A path planning method for autonomous formation of multiple tugboats to dock a target ship

Abstract

The application discloses a kind of multi-tug autonomous formation berthing target ship's path planning method, comprising S1: according to the preset berthing task issued, construct the single-ship berthing planning strategy of assisting tugboat;S2: define virtual guiding ship, and obtain the initial position coordinates of virtual guiding ship according to the ship position of multiple assisting tugboats, and based on single-ship berthing planning strategy, it is guided to be served to the ship;And based on virtual guiding ship, the formation path planning strategy of multiple assisting tugboats is constructed, to realize the path planning of multi-tug autonomous formation berthing target ship.Solved the current port tugboat operation mainly relies on manual experience operation, in the path planning of tugboat berthing target ship, especially in the process of multiple assisting tugboat collaborative work, cannot accurately and effectively satisfy the preset angle, speed, position and be served to the ship to realize the collaborative formation operation of assisting tugboat, cause the problem of low operation accuracy and efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ship path planning and berthing control, and particularly relates to a path planning method for multi-tug autonomous formation berthing of a target ship. BACKGROUND

[0002] In today's port throughput continues to climb, tug as an important auxiliary tool for port operations, but also shoulder the responsibility and pressure. Large ships maneuverability is poor, can not rely on its own ability to stop at the port, usually need to apply for tug assistance. Tug needs to be based on the requirements of the target ship for escort, pushing, towing and other services to control the attitude of the target ship, to avoid damage to personnel, ship, other ships, port equipment, etc. in the process of berthing.

[0003] The progress of science and technology has driven the shipbuilding industry to rapidly move towards intelligentization, and unmanned ships have been widely used in various application scenarios. Compared with traditional ships, maritime autonomous surface ships (MASS) exhibit more significant advantages in safety, economy, convenience, and environmental protection, and have broad research and application prospects. In addition, tugs have unique advantages in the development process of intelligentization, such as complete hydrological, meteorological and environmental information, strong port infrastructure support, efficient emergency response capability, and superior safety measures. These factors together lay a solid foundation for the development of unmanned tugs.

[0004] Current research on tugs mainly focuses on two directions: escort and auxiliary berthing. Escort refers to the tug following the target ship at a predetermined position until the target ship enters the berth, and most scholars consider this research as a path tracking problem of the escort position. Auxiliary berthing refers to the tug performing operations such as keeping the target ship's orientation, turning, U-turning, and changing speed to assist the target ship in executing turning and speed-changing decisions to help it enter the berth more safely and efficiently. In this research direction, the tug and the target ship are usually described as a coupled system, and the auxiliary berthing target is achieved through cooperative control methods. Future intelligent tug operations can cover the three stages of escort, alongside, and auxiliary operations. In this process, the tug first follows the target ship at the escort position, then chooses the appropriate opportunity to approach the target ship, and after the mooring is completed, it enters the auxiliary operation stage until the target ship safely enters the berth.

[0005] Currently, the research on the accompanying and assisting berthing operation has been widely concerned, however, the research on the alongside behavior is relatively less, and the current port tug operation mainly relies on manual experience operation, in the path planning of the tugboat for the berthing target ship, especially in the process of the cooperation of multiple assisting tugs, it is difficult to accurately and effectively satisfy the preset angle, speed and position to berth the served ship to realize the cooperative formation operation of the assisting tugs, resulting in low operation accuracy and efficiency, and in view of the current economic growth trend, the future port will have greater throughput, and the pressure of the tug operation will also increase. SUMMARY

[0006] The present application provides a path planning method for multiple tugs to autonomously form a formation to berth a target ship, so as to overcome the above technical problems.

[0007] In order to achieve the above purpose, the technical scheme of the present application is:

[0008] A path planning method for multiple tugs to autonomously form a formation to berth a target ship, specifically comprising the following steps:

[0009] S1: According to the preset berthing task issued, a single-ship berthing planning strategy of the assisting tug is constructed;

[0010] Specifically comprising the following steps:

[0011] S11: The berthing position control line of the served ship is defined and obtained based on the served ship;

[0012] S12: The direction vector of the assisting tug relative to the served ship in a static state is obtained, and the current expected heading of the assisting tug is obtained according to the berthing position control line;

[0013] S13: The current expected heading is taken as the relative motion heading, and the turning position vector of the assisting tug is obtained according to the current speed of the assisting tug;

[0014] And the berthing guide force of the served ship is obtained based on the turning position vector;

[0015] S14: The direction of the berthing guide force is taken as the expected heading of the assisting tug at the current time, and the expected heading at the next time is updated and obtained based on the constructed turning constraint;

[0016] S15: A speed gradient planning model of the assisting tug is constructed;

[0017] And based on the speed gradient planning model, the ship position of the assisting tug at the corresponding time is obtained according to the expected heading at the next time;

[0018] S2: The ship position, ship heading and ship speed of multiple assisting tugs are obtained;

[0019] The virtual guiding ship is defined, and initial position coordinates of the virtual guiding ship are obtained according to positions of the plurality of assisting tugboats, and the virtual guiding ship is guided to berth to the served ship based on a single-ship berthing planning strategy;

[0020] And a formation path planning strategy of the plurality of assisting tugboats is constructed based on the virtual guiding ship to realize path planning of the plurality of tugboats to autonomously berth to the target ship.

[0021] Further, the berthing position control line in S11 is a straight line where a resultant direction of a sailing speed vector and a berthing speed vector of the served ship TS is located;

[0022] And the vector expressions of the sailing speed vector and the berthing speed vector are

[0023]

[0024] In the formula: u ts represents a sailing speed of the TS; represents a heading of the TS; u ap represents a berthing target speed of the TS; θ ap represents a berthing target angle; v ts represents a sailing speed vector; v ap represents a berthing speed vector.

[0025] Further, S12 specifically includes the following steps:

[0026] S120: defining a direction vector of the berthing position control line as v ls , a direction vector of a side angle of the assisting tugboat relative to the served ship in a static state as v to , and recording v ls as (x ls , y ls ), and recording v to as (x to , y to );

[0027] S121: obtaining a vector included angle θ1 between v to and v ls , and the obtaining formula is

[0028]

[0029] v ls ·v to =x ls x to +y ls y to (5)

[0030]

[0031]

[0032] wherein ||v to represents the modulus of v to ; ||v ls represents the modulus of v ls ;

[0033] S122: obtaining the rotation angle θ r of the served ship TS relative to the direction vector of the bow angle of the assisting tug OS according to step S121

[0034]

[0035] wherein LC represents the berthing position control line;

[0036] S123: obtaining the rotation matrix R(θ r ) according to the rotation angle θ r , and the expression is

[0037]

[0038] and obtaining the current expected heading of the assisting tug according to the rotation matrix R(θ r );

[0039] and the expression of the current expected heading vector of the assisting tug is

[0040]

[0041] wherein v co represents the current expected heading of the assisting tug.

[0042] Further, the S13 specifically comprises the following steps:

[0043] S131: taking the current expected heading vector as the relative motion heading, and the expression is

[0044] v co = v to - v ts (11)

[0045] S132: obtaining the center o of the circle according to the sailing speed vector v ts and the position p os of the assisting tug, and defining and obtaining the relative motion vector circle O r with the sailing speed u os of the assisting tug as the radius;

[0046] and the center of the relative motion vector circle O r is obtained by the formula

[0047] o=p os -v ts (12)

[0048] Assuming the tugboat's position p will assist it os As v co The starting point is the relative motion vector circle O. r Any point on v co The undetermined endpoint is determined, and v is confirmed according to the preset vector direction vector d. co The end point;

[0049] Let the preset vector direction vector be d = (a, b), where a and b represent the horizontal and vertical components of the vector direction vector d, respectively. Then, its formula is:

[0050]

[0051] S133: Obtain the unknown parameter equation of the current desired heading vector direction ray based on the preset vector direction vector;

[0052] And the unknown parameter equation of the direction ray P(n) of the current desired heading vector is:

[0053] P(n)=P os +n·d=(x os +an,y os +bn) (14)

[0054] In the formula: n represents the parameter to be solved and n≥0;

[0055] S134: Define the relative motion vector circle O r The standard equation is

[0056] (xh) 2 +(yk) 2 =r 2 (15)

[0057] In the formula: h,k represent the coordinates of the center of the relative motion vector circle; r represents the radius;

[0058] Substituting formula (14) into (15) yields the following result:

[0059] (x os +an-h) 2 +(y os +bn-k) 2 =r 2 (16)

[0060] Rewrite (16) as a quadratic equation in n as follows:

[0061] (a2 +b 2 )n 2 +2(a(x os -h)+b(y os -k))n+((x os -h) 2 +(y os -k) 2 -r 2 )=0(17)

[0062] Simplify (17) to obtain a simplified formula

[0063] A=a 2 +b 2 (18)

[0064] B=2(a(x os -h)+b(y os -k))(19)

[0065] C=(x os -h) 2 +(y os -k) 2 -r 2 (20)

[0066] An 2 +Bn+C=0(21)

[0067] S135: Quadratic equation root is performed on the simplified formula to obtain a parameter solution;

[0068] The expression of the quadratic equation root is

[0069]

[0070] According to the parameter solution, a final current expected heading vector direction ray is confirmed;

[0071] S136: Based on the final current expected heading vector direction ray, a turning bearing vector of the assisting tugboat is obtained according to a current speed of the assisting tugboat, and the expression is

[0072] v co =P(n)-p os (23)

[0073] v to =v co +v ts (24)

[0074] In the formula, v to represents the turning bearing vector;

[0075] S137: The berthing guidance force of the vessel being served is obtained based on the steering azimuth vector, and the berthing guidance force of the vessel being served is...

[0076] F m =k m ·v to (25)

[0077] In the formula: F m Indicates berthing guidance force; k m This represents the position-guided gravity gain coefficient.

[0078] Furthermore, the expression for the steering constraint constructed in S14 is:

[0079]

[0080] In the formula: F represents m The angle of the hull relative to the OS of the assisting tugboat, with the value being positive on the starboard side and negative on the port side; θ c Δθ represents the steering constraint angle; Δθ represents the steering angle. This indicates the heading of the tugboat OS at time t; This indicates the heading of the tugboat OS at time t+1.

[0081] Furthermore, S15 specifically includes the following steps:

[0082] S151: Construct a velocity gradient programming model for the assisted tugboat, and the expression for the velocity gradient programming model is as follows:

[0083]

[0084] In the formula: u m Indicates maximum speed; d (os,ts) Indicates the distance between the assisting tugboat and the vessel being served; d c Indicates the distance threshold; u t Indicates the desired course; This represents the speed of the assisting tugboat OS at time t; u c Indicates the speed change threshold; Δu represents the speed change value; This indicates the speed of the tugboat OS at time t+1;

[0085] S152: Based on the velocity gradient programming model, the position of the assisting tugboat at the corresponding moment is obtained according to the expected heading at the next moment. Its expression is as follows:

[0086]

[0087] In the formula: Indicates the position of the assisting tugboat OS at time t; represents the position of the assisting tugboat OS at t+1 time.

[0088] Further, the S2 specifically comprises the following steps

[0089] S21: obtaining the ship position, ship heading and ship speed of the plurality of assisting tugboats;

[0090] defining a virtual guiding ship and obtaining the initial position coordinates of the virtual guiding ship according to the ship positions of the plurality of assisting tugboats;

[0091] and the formula for obtaining the initial position coordinates of the virtual guiding ship is

[0092]

[0093] wherein x i ,y i represents the position coordinates of each assisting tugboat; p c represents the coordinate center of the plurality of assisting tugboats, k sd represents the guiding coefficient; p v represents the initial position coordinates of the virtual guiding ship;

[0094] and guiding it to berth to the served ship based on the single-ship berthing planning strategy to obtain a virtual berthing point;

[0095] S22: constructing a formation path planning strategy for the plurality of assisting tugboats based on the virtual guiding ship to achieve path planning of the plurality of assisting tugboats to autonomously form a formation to berth to the target ship;

[0096] and the formation path planning strategy for the plurality of assisting tugboats specifically comprises the following steps:

[0097] S221: constructing a formation formation planning principle to achieve coordinated formation of the plurality of assisting tugboats;

[0098] and the formation formation planning principle is specifically

[0099] defining a berthing reference line including a plurality of berthing points based on the virtual berthing point, and sequentially coding each berthing point to obtain a berthing point sequence table from near to far in the direction of the bow to the stern of the served ship;

[0100] and the berthing reference line is a straight line passing through the virtual berthing point and parallel to the ship side of the served ship;

[0101] S222: obtaining the real-time positions of the plurality of assisting tugboats to obtain the relative distances of each assisting tugboat with respect to the berthing reference line;

[0102] and arranging the relative distances in descending order to obtain a real-time distance sequence table;

[0103] According to the real-time distance sequence table, the berthing point positions of each assisting tug are allocated;

[0104] The rules for allocating the berthing point positions are as follows:

[0105] Based on the berthing point position sequence from near to far in the berthing point sequence table, the berthing positions of the tug in the real-time distance sequence table are sequentially allocated to the berthing positions of the tugs, i.e., the berthing points;

[0106] S223: After obtaining the allocated positions, the direction vectors of each assisting tug relative to the corresponding berthing point are obtained to obtain the position guiding force of the assisting tug;

[0107] And the expression of the position guiding force is

[0108] F p =k p ·v p (34)

[0109] In the formula, k p represents the position guiding gain coefficient; v p represents the direction vector of the assisting tug relative to the corresponding berthing point; and F p represents the position guiding force.

[0110] Based on the position guiding force, the formation dynamic guiding force is obtained according to the position distance between each assisting tug and the corresponding berthing point, and the expression of the formation dynamic guiding force is

[0111]

[0112] In the formula, F mp represents the formation dynamic guiding force; represents the position distance between the assisting tug and the corresponding berthing point, and i represents the number of the assisting tug; j represents the number of the berthing point; k dm represents the formation guiding force dynamic guiding coefficient; k dp represents the formation position guiding force dynamic guiding coefficient.

[0113] S224: A repulsive force dynamic gain function between any two assisting tugs in the assisting tug formation is constructed.

[0114] And the expression of the repulsive force dynamic gain function is

[0115]

[0116] vec r =vec1-vec2(38)

[0117] In the formula, vec rrepresents the relative motion velocity vector between any two assisting tugboats; θ represents the included angle between the line connecting any two assisting tugboats and vec r ; represents the distance between two ships; d s represents the safety distance boundary; represents a direction vector of one assisting tugboat pointing to another assisting tugboat; F s represents the safety guiding force; k v represents the relative motion repulsion force factor; vec1, vec2 represent the velocity vectors of two assisting tugboats;

[0118] S225: Obtain the formation berthing guiding force according to the formation dynamic guiding force and the repulsion dynamic gain function, and the expression of the formation berthing guiding force is

[0119] F t =k mp ·F mp +k s ·F s (39)

[0120] wherein: k mp represents the dynamic guiding gain coefficient; k s represents the safety guiding gain coefficient; F ι represents the formation planning resultant force, i.e., the formation berthing guiding force; v i represents the velocity vector of the ith assisting tugboat OS i ;

[0121] Based on the formation berthing guiding force, the position update of the assisting tugboat formation can be obtained according to formula (26)

[0122]

[0123] and the position update of the assisting tugboat formation is realized according to formula (40) combined with formula (27);

[0124] S226: Obtain the distance between the expected position of each assisting tugboat in the assisting tugboat formation and the current position of the assisting tugboat, to obtain the distance d h between the two ships of each assisting tugboat and the served ship, and the expression is

[0125]

[0126] wherein: d(p i , p os ) represents the distance between the expected position of each assisting tugboat and the current position of the assisting tugboat; p i represents the ith assisting tugboat; represents the flank angle of the ith assisting tugboat;

[0127] And according to formula (41) to formula (28) is rewritten, can obtain

[0128]

[0129] According to formula (42) in combination with formula (29) to (30) realize the speed update of the assisting tug formation, and then realize the path planning of the target ship of the multi-tug autonomous formation.

[0130] Beneficial effects: the present application provides a kind of path planning method of multi-tug autonomous formation docking target ship, by constructing the single ship docking planning strategy of assisting tug, and according to the preset docking task issued, realize the path planning task of single ship docking, by defining virtual guiding ship, and according to the initial position coordinates of virtual guiding ship obtained by the ship position of multiple assisting tugs, and based on single ship docking planning strategy, it is guided to be docked to the served ship, and by introducing the dynamic guiding force and repulsive force dynamic gain function of formation, the formation path planning strategy of multiple assisting tugs is constructed, to realize the path planning of the target ship of multi-tug autonomous formation docking, solve the current port tug operation mainly relies on artificial experience operation, in the path planning of tug docking target ship, especially in the process of multiple assisting tugs collaborative work, cannot accurately and effectively satisfy the preset angle, speed, position and be served ship to realize the cooperative operation of assisting tug cooperative formation, cause the problem of low operation precision and efficiency, greatly reduce the operation pressure and difficulty of tug, and reduce manpower investment, improve the intelligent degree and operation precision of the path planning of the target ship of multi-tug autonomous formation docking. BRIEF DESCRIPTION OF DRAWINGS

[0131] In order to more clearly illustrate the technical scheme in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0132] Figure 1 Flow chart of the path planning method of the target ship of multi-tug autonomous formation docking of the present application;

[0133] Figure 2 Definition principle diagram of docking position control line in the present embodiment;

[0134] Figure 3 Principle diagram of docking task guiding method in the present embodiment;

[0135] Figure 4 Schematic diagram of formation task planning in the present embodiment;

[0136] Figure 5A schematic diagram of the formation shape planning in the embodiment;

[0137] Figure 6 A schematic diagram of the formation safety planning in the embodiment;

[0138] Figure 7 A schematic diagram of the target contact point calculation of the OS in the embodiment;

[0139] Figure 8 A system architecture diagram of the path planning method of the multi-tug autonomous formation berthing target ship in the embodiment;

[0140] Figure 9 A simulation diagram of the single-ship berthing simulation experiment in the embodiment;

[0141] Figure 10 A simulation diagram of the formation berthing simulation experiment in the embodiment. DETAILED DESCRIPTION

[0142] To make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in connection with the drawings of the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0143] The embodiment provides a path planning method for multi-tug autonomous formation berthing target ship, as shown in Figure 1 and Figure 8 , specifically comprising the following steps:

[0144] S1: According to the issued preset berthing task, a single-ship berthing planning strategy of the assisting tug is constructed, specifically comprising the following steps:

[0145] The embodiment faces the path planning of the tug berthing target ship, and the assisting tug needs to berth the served ship at a preset angle, speed and position. For the three-target coupling planning problem, the embodiment proposes the concept of berthing position control line LC, and designs a guiding method, i.e., a single-ship berthing planning strategy, according to the berthing position control line LC and the ship motion characteristics;

[0146] S11: The berthing position control line is defined and acquired based on the served ship;

[0147] Specifically, as shown in Figure 2 , the berthing position control line in S11 is a straight line where the resultant direction of the sailing speed vector of the served ship TS and the berthing speed vector is located;

[0148] And the vector expressions for the sailing speed vector and the berthing speed vector are:

[0149]

[0150] In the formula: u ts This indicates the speed of TS; Indicates the heading of TS; u ap θ represents the berthing speed of the target at TS; ap This indicates the target berthing angle. In this embodiment, the assisted tugboat OS berths from the side of the serviced vessel TS by default. If berthing is done from the starboard side, then θ is subtracted. ap Conversely, add θ. ap ;v ts Represents the speed vector; v ap This represents the berthing velocity vector;

[0151] like Figure 2 As shown, the berthing position control line LC is formed by v ts and -v ap Synthesizing, if the assisting tug OS is exactly above the LC, by adjusting the course and speed of the assisting tug OS to precisely match the target value, the assisting tug OS can be kept stably on the LC until it berths the servicing vessel TS.

[0152] S12: Obtain the direction vector of the assisted tugboat's hull angle relative to the stationary vessel being served, and obtain the assisted tugboat's current desired course based on the berthing position control line;

[0153] like Figure 3 The illustration demonstrates how to simultaneously control the vessel's position on the LC (Loop Position Control Line) and adjust its navigation state to achieve precise berthing. While this embodiment achieves precise berthing by controlling the vessel's position on the LC and adjusting its navigation state, realizing this goal presents another challenge. Typically, tugboat berthing operations are conducted at low speeds. If the OS (Stage Position) is controlled on the LC too early, it will lead to... ap Approaching TS slowly will reduce operational efficiency; ideally, OS should contact TS simultaneously with reaching LC, and the heading and speed should also be at the target value. Due to the characteristics of ship motion, the ship cannot make large-angle turns in a short period of time. The heading adjustment required from the initial state to the berthing state should be gradually achieved throughout the voyage. Without considering sway, the bow heading is the same as the track heading. Therefore, the above-mentioned heading problem needs to be solved in the following way:

[0154] Specifically, the following steps are included:

[0155] S120: Assuming that the TS is static, the optimal track line of the OS at the end of berthing should be tangent to the LC, and the direction vector of the berthing position control line is defined as v ls , the direction vector of the relative angle of the assisting tug with respect to the served ship in a static state is v to , and v ls is recorded as (x ls , y ls ), v to is recorded as (x to , y to ); wherein x ls , y ls represent the horizontal and longitudinal vectors of the direction vector v ls , and x to , y to represent the horizontal and longitudinal vectors of the direction vector v to ;

[0156] S121: Obtain the vector angle θ1 between v to and v ls , and the formula is

[0157]

[0158] v ls ·v to = x ls x to +y ls y to (5)

[0159]

[0160] In the formula: ||v to || represents the length of v to ; ||v ls || represents the length of v ls ; v ls ·v to represents the dot product of v to and v ls ;

[0161] S122: According to step S121, the rotation angle θ r of the direction vector of the served ship TS with respect to the assisting tug OS is obtained, and the expression is

[0162]

[0163] In the formula: LC represents the berthing position control line;

[0164] S123: According to the rotation angle θ robtaining a rotation matrix R(θ r ), the expression of which is

[0165]

[0166] and a current desired heading of the assisting tug is obtained according to the rotation matrix R(θ r );

[0167] and the expression of the current desired heading vector of the assisting tug is

[0168]

[0169] wherein v co represents the current desired heading of the assisting tug;

[0170] S13: if the served ship TS has a speed, in order to ensure the effectiveness and applicability of the design, the current desired heading is taken as a relative motion heading, a turning bearing vector of the assisting tug is obtained according to a current speed of the assisting tug, and a berthing guide force of the served ship is obtained based on the turning bearing vector;

[0171] Specifically, the following steps are included:

[0172] S131: the current desired heading vector is taken as a relative motion heading, the expression of which is

[0173] v co =v to -v ts (11)

[0174] S132: a center o of a circle is obtained according to the sailing speed vector v ts and a position p os of the assisting tug, a relative motion vector circle O os is defined and obtained with the sailing speed u r of the assisting tug as a radius;

[0175] and the center o of the relative motion vector circle O r is obtained by the formula

[0176] o=p os -v ts (12)

[0177] assuming that the position p os of the assisting tug is taken as the starting point of v co , any point on the relative motion vector circle O r is taken as the undetermined end point of v co , and the end point of v co is confirmed according to a preset vector direction vector d;

[0178] A preset vector direction vector d = (a, b) is recorded, wherein a and b respectively represent a horizontal component and a vertical component of the vector direction vector d, and an acquisition formula thereof is

[0179]

[0180] S133: An unknown parameter equation of a current desired heading vector direction ray is acquired according to a preset vector direction vector;

[0181] and the unknown parameter equation of the current desired heading vector direction ray P(n) is

[0182] P(n) = P os +n·d = (x os +an, y os +bn) (14)

[0183] In the formula, n represents a parameter to be solved and n ≥ 0;

[0184] S134: A standard equation of a relative motion vector circle O r is defined as

[0185] (x-h) 2 +(y-k) 2 =r 2 (15)

[0186] In the formula, h and k represent center coordinates of the relative motion vector circle, and r represents a radius;

[0187] The formula (14) is substituted into (15) to obtain

[0188] (x os +an-h) 2 +(y os +bn-k) 2 =r 2 (16)

[0189] and the (16) is rewritten into a quadratic equation about n as

[0190] (a 2 +b 2 )n 2 +2(a(x os -h)+b(y os -k))n+((x os -h) 2 +(y os -k) 2 -r 2 ) = 0 (17)

[0191] The (17) is simplified to obtain a simplified formula as

[0192] A = a 2 +b 2 (18)

[0193] B=2(a(x os -h)+b(y os -k)) (19)

[0194] C=(x os -h) 2 +(y os -k) 2 -r 2 (20)

[0195] An 2 +Bn+C=0 (21)

[0196] S135: Solve the quadratic equation using the simplified formula to obtain the parametric solution;

[0197] The expression for finding the roots of the quadratic equation is:

[0198]

[0199] The final desired heading vector direction ray is determined based on the parameter solution;

[0200] In this embodiment, v co As shown in equation (11), the relative motion heading needs to be determined based on the current speed of the OS to ensure that v co This embodiment can meet the berthing guidance requirements. In the previous design, this embodiment only constrained v. co The direction is not considered, and its length is determined by the sum of vectors; by defining a relative motion vector circle O r , set the OS's ship position p os According to vector -v ts The center O is obtained by translation. r The radius r is the speed u of OS. os If p is set os For v co The starting point, then O r Every point on it can become v co The endpoint; in this embodiment, it is only necessary to obtain v through a preset vector direction. co The endpoint, simply put, is through O r and v co The direction of the ray can determine v co The model, in v co v can be obtained when the magnitude and direction are both determined. to, which will be used as the turning basis for the ship to perform the berthing task. The specific formula derivation is shown in equations (12)-(22). In addition, equation (22) is used to solve n corresponding to the intersection point of the straight line and the circle. If n≥0, it is the intersection point of the ray and the circle. Before solving n, the embodiment needs to use the discriminant formula D=B 2 -4AC to determine whether there is an intersection point. If D>0, there are two real solutions, i.e., the straight line and the circle have two intersection points; if D=0, there is one real solution, i.e., the straight line is tangent to the circle; if D<0, there is no real solution, i.e., the straight line and the circle have no intersection point. After n is solved, the solution of n<0 can be eliminated. If n has two solutions, the larger value is taken, and at this time P(n)=(x os +an, y os +bn) is the intersection point of the ray and the circle. At this time, v to and the corresponding berthing guide force F m can be obtained as shown in equations (23) and (24). to will be output as the output of the task planning layer, and will embody the guidance of the task in subsequent heading and speed planning.

[0201] S136: Based on the final current expected heading direction ray, the turning position vector of the assisting tugboat is obtained according to the current speed of the assisting tugboat, and the expression is

[0202] v co =P(n)-p os (23)

[0203] v to =v co +v ts (24)

[0204] wherein v to represents the turning position vector.

[0205] S137: The berthing guide force of the served ship is obtained based on the turning position vector, and the berthing guide force of the served ship is

[0206] F m =k m ·v to (25)

[0207] wherein F m represents the berthing guide force; and k m represents the position guide force gain coefficient.

[0208] S14: The direction of the berthing guide force is taken as the expected heading of the assisting tugboat at the current time, and the expected heading at the next time is updated and obtained based on the constructed turning constraint.

[0209] The expression of the constructed turning constraint is

[0210]

[0211] wherein: represents F m with respect to the side angle of the assisting tug OS, and the right side value is positive and the left side value is negative; θ c represents the turning constraint angle; Δθ represents the turning angle; represents the heading of the assisting tug OS at time t; represents the heading of the assisting tug OS at time t+1;

[0212] The embodiment obtains F m After that, the direction is taken as the expected heading of the OS, the OS adjusts to the expected heading at each time, and the embodiment sets a turning constraint, that is, the turning amplitude of the OS at each time cannot exceed a limited value, and the calculation formula is shown in (26) and (27);

[0213] S15: constructing a speed gradient planning model of the assisting tug;

[0214] and based on the speed gradient planning model, obtaining the ship position of the assisting tug at the next time according to the expected heading at the time;

[0215] Specifically, the following steps are included

[0216] S151: constructing a speed gradient planning model of the assisting tug, and the expression of the speed gradient planning model is

[0217]

[0218]

[0219] wherein: u m represents the maximum speed; d (os,ts) represents the distance between the assisting tug and the served ship; d c represents the distance threshold; u t represents the expected heading; represents the speed of the assisting tug OS at time t; u c represents the speed threshold; Δu represents the speed change value; represents the speed of the assisting tug OS at time t+1;

[0220] S152: based on the speed gradient planning model, obtaining the position of the assisting tug at the next time according to the expected heading at the time, and the expression is

[0221]

[0222] wherein: represents the position of the assisting tugboat OS at time t; represents the position of the assisting tugboat OS at time t+1;

[0223] In terms of speed planning, the embodiment designs a speed gradient planning model for the assisting tugboat. The model first calculates the distance between the two ships. If the distance is less than a preset distance threshold, gradient planning is performed between the maximum speed and the target speed to determine the expected speed. After obtaining the expected speed, the OS will target the speed for speed decision-making, but the speed change amplitude is also subject to certain constraints. The calculation formulas are shown in equations (28) to (30). After updating the heading and speed, the ship position at the next time can be calculated based on this, and the calculation formula is shown in equation (31);

[0224] S2: Obtain the ship positions, ship headings, and ship speeds of multiple assisting tugboats;

[0225] Define a virtual guiding ship, and obtain the initial position coordinates of the virtual guiding ship based on the ship positions of the multiple assisting tugboats, and guide it to berth to the served ship based on a single-ship berthing planning strategy;

[0226] And based on the virtual guiding ship, construct a formation path planning strategy for the multiple assisting tugboats to achieve path planning for the multiple tugboats to autonomously form a formation and berth to the target ship;

[0227] Specifically, the following steps are included

[0228] S21: Obtain the ship positions, ship headings, and ship speeds of multiple assisting tugboats;

[0229] Define a virtual guiding ship, and obtain the initial position coordinates of the virtual guiding ship based on the ship positions of the multiple assisting tugboats;

[0230] And the formula for obtaining the initial position coordinates of the virtual guiding ship is

[0231]

[0232] In the formula, x i ,y i represents the position coordinates of each assisting tugboat; p c represents the coordinate center of the multiple assisting tugboats, k sd represents a guiding coefficient; p v represents the initial position coordinates of the virtual guiding ship;

[0233] And based on a single-ship berthing planning strategy, guide it to berth to the served ship to obtain a virtual berthing point;

[0234] The core idea of ​​formation planning in this embodiment is to treat all berthed ships as a unified whole, then plan their tasks accordingly, and guide each ship based on the planning results. This method ensures that the formation maintains a high degree of coordination and consistency when executing tasks. This embodiment defines a virtual guided ship OS. v Its initial coordinates p v Located at the average coordinates of each ship and p ts Between, and OS v The initial ship position is set at p c With p ts This allows for effective guidance of the formation group in the initial stage, as shown in equations (32) to (33); for example, as Figure 4 The four assisting tugboats shown need to berth at berthing points 1-4 respectively, but a fixed order is not required. This embodiment is based on a single-ship berthing planning strategy, according to OS. v Task planning is performed based on the state of the OS, that is, the OS is obtained through task planning. v After the task is directed, F is obtained using equation (25). m And boot the OS v Mooring;

[0235] S22: Based on a virtual guide ship, construct a formation path planning strategy for multiple assisting tugboats to realize the path planning for multiple tugboats to autonomously form up and berth at the target ship;

[0236] Furthermore, the formation path planning strategy for the multiple assisting tugboats specifically includes the following steps:

[0237] S221: Establish formation planning principles to achieve coordinated formation of multiple assisting tugboats;

[0238] Furthermore, the formation planning principles are specifically as follows:

[0239] A berthing baseline consisting of multiple berthing points is defined using virtual berthing points, and each berthing point is sequentially encoded from near to far in the direction from bow to stern of the vessel being served to obtain a berthing point sequence list;

[0240] Furthermore, the berthing baseline is a straight line that passes through the virtual berthing point and is parallel to the side of the ship being served.

[0241] S222: Obtain the real-time positions of multiple assisting tugboats to obtain the relative distance of each assisting tugboat relative to the berthing baseline;

[0242] The relative distances are then sorted in descending order to obtain a real-time distance sequence table.

[0243] The berthing positions of each assisting tugboat are assigned according to the real-time distance sequence table;

[0244] The rules for allocating berthing points are as follows:

[0245] Based on the order of berthing point locations from nearest to farthest in the berthing point sequence table, berthing positions (i.e., berthing points) are assigned to the tugboats in the real-time distance sequence table according to their sorting results.

[0246] In a further example, the allocation rule for the berthing point location is as follows:

[0247] Tugs that are ranked higher in the real-time distance sequence list (such as those farthest from the berthing baseline) will be preferentially assigned to the berthing point sequence position that is closest to the bow of the vessel being served.

[0248] Conversely, tugboats ranked lower in the real-time distance sequence list (those closest to the berthing baseline) are sequentially assigned to positions further from the bow of the vessel being served in the berthing point sequence list. This allocation method ensures efficiency and safety during the berthing process, allowing the assisting tugboats to be rationally distributed based on their distance from the berthing baseline, thus optimizing the entire berthing operation.

[0249] like Figure 5 As shown in this embodiment, in the study of multiple tugboats coordinating the berthing of a large ship, the prior berthing of individual tugboats may adversely interfere with the mission execution of subsequent tugboats; therefore, ensuring the synchronization of tugboat berthing is crucial, and ideally, all tugboats should berth simultaneously as much as possible. To meet this requirement, the group formation must be flexibly adjusted during convoy navigation. In the mission scenario studied in this embodiment, all tugboats need to berth on the same side of the target large ship TS, and the group formation should be based on OS. v Centered on the OS, the four tugboats are distributed according to preset points 1-4, ensuring that the formation remains parallel to the bow of the TS. To enhance the dynamic adaptability of this embodiment, the four tugboats do not need to be strictly arranged in a fixed order at fixed points; instead, their arrangement can be flexibly adjusted according to the real-time position distribution of each tugboat, and the overall formation presents an OS-shaped arrangement. v Based on the straight line arrangement of the TS, this embodiment pre-establishes a corresponding coordinate system according to the heading of the TS. By sorting the coordinate longitudinal values ​​of each tugboat, the specific positions in the formation can be allocated more reasonably. This dynamic adjustment rule not only improves the overall coordination of the formation, but also significantly enhances the system's adaptability in complex environments.

[0250] S223: After obtaining the assigned position, obtain the direction vector of each assisting tugboat relative to the corresponding berthing point, so as to obtain the position guiding gravity of the assisting tugboat;

[0251] And the expression for position-guided gravity is

[0252] F p =k p ·vp (34)

[0253] wherein k p represents the position-oriented gain coefficient; v p represents the direction vector of the assisting tug relative to the corresponding berthing point; F p represents the position-oriented attractive force;

[0254] Based on the position-oriented attractive force, the formation dynamic guiding force is obtained according to the position distance between each assisting tug and the corresponding berthing point, and the expression of the formation dynamic guiding force is

[0255]

[0256] wherein F mp represents the formation dynamic guiding force; represents the position distance between the assisting tug and the corresponding berthing point, and i represents the number of the assisting tug; j represents the number of the berthing point; k dm represents the formation guiding force dynamic guiding coefficient; k dp represents the formation position-oriented force dynamic guiding coefficient;

[0257] After obtaining the assigned position, the expected position-oriented force can be obtained, as shown in formula (34). In order to ensure the stability of the formation, when each ship approaches the target position, it is necessary to dynamically adjust the heading to the expected direction under the task guidance. This process should be dynamically corrected according to the real-time distance between each ship and the target position, so as to meet the dual requirements of formation task and formation keeping, as shown in formula (35). Through the above method, the formation can flexibly cope with the complex dynamic environment, and realize the stability and efficiency of formation navigation;

[0258] S224: Construct the repulsive force dynamic gain function between any two assisting tugs in the assisting tug formation;

[0259] And the expression of the repulsive force dynamic gain function is

[0260]

[0261] vec r = vec1- vec2 (38)

[0262] wherein vec r represents the relative motion velocity vector between any two assisting tugs; θ represents the included angle between the line connecting any two assisting tugs and vec r ; represents the distance between the two ships; d s represents the safety distance boundary; represents the direction vector of one assisting tug pointing to the other assisting tug; F srepresents the safety-oriented force; k v represents the relative motion repulsion factor; vec1, vec2 represents the velocity vector of the two assisting tugboats; In addition to the relative motion, the collision avoidance repulsion dynamic gain function of the present embodiment also needs to consider the distance between the two ships, which weakens the influence of the distance between the two ships, and a safety distance boundary is designed, and a large repulsion constant factor k will be generated when the distance between the ships is less than the safety distance boundary v , to avoid the close distance between the ships;

[0263] As Figure 6 shown, the present embodiment designs a collision avoidance repulsion dynamic gain function, and by introducing the traditional APF framework, the stability, safety and cooperation of the near-distance collision avoidance decision of each assisting tugboat in the formation are improved; During the cooperative operation of the multi-ship formation, internal safety is crucial; Due to factors such as task planning and formation planning, each ship needs to frequently adjust its own position, and if the coordination is not proper, it is extremely likely to cause collision between the ships in the formation, thereby affecting the smooth progress of the task and the overall stability of the formation. Therefore, each ship must take effective measures to ensure that it maintains an appropriate safety distance from other ships in the formation, so as to minimize the risk of collision and ensure the safe operation of the formation;

[0264] In formation navigation, due to the high density of ships, small collision avoidance space and usually same-direction travel with small distance, the traditional "early, large, wide and clear" collision avoidance principle is no longer applicable. Therefore, the collision avoidance algorithm needs to pay more attention to the analysis of the relative motion state, reduce the weight of the distance between the ships, and realize safe collision avoidance in the high-density same-direction navigation environment through fine dynamic adjustment and path planning, to ensure the stability and efficient operation of the formation as a whole; In the field of ship collision avoidance algorithm research, APF is widely used due to its strong real-time performance; However, the classic APF often shows oscillation and instability when dealing with near-distance collision avoidance, which may affect the collision avoidance effect and navigation safety. In order to overcome this problem, the present embodiment innovatively designs a collision avoidance repulsion dynamic gain function based on the classic APF framework, which takes into account factors such as ship distance and relative motion state in the decision-making process, aiming to improve the safety and cooperation of formation navigation;

[0265] S225: obtaining a formation berthing guide force according to the formation dynamic guide force and the repulsion dynamic gain function; and the expression of the formation berthing guide force F t is

[0266] F t = k mp · F mp + k s · F s (39)

[0267] In the formula: k mprepresents dynamic guidance gain coefficient; k s represents safety guidance gain coefficient; F t represents the resultant force of formation planning, i.e., the formation berthing guidance force; v i represents the velocity vector of the ith assisting tugboat OS i .

[0268] Based on the formation berthing guidance force, the position of the assisting tugboat OS

[0269]

[0270] According to formula (40) combined with formula (27), the position of the assisting tugboat OS

[0271] S226: Obtain the distance between the expected position of each assisting tugboat OS h and the current position of the assisting tugboat, to obtain the two-ship distance d i between each assisting tugboat and the serviced ship.

[0272]

[0273] In the formula, d(p os , p i ) represents the distance between the expected position of each assisting tugboat and the current position of the assisting tugboat; p m represents the ith assisting tugboat; represents the side angle of the ith assisting tugboat;

[0274] According to formula (41), formula (28) is rewritten, and the following formula is obtained:

[0275]

[0276] According to formula (42) combined with formula (29) to (30), the speed of the assisting tugboat OS t is updated, and the path planning of the multi-tugboat autonomous formation berthing target ship is realized.

[0277] The heading planning of each assisting tugboat in the formation of the present embodiment is similar to the heading planning of a single ship. F m in formula (26) is replaced by the resultant force F t obtained by the formation planning layer, and the specific calculation formula is shown in formula (39) and formula (40). Through the heading planning, each ship can move towards the expected position in the formation planning. However, this method cannot ensure that the ship remains in the expected position for a long time, and it is easy to cross the expected position, resulting in poor formation stability. To this end, the present embodiment innovatively designs a speed planning method for formation stability, i.e., OS vThe speed of the first ship is still calculated according to formulas (28) to (30). When planning the speed of the other ships, the course, position and desired position must be included in the calculation formula to avoid the ith assisting tug's OS i Once the desired position is reached, the specific formulas for the expected speed planning of each assisting tug are (41) to (42), and the formulas for speed change and position update of the assisting tug are the same as those for single-ship attitude planning.

[0278] This embodiment also includes the principle of calculating the contact points of the OS based on the actual berthing operation:

[0279] like Figure 7 As shown, during the berthing experiment, the ship has volume and cannot be considered a point mass. In this embodiment, the length of the ship OS is set to 38m and the width to 10m; the bow is a semicircular arc with a diameter of 10m and the center at p. h ;p os Let p be the OS coordinate, located at the center of the ship, and can be obtained using equation (43). h In this embodiment, the contact point of OS is obtained by calculating the relative motion states of the two ships; θ s It is the angle between the headings of the two ships; θ c It is θ s The supplementary angle, through θ c Then P can be obtained. t As shown in equation (44); based on the current motion states of the two ships, the future contact point of OS is P. t At this time θ s Instead of a preset berthing angle, θ s Replace with preset values, the desired P t This is the target contact point of the OS. When planning tasks and formations, P needs to be included. t As coordinates rather than p os ;

[0280]

[0281] In the formula: Indicates OS heading, while Figure 7 Since the OS intends to berth on the starboard side of the TS, θ needs to be subtracted. c Conversely, add θ. c .

[0282] This embodiment also includes simulation experiment results: such as Figure 9The simulation experiment diagram of single ship berthing is shown, and the trajectories and historical positions of two ships are plotted. In the experiment, the OS is located on the left side of the TS, and is planned to be alongside the TS at point 5 with an absolute speed of 2 m / s and a relative angle of 10°. The TS should keep the planned direction and speed. During the experiment, the speed of the TS is kept at 1.5 m / s, and in order to verify the robustness of the planning algorithm in the wind and wave environment, the TS is randomly turned by 0.5 degrees per second. It can be seen that the TS has a slight turning during the entire navigation procedure, which is consistent with the actual berthing operation environment. From the local enlarged diagram at the berthing time, it can be seen that the berthing effect is excellent. The high accuracy of single ship berthing provides support for the accuracy of subsequent formation berthing.

[0283] As shown in Figure 10 The simulation experiment diagram of formation berthing is shown, and the trajectories and historical positions of TS, OS1-4, OS v are plotted, wherein the OS v is a virtual guiding ship guided to berth at point 9 of the TS by the single ship berthing algorithm, and the OS 1-4 is guided to perform formation path planning by the OS v . It can be seen that the four ships realize coordinated and orderly berthing, and the entire process strictly follows the safety principle. In the local enlarged diagram, it can be clearly observed that the OS v accurately stops at point 9, and the remaining ships automatically adjust the berthing order according to the real-time situation and stop at points 1-4 in turn.

[0284] In summary, the single ship berthing planning strategy of the assisting tug is constructed, the path planning task of single ship berthing is realized according to the preset berthing task issued, the initial position coordinates of the virtual guiding ship are obtained according to the positions of the multiple assisting tugs, the virtual guiding ship is guided to berth at the served ship based on the single ship berthing planning strategy, and the formation path planning strategy of the multiple assisting tugs is constructed by introducing the dynamic guiding force and repulsive force dynamic gain function of the formation, so as to realize the path planning of the multiple tugs to autonomously form a formation to berth at the target ship, solve the problem that the current port tug operation mainly relies on manual experience operation, and in the path planning of the tug to berth at the target ship, especially in the cooperative working process of the multiple assisting tugs, the assisting tugs cannot accurately and effectively satisfy the preset angle, speed and position to berth at the served ship to realize the cooperative formation operation of the assisting tugs, resulting in low operation precision and efficiency, greatly reducing the operation pressure and difficulty of the tugs, and reducing the labor input, improving the intelligent degree and operation precision of the path planning of the multiple tugs to autonomously form a formation to berth at the target ship.

[0285] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application 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 recorded in the above embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A path planning method for autonomous formation berthing of a target ship by multiple tugboats, characterized in that, Specifically comprising the following steps: S1: constructing a single-ship berthing planning strategy of an assisting tug according to a preset berthing task issued; Specifically comprising the following steps: S11: defining and obtaining a berthing position control line of the served ship based on the served ship; the berthing position control line is a straight line where a resultant direction of a sailing speed vector and a berthing speed vector of the served ship TS is located; S12: obtaining a direction vector of a side angle of the assisting tug relative to the served ship in a static state, and obtaining a current expected heading of the assisting tug according to the berthing position control line; S13: taking the current expected heading as a relative motion heading, and obtaining a turning position vector of the assisting tug according to a current speed of the assisting tug; and obtaining a berthing guide force of the served ship based on the turning position vector; S14: taking a direction of the berthing guide force as an expected heading of the assisting tug at a current moment, and updating and obtaining an expected heading at a next moment based on a turning constraint constructed; S15: constructing a speed gradient planning model of the assisting tug; and obtaining a ship position of the assisting tug at the moment according to the expected heading at the next moment based on the speed gradient planning model; S2: obtaining ship positions, ship headings and ship speeds of a plurality of assisting tugs; defining a virtual guide ship, and obtaining initial position coordinates of the virtual guide ship according to the ship positions of the plurality of assisting tugs, and a formula for obtaining the initial position coordinates of the virtual guide ship is （32） （33） In the formula: represents the position coordinates of each assisting tugboat; represents the coordinate center of a plurality of assisting tugboats, represents a guide coefficient; represents the initial position coordinates of the virtual guide ship; and guiding the virtual guide ship to berth to the served ship based on the single-ship berthing planning strategy; and constructing a formation path planning strategy of the plurality of assisting tugs based on the virtual guide ship to realize path planning of the plurality of assisting tugs to the target ship.

2. The path planning method for autonomous formation berthing of a target ship by a plurality of tugboats according to claim 1, characterized in that, vector expressions of the sailing speed vector and the berthing speed vector in S11 are （1） （2） wherein: represents a speed of the TS; represents a heading of the TS; represents a berthing target speed of the TS; represents a berthing target angle; represents a sailing speed vector; represents a berthing speed vector.

3. The path planning method for autonomous formation berthing of a target ship by a plurality of tugboats according to claim 2, characterized in that, S12 specifically comprises the following steps: S120: define the direction vector of the berthing position control line as , the direction vector of the tugboat relative to the side angle of the served ship in the static state as , and recorded as , recorded as ; S121: obtaining between the vector angle between the vector angle whose obtaining formula is （3） （4） （5） （6） （7） wherein: denotes the module length of denotes the module length of denotes the module length of​ S122: the rotation angle of the served ship TS with respect to the direction vector of the bow angle of the assisting tug OS is acquired according to step S121 whose expression is （8） In the formula: represents the berthing position control line; S123: According to the rotation angle Obtaining a rotation matrix , the expression is （9） and according to the rotation matrix obtaining a current desired heading of the assisting tug and an expression of the current expected heading vector of the assisting tug is （10） In the formulae: represents the current desired heading of the assisting tug.

4. The path planning method for autonomous formation berthing of a target ship by a plurality of tugboats according to claim 3, characterized in that, S13 specifically comprises the following steps: S131: taking the current expected heading vector as a relative motion heading, and an expression thereof is （11） S132: Obtain the relative motion vector circle with the center at the position of the assisting tugboat and with the radius of the sailing speed vector of the assisting tugboat Obtain the position of the assisting tugboat Obtain the center of the circle Obtain the sailing speed of the assisting tugboat Obtain the relative motion vector circle with the center at the position of the assisting tugboat and with the radius of the sailing speed vector of the assisting tugboat ; and the relative motion vector circle The formula for the center of the circle is （12） Assume the position of the tugboat that will assist As the starting point, any point on the relative motion vector circle is taken as the undetermined end point, and the end point of is determined according to the preset vector direction vector ; a preset vector direction vector wherein respectively represent a transverse component and a longitudinal component of the vector direction vector , the acquisition formula of which is （13） S133: obtaining an unknown parameter equation of a current expected heading vector direction ray according to a preset vector direction vector; and the direction ray of the current desired heading vector the unknown parameter equation of （14） In the formulae: denote the parameters to be solved and ; S134: Define relative motion vector circle The standard equation for （15） In the formulae: denotes the center coordinate of the relative motion vector circle; denotes the radius; substituting formula (14) into (15) can obtain （16） and (16) is rewritten as a quadratic equation in terms of x = -b ± sqrt(b2- 4ac) （17） simplifying (17) to obtain a simplified formula （18） （19） （20） （21） S135: obtaining a parameter solution by solving a quadratic equation of the simplified formula; an expression of solving the quadratic equation is （22） confirming a final current expected heading vector direction ray according to the parameter solution; S136: obtaining a turning position vector of the assisting tug according to a current speed of the assisting tug based on the final current expected heading vector direction ray, and an expression thereof is （23） （24） In the formulae: denotes the steering orientation vector; S137: obtaining a berthing guide force of the served ship based on the turning position vector, and the berthing guide force of the served ship is （25） In the formula: represents the berthing guidance force; represents the position guidance attraction gain coefficient.

5. The path planning method for autonomous formation berthing of a target ship by a plurality of tugboats according to claim 4, characterized in that, an expression of the turning constraint constructed in S14 is （26） （27） In the formula: represents the side angle relative to the assisting tug OS, and the right side takes a positive value and the left side takes a negative value; represents the turning angle constraint; represents the turning angle; represents the heading of the assisting tug OS at the time t t; represents the heading of the assisting tug OS at the time t +1.

6. The path planning method for autonomous formation berthing of a target ship by a plurality of tugboats according to claim 5, characterized in that, S15 specifically comprises the following steps S151: constructing a speed gradient planning model of the assisting tug, and an expression of the speed gradient planning model is （28） （29） （30） wherein: Vmax represents the maximum speed of the assisting tug; D represents the two-ship distance between the assisting tug and the served ship; Dth represents the distance threshold; ψdes represents the desired heading; VOS represents the speed of the assisting tug OS at time t; t VOS represents the speed of the assisting tug OS at time t + 1; Vth represents the speed threshold; ΔV represents the speed change value; VOS represents the speed of the assisting tug OS at time t; t VOS represents the speed of the assisting tug OS at time t + 1; S152: obtaining a position of the assisting tug at the moment according to the expected heading at the next moment based on the speed gradient planning model, and an expression thereof is （31） wherein: represents the position of the assisting tug OS at t time t; represents the position of the assisting tug OS at t +1 time t.

7. The path planning method for autonomous formation berthing of a target ship by a plurality of tugboats according to claim 6, characterized in that, S2 specifically comprises the following steps S21: obtaining ship positions, ship headings and ship speeds of a plurality of assisting tugs; Define a virtual guiding ship, and obtain initial position coordinates of the virtual guiding ship according to positions of the plurality of assisting tugboats; and guide the single ship to berth to the served ship based on a single-ship berthing planning strategy, and obtain a virtual berthing point; S22: Construct a formation path planning strategy of the plurality of assisting tugboats based on the virtual guiding ship, to realize path planning of the plurality of assisting tugboats for autonomously forming a formation to berth to the target ship; And the formation path planning strategy of the plurality of assisting tugboats specifically includes the following steps: S221: Construct a formation formation planning principle to realize cooperative formation of the plurality of assisting tugboats; And the formation formation planning principle is Define a berthing reference line including a plurality of berthing points with the virtual berthing point, and encode each berthing point in order from near to far to obtain a berthing point sequence table in the direction from the bow of the served ship to the stern of the served ship; And the berthing reference line is a straight line passing through the virtual berthing point and parallel to the side of the served ship; S222: Obtain real-time positions of the plurality of assisting tugboats to obtain relative distances of each assisting tugboat with respect to the berthing reference line; And arrange the relative distances in descending order to obtain a real-time distance sequence table; Distribute berthing point positions to each assisting tugboat according to the real-time distance sequence table; Wherein the rule for distributing the berthing point positions is: Distribute the berthing positions, i.e. the berthing points, to the tugboats in the order of the sorting results in the real-time distance sequence table based on the order of the berthing point positions from near to far in the berthing point sequence table; S223: After obtaining the distribution positions, obtain a direction vector of each assisting tugboat with respect to the corresponding berthing point to obtain a position guiding force of the assisting tugboat; And the expression of the position guiding force is （34） In the formulae: represents a position-oriented gain coefficient; represents a direction vector of the assisting tug relative to the corresponding berthing point; represents a position-oriented attractive force; And based on the position guiding force, obtain a formation dynamic guiding force according to the position distance between each assisting tugboat and the corresponding berthing point, and the expression of the formation dynamic guiding force is （35） In the formula: represents the formation dynamic guiding force; represents the position distance of the assisting tugboat and the corresponding berthing point, and represents the number of the assisting tugboat; represents the number of the berthing point; represents the formation guiding force dynamic guiding coefficient; represents the formation position guiding force dynamic guiding coefficient; S224: Construct a repulsive dynamic gain function between any two assisting tugboats in the assisting tugboat formation; And the expression of the repulsive dynamic gain function is （36） （37） （38） In the formula: This represents the relative velocity vector between any two assisting tugboats; Indicates any two assisting tugboats connected by a line. The included angle; Indicates the distance between the two ships; Indicates the safety distance boundary; This represents the direction vector from which one assist tugboat points to the direction pointed by another assist tugboat; Indicates safety guidance force; Represents the repulsive force factor of relative motion; This represents the velocity vector of the two assisting tugs; S225: Obtain a formation berthing guiding force according to the formation dynamic guiding force and the repulsive dynamic gain function; And the expression of the formation berthing guiding force is （39） In the formula: represents a dynamic guidance gain coefficient; represents a safety guidance gain coefficient; represents a platoon planning resultant force, i.e., a platoon berthing guidance force; represents a speed vector of the th assisting tugboat ; And based on the formation berthing guiding force, the position update of the assisting tugboat formation can be obtained according to formula (26); （40） And the formula (28) can be rewritten according to formula (41) to obtain S226: Obtain the distance between the expected position of each assisting tug and the current position of each assisting tug in the assisting tug formation to obtain the two-ship distance between each assisting tug and the served ship The expression is （41） wherein: represents the distance of the desired position of each assisting tug from the current position of the assisting tug; represents the first assisting tug; represents the first assisting tug's side angle; The speed update of the assisting tugboat formation can be realized according to formula (42) combined with formula (29) to (30), thereby realizing the path planning of the plurality of assisting tugboats for autonomously forming a formation to berth to the target ship. （42） ​

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