Maritime Autonomous Surface Ships in Use with LMI and Overriding Trajectory Controller

Abstract

Concepts in maritime issues such as Maritime Autonomous Surface Ships (MASS) have been known for several years. At present, it is difficult to define clear rules for the cooperation of multiple systems for autonomous control, i.e., unmanned operation, which is written in the MASS requirements for the various degrees of control (four degrees). The paper proposes a multidimensional control of a ship on a certain determined trajectory, where a model of a training ship sails autonomously in restricted waters in a port. The control algorithm is based on the synthesis of a Linear Matrix Inequalities (LMI) controller and an overriding trajectory controller. The automation is divided into two parts. The master trajectory controller converts the ship’s position and course into small velocities, which, with the help of the LMI controller through an allocation system, control the operation of the ship’s propellers. The setpoints are specific twelve trajectory points given in the form of x, y coordinates and the ship’s course. The tests were carried out under real conditions and showed a silhouette of the ship performing the maneuver and a reading of the individual speeds, wind parameters and GPS mode. The solution presented is used to address MASS 3 level control.

1. Introduction

Today, the ship is one of the primary means of transportation. As reported in Baltic and International Maritime Council (BIMCO) [1], the need for 147,500 ship officers is projected to increase by 2025. At the same time, authors in [2] write that there is a shortage of nearly twenty thousand captains and officers on ships of virtually all types in shipping, and, in many countries, there is a shortage of pilots bringing ships in and out of port. Hence, it is worth considering the introduction of autonomous ships into service. This applies to vessels with different levels of autonomy, starting from the first level, such as Maritime Autonomous Surface Ships (MASS) 1, according to the IMO (ships equipped with devices that assist maneuverers in decision making and thus increase the safety of navigation, also giving the possibility of a partial reduction in the crew), to the fourth level MASS 4, describing fully autonomous ships, equipped with operational systems capable of making and executing the developed decision on their own.

It should be remembered that autonomous navigation is a complex issue, requiring a huge amount of research and the application of various technologies, including the principles and rules that define safe sea travel. The authors in the papers [2,3,4] attempted to analyze the laws for shipping. Within the framework of this article, it does not propose a solution covering all research challenges, but focuses its attention mainly on multidimensional steering in restricted waters.

Currently, the term Maritime Autonomous Ship System (MASS) [5,6] is used, which refers to autonomous ship control. Commonly known is the autonomous ship control introduced by the commercial companies Rolls-Royce and Kongsberg [7,8,9]. Scientifically, it is considered in the one-dimensional plane, which means controlling a ship only on a course, or multidimensional, but not based on the identification of a real model with dimensions of more than 4 m in length and 1 m in width of the ship. To the authors’ knowledge, currently, the work on autonomous ship control is carried out only in computer simulations [10,11,12,13,14] or on ship models, but with dimensions where the length of the ship (ship model) is 1 m by 2 m [15,16]. Very impressive is the model USV and real experiment in publication [17]. The authors of paper [18] present mechanical and electronic design strategies. Their focus is on reliability and power management. Another part of the research is engaged in the study of multidimensional ship control, where the simulated nonlinear object is not identified according to the actual ship model.

In this publication, the authors propose a technological solution in the area of MASS 3. The effect of the algorithms associated with the unmanned control of a ship in a port at low speeds, which sails on a route determined by the navigator, will be presented. This means that the training model of the ship "Blue Lady" will sail without interference from the crew on the designated route from point A through twelve coordinate points to point B.

2. Materials and Research

The multidimensional object under study was a training ship model belonging to the Foundation for Safety of Navigation and Environmental Protection located in Ilawa-Kamionka [19]. The foundation is recommended by the IMO [20] as a center that conducts effective courses for navigators to improve the safe navigation of ships with unusual maneuvering characteristics. The research was carried out on Lake Silm, located northwest of the Iława city and extending in east-west directions for approximately 1030 m and north-south for approximately 1720 m (a fragment of the lake with a detailed view of the harbor is included in Figure 1).

In the port area, maneuvers were performed on area as shown in Figure 1. The controller synthesis was performed for a multidimensional object, which is a floating model of a Very Large Crude Carrier (VLCC) class tanker named “Blue Lady”. This model ship is described in [21,22,23,24,25]. A model of the ship is presented in Figure 2.

The ship model is equipped with four thrusters, i.e., two tunnel thrusters and two rotary thrusters, designed by SCHOTTEL, simulating the operation of tugs (60 tonnes).

Table 1. Input signals of the propulsion and control devices of the “Blue Lady” ship M Rybczak adapted with permission from Ref. [26].

Symbol	Name of the Signal	Range	Unit
ng	Main propeller rotational speed	(−200; +480)	[rpm]
$\delta$	Rudder deflection angle	(−35; +35)	[deg]
sstd	Relative thrust of the bow tunnel thruster	(−1, +1)	[-]
sstr	Relative thrust of the stern tunnel thruster	(−1, +1)	[-]
ssod	Relative thrust of the bow rotary thruster	(0, +1)	[-]
${\alpha }_d$	Bow rotary thruster deflection angle	(−120, +120)	[deg]
ssor	Relative thrust of the stern rotary thruster	(0, +1)	[-]
${\alpha }_r$	Stern rotary thruster deflection angle	(−120, +120)	[deg]

records the main working ranges of the various drive rudders.

The chapter “Results” also presents the behavior of the thrusters during the autonomous operation of the “Blue Lady” ship.

3. Problem Research

Researchers in this work want to solve the problem of autonomous ship control at the level of the third MASS, which should be performed under real atmospheric conditions in infrastructure adapted for the port. Since the issue is very broad, they divided the work on MASS into four groups. The focus was on proving that it is possible to control a 14 m training model of a ship on a lake.

3.1. MASS Problem

MASS was formulated in 2018 by the International Maritime Organization (IMO) and includes four successive levels, where MASS 1 is the base level of ship autonomy, with level 4 understood as fully unmanned ships sailing according to their control system. Figure 3 quotes MASS definitions generally written by the IMO [6,20].

The authors of this paper believe the above definitions should be considered together with the problems presented below, in Figure 4, by scientists working with issues of autonomous (unmanned) control.

Scientists are dealing with the problems of autonomous (unmanned) ship control [27]. According to the authors, the issues in Figure 4 are four areas that are related to MASS. The concept of MASS problems addresses issues in automation, computer science, electronics, energy, navigation, and maritime law. Therefore, these issues are very extensive. The proposal to divide MASS makes it possible to define scientific work on autonomous control.

1.

PILOT-CAPTAIN, communication technology. For example, the performance of research in a port in Poland requires consideration of the maritime law in the port. It is currently impossible to perform research without the permission of the port of authority. The main rule is related to the presence of a captain and a minimum number of crew on the vessel.

2.

Legal rules in ports and on the high seas. Quite an elaborate issue turns out to be the work on maritime law (for example, during a collision, who will bear the responsibility: machine or man, captain or the quay?).

3.

Security and navigation. Safety principle nowadays is probably the most and best described scientific issue. Many interesting algorithms related to optimization are proposed [18,28,29,30], anthill algorithms [31,32].

4.

Ship control technology. Ship control is so complicated that it is necessary to consider risks not only by computer simulations, but based on real models, which is also realized by scientists from University in Trontheim [33,34], Volda University Colege [35], School of Marine Engineering [36,37], and Gdynia Maritime University [23,38,39,40,41,42,43,44,45,46].

3.2. Ship Control Technology Problem

Gdynia Maritime University (GMU) researchers are working on tasks closely related to ship control technology at MASS 2 and MASS 3 levels. Referring to the point related to ship control, a controller synthesis for low speed and a controller synthesis for ship trajectory were performed. The calculations involve two parts.

-

The first concerns the synthesis of the controller for the multidimensional nonlinear object of the ship “Blue Lady” (Figure 5). The whole process is described in detail in papers [21,25].

-

The second part describes the concept of using a trajectory override controller that converts the received points into velocity setpoints for the LMI controller (Figure 6).

3.2.1. Linear Matrix Inequalities in Use

As a case-study, this paper shows the results of testing on lake Silm of a multidimensional controller for ship motions in a 3DOF space with the use of LMI [48]. Linear matrix inequalities are a tool of convex optimization from a convex set of constraints to be formulated for the process of synthesizing a controller from a state. The canonical form of linear matrix inequalities has the form:

$$\mathbf{F}\left(x\right)={\mathbf{F}}_0+\sum _{i=1}^m{\mathbf{F}}_i{x}_i\succ 0$$

(1)

where $x={[x_1,x_2,\dots ,x_i]}^T\in \mathbf{R}m$ is a decision variable vector (unknown); ${\mathbf{F}}_0,{\mathbf{F}}_i\in {\mathbf{R}}^{nxn}$ are real and symmetrical matrices. In Equation (1), the notation “$\succ 0$” means that matrix F(x) is positively determined.

Lyapunov noted that a necessary and sufficient condition for a linear system to be asymptotically stable is to find a symmetric and positively specified matrix $\mathbf{P}={\mathbf{P}}^T$, $\mathbf{P}\succ 0$ (the problem of finding a symmetric, positively defined matrix $\mathbf{P}$ is often referred to as the existence problem (feasibility problem). $\mathbf{P}$ is the unknown variable when satisfying the inequality called Lapunov’s inequality:

$${\mathbf{A}}^T\mathbf{P}+\mathbf{PA}\prec 0.$$

(2)

The first condition related to the existence issue (2) and the second condition $\mathbf{P}\succ 0$ can be written together as a composite of the two conditions into a single LMI condition:

$$\left[\begin{array}{cc}-{\mathbf{A}}^T\mathbf{P}-\mathbf{PA}& 0\\ 0& \mathbf{P}\end{array}\right]\succ 0,$$

(3)

where the matrix A is the matrix of the object under study, and the matrix P is the search matrix.

The following is a methodology for synthesizing a state regulator using linear matrix inequalities.

1.

The first stage of synthesis is concerned with determining the desired pole position region, located in the left half-plane of the complex variable s in order to specify the dynamic properties of the closed system under study. The zone (Figure 7) was bounded by two vertical strips ${\alpha }_1$ and ${\alpha }_2$, and a sector with an opening angle of $\varphi$.

$${\mathbf{F}}_{\mathbb{D}\varphi }=\left[\begin{array}{cc}sin\left(\varphi \right)& cos\left(\varphi \right)\\ -cos\left(\varphi \right)& sin\left(\varphi \right)\end{array}\right]s+\left[\begin{array}{cc}sin\left(\varphi \right)& cos\left(\varphi \right)\\ -cos\left(\varphi \right)& sin\left(\varphi \right)\end{array}\right]\overline{s},$$

(4)

The vertical stripe is defined by two vertical strips ${\alpha }_1$ and ${\alpha }_2$ on the assumption that the $Re\left(s\right)=\frac{1}{2}(s+\overline{s})$ area is defined as follows:

$${\mathbf{D}}_{\alpha 1,\alpha 2}=\left\{s;{\alpha }_1<\frac{1}{2}(s+\overline{s})<{\alpha }_2\right\},$$

(5)

The first condition of the LMI:

$${\mathbf{R}}_{\mathbb{D}}\left({\mathbf{A},\mathbf{X}}_{zone}\right)=\mathbf{L}\otimes {\mathbf{X}}_{zone}+\mathbf{M}\otimes \left({\mathbf{AX}}_{zone}\right)+{\mathbf{M}}^T\otimes {\left({\mathbf{AX}}_{zone}\right)}^T\prec 0$$

(6)

is satisfied if and only if there is a symmetric and positively defined matrix ${\mathbf{X}}_{zone}$, where: $\mathbf{A}$—matrix of the object (ship “Blue Lady”); ${\mathbf{X}}_{zone}$—the symmetric and positively defined matrix being the sought Laypunov $\mathbf{X}\succ 0,\mathbf{X}={\mathbf{X}}^T$; $\mathbf{L},\mathbf{M}$—the corresponding matrices, which have been defined by the user of the zone according to the theorem.

The LMI notation for determining the controller matrix is shown below:

$${\mathbf{Y}}_{zone}={\mathbf{K}}_{zone}\ast {\mathbf{X}}_{zone}$$

(7)

1

It is necessary to transform the form of the BMI (two unknowns X and Y) condition to the LMI condition; therefore, an additional matrix ${\mathbf{Y}}_{zone}$ is introduced. The use of such a “treatment” is due to the assumption that, since the matrix ${\mathbf{X}}_{zone}$ is positively defined, its inverse is present, e.g., ${\mathbf{Y}}_{zone}={\mathbf{X}}_{zone}^{-1}$. Therefore, the gain matrix ${\mathbf{K}}_{zone}$ of the controller from the state is described by the following equation:

$${\mathbf{K}}_{zone}={\mathbf{Y}}_{zone}·{\mathbf{X}}_{zone}^{-1}.$$

(8)

2

The second stage is the minimization of the $H_{\infty }$ norm, associated with the estimation of the scalar value ${\gamma }_{\infty }$, which is the upper limit of the norm. When determining the smallest value of the norm ${\gamma }_{\infty }$ for a given area of the position of the poles of a closed system, the obtained scalar value ${\gamma }_{\infty }$ is assumed to be a constant value. The scalar value of ${\gamma }_{\infty }$ can be calculated on the basis of the minimization of the norm, or it can be assumed that ${\gamma }_{\infty }$ is a constant value constraint.

The controller determined from the second step of the so-called second limiting tool, called the $H_{\infty }$ norm, has an indirect effect on obtaining robust stability for the system. It is needed to evaluate the control lag in linear matrix inequalities. The definition of the $H_{\infty }$ norm is derived from Riccati’s algebraic inequality proof in [48,49]:

$$({\mathbf{X}}_{\infty }\mathbf{A}+{\mathbf{A}}^T{\mathbf{X}}_{\infty }+{\mathbf{C}}^T\mathbf{C})+({\mathbf{X}}_{\infty }\mathbf{B}+{\mathbf{C}}^T\mathbf{D}){({\gamma }_{\infty }^2\mathbf{I}-{\mathbf{D}}^T\mathbf{D})}^{-1}({\mathbf{B}}^T{\mathbf{X}}_{\infty }+{\mathbf{D}}^T\mathbf{C})\prec 0$$

(9)

Referring to the lemma of Schur’s complement for a matrix $\mathbf{X}$ of dimension $[3\times 3]$ and based on the inequality (9), the following theorem that is useful for controller synthesis can be quoted.

Theorem 1 

(Theorem 5.4 [49]). The notation $\mathit{G}{\left(s\right)}_{\infty }<{\gamma }_{\infty }$ is true if and only if there exists a matrix $\mathit{X}\succ 0$ for which one of the following three inequalities is satisfied:

$$\left[\begin{array}{ccc}{\mathit{X}}_{\infty }{\mathit{A}}^T+\mathit{A}{\mathit{X}}_{\infty }& \mathit{B}& {\mathit{XC}}^T\\ {\mathit{B}}^T& -{\gamma }_{\infty }\mathit{I}& {\mathit{D}}^T\\ \mathit{CX}& \mathit{D}& -{\gamma }_{\infty }\mathit{I}\end{array}\right]\prec 0$$

(10)

or

$$\left[\begin{array}{ccc}{\mathit{AX}}_{\infty }+{\mathit{X}}_{\infty }{\mathit{A}}^T& \mathit{B}& {\mathit{XC}}^T\\ {\mathit{B}}^T& -{\gamma }_{\infty }^2\mathit{I}& {\mathit{D}}^T\\ \mathit{CX}& \mathit{D}& -\mathit{I}\end{array}\right]\prec 0,$$

(11)

or

$$\left[\begin{array}{cc}{\mathit{AX}}_{\infty }+{\mathit{X}}_{\infty }{\mathit{A}}^T+{\mathit{BB}}^T& {\mathit{X}}_{\infty }{\mathit{C}}^T+{\mathit{BD}}^T\\ {\mathit{CX}}_{\infty }+{\mathit{DB}}^T& -{\gamma }_{\infty }^2\mathit{I}+{\mathit{DD}}^T\end{array}\right]\prec 0.$$

(12)

Theorem 1 has three conditions. The paper uses condition 2 and makes use of the Yalmip [50] and SeDuMi [51] library. For a system described by equations in their own state space with transmittance $\mathbf{G}\left(s\right)$, the dependence of the norm $H_{\infty }$ on the parameter ${\gamma }_{\infty }$ is as follows:

$${\parallel \mathbf{G}\left(s\right)\parallel }_{\infty }^2<{\gamma }_{\infty }^2$$

(13)

The state controller synthesis problem has a solution if the second LMI condition is satisfied. Referring to the property about the existence of the inverse of the matrix ${\mathbf{Y}}_{\infty }={\mathbf{X}}_{\infty }^{-1}$, the matrix ${\mathbf{K}}_{\infty }$ is written by the following relation:

$${\mathbf{K}}_{\infty }={\mathbf{X}}_{\infty }^{-1}·{\mathbf{Y}}_{\infty }.$$

(14)

If matrix ${\mathbf{X}}_{\infty }$ (${\mathbf{X}}_{\infty }={\mathbf{X}}_{\infty }^T,{\mathbf{X}}_{\infty }\succ 0$), we can write:

$${\mathbf{K}}_{\infty }={\mathbf{Y}}_{\infty }·{\mathbf{X}}_{\infty }^{-1}.$$

(15)

For a proof of the Theorem 1, see the paper [49].

3.

The third step is the minimization of the $H_2$ norm. For a fixed value of

$${\gamma }_{\infty }>{\gamma }_{\infty min}$$

(16)

the value of ${\gamma }_2$ is sought. On the basis of the Pareto curve, the relationship between the fixed value of the $H_{\infty }$ norm (which is the minimum value of ${\gamma }_{\infty }$) and the minimized value of the $H_2$ norm (which is the value of ${\gamma }_2$) is obtained. The third LMI condition of the form:

$$\left\{\begin{array}{c}\left[\begin{array}{cc}{\mathbf{AX}}_2+{\mathbf{X}}_2{\mathbf{A}}^T& \mathbf{B}\\ {\mathbf{B}}^T& -\mathbf{I}\end{array}\right]\prec 0\\ \left[\begin{array}{cc}\mathbf{Q}& {\mathbf{C}}^T\\ \mathbf{C}& {\mathbf{X}}_2\end{array}\right]\succ 0\\ Tr\left(\mathbf{Q}\right)<{\gamma }_2^2,\end{array}\right.$$

(17)

is satisfied if and only if there exists a symmetric and positively defined ${\mathbf{X}}_2$ matrix and a symmetric $\mathbf{Q}$ matrix. The state controller synthesis problem finds a solution if the third condition of LMI, ${\gamma }_2$, is satisfied. Invoking the property about the existence of the inverse of the matrix ${\mathbf{Y}}_2={\mathbf{X}}_2^{-1}$, the matrix ${\mathbf{K}}_2$ of the state controller is written by the following relation:

$${\mathbf{K}}_2={\mathbf{Y}}_2·{\mathbf{X}}_2^{-1}$$

(18)

4.

The fourth step is equivalent to the notation in which the authors of [47,49] use the statement (25 in [47]) and assume that the matrix $H_{\mathbf{X}}$ is equivalent to the notation $\mathbf{X}={\mathbf{X}}_2={\mathbf{X}}_{\infty }={\mathbf{X}}_{zone}$. The LMI conditions, defined for $X_{\infty }$, $X_2$, and for the area of pole placement in the left half-plane of the complex variable s, are satisfied if there is a symmetric and positively defined Lyapunov matrix. The assumption (forcing) that all Lyapunov matrices are equal in all variants, and that all three LMI conditions are treated as a single constraint, allows for the synthesis of the state controller.

Regarding the final form of state space controller gain matrix K, which stabilizes the whole control system and minimizes $H_{\infty }$ and $H_2$ norms, the assumptions are of the form:

$$\mathbf{K}=\left[\begin{array}{cccccc}1595.3& 0.000& -0.100& -807.800& -0.000& 0.000\\ -0.100& 1664.800& -0.036& 0.000& -897.900& 0.200\\ -6.100& -0.280& 435.400& 0.350& 0.160& -234.4\end{array}\right]$$

(19)

The controller from condition K was obtained based on the conditions and assumptions. The result is often called a suboptimal solution, which means that the listed matrices $\mathbf{X}={\mathbf{X}}_2={\mathbf{X}}_{\infty }={\mathbf{X}}_{zone}$ are the same for the three LMI conditions. The K-matrix calculated using the aforementioned four steps is inserted into the scheme shown in Figure 5.

3.2.2. Trajectory Control in Use

The research was conducted using a simple master system. It converts the desired trajectory and the set course at each section into the corresponding signals preset linear velocities $u,v$ and angular velocity r. A detailed description of the workings of the system is recorded in the paper [24]. The set values in the experiment in question are represented by a set of numbers: the coordinate values of the next point of the trajectory and the ship’s course on the section to that point: [$x_1$,$y_1$, ${\psi }_1$], [$x_n$,$y_n$, ${\psi }_n$], [$x_{n+1}$,$y_{n+1}$, ${\psi }_{n+1}$].

In the system that determines the set values of the linear components of velocity, two angles can be defined: $\kappa$ as the angle of the current section of the trajectory, which is calculated relative to north, and $\rho$ as the angle between the longitudinal axis of symmetry of the ship and the line from the ship to the end of the current section of the trajectory, as shown in Figure 8.

The angle $\rho$ determines the maximum instantaneous values of the set velocity u and v. The values are determined as shown in Figure 9.

The points, located on its sides, determine the values of $u_{max}$ and $v_{max}$ from the ranges given in the point (Figure 10). The instantaneous setpoint r at a given section $\kappa$ of the trajectory (Figure 11) and at a given course ${\psi }_1$ is determined from the relation.

Where $\psi$ is the instantaneous value of the exchange rate. The quantities ${\psi }_{min}$ = 2 deg and ${\psi }_{miax}$ = 40 deg are the limiting values of the course deviation, determining the change (switch) in the formula for calculating r. They were determined on the basis of the analysis of the course of the training ship during turns, so that course changes are made as far as possible without overshooting. The concept of determining the set value of angular velocity is shown in Figure 12.

For the calculation of the current values of the u and v components, it was assumed that the ship, while moving between one point of the trajectory and the next, could be in one of three zones—see also Figure 13.

-

A circle with a fixed radius of 1 m around each trajectory point (Zone III),

-

An approximation ellipse with the center at the trajectory point and a long axis coinciding with the current trajectory segment (Zone II),

-

The space outside the ellipse (Zone I).

The dimensions of the ellipse are not fixed. The lengths of the two axes depend proportionally on the maximum values of $u_{max}$ and $v_{max}$.

According to the proposed algorithm, the dimensions may change ($u_{max}$ and $v_{max}$) as the vessel moves if the vessel deviates from the path leading to the next point in the trajectory (e.g., due to external disturbances), as the angle $\rho$ will then change. However, it was assumed that the dimensions of both axes cannot be completely arbitrary (e.g., zero), but can take values from the ranges:

-

For the long axis: a range of (8–20) m,

-

For the short axis: a range of (2–5) m.

The limiting values of the angles ${\rho }^I$ and ${\rho }^{II}$ are derived from the assumed range of velocity components u and v and are: ${\rho }^I$ = arc tg (0.08/0.2) and ${\rho }^{II}$ = arc tg (0.08/0.1).

These values are derived from the maximum permissible velocities $u_{max}$ and $v_{max}$. It was also assumed that, in zone I (outside the ellipse), the ship moves with maximum velocities, resulting from the instantaneous value of the angle $\rho$. Inside the ellipse, both velocities decrease in proportion to the distance of the vessel from the trajectory point.

The position of the vessel relative to the next point of the trajectory (Figure 13). The current trajectory of a vessel outside the current trajectory section (dotted line) determines the angle $\rho$, and this, in turn, determines the maximum values of $u_{max}$ and $v_{max}$. The waveforms of both velocities during the approach to the turning point here are included in the time diagrams: parallel to the trajectory section—the velocity u—whereas perpendicular—velocity v. It can be noted that the boundaries of the ellipse and circle change the calculation of these velocities. It was also assumed that, in zone I (outside the ellipse), the ship moves with maximum velocities, resulting from the instantaneous value of the angle $\rho$. Inside the ellipse, both velocities decrease in proportion to the distance of the vessel from the trajectory point. If the vessel finds itself in zone III, the further behavior of the trajectory controller depends on whether the point reached is the last one ($x_N$, $y_N$) or just the next one ($x_k$, $y_k$). In the first situation, both velocities are set to zero. Otherwise, the algorithm is switched to the next trinity of numbers ($x_{k+1}$, $y_{k+1}$, ${\psi }_{k+1}$), determining the next point of the trajectory. Under such circumstances, the ship will be in zone I relative to the new point and the control begins again. “Hitting” zone III (circle) is not an easy task, especially when accompanied by stronger external disturbances. Atmospheric conditions in this case refer to the strength of the wind and the waves that occur on Lake Silm. A mathematical model of the wave module of Lake Silm is currently being developed. A number of wind measurements were made using an ultrasonic anemometer made by GILL Instruments located on the training ship model. Wave measurements were made using a capacitive sensor described in the work [52]. Additional wave measurements were taken on the lake using an experimental system designed and built by Dr. inż. Anna Miller, and Dr. inż. Andrzej Rak. This team of researchers is currently working on a paper about this. Currently, the authors of this paper, in cooperation with Prof. Witold Cieślukiewicz of the University of Gdansk, are analyzing these measurements in order to create a mathematical model of the waves of Lake Silm. Due to the complexity of the problem, this will be the subject of another article. However, it should be emphasized that atmospheric conditions significantly affect the operation of a ship, which is difficult to verify with computer simulations. Therefore, it is important to test the system performance in real conditions.

4. Results

The research includes the implementation of the autonomous control of a ship: in this case, the training model “Blue Lady”. The tests presented here were carried out in the summer under atmospheric conditions recorded during maneuvering in the port on Lake Silm in Ilawa Kamionka. Wind measurements were recorded and the GPS mode was read. The recorded maneuver was composed of a preset route with x and y coordinates and the course of the vessel was given, which, according to the authors, is a level 3 implementation of MASS due to the vessel’s independent execution of the maneuver without human intervention. The chapter presents a list of 13 coordinates of the trajectory that the ship had to perform. Velocity measurements and the operation of the training model’s thrusters are presented.

Figure 14 shows part of a map of Lake Silm. In the marked part of the port, the task was completed. The executed maneuver is marked in yellow. The trajectory consists of 13 set points. The specified coordinates start at the berth and are marked in red. The route of the training model “Blue Lady” is shown in Figure 15.

The silhouette of the ship is shown in blue. Figure 15 shows how the maneuver was performed, including how the ship’s silhouette was laid out; that is, the beginning of the executed trajectory started with a movement to the starboard (right) side. It then sailed forward. After completing the entire maneuver, the ship docked at the second berth with its port (left) side.

During the trials, the following were recorded:

-

Low velocity results $u,v,r$.

-

Parameters of the anenometer.

-

GPS modes.

-

Ship’s propulsion signals.

The maneuver lasted 4000 s. The list includes graphs of longitudinal velocity u [m/s], lateral velocity v [m/s], rational velocity r [rad/s], instantaneous wind registration [m/s], and GPS [modes].

Note that changing the GPS mode (independent of the author) from the value of 3 to the value of 2 causes the reading of the coordinate values to be able to change from a few centimeters up to 1 m. Therefore, as can be seen in Figure 16, between 400 and 900 s, the adjusted values of the longitudinal and transverse velocity change. The wind was at 3 m/s and, according to the author’s observations, the lake wave was 2 to 4 cm high.

Figure 17 presents four charts for each control and drive device (their list is given in Table 1).

Similarly, Figure 16 and Figure 17 also notes that, between 400 and 900 s, there is an increased operation of the bow and stern tunnel thrusters. This confirms the impact of GPS mode changes. It should be noted that the maneuver after the 1000th second forces a balanced operation of the thrusters, which work in accordance to their ranges.

5. Discussion

The executed ship maneuver on Silm Lake demonstrates that work on MASS 3 level ship control systems is available under real conditions. The autonomous passage of the ship from berth to berth in restricted waters proves that the concept of an unmanned ship can be realized. Moreover, the use of an LMI controller and am override controller converting the set points of the trajectory into velocities $u,v,r$ resulted in the reproduction of the determined trajectory despite the occurring (recorded) atmospheric conditions (wind and wave). On the other hand, it is necessary to look at new solutions related to the acceleration of the maneuver that is to be performed faster than 4000 s. Certainly, the next step in the evaluation of the autonomy of the ship will be the introduction of autonomous navigation, which is equivalent to MASS level 4, where the unmanned vessel makes decisions independently on which way to sail to a specific destination.