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A Neural-Network-Based Methodology for the Evaluation of the Center of Gravity of a Motorcycle Rider

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A correct reproduction of a motorcycle rider’s movements during driving is a crucial and the most influential aspect of the entire motorcycle–rider system. The rider performs significant variations in terms of body configuration on the vehicle in order to optimize the management of the motorcycle in all the possible dynamic conditions, comprising cornering and braking phases. The aim of the work is to focus on the development of a technique to estimate the body configurations of a high-performance driver in completely different situations, starting from the publicly available videos, collecting them by means of image acquisition methods, and employing machine learning and deep learning techniques. The technique allows us to determine the calculation of the center of gravity (CoG) of the driver’s body in the video acquired and therefore the CoG of the entire driver–vehicle system, correlating it to commonly available vehicle dynamics data, so that the force distribution can be properly determined. As an additional feature, a specific function correlating the relative displacement of the driver’s CoG towards the vehicle body and the vehicle roll angle has been determined starting from the data acquired and processed with the machine and the deep learning techniques.
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Article
A Neural-Network-Based Methodology for the Evaluation of
the Center of Gravity of a Motorcycle Rider
Francesco Carputo 1, Danilo D’Andrea 2, Giacomo Risitano 2, Aleksandr Sakhnevych 1, Dario Santonocito 2
and Flavio Farroni 1, *


Citation: Carputo, F.; D’Andrea, D.;
Risitano, G.; Sakhnevych, A.;
Santonocito, D.; Farroni, F. A
Neural-Network-Based Methodology
for the Evaluation of the Center of
Gravity of a Motorcycle Rider.
Vehicles 2021,3, 377–389. https://
doi.org/10.3390/vehicles3030023
Academic Editor: Chen Lv
Received: 1 June 2021
Accepted: 9 July 2021
Published: 15 July 2021
Publisher’s Note: MDPI stays neutral
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Copyright: © 2021 by the authors.
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This article is an open access article
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Attribution (CC BY) license (https://
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4.0/).
1Department of Industrial Engineering, University of Naples Federico II, 80125 Naples, Italy;
francesco.carputo@unina.it (F.C.); ale.sak@unina.it (A.S.)
2Department of Engineering, University of Messina, Contrada di Dio (S. Agata), 98166 Messina, Italy;
dandread@unime.it (D.D.); giacomo.risitano@unime.it (G.R.); dsantonocito@unime.it (D.S.)
*Correspondence: flavio.farroni@unina.it
Abstract:
A correct reproduction of a motorcycle rider’s movements during driving is a crucial and
the most influential aspect of the entire motorcycle–rider system. The rider performs significant
variations in terms of body configuration on the vehicle in order to optimize the management of the
motorcycle in all the possible dynamic conditions, comprising cornering and braking phases. The
aim of the work is to focus on the development of a technique to estimate the body configurations
of a high-performance driver in completely different situations, starting from the publicly available
videos, collecting them by means of image acquisition methods, and employing machine learning
and deep learning techniques. The technique allows us to determine the calculation of the center
of gravity (CoG) of the driver’s body in the video acquired and therefore the CoG of the entire
driver–vehicle system, correlating it to commonly available vehicle dynamics data, so that the force
distribution can be properly determined. As an additional feature, a specific function correlating
the relative displacement of the driver’s CoG towards the vehicle body and the vehicle roll angle
has been determined starting from the data acquired and processed with the machine and the deep
learning techniques.
Keywords: motorcycle driver; multibody co-simulation; machine learning; deep learning
1. Introduction
Human body movement is an object of a crucial interest, especially in the biomedical
field [
1
,
2
]. Technological evolution has allowed considerable progress, especially in motor
rehabilitation techniques in sports, in the study of motor problems related to behavioral
pathologies and in the analysis of dynamic systems in which a person interacts with the
surrounding environment both it real or virtual situations.
The fields of application of such a discipline can be various and most of the related
issues concern the study of the balance characteristics of a human body and the determina-
tion of its center of gravity during motion, which is fundamental for a proper calculation
of the inertial components and to evaluate the load distribution in motion phases [
3
,
4
]. In
particular, the vehicular simulation field nowadays is lacking robust and usable methodolo-
gies to account for the driver/rider position in the vehicle, and for the two-wheel domain
the problem is even deeper, due to the significant influence that the rider’s mass has on the
overall rider + vehicle system [5].
Due to the difficulty in sensing the rider with specific sensors aimed to measure
the CoG position, the optimal method to acquire data on his position is based on image-
processing. For this reason, an analysis aimed to obtain a preliminary comprehension of
the state of the art in such a field has been carried out.
In recent years, motion analysis has evolved substantially, alongside major technologi-
cal advances, and there is growing demand for faster and more sophisticated techniques
Vehicles 2021,3, 377–389. https://doi.org/10.3390/vehicles3030023 https://www.mdpi.com/journal/vehicles
Vehicles 2021,3378
for capturing motion in a wide range of contexts, ranging from clinical gait assessment [
6
]
to videogame animation.
Biomechanical tools have greatly developed, from manual image annotation to marker-
based optical trackers, inertial sensor-based systems, and marker-free systems using sophis-
ticated human body models, by double energy X-ray absorptiometry (DXA) [
7
], machine
vision, and machine learning algorithms. With such scope, the use of sophisticated sen-
sors based on the presence of physical markers applied to humans’ bodies allows one to
measure the physical quantities (force, speed, acceleration and displacement) linked to the
different movements made by the body which, for example, in the sports field, allows one
to carry out studies aiming at the improvement of the athlete’s performance [8,9].
An alternative method, markerless motion capture, based on the use of video acquisi-
tions processed by machine learning techniques, aims to identify the positions of various
key points belonging to the human body starting from a singular video frame or images,
with no need of uncomfortable and impractical physical markers [10,11].
The major difficulty of this technique is that some body parts cover some others
during the movement or in some given postures. As a result, automatic and marker-
less identification of body segments faces many difficulties that turn it into a complex
problem [12].
In recent years, thanks to the evolution of image-processing tools, the interest in
marker-free motion capture systems has significantly increased and different software
methods allowing one to automatically identify the anatomical landmarks have been
developed, among them the OpenPose software [
13
]. The OpenPose package is capable
of performing real-time skeleton tracking on a large number of subjects analyzing 2D
images [14].
Starting from the research output of the collaboration between the University of
Messina and the University of Naples Federico II [
15
], based on the employment of the
OpenPose software aiming to predict the center of gravity (CoG) of a human subject posing
in a specific set of 2D images, the present work focuses on a motorcycle rider adopting the
images acquired from a motorcycle simulation game, MotoGP19.
The work aims to develop of a technique employing the neural network technology
for correlation with vehicle data, applied in a deep learning environment, which, starting
from a partial capture of the driver position acquired in each video frame, allows one to
determine the key points not visible from the camera and corresponding to the entirety of
the driver’s body. Starting from the information collected, the calculation of the CoG of
the driver’s body is evaluated by adopting deep learning technology. The neural network
technique is then employed to determine the correlation between the relative displacement
of the driver’s center of gravity and the motorcycle’s body roll angle. The continuous
availability of information on the position of the driver/rider’s CoG is fundamental in the
motorcycle industry, both for racing and safety applications, due to the need to consider
the influence of the human body on the rider + vehicle system in design and simulations
activities [16,17].
2. Materials and Methods
The presented work aims to illustrate a methodologic approach, developed by using
data acquired from a reference scenario, that will eventually be substituted by real video
data. Each rider moves in a different way, as the driving style of racing riders demonstrates,
and once the methodology is validated, the developed algorithms can be trained for
each different rider, reproducing their typical motion and style, with the final aim of
determining the continuous position of the center of gravity, which is fundamental for
simulation activities and usually hard to determine for motorcycles. Such consideration
has been better expressed in the text. In order to obtain a reliable dataset with repeatable
and robust data, an approach based on the use of the MotoGP19 simulation videogame has
been chosen in the acquisition phase, in which several runs have been captured. The video
frames acquired in the various dynamic conditions of the motorcycle and the body driver
Vehicles 2021,3379
configuration constitute a suitable and repeatable dataset on which the OpenPose software
processing has been employed to calculate all the necessary body markers’ positions
and, therefore, the center of gravity of the driver’s body. The particular choice to start
with the videogame is motivated by the fact that modern simulation and sports games
are generally very faithful to the real movements of the athletes and drivers, since their
modelling is based on the extrapolation of Active Marker Mocap real data [
18
20
]. As a
result, the simulation output reproduces all the athlete’s movements in a realistic way, and
in the particular case under analysis, it allows one to have a great coherence with the real
movements assumed by motorcycle riders during the operation of the motorcycle even in
extreme dynamic conditions. Eventual distortions and inaccuracies of the virtual camera
did not represent a particular issue, due to the methodologic spirit of the study, whose data
can be progressively improved in terms of quality in the following activities, keeping the
value of the demonstrated feasibility.
Modern gyroscopic cameras, represented in Figure 1a, installed on racing motorcycles
provide only a partial shape of the driver’s body, being limited to acquiring the movement
information regarding only of the upper part of the rider’s body (as shown in
Figure 1b
).
The missing part, mainly comprising legs and the bottom part of the torso, becomes
necessary to correctly evaluate the CoG of the rider’s body [2124].
Vehicles 2021, 3, FOR PEER REVIEW 3
with repeatable and robust data, an approach based on the use of the MotoGP19
simulation videogame has been chosen in the acquisition phase, in which several runs
have been captured. The video frames acquired in the various dynamic conditions of the
motorcycle and the body driver configuration constitute a suitable and repeatable dataset
on which the OpenPose software processing has been employed to calculate all the
necessary body markers’ positions and, therefore, the center of gravity of the driver’s
body. The particular choice to start with the videogame is motivated by the fact that
modern simulation and sports games are generally very faithful to the real movements of
the athletes and drivers, since their modelling is based on the extrapolation of Active
Marker Mocap real data [18–20]. As a result, the simulation output reproduces all the
athlete’s movements in a realistic way, and in the particular case under analysis, it allows
one to have a great coherence with the real movements assumed by motorcycle riders
during the operation of the motorcycle even in extreme dynamic conditions. Eventual
distortions and inaccuracies of the virtual camera did not represent a particular issue, due
to the methodologic spirit of the study, whose data can be progressively improved in
terms of quality in the following activities, keeping the value of the demonstrated
feasibility.
Modern gyroscopic cameras, represented in Figure 1a, installed on racing
motorcycles provide only a partial shape of the driver’s body, being limited to acquiring
the movement information regarding only of the upper part of the rider’s body (as shown
in Figure 1b). The missing part, mainly comprising legs and the bottom part of the torso,
becomes necessary to correctly evaluate the CoG of the rider’s body [21–24].
Figure 1. (a) Gyroscopic camera; (b) rear shot with gyroscopic camera.
2.1. Acquisition of the Video Frames
A series of simulations were carried out via MotoGP19 on different tracks in order to
explore as many dynamic conditions as possible concerning the motorcycle behavior and
the driver’s body configurations.
For each track under analysis, the best track lap was selected as a reference and was
recorded in two different video acquisitions using the two different points of view
available in the simulator game:
Rear view camera 1 (Figure 2a);
Rear view camera 2 (Figure 2b).
Figure 2. (a) Rear view camera 1; (b) rear view camera 2.
Figure 1. (a) Gyroscopic camera; (b) rear shot with gyroscopic camera.
2.1. Acquisition of the Video Frames
A series of simulations were carried out via MotoGP19 on different tracks in order to
explore as many dynamic conditions as possible concerning the motorcycle behavior and
the driver’s body configurations.
For each track under analysis, the best track lap was selected as a reference and was
recorded in two different video acquisitions using the two different points of view available
in the simulator game:
Rear view camera 1 (Figure 2a);
Rear view camera 2 (Figure 2b).
Vehicles 2021, 3, FOR PEER REVIEW 3
with repeatable and robust data, an approach based on the use of the MotoGP19
simulation videogame has been chosen in the acquisition phase, in which several runs
have been captured. The video frames acquired in the various dynamic conditions of the
motorcycle and the body driver configuration constitute a suitable and repeatable dataset
on which the OpenPose software processing has been employed to calculate all the
necessary body markers’ positions and, therefore, the center of gravity of the driver’s
body. The particular choice to start with the videogame is motivated by the fact that
modern simulation and sports games are generally very faithful to the real movements of
the athletes and drivers, since their modelling is based on the extrapolation of Active
Marker Mocap real data [18–20]. As a result, the simulation output reproduces all the
athlete’s movements in a realistic way, and in the particular case under analysis, it allows
one to have a great coherence with the real movements assumed by motorcycle riders
during the operation of the motorcycle even in extreme dynamic conditions. Eventual
distortions and inaccuracies of the virtual camera did not represent a particular issue, due
to the methodologic spirit of the study, whose data can be progressively improved in
terms of quality in the following activities, keeping the value of the demonstrated
feasibility.
Modern gyroscopic cameras, represented in Figure 1a, installed on racing
motorcycles provide only a partial shape of the driver’s body, being limited to acquiring
the movement information regarding only of the upper part of the rider’s body (as shown
in Figure 1b). The missing part, mainly comprising legs and the bottom part of the torso,
becomes necessary to correctly evaluate the CoG of the rider’s body [21–24].
Figure 1. (a) Gyroscopic camera; (b) rear shot with gyroscopic camera.
2.1. Acquisition of the Video Frames
A series of simulations were carried out via MotoGP19 on different tracks in order to
explore as many dynamic conditions as possible concerning the motorcycle behavior and
the driver’s body configurations.
For each track under analysis, the best track lap was selected as a reference and was
recorded in two different video acquisitions using the two different points of view
available in the simulator game:
Rear view camera 1 (Figure 2a);
Rear view camera 2 (Figure 2b).
Figure 2. (a) Rear view camera 1; (b) rear view camera 2.
Figure 2. (a) Rear view camera 1; (b) rear view camera 2.
The video was subsequently processed via the OpenPose package as described later.
Vehicles 2021,3380
2.2. OpenPose Processing
OpenPose is an open source software package for the detection of multiperson key
points in real time starting from video frame acquisitions. It is able to jointly detect the key
points of the human body, namely the hands, face and feet on individual images, up to a
total of 135 key points [25].
It is capable of processing, in real time, single frames or direct videos in the input,
providing, in output, the same images and videos with a further level of physics represented
by the key points detected and added to the input frames.
For the recognition of key points, OpenPose uses a preadded neural convolution net-
work (CNN) called Vggnet [
26
,
27
]. The network accepts a color image as input (
Figure 3a
),
returning 2D positions of the key points for each person in the frame (Figure 3b). The
additional processing layer, representing the extracted points, is represented in Figure 3c.
Vehicles 2021, 3, FOR PEER REVIEW 4
The video was subsequently processed via the OpenPose package as described later.
2.2. OpenPose Processing
OpenPose is an open source software package for the detection of multiperson key
points in real time starting from video frame acquisitions. It is able to jointly detect the
key points of the human body, namely the hands, face and feet on individual images, up
to a total of 135 key points [25].
It is capable of processing, in real time, single frames or direct videos in the input,
providing, in output, the same images and videos with a further level of physics
represented by the key points detected and added to the input frames.
For the recognition of key points, OpenPose uses a preadded neural convolution
network (CNN) called Vggnet [26,27]. The network accepts a color image as input (Figure
3a), returning 2D positions of the key points for each person in the frame (Figure 3b). The
additional processing layer, representing the extracted points, is represented in Figure 3c.
Figure 3. (a) Original frame; (b) postprocessed frame by OpenPose; (c) plot of the key points.
3. Training Dataset
The output data obtained by means of the OpenPose package were divided into two
key points sets depending on their positions towards the human body to constitute
suitable datasets of input and target indispensable for the machine learning training. In
particular, the processed key points have been split as follows:
Input: 10 points for the upper body part (Figure 4a);
Target: 10 points for the lower body part (Figure 4b).
The neural network is set to evaluate 10 points relative to the lower part of the body,
starting from the 10 key points of the upper part acquired through camera 2 (Figure 2b).
Due to the different framings between the two chosen cameras, it was necessary to
scale the shapes obtained from the two different sets of key points to the same proportions.
Furthermore, the data were divided into x and z coordinates because it is necessary
to train two distinct neural networks for the x and z coordinates, respectively, to optimize
Figure 3. (a) Original frame; (b) postprocessed frame by OpenPose; (c) plot of the key points.
3. Training Dataset
The output data obtained by means of the OpenPose package were divided into two
key points sets depending on their positions towards the human body to constitute suitable
datasets of input and target indispensable for the machine learning training. In particular,
the processed key points have been split as follows:
Input: 10 points for the upper body part (Figure 4a);
Target: 10 points for the lower body part (Figure 4b).
The neural network is set to evaluate 10 points relative to the lower part of the body,
starting from the 10 key points of the upper part acquired through camera 2 (Figure 2b).
Due to the different framings between the two chosen cameras, it was necessary to
scale the shapes obtained from the two different sets of key points to the same proportions.
Vehicles 2021,3381
Vehicles 2021, 3, FOR PEER REVIEW 5
the calibration algorithms response. In the y-direction, the hypothesis of the fixed CoG
coordinate has been introduced, due to the lower variability of the rider’s motion in said
direction. Four distinct matrices of points have thus been prepared for the training
procedure:
x coordinates of the upper points;
z coordinates of the upper points;
x coordinates of the lower points;
z coordinates of the lower points.
Figure 4. (a) The top 10 points as network input; (b) the bottom 10 points as a network target.
3.1. Assessment of the Centre of Gravity of the Driver’s Body
Assuming that the body density is constant and all the body parts can be described
by simple geometrical features, the calculation of the center of gravity can be easily
achieved geometrically [28].
However, it has to be taken into account that the human body is characterized by a
nonuniform distribution of density between each couple of defined markers. With such
reference, specific methodologies and more accurate methods for calculating the center of
gravity could be employed [29].
Schematizing the human body as a series of discrete mass parts, the center of gravity
can be assessed as follows:
𝑥𝑚𝑥𝑖
𝑀
𝑧𝑚𝑦𝑖
𝑀
(1)
where:
m
i
is the mass of i-th element;
M is the mass of body (including clothing).
In order to employ the described equivalent system method, it is necessary to
individuate the position of the CoG of each individual part of the human body, as
described in Table 1, obtained by processing data available from the literature. It was
designed to describe body segment mass as a proportion of total body mass and the
location k of each segment’s center of mass as a proportion of segment length, in the three
transverse, sagittal and longitudinal planes. Among the papers that provide such data,
Figure 4. (a) The top 10 points as network input; (b) the bottom 10 points as a network target.
Furthermore, the data were divided into x and z coordinates because it is necessary to
train two distinct neural networks for the x and z coordinates, respectively, to optimize the
calibration algorithms response. In the y-direction, the hypothesis of the fixed CoG coordi-
nate has been introduced, due to the lower variability of the rider’s motion in said direction.
Four distinct matrices of points have thus been prepared for the training procedure:
x coordinates of the upper points;
z coordinates of the upper points;
x coordinates of the lower points;
z coordinates of the lower points.
3.1. Assessment of the Centre of Gravity of the Drivers Body
Assuming that the body density is constant and all the body parts can be described by
simple geometrical features, the calculation of the center of gravity can be easily achieved
geometrically [28].
However, it has to be taken into account that the human body is characterized by a
nonuniform distribution of density between each couple of defined markers. With such
reference, specific methodologies and more accurate methods for calculating the center of
gravity could be employed [29].
Schematizing the human body as a series of discrete mass parts, the center of gravity
can be assessed as follows:
xG=mixi
M
zG=miyi
M
(1)
where:
miis the mass of i-th element;
Mis the mass of body (including clothing).
In order to employ the described equivalent system method, it is necessary to indi-
viduate the position of the CoG of each individual part of the human body, as described
in Table 1, obtained by processing data available from the literature. It was designed to
describe body segment mass as a proportion of total body mass and the location kof each
segment’s center of mass as a proportion of segment length, in the three transverse, sagittal
and longitudinal planes. Among the papers that provide such data, obtainable through
experimental tests, this works adopts the approach described by Zatsiorsky et al. in [
30
],
modified by de Leva in [31,32].
Vehicles 2021,3382
Table 1.
Percentage values of mass and position of the center of gravity in adult men and
women [30,31]
(copyright has
been permitted).
Segment
Mass
(% Mass)
CM
(% Length)
Sagittal k
(% Length)
Transverse k
(% Length)
Longitudinal k
(% Length)
Female Male Female Male Female Male Female Male Female Male
Head 6.68 6.94 58.94 59.76 30.1 33.2 32.7 34.5 28.8 28.6
Trunk 42.57 43.46 41.51 44.86 34.6 36 33.2 33.3 16.2 18.1
Upper Trunk 15.45 15.96 20.77 29.99 60 60.57 41.1 38.7 58.6 55.9
Mid Trunk 14.65 16.33 45.12 45.02 43.3 48.2 35.4 38.3 41.5 46.8
Lower Trunk 12.47 11.17 49.2 61.15 43.3 61.5 40.2 55.1 44.4 58.7
Upper Arm 2.55 2.71 57.54 57.72 27.8 28.5 26 26.9 14.8 15.8
Forearm 1.38 1.62 45.59 45.74 26.2 27.7 25.8 26.6 9.45 12.15
Hand 0.56 0.61 74.74 79 35.4 45.2 32.7 36.9 23.4 29
Thigh 14.78 14.16 36.12 40.95 36.9 32.9 36.4 32.9 16.2 14.9
Shank 4.81 4.33 44.16 44.59 27.1 25.4 26.8 24.2 9.3 10.3
Foot 1.29 1.37 40.14 44.15 29.9 25.7 27.9 24.5 13.9 12.4
In particular, two procedures to evaluate the CoG are compared: the geometric method
and the kinematic method [13].
The overall procedure consists, therefore, of the following steps:
1. Capture of video frames from the MotoGP19 simulator (rear camera 2);
2.
Data processing with OpenPose software to evaluate the center of gravity of the
individual body elements;
3. Evaluation of the center of gravity of the whole body using the data in Table 1.
3.2. Application on the Acquired Data
The recorded video was processed with the OpenPose software for both rear cameras,
available in the MotoGP19 simulator, as illustrated in Figure 5(rear camera 1, including data
regarding the bottom part of the rider’s body) and in Figure 6(rear camera 2, simulating
the capabilities of a common onboard camera):
Vehicles 2021, 3, FOR PEER REVIEW 6
obtainable through experimental tests, this works adopts the approach described by
Zatsiorsky et al. in [30], modified by de Leva in [31,32].
In particular, two procedures to evaluate the CoG are compared: the geometric
method and the kinematic method [13].
Table 1. Percentage values of mass and position of the center of gravity in adult men and women [30,31] (copyright has
been permitted).
Segment
Mass
(% Mass)
CM
(% Length)
Sagittal k
(% Length)
Transverse k
(% Length)
Longitudinal k
(% Length)
Female Male Female Male Female Male Female Male Female Male
Head 6.68 6.94 58.94 59.76 30.1 33.2 32.7 34.5 28.8 28.6
Trunk 42.57 43.46 41.51 44.86 34.6 36 33.2 33.3 16.2 18.1
Upper Trunk 15.45 15.96 20.77 29.99 60 60.57 41.1 38.7 58.6 55.9
Mid Trunk 14.65 16.33 45.12 45.02 43.3 48.2 35.4 38.3 41.5 46.8
Lower Trunk 12.47 11.17 49.2 61.15 43.3 61.5 40.2 55.1 44.4 58.7
Upper Arm 2.55 2.71 57.54 57.72 27.8 28.5 26 26.9 14.8 15.8
Forearm 1.38 1.62 45.59 45.74 26.2 27.7 25.8 26.6 9.45 12.15
Hand 0.56 0.61 74.74 79 35.4 45.2 32.7 36.9 23.4 29
Thigh 14.78 14.16 36.12 40.95 36.9 32.9 36.4 32.9 16.2 14.9
Shank 4.81 4.33 44.16 44.59 27.1 25.4 26.8 24.2 9.3 10.3
Foot 1.29 1.37 40.14 44.15 29.9 25.7 27.9 24.5 13.9 12.4
The overall procedure consists, therefore, of the following steps:
1. Capture of video frames from the MotoGP19 simulator (rear camera 2);
2. Data processing with OpenPose software to evaluate the center of gravity of the
individual body elements;
3. Evaluation of the center of gravity of the whole body using the data in Table 1.
3.2. Application on the Acquired Data
The recorded video was processed with the OpenPose software for both rear
cameras, available in the MotoGP19 simulator, as illustrated in Figure 5 (rear camera 1,
including data regarding the bottom part of the rider’s body) and in Figure 6 (rear camera
2, simulating the capabilities of a common onboard camera):
Figure 5. OpenPose postprocessing of MotoGP19 rear camera 1.
Figure 5. OpenPose postprocessing of MotoGP19 rear camera 1.
Vehicles 2021, 3, FOR PEER REVIEW 7
Figure 6. OpenPose postprocessing of MotoGP19 rear camera 2.
The processing of the acquisitions performed with camera 1 has a good quality with
little presence of corrupt frames and undetected key points. On the contrary, the
processing of the acquisition with camera 2 presents several corrupt frames, in which the
algorithm is not able to recognize parts of the body shape, as illustrated in Figure 7.
Figure 7. Errors in the OpenPose processing of the MotoGP19 frame regarding rear camera 2.
3.3. Machine Learning Technique
The data used to train the neural network consist of point arrays from OpenPose
processing. Machine learning algorithms employing the MATLAB neural fitting tool [33]
have been used to train the neural network. In particular, 20 different runs, each one
comprising about 10 laps, for a global acquired time of 20,000 s, with an acquisition
frequency of 20 Hz, have been used to build the global dataset. The data have been
organized into 10 input points of the upper body and 10 target points of the lower body,
while the hidden and the output layers of the neural network have the dimensions of 6
and 10 neurons, respectively [33,34], as reported in Figure 8.
Figure 8. Neural network layout.
The designed neural network is a two-layered feed-forward network with six hidden
neurons based on the sigmoid (activation function of the nonlinear “neuron”) and with 10
linear output neurons (linear regression output function).
Figure 6. OpenPose postprocessing of MotoGP19 rear camera 2.
Vehicles 2021,3383
The processing of the acquisitions performed with camera 1 has a good quality with
little presence of corrupt frames and undetected key points. On the contrary, the processing
of the acquisition with camera 2 presents several corrupt frames, in which the algorithm is
not able to recognize parts of the body shape, as illustrated in Figure 7.
Figure 7. Errors in the OpenPose processing of the MotoGP19 frame regarding rear camera 2.
3.3. Machine Learning Technique
The data used to train the neural network consist of point arrays from OpenPose
processing. Machine learning algorithms employing the MATLAB neural fitting tool [
33
]
have been used to train the neural network. In particular, 20 different runs, each one
comprising about 10 laps, for a global acquired time of 20,000 s, with an acquisition
frequency of 20 Hz, have been used to build the global dataset. The data have been
organized into 10 input points of the upper body and 10 target points of the lower body,
while the hidden and the output layers of the neural network have the dimensions of 6
and 10 neurons, respectively [33,34], as reported in Figure 8.
Vehicles 2021, 3, FOR PEER REVIEW 7
Figure 6. OpenPose postprocessing of MotoGP19 rear camera 2.
The processing of the acquisitions performed with camera 1 has a good quality with
little presence of corrupt frames and undetected key points. On the contrary, the
processing of the acquisition with camera 2 presents several corrupt frames, in which the
algorithm is not able to recognize parts of the body shape, as illustrated in Figure 7.
Figure 7. Errors in the OpenPose processing of the MotoGP19 frame regarding rear camera 2.
3.3. Machine Learning Technique
The data used to train the neural network consist of point arrays from OpenPose
processing. Machine learning algorithms employing the MATLAB neural fitting tool [33]
have been used to train the neural network. In particular, 20 different runs, each one
comprising about 10 laps, for a global acquired time of 20,000 s, with an acquisition
frequency of 20 Hz, have been used to build the global dataset. The data have been
organized into 10 input points of the upper body and 10 target points of the lower body,
while the hidden and the output layers of the neural network have the dimensions of 6
and 10 neurons, respectively [33,34], as reported in Figure 8.
Figure 8. Neural network layout.
The designed neural network is a two-layered feed-forward network with six hidden
neurons based on the sigmoid (activation function of the nonlinear “neuron”) and with 10
linear output neurons (linear regression output function).
Figure 8. Neural network layout.
The designed neural network is a two-layered feed-forward network with six hidden
neurons based on the sigmoid (activation function of the nonlinear “neuron”) and with
10 linear output neurons (linear regression output function).
The training process of the neural networks is substantially based on a trial-and-error
approach. Therefore, it is usually necessary to train the network several times varying its
parameters until converging to the desired results. The dataset was divided into training,
validation, and testing sets, assigning 60%, 35% and 5% of data to the three subsets,
respectively, obtaining the datasets showed in Figure 9. Such figure shows the results of
the training process, highlighting the convergence obtained for both xand z coordinates of
the target points belonging to the lower part of the driver’s body.
The neural network outputs in terms of the entire body representation are illustrated
in Figure 10, focusing in particular on the validation of the lower points calculated by
means of the described technique, which are in a good agreement with the ones acquired
in the same frames from a different point of view. The plot reports the best performance
obtained, defined as the lowest validation error.
Vehicles 2021,3384
Vehicles 2021, 3, FOR PEER REVIEW 8
The training process of the neural networks is substantially based on a trial-and-error
approach. Therefore, it is usually necessary to train the network several times varying its
parameters until converging to the desired results. The dataset was divided into training,
validation, and testing sets, assigning 60%, 35% and 5% of data to the three subsets,
respectively, obtaining the datasets showed in Figure 9. Such figure shows the results of
the training process, highlighting the convergence obtained for both x and z coordinates of
the target points belonging to the lower part of the driver’s body.
Figure 9. Best training performance (a) x coordinates; (b) z coordinates.
The neural network outputs in terms of the entire body representation are illustrated
in Figure 10, focusing in particular on the validation of the lower points calculated by
means of the described technique, which are in a good agreement with the ones acquired
in the same frames from a different point of view. The plot reports the best performance
obtained, defined as the lowest validation error.
Two distinct acquisitions were made, relating to the same lap, through the use of the
two cameras:
Acquisition 1 with camera 1: number of frames acquired 3596 (Figure 5);
Acquisition 2 with camera 2: number of frames acquired 3583 (Figure 6).
Using the formulations described in Equation (1), an example of the points position,
in terms of the center of gravity, obtained thanks to the OpenPose processing and thanks
to the machine learning techniques (starting from the OpenPose estimated data) are
represented in Figures 11 and 12.
In such figures, the confidence ellipse (or sway area) is depicted. It represents the
surface that contains (with 86% probability) the positions of the calculated centers of
gravity [35].
Table 2 evidences the further similarity, in terms of standard deviation, relating to
the x and z coordinates, between the OpenPose calculations and the results of the machine
learning techniques, starting from the same OpenPose raw dataset.
Table 2. Standard deviation value comparison highlighting consistency between the points acquired
and processed by means of OpenPose and estimated by means of neural network.
Standard Deviation [cm]
X Z
OpenPose 5.43 8.19
Neural Network 5.01 9.1
Figure 9. Best training performance (a)x coordinates; (b)z coordinates.
Vehicles 2021, 3, FOR PEER REVIEW 9
Figure 10. Comparison between estimated and acquired key points in different body configurations.
Figure 11. Dispersion of points obtained thanks to OpenPose software compared with the neural
network results (for acquisition 1).
KCOMz [cm]
Figure 10.
Comparison between estimated and acquired key points in different body configurations.
Two distinct acquisitions were made, relating to the same lap, through the use of the
two cameras:
Acquisition 1 with camera 1: number of frames acquired 3596 (Figure 5);
Acquisition 2 with camera 2: number of frames acquired 3583 (Figure 6).
Using the formulations described in Equation (1), an example of the points position, in
terms of the center of gravity, obtained thanks to the OpenPose processing and thanks to the
machine learning techniques (starting from the OpenPose estimated data) are represented
in Figures 11 and 12.
In such figures, the confidence ellipse (or sway area) is depicted. It represents the
surface that contains (with 86% probability) the positions of the calculated centers of
gravity [35].
Table 2evidences the further similarity, in terms of standard deviation, relating to
the xand z coordinates, between the OpenPose calculations and the results of the machine
learning techniques, starting from the same OpenPose raw dataset.
Vehicles 2021,3385
Vehicles 2021, 3, FOR PEER REVIEW 9
Figure 10. Comparison between estimated and acquired key points in different body configurations.
Figure 11. Dispersion of points obtained thanks to OpenPose software compared with the neural
network results (for acquisition 1).
Figure 11.
Dispersion of points obtained thanks to OpenPose software compared with the neural
network results (for acquisition 1).
Vehicles 2021, 3, FOR PEER REVIEW 10
Figure 12. Dispersion of points obtained thanks to OpenPose software compared with the neural
network results (for acquisition 2).
3.4. Correlation with Roll Angle
The capacity to predict the motorcycle rider’s behavior becomes crucial when it
comes to correctly define and design the dynamic characteristics of the entire motorcycle
rider system [36,37]. The center of gravity of a motorcycle body can be determined
through geometric and dynamic parameters, usually already available during the design
phase and partly extrapolated through data acquisition systems [38,39].
Regarding the driver inertia system, it varies instant by instant depending on the
driving style and the specific dynamic maneuver [40]. For this reason, one of the aims of
this work is to understand if there is any correlation between the driver’s configuration
and the main telemetry channels, the rolling angle being among them. The study has re-
garded the relative movement between the motorcycle and rider systems, calculated as
the minimum distance “d” between the driver’s center of gravity and the vehicle rolling
axle, the straight line belonging to the symmetric geometrical plane ISO-xz of the moving
frame of the vehicle, as illustrated in Figure 13.
Figure 13. Distance d between the driver’s center of gravity and the vehicle’s rolling axle.
The explicit equation of the distance “d” is defined in Equation (2).
The value of d was calculated as the minimum distance between a point and a
straight line using the equation in explicit form (Equation (2)) per each video frame:
  

(2)
where:
Figure 12.
Dispersion of points obtained thanks to OpenPose software compared with the neural
network results (for acquisition 2).
Table 2.
Standard deviation value comparison highlighting consistency between the points acquired
and processed by means of OpenPose and estimated by means of neural network.
Standard Deviation [cm]
X Z
OpenPose 5.43 8.19
Neural Network 5.01 9.1
3.4. Correlation with Roll Angle
The capacity to predict the motorcycle rider’s behavior becomes crucial when it comes
to correctly define and design the dynamic characteristics of the entire motorcycle rider
system [
36
,
37
]. The center of gravity of a motorcycle body can be determined through
geometric and dynamic parameters, usually already available during the design phase and
partly extrapolated through data acquisition systems [38,39].
Vehicles 2021,3386
Regarding the driver inertia system, it varies instant by instant depending on the
driving style and the specific dynamic maneuver [
40
]. For this reason, one of the aims of
this work is to understand if there is any correlation between the driver’s configuration
and the main telemetry channels, the rolling angle being among them. The study has
regarded the relative movement between the motorcycle and rider systems, calculated as
the minimum distance “d” between the driver’s center of gravity and the vehicle rolling
axle, the straight line belonging to the symmetric geometrical plane ISO-xz of the moving
frame of the vehicle, as illustrated in Figure 13.
Vehicles 2021, 3, FOR PEER REVIEW 10
Figure 12. Dispersion of points obtained thanks to OpenPose software compared with the neural
network results (for acquisition 2).
3.4. Correlation with Roll Angle
The capacity to predict the motorcycle rider’s behavior becomes crucial when it
comes to correctly define and design the dynamic characteristics of the entire motorcycle
rider system [36,37]. The center of gravity of a motorcycle body can be determined
through geometric and dynamic parameters, usually already available during the design
phase and partly extrapolated through data acquisition systems [38,39].
Regarding the driver inertia system, it varies instant by instant depending on the
driving style and the specific dynamic maneuver [40]. For this reason, one of the aims of
this work is to understand if there is any correlation between the driver’s configuration
and the main telemetry channels, the rolling angle being among them. The study has
regarded the relative movement between the motorcycle and rider systems, calculated as
the minimum distance “d” between the driver’s center of gravity and the vehicle rolling
axle, the straight line belonging to the symmetric geometrical plane ISO-xz of the moving
frame of the vehicle, as illustrated in Figure 13.
Figure 13. Distance d between the driver’s center of gravity and the vehicle’s rolling axle.
The explicit equation of the distance “d” is defined in Equation (2).
The value of d was calculated as the minimum distance between a point and a
straight line using the equation in explicit form (Equation (2)) per each video frame:
𝑑𝑃,𝑟|

|

(2)
where:
KCOMz [cm]
Figure 13. Distance d between the driver ’s center of gravity and the vehicle’s rolling axle.
The explicit equation of the distance “d” is defined in Equation (2).
The value of d was calculated as the minimum distance between a point and a straight
line using the equation in explicit form (Equation (2)) per each video frame:
d(P,r)=|zP(mxP+q)|
1+m2(2)
where:
xp,yprepresent the coordinates of point P;
mis the angular coefficient of the straight line r;
qis the intercept on the ordinate.
Figure 14a shows the trend of the quantity “d” as a function of the roll angle relative to
the points acquired and processed by OpenPose. Figure 14b, in analogy, shows the trend of
the quantity “d” as a function of the roll angle relative to the points estimated by means of
the machine learning technique. In both cases, steady state conditions have been selected
and reproduced with a third order polynomial to fit the main trends, highlighting similar
shapes. The low availability of acquired vehicle channels did not allow us to produce
a clear fitting and to provide further correlations, but the qualitative results encourage
persisting with following studies, able to involve also other variables and a wider dataset.
The negative and positive values of the roll angle represent the vehicle cornering on
the left and on the right, respectively.
Performing a specific data processing technique, consisting in removing the nonphys-
ical outliers and transient stages with tresholds on “d” at 50 cm and on the roll angle
derivative, filtering the data with a 1Hz low-pass filter, reporting the rolling angle values
in the positive quadrant, and performing a linear regression, a preliminary trend of the
distance d with the roll angle could be pointed out, as highlighted in Figure 15.
It can be clearly seen how, in order to better tackle the corners, the riders move
their bodies internally in order to achieve a lower centre of gravity of the entire driver–
motorcycle inertial system, therefore allowing the vehicle to achieve a greater forward
speed during cornering for the level of the roll angle. All this is strictly related to the travel
speed and relative forces, longitudinal and lateral, exchanged between the tire and the
asphalt, designed to ensure the balance of the motorcycle when cornering.
Finally, the points where the roll angle values are high and the “d” values are very
small are due to the intrinsic characteristics of the rider’s movements during the direction
Vehicles 2021,3387
change maneuvers. Points (0,0) of the diagrams, expected to be physical (the rider position
should be symmetrical at zero roll angle) in Figure 15, do not belong to the linear regression
because it interpolates the data giving priority to the linear part of the dataset at roll
angles > 3.
Vehicles 2021, 3, FOR PEER REVIEW 11
xp,yp represent the coordinates of point
𝑃
;
m is the angular coefficient of the straight line
𝑟
;
q is the intercept on the ordinate.
Figure 14a shows the trend of the quantity “d” as a function of the roll angle relative
to the points acquired and processed by OpenPose. Figure 14b, in analogy, shows the
trend of the quantity “d” as a function of the roll angle relative to the points estimated by
means of the machine learning technique. In both cases, steady state conditions have been
selected and reproduced with a third order polynomial to fit the main trends, highlighting
similar shapes. The low availability of acquired vehicle channels did not allow us to pro-
duce a clear fitting and to provide further correlations, but the qualitative results encour-
age persisting with following studies, able to involve also other variables and a wider
dataset.
Figure 14. Correlation of roll angle vs. d” with Fourier fitting curve: OpenPose (on left) and neural
network (on right).
The negative and positive values of the roll angle represent the vehicle cornering on
the left and on the right, respectively.
Performing a specific data processing technique, consisting in removing the non-
physical outliers and transient stages with tresholds on “d” at 50 cm and on the roll angle
derivative, filtering the data with a 1Hz low-pass filter, reporting the rolling angle values
in the positive quadrant, and performing a linear regression, a preliminary trend of the
distance d with the roll angle could be pointed out, as highlighted in Figure 15.
It can be clearly seen how, in order to better tackle the corners, the riders move their
bodies internally in order to achieve a lower centre of gravity of the entire drivermotor-
cycle inertial system, therefore allowing the vehicle to achieve a greater forward speed
during cornering for the level of the roll angle. All this is strictly related to the travel speed
and relative forces, longitudinal and lateral, exchanged between the tire and the asphalt,
designed to ensure the balance of the motorcycle when cornering.
Finally, the points where the roll angle values are high and the dvalues are very
small are due to the intrinsic characteristics of the riders movements during the direction
change maneuvers. Points (0,0) of the diagrams, expected to be physical (the rider position
should be symmetrical at zero roll angle) in Figure 15, do not belong to the linear regres-
sion because it interpolates the data giving priority to the linear part of the dataset at roll
angles >3°.
Figure 14.
Correlation of roll angle vs. d” with Fourier fitting curve: OpenPose (
a
) and neural
network (b).
Vehicles 2021, 3, FOR PEER REVIEW 12
Figure 15. Linear regression line: OpenPose (on left) and neural network (on right).
4. Conclusions
The objective of determining the motion of a motorcycle rider using machine learning
algorithms processing images through CNN motion capture techniques has been pursued
in this paper, due to the complexity of developing and run physical-based algorithms, and
the difficulty in parameterization, vehicle design and performance optimization applica-
tions.
The CoG parameter plays, in fact, a fundamental role in vehicle dynamics simula-
tions and in the design phase of the motorcycle, since the rider and the motorcycle are not
two separate systems, but fully integrated bodies whose deep understanding is a starting
point to achieve maximum performance both in terms of safety and racing competitive-
ness.
The application of a technique based on the use of neural networks has made it pos-
sible to identify the position of several key points belonging to the human body, starting
from the video frames acquired at the rear edge of a motorcycle from a gaming simulator.
Such a choice was made because the reliability of the video data is not a main focus of the
work, which aims to set a methodology that will be then replicated with real vehicle video
data.
The quality of the results obtained is closely linked with the OpenPose software po-
tential, which, as illustrated, could have significant limits in the recognition of key points
in particular positions. Despite such an aspect, the presented activity presents a method-
ologic approach which could be further improved in terms of data quality, thanks to the
availability of a more reliable acquisition system, retaining its feasibility.
The training of a neural network, even applied to frames reproducing partial visibil-
ity of the driver, allowed us to determine the key points not visible to the camera, thus
also guaranteeing the calculation of the center of gravity in conditions in which such a
task could hardly be achievable.
Finally, a preliminary function, linking the relative displacement of the drivers cen-
ter of gravity towards the vehicle rolling axis as a function of the roll angle, has been pro-
posed.
The determination of the drivers center of gravity plays a fundamental role in the
overall dynamics of the system. Video analysis techniques represent a novel and under
development discipline, through which it will be increasingly possible to better under-
stand the motorcyclerider relationship.
The practical implications of the presented study will involve the use of the devel-
oped algorithms in activities regarding vehicle design and motorsport analysis, for which
the continuous and correct information on the rider’s CoG is an element of crucial interest
as concerns the effect of the body motion on vehicle dynamics and the ride/handling atti-
tude of the vehicle to be virtually prototyped.
Figure 15. Linear regression line: OpenPose (on left) and neural network (on right).
4. Conclusions
The objective of determining the motion of a motorcycle rider using machine learning
algorithms processing images through CNN motion capture techniques has been pursued in
this paper, due to the complexity of developing and run physical-based algorithms, and the
difficulty in parameterization, vehicle design and performance optimization applications.
The CoG parameter plays, in fact, a fundamental role in vehicle dynamics simulations
and in the design phase of the motorcycle, since the rider and the motorcycle are not two
separate systems, but fully integrated bodies whose deep understanding is a starting point
to achieve maximum performance both in terms of safety and racing competitiveness.
The application of a technique based on the use of neural networks has made it possible
to identify the position of several key points belonging to the human body, starting from
the video frames acquired at the rear edge of a motorcycle from a gaming simulator. Such a
Vehicles 2021,3388
choice was made because the reliability of the video data is not a main focus of the work,
which aims to set a methodology that will be then replicated with real vehicle video data.
The quality of the results obtained is closely linked with the OpenPose software
potential, which, as illustrated, could have significant limits in the recognition of key
points in particular positions. Despite such an aspect, the presented activity presents a
methodologic approach which could be further improved in terms of data quality, thanks
to the availability of a more reliable acquisition system, retaining its feasibility.
The training of a neural network, even applied to frames reproducing partial visibility
of the driver, allowed us to determine the key points not visible to the camera, thus also
guaranteeing the calculation of the center of gravity in conditions in which such a task
could hardly be achievable.
Finally, a preliminary function, linking the relative displacement of the driver’s center
of gravity towards the vehicle rolling axis as a function of the roll angle, has been proposed.
The determination of the driver’s center of gravity plays a fundamental role in the
overall dynamics of the system. Video analysis techniques represent a novel and under
development discipline, through which it will be increasingly possible to better understand
the motorcycle–rider relationship.
The practical implications of the presented study will involve the use of the developed
algorithms in activities regarding vehicle design and motorsport analysis, for which the
continuous and correct information on the rider’s CoG is an element of crucial interest as
concerns the effect of the body motion on vehicle dynamics and the ride/handling attitude
of the vehicle to be virtually prototyped.
Author Contributions:
Data curation, F.C.; Funding acquisition, G.R.; Methodology, D.S.; Software,
D.D.; Supervision, F.F.; Validation, A.S. All authors have read and agreed to the published version of
the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
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... The transient dynamics of the tyre is a rather intriguing and elusive phenomenon [1][2][3], involving several interconnected aspects. Amongst the external stimuli that may excite nonstationary behaviours in the tyre-wheel assembly there are, for example, time-varying slip and spin inputs [4,5], unsteady effects due to the compliance of the tyre tread and carcass, and even abrupt discontinuities in the available friction at the tyre-road interface. In order to synthesise and implement ad-hoc algorithms and strategies for vehicle state estimation and control [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], it is crucial to rely on simple and plausible physical models, capable of explaining at least qualitatively all the above-mentioned processes, and their influence upon the transient generation of tyre forces and moments [2,22,23]. ...
... The closure relationships to Eqs. (1), (5) and (6) are finally provided by the constitutive and equilibrium equations. The first set of equations relates the shear stresses q t (ξ, s) = [q x (ξ, s) q y (ξ, s)] T acting at the contact patch to the deformation of the bristles, and the global tyre forces to the deflection of the tyre carcass, respectively. ...
... Artificial neural networks have recently been utilized in many diverse applications for (1) classification, (2) optimization, (3) clustering, and (4) pattern recognition [24,25]. Their implementation fields include CM of gearboxes [26], motor vehicles (e.g., race cars and motorcycles) [27,28], mining (e.g., thrust and moment prediction) [29], etc. However, machine learning (ML) algorithms, such as the k-nearest neighbor, support vector machines, and decision tree classifiers, comprise shallow structures, making learning pertinent hidden faults (for example, tooth root crack) features more compelling [19]. ...
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... The transient behaviour of the tyre is an extremely complicated and fascinating subject [1][2][3], which involves the interaction of several interconnected phenomena. These may include, for example, continuous variations in the slip inputs [4], camber angles and vertical load acting on the tyre [5], nonstationary effects due to the compliance of the tyre tread and carcass, and even abrupt discontinuities in the available friction at the tyre-road interface. An exhaustive understanding of all these phenomena, and their influence upon the transient mechanism of tyre forces and moment generation, is an essential prerequisite when it comes to the design and implementation of algorithms for vehicle state estimation and control [2,6,7]. ...
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This paper presents a novel tyre model which combines the LuGre formulation with the exact brush theory recently developed by the authors, and which accounts for large camber angles and turning speeds. Closed-form solutions for the frictional state at the tyre-road interface are provided for the case of constant slip inputs, considering rectangular and elliptical contact patches. The steady-state tyre characteristics resulting from the proposed approach are compared to those obtained by employing the standard formulation of the LuGre-brush tyre models and the exact brush theory for large camber angles. Then, to cope with the general situation of time-varying slips and spins, two approximated lumped models are developed that describe the aggregate dynamics of the tyre forces and moment. In particular, it is found that the transient evolution of the tangential forces may be approximated by a system of two coupled ordinary differential equations (ODEs), whilst the dynamics of the self-aligning moment may described by combining two systems of two coupled ODEs. Given its stability properties and ease of implementation, the lumped one may be effectively employed for vehicle state estimation and control purposes.
... In addition to the mathematical modelling, the increasing usage of machine learning and neural network algorithms [25][26][27][28][29] has led to new vehicle control and design strategies [30]. An important aspect to investigate is the stress state acting on the mechanical components when the vehicle is hybridized, starting from a conventional configuration i.e., only with the ICE engine propulsion. ...
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This work aimed to develop an automatic new methodology based on establishing if a mechanical component, designed for a conventional propulsion system, is also suitable for hybrid electric propulsion. Change in propulsion system leads to different power delivery and vehicle dynamics, which will be reflected in different load conditions acting on the mechanical components. It has been shown that a workflow based on numerical simulations and experimental tests represents a valid approach for the evaluation of the cumulative fatigue damage of a mechanical component. In this work, the front half-shaft of a road car was analyzed. Starting from the acquisition of a speed profile and the definition of a reference vehicle, in terms of geometry and transmission, a numerical model, based on longitudinal vehicle dynamics, was developed for both conventional and hybrid electric transmission. After the validation of the model, the cumulative fatigue damage of the front half-shaft was evaluated. The new design methodology is agile and light; it has been dubbed “Smart Design”. The results show that changing propulsion led to greater fatigue damage, reducing the fatigue life component by 90%. Hence, it is necessary to redesign the mechanical component to make it also suitable for hybrid electric propulsion.
... The technical literature is plenty of articles about VSA estimation. There are different approaches to estimate the VSA starting from the observer-based methods [5], [6], [7] up to neural network data-based techniques [8], [9]. The observer-based methods are characterized by the type of state estimator adopted, e.g. ...
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