Handbook of marine craft hydrodynamics and motion control= Vademecum de Navium Motu Contra Aquas et de Motu Gubernando

The technology of hydrodynamic modeling and marine craft motion control systems has progressed greatly in recent years. This timely survey includes the latest tools for analysis and design of advanced guidance, navigation and control systems and presents new material on underwater vehicles and surface vessels. Each section presents numerous case studies and applications, providing a practical understanding of how model-based motion control systems are designed.

Key features include:

a three-part structure covering Modeling of Marine Craft; Guidance, Navigation and Control Systems; and Appendices, providing all the supporting theory in a single resource kinematics, kinetics, hydrostatics, seakeeping and maneuvering theory, and simulation models for marine craft and environmental forces guidance systems, sensor fusion and integrated navigation systems, inertial measurement units, Kalman filtering and nonlinear observer design for marine craft state-of-the-art methods for feedback control more advanced methods using nonlinear theory, enabling the user to compare linear design techniques before a final implementation is made. linear and nonlinear stability theory, and numerical methods companion website that hosts links to lecture notes and download information for the Marine Systems Simulator (MSS) which is an open source Matlab/Simulink® toolbox for marine systems. The MSS toolbox includes hydrodynamic models and motion control systems for ships, underwater vehicles and floating structures

With an appropriate balance between mathematical theory and practical applications, academic and industrial researchers working in marine and control engineering aspects of manned and unmanned maritime vehicles will benefit from this comprehensive handbook. It is also suitable for final year undergraduates and postgraduates, lecturers, development officers, and practitioners in the areas of rigid-body modeling, hydrodynamics, simulation of marine craft, control and estimation theory, decision-support systems and sensor fusion. www.wiley.com/go/fossen_marine

Author Notes

Professor Thor Fossen, Department of Engineering Cybernetics, Norwegian University of Science and Technology (NTNU), Norway
Thor Fossen was appointed Professor in Guidance, Navigation and Control at the Department of Engineering Cybernetics, NTNU in 1993, and now teaches mathematical modeling of marine craft and control theory. He is one of the founders of the company Marine Cybernetics, where he was Vice President in R&D between 2002 and 2007.
Professor Fossen was a senior scientific advisor for ABB, Kongsberg and MARINTEK in 2002. He was involved in the design of nonlinear and passive state estimators for marine vessels, autopilots, trajectory tracking and maneuvering control, identification of ship dynamics from sea-trials and strapdown DGPS/INS navigation systems. He was granted a patent for weather optimal positioning control of marine vessels in 1998 and in 2002 this work won the Automatica Prize Paper Award. Professor Fossen has authored 250 scientific papers and three international textbooks, one of which being the John Wiley and Sons publication Guidance and Control of Ocean Vehicles in 1994. In 2008 his paper entitled 'Nonlinear Observer for Vehicle Estimation' won the Arch T. Colwell Merit Award at the SAE 2008 World Congress.

About the Author	p. xv
Preface	p. xvii
List of Tables	p. xix
I Marine Craft Hydrodynamics	p. 1
1 Introduction	p. 3
l.1 Classification of Models	p. 6
1.2 The Classical Models in Naval Architecture	p. 7
1.2.1 Maneuvering Theory	p. 9
1.2.2 Seakeeping Theory	p. 11
1.2.3 Unified Theory	p. 12
1.3 Fossen's Robot-Like Vectorial Model for Marine Craft	p. 12
2 Kinematics	p. 15
2.1 Reference Frames	p. 16
2.2 Transformations between BODY and NED	p. 20
2.2.1 Euler Angle Transformation	p. 22
2.2.2 Unit Quaternions	p. 27
2.2.3 Quaternions from Euler Angles	p. 32
2.2.4 Euler Angles from Quaternions	p. 33
2.3 Transformations between ECEF and NED	p. 34
2.3.1 Longitude and Latitude Transformations	p. 34
2.3.2 Longitude and Latitude from ECEF Coordinates	p. 36
2.3.3 ECEF Coordinates from Longitude and Latitude	p. 38
2.4 Transformations between BODY and FLOW	p. 39
2.4.1 Definitions of Course, Heading and Sideslip Angles	p. 39
2.4.2 Sideslip and Angle of Attack	p. 41
3 Rigid-Body Kinetics	p. 45
3.1 Newton-Euler Equations of Motion about CG	p. 45
3.1.1 Translational Motion about CG	p. 47
3.1.2 Rotational Motion about CG	p. 48
3.1.3 Equations of Motion about CG	p. 49
3.2 Newton-Euler Equations of Motion about CO	p. 49
3.2.1 Translational Motion about CO	p. 50
3.2.2 Rotational Motion about CO	p. 50
3.3 Rigid-Body Equations of Motion	p. 51
3.3.1 Nonlinear 6 DOF Rigid-Body Equations of Motion	p. 51
3.3.2 Linearized 6 DOF Rigid-Body Equations of Motion	p. 56
4 Hydrostatics	p. 59
4.1 Restoring Forces for Underwater Vehicles	p. 59
4.1.1 Hydrostatics of Submerged Vehicles	p. 59
4.2 Restoring Forces for Surface Vessels	p. 62
4.2.1 Hydrostatics of Floating Vessels	p. 62
4.2.2 Linear (Small Angle) Theory for Boxed-Shaped Vessels	p. 64
4.2.3 Computation of Metacenter Height for Surface Vessels	p. 65
4.3 Load Conditions and Natural Periods	p. 68
4.3.1 Decoupled Computation of Natural Periods	p. 68
4.3.2 Computation of Natural Periods in a 6 DOF Coupled System	p. 69
4.3.3 Natural Period as a Function of Load Condition	p. 71
4.4 Ballast Systems	p. 74
4.4.1 Conditions for Manual Pretrimming	p. 76
4.4.2 Automatic Pretrimming using Feedback from z, ¿ and ¿	p. 78
5 Seakeeping Theory	p. 81
5.1 Hydrodynamic Concepts and Potential Theory	p. 82
5.1.1 Numerical Approaches and Hydrodynamic Codes	p. 84
5.2 Seakeeping and Maneuvering Kinematics	p. 85
5.2.1 Seakeeping Reference Frame	p. 85
5.2.2 Transformation between Body and Seakeeping	p. 86
5.3 The Classical Frequency-Domain Model	p. 90
5.3.1 Potential Coefficients and the Concept of Forced Oscillations	p. 90
5.3.2 Frequency-Domain Seakeeping Models	p. 93
5.4 Time-Domain Models including Fluid Memory Effects	p. 96
5.4.1 Cummins Equation in Seakeeping Coordinates	p. 96
5.4.2 Linear Time-Domain Seakeeping Equations in Body Coordinates	p. 99
5.4.3 Nonlinear Unified Seakeeping and Maneuvering Model with Fluid Memory Effects	p. 103
5.5 Case Study: Identification of Fluid Memory Effects	p. 104
5.5.1 Frequency-Domain Identification using the MSS FD1 Toolbox	p. 104
6 Maneuvering Theory	p. 109
6.1 Rigid-Body Kinetics	p. 110
6.2 Potential Coefficients	p. 111
6.2.1 3 DOF Maneuvering Model	p. 113
6.2.2 6 DOF Coupled Motions	p. 113
6.3 Nonlinear Coriolis Forces due to Added Mass in a Rotating Coordinate System	p. 115
6.3.1 Lagrangian Mechanics	p. 115
6.3.2 Kirchhoff's Equations in Vector Form	p. 116
6.3.3 Added Mass and Coriolis-Centripetal Forces due to the Rotation of Body Relative to Ned	p. 117
6.4 Viscous Damping and Ocean Current Forces	p. 122
6.4.1 Linear Viscous Damping	p. 123
6.4.2 Nonlinear Surge Damping	p. 125
6.4.3 Cross-Flow Drag Principle	p. 127
6.5 Maneuvering Equations	p. 128
6.5.1 Hydrodynamic Mass-Damper-Spring System	p. 128
6.5.2 Nonlinear Maneuvering Equations	p. 130
6.5.3 Linearized Maneuvering Equations	p. 131
8 Models for Ships, Offshore Structures and Underwater Vehicles	p. 133
7.1 Maneuvering Models (3 DOF)	p. 133
7.1.1 Nonlinear Maneuvering Models Based on Surge Resistance and Cross-Flow Drag	p. 136
7.1.2 Nonlinear Maneuvering Models Based on Second-order Modulus Functions	p. 136
7.1.3 Nonlinear Maneuvering Models Based on Odd Functions	p. 138
7.1.4 Linearized Maneuvering Models	p. 140
7.2 Autopilot Models for Heading Control (1 DOF)	p. 142
7.2.1 Second-Order Nomoto Model (Yaw Subsystem)	p. 142
7.2.2 First-Order Nomoto Model (Yaw Subsystem)	p. 143
7.2.3 Nonlinear Extensions of Nomoto's Model	p. 145
7.2.4 Pivot Point (Yaw Rotation Point)	p. 146
7.2.5 Nondimensional Maneuvering and Autopilot Models	p. 148
7.3 DP Models (3 DOF)	p. 152
7.3.1 Nonlinear DP Model using Current Coefficients	p. 153
7.3.2 Linearized DP Model	p. 157
7.4 Maneuvering Models Including Roll (4 DOF)	p. 158
7.4.1 The Nonlinear Model of Son and Nomoto	p. 163
7.4.2 The Nonlinear Model of Blanke and Christensen	p. 164
7.4.3 Nonlinear Model Based on Low-Aspect Ratio Wing Theory	p. 165
7.5 Equations of Motion (6 DOF)	p. 167
7.5.1 Nonlinear 6 DOF Vector Representations in Body and NED	p. 167
7.5.2 Symmetry Considerations of the System Inertia Matrix	p. 171
7.5.3 Linearized Equations of Motion (Vessel Parallel Coordinates)	p. 173
7.5.4 Transfonning the Equations of Motion to a Different Point	p. 176
7.5.5 6 DOF Models for AUVs and ROVs	p. 182
7.5.6 Longitudinal and Lateral Models for Submarines	p. 183
8 Environmental Forces and Moments	p. 187
8.1 Wind Forces and Moments	p. 188
8.1.1 Wind Forces and Moments on Marine Craft at Rest	p. 188
8.1.2 Wind Forces and Moments on Moving Marine Craft	p. 191
8.1.3 Wind Coefficients Based on Flow over a Helmholtz-Kirchhoff Plate	p. 192
8.1.4 Wind Coefficients for Merchant Ships	p. 194
8.1.5 Wind Coefficients for Very Large Crude Carriers	p. 195
8.1.6 Wind Coefficients for Large Tankers and Medium-Sized Ships	p. 195
8.1.7 Wind Coefficients for Moored Ships and Floating Structures	p. 195
8.2 Wave Forces and Moments	p. 199
8.2.1 Sea State Descriptions	p. 200
8.2.2 Wave Spectra	p. 202
8.2.3 Wave Amplitude Response Model	p. 208
8.2.4 Wave Force Response Amplitude Operators	p. 211
8.2.5 Motion Response Amplitude Operators	p. 213
8.2.6 State-Space Models for Wave Responses	p. 214
8.3 Ocean Current Forces and Moments	p. 221
8.3.1 3-D Irrotational Ocean Current Model	p. 224
8.3.2 2-D Irrotational Ocean Current Model	p. 224
II Motion Control	p. 227
9 Introduction	p. 229
9.1 Historical Remarks	p. 229
9.1.1 The Gyroscope and its Contributions to Ship Control	p. 230
9.1.2 Autopilots	p. 231
9.1.3 Dynamic Positioning and Position Mooring Systems	p. 231
9.1.4 Waypoint Tracking and Path-Following Control Systems	p. 232
9.2 The Principles of Guidance, Navigation and Control	p. 232
9.3 Setpoint Regulation, Trajectory-Tracking and Path-Following Control	p. 235
9.4 Control of Underactuated and Fully Actuated Craft	p. 235
9.4.1 Configuration Space	p. 236
9.4.2 Workspace and Control Objectives	p. 237
9.4.3 Weathervaning of Underactuated Craft in a Uniform Force Field	p. 238
10 Guidance Systems	p. 241
10.1 Target Tracking	p. 242
10.1.1 Line-of-Sight Guidance	p. 243
10.1.2 Pure Pursuit Guidance	p. 244
10.1.3 Constant Bearing Guidance	p. 244
10.2 Trajectory Tracking	p. 246
10.2.1 Reference Models for Trajectory Generation	p. 248
10.2.2 Trajectory Generation using a Marine Craft Simulator	p. 251
10.2.3 Optimal Trajectory Generation	p. 253
10.3 Path Following for Straight-Line Paths	p. 254
10.3.1 Path Generation based on Waypoints	p. 255
10.3.2 LOS Steering Laws	p. 257
10.4 Path Following for Curved Paths	p. 266
10.4.1 Path Generation using Interpolation Methods	p. 267
10.4.2 Path-Following Kinematic Controller	p. 278
11 Sensor and Navigation Systems	p. 285
11.1 Low-Pass and Notch Filtering	p. 287
11.1.1 Low-Pass Filtering	p. 288
11.1.2 Cascaded Low-Pass and Notch Filtering	p. 290
11.2 Fixed Gain Observer Design	p. 292
11.2.1 Observability	p. 292
11.2.2 Luenberger Observer	p. 293
11.2.3 Case Study: Luenberger Observer for Heading Autopilots using only Compass Measurements	p. 294
11.3 Kalman Filter Design	p. 296
11.3.1 Discrete-Time Kalman Filter	p. 296
11.3.2 Continuous-Time Kalman Filter	p. 297
11.3.3 Extended Kalman Filter	p. 298
11.3.4 Corrector-Predictor Representation for Nonlinear Observers	p. 299
11.3.5 Case Study: Kalman Filter for Heading Autopilots using only Compass Measurements	p. 300
11.3.6 Case Study: Kalman Filter for Dynamic Positioning Systems using GNSS and Compass Measurements	p. 304
11.4 Nonlinear Passive Observer Designs	p. 310
11.4.1 Case Study: Passive Observer for Dynamic Positioning using GNSS and Compass Measurements	p. 311
11.4.2 Case Study: Passive Observer for Heading Autopilots using only Compass Measurements	p. 319
11.4.3 Case Study: Passive Observer for Heading Autopilots using both Compass and Rate Measurements	p. 327
11.5 Integration Filters for IMU and Global Navigation Satellite Systems	p. 328
11.5.1 Integration Filter for Position and Linear Velocity	p. 332
11.5.2 Accelerometer and Compass Aided Attitude Observer	p. 336
11.5.3 Attitude Observer using Gravitational and Magnetic Field Directions	p. 340
12 Motion Control Systems	p. 343
12.1 Open-Loop Stability and Maneuverability	p. 343
12.1.1 Straight-Line, Directional and Positional Motion Stability	p. 344
12.1.2 Maneuverability	p. 353
12.2 PID Control and Acceleration Feedback	p. 365
12.2.1 Linear Mass-Damper-Spring Systems	p. 365
12.2.2 Acceleration Feedback	p. 370
12.2.3 PID Control with Acceleration Feedback	p. 372
12.2.4 M1MO Nonlinear PID Control with Acceleration Feedback	p. 375
12.2.5 Case Study: Heading Autopilot for Ships and Underwater Vehicles	p. 377
12.2.6 Case Study: Heading Autopilot with Acceleration Feedback for Ships and Underwater Vehicles	p. 384
12.2.7 Case Study: Linear Cross-Tracking System for Ships and Underwater Vehicles	p. 385
12.2.8 Case Study: LOS Path-Following Control for Ships and Underwater Vehicles	p. 387
12.2.9 Case Study: Path-Following Control for Ships and Underwater Vehicles using Serret-Frenet Coordinates	p. 389
12.2.10 Case Study: Dynamic Positioning Control System for Ships and Floating Structures	p. 391
12.2.11 Case Study: Position Mooring Control System for Ships and Floating Structures	p. 396
12.3 Control Allocation	p. 398
12.3.1 Actuator Models	p. 398
12.3.2 Unconstrained Control Allocation for Nonrotatable Actuators	p. 404
12.3.3 Constrained Control Allocation for Nonrotatable Actuators	p. 405
12.3.4 Constrained Control Allocation for Azimuth Thrusters	p. 408
12.3.5 Case Study: DP Control Allocation System	p. 411
13 Advanced Motion Control Systems	p. 417
13.1 Linear Quadratic Optimal Control	p. 418
13.1.1 Linear Quadratic Regulator	p. 418
13.1.2 LQR Design for Trajectory Tracking and Integral Action	p. 420
13.1.3 General Solution of the LQ Trajectory-Tracking Problem	p. 421
13.1.4 Case Study: Optimal Heading Autopilot for Ships and Underwater Vehicles	p. 429
13.1.5 Case Study: Optimal Fin and Rudder-Roll Damping Systems for Ships	p. 433
13.1.6 Case Study: Optimal Dynamic Positioning System for Ships and Floating Structures	p. 446
13.2 State Feedback Linearization	p. 451
13.2.1 Decoupling in the Body Frame (Velocity Control)	p. 451
13.2.2 Decoupling in the NED Frame (Position and Attitude Control)	p. 452
13.2.3 Case Study: Feedback Linearizing Speed Controller for Ships and Underwater Vehicles	p. 454
13.2.4 Case Study: Feedback Linearizing Ship and Underwater Vehicle Autopilot	p. 455
13.2.5 Case Study: MIMO Adaptive Feedback Linearizing Controller for Ships and Underwater Vehicles	p. 455
13.3 Integrator Backstepping	p. 457
13.3.1 A Brief History of Backstepping	p. 458
13.3.2 The Main Idea of Integrator Backstepping	p. 458
13.3.3 Backstepping of SISO Mass-Damper-Spring Systems	p. 465
13.3.4 Integral Action by Constant Parameter Adaptation	p. 469
13.3.5 Integrator Augmentation Technique	p. 472
13.3.6 Case Study: Backstepping of MIMO Mass-Damper-Spring Systems	p. 475
13.3.7 Case Study: MIMO Backstepping for Fully Actuated Ships	p. 480
13.3.8 Case Study: MIMO Backstepping Design with Acceleration Feedback for Fully Actuated Ships	p. 484
13.3.9 Case Study: Nonlinear Separation Principle for PD Controller-Observer Design	p. 487
13.3.10 Case Study: Weather Optimal Position Control for Ships and Floating Structures	p. 491
13.3.11 Case Study: Heading Autopilot for Ships and Underwater Vehicles	p. 509
13.3.12 Case Study: Path-Following Controller for Underactuated Marine Craft	p. 512
13.4 Sliding-Mode Control	p. 519
13.4.1 SISO Sliding-Mode Control	p. 519
13.4.2 Sliding-Mode Control using the Eigenvalue Decomposition	p. 522
13.4.3 Case Study: Heading Autopilot for Ships and Underwater Vehicles	p. 525
13.4.4 Case Study: Pitch and Depth Autopilot for Underwater Vehicles	p. 526
Appendices	p. 529
A Nonlinear Stability Theory	p. 531
A.l Lyapunov Stability for Autonomous Systems	p. 531
A.1.1 Stability and Convergence	p. 531
A.1.2 Lyapunov's Direct Method	p. 532
A.1.3 Krasovskii-LaSalle's Theorem	p. 533
A.1.4 Global Exponential Stability	p. 534
A.2 Lyapunov Stability of Nonautonomous Systems	p. 535
A.2.1 Barbalat's Lemma	p. 535
A.2.2 LaSalle-Yoshizawa's Theorem	p. 536
A.2.3 Matrosov's Theorem	p. 536
A.2.4 UGAS when Backstepping with Integral Action	p. 537
B Numerical Methods	p. 541
B.l Discretization of Continuous-Time Systems	p. 541
B.1.1 Linear State-Space Models	p. 541
B.1.2 Nonlinear State-Space Models	p. 543
B.2 Numerical Integration Methods	p. 544
B.2.1 p. Euler's Method
B.2.2 Adams-Bashford's Second-Order Method	p. 546
B.2.3 Runge-Kutta Second-Order Method	p. 547
B.2.4 Runge-Kutta Fourth-Order Method	p. 547
B.3 Numerical Differentiation	p. 547
References	p. 549
Index	p. 567

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