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Research on Auv Model at Hanoi University of Science and Technology [7]


Applications of AUV:

Military: AUVs can be combined with sonar technology to detect unidentified objects to ensure the safety of a sea area, which is especially important in counter-sea warfare strategies.

Mining: The mining capabilities of AUVs are demonstrated in their ability to detect metal ore on the ocean floor, instead of having to search on ships with lower reliability. Not only that, AUVs can scan areas with a lot of seafood, allowing ships to fish with the highest efficiency.

Research: Exploring ocean floors, studying life deep under the seabed, geological cross-sections, water samples, and material samples will be sent ashore for analysis and processing.

Environment: Using advanced tools such as digital cameras, infrared cameras, ultrasonic waves... to monitor the impact of corrosion, blockages, cracks of marine structures. Following oil and gas pipelines to check for leaks, determine the durability of the pipeline, ensuring the fastest possible troubleshooting. If problems such as cracks or leaks occur, the AUVs equipped with robotic arms will perform cutting, welding, connecting functions... to prevent oil and gas from spreading into the sea causing pollution. According to statistics in [10], the types of AUVs and their functions and tasks can be listed as in Table 1.2.

Table 1. 2 Statistics of AUV autonomous vessels


Nation

Year

Device Name

Application


America


2000


C-series AUVs

Stability testing, environmental survey

FENRIR

UUV Transport



Sentry

Port survey and protection



2003

SWIMS

Mineral mine investigation



SeaFox

Combined Adaptability Test

locate, control, navigate




2004


Springer

Environmental survey, teaching experiment sample


Maybe you are interested!


2011

MUSCL

reconnaissance, military defense


Older brother

2000

Barracuda

Detect targets at sea

2008

Blackfish

Port Surveillance



thin here


C –Enduro USV

Solar energy applications for autonomous ships to monitor the marine environment



Canada


2000


HammerHead

Simulate the ability to avoid threats

2004

SESAMO

Environmental monitoring


2005

Charlie

Environmental monitoring


2007

ALANIS

Environmental monitoring


Recently

Kingfisher

Military service


Italy

2000

CARVELA

Mapping

2004

DELFIM

Communicate with UUV


2008

U-Rangger

Military service



Portugal

2006

Swordfish

Environmental monitoring


2008


Kaasboll

Check the navigation and control system


2008

Vikings

Check multiple items

destination


Israel

2007

Silver Marlin

Surveillance, reconnaissance

Virtue

2005

Basil

Offshore Pipeline Survey

France

2007

Inspector

Surveillance, reconnaissance

Singapore

2008

Tianxiang One

Meteorological survey

2010

Venus

Multiple applications



China


2010


USV-ZhengHe

Hydrological environmental data collection

Japan

2004

UMV series

Marine environmental survey

Source: Technology trend analysis report: "Research and application trends of autonomous underwater robots for environmental monitoring, river and lake surveys and search and rescue" - Ho Chi Minh City Department of Science and Technology

Ho Chi Minh 2019.

1.1.2 Applications of AUV in Vietnam

Along with the development of technology, autonomous underwater vehicles (Autonomous Underwater Vehicles - AUVs) are becoming increasingly popular. As an unmanned underwater vehicle that performs survey, research or military tasks with many outstanding advantages to replace humans, in Vietnam there have been studies and developments.


development. AUVs are currently present in many different applications, from military to civilian, from economic to scientific research [7], [10].

In Vietnam, AUVs have only been studied in recent years. The first AUVs were developed by robotics research groups with the sole purpose of building small models for theoretical research, with relatively simple structures, such as fish robots with biomimetic mobility, AUV models, and ROVs.


Figure 1.1 Research on AUV model at Hanoi University of Science and Technology [7]




Figure 1.2 KIAL – AUV of Ho Chi Minh City University of Technology in collaboration with Korea [10]


1.1.3 Mathematical model and general dynamic equation of AUV


AUV modeling is often based on mechanical design, dynamic and static principles. Statics here is concerned with the equilibrium of the AUV when there is no force applied or moving at a constant velocity. Kinematics solves the problem of acceleration of motion when there is a force from the propeller or an external force [4], [7], [8], [9], [10].

To build a mathematical model for AUV, we can consider AUV in space as a robot with 6 independent degrees of freedom (6 DOF), consider AUV as a rigid body, the rotation of the Earth does not affect the acceleration of the center of mass and the hydrodynamic coefficients are constant [21], [22], [26-28], [31].

When analyzing the motion of the ship in 6 DOF, for convenience, people introduce 2 coordinate systems with the center of the earth as reference as shown below. In addition, there are many other coordinate systems suitable for each research purpose.

Figure 1.3 ECEF coordinate system

Coordinate system referenced to the center of the Earth:

• The ECI (the Earth-centered Earth-fixed) coordinate system : {i} = (xi, yi, zi) is an inertial coordinate system used for ground-based navigation, in which Newton's laws of motion apply. Including systems


inertial orientation system. The origin {i} is located at the center Oi of the Earth as shown in Figure 1.3

• The ECEF coordinate system (the Earth-centered Earth-fixed) : {e} = (xe, ye, ze) has the center Oe located at the center of the Earth but the axes rotate relative to the ECI coordinate system (fixed in space) with an angular velocity of

𝜔 𝑒 = 7.2921 × 10 −5 rad/s. For devices moving at relatively low speeds, the effect of the Earth's rotation can be eliminated, so the system

{e} can be considered as an inertial system. However, when considering ship drift, the rotation of the Earth should not be ignored. The {e} coordinate system is often used for global navigation, navigation and control, for example to describe the motion and position of ships moving from one continent to another.

Geographic coordinate systems:

• The NED (the North-East-Down) coordinate system : This is the coordinate system that we always refer to in everyday life. {n} = (xn, yn, zn) with origin On defined relative to the reference ellipsoid of the Earth. It is usually defined as a tangent plane on the Earth's surface that moves with the AUV, but has axes pointing in different directions than the fixed axes of the AUV. For this coordinate system, the x-axis points to the North, the y-axis points to the East and the z-axis points down below the Earth's surface. The position of {n} relative to {e} is determined using two angles l and μ (longitude and latitude).

• The AUV's BODY coordinate system (the body-fixed reference frame):

{b}=(xb, yb, zb) with origin Ob being a moving coordinate system, but fixed relative to the AUV. The position and orientation of the AUV are described relative to the inertial coordinate system (approximated by {e} or {n} ) while the linear and angular velocity of the AUV should be described in the body-fixed coordinate system. The origin Ob is usually chosen to coincide with the midpoint of the AUV, called CO. For marine vehicles, the axes of the BODY system are chosen as shown in Figure 1.4:



Figure 1.4 Velocities u, v, w, p, q, r in the Body-fixed coordinate system .

- x b : longitudinal axis (from stern to bow)

- y b : horizontal axis (ship's side from left to right).

- z b : perpendicular axis (direction from top to bottom of ship).

Table 1.3 Conventional table of quantities



DOF


Move

Force and Moment

Linear velocity and angular velocity

Location and

Euler angle

1

Movement in the x-axis

(surge)

X

u

x

2

Movement in the y-axis

(sway)

Y

v

y

3

Movement in the z axis

(heaven)

Z

w

z

4

Roll, heel

K

p

𝜙

5

Rotate around the y axis (pitch,

trim)

M

q

𝜃

6

Rotate around the z axis (yaw)

N

r

𝜓

The general movements of the AUV in the 6 DOF coordinate system can be described as the following vectors:

𝜂 = [𝑝 𝑇 , Θ 𝑇 ] , 𝑝 = [𝑥, 𝑦, 𝑧] 𝑇 , Θ = [𝜙, 𝜃, 𝜓] 𝑇 ;

V = [𝑣 𝑇 , 𝜔 𝑇 ] , 𝑣 = [𝑢, v, 𝑤] 𝑇 , 𝜔 = [𝑝, 𝑞, 𝑟] 𝑇 ;


𝜏 = [𝑓 𝑇 , ɱ 𝑇 ] , 𝑓 = [𝑋, 𝑌, 𝑍] 𝑇 , ɱ = [𝐾, 𝑀, 𝑁] 𝑇 ;

In there:

𝜂 : position and orientation vector of AUV in coordinate system {n}.

𝑝 : position of coordinate system {b} relative to coordinate system {n}. Θ: rotation angle between coordinate system {b} and coordinate system {n}.

𝑉 : linear velocity vector and angular velocity of AUV ({b} relative to {n}) in coordinate system {b}.

𝑣 : linear velocity of AUV ({b} relative to {n}) in coordinate system {b}.

𝜔 : angular velocity of AUV ({b} relative to {n}) in coordinate system {b}.

𝜏 : force and moment acting on AUV in coordinate system {b}.

𝑓 : force acting on AUV in coordinate system {b}.

ɱ : moment acting on AUV in coordinate system {b}.

Conversion between BODY system and NED system:

The coordinate system {b} is oriented relative to the reference coordinate system.

{n} is equal to the three angles roll ( 𝜙 ), pitch ( 𝜃 ) and yaw ( 𝜓 ).

If the coordinate system {b} is rotated around the z, y, x axes of the coordinate system

{n} we have the following transformation matrices:


𝑐𝜃 0 −𝑠𝜃

𝑅 𝑥,𝜙 = [ 0 𝑐𝜙 𝑠𝜙] , 𝑅 𝑦,𝜃 = [ 0 1 0 ] , 0 −𝑠𝜙 𝑐𝜙 𝑠𝜃 0 𝑐𝜃

𝑐𝜓 𝑠𝜓 0

𝑅 𝑧,𝜓 = [−𝑠𝜓 𝑐𝜓 0]

0 0 1

1 0 0


(1.1)

𝑏

We combine the above 3 rotations to get the transformation matrix 𝑅 𝑛 :



𝑛 𝑧,𝜓 𝑦,𝜃 𝑥,𝜙

𝑏

𝑐𝜓𝑐𝜃 𝑐𝜓𝑠𝜃𝑠𝜙 − 𝑠𝜓𝑐𝜙 𝑐𝜓𝑠𝜃𝑐𝜙 + 𝑠𝜓𝑠𝜙

= [ 𝑠𝜓𝑐𝜃 𝑠𝜓𝑠𝜃𝑠𝜙 + 𝑐𝜓𝑐𝜙 𝑠𝜓𝑠𝜃𝑐𝜙 − 𝑐𝜓𝑠𝜙 ]

−𝑠𝜃 𝑐𝜃𝑠𝜙 𝑐𝜃𝑐𝜙

𝑅= 𝑅𝑅𝑅

(1.2)



Figure 1.5 Euler rotation angles.

We get the formula:


𝑛 𝑏

𝑏 𝑏/𝑛

𝑝̇ = 𝑅𝑣

(1.3)


According to document [5], we get the angular velocity conversion matrix from coordinate system {b} to coordinate system {n} as follows:

𝑛 ̇​

𝑏 𝑏

𝜔= 𝑇Θ

(1.4)

1 𝑠𝜙𝑡𝜃 𝑐𝜙𝑡𝜃

𝑇 𝑛 = [ 0 𝑐𝜙 −𝑠𝜙 ]

𝑏

0 𝑠𝜙/𝑐𝜃 𝑐𝜙/𝑐𝜃

(1.5)

𝑏

𝑏

It should be noted that the matrix 𝑇 𝑛 is undefined at pitch angle 𝜃 = ±90 0 . For a small amount of rotation angle 𝛿𝜙 , 𝛿𝜃 , 𝛿𝜓 the matrix 𝑇 𝑛 is simply written

simplified to:


𝑇 𝑛 = [ 0 1 −𝛿𝜙 ]

𝑏

0 𝛿𝜙 1

1 0 𝛿𝜃

(1.6)

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