# Построение маршрута с помощью улучшенного метода изохрон при минимизации времени плавания и с учетом прогноза погоды

Хунбо Ван, Пэнгфэй Ли, Юаньюань Сюэ, Максим Васильевич Коровкин

Research output

6 Citations (Scopus)

### Abstract

Optimal control theory is the core of modern control theory. The development of control theory comes from the requirements of the control object. With the continuous progress of social science and technology, optimal control theory is widely used for such issues as the minimum time problem, the minimum energy consumption problem, the linear quadratic index optimal problem, and others. In this paper, a method of calculating the minimum time route of the ship using rhumb lines combined with isochrones is proposed. Firstly, a mathematical model of the minimum time route is constructed and the ship motion equation is discretized. Secondly, the distance between the starting point and the end point is divided into several rhumb segments with equal traveling time so that each isochrone corresponds to different rhumb line. Then, N parallel lines of equal spacing ΔD are arranged on both sides of each rhumb segment to form 2N sub-channels. Stipulate that the ship can only sail within the interval of 2N×ΔD and constrain the navigation area in order to find the optimal solution faster. At each unit of discrete time the course of the ship remains constant. Select the optimal arrival points on each sub-lane interval in the same time to form the local optimal isochrone. After calculating the minimum time of the ship's voyage, the minimum time route is derived using step-by-step recursion. In addition, in order to improve the obstacle avoidance capability of the improved isochrone method, the paper also proposes the algorithm based on a bitmap image in order to avoid a danger zone which may be encountered in the course of navigation, so as to ensure the safe navigation of the ship at sea. Finally, the improved isochrone method is applied to the problem of the minimum time route of the ship under meteorological conditions. The simulation results in MATLAB show that the algorithm can not only find the minimum time route from the starting point to the end point and ensure the route is relatively short, but also avoid dangerous areas encountered in the course of navigation in time and assure safety of navigation.

Original language Russian 6 286-299 13 ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. СЕРИЯ 10: ПРИКЛАДНАЯ МАТЕМАТИКА, ИНФОРМАТИКА, ПРОЦЕССЫ УПРАВЛЕНИЯ 13 3 https://doi.org/10.21638/11701/spbu10.2017.306 Published - 2017

### Fingerprint

Ship
Weather
Ships
Routing
Isochrone
Control theory
Loxodrome
Optimal Control Theory
End point
Control Theory
Social sciences
Collision avoidance
Ship Motion
MATLAB
Equations of motion
Interval
Obstacle Avoidance
Energy utilization
Social Sciences

### Scopus subject areas

• Computer Science(all)
• Control and Optimization
• Applied Mathematics

### Cite this

@article{8e2d5fb1233b4210886963b7ed46cd09,
title = "Построение маршрута с помощью улучшенного метода изохрон при минимизации времени плавания и с учетом прогноза погоды",
abstract = "Optimal control theory is the core of modern control theory. The development of control theory comes from the requirements of the control object. With the continuous progress of social science and technology, optimal control theory is widely used for such issues as the minimum time problem, the minimum energy consumption problem, the linear quadratic index optimal problem, and others. In this paper, a method of calculating the minimum time route of the ship using rhumb lines combined with isochrones is proposed. Firstly, a mathematical model of the minimum time route is constructed and the ship motion equation is discretized. Secondly, the distance between the starting point and the end point is divided into several rhumb segments with equal traveling time so that each isochrone corresponds to different rhumb line. Then, N parallel lines of equal spacing ΔD are arranged on both sides of each rhumb segment to form 2N sub-channels. Stipulate that the ship can only sail within the interval of 2N×ΔD and constrain the navigation area in order to find the optimal solution faster. At each unit of discrete time the course of the ship remains constant. Select the optimal arrival points on each sub-lane interval in the same time to form the local optimal isochrone. After calculating the minimum time of the ship's voyage, the minimum time route is derived using step-by-step recursion. In addition, in order to improve the obstacle avoidance capability of the improved isochrone method, the paper also proposes the algorithm based on a bitmap image in order to avoid a danger zone which may be encountered in the course of navigation, so as to ensure the safe navigation of the ship at sea. Finally, the improved isochrone method is applied to the problem of the minimum time route of the ship under meteorological conditions. The simulation results in MATLAB show that the algorithm can not only find the minimum time route from the starting point to the end point and ensure the route is relatively short, but also avoid dangerous areas encountered in the course of navigation in time and assure safety of navigation.",
keywords = "Algorithm of avoiding the danger zone, Improved isochrone method, Meteorological navigation, Route optimization",
author = "Хунбо Ван and Пэнгфэй Ли and Юаньюань Сюэ and Коровкин, {Максим Васильевич}",
year = "2017",
doi = "10.21638/11701/spbu10.2017.306",
language = "русский",
volume = "13",
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T1 - Построение маршрута с помощью улучшенного метода изохрон при минимизации времени плавания и с учетом прогноза погоды

AU - Ван, Хунбо

AU - Ли, Пэнгфэй

AU - Сюэ, Юаньюань

AU - Коровкин, Максим Васильевич

PY - 2017

Y1 - 2017

N2 - Optimal control theory is the core of modern control theory. The development of control theory comes from the requirements of the control object. With the continuous progress of social science and technology, optimal control theory is widely used for such issues as the minimum time problem, the minimum energy consumption problem, the linear quadratic index optimal problem, and others. In this paper, a method of calculating the minimum time route of the ship using rhumb lines combined with isochrones is proposed. Firstly, a mathematical model of the minimum time route is constructed and the ship motion equation is discretized. Secondly, the distance between the starting point and the end point is divided into several rhumb segments with equal traveling time so that each isochrone corresponds to different rhumb line. Then, N parallel lines of equal spacing ΔD are arranged on both sides of each rhumb segment to form 2N sub-channels. Stipulate that the ship can only sail within the interval of 2N×ΔD and constrain the navigation area in order to find the optimal solution faster. At each unit of discrete time the course of the ship remains constant. Select the optimal arrival points on each sub-lane interval in the same time to form the local optimal isochrone. After calculating the minimum time of the ship's voyage, the minimum time route is derived using step-by-step recursion. In addition, in order to improve the obstacle avoidance capability of the improved isochrone method, the paper also proposes the algorithm based on a bitmap image in order to avoid a danger zone which may be encountered in the course of navigation, so as to ensure the safe navigation of the ship at sea. Finally, the improved isochrone method is applied to the problem of the minimum time route of the ship under meteorological conditions. The simulation results in MATLAB show that the algorithm can not only find the minimum time route from the starting point to the end point and ensure the route is relatively short, but also avoid dangerous areas encountered in the course of navigation in time and assure safety of navigation.

AB - Optimal control theory is the core of modern control theory. The development of control theory comes from the requirements of the control object. With the continuous progress of social science and technology, optimal control theory is widely used for such issues as the minimum time problem, the minimum energy consumption problem, the linear quadratic index optimal problem, and others. In this paper, a method of calculating the minimum time route of the ship using rhumb lines combined with isochrones is proposed. Firstly, a mathematical model of the minimum time route is constructed and the ship motion equation is discretized. Secondly, the distance between the starting point and the end point is divided into several rhumb segments with equal traveling time so that each isochrone corresponds to different rhumb line. Then, N parallel lines of equal spacing ΔD are arranged on both sides of each rhumb segment to form 2N sub-channels. Stipulate that the ship can only sail within the interval of 2N×ΔD and constrain the navigation area in order to find the optimal solution faster. At each unit of discrete time the course of the ship remains constant. Select the optimal arrival points on each sub-lane interval in the same time to form the local optimal isochrone. After calculating the minimum time of the ship's voyage, the minimum time route is derived using step-by-step recursion. In addition, in order to improve the obstacle avoidance capability of the improved isochrone method, the paper also proposes the algorithm based on a bitmap image in order to avoid a danger zone which may be encountered in the course of navigation, so as to ensure the safe navigation of the ship at sea. Finally, the improved isochrone method is applied to the problem of the minimum time route of the ship under meteorological conditions. The simulation results in MATLAB show that the algorithm can not only find the minimum time route from the starting point to the end point and ensure the route is relatively short, but also avoid dangerous areas encountered in the course of navigation in time and assure safety of navigation.

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KW - Improved isochrone method

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