Rollover Risk Prediction of Heavy Vehicle Using High-Order Sliding-Mode Observer: Experimental...

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TVT.2013.2292998, IEEE Transactions on Vehicular Technology

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Rollover risk prediction of heavy vehicle using high ordersliding mode observer: experimental results

H. Imine, A. Benallegue, T. Madani and S. Srairi

Abstract—In this paper, an original method about heavyvehicles rollover risk prediction is presented and validatedexperimentally. It is based on the calculation of the LTR(Load Transfer Ratio) which depends on the estimatedvertical forces using high order sliding mode observers.Previously, a tractor model is developed. The validationtests were carried out on an instrumented tractor rollingon the road at various speeds and lane-change manoeuvres.Many scenarios have been experienced: driving on straightline, curve line, zigzag and brake tests to emphasize therollover phenomenon and its prediction to set off analarm to the driver. In this study, the vehicle dynamicparameters (Masses, Inertias, stiffness..) and the staticforces infrastructure characteristics (road profile, radius ofcurvature, longitudinal and lateral slope, skid resistance)are measured or calculated before the tests.

Index Terms—Heavy vehicle modeling; Rollover; Slidingmode observer; Estimation; Prediction

I. INTRODUCTION

AS mentioned in ([1], [2]), the rollover occurswhen the lateral acceleration equals or ex-

ceeds the vehicle’s rollover limit (which may beassisted by roadway cross-fall or camber). Lateralacceleration in a curve is highly sensitive to speed.The required speed to produce rollover reduces asthe radius of curvature reduces. Roll stability isinfluenced by the centre of gravity height(COG), theeffective track width provided by the axles and tires,and the suspensions characteristics. The COG height

Copyright (c) 2013 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposesmust be obtained from the IEEE by sending a request to [email protected].

H. Imine is with Universite Paris-Est, LEPSIS/IFSTTAR, 14-20Boulevard Newton, Champs sur Marne, F-77447 Marne la ValleeCedex 2, France, email:[email protected].

A. Benallegue and T. Madani are with Univ of Ver-sailles, 10-12 Avenue de l’Europe, Velizy, France, email:{tarek.madani,aziz.benallegue}@lisv.uvsq.fr.

S. Srairi is with ministere de l’Ecologie, du Developpement durableet de l’Energie, 12 rue Teisserenc de Bort-78197 TRAPPES-en-Yvelines, email:[email protected].

is affected by the chassis height and the heavyvehicle load. This performance measure is evaluatedin terms of the steady-state lateral acceleration atwhich all wheels on the inside of curvature havelifted off the road surface. This is accomplished byincreasing the steering angle of a vehicle until allaxles of one side of a given vehicle lift off. Therollover can occur when one wheel of the same axleof the vehicle, lifts off the road surface, as illustratedin figure 1.

Fig. 1. Wheel lifts off the road

Several works have been reported in the literaturewhich deal with rollover of heavy vehicles and sev-eral simulation results were presented ([2], [3], [4],[5], [6], [7], [27]). However, most of these workshave not presented experimental results. In fact, theinstrumentation of a heavy vehicle is very expensiveand not easy to reach at all. Another advantage ofthe predictive system developed here is that it isbased on use of robust tools, namely high ordersliding mode observer, which permits, as developedin the paper, to estimate in finite time the unknownstates of vehicle, positions, speeds and accelerations.Adding to that the fact, that the infrastructure data



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base has been built and embarked in the vehicle.The infrastructure characteristics have been used inthe system in order to evaluate the trajectory of thevehicle and therefore predict the risk 3s before.

In this paper, the first experimental results of a de-veloped predictive rollover system of heavy vehicleare presented. This work represents the extensionof the paper presented during ICRA conference [8].Even if there are common developments with thepaper presented in ICRA, many works have beenadded in this paper:

- The vehicle model has been developedmore and detailed.

- The sliding mode observer is discussedmore and its convergence study is detailed. In effect,the gains of observer are given and the method toobtain them is discussed.

- Details about infrastructure data base havebeen given.

- Signals processing (statistic study) is stud-ied in order to compute and find the values of theobserver gains.

- Real time experimentation is presented andother test, namely brake test is shown and the resultsare given and discussed.

In conclusion, one can say that ICRA paper isan introduction of the paper presented here. Moredetails, developments and results have been givenand discussed in the work presented here.

The predictive system is based on the computingof the Load Transfer Ratio (LTR) which is anindicator of rollover stability. This LTR is definedas the proportion of load on one side of a vehicleunit transferred to the other side in a transientmanoeuvre. Thus, it depends on vertical forces atthe tires that are estimated via a high order slidingmode observer ([9], [10], [11], [12]). Actually, theobserver outputs are the estimated state variablesof the vehicle (positions and especially the COGheight, speeds and accelerations). Then the verti-cal forces acting on the wheels, which depend onthe road inputs are deduced from these estimatedvariables. The used sliding mode observer is of thethird order. It estimates in the same and finite time,positions, speeds and accelerations of the heavyvehicle ([13], [14], [15], [16], [17]). In absenceof external disturbances, some existing tools andmethods, such as kalman filters or Luenberger ob-servers can be applied directly for asymptoticalreconstruction of the system states. However, in

the presence of disturbances, the standard techniqueis not accurate; the Luenberger observer can onlyensure the convergence to a bounded region nearthe real value of the state.

Sliding Mode Based Observers are presented asan alternative to the problem of observation ofperturbed systems. In particular, High Order SlidingMode (HOSM) Based Observers can be consideredas a successful technique for the state observationof perturbed systems due their high precision androbust behavior with respect to parametric uncer-tainties. The existence of a direct relation betweendifferentiation and the observability problem makesSliding Mode Based Differentiators, a techniquethat can be applied directly for state reconstruction.Even when the differentiators appear as a naturalsolution to the observation problem, the use of thesystem knowledge for the design of an observationstrategy results in a reduction of the gains for thesliding mode compensation terms. This reductionis evidenced in the improvement of the accuracy.Moreover, the complete or partial knowledge of thesystem model can give place to the application oftechniques for parametric reconstruction or distur-bance reconstruction. In this paper, how the higherorder sliding mode concept can be applied for statesobservation of the vehicle is shown.

In figure 2, the diagram of the developed pre-dictive rollover system is showed with its differ-ent components: the instrumented heavy vehicle,the infrastructure data base (road profile, radius ofcurvature, skid resistance, longitudinal and lateralslope) and the observer/estimator system.

In order to show the effectiveness of the proposedsystem, some validation tests were carried out onan instrumented tractor driving on the road at var-ious speeds and maneuvers. Many scenarios havebeen experienced: driving in straight line, in curve,zigzag and brake tests to emphasize the rolloverphenomenon and its prediction and send an alarmto the driver with recommended speed in order toavoid the rollover.

This paper is organized as follows: the secondsection is devoted to the description of the heavyvehicle model. In section three, the used slidingmode observer to predict rollover is developed. In-strumented heavy vehicle is described in the sectionfour. In section five, some validation results are pre-sented. Finally some conclusions and perspectivesare given in the last section.



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Fig. 2. Rollover risk prediction system

II. HEAVY VEHICLE MODELLING

Various studies have dealt with the heavy vehi-cle modeling taking into account the infrastructurecharacteristics ([18], [19], [20], [21], [26]). To go inthis way, the measurements carried out on the realvehicle are exploited in order to constitute a database which was used to study the various drivingrisks such as rollover or jack-knifing. In this part, aheavy vehicle model using the infrastructure database is developed. A tractor with 2 axles and 5degrees of freedom is considered and presented infigure 3.

Fig. 3. Instrumented heavy vehicle

The suspension is modeled as the combination ofsprings and damper elements. The front view of thismodel is shown in figure 4.

Fig. 4. Suspension model

The tractor chassis (with the mass M ) is sus-pended on its axles through two suspension systems.The tire of the wheel i is modeled by the springswith coefficients ki and the suspension is modeledby both springs with coefficient Ki and damperelements Bi. The wheel masses are given by mi

(i = 1, · · · , 4). At the tire contact, the road profile,longitudinal and lateral slope, skid resistance andradius of curvature are considered as inputs ofthe system. The road profile is represented by thevariable ui (i = 1, · · · , 4). The pitch angle of theheavy vehicle is neglected.

The figure 5 represents the lateral model of thetractor.

Fig. 5. Lateral model of the tractor



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The equations of motion of this model in thelongitudinal axis are given by :

Ffy sin(δ) + Ffx cos(δ) + Frx −Xh =M1x (1)

in the lateral axis, it gives:

Ffy cos(δ)− Ffx sin(δ) + Fry − Yh =M1y (2)

The yaw motion of the vehicle gives the followingequation:

Iz1α1 = (lf + lh)(Ffy cos(δ)− Ffx sin(δ))−(lr − lh)Fry

(3)

where M1 is the total mass of the tractor, Ffx andFfy are respectively the tractor front longitudinaland lateral tire forces, Frx and Fry are respectivelythe tractor rear longitudinal and lateral tire forces,x and y are respectively the longitudinal and lateraltractor accelerations, lf and lr are the distancesbetween the centre of gravity of the tractor and re-spectively the front and the rear axles, lh representsthe distance between the centre of gravity of thetractor and the hitch, Xh and Yh are respectivelythe longitudinal and lateral forces in the hitch, δ isthe steering angle and α1 is the yaw angle.

The parameter Iz1 represents the moment of iner-tia of the tractor around a vertical axis crossing thehitch. It is obtained by the use of Huyghens theorem: Iz1 = Izloc+M1l

2h where Izloc is the inertia moment

according to the vertical axle crossing the centre ofgravity of the tractor.

Therefore, the dynamic model of the vehiclederived from the Lagrangian’s equations is givenby:

M(q)q +B(q, q)q +K(q) = Fg (4)

where M ∈ <5×5 is the inertia matrix (mass matrix),B ∈ <5×5 is the matrix taking into account thedamping effects, K ∈ <5 is the sprungs stiffnessvector and Fg ∈ <5 is the generalized forces. Thecoordinates variable vector q ∈ <5 is defined by:

q = [q1, q2, q3, q4, φ]T (5)

where q1 and q2 are respectively the left and rightfront suspension deflection of the tractor, q3 and q4are respectively the left and right rear suspensiondeflection of the tractor and φ is the roll angle.

The vertical acceleration of the chassis (tractor’sbody) is function of vector q and its time derivativeq:

z = f(q, q) (6)

where the variable z is the vertical displacement ofthe tractor sprung mass which is the centre heightof the gravity.

The vertical displacements of the wheels withrespect to the ground (road) are represented by zri(i = 1, · · · , 4) and can be calculated for the frontwheels as follows:{

zr1 = z − (q0 + q1) +Tw

2sin(φ)− r

zr2 = z − (q0 + q2)− Tw

2sin(φ)− r (7)

where q0 is the static distance between the COGand the axles of the vehicle, Tw is the tractor trackwidth and r is the wheel’s radius.

From the equation (7), the centre height of gravityz is as follows :

z =1

2(zr1 + zr2 + q1 + q2) + q0 + r (8)

The vertical accelerations of the wheels are ob-tained using the following equations:

zr1= (B1q1+K1Tw

2 sin (φ) +B1Tw

2 cos (φ)φ

+K1q1−k1zr1+k1u1)/m1

zr2= (B2q2−K2Tw

2 sin (φ)−B2Tw

2 cos (φ)φ

+K2q2−k2zr2+k2u2)/m2

(9)

The normal forces Fni (i = 1, · · · , 4) actingon the wheels are calculated using the followingexpression:

Fni = Fci + ki(ui − zri), i = 1, · · · , 4 (10)

where Fci is the static force due to the static massof the vehicle.

In this study, the force generated by dampingeffects is neglected comparing to the spring forceski(ui − zri).

On the other hand, the dynamic rolling of thevehicle is described using the following differentialequation:

Ixxφ = mayh cos(φ+ ς) (11)+mgh sin(φ+ ς)− CRφ−KRφ

where Ixx is the inertia moment in the roll axis,CR represents a damping coefficient of the rollmotion, KR is spring coefficient of the roll motion,φ is the roll rate, φ is the roll acceleration with



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respect to the road, ς is the lateral slope, h isthe centre height of gravity with respect to theroll axis, g represents the gravity acceleration anday is the lateral acceleration of the heavy vehicle.This latter variable is measured using accelerometersensor as described in the section devoted to theexperimentation description.

III. ROLLOVER PREDICTION

In order to evaluate the rollover risk, high ordersliding mode observer is developed to estimate thestate variables and the vertical forces of the vehicle([3], [13], [14], [15], [16]).

In state space form, the system equation (4) canbe rewritten as:{

x1 = x2x2 =M−1(Fg −B(x1, x2)x2 −K(x1))

(12)

where x = (x1, x2)T = (q, q)T ∈ <10 is the state

variables vector and x1 = [q1, q2, q3, q4, φ]T is the

measured outputs vector of the system. The rollangle is calculated using the following formula:

φ = arcsin(q1 − q2Tw

) (13)

To be able to estimate the state variables and thevertical forces, the following observer is developedand the convergence is proved [17].

˙x1 = x2 − λ0∇(v1)Sign(v1)˙x2 = x3 − λ1∇(v2)Sign(v2)˙x3 = −λ2Sign(v3)

(14)

where x1, x2 and x3 are respectively the estimateof x1, x2 and x2, xi = xi − xi (i = 1, · · · , 3) is theestimation error of the variable xi, λ0, λ1 and λ2are the observer gains.

By setting v1 = x1 = x1 − x1, v2 = x2 − ˙x1,v3 = x3− ˙x2 and ∇(v1) = |v1|2/3 , ∇(v2) = |v2|1/2,we define the functions Sign and ∇() as following:

∇(v1) = diag{|v11 |

2/3, .., |v15 |

2/3}∇(v2) = diag{|v21 |

1/2, .., |v25 |

1/2}, i = 1, 2, 3

Sign(vi) = [sign(vi1), .., sign(vi5)]T

(15)

The observer defined in (14) permits to estimatepositions, velocities and accelerations of the system.The jerk of the system is bounded and it satisfiesthe inequality:

f+ ≥ 2 |...x1i | , i = 1..5 (16)

where f+ is some known positive scalar.Remark 1: When the accelerations in the me-

chanical system are bounded, the constant f+ canbe found as the double maximal possible jerk ofthe system. Moreover, the estimation constant f+

does not depend on the nominal elasticity or controlterms. Such assumption of the state boundedness istrue as well, if, for example, system (12) is BIBS(Bounded Input, Bounded State) stable, and thecontrol input u = U(t, x1, x2) is bounded.

The vehicle is a dynamic system with a boundedjerk. The derivative of the measured accelerations,namely, double derivative of roll rate measured bygyrometer sensor for roll angle and the jerk comingfrom the third derivative of suspension deflection,are performed in order to prove the condition 16.

The estimation errors are obtained using the equa-tions (12) and (14) as following:

˙x1 = x2 − x2 + λ0∇(v1)Sign(v1)˙x2 = x2 − x3 + λ1∇(v2)Sign(v2)˙x3 = x2 + λ2Sign(v3)

(17)

Chosen the ith components of λi0, λi1 and λi2 as:

λi0 = 3 3√f+, λi1 = 1.5 2

√f+ and λi2 = 1.1f+, the

estimation errors x1, x2 and x3 converge in finitetime t0 toward 0.

Then, after convergence of the differentiator, theequality ˙x2 = x2 holds, and given the equivalencebetween equations (12) and (14), the followingequality is satisfied:

M−1(Fg −B(x1, x2)x2 −K(x1))−x3 + λ1∇(v2)Sign(v2) = 0

(18)

The third term of the above mentioned equalityis equal to zero as a result of the differentiator con-vergence, so it is possible to obtain the equivalentoutput injection as:

zeq = x3 =M−1(Fg −B(x1, x2)x2−K(x1)) (19)

In this case, x3 is a continuous term, and nofiltration is required to obtain the equivalent outputinjection. This is an important fact, because giventhe finite time convergence of the differentiator, it’spossible now to reconstruct in finite time the equiv-alent output injection. Moreover, the variable x3 isnot affected by any filtration process, hence x3 is anexact estimation of M−1(Fg−B(x1, x2)x2−K(x1)).

More details about the convergence study of thisobserver can be found in [17].



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In this case, by means of the equation (9), thevertical displacements of the wheels are estimatedin finite time, since the vertical accelerations of thewheels zri are measured using accelerometers:

zr1 = (−m1zr1 +B1˙q1 +K1

Tw

2sin(φ)

+B1Tw

2cos(φ)

˙φ+K1q1 + k1u1)/k1

zr2 = (−m2zr2 +B2˙q2 −K2

Tw

2sin(φ)

−B2Tw

2cos(φ)

˙φ+K2q2 + k2u2)/k4

(20)

From the equation (8), the centre height of gravityz is deduced :

z =1

2(zr1 + zr2 + q1 + q2) + q0 + r (21)

Using the equation (10), the vertical forces Fni

can be estimated by:

Fni = Fci + ki(ui − zri), i = 1, · · · , 4 (22)

Finally, the Load Transfer Ratio (LTR) used toindicate the rollover risk, is calculated as follows[22]:

LTR =Fnr − Fnl

Fnr + Fnl

(23)

When Fnr = 0 (Fnl = 0) the right (left) wheelslift off the road and the rollover coefficient takes onthe limit value LTR = −1 (LTR = 1). For straightdriving on a horizontal road for the tire verticalforces, it holds that Fnr = Fnl which means thatLTR = 0.

IV. EXPERIMENTATION

A. Description of the test bench

In order to validate theoretical study and the sim-ulations results, an instrumented Renault tractor isused, as shown in figure 3. The vehicle is equippedwith several sensors to measure the dynamics of thevehicle, such as the angular speeds, accelerations,and the suspension deflections.

The figure 6 illustrates the added sensors whichare needed for the proposed technique:

• four sensors, LVDT (Linear Variable Differen-tial Transformers) installed between the wheeland the chassis in order to measure the deflec-tions of suspensions,

• four accelerometers installed on the axle inorder to measure the vertical accelerations ofwheels,

Fig. 6. The used sensors on the Vehicle

• three axial gyrometers installed on the chassisin order to measure the angular speeds (roll,pitch and yaw rate),

• two lasers installed at the bottom of the chassisin order to measure its height.

The figure 7 illustrates the positions of installedsensors in the vehicle. Two LVDT sensors areinstalled in the front of the vehicle and two othersare installed in the rear of the tractor. The two lasersensors are installed respectively in the left and inthe right side in order to measure the height of thevehicle. The tri-axial gyrometer is installed in thecentre of the vehicle in order to measure the threerotations of the tractor.

Fig. 7. Sensors position on the heavy vehicle



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Remark The LVDT are the only sensors whichare necessary and needed to be added in orderto product the predictive rollover system. The rollangle is deduced using LVDT sensors, as explainedin the previous section. The other sensors are onlyused in order to test the robustness of the approachby comparing their measures to the estimatedvariables.

The acquisition part of the bench, consists ofuse of laptop computer, a dSPACE MicroAutoBoxreal-time hardware system, and the softwares: Mat-lab/Simulink, Real Time Workshop and dSPACEacquisition system. This acquisition board delivershigh performance and reliable data acquisition ca-pabilities with 16 single-ended analogical inputs.It delivers both analogical and digital triggeringcapability, as well as two 12-bit analogical outputs,two 24-bit and 8 digital I/O lines. The samplingfrequency used during the tests is 100Hz.

The algorithms written in Matlab/Simulink coor-dinate all the data acquisition and the test measure-ment processes.

The developed program can be easilymanipulated and integrated in the vehicle.

B. Infrastructure measurementsBefore the tests, the infrastructure data have been

measured by different devices.The road profile is measured by Longitudinal

Profile Analyser shown in figure 8. The technicaldescription and the functionalities of this device aregiven in [23].

The radius of curvature, longitudinal and lat-eral slope are measured using VANI (Vehiculed’Analyse d’Itineraire). This vehicle equipped withdifferent sensors, such as Gyrometers, GPS andlasers is realized by Regional Laboratory of Lyon,in France in 1987. More details about VANI can befound in [24].

The CFT (transversal friction coefficient) of theroad surface is measured by SCRIM device (Side-way force Coefficient Routine Investigation Ma-chine) which is described in [25].

C. Test resultsMany tests and scenarios have been realized with

the instrumented vehicle driving at various speeds.

Fig. 8. Longitudinal Profile Analyzer

Some results on the states, the vertical forces andthe risk estimations are presented in this section.

The dynamic parameters and the static verticalforces are measured before the tests. The measuredstatic front left and static right vertical forces arerespectively 24200N and 25250N . The values ofstatic rear left and right vertical forces are respec-tively 9450N and 12050N .

1) Zigzag test: The zigzag test is illustrated byfigure 9. This test is very interesting for rolloverstudy since it can cause dangerous situations. Thedriver changes abruptly the direction of his vehiclewhich implies load transfer between the left andright side of the vehicle.

Fig. 9. The zigzag test on real situation



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The steering angle of the vehicle during this testis presented in the figure 10. The critical times areoccurred at 15s, 30s and 45s. One notices that atthese times, the absolute steering angle is more than3rad (180◦).

Fig. 10. Steering angle

In order to verify the condition 16, let us representthe jerk of the systems which corresponds to thedouble derivative of roll rate measured by gyrometersensor and the jerk coming from the third derivativeof suspension deflection, measured by LVDT sensor.The result is shown in the figure 11. One remarksthat the maximum values of jerks of suspensiondeflection shown in the left side of the figure 11is about 800m/s3 and the maximum values of jerksof roll angle shown in the right side of this figure isabout 150rad/s3. In this case, the value of the gainf+ is then deduced to be equal to 1600m/s3. Thevehicle speed is shown in figure 12.

In the figure 13, suspension deflections of thefront of the vehicle are estimated and comparedto the measured one. The right side of this figureshows that the observer converges quickly and theestimation error is around zero shown in the leftside of this figure. Therefore, the two graphs arepractically indistinguishable. At the critical times,the effect of the zigzag on the vehicle dynamics isclearly shown at 15s, 30s and 45s.The suspensiondeflection at the front right decreases from its staticvalue 0.01m to −0.03m, whereas the suspensiondeflection at the front left increases from 0.01m to0.025m. From this behavior, the roll angle shown inthe figure 14 occurred. Indeed, at the times 15s, 30sand 45s, the roll angle increased. One can notice the

Fig. 11. Jerk of the system in case of zigzag test

Fig. 12. Vehicle speed for zigzag test

quality of the estimation compared to the measure.It is clearly shown that the estimated and measuredroll angles are in good agreement.

The figure 15 shows the estimation of the centreheight of gravity compared to the front left suspen-sion deflection. Since, there is no existing sensorto measure this displacement, it’s then difficultto judge the quality of the estimation. However,one notices that at 15s, the suspension deflectionincreased up to 0.025m and at the same time, theestimated centre height of gravity increased up to0.71m. The same phenomena are produced at thetimes, 30s and 45s. This implies that the estimatedcentre height of gravity correctly tracks the LVDTmeasure.

This result represents a good indicator to evaluatethe quality of this estimation.



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Fig. 13. Suspension deflection estimation

Fig. 14. Roll angle estimation

Fig. 15. Estimation of centre height of gravity

In the figure 16, the vertical forces of the frontwheels are presented. The force of the front leftwheel is presented at the left. One notices that at thetimes 15s, 30s and 45s, this force increases up to28kN, following then the the measured suspensiondeflection. A zoom on the time interval [0 5]s isgiven in the right side of this figure.

Fig. 16. Estimation of vertical force: left wheel

The figure 17 shows the estimated vertical forceof the front right wheel. As explained before, thesame conclusion can be given here. indeed, at thesame times, this force decreases up to 19kN . Thisphenomena can be explained by the fact, that theload transfer from the right side to the left side ofthe vehicle is produced. A zoom on the time interval[0 5]s is given in the right side of this figure 17 inorder to confirm out last remark.

Fig. 17. Estimation of vertical force: right wheel



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In the figure 18, the vertical forces are comparedto suspension deflections measures. As for the cen-tre height of gravity, there are no sensors, during thistest, to measure the vertical forces. It’s then difficultto conclude on the quality of the estimation. How-ever, it is clearly shown that the estimated forcesand the equivalent measured suspension deflectionsare well correlated. This gives us an idea aboutthe quality of estimation. From figures 18, the loadtransfer ratio between the two wheels is computedand shown in the figure 19. The values of LTR aresituated between −0.15 and 0.2. These values aremuch smaller than the risk limit LTR=1, where onwheel of the same axle lifts off the road. This isdue to the fact that, during the test and for safetyreasons, the driver is not allowed to reach this limit.

Fig. 18. Vertical forces estimation compared to LVDT measures

However, in order to test the approach and sendan alarm to the driver, the coefficient limit of LTRis reduced to 0.2.

2) Braking test: In this section, the brake testis presented in order to show the rapidity and therobustness of the proposed method using observers.This test allows to determine if the rollover risk canoccur in the case of braking.

In the figure 20, the vehicle speed during this testis shown. The successive brakings occur at times 9s,29s and 49s.

In the following, the influence of the brakingon the vehicle behavior and the rollover risk is

Fig. 19. Load Transfer Ratio (LTR)

Fig. 20. Vehicle speed for brake test

shown. In this case, the jerk of the systems whichcorresponds to the double derivative of roll ratemeasured by gyrometer sensor and the jerk comingfrom the third derivative of suspension deflectionmeasured by LVDT sensor are shown respectivelyin the right and left side of the figure 21.

One remarks that the jerks of suspension de-flection and roll angle are respectively bounded by800m/s3 and 250rad/s3. Also in this case, the valueof the gain f+ is chosen to be equal to 1600m/s3.

In the figure 22, the estimation of the suspensiondeflections of the front of vehicle are representedand compared to measures. At the braking times 9s,29s and 49s, these vertical displacements decrease.The right and the left side have almost the samevalue of about −0.08m. In this case, no load transferis occurred between the left and the right side.



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Fig. 21. Jerk in the brake test

Fig. 22. Suspension deflection estimation

The data of the table I which come from statisticstudy, show the correlation between the measureddisplacement and the estimated one. To show thequality estimation of the roll angle, a zoom is donein the time interval [0 2]s of the figure 23.

TABLE ISUSPENSION DEFLECTION ESTIMATION ERROR

One notices that in this case, the roll angle isnot high even in the braking times. The estimationerror tends to zero as shown in the figure 24. Themaximum value is around 10−4rad.The data of thetable II show the correlation between the estimatedand the measured roll angle.

Fig. 23. Roll angle estimation

Fig. 24. Roll angle estimation error

TABLE IIROLL ANGLE ERROR



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The figure 25 shows that the estimated roll ratecompared to the gyrometer’s measure. One remarksthat the estimation converges quickly toward themeasure. This remark is confirmed by the data ofthe table III and by the estimation error shown in thefigure 26. Indeed, the minimum values for respec-tively the measured roll rate and for the estimatedroll rate are −0.03rad/s and −0.04rad/s.

The maximum value of 0.03rad/s is almost thesame for the two signals.

Fig. 25. Roll rate estimation in the case of brake test

TABLE IIIROLL RATE ESTIMATION ERROR

The figure 27 shows the estimation of the centreheight of gravity. At the braking times 9s, 29s and49s, the centre height of gravity increased up to0.8m and between these times, the value of thisdisplacement stays at its static value, namely 0.68m.

In the figure 28, the vertical forces of the wheelsare presented. In the left, the front left and rightforces are presented. One notices that these forcesare quit close. That is confirmed by the small value

Fig. 26. Roll rate estimation error

Fig. 27. Estimation of centre height of gravity

of the roll angle shown previously in the figure 23.The second remark, is about the values of these twoforces at the times 9s, 29s and 49s, which decreaseto 8000N . Between these times, the forces keeptheir static values. In the right side of this figure 28,the rear left and right forces are shown. These forcesvary around their static values, which is conform tothe braking test.

The figure 29 shows the Load Transfer Ratio(LTR). One notices an increase of its value from0.02 until respectively 0.11, 0.13 and 0.135, at brak-ing times, respectively 9s, 29s and 49s. However,these values still far from the limit value of 1 andthe limit fixed in this work, namely 0.2. In thiscondition, no rollover risk is detected and therefore,no alarm is sent to the driver.



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Fig. 28. Estimation of vertical forces in case of brake test

Fig. 29. Load Transfer Ratio for brake test

V. CONCLUSION

In this work, an original system of heavy vehiclesrollover risk prediction has been proposed. The mainadvantage of the method is its simplicity. The otheradvantage is the fact that it is based on verticalforces estimation using high order sliding modeobserver. It has been validated experimentally ona real heavy tractor rolling on the road at variousspeeds and lane-change manoeuvres. A well agree-ment has been noticed between the experimental andtheoretical results.

In order to show the robustness of the proposedapproach, two tests have been presented in thisstudy: zigzag and braking test. The results show thatdynamic states are well estimated (estimation of thecentre height of gravity is presented). Then, verti-cal forces are estimated and the rollover indicator,

namely LTR is calculated. The results are discussed.It is shown that the estimation results are quite closeto experimental ones and the rollover is predicted.In this test, the LTR does not reach its limit of 1. Inreal situation and for safety reason and only for thisreason, we were not allowed to test this situation(on wheel lifts of the road) because the tractor isnot equipped with safety device. However, in orderto send an alarm to the driver and to test its effect onthe deriver’s behavior, this limit is reduced to 0.2.In this case, and during the zigzag test, this limit isreached and the alarm has been sent to the driver inorder to reduce his speed. The method proved thatin the case of braking test, there is no rollover risk(LTR< 0.2).

The proposed method is tested on an instrumentedtractor. In the future work, it can be interesting totest the robustness of this approach on tractor semi-trailer. All vehicle parameters are supposed knownand measured. The obtained results encourage theimprovement of the proposed system in the futurework in order to take into account that some param-eters may be unavailable. One challenging issue westarted to address is to apply an adaptive observerin order to estimate in real time these parameters.

VI. ACKNOWLEDGMENTS

This works is supported by the French Ministry ofIndustry and the Lyon Urban Trucks&Bus competi-tiveness cluster; the authors gratefully acknowledgetheir contributions.

This work was supported and developed by IF-STTAR (The French Institute of Science and Tech-nology for Transport, Development and Networks)in collaboration with French industrial partners, Re-nault Trucks, Michelin and Sodit in the frameworkof French project VIF (Vehicule Lourd Interactif duFuture).

REFERENCES

[1] P. Milliken and J. de Pont, ”The Effect of Cross-Sectional Ge-ometry on Heavy Vehicle Performance and Safety” TransfundNew Zealand Research Report No. 263.

[2] H. Imine and V. Dolcemascolo, ”Rollover risk prediction ofHeavy Vehicle in interaction with infrastructure”, InternationalJournal of Heavy Vehicle Systems, Vol. 14 No. 3, 2007.

[3] H. Imine and V. Dolcemascolo, ”Vertical tyre forces estimationto calculate the Rollover risk of heavy Vehicles ”, FISITA’06,World Automotive Congress, 22-27 October 2006, Yokohama,Japan.



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[4] C. Chen and M. Tomizuka, ”Dynamic Modeling of ArticulatedVehicles for Automated Highway Systems”, American ControlConference, pp. 653-657, 1995.

[5] C. Chen and H. Peng, ”A real-time rollover threat indexfor sports utiliy vehicles”, American Control Conference, pp.1233–1237, San Diego, USA, 1999.

[6] R. W. Goldman, M. El-Gindy and B. T. Kulakowski, ”Rolloverdynamics of road vehicles: literature survey”, InternationalJournal of Heavy Vehicle Systems, Vol. 8, pp. 103-141, 2001.

[7] R. W. Allen, H. T. Szostak, D. H. Klyde, T. J. Rosenthal andK. J. Owens, ”Vehicle dynamic stability and rollover”, technicalreport, Systems Technology, Inc, NHTSA 263, Hawthorne, CA,U.S.-D.O.T., NHTSA, USA, 1992.

[8] H. Imine, A. Benallegue, T. Madani and S. Srairi, ”Rolloverrisk prediction of an instrumented heavy vehicle using highorder sliding mode observer”, ICRA’09, IEEE InternationalConference on Robotics and Automation, pp. 523-527, May12-17, 2009, Kobe, Japan.

[9] T. D. Gillespie and S. M. Karamihas, ”Characterising trucksfor dynamic load prediction”, Int. J. Vehicle Design, Vol. 1,No. 1,pp. 3-19, 1993.

[10] H. Imine, L. Fridman and T. Madani, ”Steering Control forRollover Avoidance of Heavy Vehicles”, IEEE Transaction onVehicular Technology, Vol. 61, No. 8, pp. 3499-3509, 2012.

[11] H. Imine, Y. Delanne and N. K. M’Sirdi, ”Road ProfilesInputs to evaluate loads on the wheels”, International Journal ofVehicle System Dynamics, Vol. 43, pp. 359-369, Supplement,November 2005.

[12] H. Imine and V. Dolcemascolo, ”Sliding Mode observers toheavy vehicle vertical forces estimation ”, IJHVS, InternationalJournal of Heavy Vehicle Systems, Vol. 15, No.1 pp. 53-64,2008.

[13] L. Fridman, A. Levant and J. Davila, ”High-Order Sliding-Mode Observation and Identification for Linear Systems withUnknown Inputs”, 45th, Conference on Decision in Control,San Diego, 2006.

[14] A. Levant, ”Robust exact differentiation via sliding mode tech-nique”, Automatica 34(3), 379-384, 1998.

[15] L. Fridman, Y. Shtessel, C. Edwards and X. G. Yan, ”Higher-order sliding-mode observer for state estimation and inputreconstruction in nonlinear systems”, International Journal ofRobust and Nonlinear Control 18(4-5):399-413, 2008.

[16] H. Imine, L. Fridman, H. Shraim and M. Djemai, ”Sliding modebased analysis and identification of vehicle dynamics”, LectureNotes in Control and Information Sciences, Vol. 414, SpringerVerlag, Juillet 2011.

[17] A. Levant, ”High-order sliding modes: differentiation andoutput-feedback control”, International Journal of Control 76(9-10), 924-941, 2003.

[18] J. Y. Wang and M. Tomizuka, ”Robust H∞ Lateral Controlof Heavy-Duty Vehicles in Automated Highway System,” 1999IEEE American Control Conference, San Diego, June 1999.

[19] D. Cebon, ”Interaction between heavy vehicles and roads”,Society of Automotive Engineers, SP-931, 81 p, 1993.

[20] B. Jacob and V. Dolcemascolo, ”Dynamic Interaction betweenInstrumented Vehicles and Pavements ”, Proceedings of the5th International Symposium on Heavy Vehicles Weights andDimensions, Maroochydore, Queensland, Australie, March 29-April 2, 1998.

[21] C. Chen and M. Tomizuka, ”Modeling And Control Of Ar-ticulated Vehicles”, Research Reports, California Partners forAdvanced Transit and Highways (PATH), 1997.

[22] J. Ackermann and D. Odenthal, ”Damping of vehicle rolldynamics by speeds scheduled active steering”, Proc. EuropeanControl Conf., Karlsruhe, Aug 31-Sept 3, 1999.

[23] H. Imine, Y. Delanne and N. K. M’Sirdi, ”Road ProfilesInputs Estimation in Vehicle Dynamics Simulation”, IAVSD,International Journal of Vehicle System Dynamics, Vol. 44,N◦4, pp. 285-303, April 2006.

[24] G. Gratia, ”VANI (Vehicule d’Analyse d’Itineraire): un materielmultifonction pour les etudes de securite”, Bulletin de liaisondes laboratoires des Ponts et Chaussees, special XVII, pp.69-74,juin, 1995.

[25] http://www.vectra.fr[26] Hyun, Dongyoon, and Reza Langari. ”Development of a parsi-

monious dynamic model of tractor-semitrailers.” InternationalJournal of Heavy Vehicle Systems 9.4 (2002): 298-318.

[27] Hyun, Dongyoon, and Reza Langari. ”Modeling to predictrollover threat of tractor-semitrailers.” Vehicle System Dynam-ics 39.6 (2003): 401-14.



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Hocine Imine received his Master Degree andhis PhD in Robotics and Automation from theVersailles University, France, respectively in2000 and 2003. He received the Accreditationto Supervise Research (Habilitation Dirigerdes Recherches, HDR) on March 2012 fromthe University of Valenciennes et du HainautCambrsis, France. In 2005, he joined IFST-TAR (French Institute of Science and Tech-

nology for Transport, Development and Networks), where he iscurrently a senior researcher. He is involved in different french andEuropean projects. He was member of the organization committeeof the international conference on heavy vehicles (HVParis’2008,merging HVTT10 and ICWIM5 in May 2008). He was Guest Editorof International Journal of Vehicle Design, Special Issue on: ”VariableStructure Systems in Automotive Applications”. He is Member ofIFAC Technical Committee on Transportation systems (TC 7.4). Hisresearch interests include Intelligent Transportation Systems, heavyvehicle modeling and stability, diagnosis, non linear observation, nonlinear control. He published 2 books, over 80 technical papers, andseveral industrial technical reports.

Abdelaziz Benallegue received his B. Sc. inElectronics from Ecole Nationale Polytech-nique d’Alger, Algeria in 1986, his M. Sc.(DEA) in Robotics and Ph.D in Robotics andAutomatic Control from Universit Pierre andMarie Curie, Paris, France, respectively in1987 and 1991. He was an associate profes-sor of Automatic control and robotics at theuniversity of Pierre and Marie Curie, Paris 6,

France since 1992 to 2002. He joined the University of VersaillesSt Quentin in September 2002 as Professor of Automatic Controland Robotics. His research interests are mainly related to linear andnonlinear control theory including adaptive control, robust controland neural network learning control, with applications to roboticsand aerial vehicles.

Tarek Madani received his Ph.D. in Roboticsand Automation from UVSQ university (Uni-versite de Versailles Saint Quentin), France in2005, his M. Sc. in Robotics from ENSAM en-gineering school (Ecole Nationale Superieured’Arts et Metiers) of Paris, France in 2000 andhis B. Sc. in Automatic Control for Electri-cal Engineering from ENP engineering school(Ecole Nationale Polytechnique) of Algiers,

Algeria in 1997. He was an Assistant Professor at UVSQ from 2005to 2007. Thereafter, he was a researcher member at LISV laboratory(Laboratoire d’Ingenierie des Systemes de Versailles) of UVSQ anda Project Manager in Automatic Control for the industrial fields ofautomotive, aeronautics and space from 2007 to 2013. He joinedUPEC University (Universite de Paris-Est Creteil) as an AssociateProfessor of Electrical Engineering in September 2013. He involvedin different projects at LISSI laboratory (Laboratoire Images, Signauxet Systemes Intelligents) of UPEC. His main research interests in-clude analysis of uncertain intelligent systems and nonlinear control,with medical applications.

Salim Srairi is researcher at CETE (Centred’Etudes Techniques de l’Equipement), Tech-nical Research Centre in Ile de France, andsince 2008 member of Mobility Team. Hereceived his Ph.D degree from the Universityof Technology Belfort-Monbeliard in 2004.He has already involved in several researchprojects such as METRAMOTO ”ANR2010”,RecyRoute and BUC. His research interests

include analytical and numerical modeling of electrical actuators,electromagnetism, Traffic safety analysis and exploitation of newtechnologies.

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