Hybrid Modeling and Identiﬁcation of Dynamic Yaw Simulator

Abdelhaﬁd Allad

2

, Lotﬁ Mederreg

2

, Hocine Imine

1

and Nouara Achour

2

1

The French Institute of Science and Technology for Transport, Development and Networks (IFSTTAR),

Marne-la-Vall

´

ee, Paris, France

2

Department of Intrumentation and Automatic, University of Science and Technology Houari Boumediene, Algiers, Algeria

Keywords:

Dynamic Driving Simulator, Light Vehicle Modeling, Cars Dynamics.

Abstract:

The objective of this work is the study and execution of a dynamic model reproducing the dynamics of a road

vehicle to implement it in a vehicle simulator. To do this we will use a generic approach using Matlab to

model different phenomenons related to the vehicle. In this research, we have taken into account all relevant

parameters in vehicle dynamics, specifying the longitudinal and lateral forces of wheel/ground contact.

For the calculation on an operational dynamic model of the vehicle, we chose the essential compnents to

reduce system complexity while ensuring a degree of realism and effectiveness of modeling, integrating a

status observer by sliding mode to reconstruct or estimate in real-time, the system status.

1 INTRODUCTION

Driving simulators have been becoming little by lit-

tle a suitable tool oriented to improve the knowledge

about the domain of driving research. The investiga-

tions that can be conducted with this type of tool con-

cern both the driver’s behaviour, the design/control of

vehicles, testing assistance systems for driving and

the roadway infrastructures impact. The beneﬁts of

simulation studies are many: lack of any real risk to

users, reproducible situations, time savings and re-

duced testing costs. In addition, their ﬂexibility al-

lows to test situations that do not exist in reality or at

least they rarely and randomly exist.

2 OVERVIEW OF THE DRIVING

SIMULATOR

Motion cueing platforms are widely employed in

driving simulator which became very accessible

through technological progress due to the fact that

computers have become more powerful and less ex-

pensive. Thus, several simulators of various architec-

tures were built with an aim of either human factors

study, or to test new car prototypes and functionali-

ties, or for driver training and education. Most will

agree that inappropriate motion cueing is likely to

induce simulator sickness through multisensory con-

ﬂict. For this reason, the INRETS-MSIS (which be-

came INRETS/LCPC LEPSIS) decided to initiate the

design of a mobile platform aimed primarily at study-

ing the importance of the modalities of yaw render-

ing on virtual vehicle control and on simulator sick-

ness. The aim of the present work is contributing to

improve the performance and the results of this ex-

isting simulator with the creation and insertion of a

new vehicle dynamic model. Dynamic driving sim-

ulator systems allow a driver to interact safely with

a synthetic urban or highway environment via a mo-

tion cueing platform that feeds back the essential in-

ertial components (acceleration and rotation) of the

vehicles movements, in order to immerse the driver

partially or completely. The complexity of dynamic

driving simulators lies in the fact that the system is

composed of interconnected subsystems of different

nature (mechatronics, control laws, computer, etc.) of

which a human subject is an integral part. Dynamic

driving simulators should thus be studied in their en-

tirety, including the human driver.

2.1 Motivation of the Platforms

Architecture Choice

The choices of simulator structure and motion bases

are motivated by the necessity to have a sufﬁcient

perception while driving as well as by ﬁnancial de-

sign constraints. Thus, the objective of the simulator

project is not to reproduce all of a real vehicles mo-

tions, but only the longitudinal movements (surge),

Allad, A., Mederreg, L., Imine, H. and Achour, N.

Hybrid Modeling and Identiﬁcation of Dynamic Yaw Simulator.

DOI: 10.5220/0005981605210526

In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2016) - Volume 1, pages 521-526

ISBN: 978-989-758-198-4

Copyright

c

2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

521

and yaw. This inertial feedback is to be perceived by

the human user in the intended applications, which

include the study of the effects of yaw cueing on sim-

ulator sickness. Indeed, one of the more nauseat-

ing manoeuvres in a driving simulator is the nego-

tiation of (sharp) curves, especially intersections in

complex environments like agglomerations (S et al.,

2009)(Hichem et al., 2010).

Figure 1: Vehicle simulator.

2.2 Platform Description

Here it is a driving simulator with an acceptable com-

promise between rendering quality, compactness and

cost limitation. The mechatronics components of

the proposed solution are described below (S et al.,

2009)(Hichem et al., 2010):

• The cabin consists of an instrumented mobile part

moving along a guide way mounted on the plat-

form. It is the interface between the driver and

the simulated environment. The cabin is equipped

with acceleration and braking pedals, steering

wheel, gearbox lever and other classical car con-

trol organs. (Figure 2)

Figure 2: Cabin of the vehicle simulator.

• Audio/video generators: the visual output is pro-

vided by a system of ﬁve projectors PROJEC-

TIONDESIGN F20 sx + with 1280x1024 resolu-

tion. (Figure 3)

Figure 3: Projector system.

• The acquisition system is composed of an indus-

trial micro controller. This allows the control of

actuators in the desired position, speed or torque

(used for the steering wheel force feedback). A

bidirectional information exchange protocol is de-

ﬁned between this card and the PCs dedicated to

vehicle and trafﬁc models. The communication

is performed through CAN port between the elec-

tronic card and the PC named XPC target: this

one is connected with other PCs by means of Eth-

ernet cables. 5 computers are involved in the data

elaboration and acquisition (Figure 4):

Figure 4: Aquisition system.

3 RELATED WORK

Various studies and researches have been done to edit

a simpliﬁed vehicle model by adopting several as-

sumptions with the aim to reduce its complexity in

terms of Degree of Freedom (Dof) and to neglect re-

dundant equations.

3.1 Type of Vehicle Dynamic Model

3.1.1 One Wheeled Model (Quarter of Vehicle)

For the study of suspension, the model quarter of ve-

hicle is the simplest one. We ﬁnd it in previous stydies

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

522

about suspension and pneumatic model with only two

degrees of freedom (NADJI, 2007).

Figure 5: A quarter of vehicle.

3.1.2 Half-vehicle Model

Depending on modelings purpose, in literature it is

possible to ﬁnd half-vehicle models which, although

far from a complete one, properly accomplish their

tasks (JABALLAH, 2011)(Samuel, 2006).

Lateral Half-vehicle Model. This model represent

a lateral view of the vehicle. It’s used to study roll

mouvements, mathematically il’s a model with four

degrees of freedom.

Figure 6: Lateral Half-Vehicle Model.

Longitudinal Half-vehicle Model (Bicycle Model).

According to simply the model, the 4 wheels system,

supposed a perfect symmetry between right and left

parts, has been reduced to a bicycle model, focusing

the study only to a half car. The forces applied are

simply multiplied by two in order to take into account

the four tires.

3.1.3 Complete Vehicle Modeling

The four wheels model is used for a complet and re-

alistic model of the vehicle dynamics (SLEIMAN,

2010).

4 VEHICLE DYNAMIC MODEL

The proposed dynamic vehicle model is nonlinear.

Figure 7: Longitudinal half-vehicle model.

Figure 8: Complete vehicle modeling.

Moreover, the kinematic elements can greatly inﬂu-

ence the vehicle dynamic behaviour. This is due to

the existing interconnection between different parts of

the vehicle. However, for the sake of simplicity, the

complexity of the model may be reduced depending

on the type of application and the purpose of mod-

elling. Due to the complexity of a complete vehicle

model, the vehicle model is limited to four intercon-

nected subsystems:(VENTURE, 2003)

• The chassis.

• Suspension.

• Wheels and their interaction with the ground.

• The driver controls.

The chassis is treated as an unconstrained body

in the space so it contains six DoFs; since it is con-

sistently integrated with vehicle body, it counts three

DoFs for translation along the longitudinal (Surge),

lateral (Sway) and vertical (Heave) axis and three for

rotations (Roll, Pitch and Yaw); they are all referred

to vehicles Centre Of Gravity (COG) (Figure 9).

Figure 9: Vehicle degrees of freedom.

Its permissible to assume that each tire belonging

to rear axis has two DoFs: one for the rotation and the

Hybrid Modeling and Identiﬁcation of Dynamic Yaw Simulator

523

other for suspension mechanism translation. Whereas

the front axis is composed by two driving wheels able

to steer, therefore they have one DoF more each (three

DoFs). Finally the entire vehicle system owns 16

DoFs.

4.1 Chassis Dynamic Behaviour

High rigidity of the vehicle chassis can limit its ﬂex-

ibility study and its inﬂuence on the suspension sys-

tem and the wheels system. In the present case, the

chassis is considered as rigid. This rigidity helps in

supporting axes with articulations of the elastic type.

Therefore it can be considered as a suspended mass.

The inertial parameters of the body are generally rep-

resented by:

• Its mass m (unsprung mass) and M (total mass of

vehicle) ;

• Position of the centre of gravity G;

• Matrix of inertia J;

The equations of motion of the chassis are ob-

tained by applying the fundamental principles of clas-

sical physics. This leads to three ordinary differential

equations for the translational motion of the centre of

gravity and three ordinary differential equations for

the rotation.

Figure 10: Translational and rotation motion of the centre

of gravity.

4.1.1 Translation Motion

The sum of external forces applied to a solid body

in motion, according to the principle of dynamics, is

equal to its mass m multiplied by its acceleration:

m ˙v

COG

=

∑

F

external f orces

(1)

The equilibrium of these forces along the three axes

leads to the following relation (JABALLAH, 2011):

m

˙

V

x

˙

V

y

˙

V

z

= T

c

r

F

x f 1

+ F

x f 2

+ F

xr1

+ F

xr2

+ F

wx

+ F

gx

F

y f 1

+ F

y f 2

+ F

yr1

+ F

yr2

+ F

wy

+ F

gy

F

z f 1

+ F

z f 2

+ F

zr1

+ F

zr2

+ F

wz

+ F

gz

(2)

Where v = (v

x

, v

y

, v

z

)

T

indicates respectively longitu-

dinal, lateral and vertical velocities.

Forces which contribute to body motion and

which affect it are the following ones:

• Contact Forces: three for each tyre, developed in

the pavement interface (for convention the sub-

scripts f and r indicate respectively front and rear,

whereas 1 and 2 indicate left and right).

• Aerodynamic Forces: F

wx

= −

1

2

C

ax

ρSV

2

x

• Gravity Forces:

F

gx

F

gy

F

gz

= T

s

v

0

0

−mg

The vehicle system is illustrated in the Figure ,

where p

f

and p

r

represent respectively the front and

rear half gauge (the sum of them provides the track

width), whereas r

1

and r

2

represent the distance be-

tween the COG and front and rear axis respectively

(the sum of them provides the wheelbase). m

1

, m

2

,

m

3

, m

4

depict the wheels weight, whereas m is the

sprung mass (of the chassis).

Figure 11: Vehicle With Suspension Model.

The system includes four road inputs u

1

, u

2

, u

3

and u provided by roadway longitudinal proﬁle. The

vertical displacements of the corners Z

r1

, Z

r2

, Z

r3

and

Z

r4

depend on the angles φ and θ and the vertical dis-

placement z of the sprung mass as shown in the fol-

lowing equations (IMINE, 2003):

z

r1

= z − p

r1

sinθ − r

2

sinφ

z

r2

= z − p

r2

sinθ + r

2

sinφ

z

f 1

= z − p

f 1

sinθ + r

1

sinφ

z

f 2

= z + p

f 2

sinθ + r

1

sinφ

(3)

4.1.2 Rotational Motion

In literature it is common to ﬁnd as the total equilib-

rium of rotational motion around (X

c

, Y

c

, Z

c

) axis the

following expression:

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

524

I

¨

θ

¨

φ

¨

ψ

=

(F

z f 1

− F

z f 2

)P

f

+ (F

zr1

− F

zr2

)P

r

+ (k

arr

+ k

ar f

)θ

−(F

z f 1

+ F

z f 2

)r

1

+ (F

zr1

+ F

zr2

)r

1

(F

y f 1

− F

y f 2

)r

1

− (F

yr1

+ F

yr2

)r

2

+ (F

x f 2

− F

x f 1

)P

f

+ (F

xr2

− F

xr1

)P

r

(4)

where [

¨

θ,

¨

φ,

¨

ψ]represents respectively the accelera-

tions of the roll, the pitch, and the yaw.

The inertia matrix referred to R

c

frame having cross

elements neglected:

I =

I

xx

0 0

0 I

yy

0

0 0 I

zz

(5)

4.2 Global Model

The equations developped before by Newton-euler

laws are synthesized in the state representation below:

˙

ˆ

x

˙x

y

˙y

z

˙z

θ

˙

θ

φ

˙

φ

ψ

˙

ψ

z

1

˙z

1

z

2

˙z

2

z

3

˙z

3

z

4

˙z

4

=

˙

ˆ

x

1

x

2

x

3

x

4

x

5

x

6

x

7

x

8

x

9

x

10

x

11

x

12

x

13

x

14

x

15

x

16

x

17

x

18

x

19

x

20

=

x

2

¨x

x

4

¨y

x

6

¨z

x

8

¨

θ

x

10

¨

φ

x

12

¨

ψ

x

14

¨z

1

x

16

¨z

2

x

18

¨z

3

x

20

¨z

4

(6)

5 SIMULATION AND TEST

For the tests we had many simulations scenarios, in

the ﬁgure below we tested a straight line followed by

two turns:

Figure 12: The simulation conditions: left engine torque,

the brake in the middle and on the right the ﬂoor signal.

Figure 13: Result of the trajectories simulated.

We see that the model respect the instructions of

the scenario, but it doesn’t mean that all the vehicle

dynamics are represented, because we neglected some

parameters. We note also, the rotations motions don’t

impacts the trajectory because the undulation of the

road are weak.

5.1 States Estimations

to improve the accuracy of the model, we chose to es-

timate the rotation angles that are the roll, pitch and

yaw. Due to measurements made on an instrumented

car Peugeot 406 provided by IFSTTAR, we compared

these results with what we’ve got in our simulation

model. Using a sliding mode observer we tried to es-

timate the equations that govern the movements of ro-

tations.

The Steps of the Estimate

• the calculation error between the simulated and

measured value

e

θ

= θ

mesur

− θ

calcul

e

φ

= φ

mesur

− φ

calcul

e

ψ

= ψ

mesur

− ψ

calcul

(7)

• Calculation of the sliding surfaces

S = (

∂

∂x

+ γ)e (8)

S

θ

= ˙e

θ

+ γ

θ

e

θ

⇒

˙

S

θ

= ¨e

θ

+ γ

θ

˙e

θ

⇒ −k

θ

sign(S

θ

)

S

φ

= ˙e

φ

+ γ

φ

e

φ

⇒

˙

S

φ

= ¨e

φ

+ γ

φ

˙e

φ

⇒ −k

φ

sign(S

φ

)

S

ψ

= ˙e

ψ

+ γ

ψ

e

ψ

⇒

˙

S

ψ

= ¨e

ψ

+ γ

ψ

˙e

ψ

⇒ −k

ψ

sign(S

ψ

)

(9)

• Study of stability through the theorems lyapunov

We put:

˜w =

˜

θ

˜

φ

˜

ψ

=

θ −

ˆ

θ

φ −

ˆ

φ

ψ −

ˆ

ψ

(10)

Hybrid Modeling and Identiﬁcation of Dynamic Yaw Simulator

525

We choose the following Lyapunov function:

V (x) =

1

2

S

T

S +

1

2

T

r

( ˜w

T

˜w)

˙

V (x) = S

T

˙

S + T

r

( ˜w

T

˙

˜w)

˙

V (x) = S

T

˙

S + T

r

( ˜w

T

˙

˜w)

(11)

˙

V (x) = (S

θ

S

φ

S

ψ

)

˙

S

θ

˙

S

φ

˙

S

ψ

+ T

r

((

˜

θ

˜

φ

˜

ψ)

˙

˜

θ

˙

˜

φ

˙

˜

ψ

)

(12)

• Equation resolution for obtaining the estimated

variables θ, φ et ψ;

Stability condition:

˙

V (x) ≤ 0 (13)

(S

θ

S

φ

S

ψ

)

˙

S

θ

˙

S

φ

˙

S

ψ

+ T

r

((

˜

θ

˜

φ

˜

ψ)

−

˙

ˆ

θ

−

˙

ˆ

φ

−

˙

ˆ

ψ

) ≤ 0

(14)

The problem posed is to appear

ˆ

θ

ˆ

φ

ˆ

ψ

in the equa-

tions that govern the accelerations, but unfortu-

nately we managed to do it only for 2 variable

from 3. That return us to think about another type

of observation, or downright invites us to recon-

sider our equations.

6 VALIDATION

To determine the reliability of the model we have de-

veloped, we rely on Prosper OKTAL software used

by the world’s leading players in the transport sec-

tor as your: AIRBUS, ENAC, RENAULT, PSA, DGA,

VALEO, SNCF, KEOLIS, RATP, ALSTOM or BOM-

BARDIER. About this tool as an expertise which

refers more and more academic and scientiﬁc com-

munity.

7 CONCLUSIONS

This work deals with the topic of modeling and esti-

mating the state of the vehicle subsystems. First, we

looked at different knowledge models and dynamics

of vehicle behavior in the literature. These models

are then used throughout this work based on the prob-

lematic of the study.

The modeling of motor vehicles was developed to

understand their dynamic behavior. Indeed, such a

study has allowed us to understand the complexity of

the various phenomena that interfere in this area.

As regards the aspects of vehicle dynamics; we re-

alized that the most comprehensible way for the study

of vehicle behavior is to split the various dynamics in

parts. In this case, the chassis model, the aerodynamic

forces, gravity, suspension and wheel.

REFERENCES

www.ifsttar.fr.

Boualem, B. (2009). Caracterisation du comportement non

lineaire en dynamique du vehicule. PhD thesis, Uni-

versit de technologie de Belfort Montbeliard, Ecole

Doctoral Sciences pour L’Ingenieur et Microtech-

niques.

Hamadi, N. (2009). Modlisation d’un vehicule en prsence

des forces de contact roues/sol. PhD thesis, Universite

EL-Hadj Lakhdar Batna Algerie.

Hanane, B. (2013). Observateur non lineaire mode glis-

sant. PhD thesis, Universite FERHAT ABBAS Setif

Algerie.

Hichem, A., Salim, H., Lamri, N., Rene J V, B., and

Stephane, E. (2010). From design to experiments of a

2 dof vehicle driving simulator. IEE.

Imine, H. (2003). Observation d’etats d’un vehicule pour

l’estimation du proﬁl dans les traces de roulement.

PhD thesis, Universite de Versailles Saint Quentin en

Yvelines.

Jaballah, B. (2011). Observateur robustes pour le diagnos-

tic et la dynamique des vehicules. PhD thesis, Uni-

versite Paul Cezanne Aix-Marseille III et l’Ecole Na-

tionale d’Ingenieurs de Monastir.

Maakaroun, S. (2011). Modelisation et simulation dy-

namique d’un vehicule urbain innovant en utilisant le

formalisme de la robotique. PhD thesis, Universite de

nantes, Ecole Doctoral de l’ecole des mines de nantes.

Nadji, M. (2007). Adequation De La Dynamique De Ve-

hicule a La Geometrie Des Virages Routiers, Apport

a La Securite Routiere. PhD thesis, Institut National

Des Sciences Appliquees Insa De Lyon.

Ouahi, M. (2011). Observation de systemes e entrees incon-

nues, applications a la dynamique automobile. PhD

thesis, Universite de Limoges Ecole Doctorale ED521

Sciences et Ingenierie pour l’information.

S, E., R, B., P, S., P, P., H, A., S, B., and D, D. (2009). Sim-

ulateur de detection des alterations du comportement

de conduite liees l’attention et la vigilance (vigisim).

Samuel, G.-B. (2006). Etude d’un systeme de controle

pour suspension automobile. PhD thesis, Universite

du Quebec.

Sleiman, H. (2010). Systemes de suspension semi-active a

base de ﬂuide magnetorheologique pour l’automobile.

PhD thesis, Paris Tech, Ecole Nationale Superieure

d’Arts et Metiers.

Venture, G. (2003). Identiﬁcation des parametres dy-

namiques d’une voiture. PhD thesis, Universite de

nantes, Ecole Doctoral de Nantes.

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

526