COLLISION AVOIDANCE BY CONSTRUCTING AND USING A PASSING AREA IN ON-BOARD CONTROLLER

The object of research is the processes of automatic optimal passing of one’s own ship with many dangerous targets, including maneuvering ones, by the method of constructing the area of permissible passing parameters in the on­board computer. According to the European Maritime Safety Agency (EMSA), the largest number of ship accidents in 2014–2019 occurred due to collision (32 %). On modern ships, for observation and passing with targets, ARPA (automatic radar plotting aid) is used, which allows to automate manual operations, and the built­in function «Playing the maneuver» provides the navigator with a convenient graphic interface for solv­ ing passing problems. At the same time, ARPA is an automated system that assumes the presence of an operator in the control circuit. The presence of a person in the control circuit is related to the «human factor», which is a prerequisite for the occurrence of various types of accidents, including ship collisions. The most effective means of reducing the influence of the «human factor» on control processes is the introduction of automatic control modules in automated systems. The paper develops a method for the passing module, which allows automatic and optimal passing with many targets, including maneuvering ones. The number of targets for passing is not limited by the method, but is limited only by the capabilities of the ARPA to track the targets. The obtained results are explained by the fact that at each step of the on­board computer, a region of permissible passing parameters is constructed for all purposes, passing parameters that optimize a given optimality criterion are selected from the constructed region, the selected parameters are used as software in the control law. The developed method can be used on ships, subject to integration into the existing automated system of an on­board computer with an open architecture, to increase the capabilities of automatic traffic control, in this case, the possibility of automatic optimal passing with many objectives, including maneuvering.


Introduction
According to the European Maritime Safety Agen cy (EMSA), the causes of ship accidents in 2014-2019 were: collision (32 %), loss of control (30 %), equip ment failure (14 %), grounding (13 %), fires (6 %), flood ing (3 %), loss of structural integrity of the hull (1 %) and others (1 %).As can be seen from the given data, the largest share of the causes of accidents is collisions.A radar station is a tool for measuring the parameters of TECHNOLOGY AUDIT AND PRODUCTION RESERVES -№ 1/2(69), 2023 ISSN 2664-9969 the relative movement of ships and targets, for calculating the passing of ships.The measured radar parameters (bearing and distance) are used for radar laying (calculation of passing parameters).Previously, it was manual laying on a maneuvering tablet, which had low accuracy and was very laborintensive.On modern ships, for tracking targets, ARPA (automatic radar plotting aid) [1,2] is used, which allows to auto mate manual operations, and the builtin function «Playing the maneuver» provides the navigator with a convenient graphical interface for solving the problems of ship passing.At the same time, ARPA has significant disadvantages: -ARPA is an automated system that assumes the pre sence of a person in the control circuit; -ARPA «Maneuver Playback» function provides the navigator only with a convenient graphical interface, but the navigator selects the passing parameters manually, which takes time; -«Maneuver playback» function allows to determine the passing parameters only for nonmaneuvering targets.
The presence of a person in the control circuit is re lated to the human factor, which is a prerequisite for the occurrence of the abovementioned accidents.Reducing human influence on control processes can be achieved through the introduction of automated decision support systems, energy systems [3], or automated systems with automatic control modules [4].An example of an auto matic module in an automated system, which is used on almost all ships today, is the autopilot.
The issue of automatic passing of ships was considered by many authors.Thus, in [5], an automatic differentiation system based on deep Qlearning was proposed.The ad vantage of this method is that the control system receives information from the environment with which the ship interacts, which allows optimizing the passing processes.The disadvantage of the proposed method is that during Qlearning, the system may not work optimally or even erroneously, which threatens with serious consequences.
The work [6] describes the method of assessing the risk of collision of ships, based on the complex nonlinear relationship between the degree of risk of collision and influencing factors.Collision risk estimates with expert information on collision avoidance experience are entered into a database for future reference.The solution proposed by the authors involves training the system, which is unac ceptable during the passing of ships.In addition, the learn ing process is associated with the longterm accumulation of information, the use of databases, the organization of a quick search for information in the database, the need for additional database maintenance.
The article [7] describes the route planning method tak ing into account the collision risk, dynamic characteristics of the control object and COLREG72 rules.Simulation results are presented, which confirm the workability of the proposed approach to ship passing.The disadvantage of the method is the assessment of the risk of collision only with nonmaneuverable targets.Also, the method does not provide for the formation of controls for passing in automatic mode.
As a result of the analysis, the authors of the article [8] came to the conclusion that the ship passing algorithms developed in recent decades do not foresee passing with maneuvering targets, allow passing with one or two targets, use simplified dynamics of the ship and targets.A col lision prevention method and system is proposed, which involves visualization of changes in the ship's course and speed leading to a collision.The collision avoidance sys tem can also offer ways to avoid collisions, consistent with the COLREG72 Rules, which are implemented with a minimum number of operations.The proposed collision avoidance method and systems can be used under manual control, in decision support systems, but do not provide automatic passing with many maneuvering targets.
The passing method using predictive models is consid ered in [9].Prediction of the trajectory of the ship and the target is carried out in the onboard computer based on the parameters of the ship's movement measured at the current time and the estimated parameters of the target's movement.This forecast, taking into account COLREG72 rules, is used to determine the optimal passing management strategy.The disadvantage of the method is the significant load on the onboard computer, as well as the possibility of passing with only one ship.
The aim of research is to develop a method of passing with ships and targets by constructing the area of passing in the onboard computer.This will make it possible to automatically pass from many maneuvering targets, signifi cantly reduce the influence of the human factor on control processes and increase the safety of shipping.

Materials and Methods
The object of research is the processes of automatic optimal passing of one's own ship with many dangerous targets, including maneuvering ones, by the method of constructing the area of permissible passing parameters in the onboard computer.The research used a systematic approach, analysis and synthesis, mathematical analysis, methods of automatic control theory, methods of conducting an experiment.As well as equipment: a personal computer with the Windows 10 operating system and a suite of MS Office 2016 application programs, a simulation stand de veloped by the authors on the basis of the Navi Trainer 5000 navigation simulator.

Results and Discussion
Fig. 1 shows the scheme of passing of own ship О with the target O j n j , .. .= 1 The own ship is placed in the center of the coordinate system OX Y g g , a circle with a radius R sa (safe passing zone) is drawn around the ship, and the speed vector of the own ship V n is depicted.The drawn Line of Relative Motion (RML j ), on which lies the vector of the relative speed ∆V j of the own ship and the target (shown in blue), as well as the expected lines of relative motion ERML ERML , there is a sec tor of dangerous courses, in which the vector of relative speed ∆V j should not be directed, in order to avoid a col lision.Circles with radii V max and V min , which correspond to the maximum and minimum speed of one's own ship, are drawn around the center O j .The area between the circles V max and V min , with the exception of the two dangerous course sectors DFB and AFC, is the area of permissible passing parameters (course and speed) with the jtarget.
Fig. 2 shows the area of permissible parameters of pass ing from the jtarget in the Cartesian coordinate system.The vertical axis of the area is the departure speed V n1 of the own ship, and the horizontal axis of the area is the departure course of the own ship K n1 .TECHNOLOGY AUDIT AND PRODUCTION RESERVES -№ 1/2(69), 2023 ISSN 2664-9969 The range Ω of acceptable passing parameters with all targets simultaneously can be determined by combin ing the ranges Ω j j n , .. = 1 of allowable passing parameters with each target separately: As can be seen from Fig. 2, the range of permissible passing parameters even with one target is quite com plex, so it is advisable to build it in an onboard com puter using numerical methods.To do this, let's set trial passing vectors = ( , ) at grid nodes (Fig. 2) and determine for each of them the relative speed of passing with each target: If the relative speed vector (2), calculated for the test vector ), is not directed inside the sector of dangerous courses of the jtarget, then such a test vector belongs to the region of safe passing Ω j .
As can be seen from Fig. 1, the vector of the relative speed ∆V j does not belong to the sector of dangerous courses of the jtarget, if the vector products ∆V e j j × + and ∆V e j j × − have the same sign: where e j + , e j − -orthogonals that specify the directions ERML ERML where e j 0 -unit vector, which sets the direc tion from the target to our ship; e i∆j -ope rator of rotation of the unit vector e j 0 by the angle ∆j clockwise to the combination with ERML j + ; e −i∆j -the operator of rota tion of the unit vectors e j 0 by an angle ∆j counterclockwise to the combination with ERML j − ; P D mj mj , -measured radar bearings and distances to targets.In formula (2), the speed vector V j of the target is not available for direct measurement, so it must be con stantly estimated with the help of observation devices: where T -time constant when evaluating the relative speed; V V ( , ) -estimation of the vector and components of the vector of the true speed of the target.
The range Ω of permissible passing parameters (1) constantly changes over time, depending on the relative position and speed of one's own ship and targets.There fore, its calculation must be performed constantly, at each step of the onboard calculator.For heading grid step , high speed grid step ∆V n1 0 5 = .knots, speed change range 0 2 0 , when passing with 10 targets, it is necessary to process N = ⋅ ⋅ = 360 1 20 0 5 10 144000 .points at each step.For a com puter with a clock frequency of f = 1-2 GHz, these costs are insignificant.At the same time, the construction of the area of permissible passing parameters in real time allows passing with maneuvering targets.At the same time, the number of targets is not limited by the passing al gorithm, but is limited only by the capabilities of ARPA to track targets.
Optimization of passing processes.Fig. 3 shows the range of allowable multiobjective passing parameters.
The presence of a region of admissible passing parame ters means the presence of an infinite number of solutions, among which there are optimal ones according to the se lected criterion of optimality.Let's consider as a criterion ISSN 2664-9969 of optimality the minimization of passings from the given course, which is associated with the minimization of fuel consumption in the process of passing.For the position of one's own ship in point 1, the best, from the point of view of the selected criterion, is point 2, which belongs to the area of permissible passing parameters and is at the closest angular distance to point 1.The transition to point 2 can be carried out by a combined maneuver (changing course and speed).For the position of the own ship in item 3, the best, from the point of view of the selected criterion, is item 4, which belongs to the area of permissible pass ing parameters and is on the same course as item 3. The transition to item 4 from item 3 is possible to carry out by changing the speed of one's own ship.
where θ -telegraph deflection angle; δ -stern deflection angle; j m -measured rate; ω zm -measured yaw angular speed; k k k j ω , , ∫ k ∫ -gain coefficients of the PID regulator.The performance and efficiency of the developed method, algorithmic and software of the automatic passing module with many dangerous targets, including maneuvering, tested on a simulation bench, in a closed circuit with models of the Navi Trainer 5000 simulator [10].
At the instructor's workplace, Fig. 4, a problem is crea ted for automatic optimal passing of own ship with nine dangerous targets. .nm. Fig. 5 shows the instructor's workplace after 5 minutes automatic passing.
Fig. 6 shows the ARPA screen in 5 minutes after passing.Fig. 7 shows the memory dump of the onboard computer at the fifth minute of passing, displayed in the simulation bench data exchange program [10].An area containing a dump value of «1» is the own ship's safe passing area for all purposes.Summing up and taking into account the results of the experiment, it can be noted that the proposed method and the algorithmic and software developed on its basis allow automatic and optimal passing of many dangerous targets, including maneuvering ones.The obtained result is explained by the use of the area of safe passing for all purposes to solve passing problems.The area of safe passing is built using numerical methods at each step of the calculation, which allows to constantly take into account changes in the relative position of your own ship and targets.The depar ture parameters (course and speed) are selected from the safe departure area according to the established optimality criterion.The passing parameters are used as program values in the PID controller to adjust the ship's current course and speed.Unlike ARPA, the proposed passing method al lows for automatic passing with maneuvering targets, which TECHNOLOGY AUDIT AND PRODUCTION RESERVES -№ 1/2(69), 2023 ISSN 2664-9969 minimizes the influence of the human factor on control pro cesses.Compared to known solutions of automatic passing, the developed method allows passing from many dangerous targets, including maneuvering ones.The maximum num ber of targets for passing is not limited by the method of passing, but is limited only by the capabilities of ARPA in terms of the number of accompanied targets.The developed method can be used on ships, subject to integration into the existing automated system of an onboard computer with an open architecture, to increase the capabilities of automatic traffic control, in this case, the possibility of automatic op timal passing with many objectives, including maneuvering.
The theoretical significance of the obtained result lies in the development of a method of automatic optimal passing of one's own ship with many dangerous targets, including maneuvering ones.The practical significance of the obtained result lies in the possibility of using the automatic optimal passing module in automated systems with expandable ar chitecture, automating and optimizing, due to this, passing operations, reducing crew fatigue and increasing reliability.
The limitations of the developed method include the impossibility of its application for manual control.
In further works, it is planned to investigate the regu larities of changes in the region during passing in order to predict its future forms.

Conclusions
A passing method has been developed that allows auto matic and optimal passing with many targets, including maneuvering ones.The result was obtained thanks to the construction at each step of the onboard calculator of the safe passing area of one's own ship for all purposes, the se lection of the passing parameters from the constructed area, in accordance with the established criterion of optimality, the use of the selected passing parameters as software in the law of controlling the movement of the ship.The developed method can be used to build automatic passing modules in an onboard computer of an automated system.This will make it possible to automate and optimize passing processes, significantly reduce the influence of the human factor on control processes, optimize the performance of a functional task, reduce crew fatigue, and generally improve shipping safety.
red lines.Between the lines ERML ERML j j + −

Fig. 2 .
Fig. 2. The area of permissible parameters of passing from the j -target in the Cartesian coordinate system the relative speed of the jtarget; D j ∧ estimation of the distance to the jtarget; V m x m y mV V = ( , )vector and components of the measured speed of the own ship; V

Fig. 1 .
Fig. 1.The scheme of the ship's passing from the j-target

Fig. 3 . 1 1
Fig. 3.The area of permissible passing parameters The defined passing parameters ( , ) V K n n 1 1 ∈Ω are used as program values in the control law:

Fig. 4 .
Fig. 4. The instructor's workplace at the beginning of the passing The own ship is depicted in red; the entire ships are depicted in blue.Planned target trajectories and their trends are shown.Some of the targets create a threat of collision at the beginning of the passing; the other part of

Fig. 7 .
Fig. 7. Memory dump of the on-board computer