This book explores topics that are central to the field of spacecraft attitude determination and control. The authors provide rigorous theoretical derivations of significant algorithms accompanied by a generous amount of qualitative discussions of the subject matter. The book documents the development of the important concepts and methods in a manner accessible to practicing engineers, graduate-level engineering students and applied mathematicians. It includes detailed examples from actual mission designs to help ease the transition from theory to practice, and also provides prototype algorithms that are readily available on the author's website. Subject matter includes both theoretical derivations and practical implementation of spacecraft attitude determination and control systems. It provides detailed derivations for attitude kinematics and dynamics, and provides detailed description of the most widely used attitude parameterization, the quaternion. This title also provides a thorough treatise of attitude dynamics including Jacobian elliptical functions. It is the first known book to provide detailed derivations and explanations of state attitude determination, and gives readers real-world examples from actual working spacecraft missions. The subject matter is chosen to fill the void of existing textbooks and treatises, especially in state and dynamics attitude determination. MATLAB code of all examples will be provided through an external website

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zlib/Engineering/F. Landis Markley, John L. Crassidis (auth.)/Fundamentals of Spacecraft Attitude Determination and Control_2348258.pdf

Markley, F. Landis, Crassidis, John L.

Adobe InDesign CS6 (Windows)

Springer New York : Imprint : Springer

Springer US

Space technology library -- 33, Space technology library -- 33., New York State, 2014

Springer Nature (Textbooks & Major Reference Works), New York, NY, 2014

Space technology library (Print), New York, NY, 2014

United States, United States of America

Space Technology Library, uuuu

2014, PS, 2014

sm23483015

producers:
Adobe PDF Library 10.0.1

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Includes bibliographical references and index.

Preface 8
Contents 12
1 Introduction 17
References 31
2 Matrices, Vectors, Frames, Transforms 33
2.1 Matrices 33
2.2 Vectors 37
2.3 Jacobian, Gradient, and Hessian 38
2.4 Orthonormal Bases, Change of Basis 40
2.5 Vectors in Three Dimensions 44
2.6 Some Useful Reference Frames 47
2.6.1 Spacecraft Body Frame 47
2.6.2 Inertial Reference Frames 47
2.6.3 Earth-Centered/Earth-Fixed Frame 48
2.6.4 Local-Vertical/Local-Horizontal Frame 52
2.7 Quaternions 53
2.8 Rotations and Euler's Theorem 56
2.9 Attitude Representations 57
2.9.1 Euler Axis/Angle Representation 57
2.9.2 Rotation Vector Representation 60
2.9.3 Quaternion Representation 61
2.9.4 Rodrigues Parameter Representation 64
2.9.5 Modified Rodrigues Parameters 66
2.9.6 Euler Angles 68
2.10 Attitude Error Representations 75
Problems 76
References 80
3 Attitude Kinematics and Dynamics 82
3.1 Attitude Kinematics 83
3.1.1 Attitude Matrix 83
3.1.2 Vector Addition of Angular Velocity 84
3.1.3 Vector Kinematics 85
3.2 Kinematics of Attitude Parameterizations 86
3.2.1 Quaternion Kinematics 86
3.2.2 Rodrigues Parameter Kinematics 87
3.2.3 Modified Rodrigues Parameter Kinematics 87
3.2.4 Rotation Vector Kinematics 87
3.2.5 Euler Angle Kinematics 88
3.2.6 Attitude Error Kinematics 91
3.3 Attitude Dynamics 92
3.3.1 Angular Momentum and Kinetic Energy 92
3.3.2 Rigid Body Dynamics 95
3.3.3 Rigid Body Motion 99
3.3.3.1 Spin Stabilization 99
3.3.3.2 Energy Dissipation 103
3.3.3.3 Poinsot's Construction 104
3.3.4 Torque-Free Motion of a Rigid Body 105
3.3.4.1 Axial Symmetry 105
3.3.4.2 Triaxial Symmetry 109
3.3.5 Internal Torques 114
3.3.5.1 Reaction Wheels and Control Moment Gyros 115
3.3.5.2 Slosh 117
3.3.6 External Torques 118
3.3.6.1 Gravity-Gradient Torque 118
3.3.6.2 Magnetic Torque 121
3.3.6.3 Aerodynamic Torque 122
3.3.6.4 Solar Radiation Pressure Torque 123
3.3.6.5 Mass-Expulsion Torques 125
3.3.7 Angular Momentum for Health Monitoring 126
3.3.8 Dynamics of Earth-Pointing Spacecraft 127
Problems 133
References 136
4 Sensors and Actuators 138
4.1 Redundancy 138
4.2 Star Trackers 140
4.2.1 Overview 140
4.2.2 Modes of Operation 141
4.2.3 Field of View, Resolution, Update Rate 142
4.2.4 Star Catalogs 144
4.2.5 Proper Motion, Parallax, and Aberration 145
4.3 Sun Sensors 148
4.4 Horizon Sensors 150
4.5 Magnetometers 150
4.6 Global Positioning System 151
4.6.1 GPS Satellites 153
4.7 Gyroscopes 155
4.7.1 Gyro Measurement Model 158
4.8 Reaction Wheels 162
4.8.1 Reaction Wheel Characteristics 163
4.8.2 Reaction Wheel Disturbances 163
4.8.3 Redundant Wheel Configurations 167
4.8.3.1 Pseudoinverse Distribution Law 170
4.8.3.2 Minimax Distribution Law 172
4.8.3.3 Comparison of Pseudoinverse and Minimax Distribution Laws 178
4.9 Control Moment Gyros 181
4.10 Magnetic Torquers 183
4.11 Thrusters 184
4.12 Nutation Dampers 185
Problems 191
References 193
5 Static Attitude Determination Methods 197
5.1 The TRIAD Algorithm 198
5.2 Wahba's Problem 200
5.3 Quaternion Solutions of Wahba's Problem 201
5.3.1 Davenport's q Method 201
5.3.2 Quaternion Estimator (QUEST) 203
5.3.3 Another View of QUEST 205
5.3.4 Method of Sequential Rotations 206
5.3.5 Estimator of the Optimal Quaternion (ESOQ) 208
5.3.6 Second Estimator of the Optimal Quaternion (ESOQ2) 209
5.4 Matrix Solutions of Wahba's Problem 210
5.4.1 Singular Value Decomposition (SVD) Method 210
5.4.2 Fast Optimal Attitude Matrix (FOAM) 212
5.4.3 Wahba's Problem with Two Observations 213
5.5 Error Analysis of Wahba's Problem 215
5.5.1 Attitude Error Vector 215
5.5.2 Covariance Analysis of Wahba's Problem 218
5.5.3 Covariance with Two Observations 221
5.6 MLE for Attitude Determination 222
5.6.1 Fisher Information Matrix for Attitude Determination 226
5.7 Induced Attitude Errors from Orbit Errors 230
5.8 TRMM Attitude Determination 232
5.9 GPS Attitude Determination 237
Problems 238
References 245
6 Filtering for Attitude Estimation and Calibration 248
6.1 Attitude Representations for Kalman Filtering 249
6.1.1 Three-Component Representations 249
6.1.2 Additive Quaternion Representation 250
6.1.3 Multiplicative Quaternion Representation 252
6.2 Attitude Estimation 253
6.2.1 Kalman Filter Formulation 253
6.2.1.1 Measurement Update 254
6.2.1.2 Reset 255
6.2.1.3 Propagation 257
6.2.1.4 Gyros for Dynamic Model Replacement 258
6.2.2 Gyro Calibration Kalman Smoother 259
6.2.3 Filtering and the QUEST Measurement Model 267
6.2.4 Mission Mode Kalman Filter 270
6.2.5 Murrell's Version 273
6.3 Farrenkopf's Steady-State Analysis 276
6.4 Magnetometer Calibration 282
6.4.1 Measurement Model 283
6.4.2 Centered Solution 285
6.4.3 The TWOSTEP Algorithm 287
6.4.4 Extended Kalman Filter Approach 289
6.4.5 TRACE Spacecraft Results 290
Problems 291
References 296
7 Attitude Control 299
7.1 Introduction 299
7.2 Attitude Control: Regulation Case 301
7.3 Attitude Control: Tracking Case 306
7.3.1 Alternative Formulation 313
7.4 Attitude Thruster Control 315
7.5 Magnetic Torque Attitude Control 319
7.5.1 Detumbling 320
7.5.2 Momentum Dumping 323
7.6 Effects of Noise 324
7.7 SAMPEX Control Design 330
7.7.1 Attitude Determination 333
7.7.2 Magnetic Torque Control Law 336
7.7.3 Science Modes 336
7.7.3.1 Vertical Pointing Mode 338
7.7.3.2 Orbit Rate Rotation Mode 339
7.7.3.3 Special Pointing Mode 340
7.7.4 Reaction Wheel Control Law 344
7.7.5 Simulations 345
Problems 349
References 353
Appendix A Quaternion Identities 356
A.1 Cross Product Identities 356
A.2 Basic Quaternion Identities 357
A.3 The Matrices Ξ(q), Ψ(q), Ω(ω), and Γ(ω) 360
A.4 Identities Involving the Attitude Matrix 361
A.5 Error Quaternions 365
A.6 Quaternion Kinematics 366
References 370
Appendix B Euler Angles 371
Appendix C Orbital Dynamics 375
C.1 Geometry of Ellipses 375
C.2 Keplerian Motion 380
C.2.1 Classical Orbital Elements 384
C.2.2 Kepler's Equation 386
C.2.3 Orbit Propagation 389
C.3 Disturbing Forces 392
C.3.1 Non-Spherical Gravity 392
C.3.2 Third-Body Forces 398
C.3.3 Atmospheric Drag 399
C.3.4 Solar Radiation Pressure 400
C.4 Perturbation Methods 402
C.4.1 Variation of Parameters 402
C.4.2 Two Line Elements 403
C.4.3 A Useful Approximation, Secular J2 Effects Only 405
C.4.4 Sun-Synchronous Orbits 407
C.5 Lagrange Points 408
References 412
Appendix D Environment Models 413
D.1 Magnetic Field Models 413
D.1.1 Dipole Model 414
D.2 Atmospheric Density 416
D.2.1 Exponentially Decaying Model Atmosphere 416
D.2.2 Harris-Priester Model Atmosphere 417
D.2.3 Jacchia and GOST Model Atmospheres 418
D.2.4 Jacchia-Bowman 2008 (JB2008) Model Atmosphere 419
D.2.4.1 Temperature Profile 419
D.2.4.2 Barometric Equation 425
D.2.4.3 Diffusion Equation 426
D.2.4.4 Density Correction Factors 428
D.2.4.5 Semiannual Variation 428
D.2.4.6 Seasonal-Latitudinal Variation 429
D.2.4.7 High Altitude Density Correction 429
D.3 Sun Position, Radiation Pressure, and Eclipse Conditions 430
D.4 Orbital Ephemerides of the Sun, Moon, and Planets 432
References 433
Appendix E Review of Control and Estimation Theory 435
E.1 System Modeling 435
E.1.1 Inverted Pendulum Modeling 435
E.1.2 State and Observation Models 438
E.1.2.1 State Models 438
E.1.2.2 Observation Models 442
E.1.3 Discrete-Time Systems 444
E.2 Control Theory 447
E.2.1 Basic Linear Control Design 447
E.2.1.1 Single Axis Attitude Control 448
E.2.2 Stability of Nonlinear Dynamic Systems 452
E.2.3 Sliding-Mode Control 454
E.3 Estimation Theory 458
E.3.1 Static-Based and Filter-Based Estimation 459
E.3.2 Batch Least Squares Estimation 461
E.3.3 Sequential Least Squares Estimation 463
E.3.4 Maximum Likelihood Estimation 464
E.3.5 Nonlinear Least Squares 466
E.3.6 Advantages and Disadvantages 472
E.3.7 State Estimation Techniques 472
E.3.7.1 Linear Kalman Filter 473
E.3.7.2 Extended Kalman Filter 476
E.3.7.3 Smoothing 478
E.3.7.4 Stability and Performance 478
E.3.8 Linear Covariance Analysis 480
E.3.9 Separation Theorem 480
References 483
Appendix F Computer Software 485
Index 486

"This book explores topics that are central to the field of spacecraft attitude determination and control. The authors provide rigorous theoretical derivations of significant algorithms accompanied by a generous amount of qualitative discussions of the subject matter. The book documents the development of the important concepts and methods in a manner accessible to practicing engineers, graduate-level engineering students and applied mathematicians. It includes detailed examples from actual mission designs to help ease the transition from theory to practice, and also provides prototype algorithms that are readily available on the author's website. Subject matter includes both theoretical derivations and practical implementation of spacecraft attitude determination and control systems. It provides detailed derivations for attitude kinematics and dynamics, and provides detailed description of the most widely used attitude parameterization, the quaternion. This title alsoprovides a thorough treatise of attitude dynamics including Jacobian elliptical functions. It is the first known book to provide detailed derivations and explanations of state attitude determination, and gives readers real-world examples from actual working spacecraft missions. The subject matter is chosen to fill the void of existing textbooks and treatises, especially in state and dynamics attitude determination. MATLAB code of all examples will be provided through an external website."--Publisher's Website

Front Matter....Pages i-xv
Introduction....Pages 1-16
Matrices, Vectors, Frames, Transforms....Pages 17-65
Attitude Kinematics and Dynamics....Pages 67-122
Sensors and Actuators....Pages 123-181
Static Attitude Determination Methods....Pages 183-233
Filtering for Attitude Estimation and Calibration....Pages 235-285
Attitude Control....Pages 287-343
Quaternion Identities....Pages 345-359
Euler Angles....Pages 361-364
Orbital Dynamics....Pages 365-402
Environment Models....Pages 403-424
Review of Control and Estimation Theory....Pages 425-474
Back Matter....Pages 475-486

Introduction -- Matrices, Vectors, Frames, Transforms -- Attitude Kinematics And Dynamics -- Sensors And Actuators -- Static Attitude Determination Methods -- Filtering For Attitude Estimation And Calibration -- Attitude Control -- Quaternion Identities -- Euler Angles -- Orbital Dynamics -- Environment Models -- Review Of Control And Estimation Theory -- Computer Software. By F. Landis Markley, John L. Crassidis. Includes Bibliographical References And Index.

2014-06-12