Design, Control, and Autonomous Navigation of Tilt

UNIVERSITY OF PATRAS

Design, Control, and Autonomous Navigation of Tilt–Rotor Unmanned Aerial Vehicles by Christos Papachristos

A Dissertation submitted for the degree of Doctor of Philosophy in the Department of Electrical & Computer Engineering

PhD Dissertation Nr: 330 September 21, 2015

ii

PANEPISTHMIO PATRWN

Tm ma Hlektrolìgwn Mhqanik¸n & Teqnologa Upologist¸n

Qr sto Papaqr sto © 2015 –

Me thn epifÔlaxh pantì dikai¸mato

PISTOPOIHSH H paroÔsa Didaktorik Diatrib me jèma:

“Sqediasmì ,

'Elegqo kai Autìnomh Plo ghsh Mh

Epandrwmènwn Enaèriwn Oqhmtwn me Rìtore Metaballìmenh

”

Klsh

tou

tou

QRHSTOU PAPAQRHSTOU

GRHGORIOU

, DiplwmatoÔqou

Hlektrolìgou MhqanikoÔ & Teqnologa Upologist¸n parousisthke dhmosw sto Tm ma Hlektrolìgwn Mhqanik¸n & Teqnologa Upologist¸n tou Panepisthmou Patr¸n thn 21h Septembrou 2015, kai exetsjhke kai egkrjhke apì thn akìloujh Exetastik Epitrop : Kmwn

Balabnh

, Kajhght kai Prìedro Tm mato Electrical and

Computer Engineering, University of Denver, Colorado, H.P.A. Euggelo Dermat

, Anaplhrwt Kajhght Tm mato Hlektrolì-

gwn Mhqanik¸n & Teqnologa Upologist¸n, Poluteqnik Sqol , Panepisthmou Patr¸n. Pètro

, Kajhght Tm mato Hlektrolìgwn Mhqanik¸n &

Groumpì

Teqnologa Upologist¸n, Poluteqnik Sqol , Panepisthmou Patr¸n. , Kajhght Tm mato Hlektrolìgwn Mhqanik¸n

Nikìlao KoÔsoula

& Teqnologa Upologist¸n, Poluteqnik Sqol , Panepisthmou Patr¸n. , Kajhght Sqol Mhqanolìgwn Mh-

Kwnstantno Kuriakìpoulo

qanik¸n, EjnikoÔ Metsobou Poluteqneou. Stamtio Mnesh

, Kajhght Tm mato Hlektrolìgwn Mhqanik¸n &

Teqnologa Upologist¸n, Poluteqnik Sqol , Panepisthmou Patr¸n. Ant¸nio Tzè

, Kajhght Tm mato Hlektrolìgwn Mhqanik¸n & Te-

qnologa Upologist¸n, Poluteqnik Sqol , Panepisthmou Patr¸n. Ptra, O Epiblèpwn

O Prìedro tou Tm mato

Ant¸nio Tzè

Gabri l Giannakìpoulo

iii

Declaration of Authorship I, Christos Papachristos, declare that this PhD Dissertation entitled, “Design, Control, and Autonomous Navigation of Tilt–Rotor Unmanned Aerial Vehicles” and the work presented in it are my own. I confirm that:

This work was done mainly while in candidature for the Doctor of Philosophy (PhD) degree at the University of Patras.

This PhD Dissertation has been submitted in its entirety exclusively for the Doctor of Philosophy (PhD) degree at the University of Patras, and no other qualification at this or any other institution.

Where I have consulted the published work of others, this is always clearly attributed.

Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this PhD Dissertation is entirely my own work.

I have acknowledged all main sources of help.

Where this PhD Dissertation is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.

Signed:

Date:

v

UNIVERSITY OF PATRAS

Abstract Department of Electrical & Computer Engineering ANeMoS Research Group Doctor of Philosophy Dissertation by Christos Papachristos

This Dissertation addresses the design and development of small-scale Unmanned Aerial Vehicles of the TiltRotor class, alongside their autonomous navigation requirements, including the fully-onboard state estimation, high-efficiency flight control, and advanced environment perception. Starting with an educated Computer Assisted Design-based methodology, a mechanically robust, customizable, and repeatable vehicle build is achieved, relying on high-quality Commercially Available Off-The Shelf equipment –sensors, actuators, structural components–, optionally aided by Rapid Prototyping technology. A high-fidelity modeling process is conducted, incorporating the rigid-body dynamics, aerodynamics, and the actuation subsystem dynamics, exploiting fistprinciple approaches, Frequency Domain System Identification, as well as computational tools. Considering the most significant phenomena captured in this process, a more simplified PieceWise Affine system model representation is developed for control purposes –which however incorporates complexities such as flight (state) envelope-associated aerodynamics, the differentiated effects of the direct thrust-vectoring (rotor-tilting) and the underactuated (body-pitching) actuation authorities, as well as their interferences through rigid-body coupling–. Despite the switching system dynamics, and –as thoroughly elaborated– their reliance on constrained manipulated variables, to maintain a meaningful controloriented representation, the real-time optimal flight control of the TiltRotor vehicle is achieved relying on a Receding Horizon methodology, and more specifically an explicit Model Predictive Control framework. This synthesis guarantees global stability of the switching dynamics, observance of state and control input constraints, response optimality, as well as efficient execution on low computational vii

power modules due to its explicit representation. Accompanied by a proper Lowand-Mid-Level Control synthesis, this scheme provides exceptional flight handling qualities to the aerial vehicle, particularly in the areas of aggressive maneuvering and high-accuracy trajectory tracking. Moreover, the utility of TiltRotor vehicles in the field of aerial robotic forceful physical interaction is researched. Exploiting the previously noted properties of the PieceWise Affine systems Model Predictive Control strategy, the guaranteedstability Free-Flight to Physical-Interaction switching of the system is achieved, effectively bringing the aerial vehicle into safe, controlled physical contact with the surface of structures in the environment. More importantly, employing rotor-tilting actuation –collectively and differentially– significant forces and moments can be applied onto the environment, while via the standard underactuated authority the vehicle maintains a stable hovering-attitude pose, where the system’s disturbance rejection properties are maximized. Overall, the complete control framework enables coming into physical contact with environment structures, and manipulating the enacted forces and moments. Exploiting such capabilities the TiltRotor is used to achieve the execution of physicallydemanding work-tasks (surface-grinding) and the manipulation of realisticallysized objects (of twice its own mass) via pushing. Additionally, the fully-onboard state estimation problem is tackled by implementing data fusion of measurements derived from inertial sensors and customdeveloped computer vision algorithms which employ Homography and Optical Flow calculation. With a proper sensorial setup, high-rate and robust ego-motion estimation is achieved, enabling the controlled aggressive maneuverability without reliance on external equipment, such as motion capture systems or Global Positioning System coverage. Finally, a hardware/software framework is developed which adds advanced autonomous perception and navigation capabilities to small-scale unmanned vehicles, employing stereo vision and integrating state-of-the art solutions for incremental environment building, dense reconstruction and mapping, and point-to-point collision-free navigation. Within this framework, algorithms which enable the detection, segmentation, (re-)localization, and mobile tracking –and avoidance– of a dynamic subject within the aerial vehicle’s operating space are developed, substantially increasing the operational potential of autonomous aircraft within dynamic environments and/or dynamically evolving missions.

Acknowledgements With every person, every PhD Candidate, it’s a different story; however we all areor-have been part of this year-long cycle of trying & failing to eventually succeed, investing huge amounts of effort only to experience countless disappointments before leading ourselves to the exceptional joy of accomplishment, and with each breakthrough serving only as a realization of the long & labyrinthian path laying ahead. From this rite of passage, we all come out changed, better-equipped and more determined to face the personal choices and scientific challenges which will allow us to play our smaller-or-larger roles in the history of humankind’s progress. It is however with great pleasure to traverse even the weariest of roads with others, supporters, advisors, companions, friends, and family –if not nearly impossible without them–. This is hence the time to address and grant a “thank you” where it is due. It has been a truly remarkable experience working alongside my PhD supervisor –but more significantly my advisor–, Professor Anthony Tzes. Since day one, there has never been a time when I did not feel encouraged when discussing over our research plans; his support for attempting even those “too-far-outside-thebox” ideas, has consistently been with me along my PhD path. And when the time for putting-those-feet-back-on-the-ground came, especially during the final preparation process, he was there to help put everything into order. I will forever remember Professor Peter Groumpos, whose aptitude in connecting science and the broader academia with a perspective on worldwide politics and the economy has also given me countless hours of talks, a source of inspiration about the impacts of scientific research on everyday life. Moreover it is important for me to mention Professor Kimon Valavanis, whose insightful contribution –even from continents afar– in robustifying the essence and content of this Dissertation is reflected in numerous points and passages throughout the full extent of this work. Additionally, I would like to thank the Professors of the “Seven-member Committee”, Vaggelis Dermatas, Nikos Kousoulas, Kostas Kyriakopoulos, and Stamatis Manesis for their well-posed and productive comments that helped revise this Dissertation to its current corroborated form. As a member of the ANeMoS group, it was an honor being beside and among friends and colleagues, partaking in everyday Lab research work and academic duties, sharing concerns and joys, helping and being aided when circumstances ix

called for it. Younger and older alike, everyone had a role to play throughout these years –and hence– became part of the complex process that produced this work: John Arvanitakis, Nikos Evaggeliou, Rania Tsilomitrou, Eleni Kelasidi, George Andrikopoulos, Dimos Tzoumanikas, Yannis Koveos, Yiannis Stergiopoulos, Stathis Kountouras, Kostis Giannousakis, and last but not least, Michalis Thanou whom we will always dearly miss. Moreover, it is important to mention those collaborations that “stuck” in time, Associate Professor George Nikolakopoulos and Assistant Professor Kostas Alexis whose endeavours in high-caliber research gave me the opportunity to partake in the formulation process –and be inspired by– the next generation of aerial robotics research objectives. A special “thank you” goes out to Kostas Alexis, whom I came to know as a PhD Candidate in this same Lab 4 years ago, I have collaborated with as an ETH-Z¨ urich Post-Doc researcher during the time since, and is now an Assistant Professor at the University of Nevada, Reno. You may be an endless source of professional motivation, but to the eyes of an “individual” you will always be the friend and companion, “Kostalexis”. It comes finally with great personal joy to dedicate this Dissertation to my family Grigoris and Rania, and Dimitris my younger brother. No matter the circumstances, no matter the size of the obstacle, they have always stood by my side throughout all these years, supporting me in every sense and manner. Through practice, they have taught me the most invaluable lesson: that the pain of remaining unyielding in support of another person’s endeavours will always fade under the shade of seeing that person grow to reach their goals.

Contents Certification –

iii

Pistopohsh

Declaration of Authorship

v

Abstract

vii

Acknowledgements

ix

List of Figures

xv

List of Tables

xxi

List of Algorithms

xxiii

Abbreviations

xxv

1 Introduction 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Scientific Objectives and Impact . . . . . . . . . . . 1.1.2 Socio-Economic Objectives and Impact . . . . . . . 1.2 State-of-the-Art . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Unmanned TiltRotor Vehicle Design . . . . . . . . 1.3.2 Unmanned TiltRotor Vehicle Modeling and Control 1.3.3 Aerial Robotic Forceful Physical Interaction . . . . 1.3.4 Autonomous Perception and Navigation . . . . . . 2 Flight and Physical Interaction Modeling 2.1 Non-Linear System Modeling . . . . . . . . . . . . . . . . 2.1.1 Flight Dynamics Model – Newton-Euler Formalism 2.1.2 Actuation Dynamics Model . . . . . . . . . . . . . 2.2 System Modeling for Control . . . . . . . . . . . . . . . . . xi

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xii

Contents Rotor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . Rotor-Tilt Mechanism Model . . . . . . . . . . . . . . . . . Considerations for Problem Simplification . . . . . . . . . . Hovering Flight Attitude Dynamics . . . . . . . . . . . . . . Hovering Flight Translational Dynamics . . . . . . . . . . . Interaction through Physical Contact Modeling . . . . . . . . Force Exertion on Rigid Environment Structures . . . . . . . Manipulation of Non-Rigid Environment Structures . . . . . Technical Discussion – Forceful Physical Interaction via RotorTilting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mode Conversion Modeling . . . . . . . . . . . . . . . . . . . Non-Linear Aerodynamics Modeling . . . . . . . . . . . . . . Considerations for Problem Simplification . . . . . . . . . . Modeling for Flight Mode Conversion Control . . . . . . . .

21 24 28 29 34 42 43 47

3 System Design 3.1 Hardware Design and Implementation . . . . . . . . . . . . . . . . . 3.1.1 Unmanned Aerial Vehicle Design . . . . . . . . . . . . . . . 3.1.2 Actuation Subsystem . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Sensorial Subsystem . . . . . . . . . . . . . . . . . . . . . . 3.1.4 End-Effector – Motorized Tool . . . . . . . . . . . . . . . . . 3.1.5 End-Effector – Pushing Manipulator . . . . . . . . . . . . . 3.1.6 Power System . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Software Design – Flight Control and Autonomous State Estimation 3.2.1 Embedded Computational Systems . . . . . . . . . . . . . . 3.2.2 Flight Control Software . . . . . . . . . . . . . . . . . . . . 3.2.3 State Estimation Software . . . . . . . . . . . . . . . . . . . 3.2.4 Software Architecture Integration . . . . . . . . . . . . . . . 3.3 Software Design – Human Operator Interface . . . . . . . . . . . . . 3.4 Complete System Architecture . . . . . . . . . . . . . . . . . . . . . 3.4.1 Architecture I . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Architecture II . . . . . . . . . . . . . . . . . . . . . . . . .

65 66 66 69 72 83 85 86 89 89 93 94 94 95 97 97 98

2.3

2.4

2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 Aerial 2.3.1 2.3.2 2.3.3 Flight 2.4.1 2.4.2 2.4.3

4 Autonomous State Estimation 4.1 Actuation Subsystem States . . . . . . . . . 4.1.1 Rotor Thrust . . . . . . . . . . . . . 4.1.2 Rotor-Tilt Angle . . . . . . . . . . . 4.2 Rigid-Body States . . . . . . . . . . . . . . . 4.2.1 Attitude and Heading, Accelerations 4.2.2 Altitude . . . . . . . . . . . . . . . . 4.2.3 Position and Velocity . . . . . . . . . 4.3 Computer Vision for Visual Odometry . . . 4.3.1 Pinhole Camera Model . . . . . . . . 4.3.2 Rotation-Compensated Optical Flow

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xiii

Contents 4.3.3

Homography Estimation for Orientation . . . . . . . . . . . 108

5 Flight and Physical Interaction Control 5.1 Actuation Subsystems Control . . . . . . . . . . . . . . . . . . 5.1.1 Rotor Thrust Control . . . . . . . . . . . . . . . . . . . 5.1.2 Rotor-Tilt Mechanism Control . . . . . . . . . . . . . . 5.2 Flight Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Attitude Control . . . . . . . . . . . . . . . . . . . . . 5.2.2 Feedforward Compensation Control . . . . . . . . . . . 5.2.3 Translation Control – Decoupled Dynamics-based . . . 5.2.4 Translation Control – Dual Authority Actuation-based 5.2.5 Complete Control Scheme . . . . . . . . . . . . . . . . 5.3 Physical Interaction Control . . . . . . . . . . . . . . . . . . . 5.3.1 Attitude Control and Feedforward Compensation . . . 5.3.2 Technical Work-Task Execution via Force Exertion . . 5.3.3 Object Manipulation via Thrust-Vectored Pushing . . . 5.4 Flight Mode Conversion Control . . . . . . . . . . . . . . . . . 5.5 Explicit Model Predictive Control . . . . . . . . . . . . . . . .

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6 Experiments and Simulations 6.1 Dual-Actuated Thrust Vectoring Flight Control . . . . . . . . . . 6.1.1 Position Hold while Hovering . . . . . . . . . . . . . . . . 6.1.2 Trajectory-Tracking Performance . . . . . . . . . . . . . . 6.1.3 Comparison of Rotor-Tilt-only and Dual-Actuated Thrust Vectoring . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.4 Augmented Teleoperation Responsiveness . . . . . . . . . . 6.1.5 Waypoint-Navigation Control Alternatives . . . . . . . . . 6.1.6 Aggressive Dual-Actuated Longitudinal Maneuvering . . . 6.2 Aerial Physical Interaction Control . . . . . . . . . . . . . . . . . 6.2.1 Forceful Work-Task Execution . . . . . . . . . . . . . . . . 6.2.2 Thrust-Vectored Pushing Manipulation . . . . . . . . . . . 6.3 Flight Mode Conversion Simulation Study . . . . . . . . . . . . .

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7 Autonomous Environment Perception and Navigation 7.1 Perception and Navigation Unit . . . . . . . . . . . . . . 7.1.1 Computational Power . . . . . . . . . . . . . . . . 7.1.2 3D Visual Perception . . . . . . . . . . . . . . . . 7.2 Environment Structure Representation . . . . . . . . . . 7.3 Autonomous Collision-Free Path-Planning . . . . . . . . 7.4 Generalized Dynamic Subject Detection and Tracking . . 7.4.1 Subject Detection Initialization . . . . . . . . . . 7.4.2 Singular Hull Detection . . . . . . . . . . . . . . 7.4.3 Viewable Aspect Feature Detection . . . . . . . . 7.4.4 Visual and Spatio-Temporal Loop Closure . . . . 7.5 Autonomous Mobile Subject Tracking . . . . . . . . . . .

171 . 171 . 172 . 173 . 176 . 176 . 177 . 178 . 178 . 183 . 186 . 187

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141 . 141 . 143 . 144 147 149 151 154 155 155 162 168

xiv

Contents 7.5.1 7.5.2 7.5.3

Environment Structure Representation . . . . . . . . . . . . 187 Autonomous Collision-Free Navigation . . . . . . . . . . . . 188 Experimental Study . . . . . . . . . . . . . . . . . . . . . . 190

8 Conclusions 8.1 Unmanned TiltRotor Vehicle Design . . . . . . . . 8.2 Unmanned TiltRotor Vehicle Modeling and Control 8.3 Aerial Robotic Forceful Physical Interaction . . . . 8.4 Autonomous Perception & Navigation . . . . . . . .

A Curriculum Vitae A.1 Biography . . . . . A.2 Research Projects . A.3 Publications . . . . A.3.1 Journals . . A.3.2 Conferences A.3.3 Workshops .

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Bibliography

Extended Abstract in Greek – Ekten Perlhyh Eisagwg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Knhtra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Suneisforè . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sqedash Mh Epandrwmènou Aeroskfou me Rìtore Metaballìmenh Klsh . . . . . . . . . . . . . . . . . . . . . . . . . Montelopohsh kai 'Elegqo Mh Epandrwmènou Aeroskfou me Rìtore Metaballìmenh Klsh . . . . . . . . . . . . . . Enaèria Rompotik Ulik Allhlepdrash . . . . . . . . . . . . . . Autìnomh Antlhyh kai Plo ghsh . . . . . . . . . . . . . . . . . . Sumpersmata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

207

221

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225 227 229 232

List of Figures 1.1

1.2 1.3

2.1 2.2 2.3 2.4 2.5 2.6 2.7

2.8 2.9 2.10 2.11 2.12 2.13

Historical evolution of Unmanned Aerial Systems: a) Hewitt-Sperry automatic airplane [6], b) V-1 flying missile [7], c) Predator (FixedWing) drone [8], d) Hummingbird (Vertical Take-Off & Landing) helicopter [9], e) Single-Wing (Fixed-Wing) UAV [10], f) MultiRotor (Vertical Take-Off & Landing) UAV [11]. . . . . . . . . . . . Indicative examples of manned aircraft with direct Thrust-Vectoring capabilities: a) Harrier Jump-Jet [12], b) V-22 Osprey TiltRotor [13]. Statistical trends in the field of UAVs: a) Number of United States Federal Aviation Administration (FAA) exemptions to companies that wish to fly Unmanned Aerial Vehicles (September 2014 – June 2015, source [18]), b) Google Trends [19] web search interest over the term “Drone” –civilian jargon for Unmanned Aerial Vehicles–. . The Tri-TiltRotor Unmanned Aerial Vehicle. . . . . . . . . . . . . . The Tri-TiltRotor’s design geometric characteristics. . . . . . . . . . Experimental setup for rotor speed -to- thrust mapping, and rotor dynamics identification. . . . . . . . . . . . . . . . . . . . . . . . . a) Frequency Domain identification process block diagram. b) Excitation -to- output coherence relation visualization. . . . . . . . . . a) Right rotor (i = 1) Frequency Domain identification. b) Right rotor speed -to- thrust nonlinear mapping. . . . . . . . . . . . . . . Experimental setup for digital servo command -to- rotor tilt angle mapping, and rotor-tilt dynamics identification. . . . . . . . . . . . a) Right rotor-tilt mechanism (i = 1) nonlinear digital command -to- tilt angle mapping. b) Right rotor-tilt mechanism actual & modeled response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hovering operation attitude control allocation principles: a) Roll-φ, b) Pitch-θ, c) Yaw-ψ. . . . . . . . . . . . . . . . . . . . . . . . . . . Frequency Domain-identified attitude roll-φ, pitch-θ, yaw-ψ dynamics. Translation control allocation principles in Free-Flight hovering operation: a) Longitudinal-x, b) Lateral-y, c) Vertical-z. . . . . . . . . Frequency Domain-identified translational longitudinal-x, lateral-y, vertical-z dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Interaction: Force exertion on a rigid environment structure surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Interaction: Force exertion on a free object for pushing manipulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

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List of Figures 2.14 Physical Interaction: Moment exertion authorities on a free object for rotating-manipulation. . . . . . . . . . . . . . . . . . . . . . . . 2.15 Physical Interaction: Technical advantage of tilt-rotor vehicles in forceful work-task execution. . . . . . . . . . . . . . . . . . . . . . . 2.16 Physical Interaction: Technical advantage of tilt-rotor vehicles in object pushing-manipulation. . . . . . . . . . . . . . . . . . . . . . 2.17 The Quad-TiltRotor tilt-wing conceptual vehicle design considered for Flight Mode Conversion modeling & control. . . . . . . . . . . . 2.18 The NACA2411 airfoil Lift and Drag coefficients interpolated data lookup tables visualization. . . . . . . . . . . . . . . . . . . . . . . . 2.19 The Quad-TiltRotor”s operating principles. . . . . . . . . . . . . . 2.20 Equilibrium path for a conversion-like maneuver, αx : 0Ĺ → 90 deg. 2.21 Visualization of the different modes modeled within the hybrid systems approach (the number at the bottom corner is the index of each N th PWA system). . . . . . . . . . . . . . . . . . . . . . . . . 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16

3.17 3.18 3.19 3.20

The Tri-TiltRotor vehicle’s CAD-based design. . . . . . . . . . . . . A QuadRotor vehicle, produced almost entirely employing 3D-printing technology, designed for autonomous navigation near human subjects. Rotor System: The BrushLess Direct Current motor and Electronic Speed Control circuit. . . . . . . . . . . . . . . . . . . . . . . . . . Rotor System: The fixed-blade propellers. . . . . . . . . . . . . . . The Rotor-Tilting Mechanism design. . . . . . . . . . . . . . . . . . The MTi-G Attitude & Heading Reference System device. . . . . . The Pixhawk autopilot, which offers Attitude & Heading Reference System functionality. . . . . . . . . . . . . . . . . . . . . . . . . . . The 3D-printable design for a vibration-isolating mount for the MTi-G AHRS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Global Positioning System: a) the MTi-G GPS antenna module, b) the Pixhawk external GPS & magnetometer module. . . . . . . . . Sonar ultrasonic rangefinder sensor: device and narrow beam pattern. Light Detection And Ranging rangefinder sensor. . . . . . . . . . . Optical incremental rotary encoder for rotor speed measurement. . . Accelerometer used for rotor-tilt angle measurement. . . . . . . . . Power supply voltage & current consumption measurement circuit. . Computer Vision sensors: a) the PS3 EyeToy camera, b) the Kinect RGB-D sensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wireles communication sensors: a) the WiFi USB module, b) the 433 MHz serial module, c) the remote-piloting transmitter & receiver module. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . End-effector with motorized grinder-tool design. . . . . . . . . . . . End-effector with active 1-DoF revolute manipulator design. . . . . Onboard electrical storage cell: 6-cell Lithium-Polymer battery. . . Power-over-Tether system for remote powering of a small UAV with increased power requirements. . . . . . . . . . . . . . . . . . . . . .

xvi

50 52 54 56 59 60 61

63 67 68 69 70 72 73 74 75 75 77 78 78 79 80 81

82 83 85 86 87

xvii

List of Figures 3.21 Low-level microcontroller for sensor measurement acquisition & actuation subsystem driving. . . . . . . . . . . . . . . . . . . . . . . 3.22 Pixhawk autopilot for sensor measurement acquisition, AHRS functionality, attitude control, & actuation subsystem driving. . . . . 3.23 Kontron pITx Single Board Computer for High-Level Control functionality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.24 ODROID U3 Single Board Computer for High-Level Control functionality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.25 ODROID XU-3 Single Board Computer for Autonomous Environment Perception & Navigation. . . . . . . . . . . . . . . . . . . . 3.26 Human operator groundstation: Graphic User Interface. . . . . . . 3.27 Hardware-Software system Architecture I. . . . . . . . . . . . . . 3.28 Hardware-Software system Architecture II. . . . . . . . . . . . . . 4.1 4.2 4.3 5.1 5.2 5.3 5.4 5.5

6.2

6.3 6.4

. 90 . 91 . 92 . . . .

93 96 97 98

Computer Vision-based Optical Flow illustration. . . . . . . . . . . 105 Illustration of the Optical Flow rotation-rate compensating algorithm.107 Computer Vision-based Homography estimation illustration. . . . . 109

Low-level control for Rotor actuation subsystem. . . . . . . . . . . Low-level MRAC rotor control experimental sequences. . . . . . . Low-level control for Rotor-Tilt actuation subsystem. . . . . . . . The Tri-TiltRotor’s Attitude Control structure. . . . . . . . . . . Experimental observation of rotor inflow introducing an acceleration phase lag over the translational dynamics. . . . . . . . . . . . 5.6 PieceWise Affine Representation of the dual-actuated longitudinalx dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 The complete Controller structure. . . . . . . . . . . . . . . . . . 5.8 Physical Interaction controller structure for Technical Work-Task execution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Physical Interaction controller structure for thrust-vectored Pushing Manipulation of a free large object. . . . . . . . . . . . . . . . 5.10 Quad-TiltRotor Flight Mode Conversion controller block diagram schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1

. 89

. . . .

113 114 115 117

. 119 . 124 . 128 . 133 . 134 . 137

Sequential frame-captures of aggressive longitudinal maneuvering experiment with the Tri-TiltRotor UAV while employing the DualAuthority Actuation strategy. . . . . . . . . . . . . . . . . . . . . . Position Hold for 2 min of Hovering Operation: a) Lag-Compensation Enabled, b) Lag-Compensation Disabled. The near-worst case position enclosing ellipsoid is sized 3 times the standard deviation in each DoF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Study for an advancing Timestamped Helical Trajectory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Study for an advancing Timestamped Square Trajectory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

142

143 145 146

List of Figure 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17 6.18 6.19

6.20 6.21

7.1 7.2 7.3 7.4 7.5

7.6

7.7 7.8

xviii

Experimental Longitudinal Step Sequence: a) Single-Authority LTIbased MPC Structure, b) Dual-Authority, PWA-based MPC Structure.148 Experimental Study for a Composite Trajectory via Tele-Operation. 150 Experimental Complex Step Sequence: Longitudinal & Lateral Reference Setpoint. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Experimental Complex Step Sequence: Longitudinal & Orientation Reference Setpoint. . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 Experimental 2 m Longitudinal Step Sequence: Dual-Authority, PWA-based MPC Structure. . . . . . . . . . . . . . . . . . . . . . . 155 The Tri-TiltRotor UAS in Physical Interaction-based technical worktask execution. Detail: The motorized-tool end-effector. . . . . . . . 156 Navigation, Docking, Technical Task Execution Maneuver . . . . . 158 Pulsating Force Control during UAS-based Technical Task . . . . . 159 Rotating-Moment Exertion in Technical Task: Side-Grinding . . . . 160 Significant Rotating-Moment Exertion in Technical Task: Oriented Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 The Tri-TiltRotor UAS in Physical Interaction-based pushing manipulation of an object / obstacle. Detail: The active end-effector. . 163 Straight Setpoint Manipulation . . . . . . . . . . . . . . . . . . . . 165 Diagonal Setpoint Manipulation . . . . . . . . . . . . . . . . . . . . 166 Sequential Setpoint Manipulation for Piecewise Trajectory . . . . . 167 Vertical Take-Off & Landing to Fixed Wing mode conversion controlled response. The last subplot depicts the switching among the different PWA modes as the response evolves over time. . . . . . . . 169 Fixed Wing to Vertical Take-Off & Landing mode conversion controlled response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Transition from a mode with αx = u = 0 to modes with α = 15 degrees. No forward velocity reference is tracked here: the vehicle accelerates as long as the airfoil drag does not compensate the forward force component due to the tilted rotors. . . . . . . . . . . 170 The add-on module for Autonomous Perception & Navigation. . . The hardware-synchronized Stereo Pair details. . . . . . . . . . . 3D-scene {x, y, z} flow and respective histograms. . . . . . . . . The Singular-Hull connection algorithm primary concepts. . . . . Qualitative Assessment of the Singular Graph-Connection Algorithm: a) 640x480 with RGB-D sensor, b) 320x240 with Stereo sensor, c) Performance for a fast-moving (running) subject. . . . . a) The Viewable Aspect Feature Detection algorithm block diagram, b) Illustration of matched keypoint w.r.t. different aspects and the subject contour. . . . . . . . . . . . . . . . . . . . . . . . The Visual and Spatio-Temporal Loop Closure Scheme . . . . . . The mobile tracking scenario Subject/UAS navigation spaces distinction, the Environment/Subject Forces, and the RRT ∗ -based trajectory generation primary concepts. . . . . . . . . . . . . . . .

. . . .

172 175 178 180

. 184

. 185 . 186

. 188

List of Figure 7.9

xix

Results of an experimental study: Visualization in the Rviz environment of the Robot Operating System . . . . . . . . . . . . . . . 191

Bþ.1 Istorik exèlixh Mh Epandrwmènwn Aeroskaf¸n Autìmata aeroskfh: a) Hewitt-Sperry [6℄, b) V-1 pÔraulo [7℄. Hmi-autìnoma aeroskfh pl rou megèjou : g) Predator aeroplno PSP [8℄, d) Hummingbird elikìptero KAP [9℄. Hm-autìnoma MEA mikroÔ megèjou : e) Mon s-ptèruga PSP [10℄, st) Polu-rìtoro KAP [11℄. Aeroskfh amèsou kateujunsiodìthsh dianÔsmato prìwsh : z) Harrier aeroskfo [12℄, h) V-22 aeroskfo me Rìtore Metaballìmenh Klsh [13℄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Bþ.2 a) Ulopohsh mikroÔ MEA me Rìtore Metaballìmenh Klsh (Leptomèreia: o mhqanismì elègqou klsh rìtora). b) Sqedash UpobohjoÔmenh apì Upologist . g) Sqedash kai ex’olokl rou ulopohsh bsei trisdistath ektÔpwsh enì exeidikeumènou tetrakìpterou gia asfal pt sh se mh isìpedo peribllon me gnwste domè kai anjr¸pinh parousa. . . . . . . . . . . . . . . . . . . . . . 224 Bþ.3 a) Arqitektonik me adraneiakoÔ aisjht re , upologistik ìrash kai Kentrik Monda Elègqou & Autìnomh Ektmhsh Katstash uyhl¸n upologistik¸n ikanot twn. b) Arqitektonik teleutaa teqnologa , me xeqwrist uposust mata elègqou se qamhlì kai uyhlì eppedo, kai th dunatìthta sundesimìthta me uyhlìterou epipèdou monda pou prosddei auxhmène ikanìthte antlhyh kai autìnomh plo ghsh . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Bþ.4 Anagn¸rish uposusthmtwn sto Pedo th Suqnìthta : a) Anagn¸rish Dunamik uposust mato epenerght Rìtora, b) Anagn¸rish Dunamik uposust mato epenerght Metabol Klsh Rìtora, g) Anagn¸rish Peristrofik Dunamik tou aeroskfou , d) Anagn¸rish Metaforik Dunamik tou aeroskfou . . . . . . . . 226 Bþ.5 Kat Tm mata Afinik dispash th dunamik tou aeroskfou gia th beltistopohsh elègqou pt sh mèsw UbridikoÔ ProbleptikoÔ Elègqou bsei Montèlou se mia eurea perioq tou fakèlou pt sh tou. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Bþ.6 a) 'Askhsh shmantik dÔnamh ep tou peribllonto mèsw Metabol Klsh Rìtorwn, en¸ to aeroskfo paramènei sthn perioq stajer (orizìntia ) ai¸rhsh . b) Mejodologa skhsh dÔnamh i) me upo-energopoioÔmeno aeroskfo , ii) me aeroskfo Metaballìmenh Klsh Rìtorwn, iii) sÔgkrish twn prohgoumènwn w pro thn apìrriyh mia realistik apìtomh diataraq se èna senrio metaknhsh barèo antikeimènou ep agn¸stou mh omoiogenoÔ dapèdou. . 228 Bþ.7 Enaèria Rompotik Fusik Allhlepdrash mèsw skhsh isqur¸n dunmewn kai rop¸n: a) Elegqìmenh metaknhsh mèsw ¸jhsh enì barèo antikeimènou, b) Efarmog mhqanikoÔ ergaleou apìxush epifneia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

List of Figures

xx

Bþ.8 Upologistik ìrash gia thn autìnomh ektmhsh th metaforik knhsh tou aeroskfou : a) Upologismì Optik Ro bsei Opik¸n Qarakthristik¸n, b) Exagwg qarakthristikoÔ dianÔsmato metaknhsh , g) Ektmhsh Omografa gia thn upobo jhsh twn algorjmwn ektmhsh prosanatolismoÔ tou aeroskfou . . . . . . . . . . . . . . 230 Bþ.9 UyhloÔ epipèdou autonoma: a) SÔsthma Antlhyh Peribllonto kai Plo ghsh , b) Pardeigma apostol akoloÔjhsh upokeimènou pou apaite trisdistath antlhyh, diaqwrismì upokeimènou apì to peribllon, anaparstash dom peribllonto , optik kai qwrik parakoloÔjhsh stìqou, plo ghsh qwr sugkroÔsei , dunatìthta epaneÔresh upokeimènou se perptwsh ap¸leia . . . . . . . . . . . . 231

List of Tables 3.1 3.2 3.3 3.4

TTR TTR TTR TTR

Mechanical Structure Parameters . . . . . . Rigid Body Dynamics Parameters . . . . . . Rotor (Motor-Propeller) Thrust Parameters Actuation Subsystem Dynamic Parameters .

5.1

Model Referencing I & Gain Scheduled PD-dD Attitude Controller Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

6.1 6.2 6.3

TTR Position Hold Error Metrics . . . . . . . . . . . . . . . . . . . 144 TTR Helical Trajectory Error Metrics . . . . . . . . . . . . . . . . . 146 TTR Square Trajectory Error Metrics . . . . . . . . . . . . . . . . . 147

7.1

Quantitative Assessment of 1-pass Singular Graph Detection . . . . 183

xxi

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

67 68 71 72

List of Algorithms 1

Explicit MPC Table Traversal Algorithm . . . . . . . . . . . . . . . . 139

2

Singular Hull Pixel-Graph Connection Algorithm . . . . . . . . . . . 179

xxiii

Abbreviations AHRS

Attitude & Heading Reference System

AIAA

American Institute of Aeronautics and Astronautics

AoA

Angle of Attack

AS

Aircraft System

BFF

Body Fixed Frame

CAD

Computer Aided Design

CFD

Computational Fluid Dynamics

CMake

Cross-Platform Make

CoM

Center of Mass

COTS

Commercially available Off The Shelf

CRC

Cyclic Redundancy Check

DoF

Degree of Freedom

EKF

Extended Kalman Filtering

EMF

Electro Motive Force

FAA

Federal Aviation Administration

FD

Frequency Domain

FF

Free Flight

FLANN

Fast Approximate Nearest Neighbor Library

FPV

First Person View

FW

Fixed Wing

GUI

Graphic User Interface

GPS

Global Positioning System

IMU

Inertial Measurement Unit

IR

Infra Red xxv

xxvi

Abbreviations LiDAR

Light Detection And Ranging

LiPo

Lithium Polymer

LTP

Locally Tangential Plane

LQR

Linear Quadratic Regulator

MEMS

Micro Electro Mechanical Systems

MPC

Model Predictive Control

MRAC

Model Referencing Adaptive Control

MutEx

Mutual Exclusion

NED

North East Down

OpenCV

Open Computer Vision

PCL

Point Cloud Library

PI

Physical Interaction

PNU

Perception & Navigation Unit

PoT

Power over Tether

PWA

Piece Wise Affine

PWM

Pulse Width Modulation

QTR

Quad Tilt Rotor

RANSAC RANdom SAmple Consensus RGB-D

Red Green Blue - Depth

ROS

Robot Operating System

RPV

Remotely Piloted Vehicle

RRT∗

Rapidly-exploring Random TreeStar

RTOS

Real Time Operating System

RVI

Rate Varying Integrator

RW

Rotary Wing

SAD-BM

Sum of Absolute Differences - Block Matching

SBC

Single Board Computer

SLAM

Simultaneous Localization And Mapping

SURF

Speeded Up Robust Features

TBB

Threading Building Blocks

TRL

Technology Readiness Level

xxvii

Abbreviations TTR

Tri Tilt Rotor

OFF

Object Fixed Frame

UAV

Unmanned Aerial Vehicle

UAS

Unmanned Aerial System

USB

Universal Serial Bus

VCP

Virtual Contact Point

VTK

Visualization Tool Kit

VTOL

Vertical Take Off & Landing

WFF

World Fixed Frame

Dedicated to my family for their unyielding support in my life’s endeavours.

xxix

Chapter 1 Introduction Unmanned Aerial Systems (UASs) have been the subject of significant attention over the past decade, attracting the focus of both the worldwide academic and research communities, as well as the interest of major technological key-players. From their historic roots –which lie in military research with respective target application scenarios in the beginning of the past century– over these recent years an astoundingly accelerating rate of technological breakthroughs, state-of-the-art scientific advances, and the ongoing refinement and commercialization of robotic systems production technologies, has brought forth a pivotal Technology Readiness Level (TRL) which paves the way for their ever-increasing utilization in civil usecases. With the term Unmanned Aerial System one commonly implies a high-level operational unit, possibly consisting of human-machine interfaces, equipment serving specialized functionalities, such as robotic manipulator arms [1], payload-carrying mechanisms for package delivery [2], video-cameras with specific surveillance capabilities –i.e. night or thermal vision [3], depth perception [4], etc.–, or even entire infrastructures of multiple robotic agents. At the basis of such a system lies the aerial robotic vehicle, commonly referred to as an Unmanned Aerial Vehicle (UAV). More formally, the UAV is defined according to the American Institute of Aeronautics and Astronautics (AIAA) [5] as “an aircraft which is designed or modified, not to carry a human pilot and is operated through electronic input initiated by the flight controller or by an onboard autonomous flight management control system that does not require flight controller intervention”. This indicates

1

Introduction

2

the long way flying robots have come to cover, from baseline-automatic missilelike systems –such as Hewitt-Sperry’s mechanical gyroscope-controlled un-piloted plane in World War I, and the more advanced German V-1 guided missiles in World War II–, to marvels of aerospace design which carry increased intelligence and guidance systems –such as the currently active Predator drone– enabling their fully autonomous navigation and/or wireless communication systems that allow for their operation as Remotely Piloted Vehicles (RPVs) via augmented tele-operated piloting. Whether smaller or larger, most of the common designs have been falling within the category of Fixed Wing–Aircraft Systems (FW–AS), or Rotary Wing–Aircraft Systems (RW–AS), the first aimed towards long-endurance high-speed flight exploiting the principles of aerodynamics for an aircraft with fixed airfoils traveling through the air –and thus generating the necessary lift force–, and the second capable of performing Vertical Take-Off & Landing (VTOL) and stable in-place hovering by employing smaller rotating airfoils –rotor blades– to support its weight while remaining airborne. In the same sense, UAV designs have mostly been influenced thus far by their manned counterparts, while leaving much room for the optimization of certain design aspects since the accommodation of a pilot onboard is no longer central to their operation, as well as for the implementation of differentiated methodologies to generate and controllably orient and direct the required lift force. One of the most particular aspects of this re-conceptualization process of flying vehicles, lies in the effort to make them smaller. Hence, the effect of –a significantly smaller– scale is introduced into the platform design principles, as illustrated in Figure 1.1. While an aerial vehicle’s target application / operation may still fall into the FW or the VTOL category, a fixed-wing aircraft can be completely rid of a fuselage –flying wing design–, or the typical helicopter’s mechanically complex swash-plated single large rotor, used to achieve thrust-vectoring via collective/cyclic blade pitching, can be replaced by a number of fixed rotors –multirotor design– which are coordinated (collective & differential thrusting) in order to control the aircraft’s motion. Moreover, the wide commercial availability of miniaturized –but high-quality– digital vision equipment (optical, night/thermal, depth cameras) has enabled their integration onboard UAVs, initially as a means to record video during flight, later on –and with high-bandwidth wireless streaming devices becoming available– as part of First-Person View (FPV) remote piloting systems, eventually exposing

3

Introduction Hewitt-Sperry

V-1

Predator

Hummingbird

Single-Wing

Multi-Rotor

Figure 1.1: Historical evolution of Unmanned Aerial Systems: a) HewittSperry automatic airplane [6], b) V-1 flying missile [7], c) Predator (FixedWing) drone [8], d) Hummingbird (Vertical Take-Off & Landing) helicopter [9], e) Single-Wing (Fixed-Wing) UAV [10], f) Multi-Rotor (Vertical Take-Off & Landing) UAV [11].

their potential to be fully integrated into the autopilot design and help to achieve fully autonomous flight, non-reliant on Global Positioning System (GPS) support. With a vast area of applications demanding such increased levels of operational autonomy, and –nonetheless– the capacity for environment perception via visual means, either to achieve obstacle avoidance in non-flat static environments, or the dense reconstruction of three-dimensional structures of interest in inspection operations, or even for the safe operation within dynamically changing environments populated by mobile agents –human or otherwise–, the incorporation of such capabilities onto small-scale airborne agents lies at the forefront of current robotics research priorities.

1.1

Motivation

As noted, there exists a strong connection between UAVs and their manned counterparts; a previously unmentioned category of aircraft design is that of aerial vehicles that possess the capacity to directly manipulate the orientation of their onboard-generated thrust –this is mentioned as Thrust-Vectoring–. Examples of such aircraft exist in military aviation, such as the ones illustrated in Figure 1.2, which employ either controllable surfaces –vanes– to re-orient the pressurized airstream from their engines, or change the orientation of their complete rotor

4

Introduction

subsystems relative to their body; the latter category is commonly referred to as TiltRotors. Such systems have been introduced as a means to cover the operational necessities of a dual-envelope aircraft, namely a vehicle that performs both Fixed Wing flight and Vertical Take-Off & Landing, by properly redirecting its thrust vector –via airstream outlet or rotor reconfiguration– as per a “normal” singleenvelope aircraft. In a similar direction, a subset of UAV-related research –and eventually certain commercial-grade platforms– coincided with this field, mostly focusing on the repurposing of a multirotor’s design to accommodate aerodynamic surfaces and an actuation mechanism capable of producing the two desired rotor configurations –the vertical one for Vertical Take-Off & Landing and the nearlongitudinal one for Fixed Wing flight–.

Harrier

V-22 Osprey

Figure 1.2: Indicative examples of manned aircraft with direct ThrustVectoring capabilities: a) Harrier Jump-Jet [12], b) V-22 Osprey TiltRotor [13].

The foremost part of this vision is dominated by approaches aiming for UAVs capable of performing as well as full-scale piloted aircraft. Initially, this implies that the vehicle additionally to operating reliably at each envelope configuration, should “transition” between them in a way that maintains flight stability; this view of an such an aircraft’s increased actuation potential is however inherently limited, as it eventually regards intermediate flight envelopes and their respective –more complex– system dynamics as a problem to be tackled. Additionally, the typical train of thought follows up to the point where unmanned aerial platforms achieve a set of desired flight characteristics levels, such as robustness to external disturbances, payload capacity for carrying sensorial equipment, operational endurance, etc., thus primarily regarding the UAV as an eye-in-thesky [14], or at most a means to grab-and-carry [15] smaller objects. However, the extensions for a robotic agent which is naturally-endowed in reaching high-altitude locations but also capable of coming into physical contact with structures in the environment, and effectively manipulate or –in general– produce a drastic physical

Introduction

5

change upon them, can open up a new perspective and a vast application field for aerial robots. It should be mentioned that already a large amount of technical work-tasks –such as maintenance and inspection-through-contact operations– on infrastructure assets are executed by human technicians carried on manned VTOL aircraft such as helicopters. To re-envision aerial agents of small-scale capable of undertaking various grades of work-tasks is to re-invest in a wide field of aircraft research –including their design– and re-think how such a robot will no longer avoid structures as obstacles constraining its free navigation airspace, or consider the effect of external forces as a disturbance onto its free-flight dynamics, but purposely utilize its actuation authority to come into safe physical contact with its environment and enact forces and moments upon it. Finally, the autonomous operation of aerial robots is typically considered in terms of self-perception, i.e. their capacity to estimate their own orientation and rotation with respect to the Earth’s frame –the attitude pose–, as well as their translating motion in the same inertial frame –termed as ego-motion estimation–. To this purpose, apart from electronic inertial measurement systems, cameras are used to procure visual feedback of their environment and extract the required information, relying on the perception of optical motion –visual odometry–, or on the localization of distinct visual features and the estimation of the camera transformation that produces their configuration onto the captured image frame –Simultaneous Localization And Mapping (SLAM)–. In this sense, unmanned agents have primarily been called to utilize visual information of their environment in order to deduce information about themselves, which –as logically follows– also leaves much potential to be explored in the area of autonomous aerial robotic operation.

1.1.1

Scientific Objectives and Impact

It is initially highlighted that as directly-actuated thrust-vectoring aircraft of the full (manned) scale represent a small subset of the world fleet, similarly a significant lack of such designs characterizes the UAV scientific and economic market. Thus, the investigation of the actuation design for a TiltRotor vehicle, which has to cover set of operational considerations, as well as its actual implementation and its eventual control in order to achieve efficiency and accuracy, consists a significant initial focus. In this process, the requirements for small-scale solutions which however have to operate reliably and provide a level of insight to the UAV regarding

Introduction

6

its actuation level –i.e. an actuator-specific sensorial setup which will provide operational feedback, to be used for real-time control or in order to understand the low-level dynamics which eventually govern the vehicle’s actuation potential–, are tackled. Additionally, the complete vehicle design is developed accordingly, –that is– upon the principle for an aerial robot which will exploit its direct thrustvectoring (rotor-tilting) authority to achieve a number of purposes. As a start, the free-flight maneuvering potential of such a class of UAVs is examined in an approach that begins from a fundamental basis: how such an increased actuation authority can impact on –and/or benefit– flight performance, given the characteristics of the associated: a) actuation dynamics, b) their effect on the vehicle’s flight dynamics, c) the interferences between them through rigid-body coupling, and d) the correlation of their efficiency to a dynamic state envelope. Apart from the requirement for a first-principle modeling of the system, the eventual objective is to synthesize and implement a highly efficient –optimal– control strategy which exploits that highly complex knowledge of the system at an appropriate level of fidelity. To this purpose, computational –multiparametric optimization– tools are integrated into the control formulation process, with attention to the necessity for real-time execution on the UAV’s onboard available computing resources. Consequently, the field of aerial robotic physical interaction is investigated regarding the benefits that arise from employing TiltRotor vehicles. To enable such a utility for UAVs in general, the initial problem to be addressed is the purposeful contact of a flying robot with a structure in its environment while retaining operational safety. The switching system dynamics in such an application have to be handled with a control scheme that guarantees system stability between the switching dynamics modes, ensures non-violation of certain safety-related system constraints, and achieves control and response optimality; all these while also being capable of real-time execution onboard a small-scale UAV. Equally importantly however, once stable physical contact is achieved, the vehicle’s longitudinal thrust vectoring authority –either via rigid body rotation or more interestingly via rotor-tilting– no longer plays the role of free-flight navigation, but becomes a means of exerting forces & moments onto the environment. Hence, this feature is examined thoroughly as per its potential to grant the UAV the capacity to actively manipulate and/or drastically change structures in its surroundings.

Introduction

7

Eventually, for a truly autonomous class of aerial vehicles to be attainable, the operational necessity of fully-onboard 6-Degrees-of-Freedom (DoF) [16] state estimation is a prerequisite. The scientific objective here is to synthesize a high-precision scheme for translational motion estimation, relying on data fusion between inertial and computer vision-derived measurements, which however remains computationally efficient in its execution and robust under aggressive maneuvering conditions. Apart from the baseline –not simplistic however– ego-motion estimation capabilities to be achieved, autonomy within realistic non-flat spaces populated with cluttered objects / obstacles requires perception of the environment’s threedimensional structure and the means to ensure collision-free navigation. On top of that, considering operation within a non-static map, with dynamic entities within it –or even missions strongly connected to mobile subjects– indicates the necessity for the UAV to be capable of at least identifying or even tracking such other entities within its operating map, while performing all the previously mentioned tasks, i.e. environment structure perception through vision and collision-free navigation. Such an increased level of advanced perception capabilities comes with numerous challenges, especially considering its eventual implementation onboard a small-scale aerial robot.

1.1.2

Socio-Economic Objectives and Impact

In general, autonomous robots are entering a state of maturity, slowly increasing the realization that the potential for their widest possible integration into everyday economic and social activities is immense. A more particular case are Unmanned Aerial Vehicles; their airborne nature allows robotic applications to intervene where ground-based systems and humans find it difficult –or more importantly unsafe and/or economically inefficient– to reach, and with the current state of technological maturity and large-scale production capacity, the numbers at which they can become available is essentially limited by application requirements. It is noteworthy how this worldwide interest is reflected in the web trends, as well as in the corporate interest, both indicatively illustrated in Figure 1.3. It should also be noted how the booming growth of such unmanned systems has even surpassed formal societal and economic structures, bringing together amateurs with their own personal fleet to carry out civil activities [17].

Introduction

8

Figure 1.3: Statistical trends in the field of UAVs: a) Number of United States Federal Aviation Administration (FAA) exemptions to companies that wish to fly Unmanned Aerial Vehicles (September 2014 – June 2015, source [18]), b) Google Trends [19] web search interest over the term “Drone” –civilian jargon for Unmanned Aerial Vehicles–.

At an initial level, achieving complete operational autonomy –with all flight control and state estimation processes capable of being robustly and efficiently executed onboard the UAV– and releasing aerial robots from human-operator reliance, can bring about a higher level of aerial robotic penetration into crucial applications. Relative examples can be visual data gathering operations, such as precision agriculture –crop monitoring [20]– or industrial –equipment & installations inspection [21]– with UAVs permanently situated in local operation bases, and being deployed in inspection cycles, significantly taking down costs and potentially helping identify and prevent malfunctions and issues through regular scheduling. Alternatively, their autonomous deployment on a per-request basis –and potentially in swarms– such as in emergency-response situations [22, 23] can prove life-saving considering the respective deployment times required for human personnel, and the low availability in manned aerial means, which often have to share the role of both intervening for rescue, but also inspecting and identifying threats and sensitive situations; the latter application field can be more efficiently

Introduction

9

addressed by aerial robots. It is highlighted here, that such operations cannot always be assumed to require only an over-the-sky view; UAVs eventually have to be capable of deployment within cluttered –and possibly dynamic– environments, and autonomously navigate through them safely in a collision-free manner, and avoid –or potentially in emergency response situations follow– mobile subjects of interest. Followingly, enabling more advanced designs –such as TiltRotors– to be implementable in small scales, but retaining operational robustness and accuracy, while minimizing mechanical complexity, serves the purpose of bringing their applicationrelated advantages to a larger audience. Apart from investigating the flying-only potential of such vehicles however, focusing on their utility in aerial robotic physical interaction, and –as demonstrated– their capacity to retain a safe disturbancerejecting state envelope while being capable of enacting significant forces and moments upon structures in the environment, indicates how Unmanned Aerial Systems are indeed capable of undertaking realistic physical work-tasks. Considering the application potential for such systems, which comes in the form of micromaintenance and inspection [24, 25] tasks at non-easily accessible remote locations, without the need for scaffolding or the deployment of large and potentially unsafe manned aerial means to enable human/technician intervention –and only in cases where infrastructure density allows the presence of e.g. manned helicopters, it is considered that UAVs have an even larger field of operations, where they can be useful. Especially regarding that the tasks of inspection, repair, and maintenance in the infrastructure sector amount to significant financial burdening [26–29], and equally importantly pose human-life and facility asset hazards [30], the possible undertaking of a subset of such tasks by aerial robots which are capable of working in the place of a technician while ensuring safety and repeatability, consists a highly-prospective application target.

1.2

State-of-the-Art

Referring to the field of direct thrust vectoring design for small-scale aircraft, standards are yet to be set; especially considering that many research –and commercial– targets approach its utility in performing certain feats in VTOL flight, such as translational maneuvering at an arbitrary attitude pose [31], or as a means to fly using only two rotors –bi-rotor design[32, 33]–, the standard servomotor-&-hinge

Introduction

10

design approach is followed at the actuation level, which is familiar for its implementation in the manipulation of airfoil control surfaces. This offers however a naturally constrained range of rotor-tilting actuation. On the other hand there exist examples of this class of aerial vehicles which employ full tilting-range mechanisms, which are however implemented with an end-to-end approach in mind (for VTOL to FW flight mode rotor re-orientation) and which manipulate both of the vehicle’s lateral rotors together [34], with differential-tilting operation disabled while also employing mechanisms which allow some natural slacking –such as gear-trained ones– in intermediate regions (at intermediate tilt angles). Additionally, even in cases where TiltRotors are implemented as dual flight-envelope aircraft [35] it is common to regard their rotational dynamics in an attitude-pose regulation sense, i.e. the fact that the aerial system retains its original underactuated control authority additionally to a direct-thrust vectoring actuation one, is not considered in an approach aiming for control and response optimality. Moreover, and focusing once again on the subject of optimality, the progresses which have been achieved in the field of multiparametric optimization and their application in Model Predictive Control [36], have come to enable the synthesis and execution of highly complex control laws that incorporate and account for the complex dynamics associated with a UAV’s flight envelope, and equally importantly allow their real-time execution, which is a crucial feature specifically in the case of multirotor VTOL aircraft which are characterized by particularly fast and inherently unstable flight dynamics. Regarding the field of autonomous state estimation, a wide number of commercial solutions for inertial measurement and attitude & orientation estimation have become readily available over the recent years; however, a large number of unmanned aircraft –in personal use, in research, and/or commercial applications– rely on external means (GPS or specialized external localization systems [37]) to fly without a human pilot. Approaches based on computer vision vary, ranging from simplistic optical flow modules [38, 39], to mid-range ones which employ a more sophisticated approach [40] closer to the formulation of the camera model equations, and eventually some very recent examples of high-end sensors [41] which implement SLAM algorithms in order to increase positional accuracy –as compared to visual odometry-based approaches– to the benefit of inspection operations. Finally, the research area of aerial robotic manipulation is one that steadily gains attention; since the initial vision of UAVs capable of coming into contact with their

Introduction

11

environment [42, 43] to apply non-destructive testing sensors onto the surface of industrial equipment [24], potentially equipped with miniaturized manipulators [44] to more efficiently carry out such tasks, much progress has been made. It is indicative how until now aerial robots have been demonstrated to snatch-lift and carry small objects employing either minimal-design grippers [45] and nature-inspired methodologies [46], or even robotic manipulator arms [47], achieve cooperative object transportation [48] and manipulation [49], or execute inspection-throughcontact flight paths –trajectories– while remaining in stable physical contact with their environment [50]. There remains a large field of industrial-style operations which has remained unaddressed however, which requires more than the capacity for manipulation of lightweight loose objects (grasping, lifting) or inspecting through interfacing contact; namely operations such as drilling, bolting, cutting and grinding. The key characteristic in these is the requirement for controlled large force exertion –of a magnitude even potentially up-to-scale with a UAV’s own weight-lifting force–, while maintaining safe and reliable operation. Relative efforts have currently come into activity [51], motivated by the new-found interest in aerial robotic work-task execution, mainly to address micro-maintenance operations which is a highly prospective field, as mentioned previously.

1.3

Contributions

The work conducted for the purposes this PhD Dissertation has been motivated by the challenges and opportunities mentioned in Section 9, and includes contributions in a number of fields, which have been published in peer-reviewed scientific journals and international conferences.

1.3.1

Unmanned TiltRotor Vehicle Design

A number of implementations have been developed, both respectively to the actuation level design that enables rotor-tilting on small-scale unmanned aircraft –with a robust and accurate mechanism that allows a full range of rotor-orientation angles–, as well as with respect to the aerial vehicle’ design, ranging from birotor to tri-rotor configurations [33, 52–55] and with various levels of actuating components. Additionally to these, with 3D-printing becoming a widely available state-of-the-art, this technology was utilized for the purposes of producing

Introduction

12

aerial robotic designs, from the separate / add-on component level for specific operational purposes [56–60], to the production of entire UAVs [61, 62]. Alongside the hardware-level design of such a vehicle, a field of significant importance where focus was applied is the software architecture and the necessary computing resources that enable the high-level functionalities of the produced UAVs. Over the course of the Dissertation low [33], to mid [54], to high-level [55] architectures were added to the autonomous system’s design, leading eventually up to the stacking of high-end resources and frameworks [61, 63] that integrate a number advanced autonomous operation capabilities.

1.3.2

Unmanned TiltRotor Vehicle Modeling and Control

An initiating point in order to achieve advanced control capabilities was the modeling of the vehicle’s attitude and baseline translational [53, 54, 64–66] flight dynamics, while focusing on realistic phenomena typically disregarded for the purposes of conventional VTOL operation –such as the aerodynamic forces appearing in highvelocity flight– was employed to derive modeling approaches of increased fidelity [55, 67] (coming at the cost of increased complexity). Consequently, with a proper set of senseful modeling simplifications, model-based control syntheses were applied in order to achieve high-quality autonomously controlled flight. Starting from simple output-feedback schemes [68], and moving on to Linear Quadratic Regulation (LQR) approaches [69, 70], and eventually to complex but computationally efficient Model Predictive Control (MPC) strategies [55, 71, 72], the objectives of constraint-guaranteed optimal –and robust– control were effectively demonstrated to be feasible onboard such a class of aerial vehicles.

1.3.3

Aerial Robotic Forceful Physical Interaction

Relying on the powerful control framework employed for free-flight navigation, which can generate complex control laws that guarantee global stability of a system with switching dynamics, the aerial vehicle at a first level became capable of safely coming into physical contact with its environment. More importantly however, it was demonstrated that the additional direct thrust-vectoring actuation principle

Introduction

13

of TiltRotor vehicles can be exploited to generate a significant forward-exerted force and rotating moments, while the attitude is being regulated near a hovering attitude pose via the standard underactuated control allocation [56, 73, 74]; therein the system’s disturbance rejection properties where shown to be at their strongest point. Following these deductions the TiltRotor vehicle was employed in order to achieve: a) pushing-manipulation of a heavy obstacle –of twice the UAV’s own mass– laying on the ground [73–75], and b) application of a motorized tool onto a rigid environment surface to conduct the work-task of grinding [56], both tasks requiring forces and moments up-to-scale with the vehicle’s own weight-lifting force in order to be successfully executed. It was thus –experimentally as well– validated that direct thrust-vectoring onboard UAVs can effectively serve the requirements for aerial robotic forceful physical interaction, an application not typically considered as part of a TiltRotor’s operational envelope.

1.3.4

Autonomous Perception and Navigation

Initially, the main level of autonomy approached was the vehicle’s fully-onboard state estimation capabilities. The developed subsystem relies on data fusion from inertial sensors and computer vision, and employs non-specialized hardware and an open-source framework [54, 55], while remaining platform-agnostic –not depending on modeling assumptions regarding the specific type of aerial vehicle employed– which makes it an expandable solution. More specifically, it is based on visual odometry via feature-based Optical Flow calculation and on Homography estimation, while applying any transformations and rotation-compensations employing the camera model equations as necessary, and achieves accurate self-localization results (especially considering its non-closed-loop nature), while more importantly being capable of reliably and robustly providing translational velocity estimations at very high rates. Regarding the autonomous external environment perception and collision-free navigation capabilities developed for the purposes of this Dissertation, the platformagnostic approach was also followed. More specifically, a separate module was implemented, equipped with a stereo-vision sensor –while also allowing evaluation with commercially-available depth sensors–. The developed framework was shown to achieve real-time three-dimensional perception of the environment, and

Introduction

14

building upon this, the necessary algorithms that enable the detection and visual & spatio-temporal segmentation & tracking of dynamic entities within the viewable 3D-scenery were developed. Additionally to those, the framework allows the fully-onboard generation of collision-free navigation trajectories within an incrementally-built environment map. Hence at the fully-integrated level, an aerial robotic agent was developed, shown to be capable of fully autonomously: a) perceiving the structure of its surroundings, b) navigating them safely, and c) acting upon a dynamically-changing environment. The modularity of this framework also allows the implementation of numerous other application-oriented high-level activities, such as inspection [76] and dynamics-based collision-free navigation [77].

Chapter 2 Flight and Physical Interaction Modeling The system modeling process follows a bottom-up approach: Employing the actuation subsystem dynamics, and proceeding to the integration of the generated driving forces and moments into a rigid-body formulation of the aerial vehicle flight dynamics, and eventually incorporating those aerodynamics of meaningful effect to the flight envelope, a non-linear model of high fidelity is derived. This is the baseline level of modeling, which is particularly useful when employed throughout the simulation processes for the initial evaluation of any developed control schemes. Followingly, the derived high-fidelity models are examined with respect to their properties, emphasizing on their reformulation in a form more appropriate for the development of mathematically more simplified control structures, to enable the application of computationally cumbersome control methodologies –which however come with multiple operational advantages crucial to unmanned robots of aerial nature–. Hence, the modeling-for-control process is of equal importance to the development of a high-quality control scheme. Initially, it is mentioned that the two basic coordinate systems utilized are the: the B Body-Fixed-Frame (BFF), which is attached onto the Unmanned Aerial Vehicle’s (UAV) Center-of-Mass (CoM) and rotates & translates along with its motion, and the W World-Fixed-Frame (WFF) which is assumed as a flat earth frame –i.e. a Locally Tangential Plane (LTP)–. The common aircraft notation is utilized, where: 15

16

Flight and Physical Interaction Modeling • Ω = [p, q, r]T marks the BFF-based angular rotation rates, • Θ = [φ, θ, ψ]T marks the WFF-based rotation angles, • U = [u, v, w]T marks the BFF-based velocities, • X = [x, y, z]T marks the WFF-based position. Additionally, a set of assumptions is the basis for the entire modeling process: • The aerial vehicle’s structure is supposed rigid. • The propellers’ structure is supposed rigid. • The aerial vehicle’s BFF origin coincides with its CoM.

2.1

Non-Linear System Modeling

As mentioned the tiltrotor aerial vehicle is initially approached on first principle, employing the Newton-Euler formalism and exploiting information derived from high-fidelity Computer-Aided Design (CAD) software-based design & modeling, as elaborated in Section 3.1.

2.1.1

Flight Dynamics Model – Newton-Euler Formalism

The Newton-Euler formulation is used: ΣFB and ΣMB are the sum forces and moments expressed in the aerial vehicle’s BFF, I is the rigid-body moment of inertia matrix, R B→W is the BFF→WFF translational velocities transformation matrix [16], and JB→W is the Tait-Bryan rotational rates transformation matrix [16]. Hence, the vehicle’s dynamic equations are captured by:

˙ + Ω × (mU) ΣFB = mU

ΣMB = IΩ˙ + Ω × (IΩ)

(2.1) (2.2)

˙ = R B →W U X

(2.3)

˙ = JB →W Ω . Θ

(2.4)

17

Flight and Physical Interaction Modeling

Figure 2.1 illustrates the Tri-Tiltrotor aerial vehicle, annotated with the utilized World Fixed Frame W = {x, y, z}, i.e. the North-East-Down [16] Locally Tan-

gential Plane, the B = {Bx , By , Bz } Body Fixed Frame, and the employed rotor

& rotor-tilting mechanism numbering, namely the {1, 2, 3} → {right, lef t, tail} correspondence.

Bx

By

E

N

Bz

D

F1 F2 +ω2

-ω1

+γ1

+γ2

F3 +γ3 +ω3 Figure 2.1: The Tri-TiltRotor Unmanned Aerial Vehicle.

Regarding the active forces on the vehicle’s CoM, GB is the BFF-expressed gravitational force, FiB are the BFF-expressed rotor thrust components –for rotors i → {1, 2, 3}–, and DfB marks the fuselage drag force due to the relative airflow:

18


h

GB = (R B→W )−1 0 0 m g h

FiB = Ri→B 0 0 −Fi h

DfB =

iT

iT

g ≃ 9.81 m/s2

,

(2.5) (2.6)

−σ(u) Ku Au u2 −σ(v) Kv Av v 2 −σ(w) Kw Aw w 2

Fi = kF,i ωi2 ,

iT

(2.7) (2.8)

where the vertical positive direction is consistent with the North-East-Down (NED) aircraft notation –i.e. positive points downwards–, and Ri→B denotes the transformation from the i-th tilting rotor frame to the BFF. In (2.7), σ denotes the signum function and {Au , Av , Aw } represent the rigid body cross-sectional area w.r.t. the

BFF motion axes. The drag parameters {Ku , Kv , Kw } can be initially estimated

via CAD-software modeling, or –for operation at low translational speeds– by employing system identification and relying on the simplified system model of the following Section 2.2. Regarding the active moments with respect to the aerial vehicle’s CoM, there exist the rotor thrust moments MiB , the rotor drag moments MD iB , the rotor gyroscopic moments MG iB which appear during tilting, and the adverse reaction moment due to rotor-tilting ViB , while the body drag forces DfB are considered to be applied on the CoM and thus enact no moment:

MiB = FiB × riB riB =

(

(2.9)

[ dix + h1,2 sin(γi )

[

−diz − h1,2 cos(γi ) ]T , i = {1, 2} (2.10) h3 sin(γi ) −diz − h3 cos(γi ) ]T , i=3 diy

dix h

MD iB = Li→B 0 0 −σ(ωi ) kF,i ωi2 h

MG iB = Li→B Ir,i ( 0 −γ˙ i 0 h

MG iB = Li→B Ir,i ( 0 0 −γ˙ i ViB 3 X i=1

=

(

0

−[

−[ IT,i γï

iT

iT

iT

(2.11)

h

× 0 0 ωi h

× 0 0 ωi

−IT,i γï − IT,j γ¨j 0

0 ]T 0

]T

iT

iT

) , i = {1, 2}

(2.12)

) , i=3

(2.13)

, i = {1, 2} , j = {2, 1}

,

i=3

˙V , ViB = diag IB,3 , IB,1 + IB,2 , 0 ∆Ω h

i

where diag denotes a diagonal matrix of the in-bracket elements.

(2.14) (2.15)

19


h1,h2

CoM

h3

d1z,d2z

d3z

CoM

d1y

d2y

Figure 2.2: The Tri-TiltRotor’s design geometric characteristics.

Also, riB is the i-th rotor’s thrust moment arm with respect to the CoM, which is a function of the geometric characteristics illustrated in Figure 2.2: a) dij which marks the j → {x, y, z}-component of the geometric distance from the CoM to

the i-th rotor-tilt axis, b) hi which marks the geometric distance from the i-th rotor-tilt axis to the i-th rotor’s hub (the apparent point where the thrust force is applied), and c) the rotor-tilt angles γi as in (2.10). These are illustrated for clarity

in Section 3.1.1, accompanied by their actual sizings. Moreover, Li→B denotes the transformation from the i-th rotor frame (tilted by γi ) to the BFF. Additionally, Ir,i is the i-th rotor’s moment of inertia; via moment conservation during rotortilting (2.15), the additional angular accelerations ∆Ω˙ V are induced by the adverse reaction moments, where IT,i is the i-th complete rotor-tilting mechanism (rotor, servo and base) moment of inertia and IB,i is the UAV rigid body moment of inertia excluding the i-th rotor-tilting mechanism –both calculated with respect to the rotor-tilt axis–.


2.1.2

20

Actuation Dynamics Model

The actuation systems incorporated onto a tiltrotor aerial vehicle are based on DC motors due to the requirement for operation relying on DC power sources –i.e. batteries–, whose established mathematical formulation is:

dimot = umot − Rmot imot − ke ωmech dt dωmech = Tmech − Td , Jmech dt Lmot

(2.16) (2.17)

which for small motors of low coil inductance can be approximated by the differential equation:

Jmech

dωmech kmot k2 umot , = − mot ωmech − Td + dt Rmot Rmot

(2.18)

It is noted that both the servomotors and the brushless motors which rotate the propellers, are driven by their own separate embedded controller boards, allowing only the manipulation of a setpoint command value, via a digital interface. Regarding the rotors, the setpoint command is the angular rotation speed ωir , while for the case of the servos it is their absolute angular rotation Ωri , where the r superscript marks the reference value. A more elaborate analysis of the actuation subsystems’ respective principles of operation is given in the following section, correlated with the selected modeling methodology.

2.2

System Modeling for Control

The presented modeling process aims to derive the most meaningful representation of the system, in order to devise an efficient control strategy for a Tri-TiltRotor aerial vehicle. A bottom-up approach is followed, starting from the actuator level –as for a realistic system the employed actuators are naturally bandwidth-limited– and integrating those with the platform’s flight dynamics.

21


2.2.1

Rotor Model

The rotors are driven by BrushLess DC motors (BLDC), with dedicated Electronic Speed Control (ESC) circuits which are essentially integrated switching power supplies which perform closed-loop control of the BLDC motor. Hence, by using the term rotor, the complete actuation subsystem consisting of: a) the BLDC motor, b) the fixed-pitch propeller, and c) the ESC circuit, is implied. While the nonlinear equations of motion for the DC motor (2.18) can be rather complex, in modeling their dynamics for small-scale systems focus is commonly put on their input-output relationship, which can be expressed in the linearized form:

δω −Km (1 + τa s) , (s) = 2 δTm (1 + τm s)(1 + τa s) + Km Ka (K iel 0)

(2.19)

with δTm (s) and δω(s) marking the input torque and output rotation speed Laplace expressions respectively, and Km & τm being the mechanical gain & mechanical time constant, Ka & τa the rotor gain & rotor time constant, and finally K depending on the electromagnetic properties of the motor & iel 0 denoting the stator current linearization point [78]. Furthermore, considering a sensorless ESC’s closed-loop control principle of achieving stable commutations –and in that effect a constant angular speed at a given power input voltage level– a 1st -order system structure with an input delay can accurately capture the rotor system closed-loop linearized dynamics:

KPmi δωi −τ s e d mi (s) = δUmi (1 + τPmi s)

,

i → {1, 2, 3} ,

(2.20)

with δUmi denoting the i-th rotor’s digital input, and KPmi & τPmi being the closed-loop system’s dc-gain and time constant, and finally τdmi its transfer delay. A Frequency Domain (FD) identification procedure [79] is utilized in order to capture each rotor’s (ESC/BLDC/propeller) dynamics around a selected steady-state (hovering) trim-point ωi0 . The data acquisition process consists of test-bench experiments with a setup as illustrated in Figure 2.3 where rotational speed encoders

22


are used to measure the motor angular velocity and a laboratory weighting scale used to determine the steady-state mapping between the propeller rotation speed -to- the generated thrust.

Weighting Scale

Battery is used to counteract the moment arm due to the rotor’s weight

Rotor

Rotational Speed Encoder under the shaft

Figure 2.3: Experimental setup for rotor speed -to- thrust mapping, and rotor dynamics identification.

Due to the frequency-domain approach of the identification process, the motors were excited using chirp signals covering the actuators’ effective bandwidth. During the data preparation process, the data are checked mainly based on the co2 between the excitation signal (ensuring good and fruitful excitation) herence γxy

and the random error. The experience of the identification community working in rotorcrafts [80] indicates that a good excitation level is achieved when the coherence is higher than 0.65 within the desired frequency area and is considered to be of very high quality when the coherence is higher than 0.85. The identification process is based on quadratic norm optimization for the estimation of the model parameters. In Figure 2.4-a), a block diagram of the FD identification process is shown, and in b) a plot that shows the unbiased (with mean values removed) experimental output and input, the coherence between the excitation signal and the response, as well as the random error noise for the case of the right main rotor when excited by a chirp signal with frequencies between 3.5Hz and 5.5Hz, is presented. As clearly indicated from the very high coherence, the recorded dataset contains fruitful information about the system, while also indicating that the system can be accurately approximated as a linear system (almost zero coherence

23


in the frequency areas that were not excited by the input). Results such as: a) near-80% data fitting values –computed as (ˆ y − y)/(y − y¯) with yˆ the estimated

response, y the experimental output and y¯ its mean value–, and b) the coherence which is 0.99, are typical, hence concluding that the identified model effectively captures the system dynamics.

a) Frequency-Domain Identi!ication Process Coherence Delay

Filter

Data Preparation & Frequency Domain / Time Domain Analysis

Recorded DATA

Coherence FFT

CZT

IDENTIFICATION

FD

TD

MODEL VALIDATION & ANALYSIS

Unbiased Input (rpm)

Unbiased Output (rpm)

b) Input-Output Coherence Metrics

Coherence

Time (s)

Time (s)

Time (s)

Normalized Frequency (rad/sample)

Normalized Frequency (rad/sample) Frequency (Hz)

Figure 2.4: a) Frequency Domain identification process block diagram. b) Excitation -to- output coherence relation visualization.

The closed-loop dynamics of each rotor subsystem are equivalently expressed in state-space form:

24


δ ω˙ i (t) = −aωi δωi (t) + aωi δωir (t − τdmi )

δ F˙i (t) = −aFi δFi (t) + aFi δFir (t − τdmi ) Fi0 = kF,i ωi20

δFi = cF,i δωi

,

cF,i = 2 kF,i ,

(2.21) (2.22) (2.23) (2.24)

in the relationship (2.21), which employs the steady-state (δUmi → δωi ) and dy-

namics information of the derived model in (2.20) to expose the desired rotational

speed δωir –as opposed as to the δUmi digital command– as the system input. Finally, employing linearization of (2.8) around the steady-state operating point Fi0 as in (2.23)(2.24), yields the closed-loop rotor thrust dynamics (2.22). Figure 2.5a) presents indicative results of the rotor identified dynamics –extended in such a way that also illustrates its bandwidth-limited nature, with ωi marking the actual values measured by the rotational speed encoders and ω ˆ i = δω ˆ i + ωi0 marking the respective values obtained by the (2.21) identified model response. Additionally, in Figure 2.5-b), the nonlinear relationship between the rotor speed and static thrust (2.8) is experimentally demonstrated; as per the commonly utilized assumption in the field of mini-&-micro UAV modeling [81], the static thrust is proportional to the square of the angular rotation speed.

2.2.2

Rotor-Tilt Mechanism Model

The term rotor-tilt mechanism refers to the complete actuation subsystem consisting of: a) the servomotor, b) the gear-reduction stage, and c) the rotor base. The driving actuator is the servomotor which comes with an integrated closed-loop circuit that controls its absolute rotation angle, and hence the tilt-orientation of the rotor after the gear-reduction stage. A system identification process is followed for this actuation subsystem as well, with the test-bench process consisting of the independent excitation of each servomotor actuator (via its digital control command Usi ) while the UAV platform is held stationary. The accelerometers are mounted on the rotating bases as illustrated in Figure 2.6, and are used to extract the rotor-tilt angles γi .

25


b)

F F

F F

Figure 2.5: a) Right rotor (i = 1) Frequency Domain identification. b) Right rotor speed -to- thrust nonlinear mapping.

A similar 1st -order structure to the one used for the rotors (2.20) can accurately capture the closed-loop dynamics of such a system:

KPsi δγi −τ s e dsi (s) = δUsi (1 + τPsi s)

,

i → {1, 2, 3} ,

(2.25)

there is however one crucial differentiation: Figure 2.7-a) illustrates the experimentally derived nonlinear relationship between the servo digital command Usi

26


UAV platform is held stationary

Angle-measuring Accelerometers attached under rotating Rotor-Tilt Mechanisms Figure 2.6: Experimental setup for digital servo command -to- rotor tilt angle mapping, and rotor-tilt dynamics identification.

and the resulting tilt angle γi as obtained after bench-test mapping. For an endto-end driving of the servomotor, a hysteretic cycle is observed in the results. Its effect can also be observed in the demonstrated rotor-tilt mechanism step response –i.e. in Figure 2.7-b)–, where the utilized reference value δγ r is derived from a mean mapping Usi → γi of the observed cycle. This results in a steady-state error, which cannot be treated as a dc-gain offset. In order to maintain a tractable model of the rotor-tilting mechanisms for control, the obtained models are formulated to have the same dynamics, and their dc-gain is set as:

δγi δγir |t→∞ = 1,

and it is finally left to a properly synthesized low-level control

structure elaborated in the Control Chapter 5 to handle the proper manipulation of the low-level command Usi and account for this non-linearity.

δ γ˙ i (t) = −aγi δγi (t) + aγi δγir (t − τdsi )

(2.26)

Hence (2.26) is extracted which reflects the rotor-tilt mechanism dynamics in linear-system form; it is additionally noted that Figure 2.7-b) illustrates the identification process’ result, marking as δγir the reference value, as δγi the actual measured values obtained by the accelerometers, and as δˆ γi the respective identified model response. It is eventually noted that an equivalent 2nd -order approximation of the dynamics captured by (2.26) can be achieved via Pade Approximation [82],


27

Figure 2.7: a) Right rotor-tilt mechanism (i = 1) nonlinear digital command -to- tilt angle mapping. b) Right rotor-tilt mechanism actual & modeled response.

γi relation (its utility which when reformulated as in (2.27) can provide a δγir → δ¨

is analyzed followingly):

28




δ γ˙ i



δ¨ γi

2.2.3

 



= 

0

1

−aγ˙ i γi −aγ˙ i γ˙ i

   

δγi δ γ˙ i





+

0

bγi

 

δγir ,

(2.27)

Considerations for Problem Simplification

At first, a collective main rotor thrust-vectoring principle can be achieved via r = δγ r . In this case, and concurrent tilting of the main rotors by δγxr = δγx,1 x,2

considering that the dynamics of the rotor-tilting mechanisms are almost matched, a unified closed-loop dynamic model in the form of (2.26) can be employed to represent the δγxr → δγx authority. Considering near-equal main rotor tilting and

their counter-rotating motion at near-identically opposite ω1 ≃ −ω2 (with similar

propeller inertias Ir,1 ≃ Ir,2 ), the effect of (2.12) becomes counteracting, and thus

the gyroscopic phenomenon during main rotor-tilting can be disregarded.

While this effect is counteracting, the adverse reaction effect (2.14) during aggressive tilting of the main rotors is additive. Via moment conservation (2.15), an additional angular rate derivative is induced onto the aerial vehicle’s body, which near the hovering attitude pose can be modeled as a pitch angular acceleration disturbance:

δ θ¨V ≃ δ q˙V = IV γ¨x , IV =

(IT,1 + IT,2 ) + (IT,2 + IT,1 ) , IB,1 + IB,2

(2.28)

where IV represents a mechanical ratio of moments of inertia (the rotors and rotor-tilting mechanisms -to- the rest of the rigid body). It is noted that during an aggressive forward-tilting action γ¨x ≫ 0, the induced angular acceleration is

positive (nose-up); hence if aggressive forward tilting is employed to navigate

longitudinally, the UAV body in free-flight will tend to be rotated in the opposing direction. Together with the 2nd -order rotor-tilt linear model (2.27), this relation can be used to describe the effect of the collective rotor-tilt authority onto the UAV’s angular acceleration δγ r → δ θ¨V . x

Finally, the drag force (2.7) acting on the UAV body after applying BFF-rotation can be approximated by:

29


2.2.4

Dx

≃

Dx

≃π

−σ(x) ˙ (Ku |Au cos(θ)| + Kw |Aw sin(θ)|) x˙ 2

θ∈[− 2 π2 ]

(2.29)

−σ(x) ˙ (Ku Au cos(θ) + Kw Aw σ(θ) sin(θ)) x˙ 2 .

(2.30)

Hovering Flight Attitude Dynamics

Initially, it is noted that by the term hovering flight a system operating point is usually defined, such that:

h

˙ φθ ˙ Θ X

iT

=

0

h

x˙ y˙ z˙

φ˙ θ˙ ψ˙

φθ

iT 0

≃ 0T1×8 ,

(2.31)

i.e. the translational and rotational rates of the UAV are zero and the system’s attitude (roll, pitch) is regulated at a near-horizontal pose. For such conditions to hold, the sum forces and moments acting on the aerial vehicle –as given in Section 2.1.1– have to be at equilibrium, thus determining a system of equations whose solution yields the respective operating points for the system’s actuation subsystems:

F10 = F20 = γ10 = γ20

=

r3Bx B +r B ) 2 (r1,2 3x x

0

mg

, F30 = , γ30 =

B r1,2 x B +r B r1,2 3x x

0

mg

,

(2.32)

whence also the rotor speed offsets ωi0 are also derived based on (2.23). This obviates that the asymmetric design of the UAV prototype –as opposed to standard multirotor configurations– also introduces a need for asymmetrical distribution of the rotor propulsion forces in order to maintain the sum moment at equilibrium. Hence, the resulting system has to be examined further in its hovering operating point, as the commonly assumed symmetrical design [81] does not hold, and the system’s rotational moment of inertia matrix also presents non-negligible Ixz crossaxes values. It is also noted that for the aerial vehicle’s attitude control as a trirotor, the common practice of assigning virtual control inputs of the attitude states which are a specific combination of the vehicle’s actuation subsystems is used, namely: a)

30


the virtual control input Uφ is used to control the roll via differential thrusting of the main rotors, b) Uθ represents the pitch virtual input which employs differential trusting of the two main (front) rotors and the tail (back) rotor, and c) Uψ is the yaw control authority which relies on the lateral tilting/lateral thrust projection of the tail rotor’s thrust to create a yawing moment w.r.t. the CoM. These principles are illustrated in elaborated in Figure 2.8, thus determining the attitude virtual control vector UΘ in relation to the actuators’ inputs Ua as:

UΘ =

h

Uφ



Ua =

Uθ 

Uψ 

r3Bx B 2 (r1,2 +r3Bx ) x

(2.33) 

δF1  −Uφ + c1,2 Uθ    r    δγ   0   1       δF r   U + c 1,2 Uθ   2  φ =     δγ r   0   2          r −c3 Uθ  δF3       r

δγ3r

c1 = c2 = c1,2 =

iT

c3 =

(2.34)

−Uψ

B r1,2 x B r1,2 +r3Bx x

B , f or : γ1 = γ2 ⇒ r1Bx = r2Bx = r1,2 x

(2.35)

where the ci , i → {1, 2, 3} terms are control mixing coefficients “translating” the

pitch manipulated value Uθ to symmetric moments from the main rotors and the tail rotor with respect to the CoM (due to the asymmetric rotor-sizing and CoMplacement, in the same sense –and value– as the ones used to achieve hovering-state equilibrium in (2.32).

The system’s dynamics are linearized around a more generalized operating point at near-zero translational velocities but maintaining non-zero rotational rate offsets, in order to examine the effect of the asymmetry-related Ixz -induced dynamics couplings, in correlation with the (2.34) attitude control allocation:

h

˙ φθ ˙ Θ X

iT 0

=

h

x˙ y˙ z˙

φ˙ θ˙ ψ˙

φθ

iT 0

≃ 0 0 0 φ˙ 0 θ˙0 ψ˙ 0 h

00

iT

. (2.36)

Hence, the compact linearized model of the system based on the quasi-steady rigid body dynamics [83] augmented by the actuator dynamics is presented as follows:

31


a)

b)

δF1

+φ

δF1,δF2 +θ

-δF2 -δF3 c)

-δγ3 +ψ

Figure 2.8: Hovering operation attitude control allocation principles: a) Rollφ, b) Pitch-θ, c) Yaw-ψ.

˙ Θ = AΘ XΘ + BΘ X a Ua XΘ = XΘ 0 =

(2.37)

δφ δ φ˙ δθ δ θ˙ δψ δ ψ˙ δF1 δγ1 δF2 δγ2 δF3 δγ3

h

iT

,



,

0 φ˙ 0 0 θ˙0 0 ψ˙ 0 F10 0 F20 0 F30 0

h



AΘ r,r

AΘ =  0[6×6]

AΘ r,a Aa,a

 



BΘ = 

0[6×6] Ba



iT

(2.38)

where An,j are the stability derivatives of the n state subsystem from the j state subsystem, Bn are the control derivatives of the n state subsystem, with ˙ θ, θ, ˙ ψ, ψ} ˙ and actuation {n, j} → {r, a} , where {r, a} the rotational {φ, φ, {F1 , γ1 , F2 , γ2 , F3 , γ3 } state subsystems respectively. For the generalized hov-

ering operating point of (2.36):

32




0  AΘ r,r =

1

 0   0   0    0 

0

0

θ˙0 p2 p1

0

φ˙ 0 p2 +ψ˙ 0 p3 p2

0

˙ − θ0pp1 3

0

0

1

0

0

0

0

0

0

0

0

0

φ˙ 0 p6 −ψ˙ 0 p2 p1

0

θ˙0 p6 p1



=

0

−φ˙ 0 p4 +ψ˙ 0 p5 Iyy

0

AΘ r,a

0

 0  p7 −  p1

  0   d1,2 x   Iyy    0 

− pp18

h

0

0

0

0

− pp91

p7 p1

p9 p1

0

0

0

0

0

−p10

d1,2x Iyy

0

0

− pp111

p8 p1

d

3x −p10 − Iyy

0

0

p11 p1

0



      0   ˙ ˙ ψ0 p4 +φ0 p5   Iyy   1   ˙

(2.39)

− θ0pp1 2 

0 

p12   p1 

 0  

(2.40)

0    

0  

p13 p1



Aa,a = diag −aω1 cF,1 , −aγ1 , −aω2 cF,2 , −aγ2 , −aω3 cF,3 , −aγ3 

Ba =

 0  aγ  1   0   a  γ2    0 

0

c1,2 =

0 −c1,2θ aω1 cF,1 −aω1 cF,1 c1,2θ aω1 cF,1

0

0

0 −c1,2θ aω2 cF,2

0

0

aω2 cF,2

c1,2θ aω2 cF,2

0

0

0

0

0

−c3θ aω3 cF,3

0

−c3θ aω3 cF,3

0

0

0

=

p8

=

p13 = g m



Izz − Ixx − Iyy

=

p11 =

−aγ3

Ixz (Ixx − Iyy + Izz )

p6

d1,2y Izz

Ixz d y d3x g m 2(d1,21,2+d 3x ) x Ixx d1,2y d3x g m 2(d1,2 +d3 ) x x d1,2x d3z Ixz −d1,2x d3x Ixx (d1,2x +d3x )

p10 =

(2.42)



= =

(2.41)

0  

p2 p4

=



2 Ixx Izz − Ixz

2 − 2I 2 = Izz (Ixx + Iyy ) − Izz xz

p9

0  

d1,2x d1,2x +d3x

p3 p7

 0  

=

d3x 2 (d1,2x +d3x )

= =

0   0  

c3

c1 = c2 =

p1 p5

0



i

2Ixz

Ixx (Ixx − Iyy + Izz ) d1,2y Ixz

d1,2z d3x 2(d1,2x +d3x )Iyy d1,2x d3z Izz −d1,2x d3x Ixz (d1,2x +d3x )

gm

p12 = g m

For the evaluation of the effect of the non-negligible Ixz term in the moment of inertia matrix –as compared to Ixx , Iyy , Izz )– at the generalized hovering operating

33


point XΘ 0 , numerical substitution is employed based on the values presented in the System Design Chapter 3; it is hence determined by the resulting rotational h

i

subsystem stability derivative matrix Ar,r Ar,a , that: • The δ φ˙ state is mainly affected by the differential main rotors thrusting, and ˙ θ˙0 } ≃ {0, 0} there is no additional influence from δ ψ, ˙ ψ˙ 0 . for {δ θ, • The δ θ˙ state is mainly affected by the differential thrusting of the front and tail rotors, and for {φ˙ 0 , ψ˙ 0 } ≃ {0, 0} there is no significant influence from ˙ δ ψ. ˙ δ φ,

• The δ ψ˙ state is mainly affected by the differential tilting of the main rotors, ˙ θ˙0 } ≃ {0, 0} there is no and by the tilting of the tail rotor, and for {δ θ, ˙ φ˙ 0 . Also, for equal main rotors tilting (γ1 = γ2 ) significant influence from δ φ, their respective effect disappears. • For {φ˙ 0 , θ˙0 , ψ˙ 0 } ≃ {0, 0, 0}, i.e. for any slow rotation-rate operating point, state coupling effects disappear.

The above justify the selected rotational subsystem control allocation principles of (2.34), as the roll-φ, pitch-θ-, and yaw-ψ states can be considered as decoupled systems, provided that there exists a control scheme which effectively damps their respective rates. Finally, once an appropriate underlying attitude control structure –such as the one elaborated in the Control Chapter 5– has been implemented, the closed-loop rotational dynamics can be extracted as effectively decoupled subsystems, which are useful for the synthesis of the model (and consequently the appropriate modelbased control structure) of the translational dynamics. Again, employing a FD˜ δ θ, ˜ δ ψ} ˜ identification process whose results are indicated in Figure 2.9, with {δ φ,

marking the respective models’ responses for reference, the aerial-vehicle’s closedloop attitude dynamics are accurately captured by 2nd order systems:

34


Figure 2.9: Frequency Domain-identified attitude roll-φ, pitch-θ, yaw-ψ dynamics.

δ φ˙ δφ 0 1 0   =     +   δφr δ φ˙ δ φ¨ bφ −aφφ −aφ˙ φ˙ ˙ 





 







0 δθ 0 1 δ θ˙    +   δθ r   =  ˙ ¨ bθ δθ −aθθ δθ −aθ˙θ˙ ˙ 





 







0 1 δψ δ ψ˙ 0    +   δψ r .   =  δ ψ˙ δ ψ¨ bψ −aψψ −aψ˙ ψ˙ ˙ 

2.2.5





 







(2.43) (2.44) (2.45)

Hovering Flight Translational Dynamics

The system’s translational dynamics are initially examined as per the effect of the actuation authorities. To this purpose, the augmented dynamics –including the translational states– are extracted around the same generalized operating point (2.36):

35


˙ X = AX XX + BX X a Ua XX = XX = 0

 

δx δ x˙ δy δ y˙ δz δ z˙ XΘ

h

x0 0 y0 0 z0 0 XΘ 0

AX t,t

0[6×6] AX =  

(2.46)

h

0[6×6]

AX t,a

AΘ r,r

AΘ r,a  

0[6×6]

Aa,a

,





AX t,r

iT

iT

(2.48)

0[6×6]



 

(2.47)

 

(2.49)

 0[6×6]  , BX =  

Ba



where An,j again the stability derivatives of the n state subsystem from the j state subsystem, with {n, j} → {t, r, a} augmented with the translational {x, x, ˙ y, y, ˙ z, z} ˙ state subsystem. It results that:



AX t,t =

0  0   0   0    0 



1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

 0   0   0   1  

0 0 0 0 0 0



AX t,a =

0    0           

0



0  0   0  X At,r =  g    0 

0

0



0 0 0

0 −g 0 0 0   0 0 0 0 0  

0

0

0

0

0 0

0

(2.50)

0 0 0   

0 0 0  

0 0 0

0

0

0

gd3x 2(d1,2x +d3x )

0

gd3x 2(d1,2x +d3x )

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1 −m

0

1 −m

0

1 −m

0



   0    0  . gd1,2x   d1,2x +d3x     0 

(2.51)

0

This representation covers a very small subset of the aerial vehicle’s hovering flight state envelope and lacks fidelity –it only examines near-zero velocity flight and does not include any natural damping terms such as the ones induced by aerodynamic drag–, however it exposes the available actuation principles to control the UAV’s translational dynamics:


36

• The δ x˙ state is mainly affected by the pitch-θ body rotation, and the collective main rotors tilting {δγ1 , δγ2 } in a degree determined by the numerical

relation between the physical measures {d1,2x , d3x } of the UAV.

• The δ y˙ state is mainly affected by the roll-φ body rotation, and the tail rotor tilting δγ3 in a degree determined by the numerical relation between the physical measures {d1,2x , d3x } of the UAV. • The δ z˙ state is mainly affected by the collective rotor thrusting {δF1 , δF2 , δF3 } for a given UAV physical mass m.

These initially obviate the fact that the aerial vehicle’s translational dynamics can be controlled in the typical cascaded sense –with the rotational states driving the translational ones employing the effect captured in AX t,r –. Additionally however, the effect of rotor-tilting also enables its exploitation in actuating those dynamics. As noted in AX t,a , the ratio between the front & tail rotor axial (longitudinally) distances from the CoM is important in determining the measure of their effect. That is, for different design configurations of the trirotor, different control allocations make sense; i.e. for a more symmetrically placed CoM (d1,2x ≃ d3x ) the

lateral-y DoF can effectively be actuated by additionally employing lateral tail rotor tilting, while concurrently compensating for the yaw-ψ rotating moment via differential main rotor tilting. For this specific configuration, where d1,2x ≪ d3x , the aforementioned principle has minimal effect over the lateral DoF, while retaining a meaningful effect over the rotational subsystem dynamics; it is hence rejected due to the additional compensation that would be required as previously discussed. On the other hand, the effect of main rotor-tilting onto the longitudinal dynamics is considerable, and it is hence considered as a meaningful actuation authority. The actuation principles are hence completed with the depiction of Figure 2.10, where it is illustrated how: a) the longitudinal-x DoF motion exhibits the exceptional trait that it can be driven by two actuation principles, namely either via main rotor-tilting/longitudinal projection of their combined thrust, and/or or via (underactuated) body θ-pitching, b) the standard underactuated approach is employed to control the vehicle’s lateral-y motion, via φ-projection of its thrust force, and c) the total rotor thrust force is used to control the altitude-z. The complete allocation of the translation UX and attitude UΘ in relation to the actuators’ inputs Ua is thus determined as:

37


UX = UΘ =

h

h

Uφ



Ua =

Uxθ = −δθr

Uxγ

Uθ 

Uψ 

Uy = δφr

iT

Uz

iT

(2.52) (2.53)



δF1  −Uφ + c1,2θ (Uθ − Uz )  r    δγ    Uxγ  1       δF r   U + c  1,2θ (Uθ − Uz )   2  φ   =  δγ r    Uxγ  2        r   c3θ (−Uθ − Uz ) δF3        r

δγ3r

(2.54)

−Uψ

wherein both longitudinal actuation principles {Uxγ , Uxθ } coexist, allowing the

manipulation of either of the two, or both concurrently.

+x

a)

+γ1,γ2

-θ

b)

c)

+y

-z δF3

δF1

δF2

-φ

Figure 2.10: Translation control allocation principles in Free-Flight hovering operation: a) Longitudinal-x, b) Lateral-y, c) Vertical-z.

The purpose of deriving a model suitable for advanced control requires the extraction of a higher-fidelity representation, which will include those terms that are


38

meaningful to the aerial vehicle’s flight dynamics in tractable fashion. Tn principle, the translational dynamics are manipulated by projecting the UAV propulsion force –either via directly actuated thrust-vectoring or via rigid-body rotation– in order to induce translational accelerations, which can be represented by:

y z x , δ¨ y = −λy δ y˙ + δF , δ¨ z = −λz δ z˙ + δF δ¨ x = −λx δ x˙ + δF m m m ,

(2.55)

where δFv the v → {x, y, z} driving force, and λv the respective natural damping

parameters. Via a set of experimental studies, and employing FD identification

on the obtained translational acceleration and velocity data with the aerial vehicle operating near hovering flight, while it is sequentially actuated/commanded via: a) rotor-tilting (δγxr ), b) rigid body rolling (δφr ), and c) sum rotor thrusting (δΣFir ), the the natural damping parameters λv around hovering operation can be estimated. Figure 2.11 presents an overview of the results achieved by the process of identifying the 1st -order systems of (2.55). Regarding the longitudinal dynamics, the inclusion of (2.30) can be used to encode a physically meaningful system state which is (in a certain sense) analogous to the UAV body’s aerodynamic efficiency while performing longitudinal flight. Considering only strictly positive or negative-definite regions for the pitch angle θ = θ0 + δθ and the longitudinal velocity x˙ = x˙ 0 + δ x, ˙ their respective signum functions σ(·) can be simplified as in (2.56), and hence yield the expression of (2.58):

σ(x) ˙ = σ(x˙ 0 ± δ x) ˙ = σ(x˙ 0 ) , σ(θ) = σ(θ0 ± δθ) = σ(θ0 )

For

:

(2.56)

i) x˙ = x˙ 0 + δx˙ , ii) θ = θ0 + δθ , iii) (2.56)

Dx ≃ −σ(x˙ 0 ) (x˙ 20 + 2x˙ 0 δx) ˙ { (Ku Au cos(θ0 ) + σ(θ0 )Kw Aw sin(θ0 )) (2.57) + (−Ku Au sin(θ0 ) + σ(θ0 )Kw Aw cos(θ0 )) δθ } Dx ≃ DDD + DDθ δθ + DDx˙ δx˙

DDD (x˙ 0 , θ0 ) = −σ(x˙ 0 ) x˙ 20 (Ku Au cos(θ0 ) + σ(θ0 )Kw Aw sin(θ0 ))

(2.58) (2.59)

DDθ (x˙ 0 , θ0 ) = −σ(x˙ 0 ) x˙ 20 (−Ku Au sin(θ0 ) + σ(θ0 )Kw Aw cos(θ0 ))

(2.60)

DDx˙ (x˙ 0 , θ0 ) = −σ(x˙ 0 ) 2x˙ 0 (Ku Au cos(θ0 ) + σ(θ0 )Kw Aw sin(θ0 )) .

(2.61)


Figure 2.11:

39

Frequency Domain-identified translational longitudinal-x, lateral-y, vertical-z dynamics.

This consists a linear parametrization in the system state-space, and it is noted that it is composed by an affine term DDD (2.59), and a δθ-multiplying term DDθ ˙ term DDx˙ (2.60) which are quadratic functions of x˙ 0 , as well as a δ x-multiplying which is a linear function of x˙ 0 . The longitudinal dynamics are thus formulated as:

40


F3 Dx F1 + F2 sin(γ − θ) + sin(−θ) + (2.62) m m m i) F1 ≃ F10 = c1,2 mg , ii) F2 ≃ F20 = c1,2 mg , iii) F3 ≃ F30 = c3 mg

x¨ ≃

For

:

iv) γ = 0 + δγ , v) θ = θ0 + δθ

Dx m DDθ DDx˙ DDD ) + (LLγ )δγ + (LLθ + )δθ + ( )δ x˙ x¨0 + δ¨ x ≃ (LLL + m m m LLL (θ0 ) = −g sin(θ0 ) x¨ ≃ −g sin(θ0 ) + 2c1,2 g cos(θ0 )δγ − g cos(θ0 )δθ +

(2.63) (2.64) (2.65)

LLγ (θ0 ) = 2 c1,2 g cos(θ0 )

(2.66)

LLθ (θ0 ) = −g cos(θ0 ) ,

(2.67)

where the previously extracted drag force representation is included, as well as the combined main rotor propulsion (F1 + F2 ) which is projected by the rotor-tilt and the body-pitch angle (γ − θ), and the tail rotor propulsion (F3 ) which is projected by the body-pitch angle (−θ).

Integrating the previously elaborated principles, yields the complete formulation of the desired high-fidelity longitudinal dynamics model in its complete form; this representation is additionally parameterized according to an operating region N around {x˙ N 0 , θ0 }, with the N superscript marking that specific region:

N N N ˙ = Alon δX δX + Blon Ulon + Flon



δ¨ x





    δ γ˙ x      δ¨ γ   x  ˙  δθ   

=

δ θ¨

N DD x˙

 m   0    0     0 

0



+

         

LN Lγ

0

LN Lθ +

0

1

0

0

−aγγ ˙

−aγ˙ γ˙

0

0

0

1

−aθθ ˙

−aθ˙θ˙

0

0

−IV aγγ −IV aγ˙ γ˙ ˙ 



0

0

0

 0   r   δγ    x  + 0   δθ r    0  

bγ 0

(2.68) N DDθ

IV bγ bθ



N LLL +

 

0 0 0 0

m

N DDD m 

          

.

0





  δ x˙    δγx       δ γ˙    x     δθ     

δ θ˙

41


This model includes the internal (closed-loop) dynamics of each actuation authority while incorporating their interferences (2.28) in a simple and tractable fashion. Additionally, the inclusion of (2.58) in state-feedback form provides a finer representation of the effects that each control authority has on the evolution of the longitudinal dynamics. The deduced model consists a PieceWise Affine mathematical formulation, however its specific implementation relies on the selection of proper operating points which are related to the intended principle of operation, a process which is elaborated in the Control Chapter 5. It is noted that the proposed approach employs the parameters {Ku Au , Kw Aw }.

Alternatively to acquiring estimates of their values from Computational Fluid Dynamics (CFD) modeling, FD identification around a small non-zero x˙ N 0 longitudinal velocity regions N can be used to yield reliable estimates of the Ku Au parameter, considering the equivalence to the natural damping term: −λN x ≃ −σ(x˙ N ˙N 0 )2Ku Au x 0 . m

In a similar process as previously presented for the results of Fig-

N ure 2.11, this time around a set of small ±x˙ N 0 values, yields similar λx values, as

expected. It is highlighted that this process relies on maintaining θ ≃ 0 throughout

the experimental sequence, which is achieved by employing exclusively rotor-tilting actuation, while successfully regulating the body-pitch angle near zero –which the system is capable of achieving as demonstrated in Figure 2.11-a)–. In a similar fashion the Kw Aw parameter is estimated by performing vertical experiments while maintaining {φ ≃ 0, θ ≃ 0}. Since the lateral and vertical dynamics lack the unique capability of two actuation authorities which can be exploited concurrently, their respective modeling representations are relatively simpler:

˙ = Alat δY + Blat Ulat δY 

y˙



     δ¨ y    ˙ δ φ  

δ φ¨



0

=

  0   0 

0

1 −λy 0 0

0

0

g

0

0

1

−aφφ −aφ˙ φ˙ ˙

(2.69) 

y



      δ y˙       δφ  

δ φ˙

+



0



    0 r   δφ   0  

,

bφ

where the lateral model incorporates the closed-loop roll dynamics (2.43), and:

42


˙ = Avert δZ + Bvert Uvert δX 

z˙



      δ¨ z    ˙  δ F1,2   

δ F˙3



0 1

=

  0   0 

0

0

0

−λz

2c1,2 m

0

−aF3

0 −aF1,2

0 0

0

(2.70) 

z



   c3      δ z ˙ m     δF1,2   

δF3

+



0



     0    δΣF r i   aF1,2   

,

aF3

where the vertical model relies on the linearized representation of the total rotor thrust, which is composed of a δF1 |t→∞ + δF2 |t→∞ ≃ 2 c1,2 δΣFir main rotor com-

aF1 +aF2 2 r c3 δΣFi tail

ponent (whose dynamic representations are approximated with aF1,2 ≃ as the main rotors are almost matched), and a separate δF3 |t→∞ ≃

rotor component (as the tail rotor dynamics differ in some degree), with the control mixing coefficients (2.35) distributing the manipulated thrust reference δΣFir among the i → {1, 2, 3} rotors such that no rotating moment is generated in steady-state.

2.3

Aerial Interaction through Physical Contact Modeling

Considering the aerial vehicle as more than an airborne agent that flies within an open airspace and regarding any physical structures as obstacles to be avoided, namely as an Unmanned Aerial System (UAS) which purposely comes into physical contact with its environment to achieve certain tasks, gives birth to the term Aerial Robotic Physical Interaction through Contact. In a generalized sense, an aerial robot with such an operational capacity should have the onboard –hardware– means to achieve contact with an environment surface/object while retaining its structural safety, and conduct conduct the physical interaction task. The employed modeling approach covers the requirements in order to achieve stability –via a proper control scheme– as the active system dynamics change between the Free Flight (FF) and the Physical Interaction (PI) modes. More importantly however, it is analyzed how the additional actuation authority gained through rotor-tilting is advantageous when a significant force –with respect to the UAS’ own weight-lifting force– is desired to be applied onto the environment, as

43


it provides safety-related benefits stability & control-wise, as well as increased efficiency as compared to other designs.

2.3.1

Force Exertion on Rigid Environment Structures

The tiltrotor aerial vehicle can achieve physical contact with the surface of a structure in its environment via a front-mounted end-effector, as illustrated in Figure 2.12-a), where the dm = {dmx , dmy = 0, dmz = 0} values are used to mark

the BFF-based geometric distance from the Center-of-Mass up to the centroid

of the end-effector front surface plane. As noted these are mechanically configured to be collinear; it is additionally mentioned that the end-effector is designed exhibit a degree of compliance, partially incorporating elastic materials in its design. Additionally, provided the UAS maintains a stable hovering attitude pose {φ ≃ 0, θ ≃ 0} while “docked”, the end-effector front centroid is regarded as a Virtual Contact Point (VCP).

Figure 2.12-b) also intuitively depicts a technical advantage of the tiltrotor design which is exploited: the control authorities of rotor-tilting & thrusting are employed concurrently to achieve both longitudinal-x force projection (which is applied onto the environment surface), but also maintain equilibrium of the vertical-z force and pitch-θ moment. This is achieved by commanding the main rotor thrust offset values such that their vertical z-axis components remain the same as in the Free Flight mode:

h

F10 F20 F30

iT

=

h

c1 mg cos(γx +δγm )

c2 mg cos(γx −δγm )

c3 mg

iT

,

(2.71)

where it is noted that due to the collinearity of the VCP with the CoM (dm = {dmx , dmy = 0, dmz = 0}), the control mixing coefficients ci are independent of

the end-effector dmx length and hold for both the Free Flight and Physical Inter-

action modes. Moreover, additionally to collective γx tilting of the main rotors for longitudinal force projection, differential ±γm thrust vectoring can be exploited

to generate a yaw-ψ moment while “docked”. The moment of the longitudinallyprojected thrust components {F1 |x , F2 |x } with respect to the VCP takes a value of:

44


γx

2

a)

-δγm 3

1

γx VCP

d2y

CoM

+δγm

d1y

d1,2x

d3 x

d mx

b) γ1,γ2

F3

F1+F2

By Bz

E

Fx Bx y z

x

Figure 2.12: Physical Interaction: Force exertion on a rigid environment structure surface.

MzE ≃ F2x d2y − F1x d1y ≤ 0 ⇒ F1 |x ≥ F2 |x ,

(2.72)

as d1y = d2y . Provided the rotor thrust offsets are adjusted as per (2.71) at the

45


same time, moment equilibrium around the roll-φ axis is also maintained as the vertical-z force components of the main rotors are equalized. It is noted that this implies differential thrusting concurrently to differential tilting, which further increases the magnitude of the generated MzE moment. Also, since as previously mentioned the end-effector design incorporates elastic materials in its design, a certain rotational freedom in the relative orientation of the UAV body to the environment surface plane at the VCP is allowed. Considering the system’s attitude dynamics, and assuming a longitudinally-exerted force component while the aerial vehicle body remains near the hovering operating point {φ, θ, ψ} ≃ {0, 0, ψE } –where ψE the environment surface normal vector

orientation–, the UAV can be considered as attached at the Virtual Contact Point. This is regarded as the new center-of-rotation, with respect to which the moment of inertia matrix I is recalculated ,again based on CAD modeling. Additionally, as the new center-of-rotation lies ahead of the main rotor axis, for the pitch-(θ) DoF collective rotor thrusting is allocated, modifying (2.34) in the Physical Interaction mode as per:

UPΘI =

h

UφP I



UPa I =

r

UθP I 



UψP I PI

iT

(2.73) PI

δF1  −Uφ − c1,2 Uθ  r   δγ   0  1     PI δF r   U P I − c 1,2 Uθ  2  φ  =  δγ r   0  2      r  −c3 UθP I δF3     

δγ3r

−UψP I

              

.

(2.74)

Concerning the system’s translation dynamics, the two distinct Free-Flight & Physical Interaction modes motivate the use of a PieceWise Affine system model representation to be used for control purposes. The objective for this Unmanned Aerial System is twofold: a) initially to safely perform contact with an environment surface at a reference location, and b) to exert a longitudinal force at the contact point while remaining safely “docked” at that location. To this purpose, contact stiction is exploited: Assuming a large enough longitudinally-projected force is enacted by the aerial vehicle onto the environment surface –and normal-to that plane as the aircraft hovers near {φ, θ, ψ} ≃ {0, 0, ψE }– interfacing stiction

46


comes into effect, thus constraining any lateral-y and vertical-z sliding motion at the point-of-contact, while the rigidity / impenetrability of the environment structure also constrains any longitudinal-x motion. Hence, the active system dynamics are considered to lie in the Physical Interaction mode once that force threshold, which achieves an adequately high friction-interface coefficient, is exceeded. The translational dynamics in the Free Flight mode are elaborated in Section 2.2.5, and in the Physical Interaction mode lateral and vertical motion is constrained at the VCP; since the rotor-tilting actuation authority is used to project the main rotor thrust and both drive the longitudinal dynamics in hovering operation, as well as to apply that force component onto the environment through physical contact, the PieceWise Affine model is developed around the longitudinal subsystem:

h

Xx = x x˙ γx

FxE

iT

X˙x = AxN Xx + BxN Ux 

0

FF : X˙x =

0

0



−λFx F 2 c1,2 g

1

0

0

  0   0 

−λPx I

0

0  



0

0

0

0

0

0

−aγ 0

0

N → {FF, PI}

(2.76)



0





−aγ



     Xx +       

(2.77)

0

0

0

−aγ

(2.75)

      0 0  Xx +   Ux    bγ  0   

  0   0 

0

PI : X˙x =

1

,

, Ux = γxr

0 0

aγ

aγ 2 c1,2 mg)



    Ux   

, (2.78)

where FxE is the externally applied longitudinal force, estimated as Fx ≃ (F10 + F 20 )sin(γx ), i.e. the longitudinally-projected main rotors’ collective thrust. This additional state encodes the guard-rules used to switch among the two distinct modes:

G FF :

E FxE ≤ Fx,t

,

G PI :

E FxE ≥ Fx,t ,

(2.79)

47


E the aforementioned stiction-maintaining threshold. It is noted that the where Fx,t

force-state FxE can be manipulated in the Physical Interaction mode as encoded in (2.78), in order to achieve exerted-force control. Finally, λPx I is a longitudinal velocity-damping term, mostly determined by the viscous damping coefficient of the degree of compliance of the end-effector.

2.3.2

Manipulation of Non-Rigid Environment Structures

A non-rigid structure is considered to be an object in the environment which can be manipulated via the application of forces and moments upon it. Since it is mobile, an O Object-Fixed-Frame (OFF) is defined, as illustrated in Figure 2.13. Let mobj mark the object mass, and for an object of arbitrary internal structure –and thus obj obj a non-centroid positioned Center-of-Mass– let dobj = {dobj x , dy , dz } mark the

OFF-based geometric distance from the Virtual Contact Point. Additionally, the end-effector possesses a rotational DoF as depicted and denoted by the angle γ˜m , taken with respect to the B longitudinal axis. Hence for such a system design, the “docked” hovering operating point for the UAV where planar contact of the end-effector and the object surface is achieved is {φ, θ, ψ} ≃ {0, 0, ψE − γ˜m }, and

the longitudinally-projected thrust components of the main rotors are applied in the γ˜m -direction. In such a scenario, the object lies on solid ground which introduces friction. For its manipulation, the UAS is required to enact a forward-thrusting (pushing) force in order to overcome stiction in the object-to-ground interface; the friction force Ff r which appears is modeled in the Stribeck [84] generalized form:

Ff r =

  −Fv (uobj ),  −F E , x

for uobj 6= 0 for uobj = 0 AND |FxE | < Fst

,

(2.80)

where uobj the object-to-ground interface relative velocity, FxE the externally applied force, Fv (uobj ) the viscous friction, and Fst the stiction force. A number of parameters of the environment’s setup that are of particular importance are unknown in a realistic scenario. The friction model parameters for the object-ground interface are unknown and even more, cannot be expected to be

48


a)

z

x y

2 ry

dmx

Bx Bz

γ~m obj

ψ -ψ

By

3

obj

Oz Oy

Ox

1

b)

mobj=4.34 kg

γ1 , γ2

m=2.254 kg

E

Bx By

Bz

Ffr Fx

dzobj dxobj

Oy Oz

Ox

Ffr Figure 2.13: Physical Interaction: Force exertion on a free object for pushing manipulation.

constant throughout the entire trajectory, as there is no guarantee that the floor texture is consistent. The object mass would be unknown and cannot be estimated using the Newton-Euler approach, as long as the friction-model force is unknown and vice-versa. Furthermore, the object structure may be compliant instead of rigid, not allowing the Moment and Energy Conservation approach for mass and friction estimation. Finally, the object CoM cannot be known prior to engaging in the pushing-manipulation operation, and it is inefficient to attempt to estimate it

49


via iterative force exertion (even more as the object-ground interface may not be obj 0}). flat and thus the friction force cannot be assumed to be acting on {dobj x , dy

In absence of a model for the complete system –as comprised of the UAS, the object, and the ground surface–, the previously developed methodology in Section 2.3.1 which aims to cover the modeling necessities to achieve force & moment exertion while retaining planar contact at the VCP and a hovering attitude pose, is combined with a model-less control scheme for pushing-manipulation in the Control Chapter 5. Consequently, it is left to examine how this airborne pushingmanipulation can play the role of an actuation subsystem for the complete mobile system: manipulation in the World-Fixed-Frame ground plane {x, y} can be

achieved via forward pushing-force and rotating moment exertion, with the ob-

ject’s CoM moving along the Object-Fixed-Frame O |x -axis and rotating around the O |z -axis. Forward thrust-vectoring is used to achieve longitudinal pushing

force manipulation, and rotating moment manipulation can be derived via either: a) differential thrust vectoring ±δγm , or b) active end-effector γ˜m control. The latter principles are illustrated in Figure 2.14: In a), the differential thrustvectoring principle (similar to differential-drive for non-holonomic bi-wheeled robots [85]) is depicted. Due to the arbitrary object-COM position –and assuming any friction forces act on the object-COM and produce no moment–, in order to control the orientation, the UAS must be able to produce a moment MzE ≥ 0 :

MzE = F2x (d2y − dobj y ) − F1x (d1y + dobj y ) ≥ 0 ⇒

d1 + dobj y F2x ≥ 1 , (2.81) ≥ y F1x d2y − dobj y

as d1y = d2y . In order to achieve F2x ≥ F1x , the rotors are tilted differentially by

±δγm , with the same principles elaborated for (2.72) applying –and for roll-φ & pitch-θ axes equilibrium (2.71) is also employed as previously discussed–. It is

noted that if d2y ≤ dobj y , (2.81) is solved for negative (pulling) forces. In Figure 2.14-b), the active end-effector γ˜m control principle is depicted. In order to generate a moment MzE ≥ 0 :

MzE = Fx sin(˜ γm )dobj x − Fx cos(˜ γm )dobj y ≥ 0 ⇒ γ˜m ≥ tan−1 (

dobj y ) = γc , (2.82) dobj x

50


γx

a)

+δγm

γx -δγm

F 2x

r1,2x rmx

r3x

r2y

obj

r

y

r1y

F1x

b)

c)

d

F 2x

~ ψ

F 2x

obj x

~ γ

m

Fx

obj

γ

~ γ

d

obj y

Fx

l my

m

Frx F 1x

Fr Fry

~ ψ

Fx

~ ~ +ψ γ m

F 1x

Figure 2.14: Physical Interaction: Moment exertion authorities on a free object for rotating-manipulation.

the end-effector has to be rotated by an angle higher than the object CoM-toVirtual Contact Point relative angle γc . However γ˜m is constrained by the requirement for non-sliding contact, i.e. the normal force component Fx cos(˜ γm ) E to guarantee stiction for the end-effector -to- the has to remain higher than Fx,t

environment surface interface.

51


2.3.3

Technical Discussion – Forceful Physical Interaction via Rotor-Tilting

Initially, it is important to note in Figure 2.14-c) that a counteracting moment appears in the event that the end-effector planar interface is lost. Calculating the total moment with respect to the end-effector centroid for a misalignment error e˜ψ and a reaction force Fr :

˜ γm + e˜ψ )(−lmy cos(δψ)) M m z = −Fr sin(˜ γm + δψ)(−l my sin(δψ)) − Fr cos(˜

γm ) , γm + e˜ψ − e˜ψ ) = Fr lmy cos(˜ M m z = Fr lmy cos(˜

(2.83)

which justifies a mechanical configuration of the end-effector interface as a rectangular frame of lmy 6= 0, instead of a point-edge one, as the resulting moment

direction is such that tends to eliminate the misalignment error.

Also, concerning attitude stability during “docking” with the surface of the environment structure, provided the {φ, θ, ψ} ≃ {0, 0, ψE } regulation is achieved

and for equally tilted rotors γx = {γ1 = γ2 }, no significant disturbing moment is induced onto the UAS, due to the fact that the end-effector is mechanically placed

in-line with the CoM (dm = {dmx , 0, 0}); additionally, due to this configuration

the control mixing coefficients ci remain the same in the Free Flight and Physi-

cal Interaction modes. Overall, this indicates the control-wise advantage that no attitude control offset needs to be applied during the F F ⇄ P I mode switching. Examining the utility of the rotor-tilting authority for such purposes, namely to exert a longitudinally-applied force onto an environment surface while the aerial vehicle remains “docked”, leads to an analysis of several alternative methodologies: First, with reference to Section 2.3.1, an application where the UAS is required to forcefully “press” a tool mounted on front side of the end-effector is examined. Figure 2.15-a) illustrates the use of the underactuated-platform dynamics approach. As elaborated in [86], this practice is based on the principle of forwardforce generation via longitudinal projection of the total thrust vector with pitch θ-rotation of the UAV body. In order to maintain static vertical-z axis force and pitch-θ moment equilibrium the underactuated UAV’s control authority, i.e. the

52


F F R

θ