# Guidance and control of ocean vehicles thor i fossen pdf

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- Thor I. Fossen
- Mathematical Models of Ships and Underwater Vehicles
- Control Of Ships And Underwater Vehicles
- Guidance and Control of Ocean Vehicles

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## Thor I. Fossen

Brisb ane. Reprinted May Hcpdntcd March ,, All rights reserved :! B21 Euler's Method.. Consequently, much of the material and inspiration for the book has evolved from this period.

Writing this book, is an attempt to draw the disci- plines of engineering cybernetics and marine engineering together. Systems for Guidance and Control have been taught by the author since for MSc students in Engineering Cybernetics at the Faculty of Electrical Engineer- ing and Computer Science NIT The book is intended as a textbook for senior and graduate students with some background in control engineering and calculus.

Some basic knowledge of linear and nonlinear control theory, vector analysis and differential equations is required. The objective of the book is to present and apply advanced control theory to marine vehicles like remotely operated vehicles ROVs , surface ships, high speed crafts and floating offshore structures The reason for applying more sophisticated autopilots for steering and dynamic po- sitioning of marine vehicles is mainly due to fuel economy, improved reliability and performance enhancement, Since , the rapid increase in oil prices has contributed to this trend.

This justifies the use of more advanced mathematical models and control theory in guidance and control applications,. Professor Thor 1. S0rensen should also be thanked for his sincere help in writing Section 7.

The subject of this textbook is guidance and control of ocean vehicles. This title covers control systems design for all types of marine vehicles like submarines, torpedoes, unmanned and manned underwater vehicles, conventional ships, high speed crafts and semi-submersibles. Examples of such systems are:. For practical purposes the discussion will concentrate on three vehicle categories: small unmanned underwater vehicles, surface ships and high speed craft.

GUIDANCE is the action of determining the course, attitude and speed of the vehicle, relative to some reference frame usually the earth , to be followed by the vehicle. CONTROL is the development and application to a vehicle of appropriate forces and moments for operating point control, tracking and stabilization. This involves designing the feedforward and feedback control laws. Based on the speed loss computations we can compute a fuel optimal route.

Finally, we have to design an optimal track-keeping controller autopilot to enSUT'e that this mute is followed by the ship. A guidance and contT'ol system for automatic weather routing of a ship is shown in FiguT'e 1. This system uses weather data measurements to compute a fuel optimal mute faT' the ship which is fed forward to the contT'ol system through a block denoted as the "feedforwaT'd contml system".

The contr-ol force and moment vector T is pmvided by the actuatoT' via the contm. We also notice that the 1'efeT'ence gener'atoT' 17d may use weather data t; wind speed, wind direction, wave height etc. J together with the ship states v, 17 to compute the optimal route. This is usually done by including constraints for fuel consumption, actuator saturation, fOT'waT'd speed, restricted areas for ship maneuvering etc.

This book deals mainly with modeling and control of unmanned untethered un- derwater vehicles remotely operated vehicles and autohomous underwater vehi- cles , surface ships cargo ships, tankers etc, and high speed craft surface effect ships and foilbome catamarans.

The design of modern marine vehicle guidance and control systems requires knowledge of a broad field of disciplines. Some of these are vectorial kinemat- ics and dynamics, hydrodynamics, navigation systems and control theory. To be able to design a high performance control system it is evident that a good mathematical model of the vehicle is required for simulation and verification of the design.

As a result of this, the book contains a large number of mathematical models intended for this purpose. The clifferent topics in the book are organized according to:. It is recommended that one should read Chapter 2 before Chapters since these chapters use basic results from vectoIial kinematics and dynamics. Chapter 2 Modeling of Marine Vehicles. Modeling of marine vehicles involves the study of statics and dynamics. Statics is concerned with the equilibrium of bodies at rest or moving with constant velocity, whereas dynamics is concerned with bodies having accelerated motion.

Statics is the oldest of the engineering sciences. In fact, important contributions were made over years ago by Archimedes BC who derived the basic law of hydrostatic buoyancy.

This result is the foundation for static stability analyses of marine vessels. The study of dynamics started much later since accurate measurements of time are necessary to perform dynamic experiments. One of the first time- measuring instruments, a "water clock", was designed by Leonardo da Vinci This simple instrument exploited the fact that the interval between the falling drops of water could be considered constant.

The scientific basis of dy- namics was provided by Newton's laws published in It is common to divide the study of dynamics into two parts: kinematics, which treats only geometrical aspects of motion, and kinetics, which is the analysis of the forces causing the motion. This study discusses the motion of marine vehicles in 6 degrees of freedom DO F since 6 independent coordinates are necessary to determine the position and orientation of a rigid body.

The first three coordinates and their time deriva- J. The moving coordinate frame XoYoZo is conveniently fixed to the vehicle and is called the body-fixed reference frame, The origin 0 of the body-fixed frame is usually chosen to coincide with the center of gravity CG when CG is in the principal plane of symmetry or at any other convenient point if this is not the case.

For marine vehicles, the body axes X o, Y o and Zo coincide with the principal axes of inertia, and are usually defined as:. Yo - transverse axis directed to starboard..

Zo - normal axis directed from top to bottom. V W sway heave y o. For marine vehicles it is usually assumed that the accelerations of a point on the surface of the Earth can be neglected. Here TJ denotes the position and orientation vector with coordinates in the earth- fixed frame, v denotes the linear and angular velocity vector with coordinates in the body-fixed frame and 7" is used to describe the forces and moments acting on the vehicle in the body-fixed frame In marine guidance and control systems, orientation is usually represented by means of Euler angles or quaternions..

In the next sections the kinematic equations relating the body-fixed reference frame to the earth-fixed reference frame will be derived. The inverse velocity trans- formation will be written:. Definition 2. Theorem 2. Let 0. Hence, the vector b can be expressed in terms of the vector 0. The rotation is described by see Hughes or Kane, Likins and Levinson :.

This implies that the off-diagonal matrix elements of S satisfy Sij - -Sji for i '" j while the matrix diagonal consists of zero elements. The set of all 3 x 3 skew-symmetric matrices is denoted by 88 3 while the set of all 3 x 3 rotation matrices is usually referred to by the symbol 80 3 1 'Special Orthogonal group of order 3.

Expanding 2. This yields the following transformation matrices:. The notation Oi,a denotes a rotation angle a about the i-a.. Notice that all Ci,a satisfy the following property:. Property 2. Note that the order in which these rotations is carried out is not arbitrary. This yields the coordinate system X2Y2Z2. The coordinate system X 2Y2Z 2 is rotated a pitch angle 0 about the Y2 axis. This yields the body- fixed coordinate system XoYoZo, see Figure 2. The orientation of the body-fixed reference fraIlle with respect to the inertial reference frame is given by:.

Figure 2. In that case, the kinematic equations can be described by two Euler angle representations with different singularities.. Another possibility is to use a quaternion representation. This is the topic of the next section. Summarizing the results from this section, the kinematic equations can be expressed in vector form as:.

Consider the following definitions:. By applying quatemions, we will show that we can describe the motion of the body-fixed reference frame relative to the inertial frame. Linear Velocity Transformation The transformation relating the linear velpcity vector in the inertial reference frame to the velocity in the body-fixed reference frame can be expressed as:. Angular Velocity Transformation The angular velocity kansformation can be derived by differentiating:.

This shows that the matrix S t is skew-symmetrical. Postmultiplying all ele-- ments in 2. Substituting the expressions for G;j from 2,24 into this expression, some calcu- lation yields:. Let 1 ::; i ::; 4 be the index corresponding to:. Compute the other three p-valu es from:. Let the elements of El be denot ed by E ij where the super script s i and j denot e the i-th row and j-th column of El' Writin g expression 2. Also, a convention for choosing the signs of the Euler angles should be adopted.

It is attractive to use the Euler angle representation since this is a three- parameter set corresponding to well known quantities like the roll, pitch and yaw angle of the vehicle. However, no continuous three-parameter description can be both global and without singularities.

This is due to the metacentric restoring forces. Another advantage with the Euler parameters is their representation and computational efficiency. The Euler angles are computed by numerical integration of a set of noulinear differential equations, This procedure involves computation of a large number of trigonometric functions.

For infinitesimal analyses this solution is quite accurate but problems arise for arbitrary displacements; The Rodrigues parameter representation is also computationally effective but this representation has one singularity. Although it is dangerous to generalize, computational efficiency and accuracy suggests that Euler parameters are the best choice, However, Euler angles are more intuitive and therefore more used,.

The Newton-Euler' formulation is based on Newton's Second Law which relates mass m, acceleration Vc and force le according to:. This result is actually known as Newton's First Law.

These laws were published in by lsaac Newton in "Philosophia Naturalis Principia Mathematica". These results are known as Euler's First and Second Axioms, respectively. Here f e and me are the forces and moments referred to the body's center of gravity, w is the angular velocity vector and I e is the inertia tensor about the body's center of gravity to be defined later.

## Mathematical Models of Ships and Underwater Vehicles

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Demonstrates how the implementation of mathematical models and modern control theory can reduce fuel consumption and improve reliability and performance. Coverage includes ocean vehicle modeling, environmental disturbances, the dynamics and stability of ships, sensor and navigation systems. Numerous examples and exercises facilitate understanding. Additional info : From the Author The Wiley book from was the first attempt to bring hydrodynamic modeling and control system design into a unified notation for modeling, simulation and control. My first book also contains state-of-the-art control design methods for ships, offshore structures and underwater vehicles up to

Embed Size px x x x x Consequently, muchofthematerial andinspirationfor the bookhasevolvedfromthis period. Writingthis book, is anattempt todrawthe disci-plines of engineering cyberneticsand marine engineering together. Systems forGuidanceandControl have been taught by the author since for MSc students in Engineering Cybernetics at the Faculty of Electrical Engineer-ing andComputer Science NIT Thebook isintendedasatextbook for seniorand graduate students with some background in control engineering and calculus. Some basic knowledgeof linear and nonlinear control theory, vectoranalysis anddifferential equationsisrequired. Theobjectiveof thebookis topresent andapply advancedcontrol theory to marine vehicles like remotely operated vehicles ROVs , surfaceships, highspeedcrafts andfloatingoffshorestructures Thereasonfor applyingmoresophisticatedautopilotsforsteeringanddynamicpo-sitioning of marinevehicles ismainlyduetofuel economy, improvedreliabilityandperformanceenhancement, Since, therapidincreaseinoil priceshascontributedtothistrend.

Get this from a library! Guidance and control of ocean vehicles. [Thor I Fossen].

## Control Of Ships And Underwater Vehicles

T1 - Control of Ships and Underwater Vehicles. AU - Do, Duc. AU - Pan, Jie.

Latest version View entry history. This entry describes the equations of motion of ships and underwater vehicles. Standard hydrodynamic models in the literature are reviewed and presented using the nonlinear robot-like vectorial notation of Fossen Nonlinear modelling and control of underwater vehicles.

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### Guidance and Control of Ocean Vehicles

Асфальт впереди становился светлее и ярче. Такси приближалось, и свет его фар бросал на дорогу таинственные тени. Раздался еще один выстрел. Пуля попала в корпус мотоцикла и рикошетом отлетела в сторону. Беккер изо всех сил старался удержаться на шоссе, не дать веспе съехать на обочину. Я должен добраться до ангара. Интересно, увидит ли пилот лирджета, что он подъезжает.

Струя горячего воздуха, напоенного фреоном, ударила ему прямо в лицо. Клубы пара вырвались наружу, подкрашенные снизу в красный цвет контрольными лампами. Далекий гул генераторов теперь превратился в громкое урчание. Чатрукьян выпрямился и посмотрел. То, что он увидел, больше напоминало вход в преисподнюю, а не в служебное помещение.

Хейл мог понять смысл лишь двух слов. Но этого было достаточно. СЛЕДОПЫТ ИЩЕТ… - Следопыт? - произнес. - Что он ищет? - Мгновение он испытывал неловкость, всматриваясь в экран, а потом принял решение. Хейл достаточно понимал язык программирования Лимбо, чтобы знать, что он очень похож на языки Си и Паскаль, которые были его стихией.