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A Comparison Among Different Methods to Estimate Vehicle Sideslip Angle


Abstract and Figures

Accurate measurement of the vehicle sideslip angle is fundamental to improve reliability of the vehicle dynamics control systems focused on stability and developed both for safety and performance optimization. Many experimental procedures to estimate the vehicle sideslip angle have been proposed in the last years, mainly based on GPS, INS and physical models. The aim of this paper is to compare different methods to estimate sideslip angle employing an instrumented vehicle, equipped with a system for data acquisition and time-synchronized storage capabilities, a stand-alone GPS, a GPS aided MEMS-based Attitude and Heading Reference System (AHRS) and specific sensors to collect data on the steering wheel angle and on the position of brake, throttle and clutch pedals. Further information is collected by capturing the available data at the OBD port of the vehicle. Data acquisitions (from all sensors) are synchronized by means of an external triggering signal. After driving sessions performed with specific manoeuvres in order to highlight the main phenomena concerned with the dynamic behaviour of the vehicle, the different estimation procedures have been applied, discussing on the advantages and the degree of reliability of each one of them.
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Abstract—Accurate measurement of the vehicle sideslip
angle is fundamental to improve reliability of the vehicle
dynamics control systems focused on stability and developed
both for safety and performance optimization. Many
experimental procedures to estimate the vehicle sideslip angle
have been proposed in the last years, mainly based on GPS,
INS and physical models.
The aim of this paper is to compare different methods to
estimate sideslip angle employing an instrumented vehicle,
equipped with a system for data acquisition and time-
synchronized storage capabilities, a stand-alone GPS, a GPS
aided MEMS-based Attitude and Heading Reference System
(AHRS) and specific sensors to collect data on the steering
wheel angle and on the position of brake, throttle and clutch
pedals. Further information is collected by capturing the
available data at the OBD port of the vehicle. Data acquisitions
(from all sensors) are synchronized by means of an external
triggering signal.
After driving sessions performed with specific manoeuvres
in order to highlight the main phenomena concerned with the
dynamic behaviour of the vehicle, the different estimation
procedures have been applied, discussing on the advantages
and the degree of reliability of each one of them.
Index Terms Differential GPS Tracking, Inertial
Navigation System, Instrumented Vehicle, Physical Modelling,
Vehicle Sideslip Angle.
I. I
knowledge of the vehicle sideslip angle (ߚ)
(the angle the vehicle center of gravity velocity (V
forms with the longitudinal vehicle axis (x)) is a
fundamental issue to manage all vehicle’s control systems
[1] such as braking [2]-[24], stability [5] and many ADAS
control systems [6], as well as a very important factor
allowing to validate driving simulators [7], [8].
In the event of low-friction situations, it is advantageous
to control the vehicle sideslip angle, preventing it from
assuming unexpected values [9], [10]. However, despite the
absolute benefits deriving from the direct measurement of
Manuscript received June XX, 20XX; revised July XX, 20XX.
F. Farroni is with Dipartimento di Ingegneria Industriale, Università
degli Studi di Napoli Federico II, via Claudio n. 21 80125 Napoli Italy (e-
E. Rocca is with Dipartimento di Ingegneria Industriale, Università degli
Studi di Napoli Federico II, via Claudio n. 21 80125 Napoli Italy (e-mail:
F. Timpone is with Dipartimento di Ingegneria Industriale, Università
degli Studi di Napoli Federico II, via Claudio n. 21 80125 Napoli Italy
(corresponding author: phone: +39 081 76 83263; fax: +39 081 2394165; e-
N. Pasquino is with Dipartimento di Ingegneria Elettrica e delle
Tecnologie dell'Informazione, Università degli Studi di Napoli Federico II,
via Claudio n. 21 80125 Napoli Italy (e-mail:
the sideslip angle and absolute vehicle velocity, these values
are not usually directly measured on production cars and
therefore must be estimated [11], [12].
While the yaw rate (r=dψ/dt) can be easily measured by a
gyroscope, Fig. 1 shows that the estimation of the vehicle
sideslip angle requires the knowledge of the vehicle heading
(ψ) and of the direction of the center of gravity’s velocity
vector (α) (all of them expressed with respect to a dedicated
reference system).
Because of the fundamental importance of ߚ for vehicle
dynamics, several methods have been developed over the
years for its estimation. All the different existing methods
display some strong points, but even some weaknesses, so
that a universally valid and advantageous method has not
been developed yet.
The most widely adopted methods are briefly described in
the following, together with their main advantages and
disadvantages, as well as their main fields of application.
A. Single Antenna GPS
The magnitude and the direction of the center of gravity
velocity vector (V
) can be easily determined once a
suitable reference system has been identified thanks to a
GPS receiver.
Depending on the specific receiver in use, the information
about the velocity vector can be obtained directly (some
models are able to provide the velocity vector’s components
expressed in the reference system the device has been
referred to) or has to be determined in an indirect way. The
latter is the case of a GPS receiver only indicating the
sequence of the taken position at any single time. In this
case, by simple kinematic considerations, being the elapsed
time between two consecutive points known, also the
velocity vector’s magnitude can be determined.
Once the velocity vector pertaining to the vehicle’s center
of gravity has been fully characterized in its components,
the ߙ angle is defined with respect to the assumed
coordinate system. If the vehicle is equipped with some
gyroscopes, then their signal can be integrated, and the
A Comparison Among Different Methods to
Estimate Vehicle Sideslip Angle
F. Farroni, N. Pasquino, E. Rocca, F. Timpone
Fig. 1. Vehicle Dynamics characteristic Angles.
vehicle’s heading angle (ψ) can be obtained. From the
knowledge of these two angles, the vehicle sideslip angle ߚ
is immediately determined.
One of the main limits affecting this procedure is
represented by its variable accuracy: position uncertainty in
a modern GPS is largely determined by the number of
satellites in view and can reach in some cases the
unacceptable magnitude of a few meters.
For these reasons, the single-antenna-GPS method is
often integrated with some correction algorithm, such as the
differential correction method [13]. Other improvements of
this method use a higher number of GPS like the Double
Antenna GPS method discussed below.
B. Double Antenna GPS
Also a double antenna GPS can be used for vehicle
sideslip angle measurement [12], [14]: either two separate
GPS receivers or a single receiver equipped with two
different antennas can be used, theoretically obtaining
equivalent accuracy. The purpose of using two different
antennas is to directly calculate the vehicle’s orientation
with respect to an ‘absolute’ reference coordinate frame,
with no necessity of using an additional gyroscope.
Using a double-antenna GPS two different points of the
same vehicle, which can be assumed as a completely rigid
body, can be simultaneously characterized.
The use of a double-antenna GPS is very easy to
understand since a single-antenna GPS cannot measure the
vehicle sideslip angle by itself, but always needs to be
flanked by a gyroscope.
C. Inertial Navigation System signals Direct Integration
One of the easiest ways to determine the vehicle sideslip
angle consists in the direct integration of the signals coming
from the accelerometers and gyroscopes (or, more often,
from the Inertial Navigation System (INS) based on the
advanced application of inertial sensors (accelerometers)
and rotational speed sensors (gyroscopes)) installed on-
board the vehicle itself [15].
Thanks to this method, no vehicle model nor other
instrument is needed. The results obtained from the adoption
of this simple procedure are not always acceptable, because
they tend to be affected by a high rate of error, since they
are based on the direct integration of the accelerometer
D. Physical models
This approach for the sideslip angle estimation is based
on the use of some physical models, possibly running in
real-time, describing the vehicle’s behavior, such as the
‘Bicycle model’ or the ‘Quadricycle model’ [16].
Once the chosen physical model is known, in order to
determine the vehicle sideslip angle, it is sufficient to
strictly apply the model’s equations.
The precision of the obtained results is highly affected by
the degree of complexity of the employed model, that is by
the reliability of the physical and geometrical parameters
inserted in the model, like the vehicle’s characteristic
lengths and dimensions, its inertial features, transmission
ratios, tyres’ behavior parameters and so on [17].
A. Vehicle
The experimental tests have been carried out on a FIAT
Multipla 1.9 JTD, made available by the DICEA
(Department of Civil, Architectural and Environmental
Engineering) of University of Naples ‘Federico II’ [18].
This vehicle has been used extensively in past researches to
monitor the behaviour of a driver both for analytical model
formulation [19], and for testing of Driving Assistance
Systems (DAS) logics.
In order to define the considered test-vehicle as precisely
as possible, its physical and geometric parameters have been
carefully evaluated by means of the available technical
Tyre behaviour has been modelled by means of a ‘Magic
Formula’ model. The vehicle was equipped with the
measurement instruments described in the following.
B. Description of the installed hardware
The vehicle is equipped with a system for data acquisition
and time-synchronized storage capabilities. The core of the
system is a National Instruments (NI) CompactDAQ
chassis, with up to eight measurement-specific modules. All
the sensors installed on-board are in direct communication
with the DAQ’s control software.
The DAQ receives digital and analog signals via
appropriate modules, as well as data and communications
via a CAN (Controlled Area Network) interface. In order to
process the big amount of acquired data, the CompactDAQ
is connected to a PC controller. The synchronization and
acquisition software is based on LabVIEW.
A TOPCON GPS supplies positioning and kinematic data
using a dual satellite constellation (GPS and GLONASS).
The GPS is equipped with an external antenna, installed on
the vehicle’s rooftop. The GPS dual-frequency receiver is
equipped with an internal memory allowing to store raw
satellite data for post-processing applications. An XSENS
MTi-G device embedding a GPS and an Inertial
Measurement Unit (IMU), together with an AHRS processor
have been placed on-board as near as possible to the center
of gravity (ܩ), with the aim of minimizing the centripetal
acceleration deriving from the rotations of the vehicle. The
GPS system complements the inertial system by providing a
stable position and velocity output. As a result, the errors
introduced by integrating accelerometer and gyroscope
signals (dead reckoning) are corrected by the position and
velocity given by the GPS receiver, resulting in an output
that is both stable and able to track fast changing
Three potentiometers are used to collect data on the
position of the brake, throttle and clutch pedals. The steering
wheel angle is measured by a draw-wire displacement
Other on-board information is also collected by capturing
the available data at the OBD (On Board Diagnostic)-II port
of the vehicle. Data acquisitions (from all sensors) are
synchronized by means of an external triggering signal.
The MTiG control logic is based on inertial sensors and a
miniature GPS receiver, also including other supporting
sensors, such as a 3D magnetometer and a static pressure
Orientation data are provided as relative orientation
between the above-defined reference system and the LTP
(Local Tangent Plane) reference system. LTP is a reference
system defined by the tangent plane to the Earth surface in
every point. According to the axes’ orientation, it is possible
to distinguish between different reference systems, such as
(‘East North Up’) or LTP
(‘North West Up’). The
‘default’ LTP reference system with respect to which the
XSENS provides the results is LTP
A. Available Data Channels
A LabVIEW script has been used for the acquisition of
data from the different on-board instruments, with a
sampling frequency of 10 Hz.
The collected GPS data are the time, the latitude, the
longitude, and the altitude of the GPS antenna, hemispheres
(North or South and East or West), the speed of the GPS
antenna and the number of visible satellites.
The following data are gathered from the XSENS sensor:
the three Euler angles (roll, pitch, and yaw components
around vehicle longitudinal, lateral and vertical axes the
three angular velocities of vehicle (roll, pitch, and yaw rate)
and the three linear accelerations of vehicle (longitudinal,
lateral, and vertical acceleration).
Data from the other sensors are the steering wheel angle
(positive for clockwise rotation out of neutral position), the
longitudinal speed of both the rear wheels of vehicle
(computed by means of a rotational encoder), the
normalized excursion of the vehicle pedals (brake, clutch,
and throttle pedals), and the engine’s rotation speed).
By direct connection to the XSENS device, some other
useful information can be retrieved, the main one being the
components of the vehicle’s velocity vector in the LTP
reference system.
In this section a description of the performed tests is
reported, together with a brief description of the particular
‘test protocol’ implemented.
A. Experimental Site
Some preliminary test drives have been performed close
to the location of the Engineering Faculty of the University
of Naples Federico II in order to become familiar with the
measurement equipment, configure it.
The final test session has been carried out on a closed race
track, an open-sky and abandoned parking area of a mall in
Northern Naples (coordinates: 40.896776° N; 14.312782°
E). The site fulfils the experimental requirements: no vehicle
transit, no considerable obstructions to GPS signals, and
quite planar area.
Some fixed elements in the site, such as road markings,
are used to define the reference points of each manoeuvres
performed in the test session.
Test drives were performed in dry road and good weather
conditions (cloud-free sky).
B. Test Protocol Definition
The test protocol has been defined following the criterion
of performing manoeuvres determining a considerable
sideslip angle occurrence.
In the following the different steps of the chosen test
protocol for the drive sessions are reported(Fig. 2):
Start: all the simulations start and finish at the same point,
marked with the chess flags.
Idle Period: before any drive is performed, a preliminary
acquisition with stationary vehicle has to be carried out,
with the aim of identifying the bias affecting all the
instrumental signals. The idle period usually lasts some tens
of seconds.
Straight drive: all drive sessions start with a set of straight
drives on a closed loop, separated by curves to revert the
direction. The straight drive are used to validate the initial
condition on yaw angle, computed by means of a compass:
if the compass procedure is correct, during the straight drive
the vehicle sideslip angle is supposed to be null, as the
centre of gravity’s velocity vector is perfectly aligned with
the vehicle’s heading.
Circle drive: performed with constant steering angle and
constant vehicle speed to get a constant sufficiently high
vehicle sideslip angle [20].
“8” shaped manoeuvres: after the circle drive some
manoeuvres on a “8-shaped” trajectory have been
performed. Also in this case, this manoeuvre has the purpose
of letting some higher vehicle sideslip angles occur.
Hard Braking: the final path consists in a straight drive,
with a very hard braking manoeuvre performed at sustained
speed, aiming to determine tyres’ lock up and subsequent
ABS logic intervention.
Stop: the drive session stops in correspondence of the
same point it started. Thanks to the white stripes on the road
surface, the exact point can be found, and the vehicle’s final
orientation is made to be approximately coincident with the
initial one.
The different phases of the above described test protocol
can be easily discerned on the sample vehicle sideslip angle
plot (obtained by means of 1Cbis differential GPS procedure
explained in the following), traced against measurement
time. The different steps of the data acquisition session can
be discerned (Fig. 3); in particular:
Idle Period: this phase can be easily recognized in the
plot, as the sideslip angle has been put null when the vehicle
is not moving (V
< 5 km/h).
Straight drive: as it is evident, during a straight drive the
vehicle sideslip angle is equal to zero, since the direction of
Fig. 2.
Vehicle’s trajectory during the performance of the defined test
protocol, superimposed to the satellite image of the selected area, and
colored according to the el
apsed time from the beginning of the drive session
[Blue=Initial position; Red=Final position]. The initial and final points
coincide, and have been marked with the chess flags.
the V
vector is coincident with the direction of the vehicle-
anchored x axis, indicating the vehicle’s heading.
In Fig. 3 it is possible to see that the straight drive
portions are characterized by null sideslip angle indeed: the
visible regular spikes represent the cyclic curves performed
to invert the vehicle’s direction, as depicted in previous Fig.
2. All the spikes have the same sign, since all the curves
have been performed in the same direction (clockwise).
Circle drive: as above described, the circle drive
manoeuvre has been performed with constant steering angle
and vehicle speed. This feature allows a very rapid
identification of this particular drive session’s step in the
plot of the vehicle sideslip angle, as the ߚ signals oscillates
around a well-defined value, different from zero.
“8” shaped manoeuvres: this path can be discerned in
the plot considering that during an “8” shaped manoeuvre
curves are performed in both directions, so that the steering
wheel has to pass through the neutral’ position at every
inversion. For this reason, it is easy to understand the
vehicle sideslip angle oscillates around an approximately
null value, reaching about the same magnitude in both
directions, as depicted in Fig. 3.
Hard Braking: the hard braking can be easily discerned
from the vehicle sideslip angle plot by the null portion of the
curve, corresponding to the vehicle complete stop after the
braking process.
The slight oscillation right before the null value (before
the vehicle has come to a complete stop) is due to the fact
the vehicle is rapidly decelerating, so that the lateral
component of velocity is comparable with the longitudinal
one, making sideslip angle value oscillating.
V. I
To estimate the vehicle sideslip angle different procedures
have been employed based on GPS, on INS Signal Direct
Integration and on Bicycle Model.
The first procedure (1A) makes use of the XSENS device,
using both the GPS receiver and the gyroscopes.
The vehicle sideslip angle is determined as the difference
between the ߙ and ߰ angles, computed with respect to the
frame (Fig. 1).
The ߙ angle is determined once the components of the
center of gravity’s velocity vector (V
) are known, from the
XSENS data acquisition. It is important to underline that the
XSENS platform automatically calculates the velocity
vector’s components in the LTP
reference system.
As it is evident in Fig. 4, starting from the vector’s
component it is immediate to obtain the ߙ angle as:
The ߰ angle can be obtained either directly from the
XSENS platform or by the integration of the vehicle’s yaw
rate signal, acquired by the INS sensor.
Also the second procedure (1B) makes use of the XSENS
device, using both the GPS receiver and the gyroscopes, and
simply applies the vehicle sideslip angle definition,
reporting the velocity vector’s components into the moving,
vehicle-anchored {ܩݔݕݖ} reference system to know the ݑ
and ݒ components.
Once the ݑ and ݒ components have been determined, the
vehicle sideslip angle is simply determined as:
The third procedure (1C) makes use of both the TOPCON
GPS and XSENS devices.
The vehicle sideslip angle is determined as in the previous
procedure 1A, but in this case the ߙ angle is obtained thanks
to a different method.
The TOPCON GPS receiver simply provides the
terrestrial coordinates of all the points belonging to the
vehicle’s trajectory (with a data rate depending on the
configured working frequency), and the magnitude of the
velocity vector needed to connect two consecutive points ܲ1
and ܲ2.
In order to compute the ߙ angle, some simple kinematic
consideration are employed (Fig. 5).
The instantaneous velocity of the vehicle in the ܲ1 point
can be obtained as:
In such cases, the instantaneous velocity vector can be
assumed to be parallel to the displacement vector at any
given time, whose direction can be easily identified through
the difference of the coordinates recorded by the GPS
receiver. Once the velocity vector has been fully identified,
its inclination angle ߙ is used for the calculations.
Regarding the ߰ angle, it can be obtained either directly
from the XSENS platform or integrating the vehicle’s yaw
rate signal acquired by the gyroscope.
One of the main limitations affecting the preciseness of
the just described procedure is represented by its heavy
dependence on the quality of the GPS signal, hence from the
Fig. 3. Sample vehicle sideslip angle plot vs. measurement time.
Fig. 4. Decomposition of the vehicle’s centre of gravity’s velocity vector
along the moving vehicle-anchored {
} reference system and along the
absolute {
} reference system.
number of satellites in view of the receiver.
For this reason, some signal improvements have been
performed in order to increase the accuracy of the sideslip
angle estimation in the following procedure.
The fourth procedure (1C bis) is very similar to the 1C
one, since it is based on the same physical and analytical
considerations. The only difference between the two
procedures is represented by the GPS data acquisition: in
order to enhance the signal’s preciseness and reliability a
differential correction has been applied [13].
In the differential procedure (DGPS) a GPS receiver
tracking a satellite always experiences a number of ranging
errors, which will be translated into positioning errors. The
commonality of range errors between two receivers
simultaneously tracking a satellite at two different locations
can be exploited: common errors can be removed by
differencing. Recording simultaneous range observations
allows differential processing at a later time, or in real time,
if a suitable communication device is available.
The differential correction considered in the current paper
has been carried out off-line, referring to the ephemeris data
published online after the data acquisition session was
A highly precise GPS device(‘Trimble’ GPS: receiver and
antenna) has been positioned in a fixed place for the
differential procedure application and has been used as the
reference station, in order to differentiate the data acquired
by the TOPCON GPS (the mobile station).
In order to allow the reference station to fix its position,
the reference GPS has been placed in position about 1 hour
before the drive sessions’ beginning.
B. INS Signal Direct Integration
These procedures only use the accelerometers’ signal,
obtained from the XSENS acquisition.
The first procedure (2A) is a purely kinematic method for
the vehicle sideslip angle determination, based on the
integration of the accelerometers’ signals; for this reason,
the only required instruments are the accelerometers and the
The accelerometers provide a measurement of
acceleration referred to the vehicle-anchored moving
reference system {ܩݔݕݖ}. To express the center of gravity’s
acceleration vector
with respect to the LTP
system it is necessary to implement a coordinate
transformation, so all the calculations are performed in the
absolute reference system. A crucial importance is assumed
by the Euler Angles used since these highly affect the
obtained accelerations in the {ܩݔݕݖ} reference system, and
in turn the resulting velocities and sideslip angle [21].
By integration of the acceleration components the
velocities, expressed in the ‘absolute’ LTP
system, are obtained.
The initial condition for the integration of the
accelerations has been set to zero as the vehicle had null
velocity during the first acquired seconds (idle period).
After integration, the velocity components have to be
reported again into the {ܩݔݕݖ} moving reference system. At
this point, the ݑ and ݒ components, namely the V
components in the {ܩݔݕݖ} reference frame, have been
obtained, hence it is immediate to obtain the desired vehicle
sideslip angle as (2).
The second Procedure (2B) calculates the vehicle sideslip
angle making use of the XSENS inertial station and of the
rotational encoder fitted on the rear wheels.
This procedure is based on the vehicle sideslip angle
definition, (2).
Regarding the ݑ component, this has been directly
measured through the rotational encoders installed on the
vehicle’s rear wheels (it is calculated as the mathematical
average of the values provided by the two encoders).
The ݒ component has been obtained from the Equation
reported below, where the lateral component of the ࢇܩ
vector with respect to the {ܩݔݕݖ} vehicle-anchored moving
reference system is defined:
Where the yaw rate ݎ is measured by the gyroscope.
Once the ݑ and ݒ components have been obtained, the
vehicle sideslip angle is obtained by applying its definition.
The third procedure (2C) aims to determine the vehicle
sideslip angle starting from the signals obtained from the
accelerometers and gyroscopes embedded into the XSENS
inertial station, installed on-board.
This procedure makes use of the following Equations:
Once the a
, a
and ݎ = dψ/dt quantities have been
obtained from the XSENS data, these equations can be
solved, determining the ݑ and ݒ.
Once the ݑ and ݒ components have been obtained, the
vehicle sideslip angle is obtained by applying its definition.
C. Bicycle Model
This procedure uses a vehicle dynamics’ physical model
to predict the vehicle sideslip angle, given the input
The physical model considered for the current paper is the
so-called bicycle model [16].
Both the kinematic bicycle model (absence of drift) and
the dynamic bicycle model (with drift) have been
considered, in order to provide a comparison between the
different cases.
In the first procedure (3A) the Classic Kinematic Bicycle
is used, which is only valid in case of low vehicle’s speed
and high curvature radius of the performed trajectory, and
therefore very uncommon to be observed in actual
conditions. The input signals for this model are the vehicle’s
longitudinal speed (u) and the steering angle of the vehicle’s
Fig. 5. Determination of the instantaneous vehicle’s velocity vector
from its centre of gravity’s trajectory.
front wheels (ߜ).
The vehicle sideslip angle, in case of kinematic
conditions, can be easily determined by means of simple
geometric and trigonometric considerations, Fig. 6. Being
the (ACB) ̂ angle equal to ߜ, it is immediate to obtain:
Combining the above reported Equations (6) it is possible
to obtain the vehicle sideslip angle according to the Classic
Kinematic Bicycle Model
In the procedure (3B) the Classic Dynamic Bicycle model
is used. Taking into consideration the presence of a certain
sideslip angle makes the model closer to reality than the
above kinematic model, since greater speeds and real
manoeuvres can be considered.
Also in this case the input signals for this subsystem are
the vehicle’s longitudinal speed (u) and the steering angle of
the vehicle’s front wheels (ߜ).
Making use of these signals, the ݑ and ݒ quantities can be
determined by means of the following Equations [16]:
∙ ܽ
− ܥ
∙ ܽ
∙ ܽ
+ ܥ
∙ ܽ
∙ ቊ
ቋ + ܥ
∙ ߜ∙ ቐ
After ݒ and ݎ have been determined, the vehicle’s slip
angle can be obtained (2).
The vehicle slip angle estimation method that exhibits the
best fit with what is physically expected is obtained by
procedures 1Cbis (GPS with differential correction), 3A and
3B (Bycicle Model) (Fig. 7). The other GPS based
procedures still provide good results (Fig. 8). In revers, INS
based methods show results not compliant with physical
expectations probably due to errors in Euler Angles’
estimation attributable to the magnetometer, whose signal is
highly affected by the metallic masses on-board the test
vehicle. Future analysis and experimental activities will
provide a sounder base for the claim of the better
performance of procedures 1Cbis, 3A and 3B. Future
experiments will also be carried out according to a designed
experimental plan, and results from the experimental
campaign will be analyzed by means of statistical data
analysis techniques to determine the influence of some
relevant factors on the estimates provided by the different
methods [22]-[26].
Future developments will also deal with a real-time GPS
differential procedure, with a double antenna GPS
procedure, with combined methods able to fuse signals
coming out from different devices treating them by means of
statistical methods.
[1] R. Rajamani, "Vehicle Dynamics and Control", Springer, 2012.
[2] R. Russo, M. Terzo, F. Timpone, "Software in the loop development
and validation of a Cornering Brake Control logic", Vehicle System
Dynamics, vol. 45, pp. 149-163, 2007.
[3] M. Carro, M. Russo, F. Timpone, "A modern approach to design
optimization and development of vehicles control systems",
Proceedings of the Mini Conference on Vehicle System Dynamics,
Identification and Anomalies, pp. 603-610, 2002.
[4] M. Terzo, F. Timpone, "The control of the handling of a front wheel
drive vehicle by means of a magnetorheological differential",
International Review of Mechanical Engineering, Volume 7, Issue 3,
Pages 395-401, 2013.
[5] D. Piyabongkarn, R. Rajamani, J. A. Grogg, J. Y. Lew, "Development
and Experimental Evaluation of a Slip Angle Estimator for Vehicle
Stability Control", IEEE transactions on control systems technology,
vol. 17, n. 1, 2009.
[6] G. N. Bifulco, L. Pariota, F. Simonelli, R. Di Pace, "Development and
testing of a fully Adaptive Cruise Control system", Transportation
Research Part C: Emerging Technologies, vol. 29, pp. 156-170, 2013.
[7] M. Doumiati, A. Victorino, D. Lechner, G. Baffet, A. Charara,
"Observers for vehicle tyre/road forces estimations: experimental
validation", Vehicle System Dynamics, vol. 48, no. 11, pp. 1345-1378,
[8] X. Gao, Z. Yu, "Nonlinear Estimation of Vehicle Sideslip Angle
Based on Adaptive Extended Kalman Filter", SAE Technical Paper,
no. 2010-01-0117, 2010.
[9] F. Farroni, M. Russo, R. Russo, F. Timpone, "A physical–analytical
model for a real-time local grip estimation of tyre rubber in sliding
contact with road asperities", Proceedings of the Institution of
Mechanical Engineers, Part D: Journal of Automobile Engineering,
vol. 228, no. 8, 2014.
[10] H. F. Grip, L. Imsland, T. A. Johansen, T. I. Fossen, J. C. Kalkkuhl,
A. Suiss, "Nonlinear vehicle side-slip estimation with friction
adaption", Automatica, vol. 44, pp. 611-622, 2008.
[11] J. Ryu, E. J. Rossetter and J. C. Gerdes, "Vehicle Sideslip and Roll
Parameter Estimation using GPS", Proceedings of the AVEC
International Symposium on Advanced Vehicle Control, 2002.
[12] D. N. Piyabongkarn, R. Rajamani, J. A. Grogg, J. Y. Lew,
"Development and Experimental Evaluation of a Slip Angle Estimator
Fig. 6. 'Classic' Kinematic Bicycle Model.
Fig. 7. Comparison between vehicle sideslip angle measured by GPS-based
Differential Procedure (Procedure 1C bis, red-colored curve), Kinematic
Bicycle Model (Procedure 3A, green
colored curve) and Dynamic Bicycle
Fig. 8. Vehicle
slip angle with Procedures 1B (red
colored curve) and
for Vehicle Stability Control," IEEE Transactions On Control
Systems Technology, vol. 17, no. 1, 2009.
[13] G. J. Morgan-Owen, G. T. Johnston, "Differential GPS Positioning",
Electronics & Communication Engineering Journal, vol. 7, no. 1,
[14] P. Misra and P. Enge, "Global Positioning System - Signals,
Measurements and Performance", Lincoln (MA), Ganga-Jamuna
Press, 2004.
[15] A. D. King; Marconi Electric Systems (MES), "Inertial Navigation -
Forty Years of Evolution", GEC (General Electric Company) Review,
vol. 13, no. 3, 1998.
[16] M. Guiggiani, "The Science of Vehicle Dynamics", Springer, 2014.
[17] F. Farroni, M. Russo, R. Russo, M. Terzo, F. Timpone, "A combined
use of phase plane and handling diagram method to study the
influence of tyre and vehicle characteristics on stability", Vehicle
System Dynamics, vol. 51, pp. 1265-1285, 2013.
[18] A. Montella, L. Pariota, F. Galante, L. Imbriani, M. Mauriello,
"Prediction of Drivers' Speed Behaviour on Rural Motorways Based
on an Instrumented Vehicle Study", Transportation Research Record:
Journal of Transportation Research Board, Transportation Research
Board of the National Academies, Washington, D.C., n. 2434, pp. 52-
62, 2014.
[19] G. N. Bifulco, L. Pariota, M. Brackstone, M. McDonald, "Driving
behaviour models enabling the simulation of Advanced Driving
Assistance Systems: revisiting the Action Point paradigm",
Transportation Research Part C: Emerging Technologies, n. 36, pp.
352-366, 2013.
[20] F. Farroni, D. Giordano, M. Russo, M. Terzo, F. Timpone, "On the
influence of anti-roll stiffness on vehicle stability and proposal of an
innovative semi-active magnetorheological fluid anti-roll bar", RAAD
2012 - 21TH International Workshop on Robotics in Alpe-Adria-
Danube Region - ISBN No: 978-88-95430-45-4.
[21] F. Farroni, "Development of a grip & thermodynamics sensitive
tyre/road interaction forces characterization procedure employed in
high-performance vehicles simulation", PhD thesis, University of
Naples "Federico II", 2014.
[22] A. M. Lesk, "On the calculation of Euler angles from a rotation
matrix", International Journal of Mathematical Education in Science
and Technology, vol 17, no. 3, 1986.
[23] L. Angrisani, M. D’Apuzzo, D. Grillo, N. Pasquino, R. Schiano Lo
Moriello, "A New Time-Domain Method for Frequency Measurement
of Sinusoidal Signals in Critical Noise Conditions", Measurement,
vol. 49, no. 1, pp. 368–381, 2014
doi: 10.1016/j.measurement.2013.11.034;
[24] P. Bifulco, A. Marrese, N. Pasquino, R. Schiano lo Moriello,
"Statistical Characterization of Human Exposure to GSM
Electromagnetic Field", 20th IMeKO TC4 Int. Symp., pp. 780-785,
Benevento – Italy, July 15-17, 2014.
[25] P. Cennamo, P. Caputo, A. Giorgio, A. Moretti, N. Pasquino,
"Biofilms on Tuff Stones at Historical Sites: Identification and
Removal by Nonthermal Effects of Radiofrequencies", Microbial
Ecology, vol. 66, no. 3, pp. 659-668, 2013.
[26] M. D’Arco, A. Liccardo, N. Pasquino, "ANOVA-Based Approach for
DAC Diagnostics", IEEE Trans. Instrum. Meas., vol. 61, no. 7, pp.
1874-1882, 2012.
[27] G. Betta, D. Capriglione, N. Pasquino, "Experimental Investigation on
Workers’ Exposure to Electromagnetic Fields in Proximity of
Magnetic Resonance Imaging Systems", Measurement, vol. 45, no. 2,
pp. 199-206, 2012.
... With this approach the model can correct for sensors inaccuracies and unwanted measurements, but information on tyre parameter and road condition is needed for the tyre model. Many observers have been developed based on this approach [4] [5] [6] [7] [8], where different tyre models have been used. This paper proposes a new method for estimating the fundamental variables of vehicle dynamics and, at the same time, thanks to the use of a simple Magic formula characterized by four parameters obtained from extensive offline testing [9][10], the estimation of the lateral friction coefficient, through the use of an extended Kalman filter. ...
Full-text available
The performance of the vehicle’s active safety systems depends on accurate knowledge of the vehicle state, and the frictional forces resulting from tyre contact and the road surface. This paper aims to estimate the vehicle states and tyre-road coefficient of friction through and Extended Kalman Filter (EKF), integrated with the Double-Track model and the Pacejka Magic Formula that allows knowledge of the lateral force of the tyre. Besides, this approach can estimate the overall coefficient of lateral friction on each side of the vehicle, left and right respectively. Simulations based on a reference vehicle model are performed on different road surfaces and driving manoeuvres to verify the effectiveness of the proposed estimation method, in order to obtain good performance from different vehicle control systems.
... In literature, it is possible to find algorithms based on GPS data acquisition both with single antenna and with double antenna [11,19,20], on Inertial Navigation Systems (INS) signals direct integration procedures [21], on identification by means of physical models and observers [1,22], on linear and nonlinear statistical based procedures [23,24]. ...
... The data acquisition has been possible thanks to all the instruments that equipped the vehicle [11,16]: the core of the system is a National Instruments (NI) Compact DAQ chassis, with up to eight measurement-specific modules. The DAQ receives digital and analogic signals via appropriate modules, as well as data and communications via a CAN (Controller Area Network) interface. ...
Conference Paper
The main idea of the present work is to define the domain in which it is possible to adopt very simple models of vehicle dynamics for applications in the testing of Advanced Driver Assistance Systems (ADAS) in lieu of complex models. The aim is to reduce the computational burden, and consequently the computing time. In particular, in the paper, the performances of a very simple model of vehicle dynamics, the Single Track with linear tires, have been compared with those of a complex and complete model, with non-linear tires, included in a commercial software (IPG CarMaker). For sake of shortness, the comparison has been carried out focusing on the lateral dynamical behaviour, and consequently the testing of a Lane Keeping Assistant (LKA) system has been carried out. Of course both the vehicle dynamic models, and the ADAS system have been integrated in a common simulation environment (Simulink), and tested in the standard traffic scenarios defined in EuroNCAP test protocols.
... In order to analyse the degradation of the performance caused by wear, the tires should start the test in brand-new conditions; use of the DATRON device, due to its optical working principle, is limited to dry tracks; a possible alternative can be provided by observers for sideslip angle estimation [27,28] or virtual sensors [20], but their full reliability still remains to be evaluated. ...
The most powerful engine, the most sophisticated aerodynamic devices or the most complex control systems will not improve vehicle performances if the forces exchanged with the road are not optimized by proper employment and knowledge of tires. The vehicle interface with the ground is constituted by the sum of small surfaces, wide about as one of our palms, in which tire/road interaction forces are exchanged. From this it is clear to see how the optimization of tire behavior represents a key-factor in the definition of the best setup of the whole vehicle.Nowadays, people and companies playing a role in automotive sector are looking for the optimal solution to model and understand tire's behavior both in experimental and simulation environments. The studies carried out and the tool developed herein demonstrate a new approach in tire characterization and in vehicle simulation procedures. This enables the reproduction of the dynamic response of a tire through the use of specific track sessions, carried out with the aim to employ the vehicle as a moving lab.The final product, named TRICK tool (Tire/Road Interaction Characterization and Knowledge), comprises of a vehicle model which processes experimental signals acquired from vehicle CAN bus and from sideslip angle estimation additional instrumentation. The output of the tool is several extra "virtual telemetry" channels, based on the time history of the acquired signals and containing force and slip estimations, useful to provide tire interaction characteristics. TRICK results can be integrated with the physical models developed by the Vehicle Dynamics UniNa research group, providing a multitude of working solutions and constituting an ideal instrument for the prediction and the simulation of the real tire dynamics.
Full-text available
Recently, land vehicle navigation, and especially by the use of low-cost sensors, has been the object of a huge level of research interest. Consumer Portable Devices (CPDs) such as tablets and smartphones are being widely used by many consumers all over the world. CPDs contain sensors (accelerometers, gyroscopes, magnetometer, etc.) that can be used for many land vehicle applications such as navigation. This paper presents a novel approach for estimating steering wheel angles using CPD accelerometers by attaching CPDs to the steering wheel. The land vehicle change of heading is then computed from the estimated steering wheel angle. The calculated change of heading is used to update the navigation filter to aid the onboard Inertial Measurement Unit (IMU) through the use of an Extended Kalman Filter (EKF) in GNSS-denied environments. Four main factors that may affect the steering wheel angle accuracy are considered and modeled during steering angle estimations: static onboard IMU leveling, inclination angle of the steering wheel, vehicle acceleration, and vehicle inclination. In addition, these factors are assessed for their effects on the final result. Therefore, three methods are proposed for steering angle estimation: non-compensated, partially-compensated, and fully-compensated methods. A road experimental test was carried out using a Pixhawk (PX4) navigation system, iPad Air, and the OBD-II interface. The average Root Mean Square Error (RMSE) of the change of heading estimated by the proposed method was 0.033 rad/s. A navigation solution was estimated while changes of heading and forward velocity updates were used to aid the IMU during different GNSS signal outages. The estimated navigation solution is enhanced when applying the proposed updates to the navigation filter by 91% and 97% for 60 s and 120 s of GNSS signal outage, respectively, compared to the IMU standalone solution.
The knowledge of the vehicle sideslip angle provides useful information about the state of the vehicle and it is often considered to increase the performance of the car as well as to develop safety systems, especially in the vehicle equipped with Torque Vectoring control systems. This paper describes two methods, based on the use of Kalman filters, to estimate the vehicle sideslip angle and the tire forces of a vehicle starting from the longitudinal and yaw velocity data. In particular, these data refer to on-track testing of a Range Rover Evoque performing ramp steer maneuvers at constant speed. The results of the sideslip estimation method are compared with the actual vehicle sideslip measured by a Datron sensor and are also used to estimate the tire lateral forces. KeywordsSideslip angleKalman filterVehicleState estimationRandom walk method
Conference Paper
A relatively new technology for the electric vehicles considers the use of brushless permanent magnet motors directly connected to the car wheels (in-wheel motors or hub motors). In order to evaluate the performance that can be obtained, a complete dynamic model of a four-wheel drive (4WD) electric vehicle equipped with four in-wheel motors is developed and a correspondent parametric simulator is implemented in Matlab/SimulinkTM. The simulator is also employed for designing, testing and comparing various control logics which reproduce the handling behavior of a real vehicle.
Full-text available
Several studies have developed operating speed prediction models. Most of the models are based on spot speed data, collected by radar guns, pavements sensors and similar mechanisms. Unfortunately, these data collecting methods force the users to assume some invalid assumptions in driver behaviour modeling: constant operating speed throughout the horizontal curves and occurrence of acceleration and deceleration only on tangents. In this study an instrumented vehicle with a GPS continuous speed tracking was used to analyze driver’s behaviour in terms of speed choice and deceleration/acceleration performances and to develop operating speed prediction models. The data used in the study were from a field experiment conducted in Italy on the rural motorway A16 (Naples-Avellino). Models were developed to predict operating speed in curves and in tangents, deceleration and acceleration rates to be used in the operating speed profiles, starting and ending points of constant operating speed in a curve, 85th percentile of the deceleration and acceleration rates of the individual drivers, and 85th percentile of the individual drivers’ maximum speed reduction in the tangent-to-curve transition.The study results show that (a) drivers’ speed was not constant along the curves, (b) the individual drivers’ maximum speed reduction was greater than the operating speed difference in the tangent-to-curve transition, and (c) deceleration and acceleration rates experienced by the individual drivers were greater than deceleration and acceleration rates used to draw the operating speed profiles.
Full-text available
Book available at HALF PRICE (50% off), shipping included worldwide till MARCH 31, 2016 here (Springer website) THE MORE YOU KNOW VEHICLE DYNAMICS, THE MORE YOU'LL BE SURPRISED Vehicle dynamics is often perceived as a quite intuitive subject. As a matter of fact, lots of people are able to drive a car. Nevertheless, without a rigorous mathematical formulation it is very difficult to truly understand the physical phenomena involved in the motion of a road vehicle. In this book, mathematical models of vehicles are developed, always paying attention to state the relevant assumptions and to provide explanations for each step. This approach allows for a deep, yet simple, analysis of the dynamics of vehicles, without having to resort to foggy concepts. The reader will soon achieve a clear understanding of the subject, which will be of great help both in dealing with the challenges of designing and testing new vehicles and in tackling new research topics. However, there is much more than that. Quite surprisingly, it is shown that several classical concepts, such as the understeer gradient or the roll axis, are either wrong or inadequate and need to be replaced. The book covers handling and performance of both road and race cars. A new approach, called MAP (Map of Achievable Performance), is presented and thoroughly discussed. It provides a global and intuitive picture of the handling features of a vehicle. Moreover, the book also deals with several relevant topics in vehicle dynamics that have never been discussed before. Even very experienced people should find the book interesting and stimulating. This new book is not a translation of the Italian Dinamica del Veicolo; by the same author. Actually, in some sense, this new book is totally different, with new topics and with new points of view for the topics covered in the Italian book as well.
Full-text available
The target of the activities described in the PhD thesis, fixed in collaboration with a motorsport racing team, with a high performance vehicle manufacturing company and with a tyre research and development technical centre is the development of a procedure able to estimate tyre interaction characteristics, reproducing them in simulation environments taking into account the fundamental friction and thermal phenomena concerning with tyre/road interaction. A first tool, called TRICK, has been developed with the aim to process data acquired from experimental test sessions, estimating tyre interaction forces and slip indices. Once characterized the vehicle, filtering and sensors output correction techniques have been employed on the available data, creating a robust procedure able to generate as an output a "virtual telemetry" and, following a specifically defined track driving routine, to provide tyre interaction experimental curves. TRICK virtual telemetry can be employed as an input for the second tool, TRIP-ID, developed with the aim to identify the parameters of a Pacejka Magic Formula tyre model. The advantage of this kind of procedure is the possibility to simulate the behaviour of a tyre without the bench characterizations provided by tyremakers, with the further benefit to reproduce the real interactions with road and the phenomena involved with it, commonly neglected in bench data. Among such phenomena, one of the most important is surely the effect that temperature induces on tyre performances, especially in racing applications. For this reason a specific model, called TRT, has been realized and characterized by means of proper thermodynamic tests, becoming a fundamental instrument for the simulation of a tyre behaviour as close to reality as possible. One of the most useful features provided by the model is the prediction of the so called "bulk temperature", recognized as directly linked with the tyre frictional performances. With the aim to analyse and understand the complex phenomena concerning with local contact between viscoelastic materials and rough surfaces, GrETA grip model has been developed. The main advantage to which the employment of the grip model conducts is constituted by the possibility to predict the variations induced by different tread compounds or soils on vehicle dynamics, leading to the definition of a setup able to optimise performances as a function of tyre the working conditions. The described models and procedures can cooperate, generating a many-sided and powerful instrument of analysis and simulation; the main features of the available employment solutions can be summarised as follows:  full geometric, thermodynamic, viscoelastic and structural characterization of tyres on which the analyses are focused;  estimation of the tyre interaction characteristic curves from experimental outdoor test data;  definition of a standard track driving procedure that employs tyres in multiple dynamic and thermal conditions;  identification of Pacejka Magic Formula tyre models parameters on the basis of the estimated tyre interaction characteristic curves;  estimation of surface, bulk and inner liner tyre temperatures for variable working conditions and real-time reproduction of tyre thermodynamic behaviour in simulation applications;  correlation of tyre thermal conditions with friction phenomena observable at the interface with road;  prediction of tyre frictional behaviour at tread compound and soil roughness variations;  modelling of tyre interaction by means of MF innovative formulations able to take into account grip and thermodynamic effects on vehicle dynamics;  definition of the optimal wheels and vehicle setup in order to provide the maximum possible performances improvement.
Conference Paper
Full-text available
Modern vehicles are equipped with several active and passive devices whose function is to increase active safety. This paper is focused on the anti-roll stiffness influence on vehicle handling, and follows a theoretical approach. The work firstly develops a quadricycle theoretical model, useful to study the influence of anti-roll stiffness on the vehicle local stability. The model, involving non-linear phenomena, is simplified by proper linearizations. This procedure allows local stability analysis with low computational load. At the same time, the linearized model takes into account the dynamic effects induced by load transfers through a tyre-road interaction model sensitive to the vertical load. The study is conducted considering the anti-roll stiffnesses of the two axles as parameters. The proposed model defines the relationship between the anti-roll bars stiffness and the system state. In order to realize an adaptive system able to provide a variable roll stiffness, a semi-active anti-roll bar prototype, employing magnetorheological fluid, is described. Such device gives the possibility to quickly change the roll stiffness, according to the system state, to preserve its stability.
This paper presents a semi-active differential, called MRF LSD (MagnetoRheological Fluid Limited Slip Differential) that allows to bias torque between the driving wheels. It is based on the magnetorheological (MR) fluid employment, that allows to change, in a controlled manner, the differential locking torque and, consequently, the torque bias ratio. The device is an adaptive one and allows to obtain an asymmetric torque distribution in order to improve vehicle handling. The device modelling and the control algorithm, realized for this activity, are described. The illustrated results highlight the advantages that are attainable regarding directional behaviour, stability and traction for a front wheel drive (FWD) vehicle. A comparison with a traditional passive limited slip differential has been conducted.
An adaptive sideslip angle observer based on discrete extended Kalman filter (DEKF) is proposed in this paper and tire-road friction adaptation is also considered. The single track vehicle model with nonlinear tire characteristics is adopted. The tire parameters can be easily obtained through road test data without using special test rig. Afterwards, this model is discretized and the maximum value of tire-road friction is modeled as the third state variable. Through the measurement of vehicle lateral acceleration and yaw rate, the tire-road adhesion coefficient can be timely updated. Simulations with experimental data from road test and driving simulator have confirmed that DEKF has very high accuracy. The convergent speed of DEKF relies on the magnitude of lateral excitation.
This paper deals with the frictional behaviour of a tyre tread elementary volume in sliding contact with road asperities. Friction is supposed as composed by two main components: adhesion and deforming hysteresis. The target, fixed in collaboration with a motorsport racing team and with a tyre manufacturing company, is to provide an estimation of local grip for on-line analyses and real time simulations and to evaluate and predict adhesive and hysteretic frictional contributions arising at the interface between tyre tread and road. A way to approximate asperities, based on rugosimetric analyses on macro and micro scale, has been introduced. The adhesive component of friction has been estimated by means of a new approach based on two different models found in literature, whose parameters have been identified thanks to a wide experimental campaign previously carried out. The hysteretic component of friction has been estimated by means of an energy balance taking into account rubber viscoelastic behaviour, characterized by means of proper DMA tests, and internal stress / strain distribution due to indentation with road. Model results are finally shown and discussed and the validation experimental procedure is described. The correct reproduction of friction phenomenology and the model prediction capabilities are highlighted making particular reference to grip variability due to changes in working conditions.
Frequency measurement of sinusoidal signals corrupted by noise is dealt with. A new time-domain, digital signal processing method, based on an enhanced version of the zero-crossing technique, is in particular proposed. To obtain the desired frequency value, the method exploits the histogram of time intervals between consecutive zero-crossing events, and works with success in the presence of zero-mean additive noise. Several tests conducted on simulated and actual sinusoidal signals highlight the good performance of the method also in critical noise conditions, which make high-end measurement instruments like digital counters poorly fail. Moreover, the obtained results concur with those granted by competitive digital signal processing proposals operating in the frequency domain. With respect to these latter, the main advantage of the method relies on the limited computational resources required, which suggests its implementation even in low-performance processing devices for the realization of cost-effective measurement instruments.
In the field of Intelligent Transportation Systems (ITS), one of the most promising sub-functions is that of Advanced Driver Assistance Systems (ADAS). Development of an effective ADAS, and one that is able to gain drivers' acceptance, hinges on the development of a human-like car-following model, and this is particularly important in order to ensure the driver is always 'in the (vehicle control) loop' and is able to recover control safely in any situation where the ADAS may release control. One of the most commonly used models of car-following is that of the Action Point (AP) (psychophysical) paradigm. However, while this is widely used in both micro-simulation models and behavioural research, the approach is not without its weaknesses. One of these, the potential redundancy of some of the identified APs, is examined in this paper and its basic structure validated using microscopic driving behaviour collected on thirteen subjects in Italy. Another weakness in practical application of the Action Point theory is the identification of appropriate thresholds, accounting for the perception, reaction and adjustment of relative speed (or spacing) from the leading vehicle. This article shows that this identification is problematic if the Action Point paradigm is analysed in a traditional way (car-following spirals), while it is easier if the phenomenon is analysed in terms of car-following 'waves', related to Time To Collision (TTC) or the inverse of TTC. Within this new interpretative framework, the observed action points can be observed to follow a characteristically linear pattern. The identification of the most significant variables to be taken into account, and their characterisation by means of a simple linear pattern, allows for the formulation of more efficient real-time applications, thereby contributing to the development and diffusion of emerging on-board technologies in the field of vehicle control and driver's assistance.