A Quadrotor Sensor Platform A dissertation presented to the faculty of the Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirements for the degree Doctor of Philosophy Michael J. Stepaniak November 2008 2 The views expressed in this dissertation are those of the author and do not reflect the official policy or position of the United States Air Force, the Department of Defense, or the United States Government. 3 This dissertation titled A Quadrotor Sensor Platform by MICHAEL J. STEPANIAK has been approved for the School of Electrical Engineering and Computer Science and the Russ College of Engineering and Technology by Frank van Graas Fritz J. and Dolores H. Russ Professor of Electrical Engineering Maarten Uijt de Haag Associate Professor of Electrical Engineering and Computer Science Dennis Irwin Dean, Russ College of Engineering and Technology 4 Abstract STEPANIAK, MICHAEL J., Ph.D., November 2008, Electrical Engineering A Quadrotor Sensor Platform (124 pp.) Directors of Dissertation: Frank van Graas and Maarten Uijt de Haag A quadrotor sensor platform capable of lifting a ten pound payload is presented. Platform stabilization is accomplished using classical control methodology and is implemented on a field programmable gate array. The flight control system relies on attitude information derived using a technique that circumvents the electromagnetic susceptibility of the inertial unit while minimizing the propagation of errors. This dissertation develops models for the high-power brushless motors. In particular, the rotational losses as a function of motor speed and the operational characteristics of the electronic speed controller are considered. Furthermore, losses within the batteries are found to dominate the power budget at planned operating speeds. Based on the models, a graphical method of predicting sortie duration is presented. An incremental build-up approach is applied, leading to a successful flight test program. This platform represents a threefold increase in payload capacity for quadrotor platforms and is the largest unmanned quadrotor to successfully fly without tethers. Approved: Frank van Graas Fritz J. and Deloros H. Russ Professor of Electrical Engineering Maarten Uijt de Haag Associate Professor of Electrical Engineering and Computer Science 5 This dissertation is dedicated to my family for their unwavering support and encouragement. 6 Acknowledgments This dissertation was possible only through the relentless support and encouragement of my wife and children. I am eternally grateful for their perseverance in light of the numerous sacrifices they made on my behalf. I am filled with deepest joy and immeasurable gratitude for having them at my side throughout this journey. In addition, I am extremely thankful for the guidance of my two advisors, Dr. Frank van Graas and Dr. Maarten Uijt de Haag. Their wisdom and patience was paramount to my success. I enjoyed working with them, especially in light of their approachable personalities, and I look forward to our continued collaborations in the future. Also, I was fortunate to have the assistance of Caleb White. He played a pivotal role in this effort by designing and building the airframe and by applying his skill as a remote- control pilot for the project. The contribution of Caleb’s experience was invaluable to the project. Others that contributed to my success include: Dean Bruckner, my officemate, for his daily camaraderie and commiseration which made the endeavor so much more enjoyable; Dr. Andrey Soloviev and Dr. Sanjeev Gunawardena for their pointers as I learned to cope with the myriad nuances of synthesizing VHDL code; and the remainder of my dissertation committee: Dr. David Diggle, Lt Col John Coulter, Dr. Todd Young, and Dr. Michael Braasch for their generous time, effort, and insight. My sincere appreciation also extends to all of my classmates and coworkers at the Avionics Engineering Center; their support and friendship made my time in Athens both enjoyable and productive. This quadrotor sensor platform supports theoretical research partially funded by the Air Force Office of Scientific Research through Dr. Jon Sjogren, Program Manager. I was graciously afforded the unique opportunity to pursue this research by the United States Air Force through sponsorship by the Air Force Institute of Technology. 7 Table of Contents Abstract.........................................4 Dedication........................................5 Acknowledgments....................................6 List of Tables...................................... 10 List of Figures...................................... 11 List of Symbols..................................... 13 List of Acronyms.................................... 16 1 Introduction..................................... 17 1.1 Summary................................... 20 1.2 Overview................................... 21 2 Background..................................... 23 2.1 Early History................................. 23 2.2 Recent Developments............................. 25 2.3 Principle of Operation............................. 27 2.4 Quadrotor Configuration........................... 31 2.4.1 Airframe............................... 31 2.4.2 Propulsion.............................. 32 2.4.3 Control................................ 32 2.4.4 Pulse Width Modulated Signals................... 34 3 Component Modeling................................ 36 3.1 Brushless Motor................................ 36 3.1.1 Motor Constants........................... 36 3.1.2 Determining Motor Parameters.................... 38 3.2 Electronic Speed Controller.......................... 39 3.3 Modeling Core Loss............................. 42 3.3.1 Variation in Core Loss as a Function of Motor Speed........ 43 3.3.2 An Empirical Model for Rotational Loss............... 44 3.4 Lithium Polymer Batteries.......................... 47 3.5 Propellers................................... 49 8 3.6 Inertial Sensor................................. 51 3.6.1 Limitations.............................. 52 3.6.2 Implementation............................ 53 3.6.3 Allan Variance Analysis....................... 54 4 Aerodynamic Model................................ 57 4.1 Notation.................................... 57 4.2 Mass Properties................................ 58 4.2.1 Center of Gravity........................... 59 4.2.2 Inertia................................. 62 4.3 Rigid Body Dynamics............................. 62 4.4 Gyroscopic Moments............................. 64 4.5 External Forces................................ 66 4.5.1 Gravity................................ 66 4.5.2 Thrust................................. 67 4.5.3 Aerodynamic Forces......................... 67 4.6 Linearized Equations of Motion....................... 69 5 Deriving Attitude.................................. 71 5.1 Reference Frames............................... 71 5.2 Attitude.................................... 72 5.2.1 Euler Angles............................. 73 5.2.2 Direction Cosine Matrix....................... 74 6 Flight Control System................................ 82 6.1 Background.................................. 82 6.2 Design Goals................................. 83 6.3 General Methodology............................. 83 6.4 Hardware Implementation.......................... 84 6.4.1 Hardware Description Language................... 85 6.4.2 Inertial Interface........................... 86 6.4.3 Bias Correction............................ 87 6.4.4 Radio Interface............................ 88 6.4.5 Attitude Update............................ 89 6.4.6 Control Loop............................. 92 7 Test Preparation................................... 96 7.1 FPGA Verification.............................. 96 7.1.1 Idealized Model........................... 96 7.1.2 Logic Model............................. 96 7.1.3 Modelsim............................... 97 9 7.1.4 FPGA Simulation........................... 97 7.1.5 Verification Process.......................... 98 7.2 Build Up Approach.............................. 98 7.3 Test Hazard Analysis............................. 100 7.3.1 Propeller Operating Limit...................... 100 7.3.2 Uncommanded motion at power-up................. 101 7.3.3 Uncommanded motion after power-up................ 102 7.3.4 Interference.............................. 102 7.3.5 Crossed sensor or motor signals................... 103 7.3.6 Loss of power............................. 104 7.3.7 Excessive battery temperature.................... 105 7.4 Mission Planning............................... 105 8 Results........................................ 109 8.1 Attitude Determination............................ 109 8.2 First Flight.................................. 111 8.3 Flight Control System Suitability....................... 112 8.4 Payload Capacity............................... 113 9 Conclusions and Recommendations........................ 115 9.1 Conclusions.................................. 115 9.2 Future Work and Recommendations..................... 116 References........................................ 119 10 List of Tables 3.1 AXi 4120/18 Motor Parameters........................ 40 3.2 Allan Variance-Derived Noise Coefficients.................. 56 4.1 Notation Used for the Aerodynamic Model................. 57 4.2 Component Mass Properties - Initial Configuration............. 60 4.3 Component Mass Properties - Payload and Carbon Fiber Sub-Frame.... 61 4.4 Quadrotor Mass Properties.........................