About the Author xvii
Preface xix
List of Tables xxi
Part One Marine Craft Hydrodynamics
1 Introduction to Part I 3
1.1 Classification of Models 6
1.2 The Classical Models in Naval Architecture 8
1.2.1 Maneuvering Theory 10
1.2.2 Seakeeping Theory 12
1.2.3 Unified Theory 14
1.3 Fossen’s Robot-inspired Model for Marine Craft 14
2 Kinematics 17
2.1 Kinematic Preliminaries 18
2.1.1 Reference Frames 18
2.1.2 Body-fixed Reference Points 21
2.1.3 Generalized Coordinates 22
2.2 Transformations Between BODY and NED 23
2.2.1 Euler Angle Transformation 26
2.2.2 Unit Quaternions 32
2.2.3 Unit Quaternion from Euler Angles 38
2.2.4 Euler Angles from a Unit Quaternion 38
2.3 Transformations Between ECEF and NED 39
2.3.1 Longitude and Latitude Rotation Matrix 40
2.3.2 Longitude, Latitude and Height from ECEF Coordinates 41
2.3.3 ECEF Coordinates from Longitude, Latitude and Height 44
2.4 Transformations between ECEF and Flat-Earth Coordinates 45
2.4.1 Longitude, Latitude and Height from Flat-Earth Coordinates 45
2.4.2 Flat-Earth Coordinates from Longitude, Latitude and Height 46
2.5 Transformations Between BODY and FLOW 47
2.5.1 Definitions of Heading, Course and Crab Angles 47
2.5.2 Definitions of Angle of Attack and Sideslip Angle 49
2.5.3 Flow-axes Rotation Matrix 51
3 Rigid-body Kinetics 55
3.1 Newton–Euler Equations of Motion about the CG 56
3.1.1 Translational Motion About the CG 58
3.1.2 Rotational Motion About the CG 59
3.1.3 Equations of Motion About the CG 60
3.2 Newton–Euler Equations of Motion About the CO 60
3.2.1 Translational Motion About the CO 61
3.2.2 Rotational Motion About the CO 61
3.3 Rigid-body Equations of Motion 63
3.3.1 Nonlinear 6-DOF Rigid-body Equations of Motion 63
3.3.2 Linearized 6-DOF Rigid-body Equations of Motion 69
4 Hydrostatics 71
4.1 Restoring Forces for Underwater Vehicles 71
4.1.1 Hydrostatics of Submerged Vehicles 71
4.2 Restoring Forces for Surface Vessels 74
4.2.1 Hydrostatics of Floating Vessels 74
4.2.2 Linear (Small Angle) Theory for Boxed-shaped Vessels 77
4.2.3 Computation of Metacenter Heights for Surface Vessels 79
4.3 Load Conditions and Natural Periods 82
4.3.1 Decoupled Computation of Natural Periods 82
4.3.2 Computation of Natural Periods in a 6-DOF Coupled System 84
4.3.3 Natural Periods as a Function of Load Condition 87
4.3.4 Free-surface Effects 89
4.3.5 Payload Effects 90
4.4 Seakeeping Analysis 90
4.4.1 Harmonic Oscillator with Sinusoidal Forcing 90
4.4.2 Steady-state Heave, Roll and Pitch Responses in Regular Waves 92
4.4.3 Explicit Formulae for Boxed-shaped Vessels in Regular Waves 94
4.4.4 Case Study: Resonances in the Heave, Roll and Pitch Modes 96
4.5 Ballast Systems 97
4.5.1 Static Conditions for Trim and Heel 99
4.5.2 Automatic Ballast Control Systems 102
5 Seakeeping Models 105
5.1 Hydrodynamic Concepts and Potential Theory 106
5.1.1 Numerical Approaches and Hydrodynamic Codes 108
5.2 Seakeeping and Maneuvering Kinematics 110
5.2.1 Seakeeping Reference Frame 110
5.2.2 Transformation Between BODY and SEAKEEPING 111
5.3 The Classical Frequency-domain Model 114
5.3.1 Frequency-dependent Hydrodynamic Coefficients 115
5.3.2 Viscous Damping 119
5.3.3 Response Amplitude Operators 121
5.4 Time-domain Models including Fluid Memory Effects 122
5.4.1 Cummins Equation in SEAKEEPING Coordinates 122
5.4.2 Linear Time-domain Seakeeping Equations in BODY Coordinates 125
5.4.3 Nonlinear Unified Seakeeping and Maneuvering Model with Fluid Memory Effects 129
5.5 Identification of Fluid Memory Effects 130
5.5.1 Frequency-domain Identification Using the MSS FDI Toolbox 131
6 Maneuvering Models 135
6.1 Rigid-body Kinetics 137
6.2 Potential Coefficients 137
6.2.1 Frequency-independent Added Mass and Potential Damping 139
6.2.2 Extension to 6-DOF Models 140
6.3 Added Mass Forces in a Rotating Coordinate System 141
6.3.1 Lagrangian Mechanics 142
6.3.2 Kirchhoff’s Equation 143
6.3.3 Added Mass and Coriolis–Centripetal Matrices 143
6.4 Dissipative Forces 148
6.4.1 Linear Damping 150
6.4.2 Nonlinear Surge Damping 151
6.4.3 Cross-flow Drag Principle 154
6.5 Ship Maneuvering Models (3 DOFs) 155
6.5.1 Nonlinear Equations of Motion 155
6.5.2 Nonlinear Maneuvering Model Based on Surge Resistance and Cross-flow Drag 158
6.5.3 Nonlinear Maneuvering Model Based on Second-order Modulus Functions 159
6.5.4 Nonlinear Maneuvering Model Based on Odd Functions 161
6.5.5 Linear Maneuvering Model 163
6.6 Ship Maneuvering Models Including Roll (4 DOFs) 165
6.6.1 The Nonlinear Model of Son and Nomoto 172
6.6.2 The Nonlinear Model of Blanke and Christensen 173
6.7 Low-Speed Maneuvering Models for Dynamic Positioning (3 DOFs) 175
6.7.1 Current Coefficients 175
6.7.2 Nonlinear DP Model Based on Current Coefficients 179
6.7.3 Linear Time-varying DP Model 180
7 Autopilot Models for Course and Heading Control 183
7.1 Autopilot Models for Course Control 184
7.1.1 State-space Model for Course Control 184
7.1.2 Course Angle Transfer Function 185
7.2 Autopilot Models for Heading Control 186
7.2.1 Second-order Nomoto Model 186
7.2.2 First-order Nomoto Model 188
7.2.3 Nonlinear Extensions of Nomoto’s Model 190
7.2.4 Pivot Point 192
8 Models for Underwater Vehicles 195
8.1 6-DOF Models for AUVs and ROVs 195
8.1.1 Equations of Motion Expressed in BODY 195
8.1.2 Equations of Motion Expressed in NED 197
8.1.3 Properties of the 6-DOF Model 198
8.1.4 Symmetry Considerations of the System Inertia Matrix 200
8.2 Longitudinal and Lateral Models for Submarines 201
8.2.1 Longitudinal Subsystem 202
8.2.2 Lateral Subsystem 204
8.3 Decoupled Models for “Flying Underwater Vehicles” 205
8.3.1 Forward Speed Subsystem 206
8.3.2 Course Angle Subsystem 206
8.3.3 Pitch–Depth Subsystem 207
8.4 Cylinder-Shaped Vehicles and Myring-type Hulls 208
8.4.1 Myring-type Hull 209
8.4.2 Spheroid Approximation 210
8.5 Spherical-Shaped Vehicles 214
9 Control Forces and Moments 217
9.1 Propellers as Thrust Devices 217
9.1.1 Fixed-pitch Propeller 217
9.1.2 Controllable-pitch Propeller 220
9.2 Ship Propulsion Systems 225
9.2.1 Podded Propulsion Units 225
9.2.2 Prime Mover System 227
9.3 USV and Underwater Vehicle Propulsion Systems 228
9.3.1 Propeller Shaft Speed Models 229
9.3.2 Motor Armature Current Control 230
9.3.3 Motor Speed Control 232
9.4 Thrusters 233
9.4.1 Tunnel Thrusters 233
9.4.2 Azimuth Thrusters 234
9.5 Rudder in the Propeller Slipstream 236
9.5.1 Rudder Forces and Moment 237
9.5.2 Steering Machine Dynamics 240
9.6 Fin Stabilizators 243
9.6.1 Lift and Drag Forces on Fins 244
9.6.2 Roll Moment Produced by Symmetrical Fin Stabilizers 245
9.7 Underwater Vehicle Control Surfaces 245
9.7.1 Rudder 247
9.7.2 Dive Planes 248
9.8 Control Moment Gyroscope 249
9.8.1 Ship Roll Gyrostabilizer 249
9.8.2 Control Moment Gyros for Underwater Vehicles 252
9.9 Moving Mass Actuators 258
10 Environmental Forces and Moments 261
10.1 Wind Forces and Moments 263
10.1.1 Wind Forces and Moments on Marine Craft at Rest 263
10.1.2 Wind Forces and Moments on Moving Marine Craft 265
10.1.3 Wind Coefficients Based on Helmholtz–Kirchhoff Plate Theory 266
10.1.4 Wind Coefficients for Merchant Ships 269
10.1.5 Wind Coefficients for Very Large Crude Carriers 271
10.1.6 Wind Coefficients for Large Tankers and Medium-sized Ships 272
10.1.7 Wind Coefficients for Moored Ships and Floating Structures 272
10.2 Wave Forces and Moments 274
10.2.1 Sea-state Descriptions 275
10.2.2 Wave Spectra 276
10.2.3 Wave Amplitude Response Model 287
10.2.4 Force RAOs 290
10.2.5 Motion RAOs 293
10.2.6 State-space Models for Wave Response Simulation 296
10.3 Ocean Current Forces and Moments 300
10.3.1 3D Irrotational Ocean Current Model 303
10.3.2 2D Irrotational Ocean Current Model 304
Part Two Motion Control
11 Introduction to Part II 309
11.1 Guidance, Navigation and Control Systems 310
11.1.1 Historical Remarks 312
11.1.2 Autopilots 314
11.1.3 Dynamic Positioning and Position Mooring Systems 315
11.1.4 Waypoint Tracking and Path-following Control Systems 316
11.2 Control Allocation 316
11.2.1 Propulsion and Actuator Models 318
11.2.2 Unconstrained Control Allocation 322
11.2.3 Constrained Control Allocation 324
12 Guidance Systems 331
12.1 Trajectory Tracking 333
12.1.1 Reference Models for Trajectory Generation 334
12.1.2 Trajectory Generation using a Marine Craft Simulator 339
12.1.3 Optimal Trajectory Generation 340
12.2 Guidance Laws for Target Tracking 341
12.2.1 Line-of-sight Guidance Law 342
12.2.2 Pure-pursuit Guidance Law 343
12.2.3 Constant Bearing Guidance Law 344
12.3 Linear Design Methods for Path Following 346
12.3.1 Waypoints 346
12.3.2 Path Generation using Straight Lines and Inscribed Circles 347
12.3.3 Straight-line Paths Based on Circles of Acceptance 349
12.3.4 Path Generation using Dubins Path 351
12.3.5 Transfer Function Models for Straight-line Path Following 352
12.4 LOS Guidance Laws for Path Following using Course Autopilots 353
12.4.1 Vector-field Guidance Law 354
12.4.2 Proportional LOS Guidance Law 356
12.4.3 Lookahead- and Enclosure-based LOS Steering 359
12.4.4 Integral LOS 361
12.5 LOS Guidance Laws for Path Following using Heading Autopilots 363
12.5.1 Crab Angle Compensation by Direct Measurements 363
12.5.2 Integral LOS 364
12.6 Curved-Path Path Following 365
12.6.1 Path Generation using Interpolation Methods 366
12.6.2 Proportional LOS Guidance Law for Curved Paths 378
12.6.3 Path-following using Serret–Frenet Coordinates 380
12.6.4 Case Study: Path-following Control using Serret–Frenet Coordinates 384
13 Model-based Navigation Systems 387
13.1 Sensors for Marine Craft 387
13.1.1 GNSS Position 388
13.1.2 GNSS Heading 389
13.1.3 Magnetic Compass 390
13.1.4 Gyrocompass 390
13.2 Wave Filtering 391
13.2.1 Low-pass Filtering 393
13.2.2 Cascaded Low-pass and Notch Filtering 396
13.2.3 Wave-frequency Estimation 397
13.3 Fixed-gain Observer Design 403
13.3.1 Observability 403
13.3.2 Luenberger Observer 405
13.3.3 Case Study: Luenberger Observer for Heading Autopilot 406
13.4 Kalman Filter Design 408
13.4.1 Discrete-time Kalman Filter 408
13.4.2 Discrete-time Extended Kalman Filter 411
13.4.3 Modification for Euler Angles to Avoid Discontinuous Jumps 412
13.4.4 Modification for Asynchronous Measurement Data 415
13.4.5 Case Study: Kalman Filter Design for Heading Autopilots 416
13.4.6 Case Study: Kalman Filter for Dynamic Positioning Systems 419
13.5 Passive Observer Design 424
13.5.1 Case Study: Passive Observer for Dynamic Positioning using GNSS and Compass Measurements 424
13.5.2 Case Study: Passive Observer for Heading Autopilots using only Compass Measurements 433
13.5.3 Case Study: Passive Observer for Heading Autopilots using both Compass and Angular Rate Sensor Measurements 440
14 Inertial Navigation Systems 443
14.1 Inertial Measurement Unit 444
14.1.1 Attitude Rate Sensors 446
14.1.2 Accelerometers 446
14.1.3 Magnetometer 449
14.2 Attitude Estimation 451
14.2.1 Static Mapping from Specific Force to Roll and Pitch Angles 451
14.2.2 Vertical Reference Unit (VRU) Transformations 452
14.2.3 Nonlinear Attitude Observer using Reference Vectors 453
14.3 Direct Filters for Aided INS 457
14.3.1 Fixed-gain Observer using Attitude Measurements 458
14.3.2 Direct Kalman Filter using Attitude Measurements 462
14.3.3 Direct Kalman Filter with Attitude Estimation 465
14.4 Indirect Filters for Aided INS 467
14.4.1 Introductory Example 469
14.4.2 Error-state Kalman Filter using Attitude Measurements 472
14.4.3 Error-state Extended Kalman Filter with Attitude Estimation 480
15 Motion Control Systems 493
15.1 Open-Loop Stability and Maneuverability 494
15.1.1 Straight-line, Directional and Positional Motion Stability 495
15.1.2 Maneuverability 504
15.2 Autopilot Design Using Successive Loop Closure 516
15.2.1 Successive Loop Closure 516
15.2.2 Case Study: Heading Autopilot for Marine Craft 518
15.2.3 Case Study: Path-following Control System for Marine Craft 519
15.2.4 Case Study: Diving Autopilot for Underwater Vehicles 521
15.3 PID Pole-Placement Algorithms 523
15.3.1 Linear Mass–Damper–Spring Systems 523
15.3.2 SISO Linear PID Control 527
15.3.3 MIMO Nonlinear PID Control 529
15.3.4 Case Study: Heading Autopilot for Marine Craft 532
15.3.5 Case Study: LOS Path-following Control for Marine Craft 538
15.3.6 Case Study: Dynamic Positioning System for Surface Vessels 540
15.3.7 Case Study: Position Mooring System for Surface Vessels 546
16 Advanced Motion Control Systems 549
16.1 Linear-quadratic Optimal Control 550
16.1.1 Linear-quadratic Regulator 550
16.1.2 LQR Design for Trajectory Tracking and Integral Action 552
16.1.3 General Solution of the LQ Trajectory-tracking Problem 554
16.1.4 Operability and Motion Sickness Incidence Criteria 560
16.1.5 Case Study: Optimal Heading Autopilot for Marine Craft 562
16.1.6 Case Study: Optimal DP System for Surface Vessels 566
16.1.7 Case Study: Optimal Rudder-roll Damping Systems for Ships 570
16.1.8 Case Study: Optimal Fin and RRD Systems for Ships 579
16.2 State Feedback Linearization 580
16.2.1 Decoupling in the BODY Frame (Velocity Control) 581
16.2.2 Decoupling in the NED Frame (Position and Attitude Control) 582
16.2.3 Case Study: Speed Control Based on Feedback Linearization 584
16.2.4 Case Study: Autopilot Based on Feedback Linearization 585
16.3 Integrator Backstepping 586
16.3.1 A Brief History of Backstepping 586
16.3.2 The Main Idea of Integrator Backstepping 587
16.3.3 Backstepping of SISO Mass–Damper–Spring Systems 594
16.3.4 Integral Action by Constant Parameter Adaptation 597
16.3.5 Integrator Augmentation Technique 599
16.3.6 Case Study: Backstepping Design for Mass–Damper–Spring 602
16.3.7 Case Study: Backstepping Design for Robot Manipulators 604
16.3.8 Case Study: Backstepping Design for Surface Craft 606
16.3.9 Case Study: Autopilot Based on Backstepping 610
16.3.10 Case Study: Path-following Controller for Underactuated Marine Craft 611
16.3.11 Case Study: Weather Optimal Position Control 616
16.4 Sliding Mode Control 634
16.4.1 Conventional Integral SMC for Second-order Systems 634
16.4.2 Conventional Integral SMC for Third-order Systems 637
16.4.3 Super-twisting Adaptive Sliding Mode Control 637
16.4.4 Case Study: Heading Autopilot Based on Conventional Integral SMC 639
16.4.5 Case Study: Depth Autopilot for Diving Based on Conventional Integral SMC 643
16.4.6 Case Study: Heading Autopilot Based on the Adaptive-gain Super Twisting Algorithm 646
Part Three Appendices
A Nonlinear Stability Theory 651
A.1 Lyapunov Stability for Autonomous Systems 651
A.1.1 Stability and Convergence 651
A.1.2 Lyapunov’s Direct Method 653
A.1.3 Krasovskii–LaSalle’s Theorem 654
A.1.4 Global Exponential Stability 655
A.2 Lyapunov Stability of Non-autonomous Systems 656
A.2 1 Barb?lat’s Lemma 656
A.2.2 LaSalle–Yoshizawa’s Theorem 656
A.2.3 On USGES of Proportional Line-of-sight Guidance Laws 657
A.2.4 UGAS when Backstepping with Integral Action 658
B Numerical Methods 661
B.1 Discretization of Continuous-time Systems 661
B.1.1 State-space Models 661
B.1.2 Computation of the Transition Matrix 663
B.2 Numerical Integration Methods 663
B.2.1 Euler’s Method 664
B.2.2 Adams–Bashford’s Second-order Method 665
B.2.3 Runge–Kutta Second-order Method 666
B.2.4 Runge–Kutta Fourth-order Method 666
B.3 Numerical Differentiation 666
C Model Transformations 669
C.1 Transforming the Equations of Motion to an Arbitrarily Point 669
C.1.1 System Transformation Matrix 669
C.1.2 Equations of Motion About an Arbitrarily Point 671
C.2 Matrix and Vector Transformations 672
D Non-dimensional Equations of Motion 675
D.1 Non-dimensionalization 675
D.1.1 Non-dimensional Hydrodynamic Coefficients 676
D.1.2 Non-dimensional Nomoto Models 677
D.1.3 Non-dimensional Maneuvering Models 678
D.2 6-DOF Procedure for Non-dimensionalization 678
References 681
Index 701
