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03-01-2011, 06:42 PM


Submitted by
August 2010



A good dynamics model is essential and critical for the successful design
of navigation and control system of an underwater vehicle. However, it is
difficult to determine the hydro2dynamics forces, especially the added mass and
the drag coefficients. In this paper, a new experimental method has been used to
find the hydrodynamics forces for the ROV II, a remotely operated underwater
vehicle. The proposed method is based on the classical free decay test, but with
the spring oscillation replaced by a pendulum motion. The experiment results
determined from the free decay test of a scaled model compared well with the
simulation results obtained from well2established computational fluid dynamics
(CFD) program. Thus, the proposed approach can be used to find the added mass
and drag coefficients for other underwater vehicles.

Page No:
Introduction 1
Classification Of Underwater Vehicle 2
Basic Rov System Components 3
Hydrodynamic Damping 6
Various methods for calculatingthe hydrodynamic coefficients 9
Free Decay Pendulum Motion Test 10
Dynamics Equation 11
Conclusions 20
References 21

Autonomous underwater vehicles are currently being utilised for
scientific, commercial and military underwater applications. These vehicles
require autonomous guidance and control systems in order to perform
underwater tasks. Modelling, system identification and control of these vehicles
are still major active areas of research and development.
In the recent past, Unmanned Underwater Vehicles (UUVs) have been
used to explore the secrets of the oceans and to mine deep sea resources.
Generally, UUVs can be classified as Remotely Operated Vehicles (ROVs) and
Autonomous Underwater Vehicles (AUVs). Between the two, the ROV is the
main workhorse used in the industry. Compare to a human diver, an ROV can go
deeper and into riskier areas. Furthermore, it can carry out a vast variety of tasks
such as underwater inspections, scientific and environmental data acquisition,
construction, maintenance as well as repair of benthic stations. In essence, the
use of underwater robotic system will greatly benefit all kinds of ocean


When a body is moving through the water, the main forces acting in the
opposite direction to the motion of the body are hydrodynamic damping forces.
These damping forces are mainly due
Drag and lifting forces
Lineal skin friction
Damping forces have a significant effect on the dynamics of an
underwater vehicle which leads to nonlinearity. Lineal skin friction can be
considered negligible when compared to drag forces, and therefore, it is usually
sufficient to only take into account the latter when calculating damping forces.

Drag = [(Density of medium * Velocity2 * Coef. of Drag *
Cross sectional Area)] / 2
Added mass is a phenomenon that affects the underwater vehicle. When
a body moves under water , the immediate surrounding fluid is accelerated along
with the body. This affects the dynamics of the vehicle in such a way that the
force required to accelerate the water can be modeled as an added mass.


A wide variety of methods to identify the hydrodynamics parameters
have been proposed. Traditionally, the hydrodynamics coefficients are identified
through tow tank tests of the vehicle itself or of its scaled model. Special
equipment called planar motion mechanism (PMM) is built above the tow tank
to move the vehicle in a planar motion. Subsequently, the hydrodynamics
coefficients are obtained using system identification techniques. Since the
measured forces and moments are available in six degree of freedoms (DOF),
the tow tank test allows complete model identification. However, building the
tow tank that equipped a PMM is very costly. In addition, the test procedures are
highly time2consuming.
More recently, the use of on2board sensor2based identification has become
popular. This technique is preferable because it makes use of onboard sensors
and thrusters in the process of identification. No other equipment is needed. The
technique is cost effective and the repeatability is high. It is very suitable for
variable configuration ROV where payload and shape of ROV may change
according to different missions. However, most of the works simplify the model
to an uncoupled one DOF model, which needs the motion of the ROV to be
constrained to a single DOF during identification. This is hard to implement in
practice. In addition, it is also hard to model the thruster forces and to measure
the vehicle’s responses accurately.
The use of free decay test in finding the hydrodynamics coefficients was
reported by Morrison in 1993. In his study, the hydrodynamics coefficients of
the ROV Hylas were determined successfully for the heave motion. The ROV
Hylas was allowed to oscillate in water by hanging it from an overhead crane by using three springs. The position of the Hylas was determined using Sonic High
Accuracy Ranging and Positioning System (SHARPS). Free decay test have also
been studied by Andrew [10] to identify a multiple2DOF model of an UUV. In
his proposed experiment, the underwater vehicle is attached to four springs. The
method was tested using a computer simulation and the results converge to true
values. The proposed free decay tests exhibit a few problems in practice. Firstly,
the vehicle’s positions are needed during identification and the main problem is
the ability to measure the vehicle states accurately. In Morrison this problem is
solved by employing an expensive underwater positioning system (SHARPS). In
Andrew, only computer simulation is done. Secondly, all the springs must
always be kept in tension during the oscillations. It is challenging for such
experiment configuration to constraint the ROV motion within the predefined
DOF. As a result, the mathematical model may not represent the motion
accurately and thus the identified results might be poor.

The hydrodynamics added mass and drag forces will be determined
experimentally using a scaled down model of the ROV. The scaled model is set
to scillatein water when it is displaced from its equilibrium position and due to
the hydrodynamics forces that resist the motion, the amplitude of the swing will
decay over time. The hydrodynamics parameters can then be extracted from the
time history of the motion. As the scaled model is allowed to oscillate freely in
the water tank, the experiment is classified as a free decay test. By applying the
laws of Similitude, the hydrodynamics parameters of the scaled model can be
scaled up to predict the corresponding values for the full scale vehicle. Then,
verification is performed by comparing the experimental values obtained with
that predicted by CFD for the full scale ROV.
The proposed method has few advantages. Firstly, the motion of the
pendulum is restricted in a plane and has only one DOF. The position of
pendulum is fully described by variable θ. The motion is appropriately
constrained and hence, the dynamics equation of motion could represent the
motion correctly. Therefore, the result will be more accurate. Secondly, the
variable θ can be measured easily using a potentiometer or an encoder. However,
in this experiment, the angle θ is obtained through visual sensing using a digital
camera. The method is very simple and reasonably accurate. As a whole, the
experimental setup is simple and is very low cost compared with the building
cost of a water tunnel facility with PMM equipment.

Various positions of ROV during Pendulum Motion Test, captured by underwater camera.
Dynamics Equation
Consider an object of interest attached at the end of the pendulum and
fully submerged in the water. The object moves in a circular path with radius r as
shown in Fig . In the earth2fixed frame, the object is rotating about the pivot
point. However, in the body2fixed frame, the object only moves in the surge
direction at any instance; the object has only velocity component in surge

M 2Mass of the scaled Model
ma2 Added Mass in single DOF
g 2Gravity term
B 2Buoyancy
θ 2Angle of rotation of the pendulum
r 2Length of the pendulum (radius)
KL 2Linear Damping Coefficient
KQ 2Quadratic Damping Coefficient
F2rod Tension Force from the rod
FH2 Hydrodynamics Force
v 2Tangential Velocity

By solving the equations 5, we get the values of the hydrodynamic
coefficients like ma, KL, KQ

A new free decay test has been proposed to identify the added mass and
drag coefficient of the ROV.
The test makes use of the pendulum swing motion to identify
coefficients in surge and heave directions.
Although the experiment setup is very simple and low cost, the result
obtained is reasonably reliable. The result can be used to predict the coefficients
for ROV.

Eng YH, Lau WS, Seet GGL and CS Chin (Engineering letters
16.03.2009)”Estimation of hydro dynamic coefficients of an ROV using free
decay pendulum motion”
“ROV Manual” Robert D Christ, Robert L Wenrli SR 2007
G. Bekey, R. Ambrose, V. Kumar, A. Sanderson, B. Wilcox, and Y.
Zheng, "International Assessment of Research and Development in
Robotics," World Technology Evaluation Center, Inc. 2006.
M. Caccia, G. Indiveri, and G. Veruggio, "Modeling and identification of
open2frame variable configuration unmanned underwater vehicles," IEEE
Journal of Oceanic Engineering, vol. 25, pp. 2272240, 2000.
A. Alessandri, R. Bono, M. Caccia, G. Indiveri, and G. Veruggio,
"Experiences on the modelling and identification of the heave motion
of an open2frame UUV," presented at Oceans Conference Record
(IEEE), Nice, Fr, 1998.
A. T. Morrison, III and D. R. Yoerger, "Determination of the
hydrodynamic parameters of an underwater vehicle during small scale,
nonuniform, 12dimensional translation," Victoria, BC, Canada, 1993.
G. Conte, S. M. Zanoli, D. Scaradozzi, and A. Conti, "Evaluation of
hydrodynamics parameters of a UUV. A preliminary study," presented at
International Symposium on Control, Communications and Signal Processing,
ISCCSP, Hammamet, 2004.
P. Egeskov, A. Bjerrum, A. Pascoal, C. Silvestre, C. Aage, and L. W.
Smitt, "Design, construction and hydrodynamic testing of the AUV MARIUS,"
Cambridge, MA, USA, 1994.
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