Self-adaptive great circle route guidance and control method based on great circle correction

Abstract

The invention relates to a self-adaptive great circle route guidance and control method based on great circle correction, which belongs to the field of ship track tracking and comprises the following steps of: establishing a ship motion nonlinear mathematical model; determining the course of the large circle based on the correction of the large circle; determining the self-adaptive foresight distance of the ship; based on the great circle course and the self-adaptive foresight distance, designing a guidance strategy of the great circle course, and obtaining an expected course of the ship sailing along the great circle course; based on the ship motion nonlinear mathematical model, a final controller is designed through a third-order closed-loop gain forming algorithm and used for controlling the ship to track the expected course, and the ship is made to sail along the large circle route. Through simulation verification, the ship can be effectively controlled to sail in a large arc line, and the sailing efficiency is improved.

Description

Technical Field

[0001] The invention belongs to the field of ship track tracking and relates to an adaptive great circle route guidance and control method based on great circle correction. Background Art

[0002] Currently, ship track tracking is mostly implemented based on traditional LOS algorithms, which utilize the heading of the rhumb line between two points. Therefore, most track tracking involves tracking straight line segments. However, for long-distance voyages at high latitudes, great circle navigation is commonly used. This method can significantly reduce voyage time, so how to enable ships to navigate according to great circle routes is of great practical significance for the practical application of ship navigation and track control.

[0003] Currently, one approach involves breaking down the Great Circle route into multiple connected straight lines, a method known as approximating the Great Circle method. While this method meets navigational needs, it is still fundamentally based on the principle of rhumb line navigation and is relatively complex to operate. Therefore, enabling ships to navigate directly along Great Circle routes in high-latitude regions is crucial for advancing navigation practice and research in navigation technology. Summary of the Invention In order to solve the above problems, the technical solution adopted by the present invention is: an adaptive great circle route guidance and control method based on great circle correction, comprising the following steps: Establish a nonlinear mathematical model of ship motion; Determine the great circle heading based on the great circle correction; Determine the adaptive foresight distance of the ship; Based on the great circle heading and adaptive foresight distance, a great circle route guidance strategy is designed to obtain the desired heading of the ship along the great circle route. Based on the nonlinear mathematical model of ship motion, a third-order closed-loop gain shaping algorithm is used to design the final controller to control the ship to track the desired heading and sail along the great circle route.

[0004] Furthermore: the formula for the great circle correction is as follows: Assume that the starting coordinates of the ship are , the end point coordinates are , use the great circle correction to find the starting point coordinates The formula for calculating the great circle correction is: (10) in, is the starting latitude, is the latitude of the arrival point, is the longitude of the starting point, is the longitude of the arrival point, is the great circle correction.

[0005] Furthermore, the process of determining the great circle heading based on the great circle correction is as follows: Rhumb line heading between two points The calculation method is: (11) in, is the starting latitude, is the latitude of the arrival point, is the longitude of the starting point, is the longitude of the arrival point, is the heading of the rhumb line between two points.

[0006] Great circle heading for: (12) in, is the great circle heading between the two points, is the heading of the rhumb line between the two points, is the great circle correction.

[0007] Furthermore, the formula for determining the adaptive forward-looking distance of a ship is as follows: (13) in, is the adaptive foresight distance, To set the base value of foresight distance, is the convergence rate, The distance off course.

[0008] Furthermore, the process of designing a guidance strategy for a great circle route based on the great circle heading and the adaptive foresight distance to obtain the desired heading of a ship sailing along the great circle route is as follows: Assume the current ship position is , then the current ship position and the starting point The great circle distance is ; Determine the great circle heading between the preceding ship's position and the starting point ; Take a point on the route , connect to the current ship position and , let its length be , let the starting point Arrive The distance is , which forms a spherical narrow triangle ,but: (16) in: Two large arcs and The angle between for and Great circle heading between for and Great circle heading between; It is known that in a narrow spherical triangle, the two sides are approximately equal, so we can get ; Determine the current position of the ship To a point on the route distance ; exist Add the foresight distance to the , let it be Right now: (18) Where, for arrive The distance of the point, for arrive The distance of the point, is the forward sight distance; The target point The coordinates of the point are: (19) (20) (twenty one) in, is the latitude of the starting point; is the longitude of the starting point; for point to T The longitude difference of a point; for The latitude of the point; yes The longitude of the point; for on great circle heading; The expected heading for: (twenty two) Where: is the latitude of the current ship position; is the longitude of the current ship's position; is the latitude of the target point; is the longitude of the target; is the rhumb line heading between the target point and the current ship position; The correction value between the target point and the current ship position is as follows: The present application discloses an adaptive great circle route guidance and control method based on great circle correction, which overcomes the traditional LOS algorithm method that can only use the rhumb line heading method, uses the correction value to obtain the great circle heading for navigation on the great circle route, and further overcomes the problem of slow heading adjustment caused by fixed foresight distance, designs an adaptive foresight distance, and effectively improves the route tracking efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0010] Figure 1 A flow chart of the method of this application; Figure 2 Find the great circle heading chart for the great circle correction; Figure 3 It is an adaptive effect diagram; Figure 4 This is the principle diagram of great circle route guidance; Figure 5 It is a schematic diagram of a narrow triangle; Figure 6 This is a comparison chart of the path tracking method; Figure 7 This is a comparison chart of heading changes for this method; Figure 8 This is a comparison chart of the rudder angle changes of this method; Figure 9 This is a comparison chart of the track error of this method; DETAILED DESCRIPTION It should be noted that, unless there is any conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0011] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is in no way intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0012] Figure 1 A flow chart of the method of this application; An adaptive great circle flight guidance and control method based on great circle correction. S1: Establish a nonlinear mathematical model of ship motion; it is a nonlinear Nomoto mathematical model; S2: Determine the great circle heading based on the great circle correction; S3: Determine the adaptive forward sight distance of the ship; S4: Based on the great circle heading and the adaptive foresight distance, a guidance strategy for the great circle route is designed to obtain the desired heading of the ship along the great circle route; S5: Based on the nonlinear mathematical model of ship motion, a third-order closed-loop gain shaping algorithm is used to design the final controller to control the ship to track the desired course and sail along the great circle route; Steps S1 / S2 / S3 / S4 / S5 are performed sequentially; This application is implemented using MATLAB software; Furthermore, the process of establishing the nonlinear Nomoto mathematical model of ship motion is as follows: When analyzing ship maneuvering, if only the drift speed is concerned, and bow angular velocity The linear equations corresponding to these two degrees of freedom for the ship are: (1) In this formula, Represents the rudder angle input, represent Taking the first derivative with respect to time, Respectively represent Take the first derivative with respect to time, the coefficient It is determined by the basic parameters of the ship. Formula (1) is converted into a simple equation describing the steering response to the bow roll, namely: (2) In this formula, Represents the rudder angle input, Indicates rudder angle input Taking the derivative with respect to time, Indicates the bow angular velocity Taking the second derivative with respect to time, All are manipulative indicators; Perform Laplace transform on Equation (2) and assume that the initial value Established, the following transfer function is obtained : (3) In this formula is the Laplace operator, represents the Laplace transform of the rudder angle input, represents the Laplace transform of the bow angular velocity, All are manipulative indicators; According to the relationship , and get the corresponding equation: (4) In formula (4), is the heading angle, is the Laplace operator, represents the Laplace transform of the rudder angle input, represents the Laplace transform of the heading angle, All are manipulative indicators; Simplify formula (4) and derive the following formula: (5) In the formula , is the Laplace operator, is the ship maneuverability index, and Equation (5) is written as the following differential equation (6) in, is the rudder angle, and Represents the heading angle Find the first and second derivatives with respect to time, is the ship maneuverability index.

[0013] Divide both sides of the equation (6) by have to: (7) in, is the rudder angle, and Represents the heading angle Find the first and second derivatives with respect to time, is the ship maneuverability index.

[0014] For some statically unstable ships, the second term on the left side of Equation (7) Need to be replaced by nonlinear terms Replace, and: (8) Thus, the nonlinear mathematical model of ship motion is established: (9) In formula (9): is the heading angle, is the rudder angle, and Represents the heading angle Find the first and second derivatives with respect to time, is the ship maneuverability index, is a nonlinear parameter.

[0015] Figure 2 The great circle correction is used to obtain the great circle heading chart; Furthermore, the process of determining the great circle heading based on the great circle correction is as follows: Calculate the great circle heading using the great circle correction: Assume that the starting coordinates of the ship are , the end point coordinates are , use the great circle correction to find the starting point coordinates The initial great circle heading at , the formula for calculating the great circle heading is: (10) in, is the starting latitude, is the latitude of the arrival point, is the longitude of the starting point, is the longitude of the arrival point, is the great circle correction; Rhumb line heading between two points The calculation method is: (11) in, is the starting latitude, is the latitude of the arrival point, is the longitude of the starting point, is the longitude of the arrival point, is the heading of the rhumb line between two points.

[0016] Great circle heading for: (12) in, is the great circle heading between the two points, is the heading of the rhumb line between the two points, is the great circle correction.

[0017] Figure 3 Adaptive renderings; The specific formula for determining the adaptive forward-looking distance of a ship is as follows: (13) in, is the adaptive foresight distance, To set the base value of foresight distance, is the convergence rate, The distance off course.

[0018] Figure 4 This is the principle diagram of great circle route guidance; Figure 5 It is a schematic diagram of a narrow triangle; Furthermore, the process of obtaining the great circle heading and the adaptive foresight distance based on the great circle correction and designing the guidance strategy for the great circle route so that the ship can navigate along the great circle route according to the desired heading is as follows: Assume the current ship position is The current ship position and the starting point The great circle distance is : (14) in, is the latitude of the current ship position; is the longitude of the current ship's position; is the difference in longitude between two points; is the great circle distance from the starting point to the current ship position.

[0019] Great circle heading between the current ship position and the starting point for: (15) in, is the latitude of the current ship position; is the longitude of the current ship's position; is the latitude of the starting point; is the longitude of the starting point; is the rhumb line heading between the starting point and the current ship position; It is the correction value between the starting point and the current ship position.

[0020] At this time, take a point on the route , connect to the current ship position and , let its length be , let the starting point Arrive The distance is . This forms a spherical narrow triangle ,but: (16) in Two large arcs and The angle between for and Great circle heading between for and Great circle heading between.

[0021] It is known that in a narrow spherical triangle, the difference between its two sides is very small, that is, the two sides are approximately equal, so we can get .

[0022] The current position of the ship To a point on the route distance for: (17) Where: for arrive distance; for arrive distance of the points; for to distance; Two large arcs and The angle between them.

[0023] exist Add the foresight distance to the , let it be Right now: (18) Where, for arrive The distance between points, for arrive The distance of the point, is the forward sight distance.

[0024] The target point The coordinates of the point can be obtained: (19) (20) (twenty one) in, is the latitude of the starting point; is the longitude of the starting point; for point to T The longitude difference of a point; for The latitude of the point; yes The longitude of the point; for Great circle heading The expected heading for: (twenty two) Where: is the latitude of the current ship position; is the longitude of the current ship's position; is the latitude of the target point; is the longitude of the target; is the rhumb line heading between the target point and the current ship position; It is the correction value between the target point and the current ship position.

[0025] When calculating the great circle heading, the longitude and latitude between the starting point and the arrival point are always used. When the ship is sailing at a short distance, the ship can stably track the planned route. When the longitude difference is 10°, errors begin to appear, causing the ship to be unable to stably track the planned route. Therefore, this paper proposes that when the longitude difference is 10°, the starting point should be re-selected on the route. In the above method, the coordinates involved are the tracking target. Since the target point must be on the intended route if the ship is to track its intended route, when the longitude difference is 10°, the target point is selected as the new starting point. The great circle heading between the new starting point and the destination point is recalculated. When the longitude difference is 10°, a new starting point is selected, and this process is repeated until the ship reaches the destination. This eliminates the error caused by the large difference between the two points, and the ship can continue to track the desired course to navigate along the great circle route.

[0026] Furthermore, the process of designing the final controller using a third-order closed-loop gain shaping algorithm based on the nonlinear mathematical model of ship motion is as follows: Assume that the bandwidth frequency of the closed-loop system of the ship is , then the compensation sensitivity function of the ship heading keeping control system is That is, the closed-loop transfer function of the control system is shown in formula (23): (twenty three) The controller for: (twenty four) From formula (24), the controller is in the form of a typical PD controller connected in series with an oscillating link. Under the PD controller, a constant , the ship heading keeping control system will greatly reduce the adjustment time without changing the stability. Adding a positive constant to the proportional part of the PD link in Equation (24) will give the final controller in the form of Equation (25): (25) In order to verify the effectiveness of the method of the present invention, the following simulation experiment was conducted to simulate the navigation path of the Yu Kun ship from Honolulu (approximate position: 21.5°N, 157°W) to Vancouver (approximate position: 48.5°N, 124°W). The main parameters of the Yu Kun ship are as follows.

[0027] Table 1 Main design parameters of "Yukun"

[0028] During the simulation, the initial ship heading was set to 040° and the wind condition was set to level 6 on the Beaufort scale. In order to reduce the simulation time, the radius of the earth was reduced by 100 times. The proposed scheme was compared with the approximate great circle route. The simulation results are as follows: Figure 6 — Figure 9 shown.

[0029] Figure 6 This is a comparison chart of the path tracking method. Both the great circle route navigation strategy proposed by this method and the approximate great circle route can stably navigate along the planned route under winds of force 6 on the Beaufort scale. A great circle route is the shortest path between two points on the Earth's surface, while the approximate great circle route appears to be a great circle, but is essentially a rhumb line. While the rhumb line maintains a fixed heading, it is actually a spiral line that continuously deviates from the great circle, circling further on the sphere and therefore covering a longer distance. Therefore, this method is more convenient for navigation than the approximate great circle route.

[0030] Figure 7 The following is a comparison chart of the course changes of this method. It can be seen that the course adjustment of this method and the approximate great circle method is different when the initial course is set to 040°. In the simulation, the course of both the approximate great circle method and the great circle method designed in this paper is constantly changing during navigation. At the beginning of the simulation, the course is in the controller adjustment stage, and the changes are large. The method proposed in this paper and the approximate great circle method both involve coordinate transformation, and both are changed every 10° of longitude difference, so the course will have sudden changes. However, it is not difficult to see from the comparison chart that the great circle method involved in this paper has a much smaller heading change, making the ship more stable.

[0031] Figure 8 The following figure compares the rudder angle changes of the proposed method. The proposed method primarily adjusts the controller during the first 500 seconds, resulting in significant rudder angle changes. After approximately 500 seconds, the controller begins to steadily track the reference signal, and the rudder angle stabilizes. Both this method and the approximate great-circle method require shifting coordinate points every 10° of longitude, resulting in sudden changes in the rudder angle during navigation. However, as can be seen in the figure, the proposed control method exhibits smaller changes and greater stability, even when the coordinate points remain the same.

[0032] Figure 9 The variation of track error is further demonstrated in the figure. The maximum deviation distance of the method proposed in this paper is about 250 meters, while the maximum deviation distance of the approximate great circle method is 400 meters. This method greatly reduces the deviation distance, and the response time is relatively short, the variation is relatively stable, and there is no jitter like the approximate great circle method, which proves that this method is more stable.

[0033] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive great circle course guidance and control method based on great circle corrections, characterized by: The following steps are involved: Establish a nonlinear mathematical model of ship motion; Determine the great circle heading of the ship based on the great circle correction of the ship; Determine the adaptive foresight distance of the ship; Based on the great circle heading and adaptive foresight distance, a great circle route guidance strategy is designed to obtain the desired heading of the ship along the great circle route. Based on the nonlinear mathematical model of ship motion, a third-order closed-loop gain shaping algorithm is used to design the final controller to control the ship to track the desired heading and sail along the great circle route.

2. The method of adaptive great circle flight path guidance and control based on great circle correction according to claim 1, characterized in that: The formula for the great circle correction is as follows: Assume that the starting coordinates of the ship are , the end point coordinates are , use the great circle correction to find the starting point coordinates The formula for calculating the great circle correction is: (10) in, is the starting latitude, is the latitude of the arrival point, is the longitude of the starting point, is the longitude of the arrival point, is the great circle correction.

3. The adaptive great circle flight path guidance and control method based on great circle correction according to claim 1, characterized in that: The process of determining the great circle heading based on the great circle correction is as follows: Rhumb line heading between two points The calculation method is: (11) in, is the starting latitude, is the latitude of the arrival point, is the longitude of the starting point, is the longitude of the arrival point, is the heading of the rhumb line between two points. Great circle heading for: (12) in, is the great circle heading between the two points, is the heading of the rhumb line between the two points, is the great circle correction.

4. The method of adaptive great circle flight path guidance and control based on great circle correction according to claim 1, characterized in that: The formula for determining the adaptive foresight distance of a ship is as follows: (13) in, is the adaptive foresight distance, To set the base value of foresight distance, is the convergence rate, The distance off course.

5. The method of adaptive great circle flight path guidance and control based on great circle correction according to claim 1, characterized in that: The process of designing a guidance strategy for a great circle route based on the great circle heading and the adaptive foresight distance to obtain the desired heading of a ship sailing along the great circle route is as follows: Assume the current ship position is , then the current ship position and the starting point The great circle distance is ; Determine the great circle heading between the preceding ship's position and the starting point ; Take a point on the route , connect to the current ship position and , let its length be , let the starting point Arrive The distance is , which forms a spherical narrow triangle ,but: (16) in: Two large arcs and The angle between for and Great circle heading between for and Great circle heading between; It is known that in a narrow spherical triangle, the two sides are approximately equal, so we can get ; Determine the current position of the ship To a point on the route distance ; exist Add the foresight distance to the , let it be Right now: (18) Where, for arrive The distance of the point, for arrive The distance of the point, is the forward sight distance; The target point The coordinates of the point are: (19) (20) (21) in, is the latitude of the starting point; is the longitude of the starting point; for point to T The longitude difference of a point; for The latitude of the point; yes The longitude of the point; for on great circle heading; The expected heading for: (22) Where: is the latitude of the current ship position; is the longitude of the current ship's position; is the latitude of the target point; is the longitude of the target; is the rhumb line heading between the target point and the current ship position; It is the correction value between the target point and the current ship position.

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