CN111007879A - Method and device for realizing automatic tracking of ship - Google Patents
Method and device for realizing automatic tracking of ship Download PDFInfo
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- CN111007879A CN111007879A CN201911195072.5A CN201911195072A CN111007879A CN 111007879 A CN111007879 A CN 111007879A CN 201911195072 A CN201911195072 A CN 201911195072A CN 111007879 A CN111007879 A CN 111007879A
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Abstract
The invention discloses a method and a device for realizing automatic tracking of a ship, wherein the method comprises the following steps: s1, selecting track points in a ship path planning route and sequentially forming track sections; s2, determining a track section to which the current position of the ship belongs and an adjacent next track section; s3, acquiring the steering speed of the ship running to the next track section and the steering starting distance of the ship steering the next track section; s4, judging whether the distance from the current position of the ship to the current track segment end point is smaller than the steering starting distance, and S5, if the distance is smaller than or equal to the steering starting distance, obtaining the expected course of the ship at the current position; s6, judging whether the difference between the current heading and the expected heading is smaller than the allowable heading variation, if so, the corrected expected heading is the expected heading obtained in the step S5; and repeating the steps S4 to S6 until the end point is reached. The method solves the problems of poor tracking effect and complex algorithm in the yaw process in the prior art.
Description
Technical Field
The invention relates to the field of ships, in particular to a method and a device for realizing automatic tracking of a ship.
Background
Ship tracking control means that a ship advances along a certain predetermined track at a constant longitudinal speed during operation or sailing, and the heading of the ship must be kept along the predetermined track during the process. The existing tracking control system mainly controls a ship to sail along a set air route, the tracking is divided into straight tracking and steering tracking, and the steering tracking adopts fixed steering rate to move ahead.
However, the algorithm logic of the tracking control system is complex to judge, and the tracking function is basically useless when yaw occurs in the steering process, that is, the experience in the actual steering operation of the ship is not considered, and the phenomenon that the ship is violently steered by small-angle steering often occurs in the tracking process, so that the running stability of the ship and the economical efficiency of sailing are influenced.
Disclosure of Invention
The invention aims to provide a method and a device for realizing automatic tracking of a ship, which solve the problems of poor tracking effect and complex algorithm in the yaw process in the prior art.
In order to achieve the purpose, the invention adopts the main technical scheme that:
in a first aspect, the present invention provides a method for implementing automatic tracking of a ship, including:
s1, selecting track points in the ship path planning route aiming at the running ship, and sequentially forming track sections according to the selected track points;
s2, determining the information of the track section to which the current position of the ship belongs and the information of the adjacent next track section according to the current position of the ship;
s3, acquiring the steering speed of the ship to the next track section and the steering starting distance of the ship for steering the next track section according to the basic information and the operation parameters of the ship;
s4, judging whether the distance from the current position of the ship to the current track section end point is smaller than the steering starting distance;
s5, if the current position of the ship is less than or equal to the current track section, calculating the expected course of the ship at the current position according to the current position of the ship and the current track section;
s6, acquiring the current course of the ship, judging whether the difference value between the current course and the expected course is smaller than the allowable course variation, if so, the corrected expected course is the expected course obtained in the step S5;
repeating the steps S4 to S6 until the tracking is switched to the next track segment, and repeating the steps S2 to S6 until the operation reaches the end.
Optionally, the step S4 includes: and if the distance from the current position of the ship to the current track section end point is judged to be greater than the steering starting distance, continuing tracking according to the current track section.
Optionally, the step S6 further includes:
if the difference between the current course and the expected course is larger than or equal to the allowable course variation, correcting the expected course to ensure that the corrected expected course is equal to the current course of the ship plus or minus the preset allowable course variation;
alternatively, the first and second electrodes may be,
and if the difference value between the current course and the expected course is larger than or equal to the allowable course variation, correcting the expected course according to the current steering speed of the ship.
Optionally, the step S2 further includes:
judging whether the track section to which the current position of the ship belongs is the last track section or not;
if yes, the steps S3 and S6 are not carried out until the ship sails to the end point of the current track section, and then the operation is finished.
Optionally, the basic information of the vessel includes one or more of the following:
the ship length and the ship width of the ship, the ship turning index K, the ship tracking index T, the steering time T and the maximum steering angle information of a ship steering engine;
the operating parameters of the vessel include: the current position of the ship, the current running speed, the current steering rate of the ship and the current rudder angle value of the ship.
Optionally, the step S5 includes:
s51, if the current position of the ship is as follows: o (x)0,y0) The current track section is MN, M (x)M,yM)、N(xN,yN) Tracking point los (x)los，ylos) And a vertical foot (x) from the current position of the ship to the straight line of the current track sectiond，yd) Obtaining the expected course according to the following formula I
The formula I is as follows:
wherein a is a preset constant;
xd＝(B2x0-A*By0-A*C)÷(A2+B2)；
yd＝(-A*Bx0+A2y0-B*C)÷(A2+B2)；
lpp is the ship length of the ship, d is the distance from the current position of the ship to the track section MN,
and 0 is the standard linear equation of the straight line where the current track section is located, and A, B, C in the formula corresponds to the coefficients in the standard linear equation one By one.
Alternatively, when xlos-x0<0 and ylos-y0When the value is more than or equal to 0, a is 450;
except that the above-mentioned numerical value of a-450 corresponds to the condition, a takes 90.
Optionally, the step S3 includes:
s31, obtaining the steering rate according to a formula II:
the formula II is as follows: r is K δ;
wherein r is a steering rate, K is a turning index of the ship, and delta is a current rudder angle value of the ship;
alternatively, the first and second electrodes may be,
s31, acquiring the steering rate according to a formula III;
the formula III is as follows: r isd＝αrmax＝α*Kδmax
α is a steering rate coefficient, delta, which varies according to the steering anglemaxThe allowable maximum rudder angle of the ship steering engine is K, and the turning index of the ship is K.
Optionally, the step S3 includes:
s33, obtaining the steering initial distance D according to the following formulaminturnThe starting position of the steering starting distance is a steering starting position;
wherein: v is the current running speed of the ship, T is the ship tracking index, K is the ship turning index, T is the steering time, deltamaxThe maximum rudder angle allowed by the ship steering engine;
let M (x)M,yM),N(xN,yN),O(xO,yO)；
Modulus of the vector MN:
modulus of vector NO:
vector product of vectors MN, NO:
in a second aspect, the present invention further provides an apparatus for implementing automatic tracking of a ship, including a memory, a processor;
the memory stores a computer program, and the processor executes the computer program stored in the memory, and is specifically configured to execute the method for implementing automatic tracking of a ship according to any one of the first aspect.
The invention has the beneficial effects that:
according to the invention, the automatic tracking of the ship is realized according to the ship performance on the basis of obtaining the track point (such as an inflection point in the track).
The method of the invention fully combines the experience in the actual ship steering operation, accurately controls the set course of the ship, and calculates the reasonable rudder starting distance by considering the inertia of the ship and the steering engine operation time.
In addition, the invention does not divide the linear tracking and the steering tracking, namely, the linear tracking and the steering tracking are processed uniformly, so that the complex logic judgment is omitted, and the problem of poor tracking effect during yawing in the steering process is solved.
Drawings
Fig. 1 is a schematic flowchart of a method for implementing automatic tracking of a ship according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart illustrating a method for performing automatic tracking of a ship according to another embodiment of the present invention;
FIG. 3 is a schematic illustration of a path segment in a path planning route provided in accordance with another embodiment of the present invention;
fig. 4 is a graph comparing the application effects of the method of the present invention and the prior art method according to another embodiment of the present invention.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
As shown in fig. 1, fig. 1 is a schematic flowchart illustrating a method for implementing automatic tracking of a ship according to an embodiment of the present invention, where the method includes the following steps:
s1, selecting track points in the ship path planning route aiming at the running ship, and sequentially forming track sections according to the selected track points;
and S2, determining the information of the track section to which the current position of the ship belongs and the information of the adjacent next track section according to the current position of the ship.
It should be noted that, in practical applications, after the track segment to which the current position of the ship belongs is determined, if it is determined that the track segment to which the current position of the ship belongs is the last track segment, the process is ended.
And S3, acquiring the steering speed of the ship to the next track section and the steering starting distance of the ship for steering the next track section according to the basic information and the operation parameters of the ship.
For example, the basic information of the ship in this step may include one or more of the following information:
the ship length and the ship width of the ship, a ship turning index K, a ship tracking index T, steering time T, maximum steering angle information of multiple ships and the like;
the operating parameters of the vessel include: the current position of the ship, the current running speed, the current steering rate of the ship, the current rudder angle value of the ship and the like.
And S4, judging whether the distance from the current position of the ship to the current track section end point is less than the steering starting distance.
In specific application, if the distance from the current position of the ship to the current track section end point is judged to be greater than the steering starting distance, tracking is continued according to the current track section until the distance is less than or equal to the steering starting distance.
When the distance is less than or equal to the steering start distance, the following steps S4 and S6 may be performed to realize automatic tracking and switch to the next track segment.
And S5, if the current position of the ship is less than or equal to the current track section, calculating the expected course of the ship at the current position according to the current position of the ship and the current track section.
It can be understood that, during the tracking navigation of the ship, the position of the ship changes from moment to moment, and the method for realizing automatic tracking of the ship outputs a desired heading in real time according to the current position of the ship, for example, the desired heading is C1 when the ship is at position P1 at time T1, and the desired heading is C2 when the ship is at position P2 at time T2, where the desired heading refers to the heading required for enabling the ship to track navigation, T1 and T2 are adjacent moments, a time period is from the time T1 to the time T2, and the time period mentioned in the description of the following step S6 is the time period.
S6, obtaining the current course of the ship, judging whether the difference between the current course and the expected course is smaller than the allowed course variation, if so, the corrected expected course is the expected course obtained in the step S5,
otherwise, the corrected expected heading is the current heading of the ship ± a preset allowed heading variation, the judgment of the sign ± is based on the expected heading obtained in the approaching step S5, for example, the current heading of the ship is 20, the allowed heading variation is 2, if the expected heading is 21, the corrected expected heading is 21, if the expected heading is 30, the corrected expected heading is 22, wherein the allowed heading variation is the steering speed × the time period, which means the maximum angle that the ship can steer in one time period;
it can be understood that if the difference between the current heading and the expected heading is greater than or equal to the allowed heading variation, the expected heading is corrected, so that the corrected expected heading is equal to the current heading of the ship plus or minus the preset allowed heading variation;
or if the difference between the current course and the expected course is larger than or equal to the allowable course variation, correcting the expected course according to the current steering speed of the ship.
Repeating the steps S4 to S6 periodically or in real time until the track switching segment is completed, i.e. switching to the next track segment for tracking.
In a specific application, the above steps S4 to S6 are repeated until the tracking is switched to the next track segment, and the steps S2 to S6 are repeated when the tracking is performed on the next track segment until the end point is reached.
In this embodiment, automatic tracking of the ship is realized according to the ship performance on the basis of obtaining a track point (for example, an inflection point in the track).
The method of the embodiment fully combines experience in actual ship steering operation, accurately controls the set course of the ship, and calculates a reasonable steering distance by considering the inertia of the ship and the steering engine operation time.
In addition, in the embodiment, linear tracking and steering tracking are not divided, namely the linear tracking and the steering tracking are processed in a unified manner, so that complicated logic judgment is omitted, and the problem of poor tracking effect in the yaw process in the steering process is solved.
Fig. 2 to fig. 4 are schematic diagrams illustrating a flow of a method for implementing automatic tracking of a ship according to an embodiment of the present invention; the method of this embodiment can be explained as follows.
201. The preparation work before the ship starts when the method of fig. 1 is executed, track points after the course planning are obtained, the first track point and the second track point are set as a first track segment, and the calculation of the advance steering distance and the steering rate is performed once.
In this embodiment, the course planning may be understood as a ship path planning route, and the course point may be a path point of the ship path planning route, or alternatively, the course point may be a path inflection point on the ship path planning route.
Usually, the distance between adjacent track points is set according to actual needs.
202. Basic parameters of the ship, such as ship length, ship width, ship gyration index K, ship tracking index T and the like are obtained.
203. And acquiring the current position, the current course, the course of the current track segment and the expected course of the next track segment of the ship.
204. Judging whether the current position reaches the end point, if so, ending, otherwise, continuing;
205. and judging whether the current position reaches the steering starting position of the steering starting distance, and if so, switching to the next track segment.
The steering starting position is a starting point of a steering distance, and the steering distance is the distance from the steering starting point to the end point of the track section.
In this embodiment, the track is a multi-segment line, and the next track segment is the next track segment of the current track segment of the ship. The switch means that the vessel will calculate the heading according to the next track segment.
206. Calculating an expected course at the current position of the ship;
and correcting the calculated expected course in real time according to the steering speed according to the real-time operation parameters of the ship.
In this embodiment, the desired heading is the heading required by the vessel for tracking navigation purposes.
The expected course of the ship may be too different from the current course of the ship, and the ship cannot be steered to the expected course at one time in actual ship operation. The difference (desired heading-actual heading) is therefore limited to the steering rate.
207. Comparing the difference between the actual course of the ship and the direction of the current track section, if the difference is smaller than a certain value, calculating the position of a steering starting point and the steering speed for one time, and preparing for the next steering point in advance;
for example, the turning point is a track point, and may also be an inflection point, which is a connection point of a track segment.
208. And according to the corrected expected heading and the set sailing speed, sailing until reaching the terminal.
All track segments in this embodiment are straight line segments.
In order to better understand the content of the foregoing steps, the following description is provided for the content of some steps:
the following is described with respect to the track point, track segment, ahead steering distance, steering rate, and the like after obtaining the course plan in step 201:
1) obtaining initial track points and selecting current track segment
A route planning route is obtained through an intelligent algorithm (such as an a algorithm), route points are further screened from the route planning route, and a track section MN formed by the obtained first route point M and the obtained second route point N is set as a first track section of the ship for tracking navigation, as shown in fig. 3.
In fig. 3, M, N, O, P is a track point; the segments MN, NO and OP are track segments; point N, O is the steering point, indicating that the vessel needs to be steered to that point; if the ship is positioned between the segments MN, the next track segment of the ship is NO.
2) Calculating an expected heading
2-1, setting the current position of the ship as O (x)0,y0)；
2-2, a track section MN linear equation: ax + By + C is 0 formula one;
passing the current position (x) of the vessel0,y0) Straight line equation with point perpendicular to MN: (y-y)0)÷(x-x0) B ÷ a formula two;
the simultaneous formula I and the formula II solve the problem that the foot drop is:
xd＝(B2x0-A*By0-A*C)÷(A2+B2)
yd＝(-A*Bx0+A2y0-B*C)÷(A2+B2)
2-3, calculating the current position O (x) of the ship0,y0) Distance d to track segment MN
2-4, calculating the distance d from the tracking point to the foot by using the pythagorean theorem1
Note: and Lpp is the ship length of the ship, and d is the distance from the current position of the ship to the track section MN.
2-5, current track segment direction CMN
CMN＝atan2(xN-xM,yN-yM)
2-6, calculating a tracking point T (x)los,ylos) Position of
xlos＝xd+d1sin(CMN)
ylos＝yd+d1cos(CMN)
2-7, judging the tracking point T (x)los,ylos) If the MT + NT is equal to MN, then the MT + NT is not equal to MN, and the MT is determined to be closer to M, N.
2-8, calculating the expected heading
Note: when x islos-x0<0 and ykos-y0When the value is more than or equal to 0, a is 450; otherwise a is 90.
3) Considering the stability problem of the ship during tracking, the required correction is carried out on the expected heading output in the step 2), and the rudder angle and the steady-state steering speed have the following relationship:
r＝Kδ
wherein r is the steering rate, K is the turning index of the ship, and delta is the rudder angle. Meanwhile, because of the rudder angle limitation, the maximum steering speed of the ship is determined by the maximum rudder angle allowed by the ship, the maximum rudder angle of the ship is usually between 25 and 35 degrees, and after the K value of the ship is obtained, the maximum steering speed of the ship can be determined:
rmax＝Kδmax
according to the experience in the actual steering operation of the ship, when the steering angle is large, a steering person wants to use a larger steering speed to shorten the steering time, and at the moment, the steering engine may be fully steered to achieve a larger steering speed. When the steering angle is small, the steering operator may wish to use a small steering speed to accurately control the vessel to the set heading.
From the perspective of steering engine use, in order to reduce the wear of the steering engine, it is desirable that the steering engine can operate smoothly, avoiding the occurrence of severe steering behavior. From this perspective, it is also desirable to use a small steering speed when the steering angle is small, to reduce the amount of strenuous steering of the steering engine. As shown in fig. 4, the left side of fig. 4 is a schematic diagram of the effect of using the method of the present invention, and the right side of fig. 4 is a schematic diagram of the effect of using the prior art solution.
For this reason, for steering control in the tracking of the ship, in a non-emergency situation, the steering rate may be set by the following formula:
rd＝αrmax
α is steering coefficient, which can be adjusted according to the situation in practical application, and when an emergency occurs, the steering speed can be set to rmaxα can be found by the following table query:
the steering angle in the following table is the difference between the current heading and the desired heading of the vessel.
| Steering angle (degree) | Steering speed coefficient (α) |
| <20 | 0.1 |
| 20～30 | 0.2 |
| 30～40 | 0.3 |
| 40～50 | 0.4 |
| 50～60 | 0.5 |
| 60～70 | 0.6 |
| 70～80 | 0.7 |
| 80～90 | 0.8 |
| 90～100 | 0.9 |
| >100 | 1 |
4) The ship can smoothly perform steering operation because necessary correction is made on the output of the expected heading in the step 3).
Further, in order to ensure that overshoot does not occur during tracking steering of the ship and to take account of the large inertia characteristic of the ship, it is necessary to advance the steering operation when the turning point is reached. Therefore, it is important to determine the steering timing.
A1, judging whether the next track segment exists, if not, indicating that the current track segment is the last track segment, and not considering the steering problem.
And A2, if the next track segment exists, calculating the difference value between the current track segment and the next track segment, and obtaining the α steering coefficient by looking up a table.
a) Calculating the difference of track directions
Let M (x)AM,yM),N(xBN,yN),O(xO,yCO)；
Modulus of the vector MN:
modulus of vector NO:
vector product of vectors MN, NO:
b) angle between two track sections
c) Assigning a steering coefficient according to Cdifα steering coefficients are obtained by table look-up.
A3, calculating the steering advance distance, i.e., the steering distance start position, in consideration of the steering advance:
wherein v is the speed of the ship, T is the ship tracking index, K is the ship turning index, T is the steering time (which is a constant), and deltamaxThe maximum rudder angle allowed by the ship steering engine.
Therefore, when the ship tracks to the last track section and is a certain distance away from the terminal point, the end of the current tracking navigation of the ship is judged.
According to the embodiment of the invention, the experience of actual ship operation is fully used for reference, the large steering speed can be adopted for a large steering angle, and the small steering speed is adopted for a small steering angle, so that the ship can run more stably.
The invention can guide the ship to quickly return to the navigation line when the ship deviates from the navigation line.
The invention fully considers the maneuverability of the ship and combines with the track point to calculate the related parameters (such as steering speed and reversing distance), thereby greatly reducing the violent operation of the ship.
By correcting for the desired heading, the tracking steering problem is solved using only a linear tracking strategy.
According to another aspect of the present invention, an apparatus for implementing automatic tracking of a ship is further provided, which includes a memory, a processor;
the memory stores a computer program, and the processor executes the computer program stored in the memory, which is specifically used for executing the method for realizing the automatic tracking of the ship in any method embodiment.
The device for realizing the automatic tracking of the ship is positioned in the ship and used for automatically tracking the navigation of the ship. The scheme of the embodiment of the invention fully refers to the experience of actual ship operation, can realize that a large steering angle adopts a large steering speed, and a small steering angle adopts a small steering speed, so that the ship can run more stably. In particular, the ship can be quickly and smoothly returned to the original track in the yawing state.
The scheme fully considers the maneuverability of the ship, and calculates related parameters (such as steering speed and reversing distance) by combining with the track point, so that violent operation on the ship is greatly reduced.
The above description of the embodiments of the present invention is provided for the purpose of illustrating the technical lines and features of the present invention and is provided for the purpose of enabling those skilled in the art to understand the contents of the present invention and to implement the present invention, but the present invention is not limited to the above specific embodiments. It is intended that all such changes and modifications as fall within the scope of the appended claims be embraced therein.
Claims (10)
1. A method for realizing automatic tracking of a ship is characterized by comprising the following steps:
s1, selecting track points in the ship path planning route aiming at the running ship, and sequentially forming track sections according to the selected track points;
s2, determining the information of the track section to which the current position of the ship belongs and the information of the adjacent next track section according to the current position of the ship;
s3, acquiring the steering speed of the ship to the next track section and the steering starting distance of the ship for steering the next track section according to the basic information and the operation parameters of the ship;
s4, judging whether the distance from the current position of the ship to the current track section end point is smaller than the steering starting distance;
s5, if the current position of the ship is less than or equal to the current track section, calculating the expected course of the ship at the current position according to the current position of the ship and the current track section;
s6, acquiring the current course of the ship, judging whether the difference value between the current course and the expected course is smaller than the allowable course variation, if so, the corrected expected course is the expected course obtained in the step S5;
repeating the steps S4 to S6 until the tracking is switched to the next track segment, and repeating the steps S2 to S6 until the operation reaches the end.
2. The method according to claim 1, wherein the step S4 includes: and if the distance from the current position of the ship to the current track section end point is judged to be greater than the steering starting distance, continuing tracking according to the current track section.
3. The method according to claim 1, wherein the step S6 further comprises:
if the difference between the current course and the expected course is larger than or equal to the allowable course variation, correcting the expected course to ensure that the corrected expected course is equal to the current course of the ship plus or minus the preset allowable course variation;
alternatively, the first and second electrodes may be,
and if the difference value between the current course and the expected course is larger than or equal to the allowable course variation, correcting the expected course according to the current steering speed of the ship.
4. The method according to claim 1, wherein the step S2 further comprises:
judging whether the track section to which the current position of the ship belongs is the last track section or not;
if yes, the steps S3 and S6 are not carried out until the ship sails to the end point of the current track section, and then the operation is finished.
5. The method of claim 1,
the basic information of the ship comprises one or more of the following information:
the ship length and the ship width of the ship, the ship turning index K, the ship tracking index T, the steering time T and the maximum steering angle information of a ship steering engine;
the operating parameters of the vessel include: the current position of the ship, the current running speed, the current steering rate of the ship and the current rudder angle value of the ship.
6. The method according to claim 1, wherein the step S5 includes:
s51, if the current position of the ship is as follows: o (x)0，y0) The current track section is MN, M (x)M，yM)、N(xN，yN) Tracking point los (x)los，ylos) And a vertical foot (x) from the current position of the ship to the straight line of the current track sectiond，yd) Obtaining the expected course according to the following formula I
The formula I is as follows:
wherein a is a preset constant;
xd＝(B2x0-A*By0-A*C)÷(A2+B2)；
yd＝(-A*Bx0+A2y0-B*C)÷(A2+B2)；
lpp is the ship length of the ship, d is the distance from the current position of the ship to the track section MN,
and 0 is the standard linear equation of the straight line where the current track section is located, and A, B, C in the formula corresponds to the coefficients in the standard linear equation one By one.
7. The method of claim 6, wherein x islos-x0< 0 and ylos-y0When the value is more than or equal to 0, a is 450;
except that the above-mentioned numerical value of a-450 corresponds to the condition, a takes 90.
8. The method according to claim 5, wherein the step S3 includes:
s31, obtaining the steering rate according to a formula II:
the formula II is as follows: r is K δ;
wherein r is a steering rate, K is a turning index of the ship, and delta is a current rudder angle value of the ship;
alternatively, the first and second electrodes may be,
s31, acquiring the steering rate according to a formula III;
the formula III is as follows: r isd＝αrmax＝α*Kδmax
α is a steering rate coefficient, delta, which varies according to the steering anglemaxThe allowable maximum rudder angle of the ship steering engine is K, and the turning index of the ship is K.
9. The method according to claim 6, wherein the step S3 includes:
s33, obtaining the steering initial distance D according to the following formulaminturnThe starting position of the steering starting distance is a steering starting position;
wherein: v is the current running speed of the ship, T is the ship tracking index, K is the ship turning index, T is the steering time, deltamaxThe maximum rudder angle allowed by the ship steering engine;
let M (x)M，yM)，N(xN，yN)，O(xO，yO)；
Modulus of the vector MN:
modulus of vector NO:
vector product of vectors MN, NO:
10. the device for realizing the automatic tracking of the ship is characterized by comprising a memory and a processor;
the memory stores a computer program, and the processor executes the computer program stored in the memory, and specifically executes the method for implementing automatic tracking of a ship according to any one of claims 1 to 9.
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| CN111538339A (en) * | 2020-05-29 | 2020-08-14 | 智慧航海（青岛）科技有限公司 | Ship track control method and device |
| CN114970140A (en) * | 2022-05-24 | 2022-08-30 | 中国人民解放军海军潜艇学院 | Ship maneuvering modeling and simulation method applied to situation deduction |
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| CN111007879B (en) | 2023-06-30 |
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