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1 INTRODUCTION

Maritime transport recently has evolved into one of

the prospective industries for the application and

development of information technologies.

Conventional conservative foundations of the

industry manifested in long cycles of ship design and

operation and, as a result, expensive

telecommunication infrastructure based mainly on

satellite technologies at a time when transmission of

large volumes of information online has already

become the main criterion of commercial relations

efficiency. The world merchant fleet, seaports and

shipping companies, national and international

regulators, seafarers and personnel engaged in

international shipping and transportation had limited

information exchange.

For many centuries, the shipping industry has

relied on the knowledge and experience of seafarers

who were the crew of the ships. Today, however,

autonomous technology is ready to restructure the

maritime sector using unmanned craft, meaning ships

with no physical presence of crew. Small-unmanned

vessels have already begun to operate, while the

technology for larger vessels is still at the

developmental stage. The maritime industry is about

to change with the advent of the autonomous

navigation concept and it is necessary to assess how

this approach will shape the future of the industry

and how it can be used most effectively. Certainly, the

design and construction of autonomous ships will

have an impact on ship operating processes,

shipbuilding projects, port infrastructure operations,

interfaces, regulatory and legislative frameworks.

Autonomous Ships Concept and Mathematical Models

Application in their Steering Process Control

O. Melnyk, O. Onishchenko, S. Onyshchenko, A. Voloshyn, Y. Kalinichenko, O. Rossomakha,

G. Naleva & O. Rossomakha

Odesa National Maritime University, Odesa, Ukraine

ABSTRACT: Advances in computer systems and innovative technologies along with their implementation into

the shipping industry not only enabled efficient data exchange between the ship and the shore, but also created

a single integrated information network linking all participants of the process and all elements of the maritime

sector. Development of the concept of autonomous ships and automated control facilities for their functionality

became the next stage in the evolution of innovations. The process of software adaptation, additional electronic

steering systems, optical and digital means of monitoring as well as satellite communication facilities for

autonomous ships are among the tasks which require search and development of the solutions. Provision of

reliable and safe functioning of such ships in the autonomous mode requires development of models and

methods for ensuring their accident-free navigation both in relation to the process of ships divergence and

improvement of automatic steering systems of movement and course steadiness. In the given work, the analysis

of realization of the crewless navigation and possibility of ship automatic movement control systems

advancement on the basis of application of mathematical model for the purpose of enhancement of process of

the autonomous ship steadiness on the set course is proposed.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 16

Number 3

September 2022

DOI: 10.12716/1001.16.03.18

554

Automation will change the onshore elements of

shipping, starting with ship maintenance and cargo

handling and ending with ship insurance as well as

changes to a large number of international

conventions and codes.

Many works are devoted to the functioning of

onboard control systems of an autonomous vessel.

Thus operational stability under impulse course

control of a vessel considered in [5,6]. In [7, 27, 28, 29]

the study of using infrared as docking aid system for

boat, autonomous ship steering techniques and the

difficulties of their operation studied. Works devoted

to the concept of autonomous ship, issues of

autonomous maritime navigation, that is, the task of

finding the optimal and safe route of autonomous

ship in the absence of the crew and the task of

movement of autonomous ship on the constructed

route with preservation of seaworthiness and control

of deviation from the route in [8-13]. Autonomous

shipping and its impact on regulations, technologies,

and industries, new technology trends in the design of

autonomous ships. [1,2]. Safety management in

remotely controlled vessel operations in [14]. Papers

[16,20,22] devoted to identifying research directions of

a remotely-controlled merchant ship by revisiting her

system-theoretic safety control structure and

development the method to identify task-based

implementation paths for unmanned autonomous

ships. General safety issues for maritime transport

considered in [17,23,24,26]. The Impact of

Autonomous Ships on Safety at Sea studied in [25].

Work [15,22] researches implications of autonomous

shipping for maritime education and training.

Regulatory documents concerning autonomous ship

navigation presented in [3,4,21].

Thus, the analysis of the presented works causes

necessity of address to the given research problem

from the aspect of additional studying of problems of

autonomous navigation and searching for tools of

increase the efficiency of steering control of the given

ships by use of mathematical models improving

steerability of ships. It is necessary to note, that some

provisions stated here are of analytical character and

do not exclude possibility of the further investigation

of such actual subject of research.

2 MATERIALS AND METHODS

In recent years, there has been a growing interest in

the concept of Maritime Autonomous Surface Ships

(MASS) in the international maritime community. A

number of well-funded initiatives have been and

continue to be undertaken in several countries. The

Nordic countries, mainly Norway and Finland, are at

the forefront of this activity. The Asia-Pacific

countries, which are actively involved in the maritime

business, both in shipbuilding and in the operation

and chartering of fleets, are also showing considerable

interest. Increased interest from commercial

organizations is predicted in the mid- and long-term

perspective. According to BIS Research, a market

analysis firm, the estimated global revenue from the

emerging autonomous vessel market is expected to be

$3.48 billion by 2035. Much of this work is focused on

the types of shipping in which both commercial and

research organizations see the greatest promise.

According to experts, in the future the volume of

maritime trade will grow, respectively, the number of

ships needed to transport goods will grow, as well as

the number of seafarers needed to operate these ships.

At the same time, the global shipping industry is

already facing a shortage of qualified maritime

professionals. At the heart of this problem is the

growing unattractiveness of maritime professions,

especially for new generations, and to some extent it

is caused by the inherent problem of lack of full

communication, detachment from family, high degree

of isolation from social life, which accompanies work

on a seagoing vessel as well as all hardships and

difficulties of this profession, weather conditions,

specificity of time zones, etc. The growing trend in

recent years to reduce the speed of ships, based on

environmental standards and requirements and

economic considerations, is further increasing the

length of a ship's voyage, and consequently the time

that seafarers spend at sea.

Considering the above mentioned factors, the

unmanned offshore autonomous surface vessel is a

certain way out of the situation where, as mentioned

above, the prevalence of a growing shortage of

qualified personnel due to the unattractiveness of the

job and the expected growing demand for seafarers,

primarily due to the increasing volume of

international maritime trade. As a result, on the one

hand, it can reduce the expected pressure on the

seafarers' labor market, because it will allow, at least

partially, to reduce the labor intensity of ship

operation. On the other hand, routine tasks on board

will be automated, and only complex but interesting

navigational and technical work will be transferred

from the ship to a shore-based operations center,

making the "seafarer" job more attractive and at the

same time shore-based. In addition, economic and

environmental benefits are expected with the

introduction of unmanned shipping.

Many governments, realizing the importance of

developing and deploying high technology, are

increasingly investing in targeted technology

development for autonomous ships, with the goal of

taking a significant share of the global market for such

ships in the foreseeable future. Projects are being

developed to build ships that meet the "third degree"

of the four degrees of autonomy defined by the IMO

Maritime Safety Committee in its assessment of

regulatory requirements for MASS. For example,

degree three describes a ship that does not require

crew on board and is operated remotely, although

noting the fact that seafarers may be required on

board for regulatory purposes at an early stage of

development, which would be degree two autonomy.

Degree four is a fully autonomous and unmanned

vessel, capable of making its own decisions and

determining its own course of action shown in

Figure 1.

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Figure 1. Degrees of MASS autonomy defined by the IMO

Project teams are already being set up everywhere

to develop the core technologies needed for

autonomous ships and to lay the groundwork for

early commercialization of new systems by

demonstrating their capabilities in real-world

environments by the end of 2025. The goal of these

projects is to replace actions that currently involve

crew decision-making with autonomous systems that

integrate artificial intelligence (AI), Internet of Things

(IoT), Big Data and sensors. Experts’ estimate that

once these systems are in place, up to 22% reduction

in ship operating costs can be achieved through fuel

savings due to improved routing and maintenance

optimization. The goal of such projects is to focus on

development in four main areas: creating an

intelligent navigation system, creating automated

decision-making systems, promoting international

standardization of technology and conducting a test

program of medium-sized merchant ship models that

are capable of operating autonomously.

Among other advantages of crewless navigation

are increased safety of navigation and reduction of the

number of crew on board or improvement of the

existing traditional ship management system. The

crew receives timely information for decision-making

and support from qualified shore personnel; the

shipping company receives the opportunity to control

everything that happens on the vessel, optimize its

movement and promptly influence decisions; ship

owners, insurance companies, and maritime

administrations receive unprecedented transparency

and reliability of information on vessel movement and

condition.

In addition to increased safety and elimination of

human factor in ship control, introduction of remote

control is beneficial due to cheaper ship design,

increased tonnage and, above all, lower operational

costs for the crew. It is expected that the introduction

of MASS global use may take several decades: first

companies will use remotely piloted vessels with

reduced crew numbers, then fully autonomous

vessels will emerge. While companies are developing

new designs, testing models in test pools and field-

testing individual models in real-world environments,

some experts acknowledge that autonomous vessels

will not become widespread in the foreseeable future,

and their use will be very limited. It is difficult to

disagree with such a restrained assessment, because it

is based on the developers' awareness of a huge

number of difficulties, which the operation of

autonomous ships will inevitably face.

Worth to point out that use of autonomous

vehicles has already found its place in many land

modes of transport including passenger

transportation as an example of automated subways,

logistics self-propelled transporters or automated

guided vehicles in container terminals, there are also

very broad approaches to the concepts of autonomous

management of objects in modern aviation.

Consequently, autonomous control can also be seen as

an opportunity for the maritime transport industry to

address competitiveness, safety and sustainability

issues.

Modular control systems and communications

technology will enable wireless monitoring and

control functions both on and off the ship, so unlike a

remote ship, where control tasks are performed by a

remote control facility such as a human operator

ashore, an automated ship is equipped with advanced

decision support systems on board independently,

without the intervention of a human operator.

Figure 2. Monitoring functions and MASS decision support.

According to the experts involved in the MUNIN

project, which aims to combine both typical

alternatives into a coherent concept based on the

symbiosis of automated and remote ships, the

development of autonomous ships mainly relies on

automatic and fully deterministic ship control

functions. However, to detect problematic situations,

such as unexpected objects at sea, bad weather

conditions or dangerous close-quarter situations, risk

assessment of collision, different sensor systems will

be required to be equipped inside the ship hull. In the

event of unforeseen situations, the autonomous

control module will be activated, which will try to

make corrections and remedy the situation within the

given limits. If the onboard system is unable to

perform these functions, it will request support from a

remote operator or initiate a safe state transition

procedure in the event that the shore-based operator

is unavailable for some reason. If properly

implemented, this approach to MASS autonomy will

reduce the need for constant human supervision

while maintaining a high and well-defined level of

safety. The main challenge, however, will be to

establish sensor systems so that all relevant hazardous

situations can be reliably detected and appropriately

accounted for.

3 RESULTS AND DISCUSSION

Frequently the task of autonomous ship motion

control is reduced to the task of course stabilization.

The automatic course control system contains: course

controller, which can be either classical or intelligent

or adaptive. The system also includes a feedback

sensor (e.g. gyrocompass) and a control object - a

556

steering gear itself and a seagoing ship.) According to

IMO Resolution A.751(18), where necessity of use of

mathematical models of a vessel at the decision of

practical tasks of management lying in the field of

safety of navigation and increase of efficiency of ship

course steadiness on the set course is shown, we

consider application of the simplified mathematical

models of a vessel in comparison with model of an

autonomous vessel. Steadiness is the ability of a vessel

to maintain a set course or to maintain a set direction

of straight motion without deviating from it.

As well known the steadiness is an element of one

of the ship's basic seaworthiness - controllability.

Steadiness on set course also determines how long the

vessel will remain on the same course without having

to change the position of wheel by any steering

devices. Ship's course steadiness achieved by steering

gear is called operational steadiness. The number of

rudder flips per unit time required to maintain the

ship on course with a given accuracy. This value is

usually calculated by the equations of ship dynamics

controlled by proportional regulator in the absence of

perturbations. When an external disturbing force

tends to change a vessel's heading angle, an unguided

ship may be unsteady, therefore, when upon

termination of this disturbance, the ship does not

return to any straight course, but enters circulation, or

it becomes asymptotically unsteady, that is, when the

ship returns to a straight course with a new heading

angle. Thus, an unguided vessel is not steady on

course, since in both cases, manual steering and other

controls by the operator or automatic motion control

systems are required to return to the original course.

Steadiness on course is evaluated either from the

vessel's equations of motion, or from the results of a

test model or a full-scale vessel. In the first case,

course steadiness is determined by direct criteria

developed on the basis of the theory of system

steadiness, in the second case - by indirect indicators,

which are controllability diagram or yaw parameters

of the vessel (periods and amplitudes of angular

speed, course angle and angles of controlling

elements).

Many technical and research centers are

developing new steering systems for use on remotely

piloted and controlled autonomous vessels, which

will be used in navigation systems and ship motion

control systems to computerize the process of steering

an autonomous vessel. Such systems use an autopilot

to control a ship underway, which includes evasive

maneuvers in accordance with the International

Regulations for Preventing Collisions at Sea

(COLREG). The autopilot has three modes: tracking

mode, heading mode and joystick slow steering. In

"tracking mode", the system steers the ship along a

pre-agreed route. If the ship detects another vessel to

be avoided, the autopilot switches to "course mode"

which allows to perform the necessary maneuvers to

evade the other ship by changing the ship's course.

The autopilot returns to "course mode" after the other

ship is avoided. When the joystick function is

activated, the controls and propulsion equipment are

set to maneuver at low speed, allowing systems to be

operated with the joystick, for example, to maneuver

the vessel alongside a berth. The autopilot is

programmed to ensure that the vessel always remains

within the specified distance of the planned route. If

these limits are exceeded, the autopilot issues a

warning and remote control is cancelled.

The staging of full-scale experiments on

maneuvering of seagoing ships and processing of

their results are subordinated to the main task -

estimation of parameters of the selected ship model.

This is a complex task, especially considering that the

model itself is usually non-linear. Therefore when

solving this problem, there is an intention to simplify

the model without loss of behavioral features inherent

to a real object, which was proposed by Nomoto, who

proposed using the simplest ship controllability

model, containing only two parameters.

It should be noted, that a number of international

conferences on the use of experimental pools

recommended the use of simplified mathematical

models of the ship, built based on models developed

by Nomoto. Nonlinear Nomoto model of the second

order proved itself well enough in practice. This

model is described by a differential equation:

( ) ( )( ) ( )

( )

1· 2 2 / 2 1 2 /

· 3 /

T T d dt T T d dt H

K r KT d r dt

   



+ + + + =

(1)

where:

ω – ship angular velocity; H(ω) = ν1|ω|ω + ν2ω3 –

nonlinear function of angular velocity; Т1, Т2, Т3, К,

ν1, ν2 – time and design parameters identified by

maneuvering experiments; αr – rudder angle.

One of the solutions to the problem of

identification of the parameters Т1, Т2, Т3, К, ν1, ν2 of

equation (1) is presented in [29].

Analytical solution of (1) is quite difficult, but, in

general, when solving the problems of ship control, it

is not necessary. It is connected with the fact that in

control problems synthesis of controllers is performed

on the basis of not only performance criteria, but also

steadiness. That is why (1) makes sense to solve

numerically with subsequent representation as a

system of equations in Cauchy form. In this case, the

transition to the structural representation of (1), which

allows, for example, in Matlab/Simulink to synthesize

regulators, is straightforward. One of the structural

descriptions of (1) in Matlab/Simulink is shown in

Figure 3.

Figure 3. Structural description of proposed model

Block diagram of the ship's course stabilization

system is presented on Figure 4;

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Figure 4. Block diagram of the ship's course stabilization

system

A vessel with a displacement of 640 tons was

selected as a modeling object. In the steering system of

which a low-inertia electric rudder turning device is

installed. In this device, there is practically no

restriction on the rudder turning frequency, which

makes it possible to create highly efficient auto-

rudder systems. The maximum rudder angle is 35

degrees.

A given system's structure is characterized by a

transfer function that describes its properties. The

performed identification of the parameters of

expression (1) allows us to accept the following

parameters of transfer functions of the stabilization

system for modeling.

1. Steering gear;

( ) .

0,2 1

(2)

The structural model of the steering gear (Fig. 5)

takes into account the limitation of the output signal

±35°.

Figure 5. Structural model of steering gear

2. Ship;

At nominal operating conditions of the ship:

1,4 1

( ) .

41 14 [1 ( )]

NOM

s s H s

+ + +

(3)

The coefficients К, ν1, ν2, included in the

expression H(s), practically do not change depending

on the ship's loading status. Therefore, they are

assumed to be constant for any ship operating

conditions (К = 0,93, ν1 = -0,016, ν2 = 0,0014). Modeling

of the nonlinear transfer function WNOM(s) is based

on the structural diagram shown in Figure 3;

3. Negative feedback;

1,0

( ) .

0,1 1

(4)

4. Wind-wave disturbances;

Perturbations that deviate ship's course from the

set value can be described by the sum of three or four

sinusoidal signals of different amplitude, frequency

and phase.

5. PID – controller (Proportional-integral regulator);

To evaluate the properties of the ship's course

stabilization system, the PID parameters are assumed

constant for sufficiently large changes in the transfer

function WNOM(s). Synthesis of tuning parameters of

PID controller with output signal limitation at level

10 is performed for the above mentioned transfer

functions of ship, steering machine and feedback

sensor. The following requirements for PID controller

tuning are put forward: overshoot not more than 1.5

with minimum transient time. For these conditions

and WNOM(s), the transfer function of the PID

controller has the following tuning parameter values.

( ) / ,

W s P I s D

PID

= + +

(5)

Proportional component: P = 0,013, integral

component I = 0,0016 с-1, differential component: D

= 0,08 с, filtration factor: N = 0,9.

Thus, as a result of application of this model in

prototypes it was demonstrated an increase in

accuracy of course stabilization, which increases by

10-17% with rudder shifting frequency decreasing by

8-12% and fuel consumption decreasing (during

average statistical voyage and average statistical

wind-wave disturbances for the particular navigation

area) by 3-7%.

Considering the complexity of navigational

conditions, especially in confined waters, the speed of

decision-making by the crew on board can determine

the safety of the ship. Therefore, in spite of all

advantages, automation of ships has its

disadvantages. For instance, ships cannot be fully

autonomous, as installed equipment needs to be

supervised by specialists. For example, the

maintenance of video surveillance equipment

installed on the ship, which can not always reproduce

a clear image to the operator on shore, especially in

low visibility conditions or in case of communication

failure. In such a case, the presence of qualified

personnel on the ship is essential in order to notice the

danger and prevent its consequences. The analysis of

accidents shows that despite the rapid development

of science and technology in the maritime industry,

autonomous ships undoubtedly have to comply with

the international regulations necessary for the safe

operation of ships in different countries and even in

maritime areas beyond national jurisdiction. While

some aspects of manned vessel regulation may be

compatible with unmanned vessels, such as some

clauses of the International Safety Management Code

(ISM), specific international regulations need to be

developed to take into account the specifics of

unmanned vessels. It is necessary to create an

infrastructure for providing autonomous navigation

based on e-Navigation, to develop and implement

ship and shore-based autonomous navigation

equipment, as well as an autonomous port fleet, and

certainly to train specialists for the operation and

management of autonomous ships.

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4 CONCLUSION

As a basis, expected that crewless technology will

eliminate the human factor in ships divergence

process and allows the system to provide more

accurate and uninterrupted information about the

location of ships and their movement parameters,

including the course steadiness quality. However, it is

necessary to pay attention to the combination of such

factors as unemployment of not only seamen but also

of many educational institutions and training and

training centers because the crew will be replaced by

robotics. On the other hand, there will be a need for

highly qualified service personnel capable to maintain

and repair electronic automated control systems and

complexes, so there are tendencies for development in

this direction. However, overall, automation allows

simplifying ship control on the basis of ready-made

software solutions.

In the context of the MASS concept, it is not about

inventing a new entity, but transforming a set of

functions, which are now prescribed to the crew on

board in terms of navigation by international and

national regulators, and consistently, each of these

functions is performed in automatic and remote

mode. Due to the implementation of MASS, shipping

companies will be able to reduce 15-30% of operating

costs. It will also make it possible to cover the

shortage of highly qualified seafarers, which now

reaches 20% of the required workforce. Application of

ship mathematical models for solving practical

navigation tasks becomes more and more actual,

mainly due to the use of computer technologies in

ship navigation systems, as well as innovative

methods and technologies in ship navigation and

innovative methods and management of an

autonomous ship when performing key ship

operations under conditions of increased risks.

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