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Development and Implementation of Guidance, Navigation and Control Systems for an Autonomous Air Vehicle

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Development and Implementation of Guidance, Navigation and Control Systems for an Autonomous Air Vehicle Development and Implementation of Guidance, Navigation and Control Systems for an Autonomous Air Vehicle by Adam Ufford, B.S.M.E. A Thesis In MECHANICAL ENGINEERING Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN MECHANICAL ENGINEERING Approved Dr. Jordan M. Berg Committee Chair Dr. Walt Oler Dr. Seon Han Fred Hartmeister Dean of the Graduate School August, 2009 Texas Tech University, Adam Ufford, August 2009 Contents List of Tables . iv List of Figures . v 1 Introduction . 1 2 Coordinate Frames and Nomenclature Preliminaries . 4 2.1 Navigational Coordinate Frames . 4 2.1.1 Earth Centered Earth Fixed Geoidal System . 4 2.1.2 Earth Centered Earth Fixed Rectangular System . 5 2.1.3 Local Tangent Plane - enu Coordinate System . 6 2.2 Aircraft Coordinate Frames . 6 2.2.1 Earth (Inertial) Axes . 7 2.2.2 Vehicle Navigation Axes . 7 2.2.3 Body Axes . 8 2.2.4 Wind Axes . 8 2.2.5 Path Axes . 9 2.3 Nomenclature . 9 3 Simulation Model . 11 3.1 State Equations . 12 3.2 Aerodynamic Forces and Moments . 12 3.2.1 Aerodynamic and Thrust Forces . 13 3.2.2 Aerodynamic Moments . 14 3.2.3 Aerodynamic Coefficients . 14 3.3 Inner Loop: Attitude Stabilization . 14 3.4 Outputs . 15 4 Attitude Stabilization System . 17 4.1 Infrared Horizon Sensing . 18 4.2 FMA FS-8 Copilot . 19 4.3 Arbitrary Pitch and Bank Angle Stabilization . 19 4.3.1 Calibration . 19 4.3.2 Stabilization . 20 5 Path Following Subsystem . 23 ii Texas Tech University, Adam Ufford, August 2009 5.1 Vector Field Path Following . 24 5.1.1 Algorithm . 24 6 Autopilot Subsystem . 27 6.1 Feedback Linearization Autopilot Algorithms . 27 6.1.1 Ground Track Heading Hold . 27 6.1.2 Altitude Hold . 28 6.1.3 Existence of Solutions and Corresponding Control Laws . 29 6.1.4 State Measurement and Estimation . 30 6.1.5 High-Gain Observer for Flight Path Angle . 31 6.2 Output Feedback Simulations . 33 6.3 Alternative Autopilot Design and Comparison . 33 6.3.1 Altitude Hold: PI Controller . 35 6.3.2 Ground Track Heading Hold: P Controller . 35 6.3.3 Simulation Results . 35 7 GNC System Implementation . 40 7.1 GNC System Hardware . 40 7.2 Radio Modem . 41 7.3 Remote Pilot Override . 42 7.4 Hardware in the Loop Simulations . 43 8 Conclusion . 45 Bibliography . 46 A Trajectory Model . 48 B Simulation Code . 52 C CCode.................................. 73 iii Texas Tech University, Adam Ufford, August 2009 List of Tables 2.1 WGS-84 Parameters . 5 2.2 Model Nomenclature . 10 5.1 Path Following Variables . 25 7.1 Telemetry Sentence Contents . 43 iv Texas Tech University, Adam Ufford, August 2009 List of Figures 1.1 Autonomous GNC System . 2 1.2 Subsystem Partitioning . 2 2.1 Earth Geoid Parameters . 5 2.2 Aircraft Coordinate Frames . 7 3.1 PID Controller: Roll to Aileron . 15 3.2 Simulation Results: PID Inner Loops . 15 4.1 Infrared Horizon Sensing: Single Axis . 19 4.2 Copilot System: Single Axis . 20 4.3 Voltage-Inclination Curve, Vmax=3.0 Volts . 21 4.4 Modified Co-pilot System: Single Axis . 21 5.1 Linear Path Segment Examples . 23 5.2 Waypoint Switching Look-Ahead, δs ................... 26 6.1 Two Stage Estimation Scheme . 31 6.2 Angle of Attack Estimation: . 32 6.3 High Gain Observer: ηγ = 10, ηh = 20 . 34 6.4 Output Feedback Controller: aχ=0.25, k1=0.18, k2=0.7 . 34 6.5 Proportional Ground Track Heading Hold Autopilot, 15o Step Input . 36 6.6 Proportional Ground Track Heading Hold Autopilot, Pφ = 1.5 . 37 6.7 Proportional Ground Track Heading Hold Autopilot, Pφ = 0.25 . 37 6.8 Altitude Hold: Tuned for 3 Second Rise Time . 38 6.9 Altitude Hold: φ(t) = sin t ........................ 38 7.1 Hardware Prototype: P,PI Autopilot . 41 7.2 DAC/Op-Amp Implementation: Single Channel . 42 7.3 Telemetry Sentence Structure . 42 7.4 Hardware in the Loop Simulation Results . 44 v Texas Tech University, Adam Ufford, August 2009 Chapter 1 Introduction Interest in unmanned and autonomous aerial vehicles in the Mechanical Engineer- ing department at Texas Tech University began in 2006 with a team of undergradu- ate mechanical engineering students who constructed and flew an RC-sized electric, flying wing aircraft via a standard RC remote pilot link. The following year, two undergraduate mechanical engineering teams were tasked with implementing video payload, autonomous navigation, and telemetry systems in hopes of entering an inter- national university competition for undergraduate students. The system was desired to autonomously follow a three dimensional path specified by a 2-D waypoints and a desired altitude. The undergraduate teams purchased hardware and began algorithm development with a simplified model. The scope of the project, however, proved too broad for such a short term assignment, and the project ended with few deliverables complete and limited success. This thesis details the development and implementa- tion of the guidance, navigation, and control system components for an autonomous system which satisfies the autonomous navigation requirements. Guidance, Navigation and Control (GNC) system design can be naturally divided (both conceptually and mathematically) in to several tractable sub-problems, the solutions of which act together in a larger, nested structure. The output of the higher level functions provides the input for the lower stages. A good example of this layered architecture and its benefits are given in [9]. A autonomous GNC system in this thesis is defined to be the system of systems which enables the vehicle to follow an externally specified path and maintain altitude. This task is summarized graphically in Figure 1.1. The available controls (δA, δE, δR) are the aileron, elevator and rudder control surface deflections, respectively. In general, the GNC system mission is to drive these controls in order to track the desired altitude and path. Methods of autonomous path path planning, along with other higher-level functions such as automatic target selection and cooperative formations are not considered here, although [9] describes how the nested design structure is expandable for such 1 Texas Tech University, Adam Ufford, August 2009 Figure 1.1 Autonomous GNC System functions. We choose to partition the autonomous GNC system design into three smaller systems as shown in Figure 1.2. Figure 1.2 Subsystem Partitioning Given a group of ordered waypoints and the current position of the aircraft, the Path Following Subsystem generates a desired ground track heading angle which will drive the aircraft to the desired path. This desired ground track and a desired altitude are inputs to the Autopilot Subsystem which generates pitch and bank angle commands. The bank and pitch angle commands are in turn fed into the Attitude Stabilization Subsystem which drives the aircraft control surfaces to track the bank and pitch angle commands. Each level of the system is designed assuming perfect performance (either instantaneous actuation or first order error dynamics) of the other levels. The necessary definitions and additional nomenclature for discussion of the air- craft dynamics are covered in Chapter 2. The nonlinear, 6-DOF aircraft model developed and used for simulation is detailed in Chapter 3 to illustrate the com- plexities inherent in control system design and motivate the following chapters. The selected solution for the Path Following Subsystem is described in Chapter 4, while the selected design for the Attitude Stabilization Subsystem is described in Chapter 2 Texas Tech University, Adam Ufford, August 2009 5. The main theoretical contribution of this thesis is given in Chapter 6, where origi- nal algorithms for the ground-track heading and altitude hold autopilots are derived and compared via simulation to more traditional autopilot designs. The hardware and software implementations of the selected algorithms are described in Chapter 7. A brief conclusion and suggestions for future work are included in Chapter 8. 3 Texas Tech University, Adam Ufford, August 2009 Chapter 2 Coordinate Frames and Nomenclature Preliminaries An accurate discussion of aircraft navigation and dynamics involves several dif- ferent coordinate systems and many variables. The coordinate systems and symbols used throughout this thesis are defined in this chapter. 2.1 Navigational Coordinate Frames The primary position information information is provided by GPS. Since the source of this information consists of an array of satellites which orbit the earth, the data is reported with respect to a Earth centered, non rectangular coordinate system. This section defines that coordinate system and its relation to the local rectangular system used for navigation. For more information on the navigational coordinate frames, see [5, 4]. 2.1.1 Earth Centered Earth Fixed Geoidal System The three dimensional position data is reported by the GPS receiver in an Earth Centered Earth Fixed, Geodetic (ECEF-g) coordinate system as latitude, longitude and altitude above Mean Sea Level (MSL) (λ, ', hMSL) values. Application of the ECEF-g requires a model for the Earth's ellipsoid. The model used in GPS measurements is the WGS-84 model, and its experimentally determined parameters are listed in Table 2.1. The other quantities necessary to transform the ECEF-g coordinates into the other coordinate systems can then be calculated. The ellipsoid flatness, f, and eccentricity, e, are expressed in terms of the axis lengths. a−b −3 f = a = 3:3528107 × 10 q (2.1) e = f (2 − f) 4 Texas Tech University, Adam Ufford, August 2009 Table 2.1 WGS-84 Parameters Symbol Quantity Value Units a Earth Semimajor Axis 6378137.0 m b Earth Semiminor Axis 6356752.3142 m The normal distance, N, is the distance from the ellipsoid surface as shown in Figure 2.1 to the ellipsoid z-axis and is calculated as a function of latitude.
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