Autonomous soaring and surveillance in wind fields with an unmanned aerial vehicle by Chen Gao A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Aerospace Science and Engineering University of Toronto (cid:13)c Copyright 2015 by Chen Gao Abstract Autonomous soaring and surveillance in wind fields with an unmanned aerial vehicle Chen Gao Doctor of Philosophy Graduate Department of Aerospace Science and Engineering University of Toronto 2015 Small unmanned aerial vehicles (UAVs) play an active role in developing a low-cost, low- altitude autonomous aerial surveillance platform. The success of the applications needs to address the challenge of limited on-board power plant that limits the endurance performance in surveillance mission. This thesis studies the mechanics of soaring flight, observed in nature where birds utilize various wind patterns to stay airborne without flapping their wings, and investigates its application to small UAVs in their surveillance missions. In a proposed integrated framework of soaring and surveillance, a bird-mimicking soaring maneuver extracts energy from surrounding wind environment that improves surveillance performance in terms of flight endurance, while the surveillance task not only covers the target area, but also detects energy sources within the area to allow for potential soaring flight. The interaction of soaring and surveillance further enables novel energy based, coverage optimal path planning. Two soaring and associated surveillance strategies are explored. In a so-called static soaring surveillance, the UAV identifies spatially-distributed thermal updrafts for soaring, while incremental surveillance is achieved through gliding flight to visit concentric expanding regions. A Gaussian-process-regression-based algorithm is developed to achieve computationally-efficient and smooth updraft estimation. In a so-called dynamic soaring surveillance, the UAV performs one cycle of dynamic soaring to harvest energy from the horizontal wind gradient to complete one surveillance task by visiting from one target to the next one. A Dubins-path-based trajectory planning approach is proposed to maximize wind energy extraction and ensure smooth transition between surveillance tasks. Finally, a nonlinear trajectory tracking controller is designed for a full six-degree-of-freedom nonlinear UAV dynamics model and extensive simulations are carried to demonstrate the effectiveness of the proposed soaring and surveillance strategies. ii Acknowledgements The past five years at UTIAS have been a challenging as well as rewarding experience in my life. I would not be able to reach the destination without the tremendous support of many people. My special appreciation goes to my supervisor, Prof. Hugh Liu, who provided me with the opportunity to start this rewarding journey. His guidance, patience, and expertise helped me conquer difficult obstacles throughout every stage of this research. I also would like to thank my research committee members: Prof. Peter Grant and Prof. Craig Steeves, for their insights, guidance, assistance, and warm encouragement throughout the journey. Their valuable feedback and constructive comments during every DEC meeting helped me improve my thesis significantly. I would like to show my sincere appreciation to all faculty members in the University of Toronto, Institute for Aerospace Studies (UTIAS) for their generous support during the past five years. My special gratitude is extended to all fellow students and colleagues in the flight system and control (FSC) group at UTIAS, especially Keith Leung, Sohrab Haghighat, Jason Zhang, Laurent Heirendt, Connie Phan, Zhongjie Lin, and Wen Fan. Their companionship and encouragement have helped me get to where I am today. Thanks are also extended to all visiting scholars, especially Zhan Li for sharing his photos with me. The last but not the least, I would like to express my deepest gratitude to my parents for their unconditional love during the past five years. This thesis would not have been possible without their consistent support, encouragement, and care. I also would like to thank my friend Kayla for providing emotional support during those difficult times. iii Contents 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Autonomous soaring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.2 Trajectory planning and control in aerial surveillance . . . . . . . . . . . . 7 1.3 Thesis contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Soaring flight 11 2.1 Soaring flight environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Wind models in the planetary boundary layer . . . . . . . . . . . . . . . . . . . . 12 2.2.1 The wind gradient model in the surface layer . . . . . . . . . . . . . . . . 12 2.2.2 Updraft models in the mixed layer . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Equations of motion derivation in the presence of winds . . . . . . . . . . . . . . 16 2.3.1 Frames of reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.2 Equations of motion for a small UAV in the presence of winds . . . . . . 18 2.4 Static soaring flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5 Dynamic soaring flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3 Soaring Surveillance Problem Formulation 27 3.1 Aerial surveillance task. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Autonomous soaring surveillance . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.3 Soaring surveillance problem statements and formulations . . . . . . . . . . . . . 29 3.3.1 Soaring surveillance problem statements . . . . . . . . . . . . . . . . . . . 29 3.3.2 Static soaring surveillance trajectory planning problem formulation . . . . 30 iv 3.3.3 Updraft identification problem formulation . . . . . . . . . . . . . . . . . 31 3.3.4 Dynamic soaring surveillance trajectory planning problem formulation . . 32 3.3.5 Trajectory tracking problem formulation . . . . . . . . . . . . . . . . . . . 33 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4 Static soaring surveillance in the quasi-static updraft field 35 4.1 Surveillance and exploring points in the surveillance area . . . . . . . . . . . . . 35 4.1.1 Surveillance and exploring points in the surveillance area . . . . . . . . . 35 4.1.2 The traveling salesman problem. . . . . . . . . . . . . . . . . . . . . . . . 36 4.1.3 The traveling salesman problem for Dubins’ vehicle . . . . . . . . . . . . . 38 4.1.4 The exploring point determination . . . . . . . . . . . . . . . . . . . . . . 40 4.2 Static soaring surveillance approach . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2.1 Visit surveillance and exploring points . . . . . . . . . . . . . . . . . . . . 43 4.2.2 Updraft identification by Gaussian process regression with boundary constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.2.3 Updraft soaring strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.4 Updraft soaring results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2.5 Sensitivity analysis of the static soaring surveillance approach . . . . . . . 58 4.3 Static soaring surveillance simulation results . . . . . . . . . . . . . . . . . . . . . 64 4.3.1 Soaring surveillance demo in a 1 km wind field . . . . . . . . . . . . . . . 64 4.3.2 Large wind field (10 km) results . . . . . . . . . . . . . . . . . . . . . . . 67 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5 Dynamic soaring surveillance in a wind gradient field 77 5.1 Dynamic soaring surveillance problem formulation . . . . . . . . . . . . . . . . . 77 5.1.1 Surveillance case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.1.2 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.2 Dynamic soaring surveillance trajectory planning . . . . . . . . . . . . . . . . . . 80 5.2.1 The UAV’s trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.2.2 Dubins’ paths analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2.3 Flight-path-angle-profile determination . . . . . . . . . . . . . . . . . . . . 82 5.2.4 Dubins’ path choices: Heading angle rate determination . . . . . . . . . . 83 5.2.5 Dynamic soaring trajectory planning approach . . . . . . . . . . . . . . . 85 v 5.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.3.1 The optimal visiting sequence . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.3.2 Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.3.3 Dynamic soaring surveillance simulation results . . . . . . . . . . . . . . . 89 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6 Trajectory tracking controller design 99 6.1 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.2 Trajectory tracking controller design . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.2.1 Nonlinear mapping in the outer loop . . . . . . . . . . . . . . . . . . . . . 102 6.2.2 Inner-loop dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.2.3 Linear Quadratic Regulator V.S. State Dependent Riccati Equation . . . 105 6.2.4 Comparison study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.3.1 Static soaring trajectory tracking results . . . . . . . . . . . . . . . . . . . 109 6.3.2 Dynamic soaring trajectory tracking results . . . . . . . . . . . . . . . . . 110 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7 Conclusions and future work 120 7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Bibliography 122 vi List of Tables 4.1 Surveillance and exploring points . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2 Quantitative analysis of the coverage and traveling distance . . . . . . . . . . . . 41 4.3 Aerosonde UAV parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.4 Updraft parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.1 The relationship between flight path angle and heading angle . . . . . . . . . . . 82 5.2 Heading angle change along {lll}-type path between each pair of points . . . . . 84 5.3 Appropriate path look-up table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.4 Energy harvesting results between two points . . . . . . . . . . . . . . . . . . . . 90 5.5 Energy harvesting results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 vii List of Figures 1.1 Static soaring: riding updrafts high in the air . . . . . . . . . . . . . . . . . . . . 2 1.2 Dynamic soaring: exploiting wind gradients near sea surface . . . . . . . . . . . . 2 2.1 Troposphere structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Planetary boundary layer (PBL) structure . . . . . . . . . . . . . . . . . . . . . . 12 2.3 The logarithmic-like (A = 1.2) wind gradient profile with a gradient slope value (β = 0.35 s−1,z = 30 m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 tr tr 2.4 A plume of rising air and updraft bubbles in the PBL . . . . . . . . . . . . . . . 15 2.5 The updraft model whose center (x ,y ) = (0,0) m, radius R = 50 m and center 1 1 1 strength W = 10 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1 2.6 Simulated wind field generated from the weather prediction system . . . . . . . . 16 2.7 Rotation relationship among the vehicle-carried east-north-up (ENU), flight-path, and wind reference frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.8 Forces analysis on the UAV in the calm air and vertical winds . . . . . . . . . . . 22 2.9 Static soaring by loitering around an updraft . . . . . . . . . . . . . . . . . . . . 23 2.10 Forces analysis on the UAV in windward climb, dive, leeward climb, and dive in horizontal wind gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.11 Dynamic soaring: windward climbing (γ = π, ψ = −π, γ˙ = 0, ψ˙ = 0) . . . . . . . 25 4 2 2.12 Dynamic soaring: leeward diving (γ = −π,ψ = π, γ˙ = 0, ψ˙ = 0) . . . . . . . . . 25 4 2 2.13 Flight states along the windward climbing . . . . . . . . . . . . . . . . . . . . . . 26 2.14 Flight states along the leeward diving . . . . . . . . . . . . . . . . . . . . . . . . 26 3.1 Surveillance area with 50 uniformly-distributed targets . . . . . . . . . . . . . . . 28 3.2 Surveillance area with 300 uniformly-distributed targets . . . . . . . . . . . . . . 28 3.3 Surveillance area with coordinate system (X-Y-Z) . . . . . . . . . . . . . . . . . . 29 viii 3.4 Soaring surveillance architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.5 The periodic characteristics of dynamic soaring . . . . . . . . . . . . . . . . . . . 32 3.6 Trajectory planning and control diagram . . . . . . . . . . . . . . . . . . . . . . . 34 4.1 Surveillance division and visiting targets . . . . . . . . . . . . . . . . . . . . . . 37 4.2 The sub-optimal visiting sequence (ETSP solution) in Region 1 and 2 . . . . . . 39 4.3 Dubins’ surveillance path in Region 1 and 2 . . . . . . . . . . . . . . . . . . . . 40 4.4 The original and augmented surveillance paths in Region 1 and 2 . . . . . . . . 42 4.5 The relationship between airspeed and ground speed . . . . . . . . . . . . . . . . 44 4.6 Airspeed of steady flight with maximum L/D for various turn rate cases . . . . . 46 4.7 Lift coefficient of steady flight with maximum L/D for various turn rate cases . . 46 4.8 Flight path angle of steady flight with maximum L/D for various turn rate cases 47 4.9 Bank angle of steady flight with maximum L/D for various turn rate cases . . . 47 4.10 Sink rate of steady flight with maximum L/D for various turn rate cases . . . . . 47 4.11 The flowchart of the Dubins’ surveillance trajectory calculation . . . . . . . . . . 48 4.12 Dubins’ surveillance trajectory in Region 1 and 2 in the presence of horizontal winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.13 Airspeed and lift coefficient along the trajectory in Region 1 . . . . . . . . . . . . 50 4.14 Airspeed and lift coefficient along the trajectory in Region 2 . . . . . . . . . . . . 50 4.15 True and estimated wind fields from Region 1 to Region 7 . . . . . . . . . . . . 53 4.16 The UAV P and estimated point P on the X −Y plane . . . . . . . . . . . . . 54 g c 4.17 Vector field: the desired heading direction . . . . . . . . . . . . . . . . . . . . . . 54 4.18 The flowchart of the proposed updraft soaring strategy . . . . . . . . . . . . . . . 57 4.19 Updraft soaring strategy: Dubins-path-based guidance and estimated point correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.20 Updraft soaring results (2D soaring path) when height gain is 100 m . . . . . . . 58 4.21 Airspeed, lift coefficient and height change along soaring flight . . . . . . . . . . 59 4.22 Bank angle, sink rate and turning radius change along soaring flight . . . . . . . 60 4.23 Dubins’ surveillance path in the [−100,100] m×[−100,100] m field . . . . . . . . 61 4.24 Estimation sensitivity with respect to thermal’s position (x (t ),y (t )) m using 1 0 1 0 19 measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 ix 4.25 Estimation sensitivity with respect to thermal’s position (x (t ),y (t )) m using 1 0 1 0 95 measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.26 Estimation sensitivity with respect to thermal’s central strength W m/s . . . . . 63 1 4.27 Estimation sensitivity with respect to thermal’s radius R m . . . . . . . . . . . 64 1 4.28 Estimation sensitivity with respect to thermal’s oscillation amplitude a m . . . . 65 4.29 Estimation sensitivity with respect to thermal’s oscillation frequency b rad/s . . 66 4.30 Vertical and horizontal components of wind speed results on 10×10 interpolation points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.31 Interpolation results based on 10×10 wind speed data when t = 0 . . . . . . . . 68 4.32 Vertical wind estimation results in Region 1 . . . . . . . . . . . . . . . . . . . . . 69 4.33 Superposing surveillance trajectory over vertical wind speed estimation error (cid:12)(cid:12)f −f¯(cid:12)(cid:12) in Region 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.34 2D updraft soaring path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.35 3D updraft soaring path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.36 Dubins’ surveillance trajectory in Region 2 . . . . . . . . . . . . . . . . . . . . . 70 4.37 Flight states along the surveillance in Region 2 . . . . . . . . . . . . . . . . . . . 70 4.38 Dubins’ surveillance trajectory in Region 3 . . . . . . . . . . . . . . . . . . . . . 70 4.39 Flight states along the surveillance in Region 3 . . . . . . . . . . . . . . . . . . . 70 4.40 Dubins’ surveillance trajectory in Region 4 . . . . . . . . . . . . . . . . . . . . . 71 4.41 Flight states along the surveillance in Region 4 . . . . . . . . . . . . . . . . . . . 71 4.42 Dubins’ surveillance trajectory in Region 5 . . . . . . . . . . . . . . . . . . . . . 71 4.43 Flight states along the surveillance in Region 5 . . . . . . . . . . . . . . . . . . . 71 4.44 Dubins’ surveillance trajectory in Region 6 . . . . . . . . . . . . . . . . . . . . . 72 4.45 Flight states along the surveillance in Region 6 . . . . . . . . . . . . . . . . . . . 72 4.46 Dubins’ surveillance trajectory in Region 7 . . . . . . . . . . . . . . . . . . . . . 72 4.47 Dubins’ surveillance trajectory in Region 8 . . . . . . . . . . . . . . . . . . . . . 73 4.48 Dubins’ surveillance trajectory in Region 9 . . . . . . . . . . . . . . . . . . . . . 73 4.49 Flight states along the surveillance in Region 7 . . . . . . . . . . . . . . . . . . . 74 4.50 Flight states along the surveillance in Region 8 . . . . . . . . . . . . . . . . . . . 74 4.51 Flight states along the surveillance in Region 9 . . . . . . . . . . . . . . . . . . . 74 4.52 Average climb rate in each region . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.53 Wind speed estimation results in the simulated field . . . . . . . . . . . . . . . . 75 x