Adaptive heading correction for an industrial heavy-duty omnidirectional robot

Abstract

The paper deals with the design and testing of a robot for industrial applications featuring omnidirectionality thanks to the use of mecanum wheels. While this architecture provides remarkable manoeuvrability in narrow or cluttered spaces, it has some drawbacks that limit its widespread deployment in practice, especially for heavy-duty and long-duration tasks. As an example, the variability in the mecanum wheel rolling radius leads to undesired dynamic ill-effects, such as slippage and vibrations that affect the accuracy of pose estimation and tracking control systems. Drawing on the modeling of the kinematic and dynamic behaviour of the robot, these effects have been tackled within an adaptive estimation framework that adjusts the robot control system based on the properties of the surface being traversed. The proposed approach has been validated in experimental tests using a physical prototype operating in real industrial settings.

Full text

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Adaptive heading correction
for an industrial heavy‑duty
omnidirectional robot
Rocco Galati*, Giacomo Mantriota & Giulio Reina
The paper deals with the design and testing of a robot for industrial applications featuring
omnidirectionality thanks to the use of mecanum wheels. While this architecture provides remarkable
manoeuvrability in narrow or cluttered spaces, it has some drawbacks that limit its widespread
deployment in practice, especially for heavy‑duty and long‑duration tasks. As an example, the
variability in the mecanum wheel rolling radius leads to undesired dynamic ill‑eects, such as slippage
and vibrations that aect the accuracy of pose estimation and tracking control systems. Drawing
on the modeling of the kinematic and dynamic behaviour of the robot, these eects have been
tackled within an adaptive estimation framework that adjusts the robot control system based on the
properties of the surface being traversed. The proposed approach has been validated in experimental
tests using a physical prototype operating in real industrial settings.
In recent years, mobile robots have been increasingly used in various applications of logistics and supply chain
management1–3. Several examples have been demonstrated to optimize and improve industrial processes, drawing
attention from both academy and industry4–6. Many companies are trying to speed up their production processes
by applying just-in-time (JIT) strategies with the aim of increasing eciency and reducing waste by receiving
goods only as needed in the production process by reducing inventory costs7. As a result of the adoption of new
technologies in many industrial plants, the eciency of the production processes has increased causing an over-
loading of the logistics area as a consequence. For this reason, a series of unmanned ground vehicles (UGV) have
been designed to operate as logistic robots for picking8, palletizing9, and handling10 products. Omnidirectional
robotic platforms have attracted much attention since they are capable of driving in any direction by minimizing
the total path between two points and they are suitable for compact and narrow industrial spaces11.
Omnidirectional vehicles have been proposed12–14 with varying wheels and chassis congurations, the most
important of which are based on three-wheel and four-wheel schemes15. Indeed, the number of mecanum wheels
aects the power consumption16,17: a four wheeled system allows to harness the motors power up to 50%, when
translating along the axis of a wheel, and to 71%, when translating 45 deg from an axis of a wheel, while a three
wheeled conguration enables the system to use up to 47% of the total motors power when translating along the
axis of a wheel and up to 68%, when translating 30 deg from an axis of a wheel18.
Most of the omnidirectional robots proposed in the literature have been used for research purposes or
lightweight applications19 where no payload20 or limited payload21 is present, whereas no heavy duty industrial
example has been discussed.
One common drawback of all vehicles using mecanum wheels is that they are aected by random slippage22
and high-speed vibration23 that lead to position errors and energy dissipation problems24,25. is is especially
true for robots that are required to carry large loads. In this research, an omnidirectional robot is presented
designed to be employed for heavy duty applications in industrial sites or service tasks that feature signicant
payload and long-duration operations. Critical issues are addressed for the practical deployment of the system,
including variability in the wheel radius and accurate pose estimation even in the presence of unpredictable slip
occurrences incurred by the mecanum wheels. A robust and adaptive trajectory tracking system is presented as
well that adjusts automatically the parameters of the control system according to the specic supporting surface.
Materials and methods
Vehicle overview. e omnidirectional vehicle used for this research, named Omnibot, is showed in Fig.1.
Ominibot is based on a rectangular plan having an overall length and width of, respectively,
b=1012
mm
and
a=1038
mm that provide a large supporting base. At each of the four corners, an assembly made up of a
OPEN
Department of Mechanics, Mathematics, and Management, Polytechnic of Bari, via Orabona 4, 70126 Bari, Italy.
*email: rocco.galati@poliba.it
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mecanum wheel, a gearbox with reduction ratio
i=30
, a 500 W brushed DC motor with a speed of 3000 rpm
and a torque of 35 Nm, and a 1024 pulse optical encoder is placed to provide an ecient and robust locomotion
system. Motors are controlled by a total of four drivers, featuring a high-performance 32-bit microcomputer and
quadrature encoder input to perform advanced motion control algorithms in both open-loop and closed-loop
modes for speed and position. In order to enable the vehicle to increase its working autonomy, a 24 VDC 200
Ah AGM battery pack has been installed in c to provide a maximum output power of 4.8 kW with a 350 A bat-
tery isolator switch based on a high-load solenoid. Each mecanum wheel has a vertical load capacity of 250 kg
and the metal frame of the robot has a total payload of 1000 kg to allow the use of large and heavy equipment
in industrial environments. e robot has been completely custom built starting from CAD design, and all the
parts have been manufactured by using laser cut and bending machines. Table1 summarizes the main mechani-
cal specications.
Omnidrivability. Omnibot fullls holonomy by adopting four mecanum wheels, whose main specications
have been collected in Table2. Both outer plates with a maximum diameter of about 278 mm are made of stain-
less steel and feature twelve teeth with a pitch of about 54 mm placed on their outer circumference and bent at 45
deg. Each pair of outer and inner teeth is used to mount a passive so nylon roller with a length of 108 mm for
a total of twelve rollers. Figure2 reports three dierent views and the overall dimensions of a single wheel. e
angled rollers translate a portion of the force in the rotational direction of the wheel to a force that is normal to
the wheel direction. Depending on each individual wheel direction and speed, the resulting combination of all
these forces allow the vehicle to move in any direction.
Figure1. e omnidirectional vehicle used for this research study: (A) top view of the real robot, (B) isometric
view of the 3D rendering.
Table 1. Omnibot main technical specications.
Omnibot specications Val ue
Number of motors 4
Overall dimensions 1012
×
1038mm
Max velocity (any direction) 1 m/s
Max Payload 1000 kg
Output power 4800 W
Vehicle weight 200 kg
Table 2. Mecanum wheel specications.
Mecanum wheel specications Va lue
Number of rollers 12
Roller angle
45◦
Diameter of mecanum wheel 280 mm
Diameter of roller at its center 46 mm
Diameter of roller at the extremities 34 mm
Wheel mass 15 kg
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Control and acquisition system. e control architecture of Ominibot is reported in Fig.3. Four power
drivers are used over a CAN Bus network where the controller for the front le wheel is the master and all the
other ones are set as slaves. e main operating system runs on an industrial computer with an Intel i7 CPU and
powered by ROS featuring also three USB 3.1 ports useful to connect dierent kind of sensors such as the Inertial
Measurement Unit, XSens Mti-300, mounted on the front bumper of the vehicle in order to detect velocities and
accelerations. Note that each motor is equipped with a Hall sensor to read the electrical current.
Kinematics and dynamics modeling
Inverse kinematics. With reference to Fig.4, the inverse kinematic model of the omnidirectional vehicle
can be derived from the knowledge of the velocity vector V, whose components along the
X−
and
Y−
axes are,
respectively,:
Figure2. Details of the mecanum wheels: (A) side view; (B) isometric view, and (C) front view where it is
possible to see the roller details. All measurements are in mm.
Figure3. e control architecture of Omnibot.
Figure4. Movement vector and coordinate system of mobile four-wheel drive vehicles.
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where
ψ
identies the orientation of the vehicle while the angular velocity is dened by
˙
ψ
. Important geometric
parameters are the mecanum wheel radius r, the distance a between the body and the wheel center along the x
axis and by the length of b which is the distance between the body and the wheel center along the y axis:
where i: 1,2,3,4 represents each mecanum wheel. e linear velocity vector and the velocity of mecanum nylon
roller direction for each wheel are indicated by
vi
and
si
, respectively. Tilted angle
γ
between v and s is
45◦
and
represents the mecanum roller angle:
e velocity vector equation of the vehicle towards the two coordinate system components can be calculated by:
By using equations (6) and (7), it is possible to derive all the linear velocities associated to each mecanum wheel:
Knowing that the wheel velocities can also be expressed as
vi=˙
ψr
, equations from (8) to (11) can be written
in compact matrix form:
Equation (12) shows the mathematical model of the inverse kinematic to obtain the angular velocities for the
mecanum wheels by using as input the three components of the velocity
vx
,
vy
and
˙
ψ
where the matrix R is
dened as follows:
By inverting the matrix R using the Moore-Penrose theorem, it is possible to obtain the direct kinematic model
to retrieve
vx
,
vy
and
˙
ψ
given the wheel angular velocities:
where
R+
is the pseudoinverse matrix of R.
Rolling radius. An important aspect of the Omnibot kinematics refers to the knowledge of the wheel radius.
By analyzing the mecanum wheel rotational motion, it is possible to observe that there is a constructive limit
(1)
vx=vcosψ
(2)
vy=vsinψ
(3)
ai={a,a,−a,−a}
(4)
bi={b,−b,b,−b}
(5)
γ
i=
π
4
,−
π
4
,−
π
4
,
π
4
(6)
vi+sicosγi=vx−bi˙
ψ
(7)
si
sinγ
i
=v
y
+a
i˙
ψ
(8)
v
1=vx−vy
tan
γ1
−a
˙
ψ
tan
γ1
−b˙
ψ
(9)
v
2=vx−vy
tan γ2
−a
˙
ψ
tan γ2
−b˙
ψ
(10)
v
3=vx−vy
tan
γ3
−a
˙
ψ
tan
γ3
−b˙
ψ
(11)
v
4=vx−vy
tan γ4
−a
˙
ψ
tan γ4
−b˙
ψ
(12)



w
1
w2
w3
w4



=1
rR

vx
vy
˙
ψ


(13)
R
=





1, −
1
tan γ1,−
a
tan γ1+b
1, −1
tan γ2,−a
tan γ2+b
1, −1
tan γ3,−a
tan γ3+b
1, −1
tan γ4
,−a
tan γ4+b





(14)


vx
vy
˙
ψ


=r
4R+



w
1
w2
w3
w4



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due to the presence of the nylon rollers that prevents the wheels from having a continuous contact surface and
therefore to keep the radius of the wheel constant. is contributes to generate dierent tangential speeds for
each individual wheel26. It is critical to address this problem in order to limit the wear of the rollers and to avoid
unpredictable deviations from the intended path that are dicult to predict by standard odometry approaches.
When one looks at the longitudinal middle section of the wheel, it is possible to obtain the radius change as
a function of the wheel rotational angle. Since each mecanum wheel is made up of twelve rollers, the radius
changes periodically every 30 deg ranging from its starting value up to the maximum measured value as it is
showed in Table3 where radius values for some intermediate wheel rotations are reported.
As showed in Fig.5, by using the relation to calculate the radius variation for each mecanum wheel position:
where s is the roller radius, d is the distance between the roller and the wheel hub,
α
is the current angular posi-
tion for each wheel, it is possible to improve the performance of the motion controller. Figure6 shows the radius
as a function of the wheel rotation. e radius variation aects not only the wear of the rollers but also the total
path of the vehicle that becomes not predictable. is path error has been reduced by integrating the function
of the radius by time in order to increase the accuracy of the total traveled distance.
Wheel slipping. When a torque is applied to a mecanum wheel, it starts to rotate without slipping as long as
the driving force, F, does not exceed the maximum static friction,
µ
, i.e.,
F<µFzsin(45)
. When the threshold
is overcome, the wheel slips as it rolls, resulting in unpredictable deviations. Under the assumption of uniform
weight distribution and a vehicle mass of 200 kg, a single wheel is subject to a quarter of the total vehicle weight
Gtot (1962 N), i.e.,
F
z=
Gtot
4
=
490.5
N. Friction values can be found in the literature, for example27, for most
common surfaces. For example,
µc=0.5
for industrial concrete oor and
µa=1
for asphalt. en, in order for
a given wheel to perform a pure rolling motion, the following condition must be satised:
where T indicates the torque applied to the wheel, and
r=0.15093
m the average radius. e maximum torque
that can be delivered by each drive motor is
Tmax =47
Nm as obtained from the following formula:
being
P=500W
and
RPM =3000/τ =100
rpm, where
τ=30
is the gearbox reduction ratio. By considering
equation (17), it is also possible to introduce the relation between the mechanical torque, and the electric cur-
rent drawn by each motor:
(15)
r(α) =s+dcos(α)
(16)
T≤Tmax =µFzsin(45)r
(17)
T
=
60P
2πRPM
Table 3. Radius values for 5-deg steps of wheel rotation.
Position (deg) Radius (m)
0 0.1524
5 0.1519
10 0.1504
15 0.1480
20 0.1504
25 0.1519
30 0.1524
Figure5. Radius variation for each mecanum wheel.
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where i is the gearbox reduction ratio,
τt=0.079
Nm/A is the motor torque constant and I is the electric current
drawn by each DC motor.
Vertical dynamics. It can be observed that the variation of the wheel radius, as described in the previous
section, forces the wheel to oscillate and the overall vehicle vibrational response can be considered as modu-
lated by the interaction of the wheel with the specic ground surface28. Even if the angular position of all four
mecanum wheels is identical when the vehicle starts to move, a perfect synchronization is very dicult during
operations due to the slipping eects between each roller and the ground surface. Although the radius variation
is independent of the ground surface, it is important to highlight that the vehicle vibration response is strictly
related to the interactions between the mecanum wheels aected by their radius variation and the ground sur-
face; it is therefore possible to nd out a specic vehicle’s behavior by studying the power spectral density func-
tion. In linear systems, it exists a direct linear relationship between input and output. A vehicle system dened by
its transfer function takes into account the input representing the terrain irregularities and generates an output
representing the vibration of the vehicle29. In this case, the frequency response function can be dened as the
ratio of the output to input under steady-state conditions.
In order to simplify the study of the vertical motion of Omnibot, a one-degree-of-freedom quarter vehicle
model has been considered30. is assumption has been widely adopted in the literature for the analysis of many
robots, e.g.31,32. Further studies33 have demonstrated how the theory of vibration of single-degree-of-freedom
systems serves as one of the fundamental building blocks in the theory of vibration of discrete and continuous
systems and the techniques developed for the analysis of single degree of freedom systems can be generalized
to study discrete systems with multi-degree of freedom as well as continuous systems. en, if it is possible to
consider a simplied single-degree-of-freedom model for the vehicle, and the surface irregularity as input is
dened in terms of displacement (or elevation of the surface prole) and the vibration of the sprung mass as
output is measured in acceleration, then the modulus of the transfer function H(f)27, can be expressed as:
where and
ζ=0.1
is the damping ratio, f is the frequency of excitation and
fn
is the natural frequency of the
system, which is approximately
fn=38Hz
for the considered vehicle as obtained experimentally by using an
inertial sensor and an impact piezoelectric hammer with a load cell tip. When the transfer function of a specic
system is known, then, it is possible to express the relation between the power spectral density of the input
Sg(f)
and the power spectral density of the output
Sv(f)
of the whole system as follows:
is relation shows how the output power spectral density is associated to the input power spectral density
through the square of the modulus of the transfer function. e power spectral density denes how the power
of a signal is distributed over frequency and it is strictly correlated to the interaction between the ground surface
and the mecanum wheels nylon rollers. e study of this important aspect allows nding the proper ngerprint
for each ground surface.
(18)
T=iτtI
(19)
|
(H(f)|=(2πf)2







1+2ζf
fn2
1−

f
fn

22
+

2ζf
fn

2
(20)
Sv
(
f
)=|
H
(
f
)
2
|
Sg
(
f)
Figure6. Radius variation against the wheel angular position.
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Omnibot pose estimation and trajectory tracking
Since vehicles that employ mecanum wheels are able to rotate and move in narrow spaces, they are very suitable
for industrial applications. However, the slipping eects on each roller can introduce a signicant trajectory error
both during straight motion and also during lateral displacements, and so it is dicult to retrieve the correct
vehicle position. In order to better dene the straying angle for the vehicle, it is possible to introduce a devia-
tion angle
θ
which is the dierence between the angle the vehicle should have and the current angle. As showed
in Fig.7, when the vehicle is commanded to move forward on a straight line, all the motors receive the same
PWM commands and they start spinning with the same velocity and towards the same direction. e surface
irregularities and the slipping eects lead to a lateral dri
dy
, which can be dened as:
where
θ
is obtained by integrating the yaw rate measured by the on board inertial sensor. e resulting value of
dy
is strictly related to vehicle geometry and to the ground properties.
In order to improve the accuracy of the pose estimation system, a Kalman lter is adopted by using the read-
ings coming from the gyroscope and the accelerometers included in the XSens Mti-300 inertial sensor despite
the presence of signicant errors in real time measurements34. Noisy accelerometers and gyro can be combined
to obtain an accurate representation of unit’s orientation and position35. e used Kalman lter basically consists
of two stages: during the rst stage, a mathematical state model is applied to make a prediction about the system
state while, during the second stage, this state prediction is compared to measured state values. e dierence
between the predicted and measured state is based on estimated noise and error in the system and measurements
while a state estimation is generated as output. Finally, this output estimation is used in conjunction with the
mathematical state model to predict the future state during the next time update, and the cycle begins again. By
considering the inertial measurement unit’s output, the system state x(t) can be expressed as:
where x(t) expresses the system state at time t, while
px(t)
and
py(t)
represent the position along the X and Y
axes, respectively,
vx(t)
and
vy(t)
are the velocities in the x–y plane and
ax(t)
and
ay(t)
are the accelerations along
the X and Y axis at time t. e Kalman ltering estimation operates through the prediction-correction cycle
expressed as follows: Prediction:
Correction:
(21)
d
y=

1
4
(d1+d2+d3+d4)

tan θ
(22)
x
(t)=







p
x
(t)
py(t)
vx(t)
vy(t)
ax(t)
a
y
(t)







(23)
ˆ
x
−
t+1
=
Ad
ˆ
xt
+
Bdut
(24)
P−
t+1
=A
d
P
k
A
T
d
+
Q
(25)
Kt
+1=P
−
t+1
H
T
d
(H
d
P
−
t+1
H
T
d
+R)
−1
Figure7. e straying angle caused by slipping episodes incurred by the mecanum wheels.
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where
ˆ
x
−
t+1
is the predicted state vector, A and B are the state transition matrix,
P−
t+1
is the variance matrix
for
ˆ
x
−
t+1
,
Kt+1
is the gain matrix,
ˆxt+1
is the updated state vector, and
Pt+1
is the updated error covariance
estimation; the noise covariance of the process is expressed by Q, while R accounts for the uncertainty in the
measurement and is set as
R=σgyro
. e updated position information from the Kalman lter, and, especially,
the heading of the vehicle is used to feed a combination of proportional, integrative and derivative controls (PID)
with the aim to keep the vehicle on its track while commanded to move straight forward, backward or laterally by
generating the proper corrections for all four motors as reported in Fig.8. Even if other advanced control strate-
gies, such as model predictive control (MPC) and slide model control (SMC), have been used in the literature
and are gaining signicant attention from both industry and academia, for this specic application, PID control
has been preferred since it requires less computational time, implementation eorts, and memory consumption
given the hardware resources installed on board the vehicle to keep the system cost-eective and easy to produce
on a large scale, as happens in conventional industrial scenarios. Typical nal applications for Omnibot, like
the automatic oor marking described later in the paper can be considered as non-delay dominant processes
and so they are particularly suitable for a PID controller. e controller continuously calculates an error e as the
dierence between a desired set-point and the measured heading value calculated by the MTi-300 by applying a
correction. Equation (28) describes the behavior of the controller implemented for trajectory correction:
where u is the measurement sent to the motors command algorithm,
Kp
is the proportional gain while
Kr
and
Kd
are the integrative and derivative gains, respectively. e parameters
Ac
and
Bc
are generated by a surface classier
algorithm based on the analysis of the power spectral density (PSD) calculated over the vertical accelerations
and motor currents: in particular, by measuring the dierent accelerations along the Z axis and the currents
drawn by each motor, it is possible to detect the features of the ground surface where the vehicle is moving on.
Experimental evidence shows how the magnitude of the trajectory error is strictly related to the interactions
between the mecanum wheels rollers and the ground surface by resulting in a dierent straying angle. Depending
on the surface characteristics, the surface estimator sets the value of
Ac
and
Bc
to improve the corrections over
the proportional and derivative gains. e output Y includes all the parameters (
vx
,
vy
and
˙
ψ
) needed to control
the motors as specied in Eq.(14).
Experimental results
Dierent tests in a real industrial setting have been run in order to assess the performance and validate the
adaptive control system. In the rst test case, the vehicle has been commanded to follow two motion primitives,
moving straight forward and sideways, over two dierent ground surfaces: industrial concrete oor and asphalt.
e rst one is made by a at and leveled slab formed by concrete and it is designed to withstand heavy-duty
vehicular trac while its elastic modulus is 40 GPa and its stiness module is 70 MPa. e asphalt surface is
made by a bituminous granular mixtures used for public roads with a stiness module of 140 MPa and an elastic
modulus of 480 MPa. Sample patches for both the ground surfaces are showed in Fig.9 and as it can be noted,
the concrete surface is regular and free of debris while the asphalt surface is irregular and dirtier. No other sur-
faces have been considered since the proposed vehicle is intended to operate in warehouses, where concrete and
asphalt are the two typical pavements.
As reported in Fig.10, the straight forward motion is obtained by making all the wheels spin in the same
direction and by setting a xed linear velocity, while, in order to make the vehicle move sideways, it is necessary
(26)
ˆxt
+1=
ˆ
x−
t+1
+K
t
+1(z
t
+1−H
d
ˆ
x−
t
+1
)
(27)
Pt
+1
=(I−Kt
+1
Hd)P−
t+1
(28)
u
=AcKpe+Kr

e dt +BcKd
de
dt
Figure8. e PID controller used for the closed-loop system used to generate motors commands.
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Figure9. e surfaces used for this research study: concrete, on the le, and asphalt, on the right.
Figure10. Wheel spinning conguration for the two motion primitives used for the tests.
Figure11. Currents drawn by motors over asphalt, on the le, and over concrete, on the right, during straight
motion.
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to control motors M1 and M3 to make them spin clockwise and motors M2 and M4 to spin counter-clockwise
at xed velocity. Figure11 highlights the motor currents drawn by the drive motors where time, expressed in
seconds, is represented horizontally on the X-axis and the current amplitude, in ampere, is reported on the Y-axis,
while the vehicle moves on asphalt (le) and industrial concrete oor (right) during straight motion. Since asphalt
has a higher friction component and unevenness level than concrete, the average currents are about 6.5A with
some maximum peaks above 10A when time t=170s during the transient starting stage. At steady-state conditions
(between t=180s and t=277s), uctuations in the electrical currents ranging from 6A to 7A can be noted due
to asphalt irregularities and to sporadic contact loss of the omni wheels. On the other hand, average currents for
concrete are about 5.4A at steady-state with maximum peaks at time t= 327s where they do not exceed 7A. e
currents in the time interval between t=340s and t=460s uctuate in quite a restrained way since concrete features
a atter and regular surface. It is very interesting to note that the sideways motion requires more power from
the motors due to the sliding of the rollers placed at
45◦
and the ground as shown in Fig.12. For this reason, the
average current drawn by the motors for sideways motion on concrete is 10.4A with a constant trend character-
ized by limited uctuations from 9.5A to 11A in the time interval between t=22s and t=55s. On asphalt, the
average current is about 16.6A with a maximum peak of 25A at t=10s and a more uctuating behavior in the
time interval between t=10s and t=45s because of the irregular surface as described for the forward motion.
Moreover, during sideways motion, the currents of motors M2 and M4 are positive while the currents of motors
M1 and M3 are negative since the vehicle is sliding on the le following the conguration reported in Fig.10.
All the plots report some spikes due to the intrinsic nature of the MDC2460 motor controller used for Omnibot
and the 500W DC brushed motors.
A second test case has been devoted to evaluate the robot vibrational response, as described in section III.D.
Figure13 shows two periodograms obtained as result of the vibrations over the vehicle’s frame on two dierent
surfaces, concrete and asphalt, as an estimation of the spectral density of the vertical accelerations by examining
the amplitude against the frequency characteristic measured by the inertial sensor. More details on the use of
the power spectral density can be found in previous research studies36–38.
e average noise power per unit of bandwidth for the industrial concrete oor is about -49.29 dB/Hz while
the average for the asphalt is -36.54 dB/Hz and this is because the asphalt provides a rough surface with small
debris that contribute to increase the vibration response compared to the concrete oor that can be considered
as totally at. e features of the ground surface also have eects on the locomotion control of the vehicle since
they introduce unpredictable slipping eects and slide motions that disturb the vehicle’s trajectory. A straight
line reference made by a laser pointer has been set up both on the industrial concrete oor and asphalt in order
to study the performance of the trajectory control. e right side wheels of Omnibot have been aligned with
the red line reference, and the vehicle has been commanded to move forward and backward following a straight
path for 10 meters with an open-loop control both on industrial concrete oor and on asphalt, for ten times for
each direction, in order to measure the total accumulated error between the red reference straight line and the
nal position of the vehicle as showed in Figs.14 and 15.
Before each test, the inertial sensor has been initialized, calibrated and set to
θ0=0 deg
in order to be able
to accurately measure the nal deviation angle
θc
on the concrete and
θa
on asphalt.
In all tests, the error has been measured thanks to a laser distance meter and the values are reported in Table4
where it is possible to see how to maximum error has been registered during test 2 on concrete with
ec=0.94m
and a maximum deviation angle
θc=4.81 deg
as highlighted in Fig.16 where the Y-axis reports the values of the
yaw angle expressed in degrees and the X-axis reports the samples acquired from the inertial sensor at 25Hz while
the maximum error obtained on asphalt during test 6 is
ea=0.72m
with a total deviation angle of
θa=3.54 deg
.
Figure12. Currents drawn by motors during sideways motion on asphalt, on the le, and on concrete, on the
right.
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It is worth noticing that the holonomic vehicle performs dierently depending on the ground surface: when it
is commanded to follow a straight line on industrial concrete oor, the slipping eects caused by the at surface
are higher than the ones introduced by the asphalt surface which, on the other hand, provides a more rougher
surface with an higher friction coecient that allows the rubber rollers from the mecanum wheels to have more
grip by minimizing the skidding eects. e average dierence between the angle deviation on concrete and on
asphalt is more than
Aθc−Aθa=1.3 deg
which is particularly relevant for longer trajectories since, for example,
a dierence on the angle deviation of just
1.3 deg
can lead to a total nal error at the goal of about 2.37 m. By
Figure13. Periodogram from vertical accelerations over concrete, on the le, and over asphalt, on the right,
during straight motion.
Figure14. e vehicle positioned at the starting point on concrete, on the le, and the nal error at goal, on the
right.
Figure15. e vehicle positioned at the starting point on asphalt, on the le, and the nal error at goal, on the
right.
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taking into account that both the average currents drawn by the motors and the PSD values can be considered
as unique ngerprints for each ground surface39, it is possible to apply a closed-loop control as already described
in Eq. (28) where the parameters
Ac
and
Bc
are generated by the ground classier and are used as adjustment
values to make the PID control outputs the motors corrections faster by avoiding waiving loitering around the
track; the PID control has been tuned by running an experimental trial-and-error method based on a total of
ten tests for each surface and by measuring each time the total nal error. In the end, the PID control has been
congured to work with
Kp=1.0
,
Kr=0.02
,
Kd=0.1
and
Ac=1.1
and
Bc=1.6
.
As reported in Table5, by applying the closed-loop control, it is possible to make the vehicle keep on its track
with a nal maximum angle deviation of
0.40 deg
on concrete with a maximum nal error of 0.17 m and 0.57
deg
on asphalt with a maximum nal error of 0.20 m as reported in Figs.17 and 18; moreover, it is interesting to
note that on the concrete, there is typically an overshoot of about
+0.2 deg
caused by the derivative control of
the PID while trying to minimize the slipping eect while the overshoot is almost null on asphalt because of its
rougher surface.
Table 4. Errors and yaw angle deviation for each test.
Tes t Dir Surface
c
deg Error m Surface
a
deg Error m
1 F Concrete 4.56 0.90 Asphalt 3.10 0.64
2 F Concrete 4.81 0.94 Asphalt 3.15 0.65
3 F Concrete 4.69 0.92 Asphalt 3.41 0.69
4 F Concrete 4.75 0.93 Asphalt 2.95 0.61
5 F Concrete 4.56 0.90 Asphalt 2.98 0.62
6 F Concrete 4.20 0.83 Asphalt 3.54 0.72
7 F Concrete 3.98 0.79 Asphalt 3.26 0.67
8 F Concrete 4.21 0.83 Asphalt 2.91 0.61
9 F Concrete 4.56 0.90 Asphalt 2.97 0.62
10 F Concrete 4.34 0.86 Asphalt 2.85 0.60
11 B Concrete 4.75 0.93 Asphalt 2.80 0.59
12 B Concrete 4.56 0.90 Asphalt 3.20 0.66
13 B Concrete 3.97 0.79 Asphalt 3.50 0.71
14 B Concrete 3.89 0.78 Asphalt 3.40 0.69
15 B Concrete 4.21 0.83 Asphalt 3.50 0.71
16 B Concrete 4.34 0.86 Asphalt 2.70 0.57
17 B Concrete 3.95 0.79 Asphalt 3.10 0.64
18 B Concrete 4.5 0.88 Asphalt 2.80 0.59
19 B Concrete 4.43 0.87 Asphalt 3.30 0.68
20 B Concrete 4.60 0.90 Asphalt 2.90 0.61
Figure16. Angle deviation on straight trajectory on concrete, on the le, and the angle deviation for asphalt,
on the right.
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Load inuence
One of the possible industrial applications of Omnibot is the automatic oor marking of large exhibition halls
where the boundaries of the single exhibition booths need to be clearly set before the event. To this aim, Omnibot
is equipped, as shown in Fig. 19, with an airless spraying unit powered by an hydraulic pump (5), commanded
by a motor driver (6), that sucks out the paint stored in two tanks (2), placed in the upper rack (1), and feeds it
to a bottom nozzle (4) usually placed at 25 cm away from the oor even if its height can be adjusted by using the
Table 5. Final errors and yaw angle deviation for each test.
Tes t Surface
c
(deg) Error (m) Surface
a
(deg) Error (m)
1 Concrete 0.38 0.17 Asphalt 0.52 0.19
2 Concrete 0.39 0.17 Asphalt 0.57 0.20
3 Concrete 0.32 0.16 Asphalt 0.56 0.20
4 Concrete 0.31 0.15 Asphalt 0.49 0.19
5 Concrete 0.40 0.17 Asphalt 0.41 0.17
6 Concrete 0.29 0.15 Asphalt 0.39 0.17
7 Concrete 0.34 0.16 Asphalt 0.54 0.19
8 Concrete 0.37 0.16 Asphalt 0.53 0.19
9 Concrete 0.34 0.16 Asphalt 0.57 0.20
10 Concrete 0.39 0.17 Asphalt 0.43 0.18
Figure17. Final angle deviation with PID on straight trajectory on concrete, on the le, and the angle deviation
with PID for asphalt, on the right.
Figure18. Final maximum error obtained on concrete, on the le, and on asphalt, on the right.
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positioning holes available on the nozzle support (7). Finally, an internal 12 VDC air compressor (3) is used to
enable or disable the nozzle. e total weight of the sprayer unit is 94 kg resulting in an increase of about 50% of
Omnibot original weight. An experimental campaign with a total of ve tests was performed by commanding the
vehicle to follow a 30 m straight line moving on a concrete surface inside the Fieramilano area in Rho, Italy. e
proposed adaptive closed-loop control algorithm was adopted in all tests. e average registered errors of 0.15
m (worst case 0.18 m) and 0.34 deg (worst case of 0.42 deg) on the nal position error and yaw deviation angle,
respectively, fulll the requirement for the automatic oor marking task. Performance can be seen in line with
the previous results obtained from Omnibot without any payload, indicating that the adaptive control shows a
high robustness to change in the payload.
Conclusion
is research presented Omnibot, an omnidirectional vehicle intended for heavy duty industrial and service
applications featuring large payload and increased energy autonomy by addressing specic issues including
variability of the wheel radius and accurate pose estimation even in the presence of unavoidable wheel slip occur-
rences. A Kalman Filter-based pose estimation system working in conjunction with a classier able to identify
the ground surface has been used to retrieve the position of the vehicle, and a PID control has been tuned to
generate the motors command in order to keep the vehicle on its track. First, the vehicle is operated in an open-
loop conguration. In this case, the path is aected by external disturbances including noise, wheel slipping,
surface unevenness and surface type. en, a PID closed-loop controller is proposed with a feedback loop that
continuously sends correction information by relying on the inertial sensor and on the PID parameters that are
issued by the ground classier and are used as adjustment values to make the controller generate the motors cor-
rections faster by avoiding the waiving loitering around the track. e use of the closed-loop controller resulted
in higher positioning accuracy and in the ability to react immediately to possible disturbances. e closed-loop
approach resulted in a reduction of about 77% and 88% of the position and orientation error, respectively. e
experimental results demonstrated that the proposed system is able to provide a nal maximum angle deviation
of 0.40
deg
with a maximum nal error of 0.17 m along a 10-m straight path on concrete and of
0.57 deg
with a
maximum nal error of 0.20 m along a 10-m straight path on concrete. e performance can be further improved
if laser detection sensors are used both to implement obstacles avoidance routine and to better retrieve the vehi-
cle’s position by using static references such as walls, pillars, and xed structures. e adoption of a suspension
system for the mecanum wheels will be also investigated along with the implementation of other advances control
strategies like the model predictive control (MPC) and the slide model control (SMC). By improving the wheel
compliance, surface irregularities may be better accommodated resulting in a lower impact of the ill-eects due
to wheel slippages and in a improved and more precise control of the robot.
Data availability
e datasets used and/or analysed during the current study available from the corresponding author on reason-
able request.
Received: 17 June 2022; Accepted: 14 November 2022
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Acknowledgements
e nancial support of the projects: Agricultural inTeroperabiLity andAnalysis System (ATLAS), H2020 (Grant
No. 857125), and multimodalsensing for individual plANT phenOtyping in agriculture robotics (ANTONIO),
ICTAGRI-FOOD COFUND (Grant No. 41946) is gratefully acknowledged.
Author contributions
All authors contributed and reviewed the manuscript.
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Competing interests
e authors declare no competing interests.
Additional information
Correspondence and requests for materials should be addressed to R.G.
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