2020 International Conference on Computer, Control, Electrical, and Electronics Engineering (ICCCEEE)

Trajectory Tracking for the Quadcopter UAV

2020 International Conference on Computer, Control, Electrical, and Electronics Engineering (ICCCEEE) | 978-1-7281-9111-9/20/$31.00 ©2021 IEEE | DOI: 10.1109/ICCCEEE49695.2021.9429636

utilizing Fuzzy PID Control Approach

Ahmed Eltayeb1, Mohd Fuaad Rahmat2, M. A Mohammed Eltoum3, Ibrahim M. H. Sanhoury 4 and Mohd Ariffanan Mohd Basri5
12,5School of Electrical Engineering, Faculty of Engineering, Universiti Teknologi Malaysia, Skudai 81310 Johor, Malaysia.
3System Engineering Dept., Faculty of Computer Science and Engineering, KFUPM University, 31261 Dhahran, Saudi Arabia.
4Dept. of Control Engineering, College of Engineering, Alneelain University, Khartoum, Sudan
ahmedtayeb5@gmail.com, fuaad@fke.utm.my, m-dm@live.com, sanhoury124@yahoo.com, ariffanan@utm.my

Abstract: Currently, the quadcopter Unmanned Aerial Vehicles The quadcopter is an underactuated system with high nonlinear
(UAVs) are playing a significant role in combating the COVID-19 dynamics. Consequently, the advanced robust control methods
pandemic crisis, which induced the researchers to design robust have been reported in the literature to ensure the smooth and
control techniques. In this paper, a fuzzy PID controller is robust trajectory tracking and navigation, such as linear control
designed to stabilize and/or track the desired trajectory of the design [1]-[4], sliding mode [5]-[7], feedback linearization [8],
quadcopter UAV. The mathematical model of the quadcopter [9], backstepping [10], [11] and adaptive control [12], [13], and
UAV has been briefly presented, where it has been divided into two to name a few more. A review on control methods that were
portions, the position dynamic and the attitude dynamic applied to UAVs has been reported in [14].
subsystems. Subsequently, a robust fuzzy PID controller has been
designed for both the inner loop and outer loop to control and In this paper, the mathematical model of the quadcopter UAV is
stabilize the position and the attitude of the quadcopter, which divided into two parts, the position dynamic, and the attitude
adaptively manipulate the system's input based on the tracking dynamic subsystems. Furthermore, a fuzzy PID (FPID)
error. The proposed controller is benchmarked with the controller has been proposed for the dynamic model of
conventional PID controller to show the robustness of the fuzzy quadcopter UAV to control the attitude and the position, where
PID controller. Fuzzy PID controller has been verified through
the controller output changes adaptively according to the
simulation work utilizing Matlab/Simulink, where better
trajectory tracking error. The obtained results of the proposed
controller are compared with a conventional PID controller. A
performance is achieved compared with the conventional PID
remarkable reduction in the trajectory tracking error has been
controller. It is found that the errors in the quadcopter’s attitude
achieved via the FPID controller compare to the conventional
and position have been significantly reduced through using fuzzy
PID control technique.
PID controller by 70% and 87%, respectively.

The residual of the paper is presented as follows; Section II

Keywords: Quadcopter UAV, PID controller, Fuzzy PID briefly presents the quadcopter UAV modeling. While Section
controller, fuzzy logic. III covers the proposed control design and its implementation to
the quadcopter UAV system. Section IV illustrates the
I. INTRODUCTION simulation results. Section V concludes the paper.

Recently, the quadcopter unmanned aerial vehicles (UAVs) are II. QUADCOPTER MODELING
playing a significant role in combating the COVID-19 pandemic
crisis. In some countries around the world, the quadcopter UAVs A. Quadcopter UA VDescription
have been used in aerial spray and disinfection, transport of
samples, remote temperature check for individuals and monitor The quadcopter consists of 4-rotors fixed in cross configuration
the curfew process, and a few more. Due to these applications
that have a direct impact on the community service, the
quadcopter UAV is receiving remarkable interest from
researchers and engineers in terms of modeling and control
design algorithms to enable it achieves the assigned tasks
successfully.

On the other hand, the fast progress on electronics kits,

computers, and lithium battery technology encouraged the
researchers to design the quadcopter UAVs with different sizes
and shapes, which can be used either for indoor or outdoor
applications. Therefore, currently, the quadcopter UAVs are
abundantly available in the markets.

978-1-7281-9111-9/20/$31.00 ©2020 IEEE

Authorized licensed use limited to: Robert Gordon University. Downloaded on May 28,2021 at 11:27:36 UTC from IEEE Xplore. Restrictions apply.
The quadcopter moves in 6-DOFs, namely (roll, pitch, yaw, x, y, —Mnop & —cos 3 sin 4 cos 3 + sin 3 sin 3
& = ------------------------------------------------------- 1
z), where Figure 2 maps quadcopter movements: take-off, m
landing, right, left, forward, backward, clockwise, and counter-
-Mfdyi —cos 3 sin 0 cos 3 —sin 3 sin 3
clockwise. The arrow's width is proportionally representing the 1 = l (8)
m
—MNOzZ —cos 3 cos 0
z = l
m

The quadcopter attitude subsystem dynamic equations:

Y
33 = Nv p 3 2 —a i 0 3 + a 20Xd + i2
W WP

0 = yVy0 2 — a 33 3 + a 4 3 X + “ l 3 (9)
Wy Wy

3 = — Nv u 3 2 — a s 3 0 + ——u 4
WZ WZ
B. Quadcopter UA VKinematic Model where,
fl d = " l < ] + ] | < ]4,
As depicted in Figure 1, where there are two different frames,
the earth frame (E-frame) symbolized by E = (&e,ye,ze) and the Wy W z y_ Wz W p y_ W
p
body frame (B-frame) denoted by B = (&b,yb,zb). The ai = W , a 2 = T" , a 3 = W , a 4 = T" , a 5 = W
wp wp Wy Wy Wz
generalized quadcopter’s coordinates can be given as: and (u i ,u2 ,u3 ,u4 ) are the quadcopter control inputs.
* = [ ,,.] 0 (1)

where the position of the quadcopter UAV is given as: III. CONTROL DESIGN
, = [&,1,z]0 (2)
A. PID Control Design
while the attitude of quadcopter UAV can be written as:
. = [ 3 ,0 ,3 ] 0 (3 ) The PID control technique is designed to stabilize and control
the quadcopter’s position and attitude dynamics illustrated in (8)
Hence, the quadcopter’s kinematic equation is given as follows: and (9). Consequently, the errors for the quadcopter’s in 6-DOFs
, = 78 (4) are defined as follows:
e p = &d —&
where, £ and V symbolize the quadcopter’s linear velocity in E-
frame and B-frame, respectively, and R denotes the rotation ey = 1 d < 1
matrix, and it's given as follows:
ez zd z
(10)
e<a = 3 d < 3
c0 c 3 s3s0c3 — c3c3 s3s0c3 + c3s3
7 = c0s3 s3s0s3 + c3c3 c3s0s3 — s3c3 (5) e e = 0 d —0
. — s0 s3c0 c3c0
= 3d < 3
Where for instance c 0 and s 0 denote cos0 and sin0,
respectively. where, eP, ey, ez and e^, eb, are the errors signals between
the actual signals (x, y, z, 3, 0 and y) and the desired signals (&d,
The quadcopter rotational motion equation is given by: 1d, Zd, 3d, 0d, and 3d ).
. = (6)
The PID controller is developed and applied as follows:
where, n and m denote the quadcopter’s angular velocity in E- j Y
frame and B-frame, respectively, and T represents the d = Mp.ee + M/gJ '¿Y t + M—. - e e (11)
transformation matrix, and it's given as follows [15]:
where, i = & ,i,z, 3 , 0,anY 3 , respectively, and Mp > 0 , Mh >
0, and M—> 0 denote the PID controller design parameters.
r1
sin 3 ta n 0 cos 3 ta n 0'
While ve represents the PID generated control output.
0 cos 3 —sin 3
(7)
sin 3 cos 3
0
cos 0 cos 0
B. Fuzzy PID Control Design
C. Quadcopter Dynamic Model
Fuzzy logic control (FLC) represents a major branch of
The quadcopter UAV dynamic equations [16] are divided into
intelligent control systems that exploit a human understanding
two subsystems and are given as follows: The quadcopter
position subsystem dynamic equations:

Authorized licensed use limited to: Robert Gordon University. Downloaded on May 28,2021 at 11:27:36 UTC from IEEE Xplore. Restrictions apply.
of the plant in the process of control design [7]. Figure 3 reveals and —e have been used to map the fuzzy logic controller output U
the general architecture of the FLC. into u . Therefore, the obtained control output u is used to
control the nonlinear dynamics of the quadcopter system, as
Figure 4 illustrates the fuzzy logic controller (FLC) structure as depicted in Figure 4.
presented in [17], where the FLC represents the core building
block. While Figure 5 shows the FLC inputs membership
functions.
Following the centroid technique, the defuzzified output can
be given as follows [18], [19]:

where,

_ X U=l + S i=L+ l
(13)
X i= i r u m / (&i ) + X i=L+l
and
w
S ì =l + X i=fl+l &ir ut/C & i) Fig u r e 5 FLC m e m b e r s h ip f u n c t io n s .
1 _ w (14)
X f = ir ;m/(& i) + X i=fl+l r ut/C & i)

N represents the number of samples, while r ; m/ and r um/

denote the lower and upper membership functions, respectively.
&e denotes the output of the iiZ sample. Whereas R and L are
switch points that can be calculated by Karnik-Mendel algorithm.

Fig u r e 6 C o n t r o l o u t pu t s u r f a c e o f t h e FLC.

Table 1 shows the FLC’s rule. A uniform set is implemented for

the FLC’s inputs as {N, Z, P}, where N, Z, and P denote
Fig u r e 3 FLC g e n e r a l a r c h it e c t u r e .
negative, zero, and positive, consequently. In contrast, the output
set has been chosen as {NB, NM, Z, PM, PB} where NB, NM,
PB, and PM represent negative big, negative medium, positive
medium, and positive big, respectively.

TABLE 1. FUZZY RULES

U E

N Z P
N NB NM Z
Z NM Z PM

Quadcopter Dynamics P Z P PB
Fig u r e 4 FPID C o n t r o l l e r .

The output u of the FPID controller presented in Figure 4 is

calculated by firstly getting the error signal e ( t ) and e ( t ) , and IV. SIMULATION MODEL
then normalize it to E and ~ E , repectively by multiplying e ( t )
The quadcopter model is simulated utilizing Matlab/Simulink,
and e ( t ) by the postive constats —e and —d, respectively. The
and the parameters of the simulated model are listed in T able 2
values of E and ~ E used as inputs to the fuzzy logic controller
[16]. Table 3 and Table 4 listed the inner and outer loop PID
to generate the output U , then the scalling postive constats —0 controllers’ parameters, respectively. While Table 5 and Table 6

Authorized licensed use limited to: Robert Gordon University. Downloaded on May 28,2021 at 11:27:36 UTC from IEEE Xplore. Restrictions apply.
presented the inner and outer loops FPID controllers’ The results compared the performance of the proposed FPID
parameters, respectively. controller against the conventional PID in terms of the error
trajectory tracking for the quadcopter UAV position and attitude.

Figure 7 presents the quadcopter position in a 3D spiral shape

Ta b l e 2 q u a d c o pt e r ’s Pa r a m e t e r s . for FPID and PID controllers, while Figure 8 illustrates the
N am e P a ra m eter V a lu e U n it quadcopter’s position in x,y, and z directions. Figure 9 illustrates
Mass m 0.486 Kg the position’s error signals wherein the FPID controller provides
The arm’s length d 0.25 m
Inertia on x-axis 3.8278e-3 Nm/rad/s2 better performance against the conventional PID.
I,
Inertia on y-axis Iy
3.8278e-3 Nm/rad/s2
Inertia on z-axis I„
7.6566e-3 Nm/rad/s2 Figure 10 and Figure 11 present the quadcopter attitude for FPID
Aerodynamic coefficient on x K fa x
5.5670e-4 N/rad/s and PID controllers, respectively. Again, as it can be seen in
Aerodynamic coefficient on y K fa y 5.5670e-4 N/rad/s
Aerodynamic coefficient on z 6.3540e-4 N/rad/s
Figure 12, which presents attitude error signals, the FPID
K fa z
Drag coefficient on x 5.5670e-4 N/m/s provided better attitude trajectory tracking compared to the
Drag coefficient on y K fd y 5.5670e-4 N/m/s conventional PID controller.
Drag coefficient on z 6.3540e-4 N/m/s
Lift force coefficient K p 2.9842e-3 Nm/rad/s
Drag coefficient C D
3.2320e-2 Nm/rad/s
Rotor inertia k
2.8385e-5 Nm/rad/s2

TABLE 3. PID pa r a m e t e r s FOR THE a t t it u d e

Pa r a m et er 0 0 tf
25 15 15
0 0 0
fcß 15 25 25

TABLE 4. PID pa r a m e t e r s FOR THE po s it io n

Pa r a m et er X Y Z
'p 40 40 40
Fig u r e 7 3D P o s it io n t r a j e c t o r y t r a c k in g f o r FPID a n d PID
0 0 0
CONTROLLERS.
fcß 80 80 80

TABLE 5. FPID pa r a m e t e r s FOR THE a t t it u d e

Pa r a m et er 0 0 tf
CP 50 50 20
Q 2 2 2
•0 5 5 2
•t 40 50 50

TABLE 6. FPID pa r a m e t e r s FOR THE POSITION

Pa r a m et er X Y Z

•e 50 50 40
2 2 2 Fig u r e 8 P o s it io n t r a j e c t o r y t r a c k in g in x , y , a n d z d ir e c t io n s
c 0 0.2 0.2 15 f o r FPID a n d PID c o n t r o l l e r s .

Ci 20 20 50

\ -...- - =£
V. SIMULATION RESULTS
10 20 30 40 50 60
This section presented the simulation results for the overall
quadcopter control system, and the results have been performed
; \ ey-PID

V
using Matlab/Simulink platform. The dynamic differential ey-FPID

equations in (8) and (9) have been used to simulate the

10 20 30 40 50 60
quadcopter model, while equation (11), along with the block
!
x 1 0 '3

diagram in Figure 4 have been used to simulate the controller.

The simulation is run for 60 seconds. The sampling time was set
to 0.01 sec, and the solver that has been used to solve the V
10 20 30 40 50 60
differential equation in SIMULINK is ode45 with a default Time (sec)

setting and relative tolerance of 0.001. Fig u r e 9 Th e p o s it io n t r a j e c t o r y t r a c k in g e r r o r f o r FPID a n d

PID c o n t r ol l er s.

Authorized licensed use limited to: Robert Gordon University. Downloaded on May 28,2021 at 11:27:36 UTC from IEEE Xplore. Restrictions apply.
 / ¿ ¿ ( a t t i t u d e ) % I (e^ + eg + e p j d t (16)
o

Ta b l e 8 ISE f o r t h e a t t it u d e e r r o r s .
Controller PID Fuzzy PID Reduction (%)
ISE value 1.1104 0.3311 70.18%

VI. CONCLUSION

In this work, the quadcopter UAV mathematical model has been

briefly presented in terms of the quadcopter kinematic and
dynamics equations. Then, a fuzzy PID controller has been
Fig u r e 10 Th e a t t it u d e t r a j e c t o r y t r a c k in g f o r PID c o n t r o l l e r . implemented to control the quadcopter that exhibits nonlinear
dynamics in order to obtain a robust performance in terms of
trajectory tracking error. The results of the proposed controller
are benchmarked with the conventional PID controller. It’s
found that the proposed fuzzy PID controller significantly
reduced the trajectory tracking error for the quadcopter position
and attitude. In the coming future works, the proposed fuzzy PID
controller will be further evaluated and tested by simulation in
the presence of uncertainties and disturbance.

REFERENCES

[1] S. Bouabdallah, A. Noth, and R. Siegwart, “PID vs LQ

control techniques applied to an indoor micro
quadrotor,” 2004 IEEE/RSJ Int. Conf. Intell. Robot.
Syst. (IEEE Cat. No.04CH37566), vol. 3, pp. 2451-
2456, 2005.

[2] L. Romero, D. Pozo, and J. Rosales, “Quadcopter

stabilization by using PID controllers,” Maskana, vol.
0, no. 0, pp. 175-186, 2015.

[3] A. L. Salih, M. Moghavvemi, H. A. F. Mohamed, and

K. S. Gaeid, “Modelling and PID controller design for
a quadrotor unmanned air vehicle,” 2010 IEEE Int.
Conf. Autom. Qual. Testing, Robot. AQTR 2010 - Proc.,
vol. 1, pp. 74-78, 2010.

[4] A. Ataka et al., “Controllability and observability

analysis of the gain scheduling based linearization for
UAV quadrotor,” Proc. 2013 Int. Conf. Robot.
PID CONTROLLERS. Biomimetics, Intell. Comput. Syst. ROBIONETICS
2013, no. November, pp. 212-218, 2013.
Furthermore, the integral square error (ISE) is calculated for the
quadcopter’s position and attitude by applying (12) and (13), [5] A. Eltayeb, M. F. Rahmat, M. A. M. Basri, and M. S.
respectively. The results of the FPID and PID controllers’ Mahmoud, “An Improved Design of Integral Sliding
performance in terms of tracking error reduction are presented Mode Controller for Chattering Attenuation and
in Table 2 and Table 3 for the quadcopter position and attitude, Trajectory Tracking of the Quadrotor UAV,” Arab. J.
respectively. The FPID controller exhibits a significant Sci. Eng., 2020.
reduction in tracking error compared to the conventional PID.
[6] A. Eltayeb, M. F. Rahmat, M. A. Mohammed Eltoum,
and M. A. Mohd Basri, “Adaptive fuzzy gain
scheduling sliding mode control for quadrotor UAV
/¿ ’¿’( p o s itio n ) % I (e p + e p + e p ) d t (15)
o systems,” in 2019 8th International Conference on
Modeling Simulation and Applied Optimization,
Ta b l e 7 ISE f o r t h e po s it io n e r r o r s . ICMSAO 2019, 2019.
Controller PID FPID Reduction (%)
ISE value 1.18733 0.14705 87.62% [7] A. Eltayeb, M. Fuaad, M. A. M. Eltoum, and M. A. M.
Basri, “Robust Adaptive Sliding Mode Control Design
for Quadrotor Unmanned Aerial Vehicle Trajectory
Tracking,” Int. J. Comput. Digit. Syst., vol. 2, no. 2, pp.

Authorized licensed use limited to: Robert Gordon University. Downloaded on May 28,2021 at 11:27:36 UTC from IEEE Xplore. Restrictions apply.
 249-257, 2020.

[8] A. Eltayeb, M. F. Rahmat, and M. A. M. Basri,

“Adaptive feedback linearization controller for
stabilization of Quadrotor UAV,” Int. J. Integr. Eng.,
vol. 12, no. 4, pp. 1-17, 2020.

[9] A. Freddi, A. Lanzon, and S. Longhi, A feedback

linearization approach to fault tolerance in quadrotor
vehicles, vol. 44, no. 1 PART 1. IFAC, 2011.

[10] Z. He and L. Zhao, “Robust chattering free

backstepping/backstepping sliding mode control for
quadrotor hovering,” Proc. 2016 IEEE Inf. Technol.
Networking, Electron. Autom. Control Conf. ITNEC
2016, pp. 616-620, 2016.

[11] M. Ariffanan and M. Basri, “Robust Backstepping

Controller Design with a Fuzzy Compensator for
Autonomous Hovering Quadrotor UAV,” Iran. J. Sci.
Technol. Trans. Electr. Eng., vol. 42, no. 3, pp. 379-
391, 2018.

[12] T. X. Dinh and K. K. Ahn, “Adaptive tracking control

of a quadrotor unmanned vehicle,” Int. J. Precis. Eng.
Manuf., vol. 18, no. 2, pp. 163-173, 2017.

[13] G. Antonelli, E. Cataldi, F. Arrichiello, P. R. Giordano,

S. Chiaverini, and A. Franchi, “Adaptive Trajectory
Tracking for Quadrotor MAVs in Presence of
Parameter Uncertainties and External Disturbances,”
IEEE Trans. Control Syst. Technol., vol. 26, no. 1, pp.
248-254, 2018.

[14] S. I. Abdelmaksoud, M. Mailah, and A. M. Abdallah,

“Control Strategies and Novel Techniques for
Autonomous Rotorcraft Unmanned Aerial Vehicles: A
Review,” IEEE Access, vol. 8, pp. 195142-195169,
2020.

[15] R. Olfati-Saber, “Nonlinear Control of Underactuated

Mechanical Systems with Application to Robotics and
Aerospace Vehicles,” PhD Thesis, Massachusetts
Institute of Technology, 2001.

[16] O. Mofid and S. Mobayen, “Adaptive sliding mode

control for finite-time stability of quad-rotor UAVs
with parametric uncertainties,” ISA Trans., vol. 72, pp.
1-14, 2018.

[17] J. M. Mendel, Uncertain Rule-Based Fuzzy Systems:

Introduction and New Directions. 2017.

[18] J. M. Mendel, H. Hagras, W. W. Tan, W. W. Melek,

and H. Ying, Introduction To Type-2 Fuzzy Logic
Control: Theory and Applications, vol. 9781118278.
New York, USA: Wiley-IEEE Press, 2014.

[19] Ahmed Eltayeb, Mohd Fua’ad Rahmat, Mohd

Ariffanan Mohd Basri, MA Mohammed Eltoum, Sami
El-Ferik “An Improved Design of an Adaptive Sliding
Mode Controller for Chattering Attenuation and
Trajectory Tracking of the Quadcopter UAV,” IEEE
Access, vol. 8, pp. 205968-205979, 2020.

Authorized licensed use limited to: Robert Gordon University. Downloaded on May 28,2021 at 11:27:36 UTC from IEEE Xplore. Restrictions apply.