# Small Unmanned Aircraft: Theory and Practice

RANDAL W. BEARD
TIMOTHY W. McLAIN
Pages: 320
https://www.jstor.org/stable/j.ctt7sbc4

1. Front Matter
(pp. i-vi)
(pp. vii-x)
3. Preface
(pp. xi-xvi)
4. 1 Introduction
(pp. 1-7)

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...

5. 2 Coordinate Frames
(pp. 8-27)

In studying unmanned aircraft systems, it is important to understand how different bodies are oriented relative to each other. Most obviously, we need to understand how the aircraft is oriented with respect to the earth. We may also want to know how a sensor (e.g., a camera) is oriented relative to the aircraft or how an antenna is oriented relative to a signal source on the ground. This chapter describes the various coordinate systems used to describe the position and orientation of the aircraft and its sensors, and the transformation between these coordinate systems. It is necessary to use several...

6. 3 Kinematics and Dynamics
(pp. 28-38)

The first step in developing navigation, guidance, and control strategies for MAVs is to develop appropriate dynamic models. Deriving the nonlinear equations of motion for a MAV is the focus of chapters 3 and 4. In chapter 5, we linearize the equations of motion to create transfer-function and state-space models appropriate for control design.

In this chapter, we derive the expressions for the kinematics and the dynamics of a rigid body. We will apply Newton’s laws: for example, f = mv in the case of the linear motion. In this chapter, we will focus on defining the relations between positions...

7. 4 Forces and Moments
(pp. 39-59)

The objective of this chapter is to describe the forces and moments that act on a MAV. Following [5], we will assume that the forces and moments are primarily due to three sources, namely, gravity, aerodynamics, and propulsion. Letting fgbe the force due to gravity, (fa, ma) be the forces and moments due to aerodynamics, and (fp, mp) be the forces and moments due to propulsion, we have

f = fg+ fa+ fp

m = ma+mp,

where f is the total force acting on the airframe and m is the total moment acting on the airframe....

8. 5 Linear Design Models
(pp. 60-94)

As chapters 3 and 4 have shown, the equations of motion for a MAV are a fairly complicated set of 12 nonlinear, coupled, first-order, ordinary differential equations, which we will present in their entirety in section 5.1. Because of their complexity, designing controllers based on them is difficult and requires more straightforward approaches. In this chapter, we will linearize and decouple the equations of motion to produce reduced-order transfer function and state-space models more suitable for control system design. Low-level autopilot control loops for unmanned aircraft will be designed based on these linear design models, which capture the approximate dynamic...

9. 6 Autopilot Design Using Successive Loop Closure
(pp. 95-119)

In general terms, an autopilot is a system used to guide an aircraft without the assistance of a pilot. For manned aircraft, the autopilot can be as simple as a single-axis wing-leveling autopilot, or as complicated as a full flight control system that controls position (altitude, latitude, longitude) and attitude (roll, pitch, yaw) during the various phases of flight (e.g., take-off, ascent, level flight, descent, approach, landing). For MAVs, the autopilot is in complete control of the aircraft during all phases of flight. While some control functions may reside in the ground control station, the autopilot portion of the MAV...

10. 7 Sensors for MAVs
(pp. 120-142)

Critical to the creation and realization of small unmanned air vehicles has been the development of small, lightweight solid-state sensors. Based on microelectromechanical systems (MEMS) technology, small but accurate sensors such as accelerometers, angular rate sensors, and pressure sensors have enabled the development of increasingly smaller and more capable autonomous aircraft. Coupled with the development of small global positioning systems (GPS), computationally capable microcontrollers, and more powerful batteries, the capabilities of MAVs have gone from being purely radio controlled (RC) by pilots on the ground to highly autonomous systems in less than 20 years. The objective of this chapter is...

11. 8 State Estimation
(pp. 143-163)

The autopilot designed in chapter 6 assumes that states of the system like roll and pitch angles are available for feedback. However, one of the challenges of MAV flight control is that sensors that directly measure roll and pitch are not available. Therefore, the objective of this chapter is to describe techniques for estimating the state of a small or micro air vehicle from the sensor measurements described in chapter 7. Since rate gyros directly measure roll rates in the body frame, the statesp,q, andrcan be recovered by low-pass filtering the rate gyros. Therefore, we begin...

12. 9 Design Models for Guidance
(pp. 164-173)

As described in chapter 1, when the equations of motion for a system become complex, it is often necessary to develop design models that have significantly less mathematical complexity, but still capture the essential behavior of the system. If we include all the elements discussed in the previous eight chapters, including the six-degree-of-freedom model developed in chapters 3 and 4, the autopilot developed in chapter 6, the sensors developed in chapter 7, and the state-estimation scheme developed in chapter 8, the resulting model is extremely complex. This chapter approximates the performance of the closed-loop MAV system and develops reduced-order design...

13. 10 Straight-line and Orbit Following
(pp. 174-186)

This chapter develops guidance laws for tracking straight-line segments and for tracking constant-altitude circular orbits. Chapter 11 will discuss techniques for combining straight-line segments and circular orbits to track more complex paths, and chapter 12 will describe techniques for path planning through obstacle fields. In the context of the architectures shown in figures 1.1 and 1.2, this chapter describes algorithms for the path following block. The primary challenge in tracking straightline segments and circular orbits is wind, which is almost always present. For small unmanned aircraft, wind speeds are commonly 20 to 60 percent of the desired airspeed. Effective path-tracking...

14. 11 Path Manager
(pp. 187-205)

In Chapter 10 we developed guidance strategies for following straight-line paths and circular orbits. The objective of this chapter is to describe two simple strategies that combine straight-line paths and orbits to synthesize general classes of paths that are useful for autonomous operation of MAVs. In section 11.1, we show how the straight-line and orbit guidance strategies can be used to follow a series of waypoints. In section 11.2, the straight-line and orbit guidance strategies are used to synthesize Dubins paths, which for constant-altitude, constant-velocity vehicles with turning constraints, are time-optimal paths between two configurations. In reference to the architectures...

15. 12 Path Planning
(pp. 206-225)

In the robotics literature, there are essentially two different approaches to motion planning:deliberativemotion planning, where explicit paths and trajectories are computed based on global world knowledge [65, 66, 67], andreactivemotion planning, which uses behavioral methods to react to local sensor information [68, 69]. In general, deliberative motion planning is useful when the environment is known a priori, but can become computationally intensive in highly dynamic environments. Reactive motion planning, on the other hand, is well suited for dynamic environments, particularly collision avoidance, where information is incomplete and uncertain, but it lacks the ability to specify and...

(pp. 226-246)

One of the primary reasons for the current interest in small unmanned aircraft is that they offer an inexpensive platform to carry electrooptical (EO) and infrared (IR) cameras. Almost all small and miniature air vehicles that are currently deployed carry either an EO or IR camera. While the camera’s primary use is to relay information to a user, it makes sense to attempt to also use the camera for the purpose of navigation, guidance, and control. Further motivation comes from the fact that birds and flying insects use vision as their primary guidance sensor [95].

This chapter briefly introduces some...

17. APPENDIX A: Nomenclature and Notation
(pp. 247-253)
18. APPENDIX B: Quaternions
(pp. 254-259)
19. APPENDIX C: Animations in Simulink
(pp. 260-269)
20. APPENDIX D: Modeling in Simulink Using S-functions
(pp. 270-274)
21. APPENDIX E: Airframe Parameters
(pp. 275-276)
22. APPENDIX F: Trim and Linearization in Simulink
(pp. 277-285)
23. APPENDIX G: Essentials from Probability Theory
(pp. 286-287)
24. APPENDIX H: Sensor Parameters
(pp. 288-290)
25. Bibliography
(pp. 291-298)
26. Index
(pp. 299-300)