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Hazard Thesis Colorlinks ABSTRACT HAZARD, MATTHEW WESLEY. Unscented Kalman Filtering for Real-Time Atmospheric Thermal Tracking. (Under the direction of Dr. C. E. Hall.) The increasing use of unmanned air vehicles in military and civilian applications has been accompanied by a growing demand for improved endurance and range. These demands have been largely met by advances in aerodynamic and structural efficiency, improved battery tech- nology, and the ongoing miniaturization of onboard computing and payload systems. Recently, more attention has been paid to the extraction of energy from the atmosphere. Aircraft can make use of atmospheric updrafts, or thermals, to gain altitude without expenditure of onboard fuel stores. By intelligently tracking thermals, an unmanned aircraft can extend its range or loiter time without carrying additional fuel or specialized sensors. Prior research has focused on the `big picture' concepts associated with autonomous soaring - determining when to stop and soar in a thermal, what speed to fly, when to return to the desired course, and so on. Finding and tracking thermals is only a single component of the complete soaring system. However, because the high-level decision making tasks rely on estimates of the thermal parameters, the accuracy and computational cost of the thermal tracking algorithm set the upper performance limit of the entire system. So, this research reformulated batch regression thermal finding algorithms used in past ef- forts into an efficient Unscented Kalman Filter. Open-loop simulation results showed the filter was capable of accurately estimating thermal position, strength, and size with low computa- tional cost for a variety of realistic flight paths. Closed-loop simulation reaffirmed this statement in the presence of realistic aircraft, sensor, and thermal dynamics. Further, the algorithm was embedded into the ALOFT soaring platform (a 4.3 m wingspan unmanned glider) for flight testing, which demonstrated its ability to track real-world thermals during cross-country flights exceeding 5 hours flight time over a 70 mile course. c Copyright 2010 by Matthew Wesley Hazard All Rights Reserved Unscented Kalman Filtering for Real-Time Atmospheric Thermal Tracking by Matthew Wesley Hazard A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Master of Science Aerospace Engineering Raleigh, North Carolina 2010 APPROVED BY: Dr. A. Gopalarathnam Dr. F. Wu Dr. C. E. Hall Chair of Advisory Committee DEDICATION For my grandfathers, who inspired me to become an engineer. ii ACKNOWLEDGEMENTS I'd like to thank my committee, friends, and family for their support in the completion of this research. Specific thanks go to Dan, who got me started on this project, and Dave, who convinced me to stop working and start writing. My dad, Donald, lent an editor's eye to my final draft - he is my grammar guru. My mom, Stephanie, deserves special credit for worrying about my health when I haven't had time. iii TABLE OF CONTENTS List of Tables .......................................... vi List of Figures ......................................... vii Chapter 1 Introduction ................................... 1 1.1 Autonomous Soaring . 2 1.1.1 Mission Management . 3 1.1.2 Autopilot and Airframe . 4 1.2 ALOFT Autonomous Soaring Framework . 5 1.2.1 Autopilot and Airframe . 7 1.2.2 Soaring Controller and Mission Management . 8 Chapter 2 Thermal Theory ................................. 10 2.1 Thermal Modeling . 10 2.2 Thermal Sensing . 14 Chapter 3 Thermal Tracking with a Kalman Filter ................. 18 3.1 Kalman Filtering Basics . 18 3.2 The Extended Kalman Filter . 20 3.3 The Unscented Transform . 21 3.4 The Unscented Kalman Filter . 25 3.5 Thermal Models in the UKF Framework . 28 Chapter 4 Implementation and Simulation ....................... 31 4.1 Open-loop Thermal Tracking Simulation . 31 4.2 Computational Performance Comparison . 37 4.3 Integration with the ALOFT Framework . 40 4.4 Closed Loop Simulation . 40 4.4.1 Closed-loop tracking using a Wharington thermal model . 42 4.4.2 Closed-loop tracking using the Gedeon thermal model . 48 4.5 Simulation Summary . 52 Chapter 5 Flight testing ................................... 53 5.1 Flight testing benefits and caveats . 53 5.2 Flight Testing Results . 54 References ............................................ 58 Appendix ............................................ 59 iv Appendix A MATLAB UKF Implementation . 60 A.1 Thermal UKF Closed-Loop Simulation Interface . 60 A.2 Thermal UKF . 66 A.2.1 Closed-Loop Simulation / Flight Testing Version . 66 A.2.2 Sigma Point Selection . 69 A.3 Quaternion Algebra . 70 A.3.1 Reconstruction of a Quaternion from Euler Angles . 70 A.3.2 Rotation of a Vector by a Quaternion . 70 v LIST OF TABLES Table 4.1 Open-Loop Simulation Parameters . 33 Table 4.2 Open-Loop Simulation Results . 35 Table 4.3 Closed Loop Simulation Parameters . 43 Table 4.4 Closed Loop UKF Configuration Parameters . 44 vi LIST OF FIGURES Figure 1.1 Autonomous Soaring Subsystems . 3 Figure 1.2 Loosely Coupled Outer and Inner Loop Controllers . 6 Figure 1.3 Ground-based and airborne subsystems . 6 Figure 1.4 ALOFT and its creator, Dan Edwards . 7 Figure 1.5 Cloud Cap Technology Piccolo II . 8 Figure 1.6 ALOFT Electronics Installation . 9 Figure 2.1 Schematic View of a Thermal . 11 Figure 2.2 Wharington thermal model, viewed in 3D . 12 Figure 2.3 Gedeon thermal model, viewed in 3D . 13 Figure 2.4 Comparison of Wharington and Gedeon thermal models . 14 Figure 3.1 Kalman Filter Flow Diagram . 19 Figure 3.2 Unscented Transform versus Monte Carlo Simulation . 24 Figure 3.3 Unscented Kalman Filter Flow Diagram . 25 Figure 4.4 Execution time per iteration for batch processing and Thermal UKF. 37 Figure 4.5 Mean Squared Error for batch processing and Thermal UKF . 38 Figure 4.6 Thermal position estimates for batch processing and Thermal UKF . 39 Figure 4.7 Energy Rate History in Closed-Loop Simulation . 44 Figure 4.8 Overview of Closed-Loop Simulation using the Wharington Model . 45 Figure 4.9 Altitude Time History in Closed-Loop Simulation . 45 Figure 4.10 Closed-Loop Tracking performance for Thermal 3 . 46 Figure 4.11 Closed-Loop Tracking performance for Thermal 1 . 46 Figure 4.12 Closed-Loop Tracking performance for Thermal 2 . 47 Figure 4.13 Overview of Closed-Loop Simulation using the Gedeon Model . 49 Figure 4.14 Closed-Loop Tracking performance for Thermal 2 . 49 Figure 4.15 Closed-Loop Tracking performance for Thermal 3 . 50 Figure 4.16 Closed-Loop Tracking performance for Thermal 1 . 50 Figure 4.17 Altitude Time History in Closed-Loop Simulation . 51 Figure 5.1 Altitude Trace for Cross Country Flight Test . 55 Figure 5.2 Flight Path for Cross Country Flight Test . 56 Figure 5.3 Altitude Trace for Cross Country Flight Test . 56 Figure 5.4 Flight Path for Cross Country Flight Test . 57 vii Chapter 1 Introduction The use of unmanned aerial vehicles (UAVs) in military and civilian applications is growing rapidly. In many unmanned aerial vehicle applications, endurance, range, and payload capacity are the factors which define the capabilities of the system (in contrast to manned aircraft, where speed, maneuverability, and stealth characteristics play a larger role). Increasing endurance and range by simply adding fuel or battery weight results in loss of payload capacity, so increased efficiency or energy density is needed. Although many advances have been made in structural, propulsion, and aerodynamic efficiency, recent research efforts have turned instead to extracting energy from the atmosphere. The most promising source of atmospheric energy is the thermal, or updraft. By autonomously tracking thermals, unmanned aerial vehicles can augment their internal energy stores, improving their endurance and range. This thesis presents a novel technique for efficiently tracking atmospheric thermals using an Unscented Kalman Filter. In the remainder of this chapter, we present background information on autonomous soaring, to show how this contribution fits within a larger framework. Chapter 2 continues with details of how thermals are modeled and how we can sense their effect on an aircraft. Next, Chapter 3 shows how an Unscented Kalman Filter (UKF) can be used to efficiently fuse information from thermal models and aircraft sensors. The remainder of the thesis details the implementation and testing of the thermal tracking UKF. Chapter 4 shows how the algorithm was exercised 1 in open-loop and closed-loop simulations. In Chapter 5, we document two flight tests which demonstrate the performance of the algorithm under favorable and adverse conditions. Finally, in the hope that this research may prove of benefit to others (just as the ALOFT framework, detailed in section 1.2, was invaluable to this work), the MATLAB implementation is presented in Appendix A. 1.1 Autonomous Soaring Atmospheric thermals, or convective updrafts, are naturally occurring sources of energy created by the interaction between solar heating, local terrain variations, and ambient meteorological conditions. An aircraft flying through a thermal can extract energy from the atmosphere. This energy gain can be used to offset energy losses due to drag, fuel expenditure, or maneuvers. Autonomous soaring involves actively tracking and engaging thermals to maximize energy gains, while achieving a mission. Because UAVs are already equipped with a suite of sensors and computers, adding soaring intelligence may simply require a software upgrade. In aircraft that are designed with soaring in mind from the outset (especially solar-powered or hybrid systems), fuel weight might be traded for increased payload capacity or simply omitted for weight savings. For instance, the algorithm developed in this work was implemented on a small glider, where all the energy expended by the system (except for the initial winch launch) was first extracted from the atmosphere. For existing UAV designs not specially designed for soaring, the energy gains may be more modest, however even slight improvements in endurance and range are of tactical utility to unmanned aircraft operators.
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