Proceedings VCM 2012 42 mô hình hóa và mô phỏng phương tiện ngầm vận hành từ xa

surge, sway and heave were calculated for each component and then added arithmetically to obtain the added mass for the complete ROV for the given direction.. Table 4 Geometrical paramet

Modelling and Simulation of a Remotely Operated Vehicle

Mô hình hóa và mô phỏng phương tiện ngầm vận hành từ xa

Hung Duc Nguyen, Sachith Malalagama and Dev Ranmuthugala

University of Tasmania / Australian Maritime College

e-Mails: nguyenhd@amc.edu.au

Abstract

This paper presents modelling of a newly-built remotely operated vehicle utilising theoretical and CFD simulation methods and the development of simulation programs to predict the behaviour of the ROV using LabVIEW In order to design and to implement precise control of a ROV during missions, mathematical models with hydrodynamic coefficients are required Hydrodynamic coefficients of the proposed mathematical model are determined by analytical and CFD simulation methods supplemented by experimental work A computer simulation is developed to verify the coefficients and mathematical model of the ROV under various manoeuvres

Tóm tắt:

Bài báo trình bày mô hình hóa thiết bị ngầm vận hành từ xa mới đuợc thiết kế bằng hai phương pháp lý thuyết và mô phỏng CFD và sự phát triển chương trình mô phỏng để ước ược động thái của thiết bị ngầm dùng LabVIEW Nhằm thiết kế và thực hiện điều khiển chỉnh xác một thiết bị ngầm vận hành từ xa trong khi làm nhiệm vụ thì cần có mô hình toán có đầy đủ hệ số thủy động học Các hệ số thủy động học của mô hình toán được xác định bằng phương pháp giải tích và mô phỏng CFD có phụ trợ bằng thực nghịệm Mô phỏng được thực hiện nhằm kiểm chứng các tham số và mô hình toán của thiết bị ngầm vận hành từ xa theo các điều động khác nhau

Nomenclature

Symbol Unit Meaning

u, v, w, p, q, r



ν η

n, e, d, , ,

   

η

G Vector of gravitational and

buoyancy forces and moments

xG, yG, zG m Coordinates of the centre of

gravity

li

(i=1,2,3)

Distance from each thruster

to centre of gravity

Abbreviation

CFD Computational Fluid Dynamics

DOF Degree of Freedom

ROV Remotely Operated Vehicle

AUV Autonomous Underwater Vehicle

HIL Hardware In the Loop

AMC Australian Maritime College

UTAS University of Tasmania

1 Introduction

When designing ROV/AUV platforms as in [11][12] for educational and research work, the physical and virtual/mathematical models play an important role enabling the designer to understand its dynamics and to develop its control system However the development of a specialist physical prototype of a ROV or AUV with off the shelf electronics is relatively expensive and in many cases prohibitive within undergraduate programmes The work in this paper incorporates the development of an inexpensive ROV using easily accessible materials

Although the vehicle in this paper is tethered, i.e

an ROV generally depends on a human operator for the guidance and control [22], it can also be untethered with pre-programmed mission control and both The ROV described in this paper was fabricated using PVC piping, submersible bilge pump motors connected to model scale propellers, fishing floats and accessories that are easily obtainable from the local hardware shops

The ROV was designed to carry out the following tasks [17][ 18]:

 observe and survey seabed conditions and

submersed objects and structures;

 observe marine farm facilities and equipment;

and

 perform basic underwater surveillance

operations

The work further develops the mathematical

models, control algorithms and computer

simulation to predict the dynamic behaviour of the

ROV Thus this paper describes the:

 newly-built low cost ROV;

 modelling of the ROV/AUV using theoretical

and CFD methods;

 calculation of the hydrodynamic coefficients of

the ROV;

 simulation of the ROV under various

manoeuvring scenarios;

 design and simulation of a trajectory tracking

control system to conduct underwater missions;

and

 conduct experimental work to determine the

hydrodynamic coefficients and validation of the

model

2 Description of AMC ROV-IV

AMC-ROV-IV was made of PVC pipes and joints,

aluminium frames, and two fishing floats as shown

in Fig 1 Three motors from submerged bilge

pumps connected to model scaled propellers were

used as thrusters for propulsion and vertical

motion All materials used were easily accessible

from a household hardware or marine supplier [18]

The main particulars of the ROV are given in

Table 1 The ROV has been tested for watertight

integrity to a depth of about 5 metres in the AMC

Survival Centre Swimming Pool and the

Circulating Water Channel

Fig 1 AMC ROV-IV

Table 1 Main particulars of AMC ROV-IV

Length overall [mm] 480 Width of frame [mm] 290 Horizontal distance

between centres of the two main thrusters [mm]

180

Overall width [mm] 400 Height without floats

[mm]

190

Height with floats [mm] 225 Weight in air [kg] 2.965 Volume [m3] 2.946 x 10-3

The ROV is equipped with the following sensors and actuators:

 actuators/thrusters: three bilge pump motors;

 three switch (relay) motor controllers;

 two forward lights; and

 instrumentation and control electronics

3 Reference Frames and Equations 3.1 Reference Frames

In the design of control systems for underwater vehicles, their kinematics and kinetics are

described using the reference frames given in Fig

2, which includes the Earth-centred reference

frames (the Earth-centred Earth-fixed frame xeyeze

and the Earth-centred inertial frame xiyizi), and the geographic reference frames (the North-East-Down coordinate system xnynzn and the body-fixed reference frame xbybzb) [3][4]

Fig 2 The ECEF frame x e y e z e is rotating with angular rate with respect to an ECI frame x i y i z i

fixed in space [3][4]

The two reference frames for the AMC ROV are

shown in Fig 3 NED is the earth-fixed reference

frame and XYZ is the body-fixed reference frame

The centre of gravity G is at the vertical central

thruster The arrangement of the three thrusters for

position control is shown in Fig 4 Two floats plus

a set of adjustable weights are used to adjust the

position of the centre of buoyancy and the

vehicle’s pitch

Fig 3 Reference frames for AMC ROV-IV

3.2 Kinematics

Referring to Fig 3, the 6-DOF kinematic

equations in the NED (north-east-down) reference

frame in the vector form are [3][4],

 





where

 

n

3 3



J η

with η  3  S 3and 3



ν 

Fig 4 Arrangement of thrsuters of AMC ROV-IV

(u i , i = 1 to 3, are the voltage inputs of thrusters)

The angle rotation matrix n  3 3

b





R Θ  is defined

in terms of the principal rotations as [3][4],

x,



   



  

z,



  

where s=sin(), c= cos().using the zyx-convention,

 

n

b : z, y, x ,

or

  n b

The inverse transformation satisfies,

 1  



The Euler angle attitude transformation matrix is:

 

0 s / c c / c



   

 

1





 

   

    

It should be noted that T Θ is undefined for a pitch angle of o

90

   and that  1  T 

2.3 Kinetics

The 6-DOF kinetic equations in the body-fixed reference frame in the vector form are therefore [3],

      0 wind wave

where

M = MRB+MA: system inertia matrix (including added mass)

 

C ν =CRB ν CA ν : Coriolis-centripetal matrix (including added mass)

 

D ν : damping matrix

 

g η : gravitational/buoyancy forces and moments vector

0

g : pre-trimming (ballast control) vector

τ: control input vector

wind

τ : wind-induced forces and moments vector

wave

τ : wave-induced forces and moments vector

G

u2

u1

u3

x

y

3.1 Mathematical Model with Environmental

Disturbances

In order to improve performance of the control

systems for underwater vehicles it is necessary to

consider the effects of external disturbances on the

vehicle, which include wind, waves and currents

According to Fossen [3], for control system design

it is common to assume the principle of

superposition when considering wind and wave

disturbances In general, the environmental forces

and moments will be highly nonlinear and both

additive and multiplicative to the dynamic

equations of motion An accurate description of

the environmental forces and moments is

important in vessel simulators and provides useful

information to the human operators

With effects of external disturbances Equation (8)

is rewritten as [3][4],

 

0

(9)

where wτwindτwave and νr  ν νc (where

6

c 

ν  is the velocity of the ocean current

expressed in the NED) Further information on

modelling environmental disturbances can be

found in [2][3]

The model without external forces and moments

[3], [4] and [10] is

       

3.2 Mathematical Models for ROV

In order to derive the differential equations

governing the kinematics and dynamics of the

vehicle of which inputs and outputs are shown Fig

5, it is assumed that:

 the origin of the body-fixed reference frame is

at the centre of gravity where the vertical

thruster is located;

 the vehicle is symmetric about the longitudinal

axis x;

 the body has an equivalent block shape; and

 the vehicle is neutrally buoyant and the mass

distribution of the vehicle is homogeneous

throughout the vehicle

Thus, the 6-DOF model in Equation (9) is applied

to the AMV ROV as follows [2][3][4][10]

Equations for kinematics:

 



Fig 5 Input and output variables of the AMC

ROV/AUV-IV

Equations for kinetics:

where x y z

 

 

 

 

  



 

 

 



 

η ;J η  as in equation (2);

u v w p q r

 

 

 

 

  

 

 

 

 

u v w

x p

z r







M













( )

0 Z w Y v 0 (I N )r (I M )q

Z w 0 X u (I N )r 0 (I K )p

Y v X u 0 (I M )q (I K )p 0

C ν

u u u

v v v

w w w

p p p

q q q

r r r

( )





D ν

B B

0 0 0 ( )

z B cos sin

z B sin 0

 

g η

;

kl kl kl

kl kl 0

B

;

and

1 2 3

u u u

 

 

  

 

 

The determination of all coefficients of (12) is discussed in the following sections

4 Parameter Identification

4.1 Theoretical Parameter Estimation

Translational added mass of the vehicle due to the

translational accelerations were determined by the

analytical method using the geometrical

parameters of the vehicle (see Table 1)

The added mass for each direction of translational

motion, i.e surge, sway and heave were calculated

for each component and then added arithmetically

to obtain the added mass for the complete ROV for

the given direction

Where the added masses for two dimensional

potential flows are not available, the projected area

of a particular component for the given direction

was obtained and using its principle dimensions

the added mass in the given direction was

calculated using the following formula [24][29]

ii

(a )(b )

4

M

3 (a b )





where Mii = translational added mass and ai, bi =

two principal dimensions of the projected area (bi

> ai)

The values of added mass in three directions are

given in Table 2

Table 2 Estimated added mass in three directions

Added mass Added mass [kg]

For estimation of added moments of inertia, it is

assumed that the added moment of inertia around

each axis of rotation is represented by half of the

moment of inertia around the particular axis as

given in Table 3

Table 3 Estimated added moments of inertia

Axis of

rotation

Moment of inertia (kgm2)

Added moment of inertia(kgm2)

X Ix = 0.067 Kp=0.0335

Y Iy = 0.091

q

M= 0.045

Z Iz = 0.05 Nr = 0.025

4.2 Experimental Parameter Estimation

The geometrical parameters measured are given in

Table 4 and the experimentally determined mass

and moments of inertia are given in Table 5

Table 4 Geometrical parameters of the ROV

Vertical distance between port and STBD thrusters to centre of gravity (l1)

0 [mm]

Longitudinal distance between vertical thrusters and centre of gravity (l2)

0 [mm]

Horizontal distance between Port and STBD thrusters to centre of gravity (l3)

180 [mm]

Table 5 Mass and inertia properties

Moment of inertia around x- axis (Ix)

0.067072131 kgm2

Moment of inertia around y-axis (Iy)

0.091018248 kgm2

Moment of inertia around z- axis (Iz)

0.050413326 kgm2

To determine the damping coefficients a series of experiments were carried out to measure the damping forces acting on the ROV in different orientations These experiments were conducted in

the AMC Circulating Water Channel shown in Fig

6

Fig 6 Schematic diagram of the CWC

In this project the forces acting on the umbilical were not considered Hence, the experiments were carried out only on the ROV (vehicle) as follows:

 The ROV was detached from the umbilical

 As the ROV is slightly positively buoyant, ballast weights were attached to the ROV to make it negatively buoyant

 Loops were attached to the neutral axis of the

ROV as shown in Fig 7

 A load cell was calibrated with known weights

 The ROV was then attached to the load cell

from the loops

 ROV was submerged in the circulating water

channel and the circulation of water was

initiated

 The calculated drag forces from the

experiments are plotted together with the

corresponding drag forces obtained from

computational fluid dynamics simulations

 The experimental results were

non-dimensionalised and then compared with the

CFD simulation results in order to validate the

obtained model

Fig 7 Attachment of loops to approximately to the

neutral axis

Fig 8 shows the experiment being carried out for

the surge direction Fig 9 shows the comparison

of the total drag force obtained by the experiments

for the surge orientation to that obtained by CFD

It can be seen from Fig 9 that the experimental

results and the CFD simulation results are

sufficiently similar

Fig 8 Drag test in the surge orientation

Fig 9 Drag force against flow velocity for surge

orientation

Fig 10 and Fig 11 show drag test and the graph

of drag force vs the flow velocity for sway orientation

Fig 10 Drag test in the sway orientation

Fig 11 Drag force against flow velocity for sway

orientation

Fig 12 and Fig 13 show the drag force in the

heave orientation and the respective graph of the drag force vs the flow velocity

Fig 12 Drag test in the heave orientation

Fig 13 Drag force against flow velocity for heave

orientation

4.3 Thruster Coefficient Identification

The thruster coefficient matrix and the thruster

input matrix were determined based on the

assumption that the characteristics of all three

thruster motors used in the ROV were identical

The experiment setup is shown in Fig 14 and Fig

15

Fig 14 Experiment setup for thruster coefficient

determination

Fig 15 Experiment setup in the laboratory

Fig 16 shows the graph of the thruster force vs the

supply voltage It is seen that from the graph no thrust is generated when the supply voltage is less than 2 V Hence, the value of thrust force coefficient, k was found as,

k = 0.373 N/V

Fig 16 Thruster force vs supply voltage

4.4 CFD Method

Simulations of the ROV using a CFD model were used to determine the linear and quadratic damping derivatives The results obtained from the CFD analysis were validated against the

experimental data The CFD was carried out using

the commercial software ANSYS-CFX

4.4.1 Geometry Creation

The 3D model used for the CFD was developed

using the AutoCAD and then imported into

ANSYS® Design Modeller in IGES 144 format

In Design Modeller the fluid domain required for

the simulation was created The complete

geometry is shown in Fig 17 and Fig 18

Fig 17 Flow domain plan front view

Fig 18 Flow domain plan side view

4.4.2 Mesh Generation

Meshing is the discretization of the fluid domain

volume into adjoining finite volumes Mesh

quality and distribution are critical to obtain accurate results from a CFD simulation

The entire fluid domain mesh was created with the

automatic method control, as shown in Fig 19

The mesh independence study was carried out by changing the curvature normal angle from 18o to 4.5o The rest of the settings were kept constant

4.4.3 Mesh Independence

A mesh independence study was done in order to establish the results obtained from the CFD simulations independent of the number of

elements in the mesh Fig 19 shows overall mesh

of the ROV The number of elements of the mess was changed by varying changing the curvature

normal angle as shown in Table 6

Fig 19 Overall mesh of the ROV

Table 6 Changed setting for mesh independence

study

(*) Quadratic damping derivative in the surge direction

The quadratic damping derivatives obtained with different mesh sizes for the surge direction are

plotted in Fig 20 [22] By considering the

accuracy compared to the experimental results as

in Section 4.2 and the time available time for simulations it could be concluded that the mesh generated with a 9o curvature normal angle is the most suitable to carry out the rest of simulations

Curvature normal angle

Number of Elements Xu u(*)

Fig 20 Quadratic damping coefficients Xu u

against the number of elements

4.4.4 Physics and Fluid Properties

When running the CFD simulations it was

necessary to set physical and fluid properties used

for translational and rotational motions These

properties are summarised in Tables 7 and 8

Table 7 Flow physics used for the CFD simulation

(translational)

Table 8 Flow physics used for the CFD simulation

(rotational)

4.4.5 Boundary Conditions

Boundary conditions for translational motion and

rotational motion are shown in Tables 9 and 10

Table 9 Boundary conditions (translational)

Table 10 Boundary conditions (rotational motion)

4.4.6 CFD Simulation Results

This section presents some of CFD simulation results for translational motion, rotational motion and hydrodynamic lift

4.4.6.1 Translational Motion

Translational motion includes surge, sway and

heave Table 11 and Fig 21 through to 23 show

main results from the CFD simulation by which coefficients were determined

Table 11 CFD simulation results (translational)

Fig 21 Drag force vs velocity (surge)

Fig 22 Drag force vs velocity (sway)

Fig 23 Friction drag force vs velocity (heave)

4.4.6.2 Rotational Motion

Rotational motion of the ROV includes roll, pitch and yaw The CFD simulation results are

summarised in Table 12 and Fig 23 through to 25

Table 12 CFD simulation results for rotational

motion

Fig 23 Torque vs angular velocity (roll)

Fig 24 Torque vs angular velocity (pitch)