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Underwater Robotics Gianluca Antonelli Thor Inge Fossen Dana Yoerger July 19, 2007
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Page 1: Underwater Robotics - Thor I. Fossen · Underwater Robotics 1.1 The expanding role of marine robotics in oceanic engineer-ing The world’s oceans cover 2/3 of the earth’s surface

Underwater Robotics

Gianluca Antonelli Thor Inge Fossen Dana Yoerger

July 19, 2007

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2

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Contents

1 Underwater Robotics 9

1.1 The expanding role of marine robotics in oceanic engineering . . . . . . . . . . . . . . . . . . . . . . 91.1.1 Historical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2 Underwater robotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2.2 Sensor systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.2.3 Actuating systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.2.4 Mission Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.2.5 Guidance and control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.2.6 Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.2.7 Underwater manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.2.8 Fault detection/tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.2.9 Multi underwater vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.4 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3

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4 CONTENTS

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List of Figures

1.1 The ROV Jason 2 (courtesy of Woods Hole Oceanographic Institute, http://www.whoi.edu) . . . . . 311.2 The fully actuated AUV ODIN (courtesy of Autonomous Systems Laboratory, University of Hawaii,

http://www.eng.hawaii.edu/∼asl/) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321.3 Motion variables for an underwater vehicle (output in vectorial form, may be edited to harmonize

fonts, available also in pdf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331.4 Guidance, navigation and control for an autonomous marine vehicle. (output in vectorial form, may

be edited to harmonize fonts, available also in pdf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331.5 Ambient water and axial flow velocities affecting the thruster behavior. (output in vectorial form,

may be edited to harmonize fonts, available also in pdf) . . . . . . . . . . . . . . . . . . . . . . . . . 341.6 Values of KT (solid), 10 ·KQ (dotted) and η0 (dash-dotted) in function of J0 [1]. (output in vectorial

form, may be edited to harmonize fonts) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351.7 An underwater vehicle-manipulator system: SAUVIM (courtesy of Autonomous Systems Laboratory,

University of Hawaii, http://www.eng.hawaii.edu/∼asl/) . . . . . . . . . . . . . . . . . . . . . . . . . 35

5

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6 LIST OF FIGURES

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List of Tables

1.1 ROVs for scientific use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.2 UUV possible instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.3 JHUROV instrumentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.4 ODIN III sensors update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301.5 Common notation for marine vehicle’s motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301.6 Lift and Drag Coefficient for a cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

7

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8 LIST OF TABLES

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Chapter 1

Underwater Robotics

1.1 The expanding role of marine

robotics in oceanic engineer-ing

The world’s oceans cover 2/3 of the earth’s surface andhave been critical to human welfare throughout history.As in ancient times, they enable the transport of goodsbetween nations. Presently, the seas represent criticalsources of food and other resources such as oil and gas.In the near term, we may soon see the emergence ofoffshore mining for metals as well as the exploitation ofgas hydrates. Conversely, the ocean can also threatenhuman safety and damage infrastructure through naturalphenomena such as hurricanes and tsunamis.

Our scientific understanding of the deep sea is ex-panding rapidly through the use of a variety of tech-nologies. The first scientific explorations were conductedprimarily through the use of diving and human occupiedsubmersibles, complemented by a variety of other tech-nologies such as towed or lowered instruments, trawls,dredges, autonomous seafloor instruments, and deep-sea drilling. More recently remotely operated and au-tonomous vehicles have begun to revolutionize seafloorexploration, often returning superior data products atreduced costs. In the near future, seafloor observato-ries linked by fiber optic cables and satellites will returnmassive amounts of data from coastal and deep sea sites.These observations will complement those from conven-tional expeditionary investigations, and will require tele-operated or robotic intervention during installation andfor service. An example of a remotely-operated vehicledeveloped for scientific study of the seafloor, the Jason 2vehicle developed at the Woods Hole Oceanographic In-stitution, is shown in figure 1.1, and a list of remotelyoperated vehicles for scientific exploration appears in ta-ble 1.1 (the last vehicle of the table, Kaiko, was lost

several years ago).

Offshore oil & gas installations are presently ser-viced almost exclusively by Remotely Operated Vehi-cles (ROVs), physically connected via a tether to re-ceive power and data, with human divers used only forthe most shallow installations. Subsea systems requireextensive work capability during installation, and needfrequent inspection and intervention to support drillingoperations, actuate valves, repair or replace subsea com-ponents, and to accomplish a variety of tasks requiredto maintain production rates and product quality. Thetrend toward robotic and teleoperated subsea interven-tion is certain to continue as offshore oil & gas productionmoves into deeper waters, and economic considerationspush key production steps from surface platforms to theseafloor. Remotely operated manipulators enable thesesystems to perform complex tasks such as debris removal,cleaning using abrasive tools and to operate a variety ofnondestructive testing tools. The effectiveness of usingROVs decreases with depth mainly due to the cost in-crease and the difficulties of handling the long tether.

AUVs (Autonomous Underwater Vehicles) are free-swimming, unoccupied underwater vehicles that canovercome the limitations imposed by ROV tethers forsome tasks. Such vehicles carry their own energy sup-plies (presently batteries, perhaps fuel cells in the future)and communicate only through acoustics and perhapsoptical links in the near future. Limited communica-tions require these vehicles to operate independently ofcontinuous human control, in many cases the vehiclesoperate completely autonomously. AUVs are currentlyused for scientific survey tasks, oceanographic sampling,underwater archeology and under-ice survey. Militaryapplications, such mine detection and landing site sur-vey, are presently operational, and more ambitious ap-plications such as long-term undersea surveillance are inengineering development. Presently, AUVs are incapable

9

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10 CHAPTER 1. UNDERWATER ROBOTICS

of sampling or manipulations tasks like those done rou-tinely by ROVs, as typical work environments tend to becomplex and challenging even to skilled human pilots.

Today, approximately 200 AUVs are operational,many of them experimental. However, they are maturingrapidly. Recently several companies now offer commer-cial services with AUVs. As an example, for the oil & gasindustry the cost reduction of a survey performed withan AUVs instead of a towed vehicle is up to 30% andthe data quality is generally higher. Likewise, commer-cial manufacturers in several countries now offer turn-keyAUV systems for specific, well-defined tasks. Currently,remotely operated manipulator are a standard equip-ment for most ROVs, on the contrary autonomous ma-nipulation still is a research challenge; the two projectsSAUVIM [2] and ALIVE [3] were devoted at studyingthis control problem.

1.1.1 Historical background

Boats have been used by humans before recorded history,but vehicles able to go under water are more recent. Per-haps the first recorded idea of an underwater machinecame from Aristotle; according to legend he built the:skaphe andros (boat-man) that allowed Alexander theGreat (Alexander III of Macedon, 356 - 323 b.C.) tostay submerged for at least half a day during the warof Tiro in 325 b.C. This is probably unrealistic, if trueit would precede Archimedess law first articulated ap-proximately 250 b.C. Leonardo Da Vinci may have beenthe first to design an underwater vehicle. His effortswere recorded in the Codice Atlantico (Codex Atlanti-cus), written between 1480 and 1518. Legends say thatLeonardo worked on the idea of an underwater militarymachine but he destroyed the results as he judged themto be too dangerous. The first use of feedback theory formarine control was probably the Northseeking device,patented in 1908, that used gyroscopic principals to de-velop the first autopilot [4]. From that point, the use offeedback theory in the marine control grew continuously;it is interesting to notice that the PID (Proportional Inte-gral Derivative) control commonly used today in numer-ous industrial applications, was first formally analyzedin 1929 by Minorsky [5]. The first remotely operatedunderwater vehicle, POODLE was built in 1953, andthe ROV evolved through the 1960s and 1970s mostlyfor military purposes. In the 1980s ROVs became estab-lished for use in the commercial offshore industry and be-gan to emerge for scientific applications. The first teth-erless, autonomous vehicles were built for experimental

purposes in the 1970s. Currently, AUVs are becoming in-creasingly commonplace for scientific, military, and com-mercial applications. Turnkey AUV systems for a rangeof tasks are available from commercial vendors, and AUVservices can be acquired from a number of companies [6].

1.2 Underwater robotics

1.2.1 Modeling

A rigid body is completely described by its position andorientation with respect to a reference frame Σi, Oi−xyz

that it is supposed to be Earth-fixed and inertial. Let usdefine η1 ∈ IR3 as

η1 =[

x y z]T

,

the vector of the body position coordinates in a Earth-fixed reference frame. The vector η1 is the correspondingtime derivative (expressed in the Earth-fixed frame). Ifone defines

ν1 =[

u v w]T

as the linear velocity of the origin of the body-fixed frameΣb, Ob − xbybzb with respect to the origin of the Earth-fixed frame expressed in the body-fixed frame (from nowon: body-fixed linear velocity) the following relation be-tween the defined linear velocities holds:

ν1 = RBI η1 , (1.1)

where RBI is the rotation matrix expressing the transfor-

mation from the inertial frame to the body-fixed frame.Let us define η2 ∈ IR3 as

η2 =[

φ θ ψ]T

the vector of body Euler-angle coordinates in a Earth-fixed reference frame. In the nautical field those arecommonly named roll, pitch and yaw. Yaw is definedas rotation around the z axis of the fixed frame, pitchis defined as rotation around the y axis resulting afterthe yaw movement and roll is defined as rotation aroundthe x axis resulting after both yaw and pitch movements.The vector η2 is the corresponding time derivative (ex-pressed in the inertial frame). Let us define

ν2 =[

p q r]T

as the angular velocity of the body-fixed frame with re-spect to the Earth-fixed frame expressed in the body-fixed frame (from now on: body-fixed angular velocity).

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1.2. UNDERWATER ROBOTICS 11

The vector η2 does not have a physical interpretationand it is related to the body-fixed angular velocity by aproper Jacobian matrix:

ν2 = Jk,o(η2)η2 . (1.2)

The matrix Jk,o ∈ IR3×3 can be expressed in terms ofEuler angles as:

Jk,o(η2) =

1 0 −sθ0 cφ cθsφ0 −sφ cθcφ

, (1.3)

where cα and sα are short notations for cos(α) andsin(α), respectively. Matrix Jk,o(η2) is not invertiblefor every value of η2. In detail, it is

J−1k,o(η2) =

1

1 sφsθ cφsθ0 cφcθ −cθsφ0 sφ cφ

, (1.4)

that it is singular for θ = (2l+ 1)π2 rad, with l ∈ IN, i.e.,for a pitch angle of ±π

2 rad.

The rotation matrix RBI , needed in (1.1) to transform

the linear velocities, is expressed in terms of Euler anglesby the following (or link to kinematic chapter instead):

RBI (η2) =

cψcθ sψcθ −sθ−sψcφ + cψsθsφ cψcφ + sψsθsφ sφcθsψsφ + cψsθcφ −cψsφ + sψsθcφ cφcθ

.

(1.5)Table 1.5 shows the common notation used for marine

vehicles according to the SNAME notation ([7]); a sketchis shown in Figure 1.3.

As for any representation of a rigid’s body orientationseveral possibilities arise, among them, the use of a 4-parameters description given by the quaternions. Theterm quaternion was introduced by Hamilton in 1840,70 years after the introduction of a four-parameter rigid-body attitude representation by Euler. An introductionto alternative orientation representations can be foundin xxx (link to kinematic chapter?) and, concerning themarine environment, in [8].

It is useful to collect the kinematic equations in 6-dimensional matrix forms. Let us define the vector η ∈IR6 as

η =

[

η1

η2

]

(1.6)

and the vector ν ∈ IR6 as

ν =

[

ν1

ν2

]

, (1.7)

and by defining the matrix Je(RIB) ∈ IR6×6

Je(RIB) =

[

RBI O3×3

O3×3 Jk,o

]

, (1.8)

where the rotation matrix RBI given in (1.5) and Jk,o is

given in (1.3), it is

ν = Je(RIB)η. (1.9)

The inverse mapping, given the block-diagonal structureof Je, is given by:

η = J−1e (RI

B)ν =

[

RIB O3×3

O3×3 J−1k,o

]

ν , (1.10)

where J−1k,o is given in (1.4).

Defining as

τ v =

[

τ 1

τ 2

]

.

the vector of generalized forces where

τ 1 =[

X Y Z]T

, (1.11)

the resultant forces acting on the rigid body expressedin a body-fixed frame, and

τ 2 =[

K M N]T

, (1.12)

the corresponding resultant moment to the pole Ob, it ispossible to rewrite the Newton-Euler equations of motionof a rigid body moving in the space. It is:

MRBν + CRB(ν)ν = τ v. (1.13)

The derivation of (1.13) can be found in (link to dynamicchapter?).

The matrix MRB is constant, symmetric and positivedefinite, i.e., MRB = O, MRB = MT

RB > O. Its uniqueparametrization is in the form:

MRB =

[

mI3 −mS(rbC)mS(rbC) IOb

]

, (1.14)

where rbC is the (3 × 1) distance vector to the Center ofGravity (CG) expressed in the body-fixed frame, I3 isthe (3× 3) identity matrix, and IOb

is the inertia tensorexpressed in the body-fixed frame (definition of S). Onthe other hand, it does not exist a unique parametriza-tion of the matrix CRB , representing the Coriolis andcentripetal terms. It can be demonstrated that the ma-trix CRB can always be parameterized such that it isskew-symmetrical, i.e.,

CRB(ν) = −CTRB(ν) ∀ν ∈ IR6 , (1.15)

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12 CHAPTER 1. UNDERWATER ROBOTICS

explicit expressions for CRB can be found, e.g., in [8].

Notice that (1.13) can be greatly simplified if the originof the body-fixed frame is chosen coincident with thecentral frame, i.e., rbC = 0.

Hydrodynamic generalized forces

Equation (1.13) represents the motion of a rigid body inan empty space, dealing with ships or underwater vehi-cles requires consideration of the presence of the hydro-dynamics generalized forces, i.e., the forces and momentscaused by the presence of the fluid. In hydrodynamicsit is common to assume that the hydrodynamics gener-alized forces on a rigid body can be linearly superim-posed [9]; in particular, those are separated in radiation-induced forces, environmental disturbances and restoringforces due to gravity and buoyancy.

The radiation-induced forces are defined as the forces

on the body when the body is forced to oscillate with

the wave excitation frequency and there are no incident

waves; those can be identified as the sum of the added

mass, due to the inertia of the surrounding fluid, and theradiation-induced potential damping , due to the energydissipated by generated surface waves.

The environmental disturbances can be identified inthe generalized forces caused by the wind, the waves andthe ocean current.

The overall equations of motions, thus, can be writtenin matrix form as [8, 10, 11]:

Mvν + Cv(ν)ν + Dv(ν)ν + gv(RIB) = τ v, (1.16)

where Mv = MRB +MA and Cv = CRB +CA includealso the added mass terms.

In the next subsections these generalized forces, spe-cific of the marine environment, will be briefly discussed.

Added mass and inertia

When a rigid body is moving in a fluid, the addi-tional inertia of the fluid surrounding the body, thatis accelerated by the movement of the body, has to beconsidered. This effect can be neglected in industrialrobotics since the density of the air is much lighter thanthe density of a moving mechanical system. In under-water applications, however, the density of the water,ρ ≈ 1000 kg/m

3, is comparable with the density of the

vehicles. In particular, at 0◦, the density of the fresh wa-ter is 1002.68 kg/m3; for sea water with 3.5% of salinityit is ρ = 1028.48 kg/m3.

The fluid surrounding the body is accelerated with thebody itself, a force is then necessary to achieve this accel-eration; the fluid exerts a reaction force which is equalin magnitude and opposite in direction. This reactionforce is the added mass contribution. The added massis not a quantity of fluid to add to the system such thatit has an increased mass. Different properties hold withrespect to the (6 × 6) inertia matrix of a rigid body dueto the fact that the added mass is function of the body’ssurface geometry.

The hydrodynamic force along xb due to the linearacceleration in the xb-direction is defined as:

XA := −Xuu where Xu :=∂X

∂u,

where the symbol ∂ denotes the partial derivative. Inthe same way it is possible to define all the remain-ing 35 elements that relate the 6 force/moment compo-nents [X Y Z K M N ]T to the 6 linear/angularacceleration [u v w p q r]T. These elements can

be grouped in the Added Mass matrix MA ∈ IR6×6.Usually, all the elements of the matrix are different fromzero.

In general, added mass and potential damping will befrequency-dependent and depend on forward speed. Thisis also the case for certain viscous damping terms (skinfriction, roll damping, etc.). This gives a pseudo dif-ferential equation describing the frequency response ofthe vehicle. Since some of the coefficients depend onthe frequency this is not an ODE (Ordinary Differen-tial Equation). The frequency equation, however, can betransformed to the time domain using the concepts de-scribed in [12] and [13] and recently in [14]. The resultingequation is an ODE where the added inertia matrix MA

is constant, speed independent and positive definite:

MA = MTA > O , MA = O . (1.17)

This result is well known from ship hydrodynamics;see [15] for instance. The matrix MA can be computedusing numerical programs such as WAMIT or Matlab,based on the U.S. Air Force Digital Datcom [16]; in thatcase, the infinity frequency result should be used, thatis MA = A(∞) where A(ω) is the frequency-dependentadded mass matrix. The potential damping matrix willbe small compared to the viscous effects and drag/liftterms. Hence, this term can be set to zero for underwa-ter vehicles. If added mass is computed experimentally,it is common practice to symmetrize the results such that

MA =1

2(Aexp + AT

exp)

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1.2. UNDERWATER ROBOTICS 13

where Aexp denotes the experimentally obtained addedmass terms.

If the body is completely submerged in the waterand it is designed with a port/starboard symmetry (xz-plane) as common for underwater vehicles in 6-Degrees-Of-Freedom (DOFs), the following structure of matri-ces MA can therefore be considered:

MA = −

Xu 0 Xw 0 Xq 00 Yv 0 Yp 0 YrZu 0 Zw 0 Zq 00 Kv 0 Kp 0 Kr

Mu 0 Mw 0 Mq 00 Nv 0 Np 0 Nr

. (1.18)

The added mass coefficients can be theoretically de-rived exploiting the geometry of the rigid body or nu-merically by strip theory [17].

In [18] the coefficients for the experimental AUVPhoenix of the Naval Postgraduate School (NPS) arereported. These coefficients have been experimentallyderived and the geometry gives a non diagonal MA

matrix. To give an order of magnitude of the addedmass terms, the vehicle has a mass of about 5000 kg, theterm Xu ≈ −500 kg.

The added mass has also an added Coriolis and cen-tripetal contribution. It can be demonstrated that thematrix expression can always be parameterized suchthat:

CA(ν) = −CTA(ν) ∀ν ∈ IR6;

whose symbolic expressions can be found, e.g., in [4].

Hydrodynamic damping

The hydrodynamic damping for marine vehicles is mainlycaused by:

- Potential damping;

- Skin friction;

- Wave drift damping;

- Vortex shedding damping;

- Viscous damping.

The radiation induced potential damping due to forcedbody oscillations is commonly known as potential damp-ing; its dynamic contribution is usually negligible withrespect to, e.g., the viscous friction for underwater vehi-cles while it may be significant for surface vessels.

Linear skin friction is due to laminar boundary layersand can affect the low frequency motion of the vehicle.Together with this effect, at high frequency it is possi-ble to observe a quadratic, or non-linear, skin frictionphenomenon caused by turbulent boundary layers.

The wave drift damping is the dominant dynamicdamping effect to surge motion of surface vessels in highsea. It can be considered as an added resistance for boatsadvancing in waves; its drift is proportional to the squareof the significant wave height. In the sway and yaw di-rections, however, its dynamic contribution is negligiblewith respect to the vortex shedding effect.

A body moving in a fluid causes a separation of theflow; this can still be considered as laminar in the up-stream while two antisymmetric vortices can be observedin the downstream. In case this body is a cylinder mov-ing in a direction normal to its axis, the result is a peri-odic force normal to both the velocity and the axis. Thiseffect may cause oscillation of cables and several under-water structures. However, concerning underwater vehi-cles, it is negligible for ROVs and may be counteracteddesigning proper small control surfaces for torpedo-likeAUVs.

Vortex shedding is an unsteady flow that takes place inspecial flow velocities (according to the size and shape ofthe cylinderical body). In this flow vortices are createdat the back of the body and periodically from both sidesof the body.

The viscosity of the fluid also causes the presence ofdissipative forces. Those are composed of drag forces andlift forces, the former are parallel to the relative velocityof the vehicle with respect to the water while the latterare normal to it. For a sphere moving in a fluid, the dragforce can be modeled as [9]:

Fdrag =1

2ρU2SCd(Rn), (1.19)

where ρ is the fluid density, U is the velocity of thesphere, S is the frontal area of the sphere, Cd is thenondimensional drag coefficient and Rn is the Reynoldsnumber. For a generic body, S is the projection of thefrontal area along the flow direction. The drag forcecan be considered as the sum of two physical effects:a frictional contribution of the surface whose normal isperpendicular to the flow velocity, and a pressure con-tribution of the surface whose normal is parallel to theflow velocity. For an hydrofoil moving in a fluid, the liftforce can be modeled as [9]:

Flift =1

2ρU2SCl(Rn, α), (1.20)

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14 CHAPTER 1. UNDERWATER ROBOTICS

where S is now the area, Cl is the nondimensional liftcoefficient and α is the angle of attack, i.e., the anglebetween the relative velocity and the tangent to the sur-face. For small angles of attack, i.e., |α| < 10 deg, thelift coefficient is approximatively proportional to α andrapidly decades to zeros as α increases [19].

The drag and lift coefficients are then dependent onthe Reynolds number, i.e., on the laminar/turbulent fluidmotion:

Rn =ρ|U |D

µ

where D is the characteristic dimension of the body per-pendicular to the direction of U and µ is the dynamicviscosity of the fluid. In Table 1.6 the drag coefficientsin function of the Reynolds number for a cylinder arereported [20].

A common simplification considers only linear andquadratic damping terms and group these terms in amatrix Dv as in Eq. (1.16) such that:

Dv(ν) > O ∀ν ∈ IR6.

Gravity and buoyancy

When a rigid body is completely or partially submergedin a fluid under the effect of the gravity two more forceshave to be considered: the gravitational force and thebuoyancy. The latter is the only hydrostatic effect, i.e.,it is not function of a relative movement between bodyand fluid.

Let us define as

gI =[

0 0 9.81]T

m/s2

the acceleration of gravity. This effect is not constant butvaries with the depth, longitude and latitude; however,this value is usually accurate enough for most applica-tions except for inertial navigation systems.

For a completely submerged body the computation ofthose dynamic effects is straightforward. The submergedweight of the body is defined as W = m‖gI‖ while itsbuoyancy B = ρ∇‖gI‖ where ∇ is the volume of thebody and m its mass. The gravity force, acting in thecenter of mass rBC is represented in body-fixed frame by:

fG(RBI ) = RB

I

00W

,

while the buoyancy force, acting in the center of buoy-

ancy rBB is represented in body-fixed frame by:

fB(RBI ) = −RB

I

00B

.

The (6 × 1) vector of force/moment due to gravity andbuoyancy in body-fixed frame, included in the left hand-side of the equations of motion, is represented by:

gv(RBI ) = −

[

fG(RBI ) + fB(RB

I )

rBG × fG(RBI ) + rBB × fB(RB

I )

]

.

In the following, the symbol rBG =[

xG yG zG]T

(withrBG = rBC) will be used for the center of gravity. Theexpression of gv in terms of Euler angles is representedby:

gv(η2) =

(W −B)sθ−(W −B)cθsφ−(W −B)cθcφ

−(yGW − yBB)cθcφ + (zGW − zBB)cθsφ(zGW − zBB)sθ + (xGW − xBB)cθcφ−(xGW − xBB)cθsφ − (yGW − yBB)sθ

,

(1.21)

Current

Ocean currents are mainly caused by tidal movement;the atmospheric wind system over the sea earth’s sur-face; the heat exchange at the sea surface; the salinitychanges and the Coriolis force due to the earth rota-tion; the nonlinear waves; the major ocean circulationsuch as the gulf stream; the effect of set-up phenomenaor storm surges or strong density gradient in the upperocean. Currents can be very different due to local cli-matic and/or geographic characteristics; as an example,in the fjords, the tidal effect can cause currents of upto 3 m/s, moreover, specific mathematical models existfor the various components [8].

Let us assume that the ocean current, expressed in theinertial frame, νIc is constant and irrotational, i.e.,

νIc =[

νc,x νc,y νc,z 0 0 0]T

and νIc = 0; its effects can be added to the dynamicof a rigid body moving in a fluid simply considering therelative velocity in body-fixed frame

νr = ν − RBI νIc (1.22)

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1.2. UNDERWATER ROBOTICS 15

in the derivation of the added Coriolis and centripetaland the damping terms:

Mvν+CRB(ν)ν+CA(νr)νr+Dv(νr)νr+gv(RIB) = τ v.

(1.23)Notice that the term CA(νr)νr includes the importantdestabilizing effect known as Munk moment [9].

If Dv(νr) is unknown, quadratic surge resistance andthe cross-flow drag principle can be used to describethe dissipative forces and moments in surge, sway, andyaw [9]. Moreover:

CA(νr)νr + Dv(νr)νr ≈[

Xc Yc 0 0 0 Nc]T

;(1.24)

for large relative current angles |βc −ψ|, where βc is thecurrent direction, the cross-flow principles models thesway force Yc and yaw moment Nc as:

Yc =ρ

2

L

H(x)CD(x)vxr (x) |vxr (x)|dx (1.25)

Nc =ρ

2

L

xH(x)CD(x)vxr (x) |vxr (x)| dx (1.26)

where L is the vehicle length, H(x) is the vehicle height,CD(x) is the 2-dimensional drag coefficient, vxr (x) =vr + rx is the relative cross-flow velocity at x. In prac-tise CD(x) can be chosen as a constant between 0 and 1.The proper value can be determined by curve fitting ofexperimental data. Along the surge direction, however,the quadratic damping contribution Xc still is well rep-resented by a term proportional to the square of the rel-ative velocity whose symbolic expression can be writtenas:

Xc = −Xu|u|ur |ur| (1.27)

where −Xu|u| > 0 is the quadratic surge damping co-efficient which can be found by curve fitting of experi-mental data or relating it to the drag coefficient Cd as ineq. (1.19).

Alternatively, the computation of the quadratic surgeresistance, nonlinear roll damping, and the cross-flowdrag effect can be made by resorting to the Datcomdatabase for aircraft as shown in [21].

Model properties

For completely submerged bodies in an ideal fluid movingat low velocity where there are no currents or waves,Eq. (1.16) satisfies the following properties:

• the inertia matrix is symmetric and positive definite,i.e.,

Mv = MTv > O;

• the damping matrix is positive definite, i.e.,

Dv(ν) > O;

• the matrix Cv(ν) is skew-symmetric, i.e.,

Cv(ν) = −CTv (ν),∀ν ∈ IR6.

Hydrodynamic modeling

The mathematical model of an underwater robot as ex-pressed in Eq. (1.16), is of great importance, even if sim-plified, in fact, it is capturing the most important part ofthe dynamics. Moreover, it is in a form appropriate forcontrol design. A wide literature exists on AUV/ROVcontrollers whose stability relies on the properties re-ported above. On the other side, there are working con-ditions in which the assumptions made are not valid any-more, i.e., when the AUV is travelling at high speed, orclose to the surface, or when its shape does not allowgeometric simplifications. The latter is the case of, e.g.,several ROVs. In addition, it is still common to designthe controllers for AUVs based on linearized models andto control ROVs with simple PID controllers.

These considerations justify a modeling effort to cal-culate the hydrodynamic terms more accurately with theaim of prediction, simulation, and performance anal-ysis rather than control design. This can be doneby switching from a coefficient-based approach, as theone presented above, to a component modeling method.The latter is based on the computational fluid dynam-ics theory. In detail, each geometry of the vehicle,with its specific angle of attack and sideslip, is takeninto consideration when computing the hydrodynamicforces/moments. This increased computational effortmade it possible to catch some dynamic effects, such asthe vortex-induced roll moment, not justifiable with thecoefficient-based approach.

The control plant model is usually a simplified modelcapturing the most important parts of the dynamics.The most accurate model of the vehicle should be usedfor prediction and simulation of motions.

1.2.2 Sensor systems

Underwater vehicles are equipped with a sensor sys-tem devoted to enabling motion control as well as ac-complish the specific mission for which the vehicle is

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16 CHAPTER 1. UNDERWATER ROBOTICS

commanded. In the latter case, sensors developed forchemical/biological measurements or mapping may beinstalled, the list of which is beyond the scope of thisChapter.

AUVs need to operate under water most of the time;one of the major problems with underwater robotics isin the localization task due to the absence of a single,proprioceptive sensor that measures the vehicle position.GPS cannot be used under the water. Redundant multi-sensor systems are commonly combined using state es-timation or sensor fusion techniques to give fault detec-tion and tolerance capability to the vehicle. Table 1.2lists sensors and the corresponding measured variablecommonly available for Unmanned Underwater Vehicles(UUVs).

A list of sensors that can be found on an underwatervehicle is as follows:

• Compass: a gyrocompass can provide an estimateof geodetic north accurate to a fraction of a degree.Magnetic compasses can provide estimates of mag-netic north with an accuracy < 1 degree if carefullycalibrated to compensate for magnetic disturbancesfrom the vehicle. Tables or models can be used toconvert from magnetic north to geodetic north.

• IMU (Inertial Measurement Unit). An IMU pro-vides information about the vehicles linear accelera-tion and angular velocity. These measurements arecombined to form estimates of the vehicles attitudeincluding an estimate of geodetic (true) north formost complex units. In most cases for slow-movingunderwater vehicles, an independent measurementof the vehicles velocity is also required to produceaccurate estimates of translational velocity or rela-tive displacement.

• Depth Sensor: measuring the water pressure givesthe vehicles depth. At depths beyond a few hundredmeters, the equation of state of seawater must beinvoked to produce an accurate depth estimate fromambient pressure [22]. With a high quality sensor,these estimates are reliable and accurate giving ansmall error whose order of magnitude is ≈ 0.01 %.

• Altitude and forward-looking sonar: they are usedto detect the presence of obstacles and the distancefrom the seafloor.

• DVL (Doppler Velocity Log): By processing re-flected acoustic energy from the seafloor and thewater column from three or more beams, estimates

of vehicle velocity relative to the seafloor and rela-tive water motion can be obtained. Bottom-trackvelocity estimates can be accurate ≈ 1 mm/s.

• GPS (Global Positioning System): it is used to lo-calize the vehicle while on the surface to initialize orreduce drift of estimates from an IMU/DVL combi-nation. GPS works only at the surface.

• Acoustic positioning: a variety of schemes exist fordetermining vehicle position using acoustics. Longbaseline navigation can determine the position of thevehicle relative to a set of acoustic beacons anchoredto the seafloor or on the surface through range es-timates obtained from acoustic travel times. Ultra-short baseline navigation uses phase information todetermine direction from a cluster of hydrophones,most often this is used to determine the direction ofthe vehicle (in two dimensions) from a surface sup-port vessel, which is then combined with an acous-tic travel-time measurement to produce an estimateof relative vehicle position in spherical coordinates.These techniques will be discussed later in the Lo-calization section.

• Vision systems: cameras can be used to obtain esti-mates of relative and in some cases absolute motionusing a type of SLAM algorithm [23] and used toperform tasks such as visual tracking of pipelines,station keeping, visual servoing or image mosaick-ing.

As an example, Table 1.3 reports some data of the in-strumentations of the ROV developed at the John Hop-kins University [24] and Table 1.4 some data of the AUVODIN III [25]. Reference [26] shows some data fusionresults with a redundant sensorial system mounted onthe AUV Oberon. Reference [27] reviews the advancesin navigation technology.

1.2.3 Actuating systems

Marine vehicle are generally propelled by means ofthrusters or hydrojets. In case of ROVs with a struc-tural pitch-roll stability, there are usually 4 thrustersthat give holonomic mobility to the 4 remained DOFs,in particular, the depth is often decoupled and the vehi-cle is controlled on a plane in the surge, sway and yawDOFs. Those vehicles, being under actuated, can not beeasily used for interaction control by means of a manip-ulator due to the impossibility to counteract the gener-alized forces exchanged with the manipulator’s base, in

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1.2. UNDERWATER ROBOTICS 17

such a case, 6 or more thrusters are required. AUVs gen-erally have a torpedo-like shape and are used for map-ping/exploration, those are propelled using one or twothrusters parallel to the fore-aft direction and a fin anda rudder; this kind of propulsion is obviously non holo-nomic and experiences a loss of mobility at low velocities.Hydrojets, also named pump jets or water jets, are sys-tems that create a jet of water for propulsion; they havecertain advantages with respect to the thrusters such asthe higher power density and usability in shallow water,but can provide thrust in one direction only.

Several efforts have been made to accurately and ef-ficiently describe the mathematical model of a thruster;[28] reports a one-state model where the state is n, thepropeller shaft speed. In [29] a two-state model is pro-posed to take into account the experimentally observedovershoot in the thrust; together with n, the additionalstate variable is up, the axial flow velocity in the pro-peller disc. In [30] a thruster model incorporating theeffects of rotational fluid velocity and inertia on thrusterresponses presented together with a method for experi-mentally determining non sinusoidal lift/drag curves. Athree-state model is described in [31]:

Jmn+Knn = τ −Q

mf up + df0up + df |up| (up − ua) = T

(m−Xu)u−Xuu−Xu|u|u |u| = (1 − t)T

where Jm is the moment of inertia for the dc-motor/propeller, Kn is the linear motor damping coef-ficient, τ is the motor control input, Q is the propellertorque, mf is the mass of water in the propeller controlvolume, up is the axial flow velocity in the propeller disc,df0 and df are the linear and quadratic damping coeffi-cients for control volume, respectively, ua is the ambientwater velocity, T is the propeller thrust, t is the thrustdeduction number; see Fig. 1.5. In case of steady statemotion, i.e., u = 0, the ambient water velocity ua isrelated to the surge by the wake fraction number w as:

ua = (1 − w)u, (1.28)

notice, also, that the unmeasured variable up can be es-timated using a non-linear observer [31].

The outputs of the non linear three-state dynamic sys-tems are the thrust T and the torque Q that are functionof several variables; in the following, the unsteady floweffects such as the air suction, the cavitation, the in-and-out-of-water (Wagner), the boundary layer and thegust (Kuessner) effects will be neglected. This leads to

a quasi-steady representation of the model:

T = ρD4KT (J0)n |n| (1.29)

Q = ρD5KQ(J0)n |n| (1.30)

where D is the propeller diameter and KT (J0), KQ(J0)are the thrust and torque coefficients. The latter arefunction of the advance ratio J0

J0 =ua

nD. (1.31)

The open water propeller efficiency in undisturbed wateris given as the ratio of the work done by the propeller inproducing a thrust force divided by the work required toovercome the shaft torque, according to

ηo =uaT

2πnQ=J0

2π·KT

KQ

. (1.32)

Figure 1.6 shows the values of KT , KQ and η0 as func-tion of the advance ratio for the Wageningen B4-70 pro-peller [1].

Controlling a marine vehicle usually requires that de-sired forces/moments act on the vehicle’s body; thesegeneralized forces are mapped into desired thrusts tobe provided by the propellers. There is, thus, a nontrivial control problem in that the motors are requiredto provide the appropriate propeller shaft speed n thatshows the non linear relationship presented above withthe thrust T .

To enable robustness with respect to possible failures,the actuating system is often redundant. In this case, aproblem of allocation of the desired force/moment act-ing on the vehicle among the thrusters is needed. Ref-erence [32] reports a survey for ships and underwatervehicles.

1.2.4 Mission Control System

The Mission Control System (MCS) can be considered asthe higher level process running during an AUV’s mis-sion; it is responsible for achieving several control ob-jectives. At the higher level it works as an interface be-tween the operator, accepting his instructions in a higherlevel language, and decomposes those instructions intomission tasks according to the implemented software ar-chitecture. The mission tasks are generally concurrent,their handling depends on the vehicle state and envi-ronmental conditions, it is the MCS, thus, that handlesthe tasks, eventually suppressing, sequencing, modifying,prioritizing them. Also, an MCS is usually equipped with

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18 CHAPTER 1. UNDERWATER ROBOTICS

a Graphical User Interface (GUI) to properly report themission state to the operator.

As for most of the advanced robotics applications, anefficient MCS should allow the use of complex roboticsystems from users that do not necessarily know all thetechnical details. While general concepts on this widetopic can be found in Chapter (link to proper chapter),concerning the underwater mission control an overviewis given in [33] that reports an interesting classificationon the MSC in use in several laboratories: four majorAUV control architectures were identified: the hierarchi-cal architecture, the heterarchical architecture, the sub-sumption architecture, and the hybrid architecture.

From a mathematical point of view, MCS generallyneeds to be designed in order to be able to face hy-brid dynamical systems, i.e., handling both event-drivenand time-driven processes. In [34], e.g., the MSC devel-oped at the Portuguese Instituto Superior Tecnico (IST),named CORAL, is implemented by resorting to a Petri-net-based architecture that properly handle all the nec-essary tasks in order to manage the navigation, the guid-ance and control, the sensing, the communications, etc.

MOOS (Motion Oriented Operating System), designedat Massachusetts Institute of Technology, is a softwaretool capable of executing and coordinating a multitudeof subsea operations. The MSC developed at the NavalPostgraduate School is in the framework of the behav-ioral control organized in three layers [35]; it is based onPROLOG, an artificial intelligence language for predi-cate logic.

1.2.5 Guidance and control

The terms guidance and control can be defined as [8]:

Guidance is the action of determining the course, atti-tude and speed of the vehicle, relative to some ref-erence frame (usually the earth), to be followed bythe vehicle.

Control is the development and application to a vehi-cle of appropriate forces and moments for operatingpoint control, tracking and stabilization. This in-volves designing the feedforward and feedback con-trol laws.

Figure 1.4 shows the corresponding block diagram wherethe navigation part is also outlined.

Guidance of underwater vehicles

Guidance algorithms may benefit from a wide range ofinputs, an overall mission information, a real-time oper-ator input, the environmental measured data such as theocean current, the environmental topological informationsuch as a bathymetric map, the exteroceptive sensors forobstacle avoidance and, obviously, the vehicle state asoutput from the navigation system.

The vehicle may be required to follow a path, i.e., acurve geometrically represented in 2D or 3D, or a trajec-tory, i.e., a path with a specific time-law assigned. More-over, when the desired position is constant, the problemis called set-point regulation or maneuvering. The guid-ance problem is commonly decomposed in simple sub-tasks of lower dimension: an attitude control problemand a path control; moreover, the attitude is usuallyconsidered as a simple depth set-point with null roll andpitch and the path is usually a line in the horizontalplane.

One of the most common guidance approaches is basedon the generations of way-points. Those are usuallystored in a data-base and are properly used to gener-ate the vehicle path/trajectory; a passing velocity, infact, may be defined together with the cartesian coor-dinates of the points. The simplest way to connect theway-points is to use the segments connecting two suc-cessive way-points. Efficient way-point-based guidanceapproaches need to take into account the presence of thecurrent and the eventual non-holonomicity of the vehi-cle [36]. A technique for adaptively tracking bathymetriccontours by proper generation of way-points is presentedin [37]; environment information are acquired by mean ofa single vertical sonar. An alternative method is basedon line-of-sight guidance [38, 39, 40]. In this case, theheading control is computed considering as input the an-gle formed by the vector from the vehicle to next way-point rather than requiring to the vehicle to exactly reachthe segment between the current and the following way-point. Specific care needs to be paid to the dock maneu-ver with algorithms designed on the scope [41].

By combining vision-based guidance with a neurocon-troller trained by reinforcement learning, in [42], an algo-rithm aimed at hold station on a reef or swim along a pipeis presented. In [43] the guidance for AUVs specificallyinvolved in pre-deployment survey of sea bottom and vi-sual inspection of pipelines is given. Reference [44] re-ports a specific guidance system aimed at mine avoidancefor AUVs. Based on a three-dimensional discretizationof the environment, the path planning technique consists

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1.2. UNDERWATER ROBOTICS 19

of computing a safe path avoiding the unsafe cells of themap. Due to the poor manoeuvrability at low speed,when some conditions occur, the vehicle has to make a360 turn to avoid stop and to map the environment closeto it and then generates a safe path.

A deep discussion on guidance for surface and under-water vehicles can be found in [8], [4].

Control of underwater vehicles

Control of underwater vehicles needs to consider the dif-ferent operating conditions and actuating configurationsin which a submerged vehicle is required to operate, inparticular, there are mainly 3 different control problems:

• An AUV traveling at high speed (> 1 m/s) generallyequipped with at least one thruster aligned in thefore-aft direction and at least two control surfaces(stern and rudder);

• An under actuated ROV, with a large metacentricstability, i.e., structurally stable in roll and pitch,and equipped with at least 4 thrusters;

• A fully actuated AUV equipped with at least 6trusters.

AUVs equipped with control surfaces are under actu-ated vehicles mainly use for survey/exploration missions.Inheriting the common practice of submarine control,they are not allowed to perform arbitrary motions in 6-DOFs but rather designed to perform specific movementssuch as: cruise along a given direction at constant depth;steer at constant depth; dive. The marine experience andthe mathematical insight, in fact, demonstrate that thesemovements are lightly coupled from the dynamic aspect.For these vehicles, moreover, specific manoeuvres suchas homing or docking requires special capabilities [41].This requires the design of vehicles structurally stable inthe roll DOF. The cruise motion requires control of thesurge velocity u(t), the steer motion requires control ofsway velocity v(t) and yaw DOF r(t), ψ(t), the dive mo-tion requires control of the heave DOF ω(t), z(t) and thepitch DOF q(t), θ(t). The simplest actuators’ configura-tion that can control an AUV along those movements iscomposed by one thruster aligned along the fore-aft di-rection, one stern and one rudder; the control variables,thus, are the propeller speed and the fins’ deflections.Several approaches can then be considered to solve thiscontrol problem, among them, in [45] the sliding modecontrol is proposed, [46] present an adaptive sliding modecontrol for the dive manoeuvre. Reference [18] reports a

successful implementation of multivariable sliding modecontrol on the NPS AUV II, lather implemented also onthe NPS ARIES AUV [47]. Being the model of an AUVtraveling at high speed nonlinear and coupled the tun-ing of the parameters is mainly based on the linearizedmodel around the working conditions.

From a descriptive point of view, an ROV is mainlya boxed-shaped underwater vehicle equipped with toolssuch as video camera or a robot manipulator, its payloadis often variable depending on the task. It is remotelyoperated and physically connected to another vehicle,either an underwater or a surface vessel. It is mainly de-signed to travel at low speed and it is structurally stablein roll and pitch; depth, surge, sway and yaw are inde-pendently controllable. Due to the absence of a specificshape, the varying payload and the relatively low re-quired performances, it is common to control a ROV bymeans of SISO (Single-Input-Single-Output) controllers.Moreover, often the PID approach is used due to its sim-plicity. A two layered guidance and control architecturefor the ROV Romeo is given in [48].

Control of a fully actuated AUV in 6 DOFs is neededin case of, e.g., an interaction task performed by a ma-nipulator mounted on a vehicle, the latter, in fact, needsto provide all the force/moment components in order todynamically counteract the presence of the manipulator.This problem is kinematically similar to the problem ofcontrolling a satellite in 6-DOFs, the underwater envi-ronment, however, makes it significatively different fromthe dynamic point of view. From the kinematic aspectthe main issue is in implementing a suitable policy forthe orientation control, any 3-parameters representationof the orientation, in fact, experiences representation sin-gularities (link to the appropriate chapter). This prob-lem may be overcome by resorting to redundant repre-sentation of the orientation such as the quaternion. Mostof the 6-DOF controllers proposed in the literature arebased on the Eq. (1.16), these equations, that model sim-plified effect of the hydrodynamic terms, show very simi-lar properties as the equations of motion of an industrialmanipulator. Based on this, it is obviously possible tofind a collection of approaches inherited from classicalrobotics, see, e.g., [8, 4] for some examples. In [49], somespecific considerations for the underwater environmentleads to a quaternion-based, adaptive controller; it isworth noticing that adaptive control requires a suitable,and simplified, expression for the hydrodynamic terms.In [50] a comparison among several 6-DOF controllers ismade.

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20 CHAPTER 1. UNDERWATER ROBOTICS

1.2.6 Localization

Localization in the underwater environment may be acomplex task mainly due to the absence of a single ex-ternal sensor that gives the vehicle position such as, e.g,the GPS for outdoor ground vehicles; moreover, the en-vironment is often poorly structured.

One of the most reliable methods is based on the useof acoustic systems such as the baseline systems: LBL(Long BaseLine system), SBL (Short BaseLine system)and USBL (UltraShort BaseLine system). These systemsare based on the presence of a transceiver mounted onthe vehicle and variable number of transponders locatedin known positions. The transceiver’s distance from eachtransponder can be measured via the echo’s delay; fromthese information its position can be known by basic tri-angulation operations. The USBL can be used with onesingle transponder that is usually mounted on a surfaceship whose position is measured by a GPS.

Another localization system is called Terrain AidedNavigation and it is based on the use of terrain elevationmaps; bathymetric maps are available specially in case ofwell known location such as harbors where they usuallyhave a resolution of ≈ 1 m. In this case, the vehicle po-sition is obtained filtering the information coming froma downward sonar. In [51], a particle filter approach isused to localize an AUV in the Sidney’s harbor.

Moving vehicles may be equipped with IMU or DVLin order to measure its velocity and/or acceleration. Thedata can be properly integrated to estimate the vehicleposition. This kind of information is subject to the driftphenomenon and may not be reliable for long durationrun or may become cost ineffective if accurate IMU de-vices are needed.

Relative localization can be obtained by resorting toany device that gives information about the relative po-sition of the vehicle with respect to the environment,even in absence of a map. In this case, filtering againthe distance measurements taken along the motion, thevehicle’s position can be measured. This is the case, e.g.,of sonar or vision-based localization techniques [52].

Often, the techniques presented above are used to-gether in a redundant system and the effective positionis obtained resorting to sensor fusion techniques such as,e.g., the Kalman filtering approach.

Simultaneous localization and mapping

Simultaneous Localization And Mapping (SLAM), alsoknown as Cuncurrent Mapping and Localization (CML),is a wide topic in mobile robotics. The problem can be

formulated as the requirement, for a mobile robot, tobe placed in an unknown environment and progressivelybuild a map while locating itself inside the map. Chap-ter (link to slam chapter) discusses in detail this topic.Concerning the marine environment an additional issuearise given by the large-scale map that needs to be usedfor long-duration missions; [53] implements a decoupledstochastic mapping to handle this computational prob-lem in an Extended Kalman Filter. Terrain-aided navi-gation with the use of a scanning sonar is implementedin [54]. [55] uses Long BaseLine range measurements asinput for a non linear least squares approach solved re-curring to the Gauss-Newton method; both the initiallyunknown position of the transponders and the vehicleposition are estimated. An interesting survey on naviga-tion and SLAM for underwater vehicles is given in [27].

1.2.7 Underwater manipulation

A manipulator may be mounted on a AUV or a ROV inorder to accomplish interaction operations. In this case,the vehicle needs to be fully actuated to counteract theforces and moment generated by the manipulator’s base.By considering a manipulator with n links, thus 6 DOFs,the UVMS (Underwater Vehicle Manipulator System) isa (6 + n)-DOF robotic system whose velocity vector is

ζ =[

νT1 νT

2 qT]T

(1.33)

where q ∈ IRn is the vector collecting the manipulatorjoints positions.

Repeating the same considerations done for an under-water vehicle, it is possible to write the equations of mo-tions of an UVMS in a matrix form:

M(q)ζ + C(q, ζ)ζ + D(q, ζ)ζ + g(q,RIB) = τ (1.34)

where M ∈ IR(6+n)×(6+n) is the inertia matrix includ-ing added mass terms, C(q, ζ)ζ ∈ IR6+n is the vectorof Coriolis and centripetal terms, D(q, ζ)ζ ∈ IR6+n isthe vector of dissipative effects, g(q,RB

I ) ∈ IR6+n is thevector of gravity and buoyancy effects. The relationshipbetween the generalized forces τ and the control inputis given by:

τ =

[

τ vτ q

]

=

[

Bv O6×n

On×6 In

]

u = Bu, (1.35)

where u ∈ IRpv+n is the vector of the control input.Notice that, while for the vehicle a generic number pv ≥ 6of control inputs is assumed, for the manipulator it issupposed that n joint motors are available.

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1.2. UNDERWATER ROBOTICS 21

Under hypothesis, that can be considered as reason-able at low velocity, it holds:

• The inertia matrix M of the system is symmetricand positive definite;

• For a suitable choice of the parametrization of C andif all the single bodies of the system are symmetric,M − 2C is skew-symmetric;

• The matrix D is positive definite.

In [20], it can be found the mathematical model writ-ten with respect to the Earth-fixed-frame-based vehicleposition and the manipulator end-effector. However, itmust be noted that, in that case, a 6-dimensional ma-nipulator is considered in order to have square Jacobianto work with; moreover, kinematic singularities need tobe avoided.

The equations of motion of UVMSs in matrix formpresented in (1.34) are formally close to the equationsof motion of ground fixed manipulators (link to dynamicchapter) for which a wide control literature exists. Thishas suggested a suitable translation/implementation ofexisting control algorithms. However, some differences,crucial from the control aspect, need to be underlined.UVMSs are complex systems characterized by severalstrong constraints:

• Uncertainty in the model knowledge, mainly due tothe poor knowledge of the hydrodynamic effects;

• Complexity of the mathematical model;

• Kinematic redundancy of the system;

• Difficulty to control the vehicle in hovering, mainlydue to the poor thrusters performance;

• Dynamic coupling between vehicle and manipulator;

• Low bandwidth of the sensor’s readings.

In 1996 T. McLain, S. Rock and S. Lee, in [56], presenta control law for UVMSs with some interesting experi-mental results conducted at the Monterey Bay Aquar-ium Research Institute (MBARI). A 1-link manipulatoris mounted on the vehicle OTTER controlled in all the6-DOFs by mean of 8 thrusters. A coordinated controlis then implemented to improve the tracking error of theend effector.

The monograph [50] is focused on the modeling andcontrol issues for such systems and that be considered as

a reference for further readings. Moreover, interactionwith the environment is also discussed.

Currently, remotely operated manipulator are a stan-dard equipment for several underwater ROVs, au-tonomous manipulation, however, still is a research chal-lenge. Figure 1.7 shows the vehicle SAUVIM, one of thefirst semi-autonomous underwater vehicle manipulatorsystems developed at the Autonomous Systems Labora-tory, University of Hawaii. A similar research project,ALIVE, were funded in the fifth Framework Program bythe European Community [3].

1.2.8 Fault detection/tolerance

Generally, AUVs must operate over long periods of timein unstructured environments in which an undetectedfailure could cause the loss of the vehicle. Failure de-tection and a fault-tolerant strategy are required to de-termine whether a mission must be terminated in thesafest manner possible or if the vehicle can continue in adiminished capacity. An example is the case of the arc-tic mission of Theseus [57]. In case of the use of ROVs,a skilled human operator is in charge of command thevehicle; a failure detection strategy is then of help inthe human decision making process. Based on the infor-mation detected, the operator can decide in the vehiclerescue or to terminate the mission by, e.g., turning off athruster.

Fault detection is the process of monitoring a systemin order to recognize the presence of a failure; fault iso-lation or diagnosis is the capability to determine whichspecific subsystem is subject to failure. Often in theliterature there is a certain overlap in the use of theseterms. Fault tolerance is the capability to complete themission also in case of failure of one or more subsystems,it is referred also as fault control, fault accommodationor control reconfiguration. In the following the termsfault detection/tolerance will be used.

The characteristics of a fault detection scheme are thecapability of isolate the detected failure; the sensitiv-ity, in terms of magnitude of the failure that can be de-tected and the robustness in the sense of the capabilityof working properly also in non-nominal conditions. Therequirements of a fault tolerant scheme are the reliabil-ity, the maintainability and survivability. The commonconcept is that, to overcome the loss of capability due toa failure, a kind of redundancy is required in the system(link to the appropriate chapter?).

In this section, a survey over existing fault detectionand fault tolerant schemes for underwater vehicles is pre-

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22 CHAPTER 1. UNDERWATER ROBOTICS

sented. For these specific systems, if proper strategies areapplied, a hardware/software (HW/SW) sensor failure oran HW/SW thruster failure can be successfully handled.In some conditions, it is required that the fault detectionscheme is also able to diagnose some external abnormalworking conditions such as a multi-path phenomena af-fecting the echo-sounder system. It is worth noticingthat, for autonomous systems such as AUVs, space sys-tems or aircraft, a fault tolerant strategy is necessary tosafely recover the damaged vehicle and, obviously, thereis no panic button in the sense that the choice of turn-ing off the power or activate some kind of brakes is notavailable.

Most of the fault detection schemes are model-based [58, 59] and concern the dynamic relationshipbetween actuators and vehicle behavior or the specificinput-output thruster dynamics. In general, the faultdetection/tolerance theory has been applied to the spe-cific case of the underwater environment even if only fewpapers concern the experimental results, see [60] for asurvey on that topic.

Concerning fault tolerant schemes, most of them con-sider a thruster redundant vehicle that, after a fault oc-curred in one of the thrusters, still is actuated in 6 DOFs.Based on this assumption a reallocation of the desiredforces on the vehicle over the working thrusters is per-formed [61]. Of interest is also the study of reconfigura-tion strategies if the vehicle becomes under-actuated.

Possible failures

The underwater vehicles are currently equipped with sev-eral sensors in order to provide information about theirlocalization and velocity. The problem is not easy. Nosingle, reliable sensor is available that gives the requiredposition/velocity measurement or information about theenvironment such as, e.g., the presence of obstacles. Forthis reason the use of sensor fusion by, e.g., a Kalman fil-tering approach, is a common technique to provide to thecontroller the required variables. This structural redun-dancy can be used to provide fault detection capabilitiesto the system.

For each of the sensors listed in sect. 1.2.2 the failurecan consist in an output zeroing if, e.g., there is an elec-trical trouble or in a loss of meaning. It can be consideredas sensor failure also an external disturbance such as amulti-path reading of the sonar that can be interpretedas a sensor fault and correspondingly detected.

Thruster blocking occurs when a solid body is betweenthe propeller blades. It can be checked by monitoring

the current required by the thruster. It has been ob-served, e.g., during the Antarctic mission of Romeo [62]:in that occurrence it was caused by a block of ice. Duringthe same mission also a thruster flooded with water hasbeen observed. The consequence has been an electricaldispersion causing an increasing blade rotation velocityand thus a thruster force higher then the desired one.

A possible consequence of different failures of thethrusters is the zeroing of the blade rotation. Thethruster in question, thus, simply stops working. Thishas been intentionally experienced during experimentswith, e.g., ODIN [61, 59], Roby 2 [58] and Romeo [62].

Other failures may be an hardware/software crash orthe occurrence of fin stuck or lost. A very common typeof failure involves loss of electrical isolation due to seawa-ter intrusion into underwater electrical cables or connec-tors. Such a condition can be detected through a tech-nique called ground-fault monitoring. Should this occur,electrical power must be removed from the effected de-vice.

1.2.9 Multi underwater vehicles

A growing research effort is recently devoted at develop-ing strategies to design coordinated control for underwa-ter vehicles. Use of multi-AUVs, in fact, might improvethe overall mission performance as well as give to the mis-sion a stronger tolerance to failures (link to multi-robotchapter)). Specific missions concerning the underwaterenvironment might consider the naval mine countermea-sure problem, the harbor monitoring and inspection, ex-ploration and mapping of large areas; the AUVs might becoordinated with one or more surface vessels, connectedto ground or aerial vehicles, to form a coordinated net-work of heterogeneous autonomous robots.

Beside several institutions that developed simulationpackages for multi-AUVs operations, use of real multi-AUVs is considered for the adaptive sampling and fore-casting plan under the Autonomous Ocean SamplingNetwork formed by several research institutions such as,concerning the robotic aspect, Caltech, MBARI, Prince-ton and WHOI [63]. Adaptive sampling is also deals within the Autonomous Systems and Controls Laboratoryof the Virginia tech that developed 5 AUVs [64]. TheAustralian National University is currently working onschool of small, autonomous robots, named Serafina [65].At IST, work is ongoing on the coordination between anAUV and a catamaran [66], i.e., a multi-robot systemconstituted by heterogeneous autonomous vehicles.

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1.3. APPLICATIONS 23

1.3 Applications

Underwater robots currently play prominent roles in anumber of scientific, commercial, and military tasks.Teleoperated remotely operated vehicles are very wellestablished in all these areas, and are becoming increas-ingly automated to relieve the burden on human op-erators and to improve performance. Increasingly, au-tonomous underwater vehicles are finding application inthese areas as well. Presently, AUVs are used almost ex-clusively for survey work, but the prospects for samplingand other intervention tasks are becoming more realistic.Additionally, the line between ROV and AUV continuesto blur, as systems evolve that have the best propertiesof both.

The offshore oil and gas industry relies heavily onROVs for installation, inspection, and service of plat-forms, pipelines, and subsea production facilities. Asthe reach for oil and gas goes deeper, this trend canonly continue. The Marine Technology Society estimatesthere are over 435 “work class” ROVs operating in thecommercial offshore industry today. AUVs are now be-ginning to appear in the commercial offshore industry forsurvey tasks, and concepts for hybrid systems that canperform intervention tasks are now appearing. The goalis not only for these robotic vehicles to replace humandivers or human occupied vehicles, but to enable an en-tire new generation of subsea equipment that is servicedwithout intervention by drill ships or other heavy-lift ves-sels. This holds the prospect for greatly reduced cost.

Scientific demand for ROVs and AUVs is also increas-ing dramatically. Scientific applications for ROVs in-clude survey, inspection, and sampling tasks previouslyperformed by human-occupied submersibles or towed ve-hicles. While ROVs operating for science are not nearlyas numerous as those in the offshore oil and gas indus-try, they are becoming commonplace. Most nations in-volved in global seafloor studies have several vehicles.Like the vehicles for the commercial offshore, these ve-hicles are becoming increasingly automated. High qual-ity electronic imaging, including High Definition Tele-vision, are increasingly common. Scientific ROVs arenow equipped with sophisticated sampling devices forsampling animals, microbes, caustic hydrothermal ventfluids, and a variety of rock samples. Moreover, ROVsare also used to deploy and operate seafloor experiments,which can involve difficult tasks such as drilling and del-icate emplacement of instruments.

ROVs have also emerged as powerful tools for investi-gating underwater shipwrecks and other cultural sites.

Applications include forensic investigations of modernshipwrecks to determine the cause of sinking, archae-ology, and salvage. For archaeology, the goals are thesame as for an excavation on land: detailed mapping fol-lowed by careful excavation. Beyond diver depths, ROVsare the preferred method for these investigations. Greatprogress has been made in the detailed mapping phase,and capabilities for excavation are evolving. Unfortu-nately, the same technology also opens the possibilityfor shipwrecks to be looted for financial gain, which usu-ally results in the loss of the most valuable historicalinformation.

After a long period of skepticism, AUVs are now ac-cepted for scientific tasks. Presently, AUVs performmapping tasks most often while tended by a vessel. Spe-cific mapping tasks include seafloor bathymetry, sidescansonar imaging, magnetic field mapping, hydrothermalvent localization, and photo surveys. AUVs have beenshown to improve productivity and data quality com-pared to towed and tethered systems. They have alsooperated in environments where no other means of gath-ering data is possible, such as under ice shelves. Likewise,the increasing availability of sophisticated in-situ chem-ical sensors, biological sensors, and mass spectrometersnow allow AUVs to build spatial and temporal maps ofenvironmental features that could previously be studiedonly by bringing samples back to the laboratory. Plansare now underway for AUVs that can dock to subseamoorings or observatory nodes to recharge batteries andto receive new instructions.

The military has always been a leader in the devel-opment of underwater robotic capabilities. They pio-neered ROVs for tasks such as recovering test weaponsand deep sea salvage, and present day commercial andscientific ROVs descended directly from these early sys-tems. Likewise, military interests are presently pushingAUV technology very hard. Many different countries op-erate AUVs for military surveys, gathering environmen-tal data as well as searching for hazards such as mines.An operational success was achieved in the surveying formines in the Persian Gulf harbor of Umm Qasr usingREMUS vehicles. AUVs in development will not only beable to detect mines, but to disable them. Bolder, moreinnovative concepts are also in development. These in-clude networks of AUVs that can act as extensions ofconventional surface vessels and submarines, enablingsurveillance over wide areas for extended periods of timeat costs far less than could be achieved with conventionalsurface vessels, submarines, and aircraft. These develop-ments will rely on improvements in acoustic communica-

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24 CHAPTER 1. UNDERWATER ROBOTICS

tions, energy systems, sensors, and on-board intelligencethat will likely find their way into commercial and scien-tific practice.

1.4 Perspectives

The underwater environment is extremely hostile for hu-man engineering activities. In addition to high pressuresand hydrodynamic forces that are both nonlinear andunpredictable, water is not an appropriate mean for elec-tromagnetic communication for all but short range. Thispushes underwater technology to rely on acoustic com-munication and positioning systems that are character-ized by low bandwidth. On the other hand, the ocean isextremely important for numerous human activities bothfrom the commercial, cultural and environmental pointof view.

The research on underwater robotic applications isactive both from the technological and the method-ological aspects. The power endurance of commer-cially AUVs currently lasts up to 50 hours; this willincrease as energy storage devices improve. Improvedenergy and power capability of the vehicle allows forlonger missions, higher speed or better/additional sen-sors such as, e.g., more powerful lighting for underwa-ter video/photography. The current trend for AUVs’prices is downward, the more and more research institu-tions of small size are building/buying AUVs enrichingthe research results, moreover the set-up of multi-AUVssystems is becoming cost-effective. The goal is to de-velop fully autonomous, reliable, robust, decision-makingAUVs.

There are a number of technology issues that areneeded in order to improve AUV capabilities: in-crease the underwater bandwidth of the current acous-tic modems; increase the onboard power to handle largertools and interact strongly with the environment; projectAUVs with significant hovering capability to allow betterinteraction; easier the launch/recovery phases.

In the near future, the ROV/AUV dichotomy willlikely diminish, with a variety of systems appearing thathave attributes of both systems:

• For offshore oil & gas intervention tasks, a vehiclecould transit to the work site as a self-powered, fullyautonomous vehicle, then dock to the work site. Uti-lizing energy and communications infrastructure atthe work site, the vehicle could then be operatedmuch like a conventional ROV.

• Battery operated ROVs can communicate to thesurface by very lightweight fiber optic links, enablingthe mobility of an AUV but with a high bandwidthconnection to skilled human operators for complexintervention or scientific sampling tasks.

• Acoustic and optical data links can provide moder-ate to high communications bandwidths over shortranges, enabling human supervision without anytether restrictions. At longer ranges, more modestacoustic bandwidths are available.

These developments make marine robotics a challengingengineering problem with very strong connections to sev-eral engineering domains. Sending an autonomous vehi-cle in an unknown and unstructured environment withlimited on-line communication requires some on boardintelligence and the ability of the vehicle to react in areliable way to unexpected situations [67, 68].

A major challenge concerning underwater robotics isthe interaction with the environment by means of one ormore manipulators. Autonomous UVMSs are still objectof research, the current trend is in developing the firstsemi-autonomous robotic devices that might be acousti-cally operated; moreover, if physically possible, the ca-pability to dock to the structure where the interventionis needed might significatively simplify the control. Thefinal aim might be to develop a completely autonomousUVMS, able to localize the intervention site, recognizethe task to be performed and act on it without docking tothe station and without human intervention. This mightmake it possible to perform missions currently impossi-ble such as an autonomous archaeological interventionin deep sites. The oil and gas industry might decreasesignificatively the costs and human risks by resorting tosuch robotic systems.

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Bibliography

[1] W.P.A. Van Lammeren, J. van Manen, M.W.C.Oosterveld: The Wageningen B-Screw Series,Transactions SNAME 77 (1969) 269 – 317

[2] J. Yuh, S.K. Choi, C. Ikehara, G.H. Kim, G. Mc-Murty, M. Ghasemi-Nejhad, N. Sarkar N., K. Sugi-hara: Design of a semi-autonomous underwater ve-hicle for intervention missions (SAUVIM), Proceed-ings 1998 International Symposium on UnderwaterTechnology 1998, 63–68 1998)

[3] P. Marty et al. ALIVE: An autonomous Light In-tervention Vehicle, Advances In Technology For Un-derwater Vehicles Conference, Oceanology Interna-tional 2004, 2004)

[4] T.I. Fossen: Marine Control Systems: Guidance,

Navigation and Control of Ships, Rigs and Under-

water Vehicles (Marine Cybernetics AS, 2002)

[5] S. Bennett: A Brief History of Automatic Control,IEEE Control Systems Magazine 16(3) (1996) 17 –25

[6] J. Yuh, M. West: Underwater Robotics, Journal ofAdvanced Robotics 15(5) (2001) 609 – 639

[7] The Society of Naval Architects SNAME, MarineEngineers: Nomenclature for Treating the Motionof a Submerged Body Through a Fluid, Technicaland Research Bulletin (1950) 1 – 5

[8] T.I. Fossen: Guidance and Control of Ocean Vehi-

cles (John Wiley & Sons, 1994)

[9] O.M. Faltinsen: Sea Loads on Ships and Offshore

Structures (Cambridge University Press, 1990)

[10] J. Yuh: Modeling and Control of UnderwaterRobotic Vehicles, IEEE Transactions on Systems,Man and Cybernetics 20 (1990) 1475 – 1483

[11] T.I. Fossen, A. Ross: Guidance and Control ofUnmanned Marine Vehicles. In: (IEE’s Control

Engineering Series, Peter Peregrinus Ltd. 2006)Chap. Nonlinear Modelling, Identification, and Con-trol of UUVs, pp. 23 – 42

[12] W.E. Cummins: The Impulse Response Functionand Ship Motions, Technical Report 1661, DavidTaylor Model Basin, Hydromechanics Laboratory,USA (1962)

[13] T.F. Ogilvie: Recent progress towards the under-standing and prediction of ship motions, 5 th Sym-posium Naval Hydrodynamics 1964, 1964) 3 – 79

[14] T. Perez, T.I. Fossen: Time-Domain Models of Ma-rine Surface Vessels for Simulation and Control De-sign Based on Seakeeping Computations, 7 th IFACConference on Manoeuvring and Control of MarineCraft 2006 (IFAC, Lisbon, P 2006)

[15] T.I. Fossen: A Nonlinear Unified State-Space Modelfor Ship Maneuvering and Control in a Seaway,Journal of Bifurcation and Chaos (2005)

[16] M. Nahon: Determination of undersea vehicle hy-drodynamic derivatives usingthe USAF Datcom,Proceedings Oceans Conference 1993, Victoria, BC1993) 283 – 288

[17] J.N. Newman: Marine Hydrodynamics (MIT Press,1977)

[18] A.J. Healey, D. Lienard: Multivariable SlidingMode Control for Autonomous Diving and Steeringof Unmanned Underwater Vehicles, IEEE Journalof Oceanic Engineering 18 (1993) 327 – 339

[19] B. Stevens, F. Lewis: Aircraft Control and Simula-

tions (John Wiley & Sons Ltd., 1992)

[20] I. Schjølberg, T.I. Fossen: Modelling and Controlof Underwater Vehicle-Manipulator Systems, 3 thIFAC Conference on Manoeuvring and Control ofMarine Craft 1994 (IFAC, Southampton, UK 1994)45 – 57

25

Page 26: Underwater Robotics - Thor I. Fossen · Underwater Robotics 1.1 The expanding role of marine robotics in oceanic engineer-ing The world’s oceans cover 2/3 of the earth’s surface

26 BIBLIOGRAPHY

[21] E.A. de Barros, A. PAscoal, E. de Sea: Progresstowards a method for predicting AUV derivatives,7 th IFAC Conference on Manoeuvring and Controlof Marine Craft 2006 (IFAC, Lisbon, P 2006)

[22] N.P. Fofonoff, R.C. Millard: Algorithms for compu-

tation of fundamental properties of seawater, No. 44edn. (UNESCO Technical papers in marine science,1983)

[23] R. Eustice, H. Singh, J.J. Leonard, M. Walter,R. Ballard: Visually navigating the RMS Ti-tanic with SLAM information filters, Proceedingsof Robotics: Science and Systems 2005, Cambridge,MA 2005)

[24] D.A. Smallwood, L.L. Whitcomb: Adaptive Iden-tification of Dynamically Positioned UnderwaterRobotic Vehicles, IEEE Transactions on ControlSystem Technology 11(4) (2003) 505 – 515

[25] S. Zhao, J. Yuh: Experimental Study on AdvancedUnderwater Robot Control, IEEE Transactions onRobotics 21(4) (Aug. 2005) 695 – 703

[26] S. Majumder, S. Scheding, H.F. Durrant-Whyte:Multisensor data fusion for underwater navigation,Robotics and Autonomous Systems 35(2) (2001)97 – 108

[27] J.C. Kinsey, R.M. Eustice, L.L. Whitcomb: A sur-vey of underwater vehicle navigation: recent ad-vances and new challenges, 7 th IFAC Conferenceon Manoeuvring and Control of Marine Craft 2006(IFAC, Lisbon, P 2006)

[28] D.R. Yoerger, J.G. Cooke, J.J. Slotine: The Influ-ence of Thruster Dynamics on Underwater VehicleBehavior and their Incorporation into Control Sys-tem Design, IEEE Journal of Oceanic Engineering15 (1990) 167 – 178

[29] A.J. Healey, S.M. Rock, S. Cody, D. Miles, J.P.Brown: Toward an Improved Understanding ofThruster Dynamics for Underwater Vehicles, IEEEJournal of Oceanic Engineering 20(4) (1995) 354 –361

[30] L. Bachmayer, L.L. Whitcomb, M.A. Grosenbaugh:An Accurate Four-Quadrant Nonlinear DynamicalModel for Marine Trhusters: Theory and Experi-mental Validation, IEEE Journal of Oceanic Engi-neering 25 (2000) 146 – 159

[31] T.I. Fossen, M. Blanke: Nonlinear output feedbackcontrol of underwater vehicle propellersusing feed-back form estimated axial flow velocity, IEEE Jour-nal of Oceanic Engineering 25(2) (2000) 241 – 255

[32] T.I. Fossen, T.I. Johansen: A Survey of Control Al-location Methods for Ships and Underwater Vehi-cles, 14th IEEE Mediterriaen Conference on Controland Automation 2006, Ancona, I 2006) 1 – 6

[33] K.P. Valavanis, D. Gracanin, M. Matijasevic,R. Kolluru: Control Architecture for AutonomousUnderwater Vehicles, IEEE Control Systems (1997)48 – 64

[34] P. Oliveira, A. Pascoal, V. Silva, C. Silvestre: Mis-sion Control of the MARIUS AUV: System Design,Implementation, and Sea Trials, International Jour-nal of Systems Science 29(10) (1998) 1065 – 1080

[35] D. Brutzman, M. Burns, M. Campbell, D. Davis,T. Healey, M. Holden, B. Leonhardt, D. Marco,D. McClarin, B. McGhee: NPS Phoenix AUV soft-ware integration and in-water testing, AutonomousUnderwater Vehicle Technology, 1996. AUV’96.,Proceedings of the 1996 Symposium on (1996) 99 –108

[36] A.P. Aguiar, A.M. Pascoal: Dynamic positioningand way-point tracking of underactuated AUVs inthe presence of ocean currents, Proceedings 41stIEEE Conference on Decision and Control 2002, LasVegas, NE 2002) 2105 – 2110

[37] A.A. Bennett, J.J. Leonard: A behavior-based ap-proach to adaptive feature detection and followingwith autonomous underwater vehicles, IEEE Jour-nal of Oceanic Engineering 25(2) (2000) 213 – 226

[38] M. Breivik, T.I. Fossen: Principles of Guidance-Based Path Following in 2D and 3D, 44th IEEEConference on Decision and 8th Control and Euro-pean Control Conference 2001, Sevilla, E 2005)

[39] F.A. Papoulias: Bifurcation analysis of line of sightvehicle guidance using sliding modes, InternationalJournal of Bifurcation and Chaos 1(4) (1991) 849 –865

[40] R. Rysdyk: UAV path following for constant line-of-sight, Proceedings of the 2nd AIAA “UnmannedUnlimited” Systems, Technologies, and Operations- Aerospace 2003, San Diego, CA 2003)

Page 27: Underwater Robotics - Thor I. Fossen · Underwater Robotics 1.1 The expanding role of marine robotics in oceanic engineer-ing The world’s oceans cover 2/3 of the earth’s surface

BIBLIOGRAPHY 27

[41] M.D. Feezor, F.Y. Sorrel, P.R. Blankinship, J.G.Bellingham: Autonomous Underwater VehicleHoming/Docking via Electromagnetic Guidance,IEEE Journal of Oceanic Engineering 26(4) (2001)515 – 521

[42] D. Wettergreen, A. Zelinsky C. Gaskett: Au-tonomous guidance and control for an underwa-ter robotic vehicle, Proceedings of the InternationalConference on Field and Service Robotics 1999,Pittsburgh, USA 1999)

[43] G. Antonelli, S. Chiaverini, R. Finotello, R. Schi-avon: Real-Time path planning and obstacle avoid-ance for RAIS: an autonomous underwater vehicle,IEEE Journal of Oceanic Engineering 26(2) (2001)216 – 227

[44] J. C. Hyland, F. J. Taylor: Mine avoidance tech-niques for underwater vehicles, IEEE Journal ofOceanic Engineering 18 (1993) 340350

[45] D.R. Yoerger, J.J. Slotine: Robust TrajectoryControl of Underwater Vehicles, IEEE Journal ofOceanic Engineering 10 (1985) 462 – 470

[46] R. Cristi, F.A. Pappulias, A. Healey: Adaptive Slid-ing Mode Control of Autonomous Underwater Ve-hicles in the Dive Plane, IEEE Journal of OceanicEngineering 15(3) (1990) 152 – 160

[47] D.B. Marco, A.J. Healey: Command, Control andNavigation Experimental Results with the NPSARIES AUV, IEEE Journal of Oceanic Engineer-ing 26(4) (2001) 466 – 476

[48] M. Caccia, G. Veruggio: Guidance and Control ofa Reconfigurable Unmanned Underwater Vehicle,Control Engineering Practice 8(1) (2000) 21 – 37

[49] G. Antonelli, F. Caccavale, S. Chiaverini, G. Fusco:A novel adaptive control law for underwater vehi-cles, IEEE Transactions on Control Systems Tech-nology 11(2) (2003) 221 – 232

[50] G. Antonelli: Underwater robots. Motion and force

control of vehicle-manipulator systems, 2nd edn.(Springer Tracts in Advanced Robotics, Springer-Verlag, 2006)

[51] S.B. Williams: A Terrain Aided Tracking Algorithmfor Marine Systems, 4 th International Conferenceon Field and Service Robotics 2003 2003, 2003) 55 –60

[52] M. Dunbabin, P. Corke, G. Buskey: Low-costvision-based AUV guidance system for reef naviga-tion, Proceedings 2003 IEEE International Confer-ence on Robotics and Automation 2004, New Or-leans, LA 2004) 7 – 12

[53] J.J. Leonard, H.J.S. Feder: Decoupled stochas-tic mapping, IEEE Journal of Oceanic Engineering26(4) (2001) 561 – 571

[54] S. Williams, G. Dissanayake, H. Durrant-Whyte:Towards terrain-aided navigation for underwaterrobotics, Advanced Robotics 15(5) (2001) 533 – 549

[55] P. Newman, J. Leonard: Pure range-only sub-seaSLAM, Proceedings 2003 IEEE International Con-ference on Robotics and Automation 2003, Taipei,TW 2003) 1921 – 1926

[56] T.W. McLain, S.M. Rock, M.J. Lee: Experi-ments in the Coordinated Control of an UnderwaterArm/Vehicle System, Autonomous Robots, J. Yuh,T. Ura, G.A. Bekey (Eds.), Kluwer Academic Pub-lishers (1996) 213 – 232

[57] J.S. Ferguson, A. Pope A, B. Butler, R. Verrall:Theseus AUV - Two Record Breaking Missions, SeaTechnology Magazine (1999) 65 – 70

[58] A. Alessandri, M. Caccia, G. Veruggio: Fault De-tection of Actuator Faults in Unmanned Underwa-ter Vehicles, Control Engineering Practice 7 (1999)357 – 368

[59] K.C. Yang, J. Yuh, S.K. Choi: Fault-Tolerant Sys-tem Design of an Autonomous Underwater Vehicle– ODIN: an experimental study, International Jour-nal of System Science 30(9) (1999) 1011 – 1019

[60] G. Antonelli: Fault diagnosis and tolerance formechatronic systems. Recent advances. In: (F. Cac-cavale, L. Villani, (Eds.), Springer Tracts in Ad-vanced Robotics, Springer-Verlag 2002) Chap. Asurvey of fault detection/tolerance strategies forAUVs and ROVs, pp. 109 – 127

[61] T.K. Podder, G. Antonelli, N. Sarkar: An Experi-mental Investigation into the Fault-Tolerant Controlof an Autonomous Underwater Vehicle, Journal ofAdvanced Robotics 15 (2001) 501 – 520

Page 28: Underwater Robotics - Thor I. Fossen · Underwater Robotics 1.1 The expanding role of marine robotics in oceanic engineer-ing The world’s oceans cover 2/3 of the earth’s surface

28 BIBLIOGRAPHY

[62] M. Caccia, R. Bono, Ga. Bruzzone, Gi. Bruzzone,E. Spirandelli, G. Veruggio: Experiences on Ac-tuator Fault Detection, Diagnosis and Accomoda-tion for ROVs, Proceedings International Sympo-sium Unmanned Untethered Submersible Technol-ogy 2001, Durham, New Hampshire 2001)

[63] E. Fiorelli, P. Bhatta, N.E. Leonard, I. Shulman:Adaptive Sampling Using Feedback Control of anAutonomous Underwater Glider Fleet, Proceed-ings International Symposium Unmanned Unteth-ered Submersible Technology 2003, Durham NH2003)

[64] C.J. Cannell, D.J. Stilwell: A comparison of twoapproaches for adaptive sampling of environmen-tal processes using autonomous underwater vehi-cles, Proceedings Oceans Conference 2005, Brest,F 2005) 1514 – 1521

[65] S. Kalantar, U. Zimmer: Distributed Shape Controlof Homogeneous Swarms of Autonomous Underwa-ter Vehicles, Autonomous Robots 22(1) (2006) 37 –53

[66] A. Pascoal, C. Silvestre, P. Oliveira: Vehicle andMission Control of Single and Multiple AutonomousMarine Robots, IEE Control Engineering Series 69

(2006) 353

[67] J. Yuh: Exploring the Mysterious UnderwaterWorld with Robots, 6 th IFAC Conference on Ma-noeuvring and Control of Marine Craft 2003 (IFAC,Girona, SP 2003)

[68] T. Ura: Steps to Intelligent AUVs, 6 th IFAC Con-ference on Manoeuvring and Control of MarineCraft 2003 (IFAC, Girona, SP 2003)

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BIBLIOGRAPHY 29

Table 1.1: ROVs for scientific use

Vehicle Depth Institution Manufacturer

Hyperdolphin 3000 JAMSTEC ISE

Dolphin 3K 3000 JAMSTEC JAMSTEC

Quest 4000 MARUM Shilling

Tiburon 4000 MBARI MBARI

ROPOS 5000 CSSF ISE

Victor 6000 IFREMER IFREMER

Jason 6500 WHOI WHOI

ISIS 6500 NOC WHOI

UROV 7K 7000 JAMSTEC JAMSTEC

Kaiko 11000 JAMSTEC JAMSTEC

Table 1.2: UUV possible instrumentation

sensor measured variable

Inertial System linear acceleration and angular velocity

Pressure-meter vehicle depth

Frontal sonar distance from obstacles

Vertical sonar distance from the bottom

Ground Speed sonar relative velocity vehicle/bottom

Current-meter relative velocity vehicle/current

Global Positioning System absolute position at the surface

Compass orientation

Acoustic baseline absolute position in known area

Vision systems relative position/velocity

Acoustic Doppler Current Profiler water current at several positions

Table 1.3: JHUROV instrumentations

measured variable sensor precision update rate

3DOF-vehicle position SHARP acoustic transponder 0.5 cm 10 Hz

depth Foxboro/ICT model n. 15 2.5 cm 20 Hz

heading Litton LN200 IMU Gyro 0.01 deg 20 Hz

roll and pitch KVH ADGC 0.1 deg 10 Hz

heading KVH ADGC 1 deg 10 Hz

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30 BIBLIOGRAPHY

Table 1.4: ODIN III sensors update

measured variable sensor update rate

xy vehicle position 8 sonars 3 Hz

depth pressure sensor 30 Hz

roll, pitch and yaw IMU 30 Hz

Table 1.5: Common notation for marine vehicle’s motion

forces andmoments ν1,ν2 η1,η2

motion in the x-direction surge X u x

motion in the y-direction sway Y v y

motion in the z-direction heave Z w z

rotation about the x-axis roll K p φ

rotation about the y-axis pitch M q θ

rotation about the z-axis yaw N r ψ

Table 1.6: Lift and Drag Coefficient for a cylinder

Reynolds number regime motion Cd Cl

Rn < 2 · 105 subcritical flow 1 3 ÷ 0.6

2 · 105 < Rn < 5 · 105 critical flow 1 ÷ 0.4 0.6

5 · 105 < Rn < 3 · 105 transcritical flow 0.4 0.6

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BIBLIOGRAPHY 31

Figure 1.1: The ROV Jason 2 (courtesy of Woods Hole Oceanographic Institute, http://www.whoi.edu)

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32 BIBLIOGRAPHY

Figure 1.2: The fully actuated AUV ODIN (courtesy of Autonomous Systems Laboratory, University of Hawaii,http://www.eng.hawaii.edu/∼asl/)

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BIBLIOGRAPHY 33

x

y

z

xb

yb

zb

η1

u (surge)

v (sway)

ω (heave)

φ (roll)

θ (pitch)

ψ (yaw)

Figure 1.3: Motion variables for an underwater vehicle (output in vectorial form, may be edited to harmonize fonts,available also in pdf)

way points

Guidance System

TrajectoryGenerator

Control System

AutopilotControlAllocation

ROV/AUV

disturbances

Navigation System

SensorsObserver

Figure 1.4: Guidance, navigation and control for an autonomous marine vehicle. (output in vectorial form, may beedited to harmonize fonts, available also in pdf)

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34 BIBLIOGRAPHY

ua

up

u

Figure 1.5: Ambient water and axial flow velocities affecting the thruster behavior. (output in vectorial form, maybe edited to harmonize fonts, available also in pdf)

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BIBLIOGRAPHY 35

−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

J0 [-]

KT,10

·KQ

,η0

[-]

Figure 1.6: Values of KT (solid), 10 ·KQ (dotted) and η0 (dash-dotted) in function of J0 [1]. (output in vectorialform, may be edited to harmonize fonts)

Figure 1.7: An underwater vehicle-manipulator system: SAUVIM (courtesy of Autonomous Systems Laboratory,University of Hawaii, http://www.eng.hawaii.edu/∼asl/)


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