The Pennsylvania State University the Graduate School ATMOSPHERIC ENERGY HARVESTING for SMALL UNINHABITED AIRCRAFT by GUST SOARI
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The Pennsylvania State University The Graduate School ATMOSPHERIC ENERGY HARVESTING FOR SMALL UNINHABITED AIRCRAFT BY GUST SOARING A Thesis in Aerospace Engineering by Nathan Thomas Depenbusch c 2011 Nathan Thomas Depenbusch Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 2011 The thesis of Nathan Thomas Depenbusch was reviewed and approved∗ by the following: Jacob W. Langelaan Assistant Professor of Aerospace Engineering Thesis Advisor Mark M. Maughmer Professor of Aerospace Engineering George A. Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering ∗Signatures are on file in the Graduate School. Abstract Applying bird-inspired flight planning and control techniques to small robotic aircraft can greatly improve flight performance. This paper discusses a method for improving cruise performance of an uninhabited glider by harvesting energy from short period stochastic phenomena (i.e. gusts). Receding horizon control is used to plan a sequence of control inputs that maximizes an energy- based reward function over a time horizon, using only local knowledge of atmospheric conditions. Parameters of the receding horizon controller and parameters in the reward function are tuned using an evolutionary algorithm. The resulting controller is tested using Monte Carlo simulations of flight through Dryden gust fields: results show significant improvement over constant speed flight. Robustness of the receding horizon control approach to changes in aircraft parameters (parasite drag) is also evaluated using Monte Carlo simulations: increasing parasite drag results in gracefully degrading performance over the nominal condition while decreasing parasite drag results in increasing performance. iii Table of Contents List of Figures vii List of Tables viii Acknowledgments ix Chapter 1 Motivating Energy Efficient Flight Strategies for Small UAVs 1 1.1 Introduction . 1 1.2 Motivation . 3 1.3 System Overview . 5 1.4 Problem Description . 6 1.4.1 Unknown Wind . 6 1.4.2 Optimal Behavior Determination . 7 1.4.3 Uncertain Vehicle Model . 7 1.5 Review of Related Work . 7 1.5.1 Forms of Atmospheric Energy . 8 1.5.2 Avian Soaring Flight . 8 1.5.3 Modeling of the Aircraft and Environment . 10 1.5.4 Thermal Soaring . 10 1.5.5 Orographic Lift . 11 1.5.6 Dynamic Soaring . 11 1.5.7 Gust Soaring . 11 1.5.8 Receding Horizon Control Strategy . 12 1.6 Contributions . 13 1.7 Reader's Guide . 13 Chapter 2 Receding Horizon Control for Energy Harvesting 14 2.1 Problem Statement . 14 2.2 Vehicle Model in a Dynamic Wind Field . 16 2.2.1 Relevant Coordinate Frames . 17 2.2.2 Derivation of Force Equations . 18 iv 2.2.3 Force Equations . 21 2.2.4 Derivation of Moment Equations . 23 2.2.5 Moment Equations . 24 2.2.6 Euler Kinematics Equations . 25 2.2.7 Navigation Equations . 26 2.2.8 Model Outputs . 27 2.2.9 Aerodynamic Forces . 27 2.2.10 Thrust Force . 28 2.2.11 Longitudinal Aircraft Model . 29 2.2.12 Aircraft Models as Applied . 30 2.3 Wind Field Prediction . 31 2.4 Total Energy . 32 2.5 Energy Maximization . 34 2.5.1 The Cost Function . 34 2.5.2 Aircraft Control Policy . 35 2.6 Computation of Problem Solution . 36 2.7 Controller Complexity . 38 2.8 Wind Fields . 38 2.8.1 Discrete gusts . 39 2.8.2 Turbulence . 39 2.9 Summary . 42 Chapter 3 Application of an Evolutionary Algorithm to Optimize Control Variables 43 3.1 Summary of Evolutionary Algorithms . 43 3.1.1 Fundamentals . 44 3.1.2 Application in Control . 45 3.2 Justification for the Use of Evolutionary Computation Methods . 45 3.2.1 Downsides . 46 3.2.2 Use in Related Literature . 47 3.3 Algorithm Choice . 48 3.4 Determining the Planning Horizon and Reward Parameters . 49 3.4.1 Evolutionary Algorithm Control Variables . 49 3.4.2 Algorithm Convergence and Interpretation . 50 3.5 Evolved Gust Soaring Controllers . 51 3.6 Summary . 52 Chapter 4 Simulation Results 53 4.1 Performance Evaluation . 53 4.1.1 Setup . 53 4.1.2 Discrete gusts . 54 4.1.3 Dryden Wind Fields . 55 4.2 Discussion . 59 4.2.1 Computation Cost of the Controller . 61 4.3 Model Uncertainty . 62 4.3.1 Robustness of the Controller . 62 4.4 Summary . 63 v Chapter 5 Conclusions 65 5.1 Summary of Contributions . 66 5.1.1 Method for Dealing with Stochastic Nature of Turbulence . 66 5.1.2 Development of Energy-Based Reward Function . 66 5.1.3 Optimization of Controller Through Evolutionary Methods . 66 5.1.4 Performance Verification through Simulation . 67 5.1.5 Demonstration of Controller Robustness . 67 5.2 Recommendations for Future Research . 67 5.2.1 Examination of Controller Variability . 67 5.2.2 Control Through Flap Actuation . 67 5.2.3 Hardware Implementation . 68 5.2.3.1 Improved Gust Data . 68 5.2.3.2 Unsteady Aerodynamic Considerations . 68 5.2.4 Three-Dimensional Gust Soaring Control . 68 Appendix A Vehicle Properties 70 References 72 vi List of Figures 1.1 Dry mass vs. endurance . 2 1.2 Small uavs employed in research. 4 1.3 Several military uavs of various sizes. 5 1.4 Sink rates of representative aircraft plotted versus airspeed. 6 2.1 Receding Horizon Control premise . 16 2.2 Longitudinal reference frames . 29 2.3 RHC for gust soaring . 36 2.4 State barrier function . 37 2.5 Spline point dependence . 39 3.1 Evolving control variables . 50 3.2 Evolutionary algorithm convergence . 50 4.1 Discrete gust performance . 54 4.2 Dryden turbulence: performance bars . 57 4.3 Dryden turbulence: mean flightpaths . 58 4.4 Gust soaring states . 59 4.5 Controller performance summary . 60 4.6 Computation time . 61 4.7 Controller robustness . 63 4.8 Robust controller flight paths . 64 A.1 Vehicle properties as modeled . 71 vii List of Tables 2.1 Turbulence conditions simulated. ..