Handbook of Marine Craft Hydrodynamics and Motion Control (2^nd Ed.)

The latest tools for analysis and design of advanced GNC systems

Handbook of Marine Craft Hydrodynamics and Motion Control is an extensive study of the latest research in hydrodynamics, guidance, navigation, and control systems for marine craft. The text establishes how the implementation of mathematical models and modern control theory can be used for simulation and verification of control systems, decision-support systems, and situational awareness systems. Coverage includes hydrodynamic models for marine craft, models for wind, waves and ocean currents, dynamics and stability of marine craft, advanced guidance principles, sensor fusion, and inertial navigation.

This important book includes the latest tools for analysis and design of advanced GNC systems and presents new material on unmanned underwater vehicles, surface craft, and autonomous vehicles. References and examples are included to enable engineers to analyze existing projects before making their own designs, as well as MATLAB scripts for hands-on software development and testing. Highlights of this Second Edition include:

• Topical case studies and worked examples demonstrating how you can apply modeling and control design techniques to your own designs
• A Github repository with MATLAB scripts (MSS toolbox) compatible with the latest software releases from Mathworks
• New content on mathematical modeling, including models for ships and underwater vehicles, hydrostatics, and control forces and moments
• New methods for guidance and navigation, including line-of-sight (LOS) guidance laws for path following, sensory systems, model-based navigation systems, and inertial navigation systems

This fully revised Second Edition includes innovative research in hydrodynamics and GNC systems for marine craft, from ships to autonomous vehicles operating on the surface and under water. Handbook of Marine Craft Hydrodynamics and Motion Control is a must-have for students and engineers working with unmanned systems, field robots, autonomous vehicles, and ships.

MSS toolbox: https://github.com/cybergalactic/mss

Lecture notes: https://www.fossen.biz/wiley

Author?s home page: https://www.fossen.biz

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 Barbălat’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

Thor I. Fossen is a naval architect, cyberneticist, and Professor of Guidance, Navigation, and Control at the Norwegian University of Science and Technology. He received his MS in Naval Architecture and his PhD in Engineering and Cybernetics from the Norwegian Institute of Technology. Fossen was elected to the Norwegian Academy of Technological Sciences in 1998 and became an Institute of Electrical and Electronics Engineers (IEEE) Fellow in 2016.