ABSTRACT
This work is aimed at modeling and carrying out state space analysis of a micro-UAV
(unmanned aerial vehicle) which is based on a modified radio controlled (RC) coaxial helicopter.
The modification involved incorporating payload such as: GPS (global positioning system)
module, Arduino microcontroller board and the Arduino Wi-Fi shield. The modeling involved
the development of a non-linear rigid body model on the basis of resolving forces and moments
that act on the micro-UAV using Euler-Newton formulation. In order to carry out the state space
analysis of controllability and observability, the non-linear model was linearized using the small
perturbation method. The desired performance specifications are: damping ratio 0.6 1, peak
overshoot 5% p M and the system should be asymptotically stable. The micro-UAV model
was shown to be controllable and observable even though asymptotically unstable due to the
presence of positive real roots (eigenvalues on the right hand of the s-plane, RHP) and repetitive
zero real roots on the s-plane. This indicated that the damping ratio of -1 and peak overshoot of
69.2% fell outside the desired specifications. Also, the time response analysis carried out
revealed unstable state responses in the dynamics and kinematics of the micro-UAV. A linear
optimal linear quadratic regulator (LQR) controller was introduced to stabilize the micro-UAV
and improved the performance specification with respect to peak overshoot of 4.27% and
damping ratio of 0.708. These values fell within the acceptable specifications and the system was
also shown to be asymptotically stable as all the eigenvalues were now on the left hand of the splane
(LHP). The time response analysis carried out showed stable state responses in dynamics
and kinematics of the micro-UAV. The communication link between the prototype micro-UAV
and the ground control station was established via a router access point (which was encrypted to
prevent unauthorized access) and a program written in visual C# programming language. This was tested
in the indoor environment of the Control Laboratory of Department of Electrical and Computer
Engineering, Ahmadu Bello University Zaria. The GPS data of longitude, latitude, time stamp and speed
at which these data were transmitted from the micro-UAV were monitored at the ground station (a laptop
PC with GUI developed program) with the aid of the GPS module, Ardiuno micro-controller and Ardiuno
Wi-Fi shield. The received signal strength indicator (RSSI) of the link was in the range -60dBm to –
41dBm operating at a frequency of 2.4GHz and data rate of 5.4Mbit/s.
TABLE OF CONTENTS
TITLE PAGE ……………………………………………………………………………………………………………… i
DECLARATION ……………………………………………………………………………………………………….. ii
CERTIFICATION …………………………………………………………………………………………………….. iii
DEDICATION ……………………………………………………………………………………………………………iv
ACKNOWLEDGEMENTS ………………………………………………………………………………………….. v
TABLE OF CONTENTS ……………………………………………………………………………………………..vi
LIST OF APPENDICES………………………………………………………………………….x
LIST OF FIGURES …………………………………………………………………………………………………….xi
LIST OF PLATES………………………………………………………………………………xiii
LIST OF TABLES ……………………………………………………………………………………………………. xiv
LIST OF ABBREVIATIONS ……………………………………………………………………………………… xv
ABSTRACT ……………………………………………………………………………………………………………xvii
CHAPTER ONE: INTRODUCTION ……………………………………………………………………………………… 1
1.1 Background Information …………………………………………………………………………………………………….. 3
1.1.1 Classification of UAVs……………………………………………………………………………….3
1.1.1.1 Classification based on Endurance and Altitude……………………………………………………3
1.1.1.2 Classification based on Rotor Configuration……………………………………………………….4
1.2 Aim and Objectives …………………………………………………………………………………………………………… 5
1.3 Statement of the Problem ……………………………………………………………………………………………………. 5
1.4 Methodology ……………………………………………………………………………………………………………………. 6
1.5 Significant Contributions…………………………………………………………………………….7
1.6 Thesis Organization …………………………………………………………………………………………………………… 8
CHAPTER TWO: LITERATURE REVIEW …………………………………………………………………………. 9
2.1 Introduction ……………………………………………………………………………………………………………………… 9
2.2 Review of Fundamental Concepts ………………………………………………………………………………………… 9
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2.2.1 Units of a micro-UAV System ………………………………………………………………………………………….. 9
2.2.2 Basis for Adopting the Coaxial Helicopter ………………………………………………………………………… 15
2.2.3 Non-Linear Systems ……………………………………………………………………………………………………… 15
2.2.3.1 Non-Linear Mathematical Models of a Micro-coaxial Helicopter ……………………………………….. 16
2.2.4.Controllability and Observability ……………………………………………………………………………………. 24
2.2.4.1 Stability ……………………………………………………………………………………………………………………. 24
2.2.5 Types of Controllers ……………………………………………………………………………………………………… 27
2.2.5.1Types of Optimal Control Problems ……………………………………………………………………………….. 28
2.2.5.2 Linear Quadratic Regulator ………………………………………………………………………………………….. 29
2.3 Review of Similar Works ………………………………………………………………………………………………….. 31
CHAPTER THREE: MATERIAL AND METHODS……………………………………………………………… 38
3.1 Introduction ……………………………………………………………………………………………………………………. 38
3.2.Modeling of the Micro-UAV System ………………………………………………………………………………….. 40
3.3 Modification of the Coaxial Helicopter ……………………………………………………………………………….. 40
3.4 Derivation of the Rigid Body Equation of the Micro-UAV Model ……………………………………………. 41
3.4.1Flapping Dyanmics of the Upper and Lower Rotors …………………………………………………………….. 41
3.4.2 Forces Acting on the Micro-UAV……………………………………..……………………………42
3.4.3 Moments Acting on the Micro-UAV ………………………………………………………………………………… 47
3.4.4 Rigid Body Non-Linear Equations of the Micro-UAV …………………………………………………………. 48
3.5 Linearization of the Non-Linear Micro-UAV Model Using Small Perturbation Techniques ………….. 53
3.5.1 Lineariztion of the Translational Dynamics……………………………………………………… …54
3.5.2 Linearized Rotational Dynamics ……………………………………………………………………………………… 55
3.5.3 Linearized Kinematics Responses…………………………………………………………………..55
3.6 Parameter Measurement………………………………………………………………………………58
3.6.1 Tools for Measurement………………………………………………………………………………59
3.7 Control Analysis………………………………………………………………………………………59
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3.7.1 Test for Control Solution……………………………………………………………………………59
3.7.2 Time Response Analysis of the Linear Micro-UAV Model……………………..…………………61
3.8 Application of the LQR Controller on the Micro-UAV Model………………..………………………64
3.9 Communication Link of the Micro-UAV………………………………………………………………66
3.9.1 Declaration, Assignment and Initialization of Variable…………………………………………….68
3.9.2 Creating Network Setup……………………………………………………………………………..69
3.9.3 Development of Various Functions…………………………………………………………………69
3.9.4 Development of the Main Program Used for Obtaining GPS Data…………………………………70
3.10 Conclusion …………………………………………………………………………………………………………………… 71
CHAPTER FOUR: RESULTS AND DISCUSSIONS …………………………………………………………….. 73
4.1 Introduction ……………………………………………………………………………………………………………………. 73
4.2 Comparative Study Before and After Application of Optimal LQR on the micro-UAV Model ……… 73
4.2.1 Verification of Asymptotic Stability …………………………………………………………………………………. 73
4.2.2 Time Responses Analysis ………………………………………………………………………………………………. 78
4.2.2.1 Translational Dynamics Responses ……………………………………………………………………………….. 78
4.2.2.2 Rotational Dynamics Responses……………………………………………………………………………………. 80
4.2.2.3 Flapping Rotor Dynamics Responses……………………………………………………………..82
4.2.2.4 Kinematics Responses……………………………………………………………………………..84
4.3 Communication Link Analysis………………………………………………………………………..86
4.3.1 Results Obtained from the Micro-UAV System…………………………………………………….87
4.4 Conclusion …………………………………………………………………………………………………………………….. 89
CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS ………………………………………… 90
5.1 Introduction ……………………………………………………………………………………………………………………. 90
5.2 Conclusion …………………………………………………………………………………………………………………….. 90
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5.3 Limitations …………………………………………………………………………………………………………………….. 91
5.4 Recommendations for Further Works………………………………………………………………………………….. 91
REFERENCES ……………………………………………………………………………………………………………………. 93
CHAPTER ONE
INTRODUCTION
1.1 Background Information
There are at the moment many research groups investigating the topic “indoor aerial robotics”.
Several groups are undertaking this research for different purposes. Some are building platforms for
testing control algorithms, while others are trying to understand the aerodynamics of flying robots
(Chen and McKerrow, 2007). This research is aimed at modeling a simple unmanned aerial vehicle
(UAV) using a modified radio controlled (RC) based coaxial helicopter with emphasis on its
stabilization and communication link between it and the ground control station.
Micro-coaxial helicopters are basically used for indoor experiments. However, an indoor
environment is faced with the challenges of limited space and varieties of obstacles (Thien et al.,
2012). There is, therefore the need to ensure that the coaxial helicopter system is stable and
operated using simplified control methods.
An unmanned aerial vehicle (UAV) is an aircraft system where the human pilot is replaced by
computer systems and other forms of wireless facilities such as radio links, GPS transmitters,
wireless cameras, etc. In reality, it is more complex than that and the aircraft must be properly
designed, from inception without consideration for the aircrew and their accommodation (Austin,
2010).
The basic components of a UAV system are divided into four (4) as follows:
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i) A control station which houses the system operator, the interface between the operator
and the rest of the system.
ii) The aircraft carrying the payload.
iii) The communication system between the control station which transmits control signal to
the aircraft and returns the payload and other data from the aircraft via the radio link to
the Control station.
iv) Support equipment which include maintenance and transport items.
The components that make up the complete system (micro-UAV) are shown in Figure
1.1
Figure 1.1: Components of the Micro-UAV System
The UAV system finds applications in both indoors and outdoors for both civilian and military
purposes. In the civilian application, it is basically used for aerial photography, boarder
surveillance, land survey, reservoir and pipeline monitoring and control of road traffic. While in the
Air Vehicle
Ground Control Station
Coaxial Helicopter
Router
Laptop
RC transmitter
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military application, it is utilized in reconnaissance activities, monitoring of nuclear, biological or
chemical contaminations, long range and high altitude surveillance, and search and rescue missions.
The intended micro-UAV is to be used indoors and for experimental purposes.
1.1.1 Classification of UAVs
UAVs can be classified based on their endurance and altitudes (Austin, 2010). Furthermore, the
classification can be extended based on rotor configuration.
1.1.1.1 Classification based on Endurance and Altitude
According to Austin (2010), the following are the classifications of the UAVs according to
endurance and altitude:
1) HALE – High altitude long endurance UAV is characterized by an altitude of over 15,000 m
and endurance duration above 24hours. It is basically used for extremely long-range
reconnaissance and surveillance missions. They are usually utilized by Air forces from fixed
bases.
2) MALE – Medium altitude long endurance UAV operates at an altitude between the range
5000–15000m over endurance duration of 24hours, their roles are similar to the HALE
systems but they operate at somewhat shorter ranges.
3) TUAV – Tactical UAV or Medium Range UAV operates between the ranges of 100 – 300
km. These aircrafts are smaller when compared to HALE or MALE and are mostly operated
by the Army and Naval forces.
4) Close-Range UAV is used by mobile army battle groups, military/naval operations and for
diverse civilian purposes. These UAVs operate at ranges of up to 100 km and find
4
application in diverse areas such as: reconnaissance, ship-to-shore surveillance, cropspraying
and traffic monitoring, etc.
5) Mini UAV is a UAV system below a certain mass (20 kg), but larger in size than a micro-
UAV (MAV). It is capable of being hand-launched and operates at a range of up to
30 km. mostly used by mobile battle groups and for diverse civilian purposes.
6) Micro UAV, also termed as MAV, is characterized by a rotor blade with a radius below
30cm. Micro-UAVs find applications in urban environments especially within buildings. A
micro-UAV is basically used to carry out indoor experiments and is attributed with the least
altitude of less than 50m and endurance capability of less than 12 minutes.
1.1.1.2 Classification based on Rotor Configuration
Micro-UAV can also be classified according to the rotor configuration as follows:
1) Single Rotor: A single rotor is a kind of UAV that utilizes only a single rotor blade.
2) Coaxial Rotor: A coaxial rotor is a kind of UAV that utilizes two rotor blades. Christoph,
(2011) suggested that coaxial UAVs can further be classified as:
i) Full-Scale coaxial helicopter: It is a UAV with fixed revolutions per minute (rpm)
and dual swash plate.
ii) Miniature-Scale coaxial helicopter: This kind of UAV has a varying rpm, single
swash plate and stabilizer and has no collective pitch. Miniature scale coaxial
helicopter is termed as a micro-UAV.
3) Quad-Rotor: A quad-rotor is a kind of UAV system that utilizes four rotors blade.
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1.2 Aim and Objectives
The aim of this research is the modeling and stabilization analyses of a micro-UAV using a
modified radio controlled (RC) based coaxial helicopter.
The objectives of the research work are therefore as follows:
a) Development of a simple micro-UAV system from a modified RC-based helicopter.
b) Development of a state space model of the micro-UAV and carrying out stabilization
analysis of the micro-UAV system using an optimal linear quadratic regulator (LQR) due to
its regulating and stabilizing abilities. All programs are developed with the aid of
MATLAB/Control toolbox.
c) Development of a program to create a communication link between micro-UAV and the
ground control station using the Arduino platform in order to facilitate GPS location data
transfer.
d) Validation of the UAV system by prototyping.
1.3 Statement of Problem
Most of the coaxial systems considered in literature did not show a complete resolution of the
forces and moments acting on an RC-based coaxial system due to the absence of some vital parts
(horizontal fin, vertical fin, payload effect, tail rotors) of the helicopter system. It is also important
to note that most micro-UAVs suffer great flight and model instability (Allan, 2010; Yuan and
Katupitiya, 2012). This work employed an analytical and computational approach, rather than using
a system identification approach that is predictive-based. This involved development of the nonlinear
model using the Euler-Newton formulation, its subsequent linearization using the small
6
perturbation technique and stabilization was carried out using the state model obtained from the
linearized model. A prototype was then developed.
1.4 Methodology
The following methodology was adopted in carrying out this research.
1. Modification of an RC-based coaxial helicopter by incorporating payload such as: GPS
module, Arduino microcontroller board and Ardiuno Wi-Fi shield to form a micro-UAV
system.
2. Rigid body modeling of the micro-UAV in order to obtain a non-linear model. This involved
the following steps:
a) Modeling the rigid body dynamics by attaching external forces and moments to body
dynamics (rotor forces and moment).
b) Modeling of forces and moments based on the upper and lower rotors thrusts, tail rotor,
horizontal fin, vertical fin, and flapping angles.
c) Based on the models obtained from step (b), the non-linear translational dynamics,
rotational dynamics and kinematic equation models were obtained.
3. Linearization of the non-linear model to obtain a linear state-space model using small
perturbation technique.
4. Determination of control solution test by verification using controllability and observability
analyses of the micro-UAV based on the state model obtained in step (3)
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5. Application of linear quadratic regulator (LQR) controller to stabilize the system and to
attain desired performance specification
6. Development of a program in Arduino platform to establish a Wi-Fi communication link
between the UAV system and the ground control station (GCS).
The program has two basic functions:
i) Creation of a network interface between the Wi-Fi Shield and the dedicated access point
router.
ii) Configuration of the GPS module in order to return the longitude and latitude
positioning of the air vehicle via the serial monitor of the ground control station.
7. Validation by prototyping.
1.5 Significant Contributions
The significant contributions derivable from this work are as follows:
1) Development of a micro-UAV model considering the effect of the tail rotor, vertical and
horizontal fins and fuselage.
2) Performance specifications of peak overshoot of 4.27% (desired is 5%) and damping ratio
of 0.708 (desired is 0.6 1) were obtained by the introduction of the LQR controller.
3) Establishment of the communication link between the micro-UAV and the ground control
station with RSSI of between -60dBm to -41dBm, data rate of 5.4Mbit/s at a frequency of
2.4GHz in order to obtain GPS data.
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1.6 Thesis Organization
The general introduction has been presented in Chapter One. The remaining chapters were
structured as follows: A detailed review of the relevant literature and pertinent fundamental
concepts about micro-UAV was carried out in Chapter Two. Mathematical modeling of the micro-
UAV non-linear model, linearization of the non-linear model, application of an optimal LQR
controller to the linear model, and establishment of the communication link were presented in
Chapter Three. The results obtained were analyzed and discussed in Chapter Four. Chapter Five is
the conclusion and recommendations. Quoted references and Appendices are also provided at the
end of the thesis.
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