Abstract—Software equipment of interactive vehicle simulators

consists of two main parts; a generator of virtual reality (generating

3D graphics and surrounding sound) and a mathematical model of

vehicle dynamics. The basic elements of mathematical dynamics

model of the vehicle consists first of a physics of an engine and a set

of parameterization files that define the current values of the

parameters of the vehicle, second of the world which with each

particular vehicle can interact. The paper describes the development,

implementation and testing of such a mathematical software model,

which was subsequently used in the latest driving simulator in the

laboratories at the Faculty of Transportation Sciences of the Czech

Technical University in Prague.

Keywords— car dynamics, driving simulator, mathematical

model

I. INTRODUCTION

OFTWARE equipment of a driving simulator consists of two

basic parts, a generator of virtual reality (generating 3D

graphics and spatial sound) and the physical model.

In 2010 at the Faculty of Transportation Sciences, we have

developed mathematical-physical model, which was

subsequently fully utilized in 2011 in the newly realized

chassis simulator (Octavia II 3D). This model was developed

as a universal module, which is expected to be used in future

interactive simulators of ground vehicles.

Our driving simulators are successfully used for analyzing

problem of HMI, reliability in transportation ([4]) or ITS

applications ([5], [6], [7]).

II. CONSTRUCTION AND FUNCTIONAL DESIGN OF DRIVING

SIMULATOR

An overall system of ‘living’ simulator (equipped with tools

enabling its modifications respecting the actual needs of each

particular experiment) can be described as a multilayer model

[1]. The next figure (Fig. 1) introduces the functional structure

of our equipment from the simulator point of view.

The whole system can be divided into four layers (they are

separated by green lines on the picture).

P. Bouchner, e-mail: bouchner@lss.fd.cvut.cz, S. Novotný, e-mail:

novotny@lss.fd.cvut.cz The authors participate in Driving Simulation Research Group, Joint

Laboratory of System Reliability, Department of Transporting Technology,

Faculty of Transportation Sciences, Czech Technical University in Prague, Konviktská 20, 110 00 Prague, Czech Republic.

Fig. 1: Functional structure of the simulator

The first layer represents the simulator device itself. It

consists of software and hardware parts. As the hardware of

our “light” simulator, we consider the cockpit that is

composed of parts of a real car and PCs connected to a

network. I/O cards (like CAN bus to PC interface) are also

included in this layer. Software of the simulator consists of

Virtual Reality Engine (for generation of 3D graphics and

spatial sound) and mathematical model of the car and

environment. The physical engine is always a compromise

between a very accurate physical behavior and a very fast

(real-time) response.

The next layer represents a database of testing tracks

(sometimes called scenarios) and cars. Each experiment

requires a more or less different scenario. To get objective

results, it is necessary to have precisely defined the difficulty

of each scenario. Sometimes we need a curveted road to study

driver’s ability to keep the car on the road while he/she is

forced to fulfill an additional task. On the other hand, a

scenario for investigation of driver’s drowsiness and fatigue is

recommended to have a very boring (almost straight) highway

road which cannot divert him/her but it lets the driver get into

relaxed state [2], [3]. By the same way, we should treat the

database of cars. Strong engine with automatic gearbox is

suitable for measurement of drowsiness while a car with

Car Dynamics Model - Design for Interactive

Driving Simulation Use

Petr Bouchner and Stanislav Novotný

S

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ISBN: 978-1-61804-034-3 285

manual gearbox and weaker engine with worthier grips serves

better for classification of one’s driving style.

The last layer represents the tools for creation of assets

constituting scenarios. Those are mainly modeling of 3D

objects and tools for automation of such processes and

databases (storages) of modeled objects. Each object in virtual

reality is accompanied by a texture or a set of textures. The

texture is a picture, which simplifies the 3D object creation in

following manner: the geometry of any real object is very

complex, on the other hand it is possible to replace it with a

very simple geometry covered by a worked out digital

photography (texture). The textures can be of different types;

general, which are tillable (i.e. repeatable - like grass, road

surface…) and the unique ones (houses, signs….). The amount

of textures over one scenario could be very high but lots of

them could be reused on several different pieces of geometry.

For that reason, it is also very practical to have a separate

database of 3D models (objects) as well as a database of

textures.

A. Modular architecture of driving simulator

The paragraph above introduces the simulator system as a

layered architecture. In fact, the architecture of the simulator

itself is usually modular.

Considering the inputs for the simulation device, they could

be divided into two groups: first one represents the inputs into

the simulation, these are real geographical data (for example

from GIS sources), data from the real world maps, data from

micro traffic simulations and finally the data from external

high-end physical simulations and models.

On the other hand, the system should be opened for imports

from various devices, which can be connected in the car.

Those could be for example: driver assistance devices,

systems of mobile communication, GPS systems and many

other systems requiring driver’s interaction. The basic system

setup can be fortunately decomposed into subsystems, which

could be treated and solved separately. The basic modules are

as follows (see the diagram Fig. 2):

• Graphic engine

• Graphic output system

• Spatial Audio system [8]

• Motion platform and vibration system

• Scene handling and generation system [9], [10]

• Car physics engine

• General input system

• General purpose output system

• Communication and interconnection module

• Safety and emergency system

Fig. 2: Advanced driving simulation system – basic structure

The modular architecture of a system that is required to

work in almost real time should be well-designed. The

interconnection system, which we use in our modular system

of our driving simulators, is composed of three levels - see

Fig. 3 (described in more details in [11]).

Fig. 3: Modular system based on Manager-Agent-Client architecture

(by [11])

The modules can be treated and operated separately but it is

INTERCONNECTION &

COMMUNICATION

MODULE

GENERAL

INPUT

GENERAL

OUTPUT

MOTION

PLATFORM

DRIVING

CAR

PHYSICS

ENGINE

GRAPHICAL

ENGINE

AUDIO

ENGINE

SCENE

HANDLING

MODULE

ASSETS

DATABASE

AUDIO

OUTPUT

SYSTEM

VIDEO

OUTPUT

SYSTEM

MOTION

PLATFORM

+

VIBRATION

ELEMENTS

SA

FE

TY

SY

ST

EM

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ISBN: 978-1-61804-034-3 286

very useful to take advantage of their interconnection. The

results from tasks computed on one particular module could be

utilized in other modules, which process the same (or very

similar) data. As an example, we can consider a geometric

representation of an area of the virtual scenery. The graphical

engine primarily cuts off an appropriate area of the virtual

world representing the actual driver’s surroundings. Then the

geometry should be worked out according to a particular level

of detail. Such data then enter into rendering process.

Fortunately, the data could be also reused in other modules.

For example, the audio system also needs the geometrical

representation of the world to be able to render the sound

realistically. Other modules, which can take advantage from

such pre-computed data, are for example:

• collision detection subsystem

• traffic management subsystem

• general output subsystem

• car simulation physics engine

III. MATHEMATICAL – PHYSICS SIMULATION ENGINE

The model of the car is done using linear integral-

differential solver. Online processing of input data (signals

from the devices representing driver’s controlling actions) is a

basic requirement on mathematical model of physical behavior

of any interactive simulation system. Such inputs, in case of

driving simulators, are represented by the following signals

(parameters):

• Rate of depression of throttle pedal

• Rate of depression of brake pedal

• Rate of depression of clutch pedal (in case of manual

gear shifting)

• Gear shifter position

• Angle of steering wheel deflection

Those are the basic ones, which can be (and in most cases

of high fidelity simulators are) accompanied with additional

inputs which tell the simulator about the driver’s orders and

intentions (handbrake, handlers, buttons etc.). The physical

“engine” (processing the mathematical car model) should be

able to react on additional inputs which are usually realized

via direct (manual setting) or indirect (realized via activation

of some assistant system) driver’s interventions.

Another important source of information upon which the

mathematical model decides about future steps in car behavior

is an actual state of the objects the car is interacting with. This

includes either road surface beneath each of the wheels or any

object inside the virtual world the car could get in touch with

(drives over or collides). The objects are characterized by a set

of parameters that can be static or dynamic. Their dynamical

behavior could come either from a preprogrammed dynamical

nature (moving objects on the road, traffic, change of road

adhesion due to changeable weather conditions) or they can

result just from driver’s actions (collision with objects etc.).

Upon this above described information and information

about inner structure of the simulated system (axle

architecture, gearbox etc.) the actual behavior (next step) is

computed. The following picture (Fig. 4) illustrates a basic

arrangement of powered wheel in contemporary road vehicles

with following elements:

• Engine with flywheel (1)

• Clutch (2)

• Gearbox (3)

• Differential (4)

• Axle with wheel and suspensions (5)

Fig. 4: A simplified transmission of the initial torque from the engine

up to the wheel surface

The mathematical model of vehicle physics makes always a

kind of compromise in between physical preciseness and

ability of computer to compute online enough short simulation

steps.

The core of the physical engine is composed from partial

function blocks respecting a real structure and links. In our

model these are:

• Engine

• Gearbox

• Wheels (tires)

• Suspensions

• Car body

• Surface of interacting terrain

• Initial parameters of the whole model

• Input parameters from driver and other simulation

models

• Inner variables

In the following picture (Fig. 5), there is the architecture of

our physical engine.

Fig. 5: Architecture of the physics engine

A. Essential elements of mathematical model of vehicle

dynamics

The system of physics of an engine is composed of a

mathematical model of vehicle dynamics and a set of

parameterizing files describing parameters of the vehicle and

terrain and surface parameters with corresponding collision

geometry.

The main processing unit is the physics of the engine, in our

Calculation of

traction forces

Input Engine

Suspension Wheels

Car position Car body tilt

Transmission

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ISBN: 978-1-61804-034-3 287

implementation represented by dynamically linked C++

library, in which a rough architecture of the car is defined

(with use of an open library ODE ver. 0.11.1 [12]). The built-

in architecture corresponds to middle class European car with

McPherson front axle and multi-element rear axle. Driving

power is possible to be applied on front or rear wheels or to be

split in between both (4x4).

The requested output from the computation step is

represented by the vector of variables describing the car body

position orientation (similarly for all wheels) and dynamical

status, i.e. velocity, engine RPM, wheel forces etc. as well as

virtually any variable which would be useful for other driving

simulator subsystems (for example any input for advanced

assistance devices, dashboard, navigation system…).

In our implementation, there are also other modules -

accompanying the rough physics engine - which are intended

to help the user control the simulation module, as well as to

allow him to change some car/surface parameters and/or to

choose from predefined ones. It also serves for visualization of

inner states of the vehicle model, what can be very useful for

early detection of possible nonstandard situations by the user.

Fig. 6: Front end to physical model of the car

The figure above (Fig. 6) shows the user interface of the

mathematical model CarDynamics. The various areas contain

control and information entries. They are as follows:

1. basic controls - restarting the simulation and closure of

an application

2. selection of input devices

3. control panel - "joystick" is intended to control the

steering wheel, throttle and brake, "+" and "-" shift, hand

brake and engine ignition

4. position and rotation of the vehicle - the actual value

after the external simulation step

5. output data of the vehicle - the actual value of the

external simulation step. Velocity (m / s), engine speed

(RPM), transmission gear, the driver inputs (steering

wheel, throttle, brake, clutch, handbrake, ignition), then

the actual duration of the external simulation step (ms).

6. tuning parameters

7. position and rotation of each wheel

8. degree of depression of springs of each of the wheel - the

bottom to the top stop (0% -100%)

B. Visualization and recording module VIS

This module is designed to visualize the detailed behavior

of a vehicle with the ability to record and playback of the car

behavior (all driving parameters). It can be used both for

tuning of the vehicle parameters, online monitoring of the

experiment or for offline playback of recorded experiments

(Fig. 7). This module also serves as a recording device, which

collects all the experimental data for further data analyses.

Fig. 7: Visualization and recording module VIS

C. System parameterization

Mathematical physical simulation module is designed in

such a way its properties can be modified according to the

requirements of possible changes in the simulated track and

the vehicle. According to actual needs, it is possible to adjust

the characteristics of the simulation library. Parameterization

of models is done with use of “ini” files, which are fetched

just before the module is ran or on demand during simulation

runtime.

Setup of mathematics and physics simulation module lays

mainly in the selection of vehicles and tracks properties. The

main parameter here is to set the simulation step, which is the

basis for simulation.

The simulation step is divided into external and internal.

Internal step is the actual simulation of the smallest unit (tick),

which does not change during the course of simulation.

External step is a period, over which the physical model

provides the current status to other modules. External step

must be a whole multiple of an internal step (or can be the

same).

D. Setup of car parameters

The model of car dynamics corresponds to middle-class

European car with front wheel drive, independent suspension

for all four wheels. The gearbox is selectable automatic (with

a hydrodynamic converter) or with a driver controlled

mechanical clutch.

Each parameter of a vehicle can be adjusted in an

appropriate ini file, except of parameters of the model of

wheel that are defined within the characteristics of surface

parameterization. In fact, there is not defined the wheel model

itself, but the model of the dynamic behavior of wheels in

contact with different surfaces.

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ISBN: 978-1-61804-034-3 288

E. Setup of track parameters

The vehicle moves over the virtual track, the visual image is

provided to the driver as the 3D view of objects via

visualization modules to each of the projection channels. The

physical equivalent is mathematical-physical model to

calculate the dynamic behavior.

The individual track parameters can be set in the respective

ini files with a help of set of collision objects. There are

defined parameters including interaction of the wheel (or other

colliding parts of the simulated of the vehicle) with elements

of the virtual track. These are especially surfaces, over which

the vehicle is moving and solid collision objects placed on the

track (or alongside).

IV. CONCLUSION

The whole system of simulator hardware and software

modules is a considerably complex system that requires a

relatively difficult testing procedures before it can be launched

in full operation in real experiments. This process took place

in several stages:

• technological testing of the whole system

• practical testing of system functionality in the form of

free rides

• technology testing of communication, recording and

measuring devices in the simulator system

• undertaking a sample experiment with several probands

The simulation module of car dynamics is a compromise

between two main requirements – first, a highest possible

precession and complexity of the model; second, the available

computer power capable to compute adequate close to real-

time computations, which can include interactively “driver in

loop”. On the other hand, the fidelity the interactive simulation

is always perceived subjectively by the drivers, whose

expectations and requirements on the driving simulator (and

its physical model as well) are often different from what

vehicle engineers suppose.

Since the model of the car dynamics (mainly model of

interaction between the tire and road surface) is still quite

simplified and range of cues the simulator can provide is

limited, the main criteria are experimental drivers’ feelings.

Validation of such a model should be done with use of

sophisticated experiments comparing the drivers’ behaviour in

real vs. simulated environment.

ACKNOWLEDGMENT

The work was supported by a grant of Czech Technology

Agency TACR, TA01030574 “Laboratory for training and

education of professional truck drivers equipped with

advanced truck driving simulator with ability of measuring

and analyzing of psycho-physiological, psychological and

performance data”.

REFERENCES

[1] P. Bouchner, S. Novotný, “System with driving simulation device for HMI measurements”, 8th WSEAS International Conference on

SYSTEMS (part of the 8th CSCC Multiconference), Athens, 2005,

ISBN 960-8457-29-7.

[2] M. Jiřina, P. Bouchner, S. Novotný, “Identification of driver's

drowsiness using driving information, Neural Network World

Volume:20, Issue:6, Pages:773-79, 2010

[3] S. Novotny, P. Bouchner, “Advanced methodology for evaluation of

driver's actual state with use of technical driving data”, PROCEEDINGS OF THE 8TH WSEAS INTERNATIONAL CONFERENCE ON

SYSTEMS THEORY AND SCIENTIFIC COMPUTATION

(ISTAC'08) Book Series: Mathematics and Computers in Science and Engineering, 160-165, 2008

[4] P. Moos, M. Novak, Z. Votruba et al., ”Estimation of failures probability

in alliances of transportation systems” , International Multi-Conference on Engineering and Technological Innovation Location: Orlando, FL

Date: JUN 29-JUL 02, 2008

[5] P. Bures, Z. Belinova, P. Jesty, “Intelligent Transport System architecture Different Approaches and Future Trends”, Data and

Mobility: Transforming Information into Intelligent Traffic and

Transportation Services, Proceedings of the Lakeside Conference 2010. vol. 81, J. Duh, et al., Springer-Verlag Berlin, 2010, pp. 115-125.

[6] P. Bures, “The architecture of traffic and travel information system

based on protocol TPEG”, Proceedings of the 2009 Euro American Conference on Telematics and Information Systems: New Opportunities

to increase Digital Citizenship, Prague, Czech Republic, 2009.

[7] T. Zelinka , M. Svitek, “Adaptive communications solutions in complex transport telematics systems”, Proceedings of the 12th WSEAS

international conference on communications - new aspects of

communications: book series: Recent advances in electrical engineering. Heraklion, Greece, 2008. pp. 206-212

[8] P. Larsson, D. Västfjäll, M. Kleiner “Perception of Self-motion and Presence in Auditory Virtual Environments”, Department of Applied

Acoustics, Chalmers University of Technology, Göteborg, Sweden.

Department of Psychology, Göteborg University, Göteborg, Sweden,Program in Architectural Acoustics, Rensselaer Polytechnic

Institute, Troy, NY, USA.

[9] B. E. Riecke, J. Schulte-Pelkum, M. N. Avraamides, M. Heyde, H. H.

Bülthoff, “Scene Consistency and Spatial Presence Increase the

Sensation of Self-Motion in Virtual Reality”, Max Planck Institute for

Biological Cybernetics, Tübingen, Germany,Department of Psychology, University of Cyprus, SCC, Bauhaus-Universität Weimar, Germany.

[10] D. Krajzewicz, G. Hertkorn, J. Ringel, P. Wagner, “Preparation of

Digital Maps for Traffic Simulation; Part 1: Approach and Algorithms”, German Aerospace Centre, Institute of Transportation Research, Berlin,

Germany.

[11] M. Lalcek ,“A Framework for Modular Architecture of Car Simulators”, (in Czech), Diploma thesis, FTS CTU, Prague, 2006

[12] Russell Smith, Open Dynamic Engine (ODE), Available at:

http://www.ode.org (accessed July 2011)

Petr Bouchner obtained his master degree (2003) in Computer Sciences from Faculty of Electrical Engineering of the Czech Technical University in Prague

and his doctor degree (2007) in Engineering Informatics from Faculty of

Transportation Sciences of the Czech Technical University in Prague. From 2002, he actively participates in projects dealing with driving simulator

development and research in a field of human factors in transportation.

Recently he works as an assistant professor and head of Department of Transporting Technology at the same faculty. He founded and leads the

Driving Simulation Research Group.

Stanislav Novotný obtained his master degree in 2005 in Automation of

Transportation and Telecommunications from Faculty of Transportation

Sciences of Czech Technical University in Prague. He finished his doctoral

studies at the same faculty in 2009 and he contemporarily works there as a

researcher in the Driving Simulation Research Group.

Recent Researches ιn Applied Informatics

ISBN: 978-1-61804-034-3 289