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Design, Construction and Control of a Large Quadrotor Micro Air Vehicle

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Design, Construction and Control of a Large Quadrotor Micro Air Vehicle Design, Construction and Control of a Large Quadrotor Micro Air Vehicle Paul Edward Ian Pounds September 2007 A thesis submitted for the degree of Doctor of Philosophy of the Australian National University Declaration The work in this thesis is my own except where otherwise stated. Paul Pounds Dedication For the past four years, I have been dogged by a single question. It was never far away - always on the lips of my friends and family, forever in my mind. This question haunted my days, kept me up at night and shadowed my every move. “Does it fly?” Without a doubt, the tenacity of this question played a pivotal role in my thesis. Its persistence and ubiquity beguiled me to go on and on, driving me to finish when I would have liked to have given up. I owe those people who voiced it gratitude for their support and motivation. So, I would like to thank you all by way of answering your question: Yes. Yes, it does. v Acknowledgements This thesis simply could not have happened without the help of my colleagues, many of whom I have come to regard as not just co-workers, but as friends. Foremost thanks to my supervisor, Robert Mahony, for his constant support, friendly ear, helpful advice, paper editing skills and frequent trips to France. He’s been invaluable in keeping me on the straight and true and preventing me from running off on pointless (yet fascinating) tangents. Special thanks to the members of my supervisory panel and research part- ners — Peter Corke, Tarek Hamel and Jongyuk Kim — for fielding questions, explaining maths in detail, reviewing papers and keeping me motivated. Particu- lar gratitude is owed to the CSIRO ICT Robotics group — Les Overs, Jonathan Roberts, and Stephen Brosnan — for their insight was a light in dark times when nothing would compile. My philosophy is never to let IT, workshop or admin staff feel unappreciated — this pays dividends when you need parts made in a hurry, or someone to explain how to use a fax machine in time-critical circumstances. Also, IT staff are also a rich source of surly wisdom and discarded electrical equipment. Much thanks goes to Andrew Wilkinson, Helen Shelper, Pam Shakespeare, Deb Piotch, Ben Nash, Joel Gresham, and David Tyson-Smith. Special appreciation is due Michael Eastwood for being my safety back-up during after-hours tests and keeping me sane. Finally, I must thank my father and editor, Robert Pounds, for spending countless hours pouring over reams of incomprehensible text, before deftly scrib- ing cryptic but precise editorial marks to turn my garble into meaningful prose. vii Abstract This thesis presents research directed towards the development of practical quad- rotor robot helicopters. Most existing quadrotor robot vehicles have been based on consumer flying toys that do not offer the performance necessary to consider commercial applications. The Australian National University’s ‘X-4 Flyer’ has been developed to investigate the enabling technologies essential for the next generation of larger (heavier than 2 kg or 1 m in length) quadrotor Unmanned Aerial Vehicles (UAV) capable of undertaking commercial tasks. It combines a custom-built chassis, rotors and avionics with off-the-shelf motors and batteries to provide a reliable experimental platform. Several major challenges must be overcome to produce a successful, large quadrotor UAV: generation of sufficient lifting thrust with compact rotors, con- trol of rotor dynamics associated with heavier rotor blades, and regulation of the unstable rigid body dynamics using low-cost sensors in a high-vibration environ- ment. In this thesis, I provide solutions to these problems for the X-4 Flyer and demonstrate their effectiveness in operation. I have developed a design for a complete micro air-vehicle thruster that com- bines fixed-pitch small-scale rotors and embedded control. This produces a me- chanically simple, high-performance thruster with high reliability. The custom rotor design requires a balance between aerodynamic performance, blade rigid- ity and manufacturability. An iterative steady-state aeroelastic simulator is used for holistic blade design. The aerodynamic load disturbances of the rotor-motor system in normal conditions are experimentally characterised to produce per- formance metrics for system sensitivity. The motors require fast dynamic re- sponse for authorative vehicle flight control. I detail a dynamic compensator that achieves satisfactory closed-loop response time. The experimental rotor- motor plant displays satisfactory thrust performance and dynamic response. Unlike typical quadrotors, the X-4 uses hinged rotors. By combining hinged rotors with the longitudinal flight dynamics of a helicopter, I develop a complete ix dynamic model, which includes often over-looked aerodynamic effects. It is shown that placement of the rotors close to the horizontal plane of the centre of mass produces favorable dynamic behaviour. From the fundamental limits of control, I use the Bode integral to identify the ideal mass and rotor configuration of the robot to simplify control design. A linear SISO controller is designed to regulate flyer attitude, and is demonstrated on a gimbal test rig. Furthermore, commercially viable aerial robotic vehicles require low-cost at- titude stabilisation systems that are robust to noise and sensor bias. A typical attitude stabilisation system consists of MEMs accelerometers, gyroscopes linked to separate attitude estimator, and attitude controller algorithms. I implement a non-linear attitude stabiliser for low-cost aerial robotic vehicles that combines at- titude and bias estimation with control. The attitude control algorithm is based on a non-linear control Lyapunov function analysis derived directly in terms of the rigid-body attitude dynamics and measurement signals. The combined estimator- controller is shown to function in simulation, even in the presence of noise. The flyer has successfully flown in the ANU Mechatronics test cage. It demon- strated ±0.5◦ attitude stability and hovered a short distance. The failure of a motor control board while on the ground halted testing before longer flights could be carried out. The X-4 has demonstrated commercially-viable attitude stabili- sation precision, payload capacity and flight-time performance. x Contents Acknowledgements vii Abstract ix Nomenclature xv 1 Introduction 1 1.1 Why UAVs? . 1 1.2 Why Quadrotors? . 2 1.3 Why the X-4 Flyer? . 3 1.4 Problems and Objectives . 4 1.5 Papers and Publications . 6 1.6 Roadmap . 7 2 Literature Review 9 2.1 Historial Context . 9 2.1.1 Early UAVs and Enabling Technologies . 9 2.1.2 Manned Quadrotors . 11 2.1.3 Micro Quadrotors . 14 2.2 Quadrotor Alternatives . 20 2.3 UAV Systems Design . 25 2.4 Classic Aerodynamics and Design . 27 2.4.1 Rotor Modelling and Design . 27 2.4.2 Rotor Flapping . 28 2.4.3 Longitudinal and Lateral Flapping Equations . 30 2.4.4 Rotor Inflow Distortion . 34 2.5 Modern Aerodynamics . 35 2.5.1 Aeroelasticity . 35 2.5.2 Unsteady Aerodynamics . 36 xi CONTENTS 2.5.3 Aerodynamic Disturbance Modelling . 36 2.6 Typical Quadrotor Models . 38 2.6.1 Rigid Body Dynamics . 38 2.6.2 Rotor Dynamics . 38 2.7 Control . 40 2.7.1 Attitude Estimation . 40 2.7.2 Attitude Control . 41 2.7.3 Fundamental Limits of Control . 44 2.8 Perspectives on Quadrotor Design . 44 3 X-4 Hardware 47 3.1 X-4 Flyer Overview . 48 3.2 Chassis . 49 3.2.1 Airframe . 49 3.2.2 Vibration Isolation . 50 3.2.3 Test Gimbal . 51 3.3 Drive System . 53 3.3.1 Rotors . 53 3.3.2 Motors . 55 3.3.3 Batteries . 57 3.4 Avionics . 58 3.4.1 Communications . 58 3.4.2 Inertial Measurement Unit . 60 3.4.3 Motor Controllers . 62 3.4.4 Attitude Controller . 64 3.4.5 Sensor Payloads . 65 3.5 Base Station . 66 3.5.1 Command and Telemetry Console . 66 3.5.2 Communications Stack . 67 3.5.3 RC Handset . 69 3.6 Safety . 69 4 Rotor Design and Motor Speed Control 73 4.1 Introduction . 73 4.2 Blade Design . 75 4.2.1 Aerodynamic Design . 76 4.2.2 Structural Design . 78 xii CONTENTS 4.2.3 Practical Issues . 80 4.2.4 Rotor Performance . 82 4.3 Dynamic Control . 84 4.3.1 System Identification . 85 4.3.2 Experimental Identification of Disturbance Model . 88 4.3.3 Control Requirements and Constraints . 90 4.3.4 Compensator Design . 92 4.3.5 Dynamic Performance . 94 5 Quadrotor Dynamics and SISO Control 97 5.1 Introduction . 97 5.2 Dynamics and Stability . 98 5.2.1 The Importance of Flapping . 98 5.2.2 Basic Dynamics . 99 5.2.3 Vertical Rotor Motion Inflow . 101 5.2.4 Generalised Rotor Flapping Equations . 102 5.2.5 Unforced Stability Analysis . 104 5.2.6 Simulation . 106 5.3 Model Parameterisation and Stability . 108 5.3.1 Measured Values and Uncertainty . 108 5.3.2 Parameterised Model Envelope . 109 5.4 Design for Optimal Sensitivity . 112 5.5 Control and Simulation . 114 5.5.1 Discretised Model and Validation . 114 5.5.2 Controller Design . 117 5.5.3 Disturbance Rejection . 118 5.5.4 Simulation . 120 5.6 Implementation and Performance . 120 6 Nonlinear Control and Estimation 125 6.1 Introduction . 125 6.2 Control With Bias Estimation . 126 6.3 Control Without Reconstructed Rotation Matrix . 131 6.4 Simulation . 133 7 Conclusion 137 7.1 Achievements . 137 7.2 Future Direction . 139 xiii CONTENTS A Flapping Angle Equation Derivation 141 A.1 Flapping in Horizontal Flight . 141 A.1.1 Centrifugal Moment . 142 A.1.2 Aerodynamic Moment . 143 A.1.3 Weight Moment . 144 A.1.4 Constant Component Solution . 144 A.1.5 Sinusoidal Component Solution .
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