(DVL+)
Automotive
engineering
TOOLBOX
for MATLAB/SIMULINK
Module: DVL-driver
(Version 09.2005)
Dr.-Ing. Aleksandar
D. Rodić
September 2005
To contact the author of
the DVL-driver
please refer to the following address:
Dr.-Eng. Aleksandar D. Rodić
Project manager
Robotics Laboratory
Mihajlo Pupin Institute
11060 Belgrade, SERBIA
Tel.: +381 (0)11 / 2776-174
Fax.: +381 (0)11 / 2775-870
E-mail:
1. PREFICE
From the
point of view of mechanics, a vehicle represents a complex, distinctly
nonlinear, dynamic system with a relatively large number of degrees of freedom
(DOFs), belonging to the class of large-scale dynamic systems. These DOFs
(independent motion directions), especially those that essentially influence
the system's stability and quality of its dynamic behavior, have to be
controlled. The vehicle stability,
quality of its dynamic behavior and maneuvering capabilities depend to a great
extent on the structure of the system and performances of its power-actuating
subsystems. Selection of a best control
strategy and its realization, within the limits of technical capacities of the
system, represents a delicate problem whose solving requires knowledge of
dynamic behavior of the vehicle under different conditions of motion. To that end, mathematical model of the driver-vehicle
system in the interaction with a dynamic environment represents a starting
point in the stage of system design and its automatic control. That was the
strong motivation for developing of the DVL+
automotive engineering toolbox. Its realization in the MathWorks’ Matlab/Simulink
background gives it necessary simplicity for implementation in the design
process, system analysis as well as in education.
2. WHAT IS DVL+?
The DVL+
represents user-oriented, Driver-Vehicle
in the Loop (Fig. 1) modelling
software operating in the MathWorks MATLAB/SIMULINK programming background.
Algorithmic fundament of this software package is extended in particular by
implementation (plus ‘+’) of the complementary knowledge
based identification structures.
Figure 1: The
structure of the hybrid, man-machine, i.e. driver-vehicle dynamic system
DVL+ automotive engineering toolbox has
few functional software modules:
1)
DVL – tyres
2)
DVL - suspension
3)
DVL – power drivetrain
4)
DVL – vehicle dynamics
5)
DVL - driver
6)
DVL – full system
DVL – tyres software module represents non-linear,
empirical model of tyre pneumatics based on
DVL – suspension software module is a linear or a non-linear
model of vehicle suspension system. It includes tyre suspension as well as
4-wheel suspension system.
DVL – power drivetrain software module represents the non-linear
model of power drivetrain (traction) system of road vehicle including the
particular models of: (i) IC engine (gasoline motor), (ii) automatic
transmission system, (iii) vehicle
drivetrain as well as (iv) planar
vehicle dynamics.
DVL – vehicle dynamics software module represents non-linear model of
an entire road vehicle dynamics including vehicle body 3D- or 2D- dynamics,
suspension dynamics as well as tyre dynamics. In that sense, this software
module represents a software simulator of automotive system.
DVL - driver software module represents empirical,
non-linear model of psychological as well as physiological behaviour of driver
as the human operator of a road vehicle. This module, apart to the driver
model, also includes: (i) CAD-model of path geometry, (ii) model of
driver-vehicle (man-machine) interface, (iii) model of power drivetrain system of
a road vehicle as well as (iv) model of planar (longitudinal, lateral, yaw
dynamics) vehicle dynamics.
DVL – full system software module represents integrated modelling
software including all previously mentioned software modules. In that sense,
this module represents a software simulator of the entire (driver-vehicle in
the loop) automotive system.
3. DVL –
driver:
USER GUIDE
DVL-driver represents
the most delicate and the most complex software module of the DVL+ automotive
engineering toolbox. It represents a mathematical description of the driver behaviour
in a realistic way. The present version of the driver modelling software is
based on the research results disposable in the open scientific literature,
author’s research experience in this field as well as on the own driving
experience. Modelling software was designed to be simple for use and flexible
for extension due to the research/developing requests. DVL-driver software, in present version, is suitable for simulation
experiments as well as for possible real-time implementation. With experimental
verification it will be a powerful tool for the synthesis of the advance,
automotive control systems.
3.1 MATLAB VERSION ISSUES
DVL – driver was designed for the MathWorks MATLAB/SIMULINK,
Version 6.5 Release 13, IBM PC compatible and Microsoft Windows XP. Also, it
works with the younger versions of Matlab (e.g. Matlab 7.0, Release 14). DVL-driver uses
standard Matlab functions as well as Simulink libraries. For a proper operation
it needs only basic Matlab toolbox and Simulink.
Remark: To use this modelling software, the basic knowledge
of the Matlab/Simulink is necessary. In that sense, it will be considered that
the customers are familiar with the Matlab/Simulink.
3.2 NECESSARY FACCILITY
For installation and work DVL-driver needs PC Pentium IV at 2.4 [GHz],
512 Mb RAM with Windows XP as the operative system.
Remark: It is recommended for a more comfortable work with DVL-driver, a PC Pentium IV with a
faster microprocessor, e.g. at 3.0 or 3.2 [GHz], to be used. Due to the model
complexity and numerical calculation the faster PC configurations are desirable
but not obliged.
3.3 HOW TO INSTALL?
Take the installation CD and copy
the folder entitled “DVLdriver” to the hard disc of your computer. In such a
way, you define the corresponding path where your modelling software will be
situated (as for example C:|projects\DVLdriver\).
3.4 HOW TO START?
Start the Matlab and set the
Matlabpath as C:\projects\DVLdriver\ including
all belonging subfolders: 22dof, images, Powtrain, Tyremod, driver, paths, suspsys and vehibody. Check if you have already
installed Simulink!? Before start of the Simulink, choose the root folder C:|projects\DVLdriver\. The main
Simulink model DVLDriverModel.mdl exists at this level. Then, start the
Simulink. Apply OPEN command of the Simulink to open the modelling task
entitled: DVLDriverModel (use the
browser for this purpose). After running the program, the following screen, as
it is presented in Fig. 2, should to appear. Then, simply click on the field
SIMULATION, and after that click the START (see Fig. 2). The driver modelling
programme will run on.
Figure 2: The main screen of the driver
modelling software DVL-driver
3.5 GRAPHICAL
INTERFACE
DVL-driver
use Matlab and Simulink graphical interface to plot (monitoring) the system
variables. DVL-driver software module
calculates in every cycle of simulation more than 100 variables. Author of the
software choose for demonstration only particular of them that are
characteristic and interesting for the analysis. Of course, all of the
variables (input, output, intermediate) can be plotted depending on user
choice. During the program operation the following plots can be observed in
this case: (i) the current position of a road vehicle along the desired path and
(ii) the plots (graphs) of the particular important variables. The current
position of the vehicle along the desired path is presented by the plots shown
in the Figs. 3 and 4.
Global
view of the test path as well as the position of the vehicle is presented in
Fig. 3. Black line represents the desired (imposed) path of the vehicle.
Figure 4
represents the “zoom” of the sector [+50,-50] m in the neighbourhood of the current mass centre position of the
car (Fig. 3). The black line denotes the desired path while the red one denotes
the actual trajectory of the vehicle, too. Measuring the shortest distance
between these two paths (black one and red one) user can estimate the
quality/accuracy of the driving skill. Green asterisk “*”
denotes, as well as in the Fig. 3, the current position of the Preview Point of
the car. Yellow circles ‘o’ on the front side
of the car indicate the front (right and left) position lights of the vehicle.
In such a way, one can make difference at the plots between the front and the
rear part of a car in all driving situations.
Figure 3: Plot of the global view of the
desired path in
one characteristic time instant of simulation
Figure 4: Zoom of the particular sector (shown
in Fig. 3) whose centre is in the
current vehicle position (mass centre of road
vehicle)
Figures 3
and 4 includes certain alphanumerical symbols in the left lower edge of graphs
denoting the actual forward speed of the car [km/h], passed time of driving
[sec] and passed effective distance from the start in [m]. Forward speed of the
vehicle can be observed by the plot entitled “[1] Forward speed”, too, as it
will be explained in the text to follow.
Plots that
are presented in Figures 3 and 4 are periodically exchanged each other in order
to present the actual situation on the road, i.e. exact location of road
vehicle along the desired trajectory. Particular
variables of interest can be viewed by the time-plots as it is shown in Fig. 5
by black plots. In this case, the modeling software shows the following plots
although all the other can be also viewed:
[1]
Forward speed [km/h]
[2] Longitudinal & lateral acceleration
[m/s^2]
[3]
Yaw angle & yaw rate [deg] or
[deg/s]
[4]
[5]
[6]
Gear box level
[7]
RPM engine [1/min]
[8]
Engine torque [Nm]
[9]
Side slip angle [deg]
[10]
Steering wheel angle [deg]
[11]
Ground steering angle [deg]
[12]
Braking force [N]
[13]
Throttle position [rad]
[14]
Side error of path tracking [m]
[15]
Longitudinal tyre forces Fxi, i=1,4
[16]
Lateral tyre forces Fyi, i=1,4
To view any of the mentioned graphs
just you need to do is to simply click at the bottom window of the screen entitled
“matlab” (see Fig. 5). Then, let choose a variable or plot from the offered
list by click on the corresponding title with a left mouse key. In order to get a better insight in to the
variables interesting for us to be viewed, look to the Fig. 6 that shows the
relative position of a car along the imposed path. To judge the quality of
driving car let observe the following variables as the results of numerical
simulation: side (lateral) error of path tracking (see Fig. 6), forward speed
of road vehicle (see Fig. 6), longitudinal & lateral accelerations (x- and
y-directions, see Fig. 6), side slip angle of road vehicle (see Fig. 6), yaw angle
(see Fig. 6) and yaw rate, etc. In that sense, in the following subsection
there will be speak a little bit about criteria that was imposed to be
satisfied designing a driver model.
Also, here
will be mentioned the input as well as the output variables of the simulated
model. As input signals to the driver model are taken: (i) variables that
describe the changes of path geometry (certain distances and angles), (ii)
current relative position of the road vehicle with respect to the desired path as
well as (iii) state variables of vehicle dynamics (forward speed, acceleration,
side slip angle, yaw angle, yaw rate, etc).
Output
variables of driver model are: (i) steering wheel angle, (ii) throttle position
(as a consequence of pressing the acceleration pedal), (iii) braking force at
the braking pedal.
Beside
the input and output variables some other interesting variables are enabled to
be displayed via plots (Fig. 5) such as: tyres’ slip ratios, tyre forces,
engine torque, RPM of engine, etc. Of course, the focus of attention is primary
directed before all to the input and output variables of driver model because
it is central point of the DVL – driver
software module.
Figure 5: Graphic interface of the Simulink
used to analyze of the simulation variables
Figure 6: Relative position of a road vehicle
along the desired path - some characteristic variables interesting to be
displayed by graphs during motion
3.5 MODUS OF OPERATION & MODEL PARAMETERS
Driver model
was designed as an empirical MIMO (multi input – multi output), non-linear
function whose parameters were determined according to the real driving
experience (experimental measurements are necessary) as well as according to
the numerous simulation experiments. In that sense the following driving
criteria were imposed to be satisfied:
1)
Criterion
of minimal side (lateral) error of
road vehicle as small as possible along the chosen desired path geometry,
2)
Criterion
of a fine speed adaptation to changes of the path geometry,
3)
Criterion
of a limited lateral acceleration,
4)
Criterion
of limited speed of motion,
5)
Criterion
of a fine driving comfort avoiding large
yaw rate, large side slip angle as well as prevention of jerky motion.
Remark: In this version of DVL-driver, algorithm for avoiding
fixed (e.g. rock on the road) and mobile obstacles (low speed vehicles)
existing on the road was not jet synthesized. This problem can be solved successfully
in the next versions of the DVL-driver modelling software extending the
existing algorithms.
According to the assumed driving
criteria the four driving modus can be defined and tested in simulation
experiments. These are:
1)
Defensive
driving
2)
Offensive
driving
3)
Driving
with constant speed
4)
Non-skill
driver
Defensive driving concerns such set of driver model parameters
that enables careful driving with small side (lateral) errors (fine tracking of
desired path), moderate forward speed of motion, lateral acceleration less then
for example 0.25*g (g is a gravity
acceleration) and without hazard motion (large yaw rate and slipping).
Offensive driving represents such set of model parameters that
ensures a “sporting way” of driving tests with “faster path” but generally with
larger side errors (as a consequence) then in the case of a defensive modus.
Such kind of driving assumes less trajectory tracking accuracy but faster path
and possible appearance a hazard motion in certain situations. The limits for
lateral acceleration, yaw rate as well as for the side slip angle of road
vehicle are enlarged in comparison to the modus 1).
Driving with constant speed is the third modus that satisfies
only one criterion – running with conditionally constant (with small variation)
forward speed of a road vehicle. This modus is suitable for certain simulation
tests where the analysis of a vehicle dynamics in cornering manoeuvres or
driving slalom is demanded.
Non-skill driver modus takes model parameters that enable simulation of
the behaviour of a non-skill driver (an aged
driver or a driver beginner). This modus takes into account larger amounts of time
delays in psychological and physiological reactions of human driver,
non-adequate control gains of manual commands, bad adaptation to changes of
road geometry, etc.
Remark: All parameters of driver model are transparent to the
customers of the software. In that sense it is possible to tune them before
simulation according to the desired driving modus. Tuning the model parameters
depends on the effects that we wish to produce in simulation experiments. By
suitable choice of the model parameters it is possible to simulate the
following driver behaviours: careful, panic, sporting, hazardous, non-skill or
any other. There are no changes of the applied algorithms (designed model) but
only the corresponding parameters. In that sense, the existing parameters in
this version of the DVL-driver should be additionally tuned in real experiments
with a real car and a human driver. In such a way we can derive two kinds of
driver models: (i) a valid model of the particular human driver (person) and,
(ii) driver model of an ideal driver. The second one will serve to design
advance driver assistance control systems.
Customers of the DVL-driver software
module can easily change the driving modus in simulation. Just, it is necessary
to set in advance the corresponding value of the parameter “driving_modus” in the data file entitled
“C:\projects\DVLdriver\driver\init_driver.m”
using Matlab editor (OPEN FILE commands). Simply choose driving_modus =0 (defensive), =1 (offensive), =2 (constant speed)
or =3 (non-skill driver) to set driving modus on a desired value.
Another driver model parameters are
also set in the data file “C:\projects\DVLdriver\driver\init_driver.m”
as well as the values of the speed (MAX_V)
and acceleration (MAX_ar) limits,
time-constants and time-delays, control gains, parameters of the non-linear membership
functions, etc.
Remark: In this version of software customers are advised
only to change the parameters concerning the driving modus as well as the value
of the desired constant speed “V_const” (in the case when choose the
driving_modus=2).
The other parameters used in the
DVL-driver software module are imposed in the following initialization data
files: C:\projects\DVLdriver\Powtrain\init_engine.m,init_trms.m,
init_drt.m, init_long.m, init_longlater.m,C:\projects\DVLdriver\22dof\init_22dof.m.
These files content the parameters of the power drivetrain system as well as
the geometry and dynamic parameters of road vehicle (VW Lupo in this case) and
tyre pneumatics. By changing of these parameters customer is able to impose the
performances of any real automotive system (change the car, engine
characteristics, transmission parameters, brake characteristics, etc.) in
accordance with own research necessities.
3.6 HOW TO IMPOSE THE DESIRED PATH?
Desired path
represents an arbitrary line (curve or linear) defined to describe desired lane
of motion of a road vehicle. In real condition it represents, for example, the
central line of the road, border (margin) line of road surface or simply an
imagined line that defines the desired direction of motion of road vehicle mass
centre in the plane of road surface.
Customer is
enabled to choose (simulate) one of twelve disposable real trajectories. By a
simple change of the flag “ichoice”
in the data-file “C:\projects\DVLdriver\driver\desired_path.m”
(numbers 1,…,12) user imposes the desired path (lane). Disposable set of the
desired trajectories are:
ichoice =1 Straight line road
=2 Move in a circle of radius R=25 m (positive)
=3 Move in a circle of radius R=25 m (negative)
=4 Move along ellipse
=5 Driving piranha slalom
=6 Change
lane manoeuvre (example of avoiding obstacle)
=7 Double change curves (curve-linear path)
=8 Street corner of 90 degrees
=9 Arbitrary defined curvilinear closed path
=10 Driving along the "Verkehr Testuebung Platz" in Braunschweig
=11 Driving around the "Nuerberger Ring" racing path (Mini
~1.7 km)
=12 Driving around the
"Nuerberger Ring" racing path (Full ~5.1 km)
… Other
ones or user own path ...
Images of the previously described
desired paths are given in the Figs. 7 and 8.
Figure 7: CAD models of path geometry of
desired trajectories ichoice=1,…,6
Figure 8: CAD models of path geometry of
desired trajectories ichoice=7,…,12
Trajectories ichoice=1,…,9 represent CAD models of the possible vehicle
trajectories defined as analytic functions (straight line, circle, ellipse) or
simply in a graphic way using COREL DRAW. On the other side, desired paths
numerically denoted as the ichoice=10,..,12
represents real, existing paths. For generation their CAD models the city map
fragment as well as a sketch taken from the Braunschweiger Zeitung have been
used. These two paths are presented in the Fig. 9.
Figure 9: Images of the real paths
“Nuerberger Ring” and “Braunschweiger Verkehrsuebungplatz” taken for designing
CAD models
of the desired paths numerated as ichoice=10,
11 and 12
Customers are also enabled to design
(create) their own desired paths to be simulated. It is possible to do
analytically using Matlab functions or graphically using some of the graphic
programs such as COREL DRAW. All that is necessary to do is to generate the
matrix “path” in the Matlab work-space.
The order of the path-matrix depends on the path length. Generaly, matrix order
has to be path(1:N,1:4) where N is a
number of data samples of the desired trajectory. The first two columns of the
matrix path(1:N,1:2) are X and Y coordinates of the desired path with reference
to the initial coordinate system (see Fig. 6). Note that the X-axis in the zero
time instant (t=0) is always directed along the longitudinal x-axis of a road
vehicle. The third column of the matrix path(1:N,3) represents vector of the
yaw angles along the desired path expressed in radians (see Fig. 6). It is
possible to design as well open as closed trajectories in a way that was
presented in Figs. 7, 8, and 9. Yaw angle values should be in the interval
. The last column in the matrix path(1:N,4) represents vector
of the successive effective distance from the path begins. It is advised that
the distance increments should be chosen to be ~0.10 [m]. It is important to stress out that the yaw angle
hodograph along the designed trajectory must not have discontinuity (to be
smooth) to enable the modelling programme to work without troubles (accurately). Matrix path(1:N,1:4),
after calculation of all rows and
columns, should to be saved as a new desired path using the Matlab command save FileName path;
Also, in the data file “desired_path.m”
the command load
FileName; should to be added in order to enable simulation of the new defined trajectory.
3.7 SIMULATION EXPERIMENTS
DVL-driver
software module enables various extensive simulation experiments with different
desired trajectories. Customer can define arbitrary car parameters as well as to
change the driving modus: offensive, defensive, constant speed or non-skill
driver. In that sense, it is possible to make simulation driving tests in
different conditions and with different set of parameters. Main indicator of
the trajectory tracking accuracy is side
(lateral) error of path tracking. Also, important variables are: forward
speed, yaw rate, side slip angle, longitudinal and lateral acceleration along
the desired path. Driver model, as a MIMO function, at its output generates the
following commands (signals): steering wheel angle, throttle position
(acceleration pedal) and braking force at the braking pedal. These commands are
forwarded to the driver-vehicle interface: steering system, traction system
(engine and drivetrain) and braking cylinders. As it was mentioned in the
previous consideration, a monitoring of all variables is possible using Matlab/Simulink
graphic interface. At the end of a simulation task (when the road vehicle
reaches the end pint of the desired path) a textual messages appear on the
screen as it is presented in Fig. 9.
Figure 10: Final messages of the simulation
task indicating the accuracy of the driving test
The
messages include information about: (i) Maximal side (lateral) error of
trajectory tracking in [m]; (ii) The exact position where the maximal lateral error
has appeared in the initial coordinate system in [m]; (iii) Average side error
along the desired path in [m]; (iv) Average forward speed of road vehicle in
[km/h]; (v) Average slip angle of road vehicle during motion in [rad]. All of
these variables (its absolute values) are also displayed during simulation.
End of
simulation, i.e. reaching the end point of the desired path is accompanied with
the set of successive beep signals in order to alert the user to stop the task.
Beep can be switched off by changing the flag beep_kraj=1 to be beep_kraj=0
in the data file “init_driver.m”.
3.8 MODELING OF SYSTEM PERTURBATION
DVL-driver enables simulation of
external disturbances that act on the system behaviour during motion. As
external perturbations of the system the following ones are considered: (i)
slope of the road, (ii) slippery road and (iii) side wind gust.
Slope of the road represents a
longitudinal inclination of a road surface with respect to the horizontal
plane. Slope influences upon the forward speed of motion of road vehicle. In
that sense, vehicle driver have to adopt the commands of acceleration as well
as braking to the real situation on the road.
Slippery road represents one of the most
significant perturbations acting on the automotive system. Due to the different
conditions of a road surface (wet, ice, oil) the Coulomb’s friction coefficient
of tyre-road interaction is changed. It influences the vehicle dynamics
especially during cornering or fast moving and braking. In this case, driver
have to adopt forward speed of road vehicle as well as steering wheel angle to
the actual surface conditions.
Side wind gust can be very dangerous
perturbation in the case of a strong blowing or changing its direction. Real
car are designed to have the air resistance as small as possible. In spite of this
fact, blowing impact forces cannot be prevented.
Simulink
blocks for modelling (simulation) of system perturbations are presented in
Figs. 11 and 12.
Figure 11:
Simulink blocks – model of power
drivetrain system, model of vehicle dynamics and models of external disturbances
By double
clicking at the left mouse key, with a previous positioning on the Simulink
block “Model of vehicle dynamics” (see the mask in Fig. 2), one enters in to
the lower level (Fig. 11). In the lower
left edge of the screen (marked by a red circle) three Simulink blocks exist.
These blocks represent models of system perturbations (Fig. 12).
Figure 12: Simulink
blocks – models of external disturbances
By
selection of the first block entitled “Slope of road surface” and double
clicking on it, the following interactive Simulink dialog is opened (see Fig.
13). Using a slider gain customer choose a slope angle of a road surface as a
percentage of maximal angle value (it is 90 [deg]). In the Fig. 13, as an
example, the 10% of 90 [deg] was imposed. That represents absolutely 9 [deg].
In a similar
way, using slider gains again, the tyre friction coefficients can be changed as
it is shown in Fig. 14. Double click by mouse on the block entitled “Tyre-road
interaction” (Fig. 12). The Simulink block shown in the Fig. 14 is opened.
Using manual switch choose the desired combination of friction changes. Upper
position of the manual switch enables different (split) friction distribution
at four tyres. Lower position ensures the same friction at the corresponding pairs
of right as well as left side tyres. The rear and front tyres of one side has
the same friction conditions. Using slider gains choose the desired friction
coefficient in the interval
. For 
the road surface is
absolutely dry and clean while for 
it is absolutely slip. The real values should be between 0.30
and 1.00. For example in the Fig. 14 the friction of the first tyre (front
right wheel) is chosen to be 
that corresponds to
the wet road. In the case of icy road or oily surface the value of should to be
introduced.
Figure 13:
Model of the slope of a road surface
Figure 14:
Model of the slippery road (split friction of tyres)
By a double
click on the Simulink block entitled “Model of side wind gust” shown in Fig.
12, corresponding model is opened as it was presented in Fig. 15. Concerning
the model of wind gust, two variables as inputs are necessary to be defined:
(i) wind speed in [km/h] and, (ii) wind direction in [rad]. Using slider gain,
customer is able to choose the speed of wind blowing (e.g. 44 km/h, see Fig.
15). The corresponding wind impact forces depend on the speed of wind blowing.
Direction of wind blowing can be imposed defining the value of corresponding angle.
As an example in the Fig. 15, angle of 
[rad] was assumed.
Zero value corresponds to the blowing direction that is collinear with the 
-axis of the absolute coordinate system (Fig. 6). The angle
changes in the direction opposite to clock wise.
Figure 15:
Model of the side wind gust
Remark: Simulink model
DRVDriver.mdl is initially set to the case of vehicle motion on a horizontal
plane. Tyres’ friction is imposed to correspond to the case of motion over the clean
and dry asphalt.
Remark: In the case of certain
confusion in understanding of this user guide or in the course of work with the
DVL-driver modeling software please contact the author using the e-mail given
at the front page.