Über die Autorin bzw. den Autor

Randal W. Beard is a professor in the Department of Electrical and Computer Engineering at Brigham Young University. He is the coauthor of Distributed Consensus in Multi-vehicle Cooperative Control.
Timothy W. McLain is a professor in the Department of Mechanical Engineering at Brigham Young University.

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"This book presents a unique and broad introduction to the necessary background, tools, and methods to design guidance, navigation, and control systems for unmanned air vehicles. Written with confidence and authority by leading researchers in the field, this effectively organized book provides an excellent reference for all those interested in this subject."--Emilio Frazzoli, Massachusetts Institute of Technology

"Presenting aircraft dynamics to nonaerospace students, this book provides a clear description and explanation for the design of navigation, guidance, and control algorithms for small to miniature unmanned aircraft systems."--Eric W. Frew, University of Colorado, Boulder

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SMALL UNMANNED AIRCRAFT

PRINCETON UNIVERSITY PRESS

Contents

Preface................................................................xi1 Introduction.........................................................12 Coordinate Frames....................................................83 Kinematics and Dynamics..............................................284 Forces and Moments...................................................395 Linear Design Models.................................................606 Autopilot Design Using Successive Loop Closure.......................957 Sensors for MAVs.....................................................1208 State Estimation.....................................................1439 Design Models for Guidance...........................................16410 Straight-line and Orbit Following...................................17411 Path Manager........................................................18712 Path Planning.......................................................20613 Vision-guided Navigation............................................226APPENDIX A: Nomenclature and Notation..................................247APPENDIX B: Quaternions................................................254APPENDIX C: Animations in Simulink.....................................260APPENDIX D: Modeling in Simulink Using S-Functions.....................270APPENDIX E: Airframe Parameters........................................275APPENDIX F: Trim and Linearization in Simulink.........................277APPENDIX G: Essentials from Probability Theory.........................286APPENDIX H: Sensor Parameters..........................................288Bibliography...........................................................291Index..................................................................299

Chapter One

1.1 System Architecture

The objective of this book is to prepare the reader to do research in the exciting and rapidly developing field of autonomous navigation, guidance, and control of unmanned air vehicles. The focus is on the design of the software algorithms required for autonomous and semiautonomous flight. To work in this area, researchers must be familiar with a wide range of topics, including coordinate transformations, aerodynamics, autopilot design, state estimation, path planning, and computer vision. The aim of this book is to cover these essential topics, focusing in particular on their application to small and miniature air vehicles, which we denote by the acronym MAV.

In the development of the topics, we have in mind the software architecture shown in figure 1.1. The block labeled unmanned aircraft in figure 1.1 is the six-degree-of-freedom (DOF) physical aircraft that responds to servo command inputs (elevator, aileron, rudder, and throttle) and wind and other disturbances. The mathematical models required to understand fixed-wing flight are complicated and are covered in chapters 2 to 5 and chapter 9. In particular, in chapter 2 we discuss coordinate frames and transformations between frames. A study of coordinate frames is required since most specifications for MAVs are given in the inertial frame (e.g., orbit a specific coordinate), whereas most of the sensor measurements are with respect to the body frame, and the actuators exert forces and torques in the body frame. In chapter 3 we develop the kinematic and dynamic equations of motion of a rigid body. In chapter 4 we describe the aerodynamic forces and moments that act on fixed-wing aircraft. Chapter 5 begins by combining the results of chapters 3 and 4 to obtain a six-DOF, 12-state, nonlinear dynamic model for a MAV. While incorporating the fidelity desired for simulation purposes, the six-DOF model is fairly complicated and cumbersome. The design and analysis of aircraft control approaches are more easily accomplished using lower-order linear models. Linear models that describe small deviations from trim are derived in chapter 5, including linear transfer function and state-space models.

The block labeled autopilot in figure 1.1 refers to the low-level control algorithms that maintain roll and pitch angles, airspeed, altitude, and course heading. Chapter 6 introduces the standard technique of successive loop closure to design the autopilot control laws. Nested control loops are closed one at a time, with inner loops maintaining roll and pitch angles and outer loops maintaining airspeed, altitude, and course.

The autopilot and the higher level blocks rely on accurate state estimates obtained by dynamically filtering the onboard sensors, which include accelerometers, rate gyros, pressure sensors, magnetometers, and GPS receivers. A description of these sensors and their mathematical models is given in chapter 7. Because it is not possible to measure all the states of small unmanned aircraft using standard sensors, state estimation plays an important role. Descriptions of several state-estimation techniques that are effective for MAVs are given in chapter 8.

A complete model of the flight dynamics coupled with the autopilot and state estimation techniques represents a high dimensional, highly complex, nonlinear system of equations. The full model of the system is too complicated to facilitate the development of high level guidance algorithms. Therefore, chapter 9 develops low-order nonlinear equations that model the closed-loop behavior of the system. These models are used in subsequent chapters to develop guidance algorithms.

One of the primary challenges with MAVs is flight in windy conditions. Since airspeeds in the range of 20 to 40 mph are typical for MAVs, and since wind speeds at several hundred feet above ground level (AGL) almost always exceed 10 mph, MAVs must be able to maneuver effectively in wind. Traditional trajectory tracking methods used in robotics do not work well for MAVs. The primary difficulty with these methods is the requirement to be in a particular location at a particular time, which cannot properly take into account the variations in ground speed caused by the unknown and changing effects of the wind. Alternatively, path-following methods that simply maintain the vehicle on a desired path have proven to be effective in flight tests. Chapter 10 describes the algorithms and methods used to provide the capabilities of the path following block in figure 1.1. We will focus exclusively on straight-line paths and circular orbits and arcs. Other useful paths can be built up from these straight-line and circular path primitives.

The block labeled path manager in figure 1.1 is a finite-state machine that converts a sequence of waypoint configurations (positions and orientations) into sequences of straight-line paths and circular arcs that can be flown by the MAV. This makes it possible to simplify the path planning problem so that the path planner produces either a sequence of straight-line paths that maneuver the MAV through an obstacle field, or a Dubin's path that maneuvers through the obstacle field. Chapter 11 describes the path manager, while chapter 12 describes the path planner. For path planning we consider two classes of problems. The first class of problems is point-to-point algorithms, where the objective is to maneuver from a start position to an end position while avoiding a set of obstacles. The second class of problems is search algorithms, where the...