Modelling and Simulation of an Autonomous Pod-Tethered
Quadcopter Drone System for Aviation Applications
Joshua D’Souza
1
, Keith J. Burnham
1
, Manolya Kavakli-Thorne
2
and James E. Pickering
1
1
School of Engineering and Innovation, Aston University, Birmingham, U.K.
2
Aston Digital Futures Institute (ADFI), Aston University, Birmingham, U.K.
Keywords: Drone, Tethered Drone, Control, PID, Autonomous Systems, Safety, Aviation.
Abstract: This paper presents the development of a novel autonomous pod-tethered quadcopter drone system tailored
for airport environments. Utilising the Aurrigo Auto-Pod (AAP), the multi-purpose system aims to securely
tether a drone that transmits real-time data such as video imagery to the AAP, whilst at the same time supplies
power to the drone. Through the development of a novel model-based design (MBD) approach, an analysis
of the dynamical behaviour of the tethered system is undertaken. Simulation results demonstrate the potential
benefits of using a tethered drone approach to enhance airport operational efficiency and safety. The study
highlights the drone's control dynamics and operational constraints within a potential airport setting
demonstrating the system's capability to operate under stringent aviation regulations.
1 INTRODUCTION
The research problem addressed in this study centres
on developing a novel autonomous pod-tethered
quadcopter drone system for airport operation, see
Figure 1. It essentially considers the integration of
three key components with an Aurrigo Auto-Pod
(AAP):
i. Quadcopter drone
ii. Tether
iii. Ground control station
This system must adhere to aviation regulations
and cater for the specific operational demands of an
airport environment. The objective is to create a
prototype tethered drone system that delivers
essential information on airport operations, for use
onboard the AAP, as depicted in Figure 1. It is
envisaged that one function would be that of
transmitting video footage from the drone. The
onboard control and communication system for the
drone is to be securely tethered to the AAP. The tether
has the role of not only providing a secure physical
link to the AAP, but it also provides a means of
transferring data as well as provide a continuous
power supply to the quadcopter drone.
Figure 1: Key operational areas of the autonomous-pod
tethered drone system.
In regard to the literature, various tethered drone
solutions exist for a range of applications. In (Chang
and Hung, 2021), the tethered drone system involves
a stationary base station. In (Talke, Birchmore and
Bewley, 2022), the tethered drone works with an
unmanned surface vehicle (USV) team and operates
based on the relative position of the drone and the
USV team using data from inertial measurement units
(IMUs). In (Kiribayashi, Yakushigawa and Nagatani,
Quadcopter
drone with camera
and back-up power
Aurri
g
o Auto-Pod (AAP)
Tether with
power and data
Ground control
station: secure
landing platform with
tether management
syste
m
156
D’Souza, J., Burnham, K., Kavakli-Thorne, M. and Pickering, J.
Modelling and Simulation of an Autonomous Pod-Tethered Quadcopter Drone System for Aviation Applications.
DOI: 10.5220/0013067700003822
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 21st International Conference on Informatics in Control, Automation and Robotics (ICINCO 2024) - Volume 1, pages 156-165
ISBN: 978-989-758-717-7; ISSN: 2184-2809
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.
2017), the tethered drone is designed for the operation
at disaster sites with a slack tether. In (Kiribayashi,
Yakushigawa and Nagatani, 2018), the authors
investigated the use of a lightweight tether to reduce
the load on the drone; with this being used for drone
flights below 10 meters. There is very limited
literature on the topic of using autonomous vehicles
with tethered drone systems. However, in (Rodrigues,
2023) an approach is proposed and developed for
landing a tethered drone on static and moving
platforms.
The challenge in this research involves how to
effectively 'control' a quadcopter drone that is subject
to a tether, which introduces additional complexities
to its motion dynamics. Unlike free-flying drones, the
tether imposes physical constraints on the drone's
range of movement, potentially affecting its stability,
maneuverability, and overall performance. The
tension in the tether can vary depending on factors
such as the drone's velocity, position, and direction,
creating nonlinear forces that must be accounted for
in the control system. The development of a robust
control algorithm that compensates for these tether-
induced forces while maintaining smooth, accurate,
and responsive flight is key to achieving optimal
functionality in tethered drone operations.
Additionally, ensuring that the control system can
adapt to real-time environmental changes, such as
wind or variable tether length, adds another layer of
complexity to the problem.
1.1 Aviation Applications of the
Tethered Quadcopter Drones
Tethered drones have the potential to be beneficial in
a range of airport applications. The tethered drone
system satisfies aviation legislation due to the
physical connection with the AAP. Applications of
tethered drone technology at an airport include:
• Security surveillance: Tethered drones have
the potential to offer continuous aerial
surveillance of airport premises, enhancing
perimeter security by monitoring unauthorised
entries, tracking suspicious activities, and
deterring potential threats.
• Traffic monitoring and management: Tethered
drones can aid in managing ground traffic at
large airports by monitoring and optimising
the flow of service vehicles, thereby reducing
delays, and increasing efficiency.
• Airport inspection: Tethered drones equipped
with high-resolution cameras and sensors can
potentially facilitate quick and safe
inspections of hard-to-reach aircraft parts,
such as the fuselage top and tail, for damage or
maintenance issues.
• Emergency response: In emergencies (e.g.,
fires or accidents on the tarmac), tethered
drones can be rapidly deployed to provide
real-time video feeds, aiding in accurate
situation assessment and effective response
coordination.
• Wildlife management: Tethered drones could
potentially be used at airports to monitor and
manage wildlife activity around runways,
preventing bird strikes and enhancing aircraft
safety during take-off and landing.
• Weather monitoring: Equipped with
meteorological instruments, tethered drones
could potentially provide real-time local
weather forecast data crucial for managing
flight schedules during adverse conditions at
airports.
• Construction and maintenance oversight:
Tethered drones provide an aerial overview for
monitoring progress and ensuring safety
protocols during airport construction and
maintenance, surpassing ground-based
monitoring capabilities.
In this initial piece of research, specific
applications such as the points mentioned above will
not be explored. Instead, the basic operation of the
tethered drone using the AAP will be explored. This
basic operation is a starting point for each of the
applications outlined above.
1.2 Research Aim and Approach
The aim of the research described in this paper is to
develop a novel autonomous pod-tethered drone
system tailored specifically to a range of aviation
applications and design requirements for these. In this
initial study, it will be assumed that the drone will aim
to hover at a reference altitude of 10 meters.
However, it is envisaged that a further study will be
required to explore the optimum altitude for the range
of applications. The specific requirements for the
tethered drone system have been identified in a series
of co-design sessions with the industry partner
Aurrigo, see (Pickering, et al, 2024).
To guide and enhance the development of a
physical prototype of the autonomous pod-tethered
drone system, a model-based design (MBD) approach
is adopted. This is used to initially understand the
dynamic behaviour of the system and to design and
tune the on-board control system. This is because
embedded control will be used later when developing
the physical prototype. Although initially this would
Modelling and Simulation of an Autonomous Pod-Tethered Quadcopter Drone System for Aviation Applications
157
Figure 2: Operation of the autonomous pod-tethered drone
system within an airport.
require additional time up-front, it is considered that
such an MBD approach over the span of the project
will save both time and cost, see (MathWorks, 2020).
Figure 2 provides a visualisation of the typical
operation of the autonomous pod-tethered drone
system at an airport. The MBD approach is used to
investigate the potential of the system and to develop
the control systems for the following:
• The operation of a tethered drone equipped
with a camera that provides the potential for
360-degree vision to scan a local land area,
denoted as 𝐿
(in Figure 2, the blue
circular area surrounding the drone
represents the 𝐿
). In this paper, the actual
camera scanning radius is not considered.
• The setup is used to assess the radius of a
land area, denoted as 𝑅
, that can be
scanned or investigated by a stationary AAP
using the tethered quadcopter drone system
(in Figure 2, the area within the black dashed
line represents the 𝑅
, with the direction of
the quadcopter drone motion about the
radius provided).
1.3 Outline of Paper
The paper is organised as follows. The novel tethered
quadcopter drone simulation model is developed in
Section 2. Simulation results are presented and
discussed in Section 3. Conclusions of this research
and proposals for further work are given in Section 4.
The novelty in the paper is the initial scope of the
ideas (i.e., tethered drone with autonomous vehicle)
and the initial mathematical modelling of the tether
between the drone and AAP to understand the
additional complexities to the drone’s motion
dynamics.
2 MODELLING AND
SIMULATION
A tethered quadcopter drone is to be modelled and
simulated to allow the operation of the quadcopter to
be explored, i.e., the potential radius of a land area,
denoted 𝑅
of the quadcopter drone when tethered.
Although beyond the scope of this paper, the
developed control systems will then be tested on the
actual tethered quadcopter drone system (i.e.,
physical prototype), using the embedded code tools
that are available within MATLAB and Simulink
The key elements of the AAP and tethered system
to be developed are the quadcopter drone, and the
tether, with the mass of each of the key elements
being denoted by 𝑚

,𝑚
, and 𝑚
, respectively.
The three masses are subject to gravitational
acceleration, denoted 𝑔 , resulting in a downward
force, and drag forces due to the presence of wind
disturbances; these are denoted 𝐹

, 𝐹
, and 𝐹
,
respectively, and modelled by:
𝐹
//
=
1
2
𝜌𝐴𝐶
𝑉
(1)
where 𝜌 is the density of the atmosphere, 𝐴 is the
cross-sectional area perpendicular to the wind flow,
𝐶
is the coefficient of drag, and 𝑉 is the velocity of
the object (White, 2011).
2.1 Quadcopter Dynamics and Control
The schematic in Figure 3 illustrates the quadcopter
to be mathematically modelled in this section, with
the quadcopter drone presented in three-dimensional
space, i.e., 𝑋, 𝑌, and 𝑍. The lift generated by the 4
rotors of the quadcopter is denoted 𝑈
and 𝑇 denotes
the tension acting on a taut line of the tether, denoted
𝑡, between the AAP and the quadcopter drone, see
Figure 3. Details of the free body diagram for the key
elements are also given in Figure 3.
𝐿
360-degree vision
𝑅
Quadcopter
drone with
camera
Tether
AAP
ICINCO 2024 - 21st International Conference on Informatics in Control, Automation and Robotics
158
Figure 3: Freebody diagram of the tether system.
The orientation of the quadcopter within the three-
dimensional space is defined by the Euler angles, roll,
denoted 𝜑, pitch denoted 𝜃 and yaw, denoted 𝜓, see
(Abdelhay and Zakriti, 2019).
This orientation of the
quadcopter drone is defined based on the
transformation between the quadcopter drone within
the three-dimensional space. This is represented by
the following rotational transformation matrix
(Abdelhay and Zakriti, 2019):
[
𝑅
]
= 
𝑐𝜓𝑐𝜃 𝑠𝜙𝑠𝜃𝑐𝜓− 𝑐𝜙𝑠𝜓 𝑐𝜙𝑠𝜃𝑐𝜓 + 𝑠𝜙𝑠𝜓
𝑐𝜃𝑠𝜓 𝑠𝜙𝑠𝜃𝑠𝜓 + 𝑐𝜙𝑐𝜓 𝑐𝜙𝑠𝜃𝑠𝜓− 𝑠𝜙𝑐𝜓
−𝑠𝜃 𝑠𝜙𝑐𝜃 𝑐𝜙𝑐𝜃
(2)
where 𝑐 is the cosine of the Euler angle, 𝑠 is the sine
of the Euler angle, and
[
𝑅
]
is the rotational matrix.
In (Abdelhay and Zakriti, 2019), the following
equations of motion are used to capture the nonlinear
dynamics of the quadcopter:
𝑚𝑥=(𝐹
+𝐹
+𝐹
+𝐹
)(𝑐𝑜𝑠𝜑𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜓
+𝑠𝑖𝑛𝜑sin𝜓)
(3)
𝑚𝑦=(𝐹
+𝐹
+𝐹
+
𝐹
)(𝑐𝑜𝑠𝜑𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜓 + 𝑠𝑖𝑛𝜑cos𝜓)
(4)
𝑚𝑧=
(
𝐹
+𝐹
+𝐹
+𝐹
)(
𝑐𝑜𝑠𝜑𝑐𝑜𝑠𝜃
)
−𝑚𝑔
(5)
𝐼
𝜑=
(
𝐹
−𝐹
)
𝑙+𝜃
𝜓
(𝐼
−𝐼
)
(6)
𝐼
𝜃
=
(
𝐹
−𝐹
)
𝑙+𝜓
𝜑(𝐼
−𝐼
)
(7)
𝐼
𝜓
=(𝑀
+𝑀
−𝑀
−𝑀
)+𝜑𝜃
(𝐼
−𝐼
)
(8)
where 𝑥 , 𝑦, and 𝑧 represent the acceleration
components. The quadcopter's moments of inertia
about the principal axes are given by 𝐼
, 𝐼
,
𝐼
. The
moments produced by the rotors are 𝑀
, 𝑀
,𝑀
and
𝑀
, and 𝐹
,𝐹
,𝐹
and 𝐹
correspond to the thrust
forces generated by each of the quadcopter's rotors.
Based on Equation (3) to (8), the model is
linearised (i.e., using small angle approximations,
thus eliminating the cosine and sine terms) and
rearranged to give the following, see (Ahmad et al.,
2020):
𝑥=
𝑈
𝑚
𝜃
(9)
𝑦=
𝑈
𝑚
𝜑
(10)
𝑧=
𝑈
𝑚
−𝑔
(11)
𝜑=
𝑈
𝐼
(12)
𝜃
=
𝑈
𝐼
(13)
𝜓
=
𝑈
𝐼
(14)
where 𝑈
, 𝑈
,𝑈
, and 𝑈
are the control variables
that can be further described with the following:
𝑈
=𝐹

=𝐾
𝜔

(15)
𝑈
=
(
𝐹
−𝐹
)
𝑙=𝐾
𝑙(𝜔
−𝜔
)
(16)
𝑈
=
(
𝐹
−𝐹
)
𝑙=𝐾
𝑙(𝜔
−𝜔
)
(17)
𝑈
=
(
𝑀
+𝑀
−𝑀
−𝑀
)
𝑙
=𝐾
𝑙(𝜔
+𝜔
− 𝜔
−𝜔
)
(18)
where 𝜔
,𝜔
,𝜔
, and 𝜔
are the angular velocities
of the 4 rotors, 𝐾
is the thrust coefficient, 𝐾
is the
drag coefficient for the 4 rotors and 𝑙 signifies the
distance from the center of the quadcopter to the
center of each rotor.
The initial method of control used for the
quadcopter in this research is PID. PID control
methods have been widely used for the control of
quadcopters, see (Ahmad et al., 2020), (Le Nhu Ngoc
Thanh and Hong, 2018), (Zouaoui, Mohamed and
Kouider, 2018) and (Xuan-Mung and Hong, (2019),
with the control architecture adopted in this research
being illustrated in Figure 4. The reference
displacements in the 𝑥 and 𝑦 axes are given by 𝑥

and 𝑦

, respectively. The PID controllers have been
configured and tuned to eliminate steady state error,
minimise overshoot and minimise rise time.
Modelling and Simulation of an Autonomous Pod-Tethered Quadcopter Drone System for Aviation Applications
159
Figure 4: Control architecture of the quadcopter drone,
where the bold line indicates multiple signals.
The desired roll and pitch angle references for the
drone, denoted 𝜑

and 𝜃

, respectively, are
determined using the conversion block in Figure 4,
which consists of the following:
𝜑

𝜃

=
𝑐𝑜𝑠𝜓 𝑠𝑖𝑛𝜓
𝑐𝑜𝑠𝜓 −𝑠𝑖𝑛𝜓
⎣
⎢
⎢
⎡
𝑈
𝑔
𝑈
𝑔
⎦
⎥
⎥
⎤
(19)
where use is made of the PID controllers’ outputs
(i.e., 𝑈
and 𝑈
) for the desired 𝑥

and 𝑦

positions in the three-dimensional space (Ahmad et
al., 2020). Note that in further work, PID control is to
be compared to other control methods, e.g., LQR and
adaptive control.
Regarding the altitude controller, 4 PID
controllers are applied to account for the
reference/desired altitude, roll angle, pitch angle, and
the yaw/heading angle, denoted 𝑧

, 𝜑

, 𝜃

and
𝜓

, respectively. The controller output accounting
for the altitude and the weight of the quadcopter
yields the control input, 𝑈
, which is the collective
thrust produced by the 4 rotors. The control inputs,
𝑈
, 𝑈
, and 𝑈
are from the PID controllers which
account for roll, pitch, and yaw, respectively.
An initial simulation is configured by considering
the parameters in (Abdelhay and Zakriti, 2019). This
is initially simulated in order to verify the adopted
models, see Figure 5 (a). It is set up such that the
initial coordinate location of the quadcopter is (0, 0,
0), with an initial way-point of (1, 0, 10), and then a
final coordinate location of (1, 1, 10).
Figure 5 displays the three-dimensional space and
trajectory of the quadcopter. Figure 5 also displays
the trajectory in each of the respective axes in sub-
plots, i.e., 𝑥-axis versus time (b), 𝑦-axis versus time
(c) and 𝑧-axis versus time (d). Displacements in the 𝑥
and 𝑦-axes give a peak overshoot amplitude of 1.004
(i.e., 0.4% overshoot), a 3 second rise time, and 6.5
second settling time. In regard to the displacement in
the 𝑧-axis, the system response has an amplitude of
10.1 metres. Overall, the quadcopter drone operated
as was expected based on results in (Abdelhay and
Zakriti, 2019).
Figure 5: Desired tractotory versus actual trajectory for the
quadcopter.
2.2 Tether Dynamics
Tether modelling literature suggests several
approaches. One study identifies primary tether
forces—drag, weight, and tension—and proposes
three configurations: partially-elevated, general fully-
elevated, and vertical fully-elevated (Ioppo, 2017). It
uses a quasi-static model assuming uniform
equilibrium tension, with equations developed for
elemental tether lengths under static force balance
and specific boundary conditions. Tether dynamics
might cause significant tension fluctuations,
potentially destabilising the drone, thus it is modelled
as a vibrating string with its dynamics defined by
wave velocities.
Another study models the tether as rigid-body
segments linked at nodes where forces act and
position sensors are attached, enabling tether profile
recording (Mahmood and Ismail, 2022).
A third study uses the tether for coordinating
drones and ground vehicles via force control
(Barawkar and Kumar., 2024). Measurable forces and
rates through sensors inform a fuzzy-based control
system that adjusts drone pitch and yaw. It also
includes a PD controller for rotor speed adjustments
and an adaptive control for active management under
wind conditions.
ICINCO 2024 - 21st International Conference on Informatics in Control, Automation and Robotics
160
The physical construction of the novel tether
model to be developed here is based on first
principles. It is characterised as a cylindrical rod with
a uniform circular cross-section of diameter, denoted
𝑑
. The model is further developed with the
assumption of being an extendable taut tether
throughout the flight operation. Inextensibility is
assumed with consideration of a high-modulus, low-
elongation material for the tether, which under
operational tensile loads exhibits negligible
elongation, or stretch. The cylindrical model assumes
that the tether's cross-section remains constant despite
the wind or aerodynamic forces, which is considered
reasonable given the high bending stiffness and the
small diameter-to-length ratio.
Consequently, the tether's influence on the
quadcopter's dynamics is assumed to be accounted for
through static tension and forces that are a function of
the tether's material properties, cross-sectional area,
and the external environmental loads. The amount of
tether required i.e., length, denoted 𝑙
, is dependent of
the desired position of the quadcopter with respect to
the AAP. The amount of tension on the tether is
dependent on the weight of the tether, 𝐹
and the drag
force produced by the wind, 𝐹
,
. These factors are
described by the following:
𝑇=
𝑇
𝑇
𝑇
 = 𝑇
+𝐹
+𝐹
=
𝐹

− 𝐹

𝐹

− 𝐹

𝐹

− 𝐹

 + 
0
0
𝜇𝑙
𝑔
+ 
𝐹
𝐹
𝐹
(20)
where 𝑇
,𝑇
, and 𝑇
are the tension components in the
𝑥,𝑦, and 𝑧 axes, 𝐹

,𝐹

, and 𝐹

are the
drag forces on the AAP, 𝐹

,𝐹

, and 𝐹

are
AAP’s driving forces, whilst 𝐹
,𝐹
, and 𝐹
are
the drag forces on the tether, and 𝜇 is the mass per
unit length of the tether.
This section formulates the effects of the
dynamics of the quadcopter due to the tether and wind
flow. These act as additional loads experienced by the
quadcopter, constraining the quadcopter’s degrees of
freedom. This is due to forces created by tension and
wind, and the drag experienced by the quadcopter.
These will vary with the quadcopter's position
relative to its anchor point. Considering Newton’s
second law and Figure 3, the translational motion,
from Equations (9) to (11) for the quadcopter and the
tether, are now given by:
𝑚𝑥
=𝑈
𝜃−𝐹
−𝑇
(21)
𝑚𝑦
=𝑈
𝜑−𝐹
− 𝑇
(22)
𝑚𝑧
=𝑈
−𝑚𝑔−𝐹
−𝑇
(23)
where 𝐹
,𝐹
, and 𝐹
are the drag forces
experienced by the quadcopter in the 𝑥,𝑦, and
𝑧 directions, respectively. The drag forces from
Equation (1) and modelling in Equation (20) are used
and substituted into Equations (21) to (23) to give the
following:
𝑥
=
𝑈
𝜃−
1
2
𝜌
𝐴
𝐶
𝑥
+𝑉
−𝑇𝑐𝑜𝑠(𝛼)
𝑚
(24)
𝑦
=
𝑈
𝜑−
1
2
𝜌
𝐴
𝐶
𝑦
+𝑉
−𝑇𝑐𝑜𝑠(𝛽)
𝑚
(25)
𝑧
=
𝑈
−
1
2
𝜌
𝐴
𝐶
𝑧
+𝑉
−𝑇𝑐𝑜𝑠(𝛾)
𝑚
−𝑔
(26)
where 𝑉
,𝑉
, and 𝑉
are the wind velocities in the
𝑥,𝑦, and 𝑧 directions, respectively, 𝛼,𝛽, and 𝛾 are
the angles of the tension vector with respect to 𝑥,𝑦,
and 𝑧, respectively, and 𝐴
, 𝐴
, and 𝐴
are reference
areas of the quadcopter. In addition to the tether and
wind effects on the translation motion of the
quadcopter, the generated tension and drag forces
introduce constraints in the rotational dynamics of the
quadcopter. Hence, Equations (12) to (14) are now
given by:
𝜑
=
𝑈
−𝐹
𝑙
−𝑇
𝑑

𝐼
(27)
𝜃
=
𝑈
−𝐹
𝑙
−𝑇
𝑑

𝐼
(28)
𝜓
=
𝑈
−𝐹
𝑙
−𝑇
𝑑

𝐼
(29)
where 𝑑

is the distance between the centre of
gravity of the quadcopter and the line of action of the
tension force. On this basis, substituting Equations (1)
and (21) into Equations (27) to (29) gives the
following:
Modelling and Simulation of an Autonomous Pod-Tethered Quadcopter Drone System for Aviation Applications
161
𝜑
=
𝑈
−
1
2
𝜌
𝐴
𝐶
𝑥+𝑉
𝑙−𝑇𝑐𝑜𝑠
(
𝛼
)
𝑑

𝐼
(30)
𝜃
=
𝑈
−
1
2
𝜌
𝐴
𝐶
𝑦+𝑉
𝑙−𝑇𝑐𝑜𝑠
(
𝛽
)
𝑑

𝐼
(31)
𝜓
=
𝑈
−
1
2
𝜌
𝐴
𝐶
𝑧+𝑉
𝑙−𝑇𝑐𝑜𝑠
(
𝛾
)
𝑑

𝐼
(32)
where 𝐶
, 𝐶
and 𝐶
are the drag coefficients in
the 𝑥, 𝑦 and 𝑧-axis, respectively.
3 RESULTS
In this Section, the scenario detailed in Figure 2 will
be investigated, i.e., determining the capability of a
tethered quadcopter drone system to assess the radius
of a land area. For this, the following will be
investigated:
i. Ability of the tethered quadcopter drone to
track the radius reference of a land area,
denoted as 𝑅
(see Section I) within a
circular path (constant radius) with a varying
time-period, denoted 𝑇
.
ii. Ability of the tethered quadcopter drone to
track 𝑅
with a fixed time-period.
iii. Ability of the tethered quadcopter drone to
track 𝑅
with a fixed time-period when
subject to wind.
3.1 Parameters
Table 1: Tethered quadcopter drone parameters.
Modelling
parameter
Value [units]
𝜇 0.0022 [𝑘𝑔/𝑚]
𝑚 5.2 [𝑘𝑔]
𝐷
3.5×10

[𝑚]
𝐶
0.7
𝑑

0.1 [𝑚]
𝜌

1.225 [𝑘𝑔/𝑚
]
𝐴
0.045 [𝑚
]
𝐴
0.045 [𝑚
]
𝐴
0.045 [𝑚
]
𝐶
𝑑𝑖𝑎𝑔(0.1 0.1 0.15)
𝐶
𝑑𝑖𝑎𝑔(0.1 0.1 0.15)
𝑔
9.81 [𝑚/𝑠
]
𝐼
3.8 ×10

[𝑘𝑔/𝑚
]
𝐼
3.8 ×10

[𝑘𝑔/𝑚
]
𝐼
7.1 ×10

[𝑘𝑔/𝑚
]
𝑙 0.32 [𝑚]
The parameters used for the simulation studies are
given in Tables I and II for the tethered quadcopter
drone and the six PID controllers, respectively.
Table 2: PID controller gains for the controlled variables.
Controlled
Variable
Controller Gain
𝑲
𝒑
𝑲
𝒊
𝑲
𝒅
𝑥 50.00 7.20 30.00
𝑦 11.00 0.16 6.50
𝑧 20.00 5.00 49.96
𝜑 12.00 0.20 7.50
𝜃 12.00 0.20 7.50
𝜓 12.00 0.20 7.50
3.2 Integral of Absolute Errors (IAE)
and Data Capture
The integral of absolute error (IAE) is used to
evaluate the effectiveness of the controller for the
range of scenarios detailed above over a specified
interval. This is useful when quantifying the error
between a desired control action (i.e., desired
position/radius, 𝑅
) and an actual output (i.e.,
actual position/radius, 𝑂
). The equation for the
IAE is given by:
𝐼𝐴𝐸=
|
𝑒(𝑡)
|
𝑑𝑡
(33)
where 𝑒(𝑡) is the error at time 𝑡, which is the
difference between the desired output and the actual
output, i.e., 𝑒
(
𝑡
)
=𝑟
(
𝑡
)
−𝑦(𝑡), with 𝑟(𝑡) being the
reference (i.e., desired radius of tethered drone, 𝑅
)
and 𝑦(𝑡) being the system output (i.e., actual radius
of the tethered drone, 𝑂
). 𝑇 is the time duration
over which the error is integrated.
The following simulation results are considered:
a) First lap (i.e., Lap 1)
b) 10 laps (not considering Lap 1)
Lap 1 of the simulation is included in the results;
this involves the tethered drone system initially
transitioning from being transient to steady-state.
Note that the initial positioning phase to achieve the
desired radius is not included in the IAE result for Lap
1 (this is included only for visual reasons).
For the 10-lap simulation, the graphical outputs
and IAE involve capturing Laps 2 to 11 (i.e., 10 laps).
As the tethered drone system is in steady state during
this period, this is viewed as being a ‘better’
comparison when comparing IAE for the three
investigations detailed above.
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3.3 Effect of Time-Period
To investigate the effect of the time period, 𝑇
, a 7-
metre radius reference is used for the tethered
quadcopter drone.
In Figure 6(a), the tethered drone is initially
‘climbing’ to the reference altitude of 10 metres. The
tethered drone then navigates to a reference radius of
7 metres (this is not included in any of the IAE
calculations) and proceeds to follow a radius
reference of 7 metres.
The full results for the first lap (i.e., Lap 1) and
the 10 laps are given in Figure 6 ((a) for Lap 1 and (b)
for 10 laps)), with the corresponding IAE results
given in Table III. Note that for these results, the IAE
is normalised with the time-period. The results
indicate that an IAE of 15 𝑠 represents the ‘best’
results, i.e., lowest error. Time periods of 10𝑠 and 20𝑠
result in a higher IAE, which would suggest that the
quadcopter drone was travelling too fast to achieve
the reference (i.e.,10𝑠), or too slow (i.e., 20𝑠).
Figure 6: Effect of the time period on achieving the
reference.
Table 3: Time period normalised IAE results for Lap 1 and
10 laps.
Time
Period [𝒔]
Normalised IAE
Lap 1 10 Laps
10.0 0.23 1.05
15.0 0.07 0.01
20.0 0.05 0.03
Figure 7: Effect of the radius on achieving the reference.
Table 4: Radius IAE results for Lap 1 and 10 laps.
Radius [𝒎] IAE
Lap 1 (10 Laps)
7 1.00 1.95
15 4.87 5.18
21 13.83 10.13
3.4 Effect of Radius
A set time-period of 15 seconds is selected (as this
gave the lowest IAE value in the previous Section),
with the tethered quadcopter drone radius reference
investigated with values of 7, 15 and 21𝑚.
The full results for the first lap (i.e., Lap 1) and 10
laps are given in Figure 7 ((a) for Lap 1 and (b) for 10
laps)), with the corresponding IAE results given in
Table IV. For Lap 1 and 10 laps, as the radius
increases, the IAE increases, i.e., reducing the ability
of the tethered drone system to follow the circular
path.
3.5 Effect of Wind
For this set of results, the radius reference is 7 metres
with a time period of 15 seconds. The velocity of the
wind in the y-axis, denoted 𝑉
has been varied with
the following values: 5, 10 and 15𝑚/𝑠. In (Choi,
2015), it is highlighted that wind acts as a disturbance,
with the wind altering the drone’s altitude and
velocity.
The full results for the first lap (i.e., Lap 1) and 10
laps are given in Figure 8 ((a) for Lap 1 and (b) for 10
laps)), with the corresponding IAE results given in
Table V.
Modelling and Simulation of an Autonomous Pod-Tethered Quadcopter Drone System for Aviation Applications
163
Figure 8: Effect of the wind on achieving the reference.
Table 5: Effects of wind IAE results for Lap 1 and 10 laps.
Wind
Velocity in
𝒚-axis [𝒎/𝒔]
IAE
Lap 1 10 Laps
5 1.02 2.20
10 130 5.51
15 2.06 13.84
For Lap 1 and 10 laps, as the wind speed
increases, the IAE increases, with the altitude of the
drone decreasing. Thus, the wind reduces the ability
of the tethered drone system to achieve the reference
altitude. This result is in agreement with the
relationship found in (Choi, 2015). It is noticeable
that when the wind velocity increases to 15𝑚/𝑠, a
large steady state error is introduced for the altitude,
i.e., approximately 40%.
4 CONCLUSIONS AND FURTHER
WORK
This study has demonstrated the feasibility of a novel
autonomous pod-tethered quadcopter drone system,
tailored for airport applications, using a novel model-
based design (MBD) approach. In particular, the
paper has proposed an approach to initially design
and tune the control system for a tethered quadcopter
drone. The simulation results that have been
presented serve to highlight the robustness of the
tethered system, under realistic operating conditions,
i.e., speed of drone, radius of an operating circle and
various wind conditions.
Overall, the results indicate the potential of the
system to enhance airport operational efficiency and
safety, i.e., offering continuous surveillance, traffic
management, as well as rapid emergency response
capabilities.
Future work is planned to focus on advancing the
modelling and simulation to enhance the overall
understanding of the tethered drone's operation. For
example, the development of a simulation model to
facilitate a comprehensive grasp of the tethered
quadcopter's functionality when paired with the
Aurrigo Auto-Pod (AAP). Following on from the
modeling and simulation, the controller will hen be
integrated into the physical prototype system of the
autonomous pod-tethered quadcopter drone.
ACKNOWLEDGEMENTS
The authors acknowledge the colleagues from
Aurrigo, namely James Heaton, Craig Cannon, Nick
Ridler and Simon Brewerton for their direction and
support with the project.
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