ABSTRACT

Title of Dissertation: TOWARDS AUTONOMOUS VERTICAL LANDING
ON SHIP-DECKS USING COMPUTER VISION

Abhishek Shastry
Doctor of Philosophy, 2022

Dissertation Directed by: Professor Anubhav Datta, and
Professor Inderjit Chopra

Department of Aerospace Engineering

The objective of this dissertation is to develop and demonstrate autonomous ship-board

landing with computer vision. The problem is hard primarily due to the unpredictable stochastic

nature of deck motion. The work involves a fundamental understanding of how vision works,

what are needed to implement it, how it interacts with aircraft controls, the necessary and sufficient

hardware, and software, how it differs from human vision, its limits, and finally the avenues of

growth in the context of aircraft landing. The ship-deck motion dataset is provided by the U.S.

Navy. This data is analyzed to gain fundamental understanding and is then used to replicate

stochastic deck motion in a laboratory setting on a six degrees of freedom motion platform, also

called Stewart platform. The method uses a shaping filter derived from the dataset to excite the

platform. An autonomous quadrotor UAV aircraft is designed and fabricated for experimental

testing of vision-based landing methods. The entire structure, avionics architecture, and flight

controls for the aircraft are completely developed in-house. This provides the flexibility and

fundamental understanding needed for this research. A fiducial-based vision system is first

designed for detection and tracking of ship-deck. This is then utilized to design a tracking

controller with the best possible bandwidth to track the deck with minimum error. Systematic



experiments are conducted with static, sinusoidal, and stochastic motions to quantify the tracking

performance. A feature-based vision system is designed next. Simple experiments are used

to quantitatively and qualitatively evaluate the superior robustness of feature-based vision under

various degraded visual conditions. This includes: (1) partial occlusion, (2) illumination variation,

(3) glare, and (4) water distortion. The weight and power penalty for using feature-based vision

are also determined.

The results show that it is possible to autonomously land on ship-deck using computer vision

alone. An autonomous aircraft can be constructed with only an IMU and a Visual Odometry

software running on stereo camera. The aircraft then only needs a monocular, global shutter,

high frame rate camera as an extra sensor to detect ship-deck and estimate its relative position.

The relative velocity however needs to be derived using Kalman filter on the position signal. For

the filter, knowledge of disturbance/motion spectrum is not needed, but a white noise disturbance

model is sufficient. For control, a minimum bandwidth of 0.15 Hz is required. For vision,

a fiducial is not needed. A feature-rich landing area is all that is required. The limits of the

algorithm are set by occlusion(80% tolerable), illumination (20,000 lux-0.01 lux), angle of landing

(up to 45 degrees), 2D nature of features, and motion blur. Future research should extend the

capability to 3D features and use of event-based cameras. Feature-based vision is more versatile

and human-like than fiducial-based, but at the cost of 20 times higher computing power which is

increasingly possible with modern processors. The goal is not an imitation of nature but derive

inspiration from it and overcome its limitations. The feature-based landing opens a window

towards emulating the best of human training and cognition, without its burden of latency, fatigue,

and divided attention.



TOWARDS AUTONOMOUS VERTICAL LANDING ON SHIP-DECKS
USING COMPUTER VISION

by

Abhishek Shastry

Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment

of the requirements for the degree of
Doctor of Philosophy

2022

Advisory Committee:
Professor Anubhav Datta, Chair/Advisor
Professor Inderjit Chopra, Co-Advisor
Professor Robert Sanner
Professor Mumu Xu
Professor Tobias Von Petersdorff



© Copyright by
Abhishek Shastry

2022



Dedicated to all the square pegs in round holes.

ii



Acknowledgments

Although it is difficult to acknowledge everyone who has touched my life for the past five years

and in some way helped to make this dissertation possible, I will give it a try. First and foremost,

I am grateful to my wonderful advisor Dr. Anubhav Datta, without whose help and patience, I

would not have made it through grad school. I must mention though that I was scared of him

in the beginning, not knowing what kind of person he was and fearing the worst possible. But

he proved otherwise. He was a constant source of support both inside and outside academics

and made my student life much easier than it would have been otherwise. He pushed me to the

boundary of my comfort zone for my optimal growth both as a human being and a researcher.

I have learned so much from him, not only about science but also about problem-solving and

different new ways of thinking. His enthusiasm about taking on the hardest problems and getting

to the bottom of it in the spirit of gaining new knowledge is infectious, and I will always carry a

part of him with me wherever I go.

I would also like to thank my second advisor, Prof. Inderjit Chopra, for his guidance and

letting me take on this challenging problem for my Ph.D. dissertation. I am grateful to him

for being patient with me whenever I disagreed with him and for patiently offering kind and

helpful suggestions throughout the last five years. It is impressive how after so many years,

he still maintains the level of enthusiasm and curiosity of that of a child. I should also thank

iii



Prof. Sanner. Many of the ideas in this dissertation have been inspired by his teachings and the

discussions that I have had with him.

My housemates for the past five years, Mrinal, Nikhil, Shashank, Animesh, and Koushik, deserve

special mention for their help and support, without which these five years might have been

torturous. I had many productive discussions with them, especially with my brother Animesh

whose research overlaps with this dissertation topic. A big thanks to my seniors from the Alfred

Gessow Rotorcraft Center, Bharath, Ananth, Dan, Elizabeth, Tyler, Thomas, Lex, Fred, Brandyn,

Wanyi, and Vera. They made sure I felt welcomed and a part of the group. I am also grateful

for all the wonderful friendships I have developed over the past five years with my colleagues,

Seyhan, Ravi, Wanyi, Amy, Emily, James, Katie, Brent, Eric, Ola, Matt, Victoria, and everyone

else in the rotorcraft center. All the time that I have spent with them will surely be cherished.

I owe unending gratitude to my parents. Nothing I have ever done would have been possible

without their sacrifices. And the love of my life, Lea who has been always there for me with all

her love and support and has pushed me to finally complete this dissertation.

I am thankful to Naval Air Systems Command (NAVAIR) for financially supporting this research

and to all the people at the organization, including Jim Bumbaugh, Daniel Schafer, and Peter

Arslanian, who continuously gave valuable feedback to improve my methods. I am also thankful

to Dr. Mahendra Bhagwat for his support and the many productive discussions I have had with

him throughout my Ph.D. life. Lastly, I would like to thank all my committee members for their

valuable advice, which has greatly improved the quality of research in this dissertation.

iv



Table of Contents

Dedication ii

Acknowledgements iii

Table of Contents v

List of Tables viii

List of Figures ix

List of Abbreviations xiii

List of Notations xiv

Chapter 1: Introduction 1
1.1 Brief History of Ship-Deck Landing . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Computer Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Vision for Ship-Deck Landing . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Autonomous Ship-Deck Landing . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6 Objectives of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.7 Technical Approach and Organization of the Dissertation . . . . . . . . . . . . . 19

Chapter 2: Ship-Deck Motion 21
2.1 Types of ship-deck motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Sea States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Deck Motion Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Construction of Shaping Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Hardware to replicate deck motion . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.6 Van Loan’s algorithm to discretize linear system . . . . . . . . . . . . . . . . . . 31
2.7 Procedure to replicate deck motion . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Chapter 3: Fabrication of Quadrotor UAV 37
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 Vehicle Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3 Propulsion System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

v



3.4 Avionics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.5.1 Inertial Measurement Unit (IMU): . . . . . . . . . . . . . . . . . . . . . 47
3.5.2 Visual Inertial Odometry (VIO) sensor: . . . . . . . . . . . . . . . . . . 47
3.5.3 Monocular Camera: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.6 Computers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.6.1 Flight controller: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.6.2 Flight Computer: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.7 Communication Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.7.1 UART: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.7.2 I2C: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.7.3 DShot: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.7.4 USB: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.8 Assembled Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.9 Flight Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.9.1 Attitude Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.9.2 Translational Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.9.3 Control mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.10 Filtering and State-estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.11 Kalman Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.11.1 For angular velocity: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.11.2 For attitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.12 Low Pass Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.13 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Chapter 4: Fiducial-Based Vision System 70
4.1 Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2 Adjusting camera focus: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.3 Camera Calibration: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4 Fiducial-based vision algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5 Verification of Vision using Vicon . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.6 Velocity Estimation From Vision Measurements . . . . . . . . . . . . . . . . . . 79

4.6.1 Low pass filter on numerical differentiation . . . . . . . . . . . . . . . . 79
4.6.2 Kalman filter with white disturbance model . . . . . . . . . . . . . . . . 80
4.6.3 Kalman filter with colored disturbance model . . . . . . . . . . . . . . . 83

4.7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Chapter 5: Motion Tracking Performance With Fiducial-Based Vision 88
5.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2 Tracking of Static Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.3 Tracking a Platform Oscillating at 0.075 Hz . . . . . . . . . . . . . . . . . . . . 90
5.4 Tracking a Platform Oscillating at 0.2 Hz . . . . . . . . . . . . . . . . . . . . . 93
5.5 Tracking a Platform Oscillating at 0.33 Hz . . . . . . . . . . . . . . . . . . . . . 96
5.6 Explanation Using Linear Systems Theory . . . . . . . . . . . . . . . . . . . . . 99
5.7 Tracking a platform with stochastic motion . . . . . . . . . . . . . . . . . . . . . 102

vi



5.8 Landing strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Chapter 6: Feature-Based Vision and Robustness 108
6.1 Problems with fiducial based vision . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.2 Feature-Based Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.3 New Feature-based vision algorithm . . . . . . . . . . . . . . . . . . . . . . . . 111
6.4 Feature Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.5 Accuracy and precision of vision measurements . . . . . . . . . . . . . . . . . . 118
6.6 Effect of occlusion on the vision system . . . . . . . . . . . . . . . . . . . . . . 121
6.7 Effect of ambient illumination on the vision system . . . . . . . . . . . . . . . . 123
6.8 Effect of motion blur on the vision system . . . . . . . . . . . . . . . . . . . . . 125
6.9 Effect of glare and water distortion . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.10 Effect of camera resolution on the vision system . . . . . . . . . . . . . . . . . . 128
6.11 Effect of processors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Chapter 7: Summary and Conclusions 134
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.3 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 138

Bibliography 142

vii



List of Tables

2.1 Douglas Sea-scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Stewart Platform Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.1 Aircraft Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2 Inner loop control Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3 Outer loop control Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.1 Camera properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.1 Effect of using different processors for the vision system . . . . . . . . . . . . . 131

viii



List of Figures

1.1 Birth of naval aviation with the first ship landing performed by Eugene Ely on
USS Pennsylvania anchored in San Francisco Bay (Photo from Naval History
and Heritage Command) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 First naval rotorcraft XOP-1, similar to the one used by Alfred M. Pride pictured
in flight over the aircraft carrier USS Langley in 1931 (Photo from Naval History
and Heritage Command) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 A rare color picture of first naval VTOL aircraft, USCG R-4/HNS-1 landing on a
ship near Floyd Bennett Field in Brooklyn, New York. (Photo from USCG/Stewart
Graham Collection Photo, Vertical Magazine) . . . . . . . . . . . . . . . . . . . 4

1.4 Helicopter Hauldown and Rapid Securing Device (HHRSD) also known as beartrap 5
1.5 Sea-King helicopter CH-SS2 is hauled down by a beartrap to a landing on the

deck of Canadian ship Assiniboine on May, 1967 . . . . . . . . . . . . . . . . . 6
1.6 First digital image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.7 Hubel and Weisel experiment to understand the visual cortex . . . . . . . . . . . 10
1.8 Standard vs event camera outputs; Standard camera pixels synchronously capture

the entire scene at a specified frame rate. Event camera only detects changes in
scene with every pixel firing asynchronously. . . . . . . . . . . . . . . . . . . . 13

1.9 Different types of landing pads proposed in vision literature for ship-deck landing 15
1.10 SNC’s UCARS system for autonomous ship-deck landing of unmanned helicopters 16
1.11 Autonomous Flight testing of Airbus DeckFinder system; . . . . . . . . . . . . . 17

2.1 6 types of ship-motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Sample ship-deck motion time series from Navy provided dataset . . . . . . . . . 24
2.3 Fourier transform of deck acceleration; different colors are from different time

histories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 Power Spectral Density of deck’s sway acceleration . . . . . . . . . . . . . . . . 27
2.5 Linear time invariant system with stochastic wide sense stationary (WSS) input

gives stochastic WSS output . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6 6-DOF stewart motion platform used to replicate ship-deck type motion in lab

environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.7 A sample stochastic deck motion trajectory generated by commanding the Stewart

platform through the designed shaping filter and measured using a VICON system 35

3.1 Quadrotor skeleton made from square aluminum tubes . . . . . . . . . . . . . . 38
3.2 Quadrotor frame ready to be mounted with propulsion and avionics components . 39
3.3 iFlight 2207 2750Kv motor used on the vehicle; Configuration: 12N14P . . . . . 40

ix



3.4 Electronic Speed Controller running BLHeli32 firmware . . . . . . . . . . . . . 41
3.5 Experimental setup used to measure thrust and torque in hover . . . . . . . . . . 41
3.6 Experimentally measured variation of thrust and torque with RPM . . . . . . . . 42
3.7 Power vs RPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.8 Motor Efficiency vs RPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.9 Aircraft’s Avionics architecture; DShot, UART, and I2C are three different digital

communication protocols used on the aircraft . . . . . . . . . . . . . . . . . . . 46
3.10 Sensors on the quadrotor vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.11 Primary computing elements on the quadrotor vehicle . . . . . . . . . . . . . . . 49
3.12 The in-house fabricated quadrotor aircraft . . . . . . . . . . . . . . . . . . . . . 53
3.13 Body-axes and direction of rotation of rotors; Z is +ve down . . . . . . . . . . . 55
3.14 Control architecture for vision-based autonomous tracking and landing on a stochastically

moving platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.15 Inner and outer loop step response of quadrotor along X-axis; response along

other axes is similar; The response time verifies the time scale separation of
attitude and translational dynamics assumed in the control design . . . . . . . . . 61

3.16 Effective outer loop control diagram . . . . . . . . . . . . . . . . . . . . . . . . 61
3.17 Bode plot of closed outer loop control system T (s) for X and Y axes . . . . . . . 62
3.18 Large noise in measurements by accelerometers . . . . . . . . . . . . . . . . . . 63
3.19 Fourier transform of the measurements show large noise is due to 1/rev vibration

from the rotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.1 Monocular global shutter camera with fixed focus and auto-exposure; Made by:
Econsystem; Product number: See3CAM 24CUG . . . . . . . . . . . . . . . . . 71

4.2 Pinhole camera model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3 Checkerboard pattern used for camera calibration . . . . . . . . . . . . . . . . . 74
4.4 Detected checkerboard points in camera image; also visible is the barrel and

pincishion distortion from lens . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.5 Fiducial 308 of the original Aruco marker library is used for the vision-based

landing system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.6 Fiducial-based vision system for deck detection and estimation of its pose . . . . 77
4.7 Vicon system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.8 Comparison of vision and vicon measurements for a static deck . . . . . . . . . . 78
4.9 Comparison of vision and vicon measurements for an oscillating deck . . . . . . 78
4.10 Velocity estimation using numerical differentiation shows large spikes . . . . . . 80
4.11 Velocity estimation using Kalman filter is less noisy but shows a lag . . . . . . . 82
4.12 Modified power spectral density function with peak at 0.34 Hz . . . . . . . . . . 83
4.13 Comparison of the two Kalman filters for vision-based velocity estimation of a

simple oscillating ship-deck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.14 Validation of Kalman filter estimates of quadrotor relative ship-deck velocity

using Vicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.1 Experimental setup for studying motion tracking performance . . . . . . . . . . . 88
5.2 Tracking of the stationary ship-deck by the quadrotor . . . . . . . . . . . . . . . 89

x



5.3 Tracking of a stationary deck by the quadrotor. Box shows the extent of landing
platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.4 Quadrotor hovering over the stationary deck. . . . . . . . . . . . . . . . . . . . . 90
5.5 Tracking performance of quadrotor for a deck oscillating at 0.075 Hz frequency . 91
5.6 Tracking of a deck oscillating at 0.075 Hz . . . . . . . . . . . . . . . . . . . . . 92
5.7 Video frames showing quadrotor tracking of the deck tracking at 0.075 Hz . . . . 93
5.8 Tracking performance of quadrotor for a deck oscillating at 0.2 Hz frequency . . 94
5.9 Tracking of a deck oscillating at 0.2 Hz . . . . . . . . . . . . . . . . . . . . . . 95
5.10 Video frames showing quadrotor tracking of the deck tracking at 0.2 Hz . . . . . 96
5.11 Tracking performance of quadrotor for a deck oscillating at 0.33 Hz frequency . . 97
5.12 Tracking of a deck oscillating at 0.33 Hz . . . . . . . . . . . . . . . . . . . . . . 98
5.13 Video frames showing quadrotor tracking of the deck tracking at 0.33 Hz . . . . . 99
5.14 Linear time invariant system with oscillatory input produces an oscillatory output

whose magnitude and phase modulated by the transfer function of the system . . 100
5.15 Effective outer loop control block diagram . . . . . . . . . . . . . . . . . . . . . 101
5.16 Outer loop bode plot showing predicted attentuation and phase lag in quadrotor

oscillations; Prediction matches experiments except for magnitude at 0.33 Hz . . 102
5.17 Tracking performance of quadrotor for the platform with ship-deck type motion . 103
5.18 Effective outer loop control block diagram . . . . . . . . . . . . . . . . . . . . . 104
5.19 Autonomous landing strategy for ship-deck landing . . . . . . . . . . . . . . . . 105
5.20 Error plot with chosen limits to start and abort descent . . . . . . . . . . . . . . . 106
5.21 Video frames showing quadrotor tracking and landing on a platform with stochastic

ship-deck type motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.1 Sample failure cases for fiducial-based vision system . . . . . . . . . . . . . . . 109
6.2 Features are image patches with special invariant properties that makes them

detectable across wide variety of different images . . . . . . . . . . . . . . . . . 110
6.3 Feature-based Vision Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.4 Vision algorithm can track any planar target as long as the target is rich in features;

lines show matching of each individual feature from model to scene image . . . . 116
6.5 Landing pad design with large number of features for improved robustness . . . . 117
6.6 Roll and pitch estimation using the new vision system; truth values are obtained

using a digital protractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.7 X-Y position estimation using the new vision system; truth values are obtained

using a ruler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.8 Deck distance estimation using the new vision system . . . . . . . . . . . . . . . 119
6.9 Noise in vision estimation increases with decrease in number of observed features;

noise multiplier is the factor by which the standard deviation in measurements
increases in comparison to the baseline at large (> 120) number of features . . . 119

6.10 Vision system works under occlusion as high as 80%; note that features of even
single occluded tags are also detected by the vision algorithm . . . . . . . . . . . 122

6.11 Vision system can detect the pad on a bright day (20,000 lux illumination), with
lighting variation created by shadows on the pad . . . . . . . . . . . . . . . . . . 123

6.12 Vision system can detect the pad even in a dark room of only 0.01 lux illumination 123
6.13 Maximum visible distance decreases for illumination lower than 10 lux . . . . . . 124

xi



6.14 Motion blur can distort features leading their non-detection and failure of the
vision system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

6.15 New vision system can detect landing pad even with glare . . . . . . . . . . . . . 127
6.16 Water distortion increases noise in detection of landing pad . . . . . . . . . . . . 128
6.17 Increasing image resolution increases the maximum distance from which the

landing pad can be observed with the side-effect of decrease in algorithm’s speed 130

7.1 Larger Stewart platform in process of being procured by University of Maryland . 140
7.2 View from cockpit during an actual ship-deck landing shows that pilots use 3D

features of the ship rather than that of the deck for manual estimation and tracking
of the ship position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.3 YP Patrol boats from Navy can be used for real-life testing of autonomous ship-
deck landing methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

xii



List of Abbreviations

ABS Acrylonitrile Butadiene Styrene
CNN Convolutional Neural Network
COTS Commercial Off The Shelf
CPU Central Processing Unit
CRC Cyclic Redudancy Check
CV Computer Vision
DOF Degree of Freedom
DShot Digital Shot
ESC Electronic Speed Controller
FFT Fast Fourier Transform
FOV Field Of View
I2C Inter-Integrated Circuit
IC Integrated Circuit
IMU Inertial Measurement Unit
LQE Linear Quadratic Estimator
MAV Micro Air Vehicle
MAVLink Micro Air Vehicle Link
MEMS Micro-Electro-Mechanical System
ONR Office of Naval Research
OS Operating System
PID Proportional Integral Derivative
PnP Perspective n Point
PWM Pulse Width Modulation
RANSAC Random Sample Consensus
ROS Robot Operating System
SBC Single Board Computer
SCONE Systematic Characterization Of the Naval Environment
SIFT Scale Invariant Feature Transform
SNR Signal to Noise Ratio
SWaP Size Weight and Power
UART Universal Asynchonous Receiver and Transmitter
UAS Unmanned Aerial System
UAV Unmanned Aerial Vehicle
USB Universal Serial Bus
VFS Vertical Flight Society
VTOL Vertical Take-off and Landing

xiii



List of Notations

CT Thrust coefficient
CQ Torque coefficient
Ixx, Iyy, Izz Quadrotor’s moment of inertia
Kp, Ki, Kd PID gains
R Blade radius
S Power Spectral Density
T (s) Closed loop tracking transfer function
cx, cy Camera optical center
f Camera focal length
k1, k2, k3 Camera distortion coefficients
km Motor constant
u, v 2D image co-ordinates
vk Measurement noise
wk Process disturbance
ρ Air density
Ω Rotor RPM
σ Blade solidity

xiv



Chapter 1: Introduction

This chapter introduces the topic of this dissertation. It begins with a history of ship-deck

landing and then explains the the motivation behind the research topic. This is followed by

history of computer vision and explanation of prior works in use of vision for ship-deck landing

and autonomous ship-deck landing methods. Next it states the objectives of the research, and

technical approach followed to achieve those objectives. Finally it ends with an organization of

the rest of the dissertation.

1.1 Brief History of Ship-Deck Landing

As we walk into the age of automation when all but high-level decision making may be

delegated to machines, there are still tasks that are extremely difficult to automate. Landing on a

ship-deck is one such tasks. The task is a formidable one even for navy pilots and yet forms the

basis many critical operations in naval aviation.

The first aircraft to be used for naval operations were sea-planes and the first ship-deck landing

was performed by Eugene Burton Ely with a Curtiss pusher biplane on board the USS Pennsylvania

anchored in San Francisco bay, on January 18, 1911 [1]. It used a braking system of sandbags

and ropes - a direct pre-cursor to modern arrester-hook and wire system used on aircraft carriers.

1



Figure 1.1: Birth of naval aviation with the first ship landing performed by Eugene Ely on USS
Pennsylvania anchored in San Francisco Bay (Photo from Naval History and Heritage Command)

The first rotary wing aircraft landing on a ship however would not happen until 30 years

later when an autogiro called Pitcairn XOP-1 (PCA-2), piloted by Lt. Alfred Metville Pride

took off and landed on the aircraft carrier USS Langley while it was underway on September 23,

1931 [2]. However, autogiros are not powered and they cannot takeoff or land vertically. Hence

the first powered vertical landing on a ship is credited to Lt. Stewart Ross Graham with Sikorsky

YR-4B onboard British ship SS Daghestan docking off from North Atlantic on January 16, 1944

under high wind [2]. This was also the first rotary wing landing on a small ship with a single

flight deck. This was important as it allowed Navy to operate helicopters from smaller combat

ships such as cruisers, destroyers, and frigates instead of only giant aircraft carriers, which have

larger landing area and are more stable due to larger mass.

2



Figure 1.2: First naval rotorcraft XOP-1, similar to the one used by Alfred M. Pride pictured
in flight over the aircraft carrier USS Langley in 1931 (Photo from Naval History and Heritage
Command)

3



Figure 1.3: A rare color picture of first naval VTOL aircraft, USCG R-4/HNS-1 landing on a ship
near Floyd Bennett Field in Brooklyn, New York. (Photo from USCG/Stewart Graham Collection
Photo, Vertical Magazine)

Helicopters are now a mainstay of naval operations, but only when the conditions on flight

deck are favorable. In bad-weather or high sea-states, they remain grounded. In the late 1950s the

Royal Canadian Navy invented a helicopter hauldown and rapid securing (HHRSD) device, also

known as beartrap. This system was cleared for service in 1967 for both day and night operations

up to 30 degrees of roll and 9 degrees of pitch in Sea State 6 [3]. It was so successful that it

was replicated by other navies around the world including the United States and is still in use

even today. In the typical functioning of the system, a cable drops from the helicopter that is

4



attached by the deck crew to a heavier cable passing through the center of beartrap and attached

to a winch below the deck. The cable is then pulled back and secured to the helicopter. Then

when the landing safety officer determines the conditions to be favorable, he instructs the pilot

to decrease and increases the tension in the cable to pull the helicopter down and attach it to the

deck by closing the beartrap. Once the helicopter is secured to the deck, the beartrap is also used

to move the aircraft in and out of the hangar using rail lines on the deck.

Figure 1.4: Helicopter Hauldown and Rapid Securing Device (HHRSD) also known as beartrap

5



Figure 1.5: Sea-King helicopter CH-SS2 is hauled down by a beartrap to a landing on the deck
of Canadian ship Assiniboine on May, 1967

6



The bear trap system improves helicopter ship-deck landing in two ways:

1. It helps to keep the helicopter aligned with the center of the ship-deck when the helicopter

is hovering over it.

2. It helps handling of the landed helicopter by securing it to the deck and preventing it from

falling over.

In some modern modified versions of beartrap, such as Aircraft Ship Integrated Secure and

Traverse (ASIST) system, the first functionality is performed ’wirelessly’ by an electro-optical

system. In case of ASIST, laser beacons placed on the helicopter are used to track the aircraft

from an optical tracking device on the ship. The precise relative position is then communicated to

the pilot through visual cues, which then uses it to better align the helicopter with the ship-deck.

However once landed, a beartrap like mechanical system is still used to secure the aircraft to the

ship. The benefit of using the electro-optical system for aligning the aircraft is that the pilot is

always in complete control of the helicopter. In a Japanese version of the system produced by

Mitsubishi Heavy Industries, a laser beam from the ship is reflected off a mirror placed on the

helicopter to calculate the relative position of aircraft with the ship.

1.2 Motivation

The modern modifications to the bear-trap makes it clear that the original beartrap landing

system has deficiencies and needs to be changed. The tethered wire approach to align the

helicopter with the ship-deck is hazardous for the helicopter pilot as he gives up control over his

aircraft. Moreover, the system needs personnel on deck for its operation which leads to the risk of

man overboard, especially during bad-weather and high sea-states. Furthermore, as automation in

7



cockpit increases, ship-deck landing needs to be automated to achieve a completely autonomous

naval helicopter. Finally with the recent rise of unmanned aerial vehicles (UAVs), an autonomous

ship-deck landing system is necessary for use of these aircrafts in naval aviation. All these form

the overarching motivation behind this research that aims to develop a vision-based autonomous

system for vertical landing on ship-deck. The vision based approach to autonomously align

the aircraft with the ship-deck seeks to replace the tethered wire approach of beartrap. The deck

handling of the landed aircraft however is still expected to be with the mechanical securing device

of beartrap. The idea is that with precise vision based measurements the helicopter autonomously

tracks and land at the center of the beartrap, which then closes and secures the aircraft to the ship.

The vision based autonomous landing approach is envisioned to be similar to a pilot on visual

flight rule but with more precise measurements of relative position between the aircraft and the

ship and with faster response due to the absence of inherent delays present in human action. The

next section goes into detail on history and methods of computer vision.

1.3 Computer Vision

Computer vision aims to replace the functionality of human eye but with greater precision

and speed. Similar to eye, the primary goal here is to recover useful information about the world

from the output of a light sensitive sensor called camera. The useful information to be extracted

depends on the actual application, but typically it is recognizing the structure of the world and

the objects present in it. The history of computer vision is primary an effort in this direction

with different breakthroughs over time establishing four different paradigms or approaches to the

same problem.

8



Figure 1.6: First digital image

The field was born when the first digital image was produced in 1957. Many algorithms

for manipulating these images were soon developed. Most of these were aimed at photographic

enhancement. But soon in 1960s researchers turned their attention to extraction of edges and

contours from images and using them to derive shapes and then infer about more complicated

patterns and objects present in the images. This was the first paradigm of vision, the method of

deriving progressively complicated structures from underlying simpler ones. A good summary

of work from this early period can be found in [4] and [5].A common misconception of the era

was that solving vision should be easy as humans do it all the time. A famous of story of the

time is that in 1966 Marvin Minsky, a professor at MIT asked his undergraduate student Gerald

Jay Sussman to “spend the summer linking a camera to a computer and getting the computer to

describe what it saw” [6]. It is now known that the problem is more difficult.

9



Figure 1.7: Hubel and Weisel experiment to understand the visual cortex

The most important work for computer vision during these early years however came

from another field. David Hubel and Torsten Wiesel, two scientists working in the field of

neurophysiology, through a series of experiments on cats between 1959-1969 described in detail

how the signals from the eye are processed by the visual cortex [7]. Their groundbreaking work

earned them the 1981 Nobel prize in medicine. And as it is shown later, their work directly

inspired two different modern paradigms of computer vision: 1)feature based vision, and 2)

Convolutional Neural Network (CNN).

The rest of the 20-th century saw steady improvements in both low level vision i.e. extraction of

image primitives such as edges, contours, and corners and high level vision i.e. detecting more

complicated shapes and objects in the images. Also, methods to obtain camera motion, and 3D

structure of the environment from multiple images based on geometry were developed during this

period. Popular optical flow methods were also developed during this time [8, 9]. These works

10



are summarized in [10–12].

An important work of the era that led to the second paradigm of computer vision was the

development of neocognitron. Neocognitron was a multilayered artificial neural network proposed

by Kunihiko Fukushima in 1980 for pattern recognition [13]. It was heavily inspired from the

previous work on visual cortex by Hubel and Weisel, and in turn inspired the development of

modern deep convolutional neural networks (CNN) used in computer vision.

The first decade of 21-st century saw the development of image point-feature extraction algorithms.

The well known paper by Lowe [14], established this third paradigm of computer vision. It uses

point features instead of lines and shapes for higher level vision tasks such as object detection or

3D reconstruction of a scene. Lowe’s work was also partly inspired by the earlier work on visual

cortex by Hubel and Weisel.

The second decade of the century saw the re-emergence of neural networks in computer vision

with the influential paper by Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton [15]. The

paper developed a deep CNN architecture that significantly outperformed the state of the art in

visual recognition. The depth of the network was necessary to achieve this result. This work was

inspired by a previous work by Yan le Cun [16] who introduced the backpropagation algorithm

to train neural networks. Yan le Cun’s work was in turn inspired from the neocognitron work

by Fukushima. Deep neural networks have now completely overtaken the field of computer

vision. This is primarily due to their very high success rate in almost all vision tasks, compared

to any other conventional method developed over the previous half a century of vision research.

11



However, there is little to no explanation as to why these deep neural networks are better or why

they even work in the first place, which limits their use in aerospace. A good summary of these

modern works in computer vision can be found in Ref. [17].

While CNN has come to dominate the field in the last decade, a new paradigm of computer vision

has also developed quietly during this time. Unlike the previous ones, this has occurred in vision

hardware. Researchers have now realized that traditional frame-based cameras are made for

photography which has different requirements than vision. As a result, researchers at University

of Zurich trying to replicate the human eye, invented the event-based camera in 2008 [18]. This

new type of camera has no shutter and is always on, but records only changes in intensity of

light. Change in intensity received by a pixel is called an event and the changes are recorded

asynchronously as they happen. This is quite different from the frame-based cameras which

record the total energy of light received by all the pixels synchronously over a specified exposure

time. The event-based cameras record dynamic phenomena and as such are not pleasant to the

eye but have significant benefits over frame-based ones such as low-latency, low power, low data

bandwidth and high dynamic range. However, conventional vision algorithms cannot be used

with them and hence they require a complete re-formulation of computer vision algorithms. This

has been slow due to low quantity and high cost of event cameras in market, which in turn is due

to low consumer use cases. A good survey of event based vision can be found in Ref [19].

12



Figure 1.8: Standard vs event camera outputs; Standard camera pixels synchronously capture the
entire scene at a specified frame rate. Event camera only detects changes in scene with every
pixel firing asynchronously.

1.4 Vision for Ship-Deck Landing

Computer vision has already found applications in many areas such as facial recognition

in surveillance and law enforcement, automatic license plate reading in traffic management, 3D

medical imaging and diagonostics in medicine, and automated sorting and monitoring of crops

in agriculture. In aerospace, vision has found use in analysis of satellite images, inspection

of aircraft parts, and in star trackers and earth sensors for satellite attitude determination and

navigation. The benefits of vision are obvious as a low cost and low SwaP sensor. Hence,

recently researchers have started exploring use of vision to detect and track ship-deck. One of the

earliest work in this area was by Sanchez Lopez [20] in 2008, who proposed a method to detect

the H marker on helipads. This approach has more recently morphed into detection and use of

custom designed fiducials [21,22] which are more reliable to detect. This fiducial based vision is

13



one of the method used in the current dissertation. Other approaches include using color LEDs

on deck [23], custom designed colored objects on deck [24, 25], and using other sensors such as

Lidar [26, 27] or acoustic sensors [28] in addition to or as a replacement of vision.

All these previous work fall under the first paradigm of computer vision that detects image

primitives such as color, lines and contours in images and uses them to detect more complicated

shapes and objects. The reason they have been widely used in practice is because they are not

robust to environmental degradation and lighting conditions. This dissertation begins fiducial

based vision, but then develops a feature based vision for deck landing, which falls under the

third paradigm of computer vision discussed earlier. It is found that this approach is far more

robust.

14



(a) Landing pad with helipad marker (b) Landing pad with red LEDs

(c) Landing area constructed with red cones

(d) Landing pad with a vision fiducial

Figure 1.9: Different types of landing pads proposed in vision literature for ship-deck landing

1.5 Autonomous Ship-Deck Landing

Landing on the deck of a small ship is hard because of three important problems:

15



1. Turbulent wake from ship’s structures

2. Confined landing area

3. Stochastic deck motion

Landing a helicopter in turbulence or in a confined area is quite common even on land. Hence of

the three factors, the one unique to ship-deck landings is the deck motion. Beartrap was invented

primary to tackle this problem. This problem is also the focus of this dissertation

In recent years, an autonomous landing method for Unmanned Air Vehicles (UAV) has been

released by Sierra Nevada Corporation (SNC). The system called UAV Common Automatic

Recovery System (UCARS) consists of a radio transponder attached to the UAV and a tracking

device on the ship (see Fig. 1.10). The tracking device localizes the UAV with respect to the ship

with the help of a microwave radar and a beacon on the airborne transponder and then guides it

to the center of the deck. The system is currently in use on the Northrop Grumman Fire Scout

UAV.

(a) Transponder to be placed on
the UAV

(b) Ground Tracker to be placed
on the ship-deck

Figure 1.10: SNC’s UCARS system for autonomous ship-deck landing of unmanned helicopters

16



More recently, Airbus has developed a similar system for local positioning of helicopters

with respect to ship-deck called DeckFinder. It consists of three airborne and six ground units

that use RF signals to triangulate and localize the aircraft similar to GPS.

Figure 1.11: Autonomous Flight testing of Airbus DeckFinder system;

Both the SNC UCARS and Airbus DeckFinder are pure localization systems and neglect

deck motion. Hence they can only be used when the deck is calm and in low sea-states, which

does not solves the main problem. Moreover, they use active communication that may not be

desirable if the ships want to maintain a low profile. This dissertation develops a vision-based

method for localization and tracking of ship-deck using only a single passive sensor, a monocular

camera.

There is literature on autonomous ship-deck landing research, but most deal with simulation

[29, 30] and only a few with actual test data [31]. They have proposed various non-linear

17



adaptive techniques but none have provided a clear demonstration. Experimental demonstration

is where the real challenge is encountered: sensor noise which thwarts any technique that tries to

dynamically adapt to deck motion without adapting to noise.

Other works on autonomous landing on ship-deck pertain to prediction of quiescent period of

deck motion during which the helicopter can descend and land on the deck. To this end, some

use an empirical formulation called energy index that is a function of deck motion and is used to

predict when a quiescent deck period might be imminent. Such a system is often called Landing

Period Designator (LPD) [32, 33] or Landing Period Indicator (LPI) [34]. A few others try to

predict the deck motion into the future by fitting a parametric model to the past values [35].

The present work does not try to predict but instead search for a quiescent period using vision

measured deck motion.

Recent studies that have used small-scale experiments on this topic can be found in Refs [36,37].

They have ignored the effect of stochasticity of deck motion in their efforts which is important

and is one of the distinguishing aspect of this dissertation.

1.6 Objectives of the Dissertation

The objectives of this dissertation are the following:

1. Develop an experimental setup to produce stochastic ship-deck type motion.

2. Fabricate an in-house 3.75-lb quadrotor platform to establish minimal sensor & computing

requirement for vision only autonomy.

18



3. Develop a ship-deck tracking/landing method using fiducial based vision.

4. Experimental evaluation of fiducial based landing method.

5. Develop a 2D-feature based vision for ship-deck detection and tracking.

6. Explore feature-based vision over fiducial based vision systematically from robustness of

algorithm to overhead weight and power penalty.

1.7 Technical Approach and Organization of the Dissertation

The first objective is achieved by developing a shaping filter based method to generate

stochastic ship-deck type motion from white noise input. This method is then used to control

the motion of a commercially procured robotic hardware called Stewart platform. The hardware

consists of six parallel actuators that together control the 6-degrees of freedom of a rigid platform.

The description of the platform and detailed derivation of shaping filter based method to excite

the platform into ship-deck type motion is provided in Chapter 2.

For the second objective, an autonomous 3.75-lb quadrotor UAV is fabricated in-house with

3 sensors and 2 flight computers. The aircraft serves as a testing platform for the fiducial

vision based landing method. The detailed description of the fabrication process, the avionics

architecture and the control algorithms for the aircraft is provided in Chapter 3.

To achieve the third objective a method to estimate both position and velocity of ship-deck using

fiducial based vision is developed. The results are validated using measurements from Vicon.

19



The description and validation of fiducial based vision is provided in Chapter 4.

For the fourth objective, systematic experiments are carried out to study the tracking performance

of the quadrotor UAV using fiducial based vision. The ground truth values about motion of both

the quadrotor and the Stewart platform is obtained using Vicon. The details of the experiment

and the results are provided in Chapter 5.

The fifth and final objectives are achieved by developing a new feature based vision system and

through systematic experiments evaluating its robustness in different environmental conditions

such as partial occlusion, illumination variation, glare and water distortion. Also, weight and

power penalty for using featured based vision are studied by evaluating its performance on

different flight computers. The details are provided in Chapter 6.

20



Chapter 2: Ship-Deck Motion

This chapter focuses on ship-deck motion and methods to replicate it in lab at a small scale.

It starts with a description of different types of ship-deck motion and sea-states, followed by a

description of the deck motion dataset obtained from the Navy. Next, it describes the construction

of a shaping filter from the dataset to generate stochastic ship-deck motion. After that, the

hardware used to replicate deck motion is described. This is followed by Van Loan’s algorithm to

discretize a linear system and the process followed to replicate the deck motion in the laboratory

setting.

2.1 Types of ship-deck motion

Ship-deck motion can be broadly categorized into six types: 3 translations and 3 rotations.

The translational motion along the longitudinal axis of ship is called surge, while the translational

motion along the lateral axis is called sway. The translational motion perpendicular to these axes

is called heave, which is the raising or lowering of the ship-deck. The rotational motions along

the longitudinal axis is called roll (positive to right), along the lateral axis is called pitch (nose

down positive), and along the axis perpendicular to these is called yaw (nose left positive). These

motions for a ship-deck are depicted in Fig. 2.1.

21



Figure 2.1: 6 types of ship-motion

Table 2.1: Douglas Sea-scale

State Wave Height Characteristic

0 0 m Calm Glassy Sea

1 0-0.1 m Calm Rippled Sea

2 0.1-0.5 m Smooth Sea

3 0.5-1.25 m Slight Sea

4 1.25-2.5 m Moderate Sea

5 2.5-4 m Rough Sea

6 4-6 m Very Rough Sea

7 6-9 m High Sea

8 9-14 m Very High Sea

9 >14 m Phenomenal Sea

22



2.2 Sea States

Sea states are numbers used to characterize the roughness of sea. It is part of the Douglas

sea scale devised in 1921 by Capt. H.P. Douglas of the Royal Navy for ship navigation. The scale

is summarized in Table 2.1.

Ship-deck motion is stochastic as the exact forces applied by sea-waves to the ship cannot be pre-

determined. However, statistical properties of these forces can be inferred from available datasets.

These properties can then be used to simulate the deck motion in the laboratory environment. This

is the approach followed here.

2.3 Deck Motion Dataset

A standard deck motion dataset for a generic surface combatant that is representative of

a DDG-51 destroyer was provided by NAVAIR. The dataset contained 30 time histories in 3

different sea-states for the ship traveling in a straight line along its surge direction. A sample

snapshot of the time history of deck motion from the dataset is presented in Fig. 2.2. Motion

histories for all six degrees of freedom are shown.

23



0 100 200 300

Time, s

0

1000

2000

3000

S
u

rg
e
, 
m

(a) Surge

0 100 200 300

Time, s

-10

0

10

S
w

a
y
, 
m

(b) Sway

0 100 200 300

Time, s

-10

0

10

H
e

a
v

e
, 

m

(c) Heave

0 100 200 300

Time, s

-10

0

10

R
o

ll
, 

d
e

g

(d) Roll

0 100 200 300

Time, s

-10

0

10

P
it

c
h

, 
d

e
g

(e) Pitch

0 100 200 300

Time, s

-10

0

10

Y
a

w
, 

d
e

g

(f) Yaw

Figure 2.2: Sample ship-deck motion time series from Navy provided dataset

The dataset when converted to frequency domain provides unique insights. Figure 2.3

shows fourier amplitude vs. frequency of deck’s sway acceleration at three different sea-states.

Each color in the figure is from a single time history. It is observed from the figure that the

primary effect of increasing sea-state is an increase in the amplitude of deck acceleration. The

frequencies always remain between 0.1-0.3 Hz. This frequency domain information is used in

the next section to construct a shaping filter used later to replicate deck motion in the laboratory.

24



(a) Sea State 2-3 (b) Sea State 4-5 (c) Sea State 7

Figure 2.3: Fourier transform of deck acceleration; different colors are from different time
histories

2.4 Construction of Shaping Filter

This section deals with the construction of a shaping filter from the Navy provided dataset.

The shaping filter is essentially a linear system which takes a white noise input and generates

ship-deck motions similar to that in the dataset.

To begin, we first analyze the power spectrum of the deck motion. The power spectrum of a

signal is the average power per unit frequency present in the signal as a function of frequency.

And power spectrum of a signal of an ergodic random process is expected power spectrum of

the process itself. Additionally, according to Weiner-Kinchin theorem, this is the same as the

Fourier transform of the process auto-correlation function. So, let X(t) be a continuous signal

generated by an ergodic random process. Then the power spectrum S(ω) of the signal, as well as

the expected power spectrum of the random process is given by the following equation:

25



S(ω) = lim
T→∞

1

T
|X̂T (ω)|2 (2.1)

where X̂T (ω) is fourier transform of XT (t) defined as

XT (t)
∆
=


X(t) if − T/2 ≤ t ≤ T/2

0 otherwise

Now if we only have a set of N discrete measurements of the signal X(t), spaced ∆t apart. Then

the power spectrum can be re-written in discrete form as,

S(ωk) ≈
∆t2

N∆t
|X(ωk)|2 =

1

FsN
X(ωk)X̄(ωk) (2.2)

whereX(ωk) =
∑N−1

n=0 X(tn)e
−inωk∆t is discrete Fourier transform of the discrete measurements

X(tn) of the signal, Fs = 1
∆t

is sampling frequency, and ωk = 2πk/(N∆t) for k = 0 to N − 1

are the N discrete circular frequencies where the power spectrum values are obtained.

Equation 2.2 is used to calculate the power spectral density of the deck’s sway acceleration time

series data for Sea State 4-5 (Fig. 2.3b). Figure 2.4 shows this calculated power spectral density

for different time series represented by different colors. Also shown in the figure is an analytical

function approximation of the power spectrum, which has the following equation

S(ω) =
Kω6

ω8 − 1.2ω4 + 1
(2.3)

26



The gain K of this power spectrum function is a parameter that controls its amplitude and hence

can be used to represent different sea-states.

Figure 2.4: Power Spectral Density of deck’s sway acceleration

Now according to the theory of linear systems and stochastic processes, a stochastic wide

sense stationary (WSS) input signal to a linear time invariant system produces a stochastic wide

sense stationary output signal whose power spectrums are related by the following equation,

Syy(ω) = |G(jω)|2Suu(ω) (2.4)

27



Figure 2.5: Linear time invariant system with stochastic wide sense stationary (WSS) input gives
stochastic WSS output

Now, if the input signal to the linear system is a white noise with unit intensity, i.e.

Suu(ω) = 1, the output is

Syy(ω) = |G(jω)|2 = G(jω)G(−jω) (2.5)

Hence the power spectrum function found above in Eq. 2.3 can be thought of as generated by

a linear system with white noise of unit intensity as input. A spectral factorization of the power

spectrum is performed to recover the linear system:

S(w) = G(jω)G(−jω)

G(jω) =

√
K(jω)3

(jω)4 + 2.406(jω)3 + 2.8944(jω)2 + 2.406(jω) + 1

(2.6)

where G(jw) is chosen so as to contain the stable poles and to have minimum order. Lifting the

factor G(jw) into laplace domain by simply replacing jω with s results in the following transfer

function. This is also called a shaping filter.

G(s) =

√
Ks3

s4 + 2.406s3 + 2.8944s2 + 2.406s+ 1
(2.7)

28



Converting it to state space results in,

ẋ =



0 0 0 −1

1 0 0 −2.406

0 1 0 −2.8944

0 0 1 −2.406


x+



0

0

0

1


u

q =

[
0 0 0 1

]
x

(2.8)

where u is white noise with intensity K.

Equation 2.8 is the shaping filter that drives the ship-deck sway with white noise input. It should

be noted that its output is deck’s sway acceleration. Hence the output should be fed into a double

integrator to get the deck sway position. Physically, Eq. 2.8 represents a model of the stochastic

forces acting on the ship-deck.

2.5 Hardware to replicate deck motion

A Stewart platform is used to replicate ship-deck motion in the lab at a small scale. The

platform is a parallel manipulator that uses six electric linear actuators to control the complete

6-DOF motion of a horizontal platform representing the ship-deck. The platform used in this

research was procured from Acrome robotics and is shown in Fig. 2.6. Its specifications are

presented in Table 2.2.

29



Figure 2.6: 6-DOF stewart motion platform used to replicate ship-deck type motion in lab
environment

Table 2.2: Stewart Platform Specifications

Parameters Value

Gross mass 5.2 kg

Platform diameter 30 cm

Linear travel range +/- 10 cm

Angular travel range +/- 30 degrees

Max speed (No load) 50 cm/s

Max force 280 N(static)

The discrete dynamic equations required to excite this platform to simulate ship-deck motion is

derived next.

30



2.6 Van Loan’s algorithm to discretize linear system

Van Loan’s algorithm with zero-order hold is used in this chapter and throughout this

dissertation to discretize continuous linear time-invariant systems. The method followed in these

cases is described here.

Any continuous linear time invariant system has the following form:

ẋ = Ax+Bu+B1w

where x is system’s state, u is control, w is white noise of intensity Q, and A,B,B1 are time

invariant matrices. From linear systems theory, the above system can be discretized into a discrete

linear system of the form:

xk+1 = Fkxk +Gkuk + wk

where xk and xk+1 are states of the system at time steps tk and tk+1 respectively, uk is control

input assumed to be held fixed between the two time steps, and wk is a Gaussian random variable

with variance Qk. The matrices Fk, Gk and Qk are related to the continuous system as given by

the following equations:

Fk = eA(tk+1−tk) (2.9)

Gk =

∫ tk+1

tk

eA(tk+1−σ)Bdσ (2.10)

Qk =

∫ tk+1

tk

eA(tk+1−σ)B1QB
T
1 e

AT (tk+1−σ)dσ (2.11)

31



Van Loan [38] gave a fast and easy way to find the matrices Fk and Qk. His algorithm is to

construct another matrix:

Λ =

−A B1QB
T
1

0 AT

 (2.12)

Then use the following identity to find Fk and Qk:

eΛ(tk+1−tk) =

− F−1
k Qk

0 F T
k

 (2.13)

where − means that term is irrelevant to the present discussion.

Hence, Fk is transpose of lower right partition of eΛ(tk+1−tk) and Qk is upper right partition pre-

multiplied by Fk.

Similarly, Gk can also be found by using the following identity,

e


A B

0 0

(tk+1−tk)

=

Fk Gk

0 I

 (2.14)

where I is identity matrix.

The matrix exponentials in this work was evaluated using the MATLAB expm function.

32



2.7 Procedure to replicate deck motion

The trajectory of the Stewart platform hardware described in Sec. 2.5 is controlled using

a Simulink model provided by Acrome robotics. The input to the model is desired position and

orientation of the platform at each time step. Hence to simulate deck motion using the platform,

we need a way to generate discrete deck positions using the shaping filter designed in Section

2.4. This is described here.

The output of the designed shaping filter is deck’s acceleration. Hence it is first augmented

with a double integrator to get a linear system whose output is deck’s position. This results in the

following linear system.

ẋ =



0 1 0 0 0 0

0 0 0 0 0 1

0 0 0 0 0 −1

0 0 1 0 0 −2.406

0 0 0 1 0 −2.8944

0 0 0 0 1 −2.406



x+



0

0

0

0

0

1



u

y =

[
1 0 0 0 0 0

]
x

(2.15)

where u is again a white noise process with intensity K. The value of K controls the amplitude

of deck disturbance and hence different values can be used to simulate different sea-state.

33



The above linear system is discretized using Van Loan’s algorithm resulting in the following

discrete linear system. The discretization time step is chosen as 0.01 s as the simulink model runs

at 100 Hz.

xk+1 =



1 1e−2 8.3e−13 4.15e−10 1.66e−7 4.96e−5

0 1 4.15e−10 1.66e−7 4.96e−5 9.88e−3

0 0 1 −1.66e−7 −4.96e−5 9.88e−3

0 0 1e−2 1 −1.19e−4 −2.38e−2

0 0 5e−5 1e−2 1 −2.87e−2

0 0 1.65e−7 4.96e−5 9.88e−3 9.76e−1



xk + wk

yk =

[
1 0 0 0 0 0

]
xk

(2.16)

where wk is a random vector with zero mean Gaussian distribution whose covariance matrix Qk

is found to be:

Qk =



4e−10 9.96e−8 −9.96e−8 −2.40e−7 −2.89e−7 1.32e−5

9.96e−8 2.65e−5 −2.65e−5 −6.39e−5 −7.70e−5 3.95e−3

−9.96e−8 −2.65e−5 2.65e−5 6.39e−5 7.70e−5 −3.95e−3

−2.40e−7 −6.39e−5 6.39e−5 1.54e−4 1.86e−4 −9.53e−3

−2.89e−7 −7.7e−5 7.7e−5 1.86e−4 2.24e−4 −1.15e−2

1.32e−5 3.95e−3 −3.95e−3 −9.53e−3 −1.15e−2 7.91e−1



(2.17)

The value of white noise intensity K used while discretizing above is chosen as 81 cm2/s3 to

bound the output positions from the discrete system to be within the range of the platform motion.

34



The discrete linear system represented by Eq. 2.16 is used to generate desired discrete deck

positions at each time-step and fed into the simulink model provided by Acrome robotics to

control the position of Stewart platform. The linear system itself is driven by Gaussian white

noise with covariance matrix given by Eq. 2.17.

A sample stochastic Stewart platform trajectory generated using the above method is shown

in Fig. 2.7. The trajectory shown is platform motion measured using a VICON system. The

trajectory is observed to be stochastic and similar to the sway motion of the original data.

Figure 2.7: A sample stochastic deck motion trajectory generated by commanding the Stewart
platform through the designed shaping filter and measured using a VICON system

2.8 Summary

In this chapter, the Navy provided dataset was used to construct a shaping filter which was

then used in this research to replicate ship-deck type motion in the lab at a small scale. The motion

itself is produced using a 6-DOF Stewart platform hardware. The properties of the platform and

35



the method to excite it into ship-deck type motion have also been discussed in this chapter. Based

on this part of the work, following conclusions are drawn.

1. Navy provided dataset showed that the effect of increasing sea-state is an increase in deck

motion disturbance amplitude; the frequency distribution of the disturbance remains the

same.

2. The frequencies of deck motion disturbances for the DDG-51 destroyer for which the data

was provided lie predominantly between 0.1-0.3 Hz irrespective of sea-state.

3. A small 30 cm diameter Stewart platform can be used to replicate the ship-deck motion in

laboratory setting.

4. The power spectrum of ship-deck disturbances derived from ship-deck motion dataset can

be used to construct a shaping filter. The filter with a white noise input can then be used to

excite the Stewart platform into stochastic deck motion similar to the original data.

36



Chapter 3: Fabrication of Quadrotor UAV

This chapter describes the design and fabrication of the VTOL UAV used in this research.

It begins with a short overview, and then it covers the structure, propulsion system, avionics,

sensors, computers, communication protocols, control system, and state estimators in deatil.

3.1 Overview

A Vertical Take-Off and Landing quadrotor UAS was fabricated in-house as a representative

vertical lift vehicle to track and land on the ship-deck represented by the Stewart platform. The

quadrotor configuration was specifically selected because of the inherent simplicity in its flight

dynamics and control allocation. So, the principal emphasis can be on the avionics, and vision-

based algorithm required for ship-deck landing, and not on system identification of the plant.

Commercial-Off-The-Shelf (COTS) quadrotors were unsuitable for this research because of the

numerous modifications required to integrate the many special purpose sensors and computing

platforms, while not being over-burden with unnecessary features. This flexibility was important

particularly as components were often replaced and upgraded as the research progressed. An

additional consideration was the use of secure source in-house designed components and software

as much as possible. Modern additive manufacturing technology with metals and carbon-fiber

made this a feasible endeavor at least at the small UAV scale studied in this research. Hence,

37



a quadrotor was designed and fabricated ground up with a scale about the same as that of the

Stewart platform and with just the right sensors and processing units required for ship-deck

landing. The final vehicle has a dimension of about 280 mm × 280 mm (11 in. × 11 in.), a

gross take-off weight of about 1700 grams (3.75 lbs), and a maximum thrust to weight ratio of

about 2. The vehicle is described in detail in the next few sections.

3.2 Vehicle Structure

The primary load-carrying component of the vehicle is an H-shape structure, as shown in

Figure 3.1. The structure is made from 10 mm hollow square aluminium-6063 T5 tubes of 1 mm

thickness. Al-6063 T5 was chosen for good strength and machinability at a low cost. The tubes

with a flexural modulus of 112.84 MPa give a factor of safety of at least 64 for material yield

under steady flight conditions. The high factor of safety is essential for this research vehicle as it

reduces the probability of structural failure during high impact landings.

Figure 3.1: Quadrotor skeleton made from square aluminum tubes

38



3D printed parts are used to secure components to the aluminum frame. Motor mounts

(Figure 3.2) used to secure motors as well as transfer loads from the motor base to the aluminum

structure are printed from Onyx, a material made of micro-carbon fibers in a nylon matrix. These

are also reinforced with 1 mm thick unidirectional 3D printed carbon fiber sheets at the top. This

gives it a similar elastic modulus and strength as Al-6061 T6.

3D printed plates made from ABS plastic are used to secure avionics components to the quadrotor

frame (Figure 3.2). The slits and cutouts of the plates are tailored to the attachment that will

secure the avionics later. The avionics components are soft-mounted with rubber dampers to

reduce vibration transfer to the components.

Figure 3.2: Quadrotor frame ready to be mounted with propulsion and avionics components

39



3.3 Propulsion System

A pair of clockwise and counter-clockwise rotating 3-bladed, 6-inch fixed-pitch rigid rotors

are used for propulsion. The rotors are driven by iFlight Xing-E 2450KV brushless direct-drive

electric motors (Fig. 3.3), each with 12 electromagnets and 14 N52SH neodymium permanent

magnets. The motors are controlled by electronic speed controllers (ESC) (Fig. 3.4) running

BLHeli32 firmware. Communication with the ESC is established using DSHOT protocol. The

benefit of this protocol over the conventional analog pulse width modulation (PWM) is that it is

digital and hence is faster and more robust to noise. This leads to more precise and faster changes

of motor RPM than what is possible with PWM signals. A brief description of the protocol is

presented in the section 3.7.

Figure 3.3: iFlight 2207 2750Kv motor used on the vehicle; Configuration: 12N14P

40



Figure 3.4: Electronic Speed Controller running BLHeli32 firmware

Figure 3.5: Experimental setup used to measure thrust and torque in hover

A simple experiment is used to characterize the propulsion system. The experimental setup is

shown in Fig. 3.5. The motor and the rotor are mounted in series to a RTS-50 torque cell and

41



a single axis MDB-2.5 load cell from Transducer Techniques. The entire setup is held in place

using a vice attached to a bench. The motor is instrumented with a hall-effect switch and a

magnet for RPM measurement. A second RPM measurement is taken using a laser tachometer

and a retro-reflective marker placed on the motor. The experimental measurements along with

quadratic curve fits are shown in Fig.3.6. From the curve fit, thrust and torque coefficients (CT

and CQ) of the rotor were calculated to be:

CT =
T

ρA(ΩR)2
=

1

ρπR4

T

Ω2
= 0.0254 (3.1)

CQ =
Q

ρA(ΩR)2R
=

1

ρπR5

Q

Ω2
= 0.0042 (3.2)

where ρ = 1.23 kg/m3. This leads to a Figure of Merit of 0.68, and with solidity(σ) = 0.095, a

blade loading CT/σ of 0.266.

(a) Thrust vs RPM (b) Torque vs RPM

Figure 3.6: Experimentally measured variation of thrust and torque with RPM

42



For the above experiment, power was supplied to the motor at a constant 11.8 V through a

DC power supply. The current consumed was measured through the power supply. From these

power consumed by the motor at different RPMs was calculated and is shown in Fig. 3.7. The

curve fit has the following equation:

Psupply = 3.9× 10−8Ω3 + 2.428× 10−11Ω4 Watts (3.3)

where the first term corresponds to mechanical power provided to rotor and the second term

represents resistive power loss. From the second term, the motor constant is calculated as:

Km =
Q√
Ploss

=
ρπR5CQ√

2.428 ∗ 10−11
= 0.0085 N-m/

√
Watts (3.4)

This motor constant is related to the torque constant KT by the well known expression Km =

KT/
√
R where R is motor’s resistance.

Since the first term in Eq. 3.3 represents power provided to rotors, it can be used to evaluate

the rotor’s power constant as:

CP =
Protor

ρA(ΩR)3
= 0.0039 (3.5)

Now CP = CQ from momentum theory of rotors. It is observed that our calculated values of CP

and CQ are quite close within 7% of each other. This serves as a sanity check and goes on to

show that use of torque cell in the experiment is redundant. Both motor constant and rotor torque

constant can be found from just Power vs. RPM measurements.

43



Figure 3.7: Power vs RPM

Figure 3.8: Motor Efficiency vs RPM

44



Figure 3.8 shows the plot of efficiency of the motor with its RPM. Efficiency of the motor

is defined as η = Protor/Psupply. From the plot, it is seen that the motor operates near its peak

efficiency for the quadrotor in hover. This is by design as the aircraft will operate in near hover

conditions throughout its operations.

3.4 Avionics

Figure 3.9 shows the complete avionics architecture of the quadrotor. The avionics sub-

system is designed to be simple, lightweight, programmable, and robust to noise and external

disturbances. It primarily consists of two computers and three sensors. The computers are 1) a

600 MHz Arm Cortex M7 core based flight controller, and 2) a 1.92 GHz Intel Atom based flight

computer. The sensors are: 1) an Inertial Measurement Unit (IMU), 2) a Visual Inertial Odometry

(VIO) sensor, and 4) a Monocular camera. These components communicate with each other

through 4 communication protocols: 1) UART, 2) I2C, 3) DSHOT, and 4) USB. The avionics is

powered through a single cell 1Ah battery that is different from that used for propulsion. This is

to isolate the avionics components from electrical transients in propulsion. Apart from the above

components, since this is a research aircraft a 2.4 GHz radio receiver is used for emergency

manual control of the quadrotor. These components of avionics are briefly described next.

3.5 Sensors

The vehicle carries a set of 3 sensors; 2 for autonomous flight and 1 for ship-deck detection.

These are:

45



Figure
3.9:

A
ircraft’s

A
vionics

architecture;
D

Shot,
U

A
R

T,and
I2C

are
three

different
digital

com
m

unication
protocols

used
on

the
aircraft

46



3.5.1 Inertial Measurement Unit (IMU):

MPU-6050 by Invensense is used as an IMU on the vehicle. The IMU consists of 3

orthogonally placed micro-electromechanical (MEMS) accelerometers and 3 orthogonally placed

MEMS gyroscopes. The gyroscopes measure the angular velocity of the vehicle, while the

accelerometers measure the linear acceleration combined with gravity vector.

3.5.2 Visual Inertial Odometry (VIO) sensor:

Realsense T265 by Intel is used as a visual-inertial sensor onboard the quadrotor. It

measures the position and velocity of the aircraft and is used in place of GPS for indoor flights. It

is essentially a stereo camera that runs Visual Odometry software fused with IMU measurements.

The software is proprietary to Intel.

3.5.3 Monocular Camera:

A monocular global shutter camera by e-consystems is used for detection and tracking of

ship-deck. It is the only sensor used to detect ship-deck and estimate its position and orientation.

The camera and the related vision system are explained in detail in the next chapter.

(a) Inertial Measurement Unit
(IMU)

(b) Visual Inertial Odometry
(VIO) sensor

(c) Monocular global shutter
camera

Figure 3.10: Sensors on the quadrotor vehicle

47



3.6 Computers

There are two computers onboard the vehicle. These are:

3.6.1 Flight controller:

A Flight controller based on Teensy 4.0 micro-controller board is used on the vehicle. It

contains an NXP MIMXRT1062 processor with a 32-bit ARM Cortex-M7 CPU core and can

execute instructions at 600 Mhz. Its primary purpose is real-time flight stabilization/attitude

control of the vehicle. It runs a single process that in sequence, estimates the vehicle’s attitude and

angular velocity using IMU data, receives attitude setpoints from the flight computer, evaluates

the inner loop control, and then finally sends motor commands to ESC. The inner loop calculates

the four rotor RPM needed to maintain vehicle’s attitude. This is repeated every millisecond,

resulting in a loop rate of 1000 Hz.

3.6.2 Flight Computer:

A Flight Computer based on Up-Board Single Board Computer (SBC) is used on the

vehicle. It contains an x64 architecture based quad-core Intel Atom processor and runs a non-

real-time version of debian Linux operating system (OS). Its primary purpose is localization and

navigation of the vehicle through outer loop control. The outer loop calculates attitude setpoints

from VIO and camera measurements. Its secondary purpose is data logging of flight variables

for debugging and post-processing. Different processes running on top of the OS are used for

executing different tasks in parallel. These tasks are reading and processing the data from the

VIO and camera sensor, executing outer loop control commands, managing communication with

48



the flight controller, and recording flight data to non-volatile memory for post-processing. The

communication between the independent processes itself is carried out using an asynchronous

publish/subscribe messaging system of the Robot Operating System (ROS) package. It is to be

noted that ROS is just an Inter Process Communication (IPC) mechanism here.

(a) Teensy Flight Controller; CPU
Core: ARM Cortex M7

(b) Up-Board Flight Computer;
CPU Core: x64 Intel Atom

Figure 3.11: Primary computing elements on the quadrotor vehicle

3.7 Communication Protocols

Three types of communication protocols are used onboard the aircraft. Low latency UART

and I2C are used for communication of time-sensitive data to the micro-controller. High bandwidth

USB on the other hand is used by the flight computer to receive camera frames and VIO data. For

communication with ESC, a special purpose UART known as DShot is used. These protocols are

briefly described below.

3.7.1 UART:

Universal Asynchronous Receiver and Transmitter (UART) is a simple method of bi-directional

(full duplex) serial communication between two devices. The data is transmitted in frames. Each

frame is 8 bits of data prepended by a start bit and appended optionally by a parity and two stop

49



bits. The rate of transmission of each bit is pre-agreed between the two devices. The entire

protocol is commonly implemented as an Integrated Circuit (IC), which offloads CPU (Central

Processing Unit) cycles for other important tasks.

In this research, a high-level protocol based on UART was written for communication between the

flight controller and the flight computer. The messages from flight controller are primarily to log

inner loop flight variables into the non-volatile memory of flight computer. The messages from

flight computer on the other hand contains outer loop control commands i.e. attitude set-points

for the flight controller to execute on. Each message for data logging from flight controller to

flight computer starts with ”Hi,”. This is followed by 3 character bytes specifying which vehicle

state or parameter is being communicated, which is then followed by bytes containing the value of

that state. The message ends with a newline character. The vehicle set points command message

from the flight computer to the flight controller starts with ”Hi,” too, and is followed by values

of thrust and the desired attitude setpoints command from the outer loop control. The message

ends with a checksum and a newline character. The checksum is important as it helps to detect

communication errors for the flight critical data being sent from flight computer to the controller.

Each message in either direction when received is evaluated against their respective format, and

is discarded if it does not match or if the checksum is invalid. The codes for either side UART

message encoder and decoder were written in C to minimize round-trip communication delay to

440 microseconds.

The 2.4 GHz radio receiver used for emergency manual control also sends the control commands

to the flight controller using UART. A decoder for the signal from this UART radio receiver was

50



also written as part of this research using the message format provided by the vendor.

3.7.2 I2C:

I2C stands for Inter-Integrated Circuit. Like UART, it is another protocol for bi-directional

but half-duplex serial communication. Unlike UART, it is synchronous, which means a clock

signal is also transmitted along with data to tell the receiver the rate of data transmission. I2C

uses a parent-child communication framework, in which one device is designated as parent and

completely controls the start and stop of communication with multiple child devices. Each I2C

communication involves the following steps:

1. The parent sends a start signal to the child devices.

2. The parent sends the address of the device it wants to communicate with, along with its

intent to either read or write from the device.

3. The child device for which the address matches, sends an acknowledgement signal back to

the parent device.

4. The parent sends or receives data in 8-bit data frames. Each frame is followed by an

acknowledgement signal from the receiver to the sender.

5. The parent sends a stop signal to stop the transmission.

The I2C protocol is more robust to noise and electromagnetic interferences and is also significantly

faster than UART. Its primary drawback is that communication can only occur in one direction

at a time and that the parent device has total control over the flow of communication. Hence it is

suitable for communication between computers and sensors where the computer acts as a parent.

51



In this research, I2C was used to transmit gyroscope and accelerometer data from the IMU to the

micro-controller for flight stabilization.

3.7.3 DShot:

Digital Shot is a special purpose UART type communication protocol made for fast digital

communication with Electronic Speed Controllers (ESCs). It is used to send motor RPM commands

to ESCs and receive telemetry data in return. Sending of command from flight-controller to ESC

happens in 16-bit data packets. The first 11 bits of a packet contain the commanded RPM value

for motors or special commands such as to reverse motor spin direction. The next bit represents

a request for telemetry if set to 1. The last 4 bits are used for communication error checking

through Cyclic Redundancy Check (CRC). In this research, an open-source DShot library for the

Teensy micro-controller was modified for use with the in-house flight controller code.

3.7.4 USB:

Universal Serial Bus is a standardized modern serial communication protocol developed

for communication between computers and peripheral devices. It has a tree-network topology

where the host computer acts as the root device and talks to the peripheral devices over different

communication branches. Similar to I2C, the host computer for USB has total control over

communication flow. USB by design is fast and reliable as it has inbuilt error-correcting mechanisms.

Its primary drawback is large communication latency which makes it unsuitable for applications

where low-latency real-time communication is needed. In this work, USB was used to send

monocular camera images and VIO data to the flight computer. It should be noted that the job of

the flight computer is guidance and navigation which are much more tolerant to latency than job

52



of the flight controller which is vehicle stabilization.

3.8 Assembled Aircraft

The assembled aircraft ready for flight is shown in Fig. 3.12, with its properties listed in

Table 3.1. Center of gravity and moment of inertia of the aircraft are calculated by measuring

the weight and location of each component. For this purpose, all components are assumed to be

point masses except for the flight battery, aluminum beams in the frame, and the ABS plates for

which the moment of inertia was evaluated using standard formulae assuming uniform internal

mass distribution.

Figure 3.12: The in-house fabricated quadrotor aircraft

53



Table 3.1: Aircraft Properties

Parameters Value

Gross Take off mass 1.7 kg

Center of gravity (0.015 m, 0 m, 0 m)

Ixx 5.8 ×10−3 kgm2

Iyy 1.8 ×10−2 kgm2

Izz 2.5 ×10−2 kgm2

Rotor diameter 0.152 m

Mean rotor chord 0.015 m

Hover tip speed 99 m/s

Hover tip Mach number 0.29

Hover tip Reynolds number 100,914

Rotor spacing 0.28 m

Landing gear footprint 0.10 m × 0.062 m

Max thrust to weight ratio 1.96

Flight time in hover 5 min

54



Figure 3.13: Body-axes and direction of rotation of rotors; Z is +ve down

3.9 Flight Control System

The flight controller for the vehicle is designed as nested PID (Proportional-Integral-Derivative)

type linear controller for vehicle dynamics linearized around hover. Time-scale separation of

attitude and translational dynamics is assumed in control design and is ensured through control

gains selection. The complete control block diagram is shown in Fig. 3.14.

55



Figure
3.14:C

ontrolarchitecture
forvision-based

autonom
ous

tracking
and

landing
on

a
stochastically

m
oving

platform

56



3.9.1 Attitude Control

Attitude control is performed through two cascaded PI controller, operating on attitude and

attitude rates. The equations for the rate PI control are

Ld = KpL(pd − p) +KiL

∫ t

0

(pd − p)dt

Md = KpM(qd − q) +KiM

∫ t

0

(qd − q)dt

Nd = KpN(rd − r) +KiN

∫ t

0

(rd − r)dt

(3.6)

where (Ld,Md, Nd) are desired moments while (pd, qd, rd) and (p, q, r) are desired and

measured angular velocities respectively.

Similarly the equations for the Attitude PI control are:

pd = Kpϕ(ϕd − ϕ) +Kiϕ

∫ t

0

(ϕd − ϕ)dt

qd = Kpθ(θd − θ) +Kiθ

∫ t

0

(θd − θ)dt

rd = Kpψ(ψd − ψ) +Kiψ

∫ t

0

(ψd − ψ)dt

(3.7)

where (ϕd, θd, ψd) and (ϕ, θ, ψ) are desired and measured attitude angles respectively. (pd, qd, rd)

are desired angular rates and are used in rate PI control (Eq. 3.6).

3.9.2 Translational Control

Translational control for the quadrotor to track the ship-deck position is performed through

a single linear PID type control. The control is designed such that only X and Y deck motions

57



(surge and sway) are tracked, while maintaining a constant altitude. The equations for translational

control are:

ẍd = Kpx(xt) +Kdx(0− ẋ) +Kd1x(ẋt) +Kix

∫ t

0

(xt)dt

θd = −ẍd/g
(3.8)

ÿd = Kpy(yt) +Kdy(0− ẏ) +Kd1y(ẏt) +Kiy

∫ t

0

(yt)dt

ϕd = ÿd/g

(3.9)

z̈d = Kpz(zd − z) +Kdz(0− ż) +Kiz

∫ t

0

(zd − z)dt

Td = m(g − z̈d)

(3.10)

where (xt, yt, zt) is quadrotor relative ship-deck position and (ẋt, ẏt, żt) is quadrotor relative

ship-deck velocity, both obtained using computer vision through monocular camera. (x, y, z)

is quadrotor inertial position, (ẋ, ẏ, ż) is quadrotor velocity in body axes obtained through the

VIO sensor. The symbol g is acceleration due to gravity, m is mass of the quadrotor and h is the

height above deck to hover the quadrotor. Td, ϕd, θd are the desired thrust, roll and pitch used in

the attitude control. It should be noted that the translational control equations makes use of small

angle assumptions in roll and pitch of the vehicle near hover.

The above translational control equations can also be used for waypoint navigation of quadrotor

58



in the absence of ship-deck. The relative error in this case is xt = xd− x, where xd is the desired

waypoint and x is the quadrotor position obtained through VIO sensor.

Another point to note is that the integral terms in all the above controller equations are implemented

using recursive summation in the actual controller.

∫ t

0

fdt = f(t)∆t+

∫ t−∆t

0

fdt

The saturation of integral terms and re-initialization to zero every time the aircraft takes off after

landing are two techniques used to prevent integral windup in the controller.

3.9.3 Control mixer

Control mixer essentially converts the desired thrust, roll, pitch and yaw moment (Td, Ld,Md, Nd)

to motor speeds. The equations for control mixer are based on the following actuation model that

assumes the thrust and torque from each rotor to be proportional to the square of its RPM, valid

for aircraft operations near hover.



Td

Ld

Md

Nd


=



kT kT kT kT

lkT lkT −lkT −lkT

lkT −lkT −lkT lkT

−kQ kQ −kQ kQ





Ω2
1

Ω2
2

Ω2
3

Ω2
4


(3.11)

59



Here l = 0.14 m is half of the distance between any two adjacent motors, while kT and kQ are

given as:

kT = ρπR4CT = 3.315× 10−6 Ns2

kQ = ρπR5CQ = 4.2× 10−8 Nms2

The inversion of Eq. 3.11 produces the equation for aircraft mixer.

The set of selected control gains for the quadrotor are given in Table 3.2 & 3.3. The inner loop

was tuned to get the fastest settling, without any overshoot and without feeding in sensor noise.

Similarly the outer loop was tuned to get the maximum tracking bandwidth without feeding in

sensor noise. The gains were arrived at through multiple subsequent iterations of linear system

analysis and flight tests.

Table 3.2: Inner loop control Gains

KpL KiL KpM KiM KpN KiN Kpϕ Kiϕ Kpθ Kiθ Kpψ Kiψ

0.2 0.2 0.3 0.2 0.7 0.2 7 0.8 7 0.8 5 1

Table 3.3: Outer loop control Gains

Kpx Kdx Kd1x Kix Kpy Kdy Kd1y Kiy Kpz Kdz Kd1z Kiz

6.0 6.0 0.5 2.0 6.0 6.0 0.5 2.0 5.0 3.2 0.3 1.0

Figure 3.15 shows simulated inner and outer loop response of quadrotor to step inputs. It

is observed that settling time of outer loop is more than an order of magnitude higher than that

of inner loop. This confirms that the selected gains maintain a timescale separation of the vehicle

attitude and position dynamics, an assumption of the presented control design.

60



(a) Inner loop step response (b) Outer loop step response

Figure 3.15: Inner and outer loop step response of quadrotor along X-axis; response along other
axes is similar; The response time verifies the time scale separation of attitude and translational
dynamics assumed in the control design

Figure 3.16 shows the effective outer loop tracking control system of the quadrotor with

the closed loop transfer function given as,

T (s) =
s2Kd1 + sKp +Ki

s3 + s2(Kd1 +Kd) + sKp +Ki

(3.12)

Figure 3.16: Effective outer loop control diagram

61



Figure 3.17: Bode plot of closed outer loop control system T (s) for X and Y axes

Figure 3.17 shows Bode plot of T (s). As observed, the tracking bandwidth is 0.15 Hz.

The bandwidth was restricted here as it was observed from experiments that further increase in

bandwidth would lead to significant feedback of noise into control. The system has infinite gain

margin, phase margin of 66.7°and delay margin 1.15 s.

62



Figure 3.18: Large noise in measurements by
accelerometers

Figure 3.19: Fourier transform of the
measurements show large noise is due to
1/rev vibration from the rotors

3.10 Filtering and State-estimation

One of the important problems associated with control design is estimation of vehicle states

reliably from a set of sensor measurements. This is a non-trivial task as sensor measurements are

always corrupted by unwanted noise from the environment. For rotary wing vehicles this is

exacerbated by vibrations from the rotors as shown in Figure 3.18 and 3.19. The figures show a

high 1/rev vibration from rotors adversely affecting the vehicle attitude measurement by MEMS

(Micro Electro-Mechanical System) accelerometers. In this work, low-pass filters and Kalman

filters have been used to filter out such noise and produce reliable estimates of vehicle states from

sensor measurements.

63



3.11 Kalman Filters

Kalman Filter also known as Linear Quadratic Estimator (LQE) is an algorithm to produce

optimal estimates of vehicle’s states using known models of state dynamics and sensor measurements.

Models for the three Kalman filters used in the control system (Figure 3.14) are described below:

3.11.1 For angular velocity:

The models for Kalman filter of roll rate is presented here. They are same for the other

angular velocity components.

Process model:

pk+1

ṗk+1

 =

1 ∆t

0 1


pk
ṗk

+

1
2
∆t2

∆t

wpk (3.13)

where wpk is the process disturbance, assumed to be in the second derivative of the roll rate.

Measurement model:

ypk+1 = pk+1 + vpk+1 (3.14)

where ypk+1 is the measurement from the gyroscope aligned along X-axis of the aircraft and vpk+1

is the measurement noise.

It should be noted that independent Kalman filter design for angular velocities along three

axes assumes no cross-coupling in attitude dynamics between the axes, which is strictly true

64



only if the off-axis terms in the moment of inertia matrix of the vehicle are zero. Typically for

quadrotors they are small because of vehicle symmetry.

3.11.2 For attitude

The Kalman filter for attitude fuses the data from gyroscopes with that from accelerometers.

The gyroscope data through angular velocity estimates are used as inputs in the process model

and are integrated to produce attitude estimates. These are then corrected with direct attitude

measurements from accelerometers. This method of sensor fusion produces much better attitude

estimates than using any one of the sensor alone.

Process model:

ϕk+1 = ϕk + (ϕ̇k + wϕk )∆t

θk+1 = θk + (θ̇k + wθk)∆t

ψk+1 = ψk + (ψ̇k + wψk )t

(3.15)

where (wϕk ,wθk ,wψk ) are the process disturbances. (ϕ̇k, θ̇k, ψ̇k) are Euler angle rates, obtained from

angular velocity estimates (pk, qk, rk) through the following transformation.


ϕ̇k

θ̇k

ψ̇k

 =


1 sin(ϕk) tan(θk) cos(ϕk) tan(θk)

0 cos(ϕk) − sin(ϕk)

0 sin(ϕk) sec(θk) cos(ϕk) sec(θk)




pk

qk

rk

 (3.16)

65



Measurement model:

yϕk+1 = ϕk+1 + vϕk+1

yθk+1 = θk+1 + vθk+1

(3.17)

where yϕk+1 and yθk+1 are pseudo measurements obtained from true accelerometer measurements

using the following equations:

yϕk+1 = tan−1(ay/az)

yθk+1 = tan−1(−ax/
√
a2y + a2z)

(3.18)

where (ax, ay, az) are accelerometer measurements along the three axes. It should be noted that

the above measurement model assumes vehicle accelerations in flight to be small when compared

to acceleration due to gravity (g).

Also, the measurement model does not include a model for yaw measurements as accelerometer

readings are unaffected by vehicle’s yaw. Hence, the Kalman filter only predicts yaw through the

integration of yaw rate in the process model and as such it drifts with time.

3.11.2.1 For ship-deck position:

Relative ship-deck position is measured through the vision system is then filtered through

Kalman filter to get both relative position and velocity. The model of the Kalman filter is:

Process model:

66



The process model is based on relative translational dynamics of quadrotor and ship-deck:

xk+1

ẋk+1

 =

1 ∆t

0 1


xk
ẋk

+

1
2
∆t2

∆t

 (ẍk + δẍk) + wxk (3.19)

yk+1

ẏk+1

 =

1 ∆t

0 1


yk
ẏk

+

1
2
∆t2

∆t

 (ÿk + δÿk) + wyk (3.20)

zk+1

żk+1

 =

1 ∆t

0 1


zk
żk

+

1
2
∆t2

∆t

 (z̈k + δz̈k) + wzk (3.21)

where xk, yk, zk are ship-deck relative quadrotor position measured through vision. The accelerations

(ẍk, ÿk, z̈k) in the process model are negative of commanded quadrotor accelerations, assuming

nominal deck acceleration to be zero. (δẍk, δÿk, δz̈k) are external disturbances to quadrotor.

wxk , wyk, and wzk are random vectors representing ship-deck disturbance by the sea-waves. The

quadrotor accelerations are obtained from outer loop PID control inputs as:

ẍk =gθdk

ÿk =− gϕdk

z̈k =Tdk/m− g

(3.22)

where (Tdk, ϕdk, θdk) are outer loop controls from the previous time step.

67



Measurement model: The measurements for the translations dynamics is the quadrotor relative

ship-deck position as measured through the monocular camera.

yxk+1 = xk+1 + vxk+1 (3.23)

yyk+1 = yk+1 + vyk+1 (3.24)

yzk+1 = zk+1 + vzk+1 (3.25)

3.12 Low Pass Filter

Kalman filter works in the time domain. It produces optimal state estimates by assuming

white Gaussian noise in measurements. But sometimes corruption of signal is not due to noise but

real phenomenon such as rotor vibrations (Figure 3.18-3.19), which are not white and have peaks

at certain frequencies. Typically notch filters are used to remove such noise. But notch filters

requires precise estimation of the frequency at which the vibration occurs. This is difficult for

variable RPM rotors where the excitation frequency can change during flight. But this excitation

frequency due to RPM of the rotors are always at frequencies that are much above those of typical

flight dynamics. This is seen from Fig. 3.19 where the vibration frequency is near 200 Hz. Hence

first order discrete low pass filters are used with the following equation:

Yi+1 = αXi+1 + (1− α)Yi (3.26)

where Xi+1 is the (i+1)-th filter input and Yi+1 is the (i+1)-th filter output. α is a parameter that

can be tuned to vary filter cut-off frequency. A 30 Hz low pass filter was used to remove the effect

of vibration in accelerometers. It should be noted that this specific solution of vibration isolation

68



is not scalable to full-scale manned aircrafts where the rotor RPMs and hence the vibration

frequencies are often at lower frequencies such as 5 Hz. Notch filters become necessary in such

cases.

3.13 Summary

This chapter covered in detail the design and fabrication of the autonomous quadrotor UAV

as a representative VTOL vehicle for ship-deck tracking/landing. Various aircraft subsystems,

including structure, propulsion, avionics and control were explained in-depth. To summarize, the

structure is made out of aluminium tubes and 3D printed parts are used to attach avionics and

propulsion to it. Commercial Off The Shelf (COTS) motors and rotors were used for propulsion

but characterized through in-house experiments. A total of 3 sensors and 2 computers make up the

avionics. Kalman filters are used for state-estimation, while linear controls are used to stabilize

the vehicle and track ship-deck motion. Based on the results presented, following conclusions

are drawn

1. A custom designed UAV provides the right flexibility to focus on vision-based tracking/landing

performance. Modern fabrication techniques such as 3D printing and CNC makes this

feasible.

2. The inner attitude stabilization loop has settling time of around 0.4 s, while outer trajectory

tracking loop settling time is 10 s. This maintains a timescale separation between translational

and rotational dynamics of the vehicle consistent with assumption of the designed control

system.

3. The tracking bandwidth of the designed control system is 0.15 Hz.

69



Chapter 4: Fiducial-Based Vision System

The quadrotor aircraft uses only a camera and computer vision algorithms to detect and

track ship-deck motion. This chapter describes the vision system in detail. In order it covers, the

camera hardware, calibration, fiducial based vision algorithm, and verification of position and

velocity measurements from the vision system.

4.1 Camera

The camera is a global shutter camera with fixed focus, high dynamic range and auto-

exposure. Global shutter was necessary to get images without motion artifacts. Auto-exposure

was necessary to prevent over and under exposed images when there are large changes in environmental

lighting. Fixed focus was chosen for repeatability and ease of calibration. High dynamic range

allows the sensor to properly perceive bright and dark areas of the scenes in sufficient detail at

the same time. The image sensor of the camera is 1920×1200