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2 DOF Low Cost Platform for Driving Simulator:
Design and Modeling
Hichem Arioui, Salim Hima, Lamri Nehaoua
To cite this version:
Hichem Arioui, Salim Hima, Lamri Nehaoua. 2 DOF Low Cost Platform for Driving Simulator: Design
and Modeling. The 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics,
Jul 2009, SINGAPOUR, Singapore. pp.1206-1211. �hal-00420879�
2 DOF Low Cost Platform for Driving Simulator: Modeling and Control
Hichem Arioui, Salim Hima and Lamri Nehaoua
Abstract—In order to be an effective tool for driver eval-
uation and education, driving simulators need to be better
designed to reduce simulator sickness. In this paper, we expose
platform design, description and the modeling aspects of a
2 DOF low cost motion platform allowing the restitution of
the longitudinal and yaw movements. To enhance the drive
immersion in the virtual world, a haptic feedback steering wheel
will be implemented.
The whole system is considered as a two coupled systems and
linked mechanically. The first system consists in motorized rail
for the longitudinal movement while the second system consists
in motorized yaw allowing either curve-taking movement.
The platform mechanics is proposed as presented in the next
sections to study the driving simulator sickness on the driver
and especially the yaw component. Experimental studies were
made to devise a characterization of the platform capabilities
and frequency responses. Experimentations were carried out
for classical drive operation. First conclusion and future works
are established.
Index Terms—Driving Simulator design, Dynamics and Mod-
eling.
I. INTRODUCTION
The use of driving simulators is increasingly widespread
and adopted by various public and private institutions. A
driving simulator is virtual reality tool allows users to drive
in safe way and test several scenarios on same system.
These motion cueing platforms were firstly used for aircraft
simulators and were democratized for cars and recently
for motorcycle [1][2][3]. Driving simulators became very
accessible by technological headway. Indeed, the calculators
become more powerful and less expensive. Thus, several
simulators of various architectures were built with an aim
of either human factor study [4][5][6][7], or vehicle dynamic
model validation, or test of new car prototypes and function-
alities [8][9][10].
However, if the cost of aircraft and passenger safety allow
investment in high-cost simulators, nothing justifies it or even
provides a tool for training and psychophysical studies in
the car [11][12] and motorcycle cases [13]. In addition, the
complexity of a simulator does not reflect its fidelity to feed
back all the movements. For this reason, it was interesting
to offer targeted solutions based low-cost mobile platforms
aimed primarily at training schools, hospitals and other users.
Furthermore, driving simulator system allows a driver to
interact in a safe manner, with a synthetic urban or highway
via a motion cueing platform by feeding back the essential
This work was supported by French National Agency of Research (ANR)
in the Framework of VIGISIM Project.
H. Arioui, S. Hima and L. Nehaoua are with IBISC-CNRS
Fre3190 at University of Evry Val d’Essonne, 40, rue du
Pelvoux, CE1455 Courcouronnes, Evry cedex, France. Email :
hichem.arioui@ibisc.fr
inertial components (acceleration and rotation) to immerse
driver partially or completely. Indeed, this clearly means that
as the complexity of such experiments is lies in the fact
that the simulation is composed of interconnected subsystems
of different nature (biological, mechatronics, control laws,
computer, etc.) and should be studied in its entirety. In this
work, we are interested by the design, mechactronics and
identification parts of the platform.
More generally, on motion cueing platform, a large range
of real-driving experienced accelerations cannot be repro-
duced. A compromise is to be found between the quality
of various inertial indices’ restitution and maintaining the
platform within its reachable workspace. Therefore, many
control strategies were developed [14][15][16][17], [18]. The
Motion Cueing Algorithms (MCA) were firstly used for flight
simulators motion cueing. Their porting to vehicle simulators
is possible, but the vehicle dynamics is of much higher
frequencies (more abrupt and frequent acceleration variation)
than what is observed on airplanes. Besides, driving a
vehicle takes place within traffic and unforeseen events (fog,
pedestrians...) conditions which could create more complex
scenarios.
All the components cited before will be taken into account
in order to facilitate the design built a low-cost motion
platform equipped with two degrees of freedom.
In the rest of this paper we present the design, description
and modeling aspects of the platform, followed by the
experiments that were carried to characterize frequentially
the motions. We finish this present work by the traditional
conclusion and future works.
II. C
HOICES’MOTIVATION OF THE PLATFORM
ARCHITECTURE
The simulator structure and motions based choices are
motivated by the necessary needs to have a sufficient percep-
tion while riding under financial constraint to make easy the
duplication in favor of driving schools and other institutions.
In this sense, the objective of the simulator project is not to
reproduce the whole vehicle motions, but only the longitu-
dinal and yaw one. These inertial effects are to be perceived
by the human user for the expected applications which aims
to study the effect of yaw component on simulator sickness.
Because of the importance of accelerating transition mo-
tion in vehicle dynamics, we also emphasize the longitudinal
movement.
Moreover, we know that the multiplication of perception
stimuli can strongly increase the riding simulation sensations
[19]. Based on this observation, the reproduction of the
dynamic tire-road contact system to assist the driver is
implemented (actuator mounted on the steering wheel). The
modeling part of this last point is not addressed in the present
paper. Figure (1) presents the experimented architecture
platform which will be described in the next section.
Fig. 1. The experimented 2 DOF simulator platform.
III. PLATFORM DESCRIPTION
A. Simulator Architecture
We present in this paper a mini driving simulator with an
acceptable compromise between the quality of restitution,
compactness and under cost constraints. The mechatronics
components of the proposed solution are described below:
• The cabin consists of an instrumented mobile part
moving along a guide-way mounted on the platform. It is
the interface that lies between the driver and the simulation
environment. The cabin is equipped with acceleration and
braking pedals, steering wheel, gearbox lever and other
classical car implements which are having appropriate sen-
sors that allow the acquisition of the driver desired input
commands (figure 1). These inputs feed the vehicle dynamic
model to update its several states. The cabin disposes also
of different visual indicators rendering the engine rpm, the
vehicle speed, etc.
• The acquisition system is composed of an industrial mi-
cro controller, and has both analog and digital input/output.
This allows the control of the actuators in the desired posi-
tion, speed or torque; this card appeared to be well adapted
for the interfacing of the simulator’s cabin. A bidirectional
information exchange protocol is settled between this card
and the PCs dedicated to vehicle-traffic model. This can be
performed either through a parallel or a CAN ports.
• The vehicle model concerns the computation of the
dynamics and the kinematics according to the driver actions
such as acceleration and brake pedals’ positions, clutch...
that are transmitted through the acquisition module and the
road characteristics. It is a simple model dedicated to our
simulator driving application. In this model, the vehicle is
considered as one body with 5DOF (longitudinal, lateral,
roll, pitch and yaw). Its complexity relates more to the
motorization part than the chassis dynamic. The engine part
is modeled by a mechanical and behavioral approaches [20]
based on the vehicle general characteristics (engine torque
curves, clutch pedal position, accelerating proportioning,
etc). After updating the vehicle’s state, resulting information
on the engine are sent to the cabin’s dashboard and to the
traffic model server.
The traffic model, visual and audio systems are not yet
operational on this platform.
Fig. 2. Simulation Synoptic Architecture.
The platform is embedded with power, sensors and control
modules to have information feedback on the control system
states. Each actuator (for the yaw and longitudinal one)
has servomotor level to ensure angular position transducer,
angular velocity and the output torque’s estimation. Data
resulting from these module are sent to the input/output
interface board that is managed by a control PC transmitted
via CAN technology.
B. Mechanical Description
The platform is composed of two metallic parts linked
mechanically. The upper part is composed by the cabin car
supported by chassis moving longitudinally on the lower part.
This last one consists of horizontal structure on which is fixed
the rotation drive system of the yaw motion (see figures 3
and 4). Overall upper system: cabin, driver and the sliding
plate have an average weight of 380 kg.
To control yaw and longitudinal motions of the platform,
two actuators have been used. Through two sliders, assem-
bled under the two edges of the cabin’s base, the platform
is able to move on a rail of 1.2 m length. To this end, a
Brushless type motor SMB 80 (nominal and peak torques
are respectively 3 and 9 N.m) with a reduction ratio of 45
are fixed at a mechanical stand related to the platform’s rails.
The motor rotation is transformed into cabin’s longitudinal
motion through a pulley-belt system. This platform achieves
linear accelerations up to ±0.408g in steady mode. At
peak current, acceleration and speed of ±1.224g and ±2.45
m/sec respectively are reached. The SMB 80 actuator is
driven with a brushless type servomotor.
Fig. 3. Upper metallic frame of the longitudinal motion
On the yaw motion, it is directly controlled by placing a
rotation system under the vertical structure and driven by a
circular ball-screw drive actuated system (the same actuator,
SMB 80, used for the longitudinal motion) operated by a
brushless servomotor and reduction red of 139.2 see figure
4. The motor rotation is transformed into ball-screw system
through a right angle transformation. This system achieves
angular accelerations up to 3.971
◦
/s
2
in steady mode. At
peak current, acceleration and speed of 58.151
◦
/s
2
and
29.075
◦
/s respectively are reached.
On the present driving simulator, the yaw rotation of the
platform can be changed or adapted to the situation that we
want simulate. Indeed, the upper part of the platform moves
manually over the lower part. This option allows us to study
better the impact of the rotation yaw (rotation speed and
radius of curvature, etc.) on the perception quality of the
restituted motion.
Fig. 4. The circular ball-screw drive actuated system
IV. PLATFORM MODELING AND IDENTIFICATION
Mainly, control of robotic mechanisms is based on the
knowledge of an accurate behavioral model that governs
their motions. Indeed, the accuracy of the model depends
essentially on the quantification of the phenomena that acts
on it, and on the precision of its parameters. We devote
this section to the derivation of the dynamic model of our
platform in response to actuators torques.
A. Platform Kinematic Modeling
The effect of the front wheel dynamics on that of the
whole system is neglected. Hence, by removing the wheel
and replace it with a resistive torque, resulting from the
friction forces of the wheel/ground interaction, and acting
on the yaw motion, the system treated in this paper can be
seen as a serial multi body system with three bodies linked
by two degrees of freedom, RP manipulator. In this case,
Three orthonormal frames are used to describe the motion
of the platform, see figure 5. Body B
0
and body B
1
are
linked with a revolute joint parametrized by the variable q
1
.
So, the transformation between frame R
0
and R
1
is given
by the rotation matrix:
R =
⎛
⎝
cos(q
1
) − sin(q
1
)0
sin(q
1
)cos(q
1
)0
001
⎞
⎠
(1)
Besides, Body B
2
performs a translation with respect
to body B
1
parametrized by the variable q
2
. Hence, the
configuration of the platform can be easily described by the
vector q =(q
1
,q
2
).
Let (x
G
1
,y
G
1
,z
G
1
) and (x
G
2
,y
G
2
,z
G
2
) denote, respec-
tively, the positions of the center of mass for bodies B
1
and
B
2
in their attached frames.
Angular velocities of bodies B
1
and B
2
are given by:
ω
1
= ω
2
=
⎛
⎝
0
0
˙q
1
⎞
⎠
(2)
Then linear velocities of G
1
and G
2
are given by:
V
G
1
=ω
1
× O
1
G
1
V
G
2
=V
O
2
+ ω
2
× O
2
G
2
(3)
By projecting these expression in their local frames we can
find:
V
G
1
=
⎛
⎝
− ˙q
1
y
G
1
˙q
1
x
G
1
0
⎞
⎠
(4)
V
G
2
=
⎛
⎝
− ˙q
1
y
G
2
+˙q
2
(x
G
1
+ q
2
)˙q
1
0
⎞
⎠
(5)
Fig. 5. Platform frames description
B. Platform Dynamics
Modeling mechanical mechanisms have attracted a great
attention for a long time and have attained a great maturity.
In fact, these development have led to a very efficient
algorithms which are accurate and rapid in order to fulfilling
requirements for robotic applications or computer animation
for example and for a large degrees of freedom [21].
There exist several methods to derive the dynamics equa-
tions of mechanisms such as: Newton-Euler’s formalism,
Hamilton’s formalism, Kane’s formalism ... etc. In this paper,
we have used the Lagrange’s formalism for its simplicity. The
equations of motion can than be obtained using Lagrange’s
equation for each generalized coordinates:
d
dt
∂T
∂ ˙q
i
−
∂T
∂q
i
= Q
i
(6)
where T = V − U is the Lagrangian function defined by the
difference between the total kinetic energy of the system V
and the total potential energy of the system U . In the case of
the platform presented in this paper, which evolves in (XY )
plan, T is reduced only to kinetic energy:
T = V =
1
2
2
i=1
V
T
G
i
M
i
V
G
i
+ ω
T
i
I
i
ω
i
(7)
where M
1
= m
1
eye(3) and M
2
= m
2
eye(3) are re-
spectively, body B
1
and B
2
matrix of masses, I
1
=
diag(I
1
xx
,I
1
yy
,I
1
zz
) and I
2
= diag(I
2
xx
,I
2
yy
,I
2
zz
) are
respectively, the moment of inertia tensors of bodies B
1
and
B
2
expressed in their local frames.
By replacing equations (4) and (5) in equation (7), the
previous expression becomes:
T =
1
2
m
1
x
2
G
1
+ y
2
G
1
+ I
1
zz
+ m
2
y
2
G
2
+ m
2
(x
G
1
+ q
2
)
2
+I
2
zz
)˙q
2
1
+
1
2
m
2
˙q
2
2
− m
2
y
G
2
˙q
1
˙q
2
(8)
It is a straightforward to show that, by application of La-
grange’s formalism, equation (6), the platform equations of
motion can take the following from:
M(q)
¨
q + C(q,
˙
q)=Q (9)
where M(q) is the system inertia matrix given by:
M(q)=
m
11
m
12
m
21
m
22
(10)
such as:
m
11
=m
1
x
2
G
1
+ y
2
G
1
+ I
1
zz
+ m
2
y
2
G
2
+ m
2
(x
G
2
+ q
2
)
2
+ I
2
zz
m
12
=m
21
= −m
2
y
G
2
m
22
=m
2
(11)
and C(q, ˙q) is a vector of centrifugal and Coriolis forces:
C(q, ˙q)=
2m
2
(x
G
2
+ q
2
)˙q
1
˙q
2
−m
2
(x
G
2
+ q
2
)˙q
2
1
(12)
Q is the external forces/torques vector acting on the platform
including traction and friction forces/torques:
Q =
τ
1
− τ
f
1
τ
2
− τ
f
2
(13)
τ
1
and τ
2
are obtained by multiplying the effective torque
delivered by motors, by the reduction ration of gears systems
integrated into their corresponding joints:
τ
1
= K
1
τ
a
1
τ
2
= K
2
τ
a
2
(14)
where : K
1
and K
2
are respectively about 139.2 and 45.
τ
f
1
and τ
f
2
are the friction torques. These torques are
modeled as a combination of dry and viscous frictions:
τ
f
i
= K
s
i
sign(˙q
i
)+K
v
i
˙q
i
i =1, 2 (15)
In next section, we will discuss the all parameters iden-
tification of the developed dynamic model and the used
approach. The frequency characterization of the system dy-
namic is also done to make an idea on the system transitions
capabilities.
V. E
XPERIMENTAL RESULTS
In this section we present the results of tests made on the
simulator for its frequency characterization. For the purpose
of experiments, a PID controllers are used to control each of
platform articulations (q
1
,q
2
)
T
.
Firstly, we are looking for frequency characteristics of
longitudinal and yaw motions. To do this, the system have
being excited with a chirp signal (sine wave with increasing
frequency) independently axel by axel. The resultant input-
ouput signals is used to identify the parameters the parame-
ters of the linear system which match this motion, by using
the least square method. Hence, the obtained system is used
to identify the bandwidth of the corresponding motion.
Figure 6 and 7 represent the experimental measures of the
longitudinal and yaw motions respectively when excited by
the chirp signal. The best fit is obtained by second order and
third order system for respectively the longitudinal and yaw
