Small Unmanned Aircraft

Preface xi

Chapter 1 Introduction 1

1.1 System Architecture 1

1.2 Design Models 4

1.3 Design Project 6

Chapter 2 Coordinate Frames 8

2.1 RotationMatrices 9

2.2 MAV Coordinate Frames 12

2.3 Airspeed,Wind Speed, and Ground Speed 18

2.4 TheWind Triangle 20

2.5 Differentiation of a Vector 24

2.6 Chapter Summary 25

2.7 Design Project 27

Chapter 3 Kinematics and Dynamics 28

3.1 State Variables 28

3.2 Kinematics 30

3.3 Rigid-body Dynamics 31

3.4 Chapter Summary 37

3.5 Design Project 38

Chapter 4 Forces and Moments 39

4.1 Gravitational Forces 39

4.2 Aerodynamic Forces andMoments 40

4.3 Propulsion Forces andMoments 52

4.4 Atmospheric Disturbances 54

4.5 Chapter Summary 57

4.6 Design Project 58

Chapter 5 Linear Design Models 60

5.1 Summary of Nonlinear Equations of Motion 60

5.2 Coordinated Turn 64

5.3 Trim Conditions 65

5.4 Transfer Function Models 68

5.5 Linear State-space Models 77

5.6 Reduced-order Modes 87

5.7 Chapter Summary 91

5.8 Design Project 92

Chapter 6 Autopilot Design Using Successive Loop Closure 95

6.1 Successive Loop Closure 95

6.2 Saturation Constraints and Performance 97

6.3 Lateral-directional Autopilot 99

6.4 Longitudinal Autopilot 105

6.5 Digital Implementation of PID Loops 114

6.6 Chapter Summary 117

6.7 Design Project 118

Chapter 7 Sensors for MAVs 120

7.1 Accelerometers 120

7.2 Rate Gyros 124

7.3 Pressure Sensors 126

7.4 Digital Compasses 131

7.5 Global Positioning System 134

7.6 Chapter Summary 141

7.7 Design Project 141

Chapter 8 State Estimation 143

8.1 Benchmark Maneuver 143

8.2 Low-pass Filters 144

8.3 State Estimation by Inverting the Sensor Model 145

8.4 Dynamic-observer Theory 149

8.5 Derivation of the Continuous-discrete Kalman Filter 151

8.6 Attitude Estimation 156

8.7 GPS Smoothing 158

8.8 Chapter Summary 161

8.9 Design Project 162

Chapter 9 Design Models for Guidance 164

9.1 AutopilotModel 164

9.2 Kinematic Model of Controlled Flight 165

9.3 Kinematic Guidance Models 168

9.4 Dynamic Guidance Model 170

9.5 Chapter Summary 172

9.6 Design Project 173

Chapter 10 Straight-line and Orbit Following 174

10.1 Straight-line Path Following 175

10.2 Orbit Following 181

10.3 Chapter Summary 183

10.4 Design Project 185

Chapter 11 Path Manager 187

11.1 Transitions BetweenWaypoints 187

11.2 Dubins Paths 194

11.3 Chapter Summary 202

11.4 Design Project 204

Chapter 12 Path Planning 206

12.1 Point-to-Point Algorithms 207

12.2 Coverage Algorithms 220

12.3 Chapter Summary 223

12.4 Design Project 224

Chapter 13 Vision-guided Navigation 226

13.1 Gimbal and Camera Frames and Projective Geometry 226

13.2 Gimbal Pointing 229

13.3 Geolocation 231

13.4 Estimating Target Motion in the Image Plane 234

13.5 Time to Collision 238

13.6 Precision Landing 240

13.7 Chapter Summary 244

13.8 Design Project 245

APPENDIX A: Nomenclature and Notation 247

APPENDIX B: Quaternions 254

B.1 Quaternion Rotations 254

B.2 Aircraft Kinematic and Dynamic Equations 255

B.3 Conversion Between Euler Angles and

Quaternions 259

APPENDIX C: Animations in Simulink 260

C.1 Handle Graphics inMatlab 260

C.2 Animation Example: Inverted Pendulum 261

C.3 Animation Example: Spacecraft Using Lines 263

C.4 Animation Example: Spacecraft Using Vertices and

Faces 268

APPENDIX D: Modeling in Simulink Using S-Functions 270

D.1 Example: Second-order Differential Equation 270

APPENDIX E: Airframe Parameters 275

E.1 Zagi Flying Wing 275

E.2 Aerosonde UAV 276

APPENDIX F: Trim and Linearization in Simulink 277

F.1 Using the Simulink trim Command 277

F.2 Numerical Computation of Trim 278

F.3 Using the Simulink linmod Command to

Generate a State-space Model 282

F.4 Numerical Computation of State-space Model 284

APPENDIX G: Essentials from Probability Theory 286

APPENDIX H: Sensor Parameters 288

H.1 Rate Gyros 288

H.2 Accelerometers 288

H.3 Pressure Sensors 289

H.4 Digital Compass/Magnetometer 289

H.5 GPS 290

Bibliography 291

Index 299