Design, Modelling and Control of a Space UAV for Mars Exploration Akash Patel Space Engineering, master's level (120 credits) 2021 Luleå University of Technology Department of Computer Science, Electrical and Space Engineering Design, Modelling and Control of a Space UAV for Mars Exploration Akash Patel Department of Computer Science, Electrical and Space Engineering Faculty of Space Science and Technology Luleå University of Technology Submitted in partial satisfaction of the requirements for the Degree of Masters in Space Science and Technology Supervisor Dr George Nikolakopoulos January 2021 Acknowledgements I would like to take this opportunity to thank my thesis supervisor Dr. George Nikolakopoulos who has laid a concrete foundation for me to learn and apply the concepts of robotics and automation for this project. I would be forever grateful to George Nikolakopoulos for believing in me and for supporting me in making this master thesis a success through tough times. I am thankful to him for putting me in loop with different personnel from the robotics group of LTU to get guidance on various topics. I would like to thank Christoforos Kanellakis for guiding me in the control part of this thesis. I would also like to thank Björn Lindquist for providing me with additional research material and for explaining low level and high level controllers for UAV. I am grateful to have been a part of the robotics group at Luleå University of Technology and I thank the members of the robotics group for their time, support and considerations for my master thesis. I would also like to thank Professor Lars-Göran Westerberg from LTU for his guidance in develop- ment of fluid simulations for this master thesis project. I would like to express my gratitude towards Dr Victoria Barabash from LTU for her considerations towards the academic deadlines and course guidance though out my master program at LTU. I also thank Maria Winnebäck for always helping in courses, administration work and also for considerations towards the thesis defence. Moreover I express my sincere gratitude towards the Faculty of department of Space Science and my fellow students from University who have been kind enough to share their knowledge and important com- ments in order to make this project scientifically strong. Last but not least, I would like to thank my friends and my family for supporting me morally to write this master thesis. i Abstract Mars : The red planet has been on top in the priority list of interplanetary exploration of the solar system. The Mars exploration landers and rovers have laid the foundation of our understanding of the planet atmosphere and terrain. Although the rovers have been a great help, they also have limitations in terms of their speed and exploration capabilities from the ground. Throughout the whole mission period the rover is limited to travel for couple of Kilometers, and the lack of terrain data in real time also limits the path planning of the exploration rovers. It would be beneficial in terms of extended range of operation to have a secondary system that can fly ahead of the rover and provide it with pre-mapped terrain so that the rover can select the optimal site to perform scientific experiments. The INGENUITY Mars helicopter is designed to test the technical demonstration of aerial flight in the thin atmosphere of Mars. This project will use some of the research and devel- opments done for the ingenuity helicopter and aims to simplify the rotor craft’s design by adding more rotors and getting rid of the variable pitch control used in ingenuity helicopter. In this thesis we have proposed a multi rotor UAV that is developed for powered flight in the Mars atmosphere. This thesis will give insights about the constraints and solutions to allow an autonomous UAV to fly in the thin atmosphere of Mars. The thesis will focus on the selection of the optimal airfoil for low Reynolds number flow on Mars, its aerodynamics which will be followed by flow simulations in CFD software to extract thrust parameters for the UAV. The later half of the thesis project will be primarily focused on designing a low level controller for the UAV to execute some basic com- mands like hold position, do roll,pitch and yaw movements and following a specific path. From the control prospective the scope of this master thesis is to make a mathematical model of the Mars UAV and design a PID controller for the vehicle. The project will conclude the simulations and control response from the PID controller and as a future work an LQR and MPC can be developed for the Mars UAV. ii Table of Contents 1 Introduction 1 1.1 Motivation . .2 1.2 UAV Flight in Mars Atmosphere . .3 1.3 Thesis Outline . .4 1.3.1 Chapter 2 . .4 1.3.2 Chapter 3 . .4 1.3.3 Chapter 4 . .4 1.3.4 Chapter 5 . .4 1.3.5 Chapter 6 . .5 1.3.6 Chapter 7 . .5 1.3.7 Chapter 8 . .5 1.3.8 Chapter 9 . .5 2 Literature review and Background 6 2.1 Computational Fluid Dynamics . .6 2.1.1 Reynolds Averaged Navier-Stokes equations . .7 2.2 Momentum theory of Rotors . .8 2.2.1 Blade Element Momentum theory . 12 3 Rotor blade optimization for Mars 15 3.1 Low Reynolds Number Aerodynamics . 16 3.1.1 Performance of Flat and Cambered Plate Airfoils . 18 3.1.2 Laminar and Turbulent Reattachments . 19 3.1.3 Ingenuity Helicopter . 21 3.1.4 Performance Evaluation of Ingenuity Blade Profile . 22 4 Two Dimensional Flow Analysis 25 4.1 Experimental Setup . 25 4.1.1 Turbulence and Laminar Separation Bubble Expectations . 26 4.1.2 Definition of 2D Geometry . 27 4.2 Result Validation of 2D Analysis . 28 iii 5 Fluent Simulation 3D 34 5.1 Co-Axial Rotor System . 34 5.2 Simulation Setup In ANSYS Fluent . 35 5.3 Simulation Results and Validation . 36 6 CAD design of Mars UAV 43 7 Vehicle Dynamics 47 7.1 Conventional Quadrotor . 47 7.2 Quadrotor Dynamics . 47 7.2.1 Euler angles . 50 7.2.2 Mathematical Model of Quadrotor . 51 7.3 Mars UAV Model Dynamics . 53 7.3.1 Equations of Motion . 55 7.3.2 State Space Representation . 56 8 Mars UAV System Control 60 8.1 Open Loop Simulation . 60 8.1.1 Motor Mixer Subsystem . 62 8.1.2 Rotation Subsystem . 63 8.1.3 Translation Subsystem . 64 8.2 Closed Loop Simulations . 65 8.2.1 Altitude Controller . 65 8.2.2 Heading and Attitude Controller . 65 8.2.3 Position Controller . 66 8.3 PID Control . 68 8.3.1 Altitude PID Control . 69 8.3.2 Roll PID Control . 69 8.3.3 Pitch PID Control . 70 8.3.4 Yaw PID Control . 71 8.3.5 Position PID Control . 72 8.4 Simulation Results for PID Control . 73 8.4.1 Position response . 74 8.4.2 Trajectory Follow response . 75 9 Conclusion 79 TABLE OF CONTENTS iv List of Figures 2.1 Control volume for streamtube representation . .9 2.2 Aerodynamic forces on blade profile . 12 3.1 subsonic and transonic airfoils . 15 3.2 Flow separation affected by Reynolds number and angle of attack . 16 3.3 CL vs Reynolds number . 18 3.4 CD vs Reynolds number . 18 3.5 Separation bubble . 20 3.6 Ingenuity Helicopter . 22 3.7 Performance of Ingenuity helicopter test model for different atmospheric conditions 23 4.1 Geometry of flat plate defined in grid . 27 4.2 Geometry of cambered plate defined in grid . 27 4.3 Cl versus Cd for a flat plate . 28 4.4 Angle of attack versus Cl and Cd for flat plate . 29 4.5 Lift/Drag coefficients versus Angle of attack for flat plate . 29 4.6 Angle of attack versus Cl and Cd for cambered plate . 30 4.7 Lift/Drag coefficients versus Angle of attack for cambered plate . 30 4.8 (a) Velocity profile over cambered plate airfoil (b) Velocity profile over ACA airfoil (c) Velocity profile over a DEP airfoil (d) Velocity profile over PAT airfoil . 31 4.9 (a) Laminar boundary layer at angle of attack a = 0° (b) shear layer separation Angle of attack a = 2°................................ 31 4.10 (a) Shear layer behaviour at angle of attack a = −2° (b) shear layer behaviour at Angle of attack a = −3°............................... 32 4.11 Extreme mach number in subsonic range showing shock wave formation . 33 5.1 (a) Thrust plot for a single rotor (b) Velocity contour with flow lines for a single rotor 36 5.2 Velocity in stationary frame contour for co axial rotors . 38 5.3 Maximum velocity value in stationary frame for 3000 rpm . 39 5.4 Force report from Fluent . 39 5.5 Pressure contours for co axial rotors . 40 v 5.6 Global velocity contour with streamlines . 41 5.7 (a) Velocity contour lines on rotor surfaces (b) Pressure contour lines on rotor surfaces . 42 6.1 Isometric view of the Mars UAV model . 43 6.2 Rotor blade of Mars UAV . 44 6.3 Side view : Rotor blade of Mars UAV . 44 6.4 Subsystems Mars UAV model . 45 7.1 World and Body frame of reference for a quadrotor . 48 7.2 Differential thrusts for roll, pitch and yaw moments . 49 7.3 Euler angles representation . 51 7.4 Mars UAV rotors representation . ..