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Fault Tolerance Control for Quad-Rotor UAV Using
Gain-Scheduling in Matlab/Gazebo
Fatima Alkhoori
Emirates Technology
and Innovation Center
Khalifa University
of Science and Technology
P.O. Box 127788,
Abu Dhabi, United Arab Emirates
Yahya Zweiri
Faculty of Science,
Engineering and Computing
Kingston University London
London SW15 3DW, UK
Visiting Associate Professor,
Robotics Institute
Khalifa University
of Science and Technology
P.O. Box 127788,
Abu Dhabi, United Arab Emirates
Ahmad Bani Younes, Tarek Taha
and Lakmal Seneviratne
Khalifa University
of Science and Technology
P.O. Box 127788,
Abu Dhabi, United Arab Emirates
Abstract—Nowadays, multi-rotor Unmanned Aerial Vehicles
(UAVs) are deployed widely in different fields to serve multiple
purposes. Safety and reliability of multi-rotor system are rapidly
growing research area, and enhancing the control design to
account for system failure. In this paper, the Fault-Tolerance
Control (FTC) is introduced as a method for recovery from
failure in quad-rotor UAV actuator in hovering mode. The
ultimate aim is to land safely with minimal damage. This research
focuses on designing a FTC method that is capable of handling
one and/or two rotors failures. Two different controllers are
designed and implemented in simulation for controlling the UAV
which are Proportional-Integral-Derivative (PID) control and
Linear Quadratic Regulator (LQR). LQR shows its effectiveness
after comparing both methods responses. Furthermore, a state
observer is designed using Linear Quadratic Estimator (LQE).
Gain scheduling (GS) method is developed to switch between
the controllers of the system in the event of failure. The
GS-PID control design is validated in ROS/Gazebo using the
new Robotics System Toolbox showing the effectiveness of the
proposed method.
Index Terms—Fault Tolerance Control, Failure, UAV, Quad-
copter, Multi-rotor, Gain-Scheduling, LQR, LQE
I. INTRODUCTION
In the last few decades, Unmanned Aerial Vehicles (UAVs)
have gained a great value in the market due to its numerous
applications. They can be widely used in various defense and
civilian applications because of their capability of carrying
various sensor payloads and specialized hardware (e.g. gimbal,
cameras, laser range finder, radars etc).
In general, UAVs are exposed to different types of failures
in their components whether in sensors or actuators. Other
failures could be in the structure partially or even a total
structural damage which are discussed in [1]. Failure could
be, also, in form of partial or total loss of effectiveness as
considered in this research. Noting that, each type is treated
differently and requires different approach.
Fault Tolerance Control (FTC) is a technique applied to
enable a system to recover and/or continue its operation in
an acceptable performance or land safely in the event of one
or/and more faults or failures [2]. An effective FTC technique
is essential to enable the system to continue operating in
a controlled manner. A FTC technique can reduce physical
damages and minimize safety risks that can occur where a
simple fault can escalate to a total system failure. Moreover,
integrating FTC in a flight system adds reliability to the
overall control system, thus increases its robustness and its
applications. Saving the expensive payloads is an important
aspect nowadays since the integrated sensors with the platform
are more valuable than the platform itself. The ultimate goal,
which should be of the highest priority, is minimizing risk
to peoples lives when operating UAV in populated areas.
A properly developed FTC technique should be capable of
dealing with worst case scenario, catastrophic failure, and
significantly reduce the risk factor by executing appropriate
safe maneuvers.
FTC could be categorized into two types; Active FTC
(AFTC) and Passive FTC (PFTC). The AFTC corresponds in
real time by reconfiguring the control system according to
the fault detected [3]. The passive FTC tolerates set of pre-
defined failures by using a pre-computed fixed-controller that
contains limited failure modes along with the free-fault mode.
The PFTC is designed to work off-line and to be sufficiently
robust to bear the pre-defined malfunctions.
Different FTC multi-rotor based algorithms were surveyed
such as: sliding mode control (SMC) [4]–[6], adaptive control
[7]–[11], feedback linearization approach [12]–[14], relaxed
hover solution [15], [16], backstepping approach [17], Model
predictive control (MPC) [18], and Gain Scheduling [19]–[21].
Many other methods are available in the literature since it is
still a vital issue.
In this paper, Gain Scheduling (GS) with PID controller
is applied to quad-rotor UAV to switch between free failure
mode and a failure mode. The failure scenario is to recover
from actuator failure in one or two opposing motors. The case
Fig. 1. UAV configuration
of failure in one motor is treated as two motor failure where the
opposite motor is switched of directly. The aim of this paper is
to test the method in the new Matlab/Simulink Robotic System
toolbox.
II. UAV DYNAM IC MO DE L AN D CON TRO L
The quad-rotor UAV, shown in Fig. (1), adopted from
[22].Two main frames are used; north-east-down (NED) frame
which is the inertial frame, and body frame (B-frame) is fixed
on the quad-rotor platform. Moreover, motor 1 and 3 spin
clock-wise and motor 2 and 4 spin counter-clock-wise. The
linearized model corresponds to the hovering mode is
˙z=w(1)
˙w=−2CT
mΩ0(Ω1−Ω2+ Ω3−Ω4)(2)
where the model is linearized around the trim point. zand
wcorrespond to the position and linear velocity in z-axis
respectively, CTis the thrust power coefficient 1.5108 ×10−5
kg.m, mis the total mass 1.32 kg, Ω0is the rotor angular
velocity in the trimming point equals 463.1rad/sec and Ωis
the angular velocity of the rotors. The brush-less motor model
is treated as first order linear system
˙
Ωm,i =−10 Ωm,i + 7 Ufor i= 1, ..., 4(3)
where Uis the motor input. Combining (1) and (3) to
develop the dynamical model for the hovering mode. The
motors speeds are considered as part of the model states for
fault tolerance purposes where the motor speed provides an
indication of failure.
The same linearized model has been used for the failure
mode in two opposite motors where (3) is used for motor 1
and 3 only and motors 2 and 4 are eliminated as shown in
Fig. (2).
A. Control law
Two controllers have been used which are PID and LQR to
control the vertical position.
Fig. 2. The quad-rotor in failure case
Fig. 3. System feedback loop with PID controller
1) PID controller: Two loops are used to control the UAV
vertical movement as shown in Fig. (3). The inner loop
is used to control the vertical velocity where P controller
was sufficient. The outer loop is used to control the vertical
position using PD controller. The detailed implementation of
PID controller is discussed in [23]. The derivative controller
is introduced as high pass filter as shown in (4)
KP D =kpp+skd
αs + 1 (4)
where α= 0.02 is the low pass filter time constant.
2) LQR: Linear Quadratic Regulator (LQR) is another
method for state feedback control that provides a systematic
procedure for determining the control gains. Considering our
system, the aim of this method is to minimize the cost function
J
J=Zt∞
t0
(xTQ x +uTR u)dt (5)
where Qand Rare the weight matrices that are positive
definite specifying the relative importance of the error and en-
ergy consumption. In order to minimize J, the state feedback
control can be
u=−K x (6)
where Kis the control gain. It is determined by solving the
steady state Riccati equation
ATP+P A −P B R−1BTP+Q= 0 (7)
and then using Pto find the control gain K
K=R−1BTP(8)
The aim of implementing this method is to control the
UAV’s altitude as shown in Fig. (4)
Fig. 4. LQR Simulink model
3) LQG: It was important to design an observer for state
estimation since measuring the states is an expensive proce-
dure. Therefore, Linear Quadratic Gaussian (LQG) is a method
that combines Linear Quadratic Regulator (LQR) and Linear
Quadratic Estimation (LQE). For the observer, the system state
space representation becomes
˙
ˆx =Aˆx +Bu +T(y−ˆy)
ˆy =Cˆx (9)
where ˆx is the estimated state vector, ˆy is the estimated
output and Tis the control gain. By substituting ˆ
yfor (9)
and re-arranging
˙
ˆx−˙x= (A−T C )ˆx+ (A−T C)x(10)
In terms of the error vector, it becomes
˙e = (A−T C)e(11)
This equation presents the error dynamics in terms of the
system matrix A, the measurement matrix Cand the observer
gain T.Tto be chosen according to two aspects. First,
(A−T C)is stable matrix (the real part of the eigenvalues
is negative), then as t→ ∞ the error vector e→0. It means
that the produced estimates are asymptotically stable. The gain
Tcan be calculated based on LQE method.
Introducing a disturbance to the system Vand a white
Gaussian noise to the measurements W, the linear dynamic
system becomes
˙x =Ax +Bu +V
y=Cx +W(12)
The optimal Kalman filter gain Tis obtained from A,C,W
and Vby solving the steady state Riccati equation
ATP+P A −P C W−1CTP+V= 0 (13)
then, the observer gain is
T=P CTW−1(14)
The results obtained by implementing the LQG method
is shown in Fig. (5). This results have been obtained after
modifying the observer gain by increasing its value in order
to reject the disturbances. However, the noise signal has
increased, therefore, a filter is used for the output signal. These
steps created a robust and reliable control law that is applied
to the system.
012345678910
Time [sec]
-5
0
5
10
15
20
25
Position [m]
Measured z
filtered z
estimated z
Fig. 5. yvs. ˆywith noise and disturbance injection, filter and modified
gain
Similar steps have been implemented to the system with
failure, where only number of states is reduced.
III. FAULT TOLERANCE CONT ROL
A. FTC using Gain Scheduling
The FTC technique, in this paper, is based on combining
both quad-rotor models developed previously and switch be-
tween them at the failure event. The models are taken with
their control law to account for the free fault mode and the
failure mode. The intended methodology is to switch the
control gains of the LQG at the instant of failure. This is
called gain scheduling. In order to test our methodology, the
failure is introduced at tfsecond. A fault detection unit is
assumed to be implemented to capture the failure. Once the
system is alerted to the existence of the failure, two opposite
motors angular velocities are set to zeros.
In the simulation, the failure is injected at tf= 8 sec in
motors 2 and 4. The switching condition is triggered by a zero
angular velocity signal which is sent by the observer. The mea-
sured data are continuously sent as a non-zero value, where
all values are multiplied together. Once a motor produces a
zero angular velocity, the switch detects the zero signal and
shifts to the control system that accounts for the failure. At the
moment of switching, the position response of the free fault
model passes its final value to the failure model. Therefore, the
switches are designed to allow for an overlap of one sample
time for the final value of the position to be passed. The sample
time is chosen as tp= 0.01 sec. Figure(6) demonstrates the
idea more clearly. First, the control signal in figure(7) is sent to
the four rotors model with consideration of the sample time
tp. Thus the four rotors model is running for 8.01 seconds.
However, the two rotors model starts running at the failure time
tf= 8, as shown in figure(8). This one sample time overlap
allows for the position final value from the four rotor model
to pass through the two rotor system as an initial condition.
Fig. 6. Switching using overlap approach
Fig. 7. Control signal block for the four rotor
Figure (9) shows the response of the system to the GS
method. A command of landing is given to the system in order
to recover with minimal damage. The figure shows a lag of
response in the lading; however, it is within our benefits since
we aim to increase the landing time in order to decrease the
impact of the platform on the ground.
IV. IMPLEMENTATION AND RESU LTS
It was essential to have a suitable environment for vali-
dation. There are multiple ways for validation such as flight-
testing, parameter identification or using a real simulated envi-
ronment. Flight testing requires an access to costly hardware,
field test with trained pilot and significant amount of time.
Moreover, field test does not produce an expected or successful
outcome from the beginning and sometimes it could damage
the UAV. Parameter identification is a suitable validation
method if there is an access to a measured data. Therefore,
the real simulation environment ROS/Gazebo is chosen due
Fig. 8. Control signal block for the two rotor
0 2 4 6 8 10 12 14 16 18 20
Time [sec]
-5
0
5
10
15
20
25
Position [m]
z (reference)
z (free-fault)
z (reference)
z (failure)
Fig. 9. FTC model response
to availability of software and expertise in Khalifa University
campus (KURI Lab). Robotics Operating System (ROS) is a
recent software that provides interface communication (e.g.
send and receive data) with a robot simulator system and
Gazebo simulate a real physical robotic machine. The firmware
used for validation was already validated and tested in actual
platform and proven its reliability. Moreover, the interface
between Matlab/Simulink and ROS/Gazebo is carried out via a
recent toolbox added to MathWorks toolboxes called Robotics
System Toolbox. It allows for direct communication with ROS
by sending and receiving messages, generating and deploying
nodes in ROS, and C++ code generation.
Figure (10) shows the Simulink model developed to inter-
face with ROS/Gazebo. The blocks shown on the left side
and magnified in Fig. (11) are the subscribers to the position
and velocity published by Gazebo. The Command Velocity
Publisher block shown in Fig. (12) describes the publishing
method where the signal is assigned with a message type.
Initially, PID controller is implemented to control the UAV.
Figure (13) shows the take-off and hover behaviors of the UAV
in Gazebo comparing to the Matlab/Simulink behavior when
constrained to the same system requirements as Gazebo. A
similar behavior between both systems is achieved, although
there is a delay in the Gazebo model due to the necessity of
the platform to reach a certain velocity prior take-off.
In Gazebo, the failure in two rotors is created by shutting-
Fig. 10. Simulink model with Gazebo interface
Fig. 11. Position and velocity subscriber blocks
off two opposite motors at random time. The behavior of the
UAV at the instant of failure is described in figure(14). The
abnormal performance is due to the spinning of the UAV and
its attempt to reach the desired altitude. The goal is to land
the UAV safely while it is spinning. Therefore, a switching
mechanism is applied where the system detects the failure
and switches to landing mode immediately. A signal taken
from Gazebo that publishes the angular velocity of the motors
is fed to the switch. This is done with the assumption of
Fig. 12. Velocity publisher block
0 5 10 15 20 25 30 35 40 45
Time [sec]
-1
0
1
2
3
4
5
6
Position [m]/Velocity [m/s]
Velocity Simulation
Position Simulation
Position Gazebo
Velocity Gazebo
Fig. 13. Simulation vs. Gazebo response for PID controller (simulation
refers to Matlab simulation)
pre-implementation of a failure detection unit. The switch
commands the system to land when a zero angular velocity
is captured. Moreover, gain scheduling is implemented where
the switching mechanism is applied to the controlling gains as
well. Another switch commands the system to stop the UAV
before reaching the ground by 15cm.
In Fig. (14), the UAV took less than 3 seconds to crash after
the abnormal behavior. It is shown in figure(15) that the UAV
landed in around 4 seconds. This is due to the gain scheduling
method used where the controller parameters are re-tuned to
account for the failure case. An acceptable performance in
following the landing command is shown which allows for
safe landing of the UAV. In this case, we demand a longer
time in the landing mode to prevent fast impact which might
damage the UAV.
V. CONCLUSION
Fault tolerance control is a wide field that can be ap-
proached from different perspectives. In this paper, failure
scenario is considered for total loss of two opposing rotors.
The simulation results showed the effectiveness of the Gain
Scheduling method applied, where the UAV was able to track
the trajectory (stay hovering) in a controlled manner and land.
Moreover, the system was validated using ROS/Gazebo and
the Robotics toolbox in Matlab/Simulink where the UAV was
0 10 20 30 40 50 60 70
Time [sec]
-4
-3
-2
-1
0
1
2
3
4
5
Position [m]/Velocity [m/s]
Velocity
Position
Fig. 14. UAV behavior in failure mode without FTC
0 2 4 6 8 10 12 14 16 18
Time [sec]
-3
-2
-1
0
1
2
3
4
5
6
Position [m]/Velocity [m/s]
Velocity
Position
trajectory
Fig. 15. UAV behavior in gain scheduling with tuning
able to recover and land safely immediately after the failure.
In future, LQR is intended to be tested in ROS/Gazebo.
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