High Angle of Attack Landing of an Unmanned Aerial Vehicle
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High Angle of Attack Landing of an Unmanned Aerial Vehicle Kristoffer Gryte Master of Science in Cybernetics and Robotics Submission date: July 2015 Supervisor: Thor Inge Fossen, ITK Norwegian University of Science and Technology Department of Engineering Cybernetics NTNU Faculty of Information Technology, Norwegian University of Mathematics and Electrical Engineering Science and Technology Department of Engineering Cybernetics MSC THESIS DESCRIPTION SHEET Name: Kristoffer Gryte Department: Engineering Cybernetics Thesis title (Norwegian): Landing av ubemanneded fly ved bruk av stor angrepsvinkel Thesis title (English): High Angle-of-Attack Landing of an Unmanned Aerial Vehicle Thesis Description: The purpose of the thesis is to investigate how a control strategy based on high angle-of-attack (AOA) can be used to automatically land an unmanned aerial vehicle (UAV) in a net. This involves mathematical modeling of the X8 fixed-wing UAV and simulation of high AOA maneuvers. Furthermore, the X8 model should be used to design and test an automatic control system for landing. The following items should be considered: 1. Define the scope of the thesis and clarify what your contributions are. 2. Development of a flight simulator the X8 UAV, which is valid for high AOA. The simulator should also include wind loads on the fuselage. 3. Development of a software-in-the-loop simulator for the X8 using JSBSim interfaced with the ArduPlane autopilot. 4. Formulate landing as an optimal control problem, that has low terminal velocity as the objective. Use this to investigate how the terminal velocity is affected by different initial conditions and constraints. 5. Extend the optimal control problem to a model predictive controller, and use this in landing simulations. 6. Conclude your results. Start date: 2015-01-05 Due date: 2015-07-01 Thesis performed at: Department of Engineering Cybernetics, NTNU Supervisor: Professor Thor I. Fossen, Dept. of Eng. Cybernetics, NTNU Abstract Motivated by the limited landing space on board a ship, this thesis investigates the landing of the Skywalker X8 fixed wing unmanned aerial vehicle (UAV)in a net. Further motivated by the way birds abruptly, and equally elegantly, reduce their velocity when landing on a perch or the branch of a tree, a perched landing strategy utilizing the increased drag experienced for large angles of attack is used to minimize the velocity at impact with the net. This is accomplished by expressing landing as an optimal control problem, taking advantage of a nonlinear model of the X8 that is valid for high angles of attack. At this stage, the optimal control problem is only concerned with the three longitudinal degrees- of-freedom. It is solved in an open source optimization framework, using a nonlinear interior point method. Further, a nonlinear model predictive controller (NMPC) that can control the X8 throughout the landing is developed. At the heart of the optimal control problem lies a linear model, blended with a flat plate model to increase its validity for high angles of attack in lift, drag and pitch moment. The linear model is developed using an easy-to-use computational fluid dynamics (CFD) modeling software. In addition a six degrees-of-freedom software-in-the-loop (SITL) simulator is developed for future use in testing of hardware-near implementations of the controller, and to allow for validation of the model through pilot testing. Comparison of six different landing scenarios yield a wide range of landing velocities, depending on the constraints of the scenario. Simulations with the developed NMPC show that the same performance is achievable through control of the X8 under minor environmental disturbances. From this it is concluded that the perched landing strategy will lead to a considerable reduction in terminal absolute velocity, compared to a low angle of attack approach. It is found to be advantageous to start from a low altitude, landing into an elevated net. However, whether an equally large reduction is possible in practice depends on the capabilities of the real-time implementation and the validity of the model, particularly the propeller model, the pitching moment and drag coefficients. Finally it depends on how the lateral degrees-of-freedom are affected by the high angle of attack flight. i ii Samandrag (Norwegian Translation of the Abstract) Motivert av den avgrensa landingsplassen ombord pa˚ skip, undersøkjer denne oppgava˚ nettlanding av det ubemanna flyet Skywalker X8. Vidare motivert av den snøgge ned- bremsinga fuglar elegant oppnar˚ ved landing pa˚ greiner, ser denne oppgava˚ nærare pa˚ ein landingsstrategi som utnyttar den drastiske auken i luftmotstand, som finn stad for store angrepsvinklar, til a˚ minimere hastigheita i landingsaugneblinken. Dette blir gjort ved a˚ formulere landinga som eit optimaliseringsproblem som nyttar seg av ein ulineær modell av X8 som er gyldig for store angrepsvinklar. Optimaliseringsproblemet har blitt forenkla til dei tre fridomsgradene i longitudinalplanet, og blir løyst ved hjelp av eit optimalis- eringsrammeverk basert pa˚ open kjeldekode som nyttar ein ulineær indre-punkt løysar. Vidare har ein ulineær modell-prediktiv regulator blitt utvikla for a˚ kunne kontrollere X8 gjennom landinga. Ein sentral del av optimaliseringsproblemet er ein eigenutvikla lineær modell, der løft-, luftmotstand- og stampkoeffisientane gradvis gar˚ over i ein flat plate modell for a˚ auke gyldigheita ved store angrepsvinklar. Den lineære modellen har blitt utvikla ved hjelp av eit enkelt program for numerisk strøymingsanalyse. I tillegg har det blitt utvikla ein programvare-i-sløyfa simulator i seks fridomsgrader for a˚ kunne nyttast i testing av maskinvarenære implementeringar av regulatoren, samt for a˚ legge til rette for modellvalidering gjennom pilottesting. Samanlikning av seks ulike landingsscenario, med ulike avgrensingar, gav ulike landingshastigheiter. Ei simulering med den modell- prediktive regulatoren har vist at tilsvarande ytelsar er oppnaelege˚ ved regulering av X8 under ytre paverknader.˚ Basert pa˚ desse resultata blir det konkludert at ein slik land- ingsstrategi, med stor angrepsvinkel, vil føre til ein stor reduksjon i absolutthastigheita i landingsaugneblinken, samanlikna med a˚ lande med ein lag˚ angrepsvinkel. Det har synt seg føremonleg a˚ starte landinga fra˚ ei lag˚ høgde, samt a˚ lande i eit heva nett. Men om ein like stor reduksjon er mogleg i praksis avhengjer av sanntidsimplementasjonen av sys- temet og gyldigheita av modellen, herunder særskildt propellmodellen, stampemoment- og luftmotstandskoeffisientane. Det vil ogsa˚ vere avhengig av korleis fridomsgradene i lateralplanet vert paverka˚ av flyging med stor angrepsvinkel. iii iv Preface This thesis is submitted in partial fulfillment of the requirements for the Master of Science degree at the Norwegian University of Science and Technology. The work presented in this thesis has been carried out at the Department of Engineer- ing Cybernetics, and would not have been possible without the inputs and contributions from many of its associates. First, I would like to thank Professor Thor Inge Fossen for his inspiring ideas and guidance into the academic world. The team at the UAV-lab deserve to be acknowledged; especially Artur Zolich, who has been an important sparring partner in my aerodynamic endeavors, and Siri H. Mathisen, whom I have worked closely with on optimization and model predictive control. I would also like to thank my fellow MSc. students from room G232B. They have given me invaluable feedback in a competitive, yet friendly environment. Finally I would like to thank my parents and brother for believing in me and encouraging me when times get tough. Kristoffer Gryte Trondheim, June 2015 v vi Table of Contents Abstracti Abstract in Norwegian iii Prefacev Table of Contentsx List of Tables xi List of Figures xiv List of Code Snippets xv Nomenclature xvi I Introduction and Background Material1 1 Introduction3 1.1 Skywalker X8................................3 1.2 Previous work................................4 1.3 Contributions................................5 1.4 Structure of this thesis...........................6 2 Theory9 2.1 UAV coordinate systems and models.................... 10 2.1.1 Body-axis.............................. 10 2.1.2 Stability-axis............................ 10 2.1.3 UAV models............................ 11 2.1.4 Mapping from elevon to aileron-elevator.............. 12 vii 2.2 Aerodynamics................................ 12 2.2.1 Parametrization of the aerodynamical coefficients......... 12 2.2.2 Flat plate model.......................... 13 2.3 Rotations between frames of reference................... 14 2.4 Wind model................................. 15 2.4.1 The Dryden turbulence model................... 16 II Methods 17 3 Model 19 3.1 From a physical UAV to aerodynamic coefficients............. 19 3.2 Choosing model structure.......................... 20 3.3 Model extension............................... 20 3.3.1 Drag depending on sideslip..................... 20 3.3.2 Nonlinear extension to lift and drag................ 21 3.3.3 Flat plate pitch moment...................... 21 3.4 Final model structure............................ 24 3.5 Adaptation of coefficient.......................... 24 4 Simulator 25 4.1 Simulink simulator............................. 25 4.1.1 Simulink structure......................... 26 4.1.2 FlightGear............................. 27 4.1.3 Calculating trim conditions..................... 29 4.2 Software-in-the-loop