

)

Measurement

Dugoff

Fig. 3. Validation of the Dugoff model.

λ =µFzij

2Cαi|tanαij |

(5)

In the above formulation,µ is the coefficient of friction of theroad andFzij is the normal load on the tire. This simplifiedtire model assumes no longitudinal forces, a uniform pressuredistribution, a rigid tire carcass, and a constant coefficient offriction of sliding rubber.In order to validate the chosen model, many tests werecarried out using a laboratory car (see section V-A). Figure3 compares measured forces and the Dugoff model. Theseresults prove the model validity.As shown in figure 3, the relationship between the lateral

force and the slip angle is initially linear (low slip angles).When operating in the linear region, a vehicle respondspredictably to the driver’s inputs. As the vehicle approachesthe handling limits, for example during an evasive emergencymaneuver, or when a vehicle undergoes high accelerations,high slip angles occur and the vehicle’s dynamic becomeshighly nonlinear and its response becomes less predictableand potentially very dangerous.

C. Relaxation model

When vehicle sideslip angle changes, a lateral tire force iscreated with a time lag. This transient behavior of tires canbe formulated using a relaxation lengthσ. The relaxation

length is the distance covered by the tire while the tire forceis kicking in. Using the relaxation model presented in [3],lateral forces can be written as:

Fyij =Vg

σi(−Fyij + Fyij), (6)

whereFyij is calculated from a Dugoff tire-force model,Vgis the vehicle velocity andσi is the relaxation length.

IV. OBSERVERS DESIGN

This section presents a description of the observer devotedto lateral tire forces and sideslip angle. The state-spaceformulation, the observability analysis and the estimationmethod will be presented.

A. Stochastic state-space representation

The nonlinear stochastic state-space representation of thesystem described in previous section is given as:

{

X(t) = f(X(t), U(t)) + w(t)Y (t) = h(X(t), U(t)) + v(t)

(7)

The input vectorU comprises the steering angle and thenormal forces considered estimated by the first block (seefigure 1):

U = [δ, Fz11, Fz12, , Fz21, Fz22]. (8)

The measure vector Y(t) comprises yaw rate, vehicle velocity(approximated by the mean of the rear wheel velocitiescalculated from wheel-encoder data), longitudinal and lateralaccelerations:

Y = [ψ, Vg, ax, ay]. (9)

The state vector comprises yaw rate, vehicle velocity, sideslipangle at the cog, lateral forces and the sum of the frontlongitudinal tire forces:

X = [ψ, Vg, β, Fy11, Fy12, Fy21, Fy22, Fx1]. (10)

The process and measurements noise vectors, respectivelyw(t) and v(t), are assumed to be white, zero mean anduncorrelated.The nonlinear functions (f ) and (h) representing the stateand the observation equations are calculated according toequations (1) and (6).

B. Observability

Observability is a measure of how well the internal statesof a system can be inferred from knowledge of its inputs andexternal outputs. This property is often presented as a rankcondition on the observability matrix. Using the nonlinearstate-space formulation of the system presented in sectionIV-A, the observability definition is local and uses the Liederivative [12]. An observability analysis of this systemwas undertaken in [14]. It was shown that the system isobservable except when:

• steering angles are null,• the vehicle is at rest (Vg = 0).

For these situations, we assume that lateral forces andsideslip angle are null, which approximately corresponds tothe real cases.

903

Kalman Gain

X=f(X,U)

K

h(X,U) +-

X

Inputs

++evolution

correction

Measurements

observer

sensors

Fig. 4. Process estimation diagram

C. Estimation method

The aim of an observer or a virtual sensor is to estimatea particular unmeasurable variable from available measure-ments and a system model in a closed loop observationscheme, as illustrated in figure 4. The observer was imple-mented in a first-order Euler approximation discrete form. Ateach iteration, the state vector is first calculated accordingto the evolution equation and then corrected online withthe measurement errors and the filter gainK in a recur-sive prediction-correction mechanism. The gain is calculatedusing the Kalman filter technique (EKF, UKF, . . . ). The EKF(Extended Kalman Filter) is probably the most commonly-used estimator for nonlinear systems. However, in this studythe UKF (Unscented Kalman Filter) [16] is chosen for thefollowing reasons:

• the high nonlinearities of the vehicle-road model,• the calculation complexity of the Jacobian matrices

which causes implementation difficulties.

1) UKF algorithm: In this subsection, the principle of theUKF is summarized. Consider the general discrete nonlinearsystem:

{

Xk+1 = f(Xk, Uk) + wkYk = h(Xk) + vk

(11)

whereXk ∈ Rn is the state vector,Uk ∈ Rr is the knowninput vector,Yk ∈ Rm is the output vector at timek. wkand vk are, respectively, the disturbance and sensor noisevector, which are assumed to be Gaussian white noise withzero mean and uncorrelated.The UKF can be formulated as follows:Initialization

{

X0 = E[X0]P0 = E[(X0 − X0)(X0 − X0)

T ](12)

where X0 and P0 are respectively the initial state and theinitial covariance.Sigma points calculation and time update

χk−1 = [Xk−1, Xk−1 ±√

(n+ λ)Pk−1]χ∗k|k−1 = f(χk−1, Uk−1)

xk|k−1 =∑2ni=0 w

mi χ

∗i,k|k−1

Pk|k−1 =∑2ni=0 w

ci (χ

∗i,k|k−1 − Xk|k−1)×

(γ∗i,k|k−1 − Xk|k−1)T +Q

χk|k−1 = [Xk−1, Xk−1 ±√

(n+ λ)Pk|k−1]γk|k−1 = h(χk|k−1)

Yk|k−1 =∑2ni=0 w

mi γi,k|k−1

(13)

where

wm0 = λn+λ

wc0 = λn+λ + (n− α2 + β)

wmi = wci = 12(n+λ) i = 1, . . . , 2n

λ = n(α2 − 1)

(14)

Measurement update

PYkYk=

∑2ni=0 w

ci (γi,k|k−1 − Yk|k−1)×

(γi,k|k−1 − Yk|k−1)T +R

PXkYk=

∑2ni=0 w

ci (χi,k|k−1 − Xk|k−1)×

(γi,k|k−1 − Yk|k−1)T

Kk = PXkYkP−1YkYk

Pk = Pk|k−1 −KkPYkYkKTk

Xk = Xk|k−1 +Kk(Yk − Yk|k−1)

(15)

where the variables are defined as follows:Xk andYk|k−1are the estimations respectively of the state and of the realmeasurement at each instantk. wi is a set of scalar weights,and n is the state dimension; the parameterα determinesthe spread of the sigma points aroundX and is usually setto 1e − 4 < α < 1. The constantβ is used to incorporatepart of the prior knowledge of the distribution ofX, andfor Gaussian distributions,β = 2 is optimal.Q andR arerespectively the disturbance and sensor-noise covariance: Rtakes into account the uncertainty in the measured data andQ is tuned depending on the model quality.

V. EXPERIMENTAL RESULTS

In this section we present the experimental car used to testthe observers potential, and we discuss and analyze the testconditions and the observers’ results.

A. Experimental carThe experimental vehicle shown in figure 4 is the

INRETS-MA (Institut National de la Recherche sur lesTransports et leur Securite - Departement Mecanismesd’Accidents) Laboratory’s test vehicle [2]. It is a Peugeot307equipped with a number of sensors including accelerometers,gyrometers, steering angle sensors, linear relative suspensionsensors, three Correvits and four dynamometric wheels. OneCorrevit is located in chassis rear overhanging position andit measures longitudinal and lateral vehicle speeds and twoCorrevits are installed on the front right and rear right tiresand they measure front and rear tires velocities and sideslipangles. The dynamometric wheels fitted on all four tires,which are able to measure tire forces and wheel torques inand around all three dimensions.We note that the correvit and the wheel-force transducer (seefigure 5) are very expensive sensors. The sampling frequencyof the different sensors is 100 Hz.

B. Test conditionsTest data from nominal as well as adverse driving condi-

tions were used to assess the performance of the observerpresented in section IV, in realistic driving situations. Wereport a lane-change manoeuvre where the dynamic contribu-tions play an important role. Figure 6 presents the Peugeot’strajectory (on a dry road), its speed, steering angle and”g-g” acceleration diagram during the course of the test.The acceleration diagram, that determines the maneuveringarea utilized by the driver/vehicle, shows that large lateralaccelerations were obtained (absolute value up to0.6g). Thismeans that the experimental vehicle was put in a criticaldriving situation.

904

Wheel transducer Correvit

Fig. 5. Wheel-force transducer and sideslip sensor installed at the tirelevel.

0 500 1000

−100

0

100

200

X position (m)

Y p

ositi

on (

m)

0 20 40

80

90

100

110

Time (s)

Spe

ed (

km.h

1 )

0 20 40−0.04

−0.02

0

0.02

0.04

Time(s)

Ste

erin

g an

gle

(rad

)

−0.4 −0.2 0 0.2 0.4 0.6

−0.1

−0.05

0

0.05

0.1

Lateral acceleration (g)

Long

itudi

nal a

ccel

erat

ion

(g)

Fig. 6. Experimental test: vehicle trajectory, speed, steering angle andacceleration diagrams for the lane-change test

The estimation process algorithm was written in C++ andhas been integrated into the laboratory car as a DLL (Dy-namic Link Library) that functions according to the softwareacquisition system.

C. Validation of observersThe observer results are presented in two forms: as

tables of normalized errors, and as figures comparing themeasurements and the estimations. The normalized error foran estimationz is defined as:

ǫz = 100 ×‖zobs − zmeasured‖

max(‖zmeasured‖)(16)

where zobs is the variable calculated by the observer,zmeasured is the measured variable andmax(‖zmeasured‖) isthe absolute maximum value of the measured variable duringthe test maneuver.Figures 7 and 8 show lateral forces on the front andrear wheels. According to these plots, the observers arerelatively good with respect to measurements. Some smalldifferences during the trajectory are to be noted. Thesemight be explained by neglected geometrical parameters,especially the camber angles, which also produce a lateralforces component [10]. It is also shown that the lateral forceson the right-hand tires exceed those on the left-hand tires.

0 10 20 30 40 50

−2000

−1000

0

1000

2000

Front left lateral force Fy11

(N)

0 10 20 30 40 50−2000

0

2000

4000

Time (s)

Front right lateral force Fy12

(N)

measurementEstimation

Fig. 7. Estimation of front lateral tire forces.

0 10 20 30 40 50

−1000

0

1000

Rear left lateral force Fy21

(N)

0 10 20 30 40 50

−1000

0

1000

2000

3000

Time (s)

Rear right lateral force Fy22

(N)

measurementEstimation

Fig. 8. Estimation of rear lateral tire forces.

This result is clearly a consequence of the load transferproduced during cornering from the left to the right-handside of the vehicle. In fact, lateral force increases as normalforce increases. Figure 9 shows how sideslip angle changesduring the test. Reported results are relatively good.Table I presents maximum absolute values, normalized meanerrors and normalized std (standard deviations) for lateraltire forces and sideslip angles. Despite the simplicity of themodel, we can deduce that for this test, the performance ofthe observer is satisfactory, with normalized error globallyless than8%.

Given the vertical and lateral tire forces at each tire-roadcontact level, the estimation process is able to evaluate theused lateral friction coefficientµ. This is defined as the ratioof friction force to normal force, and is given by [10]:

µij =Fyij

Fzij(17)

905

10 20 30 40 50 60

−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

Time (s)

Sideslip angle at the cog (rad)

measurementEstimation

Fig. 9. Estimation of the sideslip angle at the cog.

0 20 40

0

0.5

1

Time (s)

µ11

0 20 40

−0.5

0

0.5

Time (s)

µ12

0 20 40

0

0.5

1

Time (s)

µ21

0 20 40

−0.5

0

0.5

Time (s)

µ22

Fig. 10. Used lateral friction coefficients developed by thetires

The lateral friction coefficients in figure 10 show that theestimatedµij are close to the measured values. A closerinvestigation reveals that the used lateral friction coefficientsµ12 and µ22 corresponding to the overloaded tires duringcornering are lower thanµ11 andµ21. This phenomenon isdue to the tire load sensitivity effect: the lateral friction coef-ficient is normally higher for the lighter loads, or conversely,falls off as the load increases [10].This test also demonstrates thatµ11 and µ21 are high,especially for lateral accelerations up to0.6, and that theyattain the limit for the dry road friction coefficient. In fact,dry road surfaces show a high friction coefficient in the range0.9-1.2 (implying that driving on these surfaces is safe),which means that for this test the limits of handling werereached.

VI. CONCLUSION

This paper presents a new method for estimating lateraltire forces and sideslip angle, that is to say two of themost important parameters affecting vehicle stability andthe

Max ‖‖ Mean % Std %Fy11 2180 (N) 8.23 4.80Fy12 4070 (N) 3.70 3.74Fy21 1441 (N) 7.51 3.52Fy22 2889 (N) 1.91 1.77

β 0.027(rad) 8.32 6.41

TABLE IMAXIMUM ABSOLUTE VALUES , NORMALIZED MEAN ERRORS, AND

NORMALIZED STD.

risk of leaving the road. The developed observer is derivedfrom a simplified four-wheel vehicle model and is based onunscented Kalman filtering technique. Tire-road interactionis represented by the Dugoff model.A comparison with real experimental data demonstrates thepotential of the estimation process. It is shown that it maybe possible to replace expensive correvit and dynamometrichub sensors by real-time software observers. This is one ofthe important results of our work. Another important resultconcerns the estimation of individual lateral forces acting oneach tire. This can be seen as an advance with respect to thecurrent vehicle-dynamics literature.Future studies will improve the vehicle/road model in orderto widen validity domains for the observer, and will take intoaccount road irregularities and road bank angle. Moreover,itwill be of major importance to study the effect of couplinglongitudinal/lateral dynamics on lateral tire behavior.

REFERENCES

[1] Y. Hsu and J. Chistian Gerdes,Experimental studies of using steeringtorque under various road conditions for sideslip and friction esti-mation, Proceedings of the 2007 IFAC Symposium on Advances inAutomotive Control, Monterey, California.

[2] D. Lechner,Embedded laboratory for vehicle dynamic measurements,9th International symposium on advanced vehicle control, Kobe,Japan, Octobre 2008.

[3] P. Bolzern, F. Cheli, G. Falciola and F. Resta,Estimation of thenonlinear suspension tyre cornering forces from experimental roadtest data, Vehicle System Dynamics, volume 31, pages 23-24, 1999.

[4] G. Baffet A. Charara, D. Lechner and D. Thomas,Experimentalevaluation of observers for tire-road forces, sideslip angle and wheelcornering stiffness, Vehicle System Dynamics, volume 45, pages 191-216, june 2008.

[5] U. Kiencke and L. Nielsen,Automotive control systems, Springer,2000.

[6] G. Baffet, A. Charara and J. Stephant,An observer of tire-roadforces and friction for active-security vehicle systems, IEEE/ASMETransactions on Mechatronics, volume 12, issue 6 pages 651-661,2007.

[7] J. Dugoff, P. Fanches and L. Segel,An analysis of tire properties andtheir influence on vehicle dynamic performance, SAE paper (700377),1970.

[8] Hans B. Pacejka,Tyre and vehicle dynamics, Elsevier, 2002.[9] J. Dakhlallah, S. Glaser, S. Mammar and Y. SebsadjiTire-road forces

estimation using extended Kalman filter and sideslip angle evaluation,American Control Conference, Seatle, Washington, U.S.A, June 2008.

[10] W.F. Milliken and D.L. Milliken, Race car vehicle dynamics, Societyof Automotive Engineers, Inc, U.S.A, 1995.

[11] M. Doumiati, A. Victorino, A. Charara, D. Lechner and G. Baffet, Anestimation process for vehicle wheel-ground contact normal forces,IFAC WC’08, Seoul Korea, july 2008.

[12] H. Nijmeijer and A.J. Van der Schaft,Nonlinear dynamical controlsystems, Springer Verlag, 1991.

[13] J. Stephant, A. Charara and D. Meizel,Virtual sensor, application tovehicle sideslip angle and transversal forces, IEEE Transactions onIndustrial Electronics. vol.51, no. 2, April 2004.

[14] G. Baffet, Developpement et validation exprimentale d’observateursdes forces de contact pneumatique/chaussee d’une automobile, Ph.Dthesis, University of Technology of Compiegne, France, 2007.

[15] N. K. M’Sirdi, A. Rabhi, N. Zbiri and Y. Delanne,Vehicle-roadinteraction modelling for estimation of contact forces, Vehicle SystemDynamics, volume 43, pages 403-411, 2005.

[16] S. J. Julier and J. K. Uhlman,A new extension of the Kalman filterto nonlinear systems, International Symposium Aerospace/DefenseSensing, Simulation and Controls, Orlando, USA, 1997.

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