An Interactive Virtual Simulator for Motion Analysis of

Underwater Gliders

Alan López-Segovia, Luis García-Valdovinos, Tomás Salgado-Jiménez, Isabel Andrade-Bustos,

Luciano Nava-Balanzar, José Luis Sánchez-Gaytán and Juan Pablo Orozco-Muñiz

Energy, CIDESI, Av. Playa Pie de la Cuesta 702, 76125, Queretaro, Queretaro, Mexico

Keywords: Virtual Reality, Underwater Gliders, Modelling and Control, Haptic Interfaces.

Abstract: Autonomous Underwater Gliders (AUG) have become a very useful and cheap tool to sample the ocean’s

environment compared with oceanographic ships to perform the same task. AUGs can glide along the ocean

up to a specific depth thanks to their aerodynamic shape, wings and rudders, and a buoyancy-driven system

composed of a bladder and an eccentric movable mass that modifies the net buoyancy and the pitch/roll

angles of the vehicle, respectively. One of the main concerns of glider’s pilots is to understand and/or

predict the behaviour of the glider when it is affected by ocean currents under the water. In this paper, an

interactive virtual simulator for motion analysis of underwater gliders is given. The simulator considers the

online solution of the full nonlinear hydrodynamics of a well-known glider. The virtual simulator is a tool

that will help technicians and pilots to increase their training process, to carry out performance analysis of

new control schemes and validation of new glider’s models before the physical construction.

1 INTRODUCTION

An Autonomous Underwater Glider (AUG) bases its

operation on its buoyancy change to move through

the ocean in saw tooth patterns, reaching a specific

depth target. The AUG missions can explore

thousands of kilometres in long time missions

(several months) because of its low power

consumption. It can have different kinds of sensors

to analyse several water columns in ocean’s

environment following a zigzag trajectory until a

specific depth is reached; this vehicle has become

more and more popular for oceanographic studies

due to its low cost in comparison to traditional

methods. However, the cost of a commercial AUG is

not negligible so a real glider mission is considered a

critical task, therefore, a glider’s pilot must have a

full knowledge of the physical glider behaviour

under different environmental conditions (e.g.

marine currents) and inherent mission conditions

(e.g. velocity changes due to glider attitude). This

paper addresses the design and development of an

interactive virtual simulator for the study of the

behaviour of an AUG. The aim of this interactive

virtual simulator is to make the learning process

faster and easier for pilots before a real mission

deployment, performance analysis of new control

schemes and validation of new glider’s models

before the physical construction.

An interactive virtual simulator is a system

where can be reproduced the behaviour of a physical

phenomenon in a computer created environment

under conditions nearly to reality, the user can

handle the phenomenon parameters while simulation

is running. Through a virtual simulator can be either

predicted or analysed the phenomenon behaviour

without a physical implementation, virtual simulator

results are nearly approximated to real phenomenon

behaviour results. An AUG’s virtual simulator

development implies three main tasks: i) validation

and analysis of a mathematical model able to

reproduce real glider behaviour, ii) validation and

analysis of a mathematical model able to reproduce

environmental conditions wherein the AUG will

interact with, and iii) design of a virtual environment

(scenario and AUG graphical design and

animations) to give a real visual sensation for users.

Graver and Leonard (Graver & Leonard, 2001),

using a Newtonian approach, proposed a

mathematical model which sat the foundations to

obtain and do a formal analysis of AUG dynamics,

until that moment, a lot of AUGs had been used in

several successful oceanographic missions but

López-Segovia, A., García-Valdovinos, L., Salgado-Jiménez, T., Andrade-Bustos, I., Nava-Balanzar, L., Sánchez-Gaytán, J. and Orozco-Muñiz, J.

An Interactive Virtual Simulator for Motion Analysis of Underwater Gliders.

DOI: 10.5220/0006476804810488

In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 2, pages 481-488

ISBN: Not Available

Copyright © 2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

481

neither a precise physical behaviour nor

mathematical properties had been comprehended

yet. Later, several research groups around the world

were dedicated to discover and understand physical

properties of that mathematical model (Bender,

Steinberg, Friedman, & Williams, 2008) (Ali

Hussain, Arshad, & Mohd-Mokhtar, 2011)

(Upadhyay, Singh, & Idichandy, 2015),

programming and computing the differential

equations system using a specific numerical method;

by their own, in (Wang, Singh, & Yi, 2013) a

Lagrangian approach has been used in order to

compute a mathematical model of the Slocum

Glider, a commercial AUG model. On the other

hand, the mathematical model presented in (Zhang,

Yu, & Zhang, 2013) captures general behaviour of

an AUG whose pitch and roll angles are generated

by an eccentric movable mass. Hydrodynamic

parameters are an important part of AUG

mathematical model that describe interaction

between vehicle and surrounding fluid and they

depend of fluid characteristics as well as vehicle

geometry. The hydrodynamic study of an AUG for

obtaining hydrodynamics parameters is a complex

task; currently there are a lot of commercial

computer software which can compute high

precision hydrodynamic parameters for complex

structures, under numerous simulated scenarios.

Using this techniques, there are several papers, like

(Zhang, Yu, & Zhang, 2013) (Seo, Jo, & Choi,

2008) (Seo & Williams, 2010) (Singh,

Bhattacharyya, & Idichandy, 2014), that employ a

CFD (Computational Fluid Dynamics) software to

estimate the coefficients and hydrodynamic forces of

an AUG.

In the literature are reported a number of AUG

simulators, most of them use the 2D mathematical

model presented in (Graver & Leonard, 2001), very

few use 3D mathematical model and none of them a

mathematical model implemented on a virtual

environment. A simulator presented in

(Phoemsapthawee, Le Boulluec, Laurens, & Deniset,

2013) represents an AUG with six degrees of

freedom. The objective of this work was the

hydrodynamic study of a vehicle to improve glider

designs and evaluate the control strategy

performance. The mathematical model used in this

work is based in Newton-Euler equations and

considers that mass centre is moved with respect to a

coordinate system fixed to the vehicle. Other work

about virtual simulator is presented in (Woithe &

Kremer, 2010), in this work a virtual simulator for

Slocum glider is presented. It’s not clear if the 3D

hydrodynamic model is used. In (Asakawa, Watari,

Nakamura, Hyakudome, & Kojima, 2013),

Tsukuyomi glider movements are observed

numerically, the depth effect produced in AUG’s

(water density change, AUG buoyancy, etc.) is

incorporated in the numerical simulation. This work

does not include interactive animations.

The discussion in this paper will procced as

follows: In section II the mathematical model used

for AUG behaviour and ocean environmental

reproduction is presented. Then, in section III

simulation testing and validation of mathematical

model is discussed. The AUG interactive virtual

simulator implementation is described in section IV.

Finally, conclusions are exposed in Section V.

2 MATHEMATICAL MODEL OF

AN UNDERWATER GLIDER

The mathematical model of an AUG used in the

interactive virtual simulator is proposed in (Zhang,

Yu, & Zhang, 2013); a well-known commercial

AUG model is incorporated in the interactive virtual

simulator. The model takes into account a moveable

eccentric mass for inducing a θ (pitch) angle and ϕ

(roll) angle.

2.1 Kinematics Model

Figure 1 shows the coordinates frame used for the

AUG mathematical model calculation: Inertial

frame, body frame and flow frame, established to

describe the motion of the AUG. The body frame

origin

is established at the Buoyancy

Center (CB) of the AUG. The axis matches with

longitudinal axis of the AUG. The axis points

downward, forming 90° with axis. The axis lie

on the wings plane and is the result of the right hand

rule. The inertial frame is described by

,

where represents the frame axis and they are

unitary vectors. At the body frame, translational

velocity and angular velocity of the AUG are

defined as

and

,

respectively. At inertial frame, AUG position and

orientation are described by

and

, respectively. Rotation matrix

maps

of the body frame to the rate of change of at

inertial frame as follows:

(1)

Rotation matrix

is defined as:

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

482

(2)

where

y .

The relationship between y

is given by:

(3)

Often is more useful and convenient to compute

and analyse at flow frame denoted by

in Figure 1. For flow frame definition,

first is necessary to define attack angle and

sideslip angle as follows:

(4)

(5)

The flow frame is defined with respect to body

frame as: First, the body frame is rotated by

angle around y axis, this yield that z axis is rotated to

a new position now called

axis. Later, the new

frame is rotated around

axis by angle. So,

both, axis is converted at

axis, and axis is

converted at

axis of flow frame.

2.2 Hydrodynamic Model

As mentioned above, the hydrodynamic model used

in the AUG’s interactive virtual simulator is

proposed in (Zhang, Yu, & Zhang, 2013), which can

reproduce the behaviour of any AUG’s.

Figure 2 shows mass distribution of an AUG:

static mass

, eccentric movable mass

, and net

buoyancy

which represents the difference

between total buoyancy () and AUG total mass

. The movable mass is modeled like

a half cylinder with eccentric offset

. Its mass

center is located at

along axis and it is rotated

by angle around axis. The vectors

and

denote mass center position of eccentric mass,

net buoyancy and static mass, respectively respect to

inertial frame. In turn, the vectors,

,

, and

express mass center position of eccentric mass, static

mass and net buoyancy respect to body frame,

respectively.

Figure 1: Coordinate frames.

The hydrodynamic equations that describe the AUG

behaviour are given by:

(6)

For more details refer to (Zhang, Yu, & Zhang,

2013).

2.3 Hydrodynamic Forces

In the flow frame, the hydrodynamic force

and hydrodynamic moment

are expressed as:

(7)

Figure 2: Mass distribution.

A rotation matrix

is defined as follows:

(8)

An Interactive Virtual Simulator for Motion Analysis of Underwater Gliders

483

maps the hydrodynamic force and

hydrodynamic moment from flow frame to body

frame as shown next:

(9)

2.4 Ocean Currents Model

In (Fossen, 2002) is described an ocean current

model widely accepted in underwater robotics.

Although the current model considers a laminar and

constant flow it is useful to analyse the

hydrodynamic behaviour of an AUG when this is

disrupted by a current with diverse directions and

intensities.

The ocean current model establishes that the

hydrodynamics can be expressed in terms of a

relative velocity as follows:

(10)

where

is the relative velocity between the

AUG velocity and the ocean current velocity

expressed in the body frame.

The ocean current components with respect to

inertial frame

can be related to

current intensity

defining two angles: attack angle

and sideslip angle

, which describe the

orientation respect to axis and axis, respectively,

as is shown in Figure 3.

The average ocean current velocity in terms of

attack angle and sideslip angle, expressed with

respect to the inertial frame is:

(11)

Figure 3: Flow frame.

To express the ocean current components from

inertial frame to body frame is necessary to use the

matrix

as follows:

(12)

The hydrodynamic model equations including

the ocean current effects now are described as:

(13)

where

. Now the mass, Coriolis-

centripetal and hydrodynamic force and moment

terms are only functions of acceleration and relative

velocity. For the hydrodynamic force and moment

described in (Graver J. , Thesis: Underwater Gliders:

Dynamics, control and design., 2005), the resultant

velocity in equation (6) is substituted by the next

resultant relative velocity:

(14)

3 MODEL VALIDATION

Once we have raised and analysed the AUG

hydrodynamic model, a validation of this becomes

necessary for its implementation in the AUG

interactive virtual simulator. The model validation is

made through a numerical simulation using the

mathematical software MATLAB/Simulink.

In a numerical simulation the results are shown

numerically through graphs for easy interpretation

and analysis. The variable values used for validation

model simulation are presented in Table I and Table

II.

Normally, an AUG does hundreds of cycles

during its mission, in one cycle the AUG sinks from

the ocean surface until a specific depth, then the

AUG rises from specific depth to ocean surface

again, that is one cycle end. For the model validation

the parameters for one cycle is summarized in Table

III and Table IV.

The eccentric mass is held at γ=0 (ϕ=0) at all time

to avoid inducing a turn in the AUG. Notice that the

Slocum glider induces a turn in the yaw angle by

means of an actuated rudder. Depending on the AUG

position the movable mass is moved to produce the

desired pitch angle .

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

484

Table 1: Physical parameters of Slocum glider (Bardolet,

2012) (Teledyne Webb Research, 2012).

Variable

Value

@

(water mass displaced by the

vehicle @

)

(rudder area)

Table 2: Hydrodinamic parameters of slocum glider

(BARDOLET, 2012).

Variable

Value

,

(rudder angle of rotation)

Table 3: Sinking trajectory conditions.

0 – 50 s

50 – 150 s

150 – 250 s

Table 4: Rising trajectory conditions.

250 – 350 s

350 – 450 s

450 – 550 s

550 – 600 s

Table 5: Ocean current parameters.

0.12 m/s

180°

0°

Figures 4 and 5 depict the behaviour of the Slocum

glider with and without ocean currents. Evidently,

when ocean current is present the glider is restricted

to move freely.

The hydrodynamic model raised shows a

coherent behaviour with reality and reported data in

literature. Numerically, as is shown in Figure 4 to 5,

it presents good stability which is reflected with

moderate transition and low frequency signals. Thus,

the hydrodynamic model with and without current

effects is validated and available for its incorporation

in the AUG interactive virtual simulator.

Figure 4: Glider behavior during a cycle, wih and without

ocean current.

Figure 5: Trajectories followed by the glider with and

without ocean current.

Next, the main contribution of the paper is given.

4 GLIDER SIMULATOR

IMPLEMENTATION

The AUG interactive virtual simulator was created by

using a set of software tools such as Unity 3D,

Blender, Visual C++ and Matlab/Simulink. Figure 6

shows the combination of this Software tools.

An Interactive Virtual Simulator for Motion Analysis of Underwater Gliders

485

Figure 6: Software tools used for the development of the

interactive virtual simulator.

Unity 3D is one of the most popular and powerful

game engines used for the development of virtual

environments. Unity works as a platform that offers a

variety of tools to develop realistic scenarios along

with the capability to interface with scripts performed

in Visual C# and to import CAD models from

Blender.

The mathematical model along with the

parameters of each glider was added to the virtual

simulator using script files under C# language, inside

this script files was programmed the Heun numerical

integrator for the model resolution.

In Figure 7 a block diagram of the interactive

virtual simulator is displayed. The virtual simulator is

formed by a high performance PC and a haptic

interface (Falcon) which can be operated by the user

for controlling the AUG control. As shown above, in

the high performance computer the hydrodynamic

model is programmed which is solved online by the

Heun integrator. The model solution is processed by

the render module to recreate visually the AUG

motion in the virtual environment.

Figure 7: Block diagram of the interactive virtual

simulator.

The interactive virtual simulator allows the users

(pilots) to analyse the AUG motion in the 3D virtual

environment by manipulating the control variables

(bladder volume, moveable mass position and

moveable mass rotation), as shown in Figure 8.

Figure 8: The pilot can modify online the main variables

of the selected glider by means of a haptic interface, a

mouse or the keyboard.

The main screen displays three different types of

information and two types of controllable variables.

The types of information are: 3D visualization,

graphic visualization of variable values and

numerical visualization of AUG state variables. The

types of controllable variables are: AUG control

variables and ocean current velocity. Figure 9 and

Figure 10 depicts, respectively, the 4 different views

and the control variables and ocean current panels.

Figure 9: (a) Isometric view, (b) Superior view (Gulf of

Mexico map), (c) plane view, (d) plane view.

Figure 10: Control variables and ocean current control

panels.

Finally, it includes a button which allows choosing

between the AUG 3D models: Seaglider, Slocum,

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486

Seawing and soon the CIDESI’s glider. Any other

commercial or academic glider can be added to the

simulator provided the whole parameters are

available. When the AUG 3D model is chosen the

corresponding hydrodynamic model and parameters

are chosen too. Once a simulation is running is not

possible to change the AUG model until the button

“Restart” is pushed.

Each control panel is fitted with a button to

expand or collapse the information. While the

simulation is running the AUG creates navigation

marks, which stores historical data about AUG

trajectory, as can be seen in Figure 11.

Figure 11: Equidistant navigation marks (red balls) draw

the glider trajectory. A green ball is a particular point

selected by the pilot to know the glider’s state in the

inertial frame.

5 CONCLUSIONS

In this paper, preliminary results of an interactive

virtual simulator are presented. The simulator solves

online the full nonlinear hydrodynamics of

underwater gliders and the solution is fed to the

rendering module (virtual environment) to display

the motion in a realistic 3D scenario in order to

analyze the behavior. The simulator is provided with

different tools to analyze the motion and the

generated information. At this moment, the virtual

simulator is interactive; it means that the pilot can

modify online the three main control variables of an

underwater glider: volume of the bladder, position of

the moveable mass and the rotation angle of the

eccentric mass. In the case of the Slocum glider, an

actuated rudder has been considered into the

hydrodynamics instead of the eccentric mass.

Additionally, the simulator has a panel to arbitrarily

set the intensity and direction of the ocean current.

The simulator represents a useful tool for the

Oceanographic Monitoring Group with Gliders

(GMOG) pilots.

Future work is to implement the functionality of

“automatic mode” and add the map of the Gulf of

Mexico wherein the pilot will be able to indicate on

it the starting point and the subsequent way points

that the glider has to reach, with or without currents.

Not only the virtual environment and the graphic

user interface have to be modified but also it is

necessary to choose the correct control law.

ACKNOWLEDGMENT

This study is part of the project number 201441

“Implementation of oceanographic observation

networks (physical, geochemical, ecological) for

generating scenarios of possible contingencies related

to the exploration and production of hydrocarbons in

the deepwater Gulf of Mexico”, granted by SENER-

CONACyT Hydrocarbons Sectorial Fund.

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