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UAV quadrotor fault detection
Citation preview
Actuator Fault Detection System
for a Mini-Quadrotor
A. Freddi, S. Longhi and A. Monteriù
Dipartimento di Ingegneria Informatica, Gestionale e dell’Automazione
Università Politecnica delle Marche
Via Brecce Bianche, 60131 Ancona, Italy
Email: [email protected], {sauro.longhi, a.monteriu}@univpm.it
Abstract—This paper addresses the problem of actuator faultdetection for a mini-quadrotor. First a model for a four-rotorvehicle, obtained via a Lagrange approach, is presented. In orderto stabilize the quadrotor at low cruise speed, a control strategybased on nested saturation controllers is presented. Using aThau’s observer, a diagnostic system has been developed for thenonlinear model of the quadrotor. Different simulation trials havebeen performed and the analysis of the results proves that thedeveloped diagnostic system represents an effective solution tothe problem of actuator fault detection in mini-flying machines.
I. INTRODUCTION
Unmanned aerial vehicles (UAVs) or flying robots have
attracted enormous interest during the last years. Recent de-
velopments in solid state disks, integrated miniature actuators
and MEMS (Micro Electromechanical Systems) technology
sensors have made autonomous miniaturized flying robots pos-
sible. One type of mini-aerial vehicle with a strong potential is
the four-rotor aerial vehicle, also called quadrotor. This vehicle
has been chosen by many researchers as a very promising
vehicle for indoor/outdoor navigation using multidisciplinary
concepts ([1], [2], [3], [4]).
A quadrotor simply consists in four DC motors on which
propellers are fixed. These motors are arranged to the extrem-
ities of a X-shaped frame, where all the arms make an angle
of 90 degrees with one another. As shown in Figure 1, the
front and rear motors (M1 and M3) spin in the clockwise
direction with angular velocities ω1 and ω3, while the other
pair of rotors (M2 and M4) spin in the counter-clockwise
direction with angular velocities ω2 and ω4. Thus, a quadrotor
is an under-actuated system with four independent inputs and
six coordinate outputs. The quadrotor has some advantages
over conventional mini-helicopters. One of the advantages of
quadrotors is that they have more lift thrusts than conventional
helicopters. Moreover, they are potentially simpler to build and
highly maneuverable.
To ensure the normal operation, and increase the safety and
reliability of such vehicles, the problem of fault detection is
very important. If a fault is rapidly detected, the structure
of the controller can be changed to get the best possible
response of the system, or even the system can be brought to
an emergency manoeuvre ([5]). The information provided by
an efficient diagnostic system could assist in the development
Fig. 1. Quadrotor rotorcraft.
of fault accommodation strategies which would guarantee fail-
safe operation of the control system.
Several methods have been proposed to control a quadrotor
vehicle ([1], [6], [7], [8]), and different approach have been
developed for detecting and isolating sensor faults on a such
vehicle ([9], [10]), however only few researches have been
devoted to the important problem of detecting the vehicle
actuator faults.
The interest of the present work is to successfully develop
and apply a diagnostic observer to the nonlinear quadrotor
model for detecting the rotorcraft actuator faults. Exploiting
the Lipschitzianity of the nonlinear model, a full order Thau
observer ([11]) is obtained and used to generate the residuals
on which the FDI system is based. In faultless situations,
residuals remain around zero, while if an actuator fault occurs,
their values change, permitting to detect the fault. The scheme
proposed in this paper permits to detect actuator faults, and to
isolate which pair of rotors is faulty.
The nonlinearity of the quadrotor model does not permit to
exploit the significant developments which have been made in
the area of fault detection in linear systems ([12]).
The paper is organized as follows. In Section II, the non-
linear model of a mini-quadrotor is presented. The strategy to
control the quadrotor is detailed in Section III. The proposed
actuator fault diagnostic nonlinear observer is described in978-1-4244-6392-3/10/$26.00 ©2010 IEEE 2055
Section IV. Section V is devoted to the presentation of the
simulation results obtained for various fault scenarios when
the proposed scheme is applied to the quadrotor. Conclusions
and future directions are presented at the end of the paper.
II. DYNAMICAL MODELING OF QUADROTOR
The mathematical model developed here is based on some
basic assumptions as given below:
• Design is symmetrical.
• Quadrotor body is rigid.
• Propellers are rigid.
• There are not external effects on quadrotor body such as
air friction, wind pressure, etc.
• Free stream air velocity is zero.
• The four electric motors’ dynamic is relatively fast and
therefore it will be neglected as well as the flexibility of
the blades.
Two frames are used to study the system motion: an
inertial earth frame {RE} (O, x, y, z), and a body-fixed frame
{RB} {OB , xB , yB , zB}, where OB is supposed to be at
the mass center of the quadrotor. {RB} is related to {RE}
by a vector ξ =[
x y z]T
describing the position of
the center of gravity in {RE}, and three independent an-
gles η =[
φ θ ψ]T
, respectively roll, pitch and yaw,
which describe the rotorcraft orientation, with(
−π2 ≤ φ < π
2
)
,(
−π2 ≤ θ < π
2
)
and (−π ≤ ψ < π) (see Figure 1).
The small rotorcraft is supposed to have six degrees of
freedom according to the earth fixed frame given respectively
by quadrotor position and its attitude. The weight force acts
at the center of mass and is always along negative z-axis. If
l is the length of each arm, then each motor can be located
by position vectors: ~L1 = lıB , ~L2 = lB , ~L3 = −lıB and~L4 = −lB , with (ıB , B , kB) as versors of (xB , yB , zB)-axis.
Analogously, all the forces shown in the Figure 1 by ~fi = fi ~kBare located in RB by position vectors ~Li (i = 1, 2, 3, 4).
With these assumptions, the quadrotor is a solid body
evolving in 3D and subject to one force and three torques.
The imbalance of the forces ~fj , where j = 1, 3 or j = 2, 4,
results in torques, along a direction perpendicular to the plane
containing the force ~fj and the vector ~Lj . This torque is
responsible for the rotation of the vehicle along xB-axis and
yB-axis. The rotation about zB-axis is due to imbalance of
clockwise and counter-clockwise torques.
The translational kinetic energy of the rotorcraft is expressed
as ([13])
Ttrans ,1
2mξT ξ (1)
where m denotes the whole mass of the rotorcraft.
The rotational kinetic energy is given by ([14])
Trot ,1
2ηT Jη (2)
where J is the inertia matrix expressed directly in terms of the
generalized coordinates η
J = WTη IWη (3)
with
Wη =
1 0 −Sθ0 Cφ SφCθ0 −Sφ CφCθ
(4)
where S(.) and C(.) represent sin (.) and cos (.) respectively,
and I is the moment of inertia tensor, which is diagonal due
to the symmetry of the quadrotor.
The only potential energy which needs to be considered is
due to the gravitational field. Therefore, potential energy is
expressed as
U = mgz . (5)
Let q =[
ξT ηT]T
= [x, y, z, φ, θ, ψ]T ∈ R6 be the
generalized coordinates vector for the flying machine, the
Lagrangian is given by
L (q, q) = Ttrans+Trot−U =1
2mξT ξ+
1
2ηT Jη−mgz (6)
The model for the full quadrotor aircraft dynamics is
obtained from the Euler-Lagrange equations with external
generalized force
d
dt
∂L
∂q−∂L
∂q= F (7)
where F =[
FTξ τTη]T
. Fξ defines the translational force
applied to the aerial robot due to the control inputs and relative
to the frame {RE}, and τη is the generalized torques vector.
The small body forces are ignored, and we only consider the
principal control inputs uf and τη , where uf represents the
total thrust, and τη is the generalized torque.
Because of each spinning propeller generates vertically
upward lifting force, labeled as f1, f2, f3 and f4, all the motion
of the quadrotor is a consequence of the sum of these forces:
uf = f1 + f2 + f3 + f4 (8)
with
fj = Klω2j (i = 1, 2, 3, 4) (9)
where ωj is the angular speed of motor Mj (j = 1, 2, 3, 4),while Kl > 0 is the lift constant depending on the air density
ρ, the lift coefficient Cz and the blade rotor characteristics S
(diameter, step, profile, ...) and it results as
Kl =1
2ρSCz . (10)
Then, the force applied to the mini-rotorcraft relative to the
frame {RB} is defined as
F =[
0 0 uf]T
. (11)
Consequently
Fξ = RB→EF (12)
where RB→E is the rotation transformation from the body
reference frame to the earth reference frame given by
RB→E =
CθCψ CψSθSφ − CφSψ CφCψSθ + SφSψCθSψ SθSφSψ + CφCψ CφSθSψ − CψSφ−Sθ CθSφ CθCφ
.2056
Indicating the generalized torque as τη ,[
τφ τθ τψ]T
,
the Euler-Lagrange equation can be rewritten as
mξ +
00mg
= Fξ (13)
Jη + Jη −1
2
∂
∂η
(
ηT Jη)
= τη . (14)
Defining the Coriolis vector as
Fc (η, η) = J−1
2
∂
∂η
(
ηT J)
(15)
the expression (14) can be rewritten as
Jη + Fc (η, η) η = τη (16)
.
Finally, the equations of motion for the mini rotorcraft are
expressed as
mξ = Fξ +
00
−mg
(17)
Jη = τη − Fc (η, η) η . (18)
Since J is nonsingular, it is possible to simplify the analysis,
without loss of generality, changing the input variables as
follows
τη = Jτ + Fc (η, η) η (19)
with τ =[
τφ τθ τψ]T
.
Then, with the new inputs, it results:
η = τ . (20)
Rewriting (17) and (18) gives
mx = (CφCψSθ + SφSψ)uf (21)
my = (CφSθSψ − CψSφ)uf (22)
mz = (CθCφ)uf −mg (23)
φ = τφ (24)
θ = τθ (25)
ψ = τψ (26)
III. CONTROL STRATEGY
A control strategy for stabilizing the quadrotor near hover
is recalled in this section. The control input uf is essentially
used to make the altitude reach a desired value. The control
input τψ is used to set the yaw displacement to zero. τθ is
used to control the pitch angle and the horizontal movement
in the x-axis. Similarly τφ is used to control the roll angle and
the horizontal displacement in the y-axis ([7]).
A. Altitude and yaw control
The control of the vertical position can be obtained by using
the following control input ([7])
uf = (−az1 z − az2(z − zd) +mg)1
CφCθ(27)
where az1 , az2 are positive constants and zd is the desired
altitude.
The control of the yaw displacement can be obtained by
using the following control input ([7])
τψ = −aψ1ψ − aψ2
(ψ − ψd) (28)
where aψ1and aψ2
are positive constants, ψd is the desired
yaw angle.
B. Attitude control
The control of the attitude can be obtained by using the
nested saturations strategy ([7]). The law for roll control is:
τφ = −σφ1(φ+ σφ2
(ν1 + σφ3(ν2 + σφ4
(ν3))))
ν3 = 3φ+ φ− 3y
g−y − yd
g
ν2 = 2φ+ φ−y
gν1 = φ+ φ
(29)
The law for pitch control is:
τθ = −σθ1(θ + σθ2(ν1 + σθ3(ν2 + σθ4(ν3))))
ν3 = 3θ + θ + 3x
g+x− xd
g
ν2 = 2θ + θ +x
gν1 = θ + θ
(30)
In both equations σa(s) is a saturation function defined as
σa (s) =
a, if s > a
s, if − a ≤ s ≤ a
−a, if s < −a(31)
while xd and yd are the desired longitudinal and lateral
positions.
IV. FDI SYSTEM
A model-based fault diagnosis system consists of a residual
generation module and a residual evaluation module. This
section recalls the theoretical aspects for developing a residual
generation module and a residual evaluation module for the
considered quadrotor system.
A. Residual generation
In literature several model-based methods have been
adopted for generating residual to be used in FDI schemes for
UAVs. Luenberger observers have been used both for sensor
and actuator fault detection (see [5]). Kalman filters (simple,
extended or unscented) have been used for fault adaptive and
tolerant control (see, e.g., [15] and [16]).
Most of the times the easiest and practical solution when
dealing with model-based techniques is to choose a proper2057
working point and linearize the system around it. However
this solution is suitable only for those vehicles operating most
of the time near the considered conditions. In all the other
cases there are two possible alternatives: linearizing the system
around different operating conditions or using a non-linear
model-based approach.
[11] developed an observer for a special class of non-linear
systems. This observer has already been applied to the fault
detection and isolation of non-linear dynamic systems and uses
the following non-linear system model ([12]):{
x(t) = Ax(t) + Bu(t) + h(x(t),u(t)) + F 1f(t)y(t) = Cx(t) + F 2f(t)
(32)
where x ∈ Rn is the state vector, u ∈ Rr is the input vector,
y ∈ Rp is the output vector, f ∈ Rh is the fault vector,
A,B and C are known system matrices with appropriate
dimensions, h(x(t),u(t)) represents the nonlinearity, and F 1
and F 2 are known fault entry matrices which represent the
effect of faults on the system.
For developing the Thau observer, the system model (32)
has to satisfy the two following conditions:
C1 - the pair (C,A) must be observable;
C2 - the non-linear function h(x(t),u(t)) must be locally
Lipschitz with constant , i.e.
||h(x1(t),u(t))−h(x2(t),u(t))|| ≤ ||(x1 −x2)||(33)
When these two conditions are satisfied, a stable observer for
the system (32) has the form{
˙x(t) = Ax(t) + Bu(t) + h(x(t),u(t)) + K(y(t) − y(t))y(t) = Cx(t)
(34)
where K is the observer gain matrix defined by
K = P−1δ CT . (35)
The matrix P δ is the solution to the Lyapunov equation
ATP δ + P δA − CTC + δP δ = 0 (36)
where δ is a positive parameter which is chosen such that (36)
has a positive definite solution.
In order to develop the Thau observer for the quadrotor
system considered in this paper, it is necessary to write the
system described by the equations (21)-(26) in a state-space
form. Defining
x =[
x y z φ θ ψ x y z φ θ ψ]T
(37)
u =[
uf τφ τθ τψ]T
(38)
f =[
fx fy fz fφ fθ fψ]T
(39)
y =[
x y z φ θ ψ]T
(40)
as the state, input, fault and output vector, respectively, then
the system described in (21)-(26) can be rewritten as a state
space system of the form (32), where
A =
[
0(12×12)I6
0(6×6)
]
, (41)
B = 012×4, (42)
C =[
I6 0(6×6)
]
, (43)
h(x,u) =
06×1
(CφCψSθ + SφSψ) um
(CφSθSψ − CψSφ)um
(CθCφ)um
− g
J−11 ((τη − Fc (η, η) η))
J−12 ((τη − Fc (η, η) η))
J−13 ((τη − Fc (η, η) η))
(44)
and
F 1 = 0(12×6) , (45)
F 2 =
[
0(6×3)0(3×3)
I3
]
, (46)
where In is the n-by-n identity matrix, 0(n×m) is the n-by-m
matrix of zeros and J−1i is the i− th row of the J−1 matrix.
The observability matrix results
O =[
CT (CA)T (CA2)T · · · (CA11)T]T
(47)
where[
CT (CA)T]T
= I12, while CAi = 0(6×12) (i =2, . . . , 11). Thus, the observability matrix has full rank, and
the pair (C,A) is observable, and condition C1 is satisfied.
h(x(t),u(t)) is a continuously differentiable function and
thus the condition C2 is satisfied as long as u(t) is bounded
([17]).
The parameter δ, and thus the gain matrix K, defines how
much the difference between the real system outputs and
the observer outputs must affect the residuals and should be
chosen as the best trade-off between the magnitude of residuals
due to faults and that due to noise. After several simulations
the gain matrix has been chosen as
K =
[
1.1I6
0.3025I6
]
. (48)
Since the considered quadrotor system is supposed to be
equipped with either a GPS receiver (outdoor operation) or
a vision system (indoor flight) and an Attitude and Heading
Reference System (AHRS), the system outputs are the position
in the earth frame (x, y and z) and the attitude angles (φ, θ
and ψ). The residuals are built as the difference between the
system outputs and the Thau observer outputs, that is to say:
r1(t) = x(t) − x(t) (49)
r2(t) = y(t) − y(t) (50)
r3(t) = z(t) − z(t) (51)
r4(t) = φ(t) − φ(t) (52)
r5(t) = θ(t) − θ(t) (53)
r6(t) = ψ(t) − ψ(t) . (54)
which are supposed to be zero as long as there are no faults
on the actuators and to differ from zero in case of faults.2058
B. Residual evaluation
The residual evaluation module detects a change in the mean
of an observed and distributed random sequence achieved by
sequential change detection algorithms. Based on the residual
evaluation algorithm developed by [18], each residual ri(i = 1, . . . , 6) has been compared to a fixed threshold, and
the following decision is made at time t:
ri(t) ≥ Hi or ri(t) ≤ hi in faulty case (55)
ri(t) < Hi or ri(t) > hi in fault-free case (56)
where Hi and hi are the upper and lower thresholds, respec-
tively, with i = 1, . . . , 6.
V. SIMULATION RESULTS
The non-linear quadrotor system along with the FDI system
have been developed using the Matlab and Simulink R© soft-
ware. The system outputs are supposed to be the linear posi-
tions in the earth frame (x, y and z) and the euler angles (φ, θ
and ψ). Noise is included in the model, affecting the sensors
measurment with an uncertainity of ±15cm on the linear
position and ±2 deg on the attitude position. The residuals
(six) are built as the difference between the nonlinear system
outputs and the Thau observer outputs. They are supposed to
be almost zero as long as there are no faults and to differ from
zero in case of faults.
The controller is set in order to allow the quadcopter to
reach a height of 25m and to remain in hover flight thereafter.
During the hover flight, a fault is introduced into one of the
actuators: indicating with T the instant time when a stuck fault
occurs, the behaviour of the actuator fi can be modelled as:
fj (t) =
{
fj (t) , t < T
fj(
T)
, t ≥ Tfor j=1, . . . ,4 (57)
The faulty actuator can no longer change its value once that
the fault has occurred. For the simulation a time T = 20s has
been chosen (fig. 2).
0 5 10 15 20 25 30 35 401.15
1.2
1.25
1.3
1.35
time [s]
f1 [N]
f1
Fig. 2. f1 in case of fault.
Once the actuator is stuck, the controller can no longer
control the position of the vehicle, due to the yaw displacement
that differs from zero, while it can still stabilize the attitude
angle on the axis in which the faulty actuator is present (that
is to say the angle θ if the fault is on f1 or f3, and φ if the
fault is on f2 or f4). Thus all the residuals should differ from
zero when a fault occurs on f1 or f3 with the exception of
the residual of θ, or with the exception of the residual of φ in
case of fault on f2 or f4.
Due to the symmetry of the system, a fault on f1 or f3produces the same results as a fault on f2 or f4: this implies
that a fault can always be detected, but the isolation logic can
only isolate the couple on which the fault has occurred and
not the single faulty actuator. These assumptions are confirmed
by the simulation results. Due to the symmetry of the problem
they are reported only for a fault on the actuators f1 and f2.
In absence of faults all the residuals show the same be-
haviour, and they are affected only by noise and slightly differ
from zero.
When the actuator f1 get stuck the dynamic of the real
system behaves in a different way then that of the observer:
the residual raises above the maximum value it had in the
faulty-free case (fig.3).
0 5 10 15 20 25 300
2
4
6
8
10
12
14
16
18
20
time [s]
r1 [m]
r1 [m]
threshold
Fig. 3. Residual 1 in case of fault on the 1st actuator.
A similar behaviour can be seen in all the other residuals,
with the exception of the residual calculated as (φ − φ), as
shown in fig. 4.
As already stated before, a similar behaviour can be seen if
the fault occurs on f3 (see table I).
In case of faults on f2 all the residual are similar to that of
fig. 5 with the exception of the residual calculated as (θ− θ),as shown in fig. 6.
As already stated before, a similar behaviour can be seen if
the fault occurs on f4 (see table I).
VI. CONCLUDING REMARKS
In this paper, the FDI problem for a quadrotor vehicle has
been faced. Using a Thau’s observer, a set of residuals have2059
0 5 10 15 20 25 300
0.01
0.02
0.03
0.04
0.05
0.06
0.07
time [s]
r4 [rad]
r4 [rad]
threshold
Fig. 4. Residual 4 in case of fault on the 1st actuator.
0 5 10 15 20 25 300
1
2
3
4
5
6
time [s]
r1 [m]
r1 [m]
threshold
Fig. 5. Residual 1 in case of fault on the 2nd actuator.
been generated for FDI tasks. The Thau observer estimates
the system states using a simple algorithm and it is accurate
enough to provide a reliable signal for the FDI system, thus
representing an effective alternative to Kalman-based filters.
Simulation trials have shown that faults on the actuators can be
correctly detected and that the couple on which the fault occurs
can be correctly isolated. A strategy for disturbance reduction
and fault tolerant control is currently under investigation.
REFERENCES
[1] E. Altug, J. Ostrowski, and R. Mahony, “Control of a quadrotor heli-copter using visual feedback,” in Proc. of IEEE Int. Conf. on Robotics
and Automation, 2002.[2] A. Mokhtari and A. Benallegue, “Dynamic feedback controller of euler
angles and wind parameters estimation for a quadrotor unmanned aerialvehicle,” 2004.
[3] A. Tayebi and S. McGilvray, “Attitude stabilization of a vtol quadrotoraircraft,” IEEE Transactions on Control Systems Technology, vol. 14,no. 3, pp. 562–571, 2006.
[4] B. Bethke, M. Valenti, and J. How, “Uav task assignment,” IEEE Trans.
on Robotics and Automation, vol. 15, no. 1, pp. 39–44, 2008.
0 5 10 15 20 25 300
0.01
0.02
0.03
0.04
0.05
0.06
0.07
time [s]
r5 [rad]
r5 [rad]
threshold
Fig. 6. Residual 5 in case of fault on the 2nd actuator.
TABLE IEFFECTS OF THE ACTUATOR FAULTS ON THE RESIDUALS
f1 f2 f3 f4
r1 1 1 1 1r2 1 1 1 1r3 1 1 1 1r4 0 1 0 1r5 1 0 1 0r6 1 1 1 1
[5] G. Heredia, A. Ollero, M. Bejar, and R. Mahtani, “Sensor and actuatorfault detection in small autonomous helicopters,” Mechatronics, 2007.
[6] S. Bouabdallah, P. Murrieri, and R. Siegwart, “Design and control of anindoor micro quadrotor,” 2004, pp. 4393–4398.
[7] P. Castillo, R. Lozano, and A. Dzul, Modelling and control of mini-flying
machines. Springer-Verlag, 2005.[8] A. Das, K. Subbarao, and F. Lewis, “Dynamic inversion with zero-
dynamics stabilisation for quadrotor control,” IET Contr. Theory &
Applications, pp. 303–314, 2009.[9] C. Berbra, S. Lesecq, and J. Martinez, “A multi-observer switching
strategy for fault-tolerant control of a quadrotor helicopter,” in Control
and Automation, 2008 16th Mediterranean Conference on, 2008, pp.1094–1099.
[10] H. Rafaralahy, E. Richard, M. Boutayeb, and M. Zasadzinski, “Si-multaneous observer based sensor diagnosis and speed estimation ofunmanned aerial vehicle,” 2008, pp. 2938–2943.
[11] F. Thau, “Observing the state of non-linear dynamic systems,” Int. Jour.
of Control, vol. 17, no. 3, pp. 471–479, 1973.[12] J. Chen and R. Patton, Robust model-based fault diagnosis for dynamic
systems, 1999.[13] S. Salazar, H. Romero, R. Lozano, and P. Castillo, “Modeling and
real-time stabilization of an aircraft having eight rotors,” Journal of
Intelligent and Robotic Systems, vol. 54, no. 1, pp. 455–470, 2009.[14] G. Raffo, M. Ortega, and F. Rubio, “An integral predictive/nonlinear
control structure for a quadrotor helicopter,” Automatica, pp. 29–39,2009.
[15] J. Qi, Z. Jiang, X. Zhao, and J. Han, “UKF-based rotorcraft UAV Faultadaptive control for actuator failure,” in IEEE International Conference
on Robotics and Biomimetics, 2007. ROBIO 2007, 2007, pp. 1545–1550.[16] C. Rago, R. Prasanth, R. Mehra, R. Fortenbaugh, S. Inc, and M. Woburn,
“Failure detection and identification and fault tolerant controlusing theIMM-KF with applications to the Eagle-Eye UAV,” in Proc. of the 37th
IEEE Conf. on Decision and Control, 1998.[17] H. Khalil, Nonlinear systems (3rd edition). Prentice Hall, 2002.[18] A. Monteriù, P. Asthana, K. Valavanis, and S. Longhi, “Real-Time
Model-Based Fault Detection and Isolation for UGVs,” Journal of
Intelligent and Robotic Systems, vol. 56, no. 4, pp. 425–439, 2009.
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