A collaborative obstacle avoidance and robust control method for ship formation based on differential game

Abstract

The present invention discloses a method for coordinated obstacle avoidance and robust control of a fleet of ships based on differential games, comprising constructing a ship obstacle avoidance function and designing an optimal virtual control law based on a first performance index function; constructing a second performance index function for stabilizing the ship's position dynamics error and combining it with the first optimal value function to obtain the ship's ocean state disturbance; designing a third performance index function for stabilizing the ship's state dynamics error to obtain an optimal response controller; obtaining a heading virtual control law based on the optimal response controller; performing order reduction processing on the derivative of the heading virtual control law to obtain the bowing motion dynamics error; constructing a fourth performance index function for describing the bowing motion disturbance and combining it with the second optimal value function to obtain the ship's bowing motion disturbance; and designing a fifth performance index function for stabilizing the ship's bowing motion dynamics error to obtain an optimal robust controller. The present invention solves two technical problems in existing ship formation motion control engineering practices: "the artificial potential field method is not conducive to high-precision and safe navigation of ships" and "the disturbance observer has weak robustness in the face of ocean environment disturbances."

Description

Technical Field

[0001] The present invention relates to the field of ship control engineering and ship automated navigation equipment application technology, and in particular to a ship formation collaborative obstacle avoidance and robust control method based on differential game. Background Art

[0002] In the field of ship formation motion control, the main design ideas of formation collaborative control include leader-follower distributed control [1] Distributed control based on graph theory [2] In order to solve the problem of autonomous obstacle avoidance and ocean interference resistance of ship formation, the existing ship formation control technology proposes a disturbance observer. [3] and artificial potential field method [4] .

[0003] However, while the artificial potential field method can generate safe and smooth reference trajectories for ships in real time, it fails to account for the ship's maneuverability and inertia, making the resulting reference trajectory unfavorable for high-precision tracking. Furthermore, the highly nonlinear and variable nature of the real ocean environment, combined with the difficulty of adjusting the disturbance observer's parameters, makes the disturbance observer difficult to apply in maritime practice.

[0004] Based on the above analysis, the existing ship formation obstacle avoidance control technology has the following two main defects:

[0005] 1) Existing autonomous obstacle avoidance strategies based on artificial potential fields are not suitable for high-precision navigation and cannot even guarantee effective obstacle avoidance. Artificial potential field methods have numerous parameters and rely heavily on parameter adjustments. When the parameters are too large, the reference trajectory is not conducive to ship tracking, while when the parameters are too small, effective obstacle avoidance cannot be achieved.

[0006] 2) Existing marine environment disturbance observers cannot be directly applied to navigation practice. Faced with complex and changing marine environments, disturbance observers often fail to achieve the desired observation effect, and the ship trajectory tracking controller designed based on them lacks strong robustness. Summary of the Invention

[0007] The present invention provides a ship formation collaborative obstacle avoidance and robust control method based on differential game to overcome the two technical problems in the current ship formation motion control engineering practice: "the artificial potential field method is not conducive to high-precision and safe navigation of ships" and "the disturbance observer is less robust in the marine environment interference."

[0008] In order to achieve the above object, the technical solution of the present invention is:

[0009] A method for coordinated obstacle avoidance and robust control of a ship formation based on differential game theory specifically includes the following steps:

[0010] S1: Obtaining a mathematical model of ship motion of the ships in the ship formation;

[0011] S2: A reference path is obtained by the set virtual ship, and the distributed kinematic error of the ship is obtained according to the mathematical model of ship motion, so as to construct a first performance indicator function for describing the coordinated obstacle avoidance of ships based on differential game theory;

[0012] S3: Construct a ship obstacle avoidance function and design an optimal virtual control law based on the first performance index function;

[0013] S4: Reduce the order of the derivative of the optimal virtual control law and define the ship position dynamics error in combination with the ship motion mathematical model; construct a second performance indicator function for stabilizing the ship position dynamics error and obtain the ship ocean state disturbance in combination with the constructed first optimal value function;

[0014] S5: Design a third performance index function for stabilizing the ship state dynamics error to obtain the optimal response controller under the ship sea state disturbance;

[0015] S6: Obtaining a heading virtual control law based on the optimal response controller; performing order reduction processing on the derivative of the heading virtual control law to obtain the heading motion dynamics error;

[0016] Constructing a fourth performance index function for describing the bow motion disturbance, and obtaining the ship bow motion disturbance in combination with the constructed second optimal value function;

[0017] S7: Design a fifth performance index function for stabilizing the ship bow motion dynamics error to obtain the optimal robust controller under the ship bow motion disturbance, so as to achieve robust control of coordinated obstacle avoidance of ship formation.

[0018] Furthermore, the expression of the mathematical model of ship motion is:

[0019]

[0020] Where: P i =[x i ,y i ] T Indicates the position status of the i-th ship; P i rate of change; express The derivative of x i ,y i They represent the x-axis coordinate and y-axis coordinate of the ship in the geodetic coordinate system respectively; Represents x i ,y i The rate of change of ψi represents the heading angle of the i-th ship; v i =[u i ,v i ,r i ] T represents the i-th ship speed matrix, which is the ship's forward speed, drift speed and bow speed respectively; F i =[f ui (v i ),f vi (v i )] T represents the nonlinear matrix of the state of i ships; f ui (v i ),f vi (v i ),f ri (v i ) represent the nonlinear terms of ship's forward, drift and pitching degrees of freedom that can be approximated online by radial basis function neural network; M i =[m ui ,m vi ] T represents the displacement matrix of the i-th ship; m ui ,m vi ,m ri Respectively represent the displacement of the ship in forward, drifting and pitching degrees of freedom; d wi =[d wui ,d wvi ] T represents the state interference matrix of the i-th ship; d wui ,d wvi ,d wri They represent the interference of the ocean environment on the ship's forward movement, drift and bow rolling directions respectively; τ ui ,τ ri They represent the propulsion force provided by the propeller of the i-th ship and the turning torque generated by the rudder blade, and serve as the control input of the ship motion control system; τ xi ,τ yi Respectively represent τ ui The decomposition amount along the x-axis and y-axis of the geodetic coordinate system; τ i =[τ xi ,τ yi ] T represents the input matrix of the ship and τ xi =τ ui cos(ψ i ),τ yi =τ ui sin(ψ i );R i represents the rotation matrix of the i-th ship and Ri =[cos(ψ i ),-sin(ψ i ); sin(ψ i ),cos(ψ i )]; Represents the additional matrix of the i-th ship.

[0021] Furthermore, the S2 specifically includes the following steps:

[0022] S21: Obtain a reference path from the set virtual ship. The expression of the reference path is:

[0023]

[0024] Where: x r ,y r ,ψ r They represent the x-axis coordinate, y-axis coordinate and heading angle of the virtual ship in the geodetic coordinate system respectively; u r ,r r They represent the forward speed and bow rolling speed of the virtual ship respectively; Represents x r ,y r ,ψ r The first derivative of

[0025] S22: Based on the reference path, the distributed kinematic error of the ship is obtained according to the mathematical model of ship motion, and its expression is:

[0026]

[0027] Where: P ei =[x ei ,y ei ] T represents the distributed kinematic error of the i-th ship; x ei ,y ei Represents the coordinate errors along the x-axis and y-axis respectively; P j =[x j ,y j ] T represents the state of the j-th ship, x j ,y j They represent the x-axis coordinate and y-axis coordinate of the j-th ship in the geodetic coordinate system; P r =[x r ,y r ] T Indicates the state of the virtual ship; Δ i With Δ j Represents the fleet structure configuration of ship i and ship j respectively; a ijrepresents the communication status between the i-th ship and the j-th ship; g i represents the communication status between the i-th ship and the virtual ship;

[0028] S23: Based on differential game theory, the first performance index function for describing the coordinated obstacle avoidance of ships is constructed, and its expression is:

[0029]

[0030] Where: represents the dynamic form of the j-th ship state, where They are The derivative of Represents x j ,y j rate of change; Indicates P j The rate of change of h i Represents variables related to the obstacle avoidance function; and They represent the kinematic critic neural network weight estimates for the i-th ship and the j-th ship respectively.

[0031] Furthermore, the S3 specifically includes the following steps:

[0032] S31: Construct the ship obstacle avoidance function, and substitute the distributed kinematic error of the ship into the expression:

[0033]

[0034] Where: K i =diag{k oxi ,k oyi} represents the obstacle avoidance parameter of the i-th ship; k oxi ,k oyi They represent the obstacle avoidance parameters for controlling the x-axis and y-axis obstacle avoidance respectively; O represents the number of obstacles; P k =[x k ,y k ] T represents the state of the target obstacle k, x k ,y k They represent the x-axis coordinate and y-axis coordinate of the target obstacle k in the geodetic coordinate system; R k represents the detection radius of the target obstacle k by the i-th ship; r k represents the safety zone radius between target obstacle k and the i-th ship; With A i represent the obstacle function and obstacle avoidance function of the i-th ship respectively;

[0035] S32: Based on the distributed kinematic error of the ship and the first performance index function substituted in step S31, an optimal virtual control law is designed to minimize the first performance index function. The expression of the optimal virtual control law is:

[0036]

[0037] Where: and They represent the inputs of the optimal virtual control of the i-th ship and the j-th ship, which are the first performance index function and Input quantity; K pi With K pj denote the virtual control parameters of the i-th ship and the j-th ship respectively; and denote the inter-ship communication topology of ship i and ship j respectively; d j represents the communication mode between the jth ship and the virtual ship; P ej is the distributed kinematic error of the jth ship; A j is the obstacle avoidance function of the j-th ship; and are the kinematic actor neural network weight estimates for the i-th ship and the j-th ship respectively; S pi With S pj represent the kinematic neural network activation functions of the i-th ship and the j-th ship respectively.

[0038] Furthermore, the S4 specifically includes the following steps:

[0039] S41: The derivative of the optimal virtual control law is reduced to the order, and its expression is

[0040]

[0041] In the formula: i express The filter time constant; β i Indicates that The dynamic reference signal obtained after filtering; β i (0), Represents β i , The initial value of

[0042] S42: Based on step S41 and combined with the ship motion mathematical model, define the ship position dynamics error Its expression is

[0043]

[0044] According to the mathematical model of ship motion and the ship position dynamics error, the derivative of the ship dynamics control error is obtained, and its expression is:

[0045]

[0046] S43: constructing a second performance indicator function for stabilizing the ship position dynamics error according to the ship dynamics control error, and obtaining the ship ocean state disturbance by combining the first optimal value function constructed to minimize the second performance indicator function;

[0047] The expression of the second performance indicator function is:

[0048]

[0049] Where: J di Denotes the performance index describing the ship status interference; D i With T i are symmetric matrices representing the magnitude of control disturbance and control performance in describing ship state disturbance;

[0050] The expression of the first optimal value function is:

[0051]

[0052] Where: represents the worst-case ocean state disturbance obtained by the i-th ship; Indicates that it is used for Performance indicators for evaluation J di The negative gradient of the optimal value function; and They represent the actor and critic neural network estimates of the ship state disturbance respectively; S di Activation function of the neural network representing the disturbance of the ship state.

[0053] Furthermore, the S5 specifically includes the following steps:

[0054] S51: Design the third performance index function for stabilizing the ship state dynamics error, expressed as

[0055]

[0056] Where: represents a performance indicator describing the dynamics of the state;

[0057] S52: Obtain the optimal response controller that minimizes the third performance index function under the disturbance of the ship's ocean state, and its expression is:

[0058]

[0059] Where: is the input of the optimal controller, which is τ in the third performance index function i The input amount; They represent the optimal controllers for controlling the x-axis and y-axis motion of the ship respectively; Control parameters representing the state dynamics; and They represent the estimated weights of the neural network for the ship reorganization state nonlinearity and state dynamics critic-only; S fi and Respectively and The activation function L i represents the intermediate parameter quantity and in and The update law is:

[0060]

[0061] and and Represent the estimated values ​​of neural network weights and The update law of Γ fi and Respectively and The update rate of σ fi Indicates that it is used to control The matrix of the change amplitude and greater than 0; h represents the time interval of each update; represents the Bellman error of the third performance index function; V 1i A value function representing the third performance indicator function.

[0062] Furthermore, the step S6 specifically includes the following steps:

[0063] S61: Obtain the reference heading angle according to the optimal response controller: And define the heading kinematic error as ψ ei =ψ di -ψ i , to obtain the heading virtual control law, which is expressed as

[0064]

[0065] Where: α ri represents the virtual control law of heading; Indicates the heading virtual control parameter; Represents ψ diThe first derivative of i Indicates the actual heading angle;

[0066] S62: The derivative of the heading virtual control law is reduced to the following expression:

[0067] α ri (0) = β ri (0)

[0068] Where: ∈ ri Represents α ri The filter time constant; β ri Indicates that α ri The heading dynamics reference signal obtained after filtering; α ri (0),β ri (0) represents α ri ,β ri The initial value of

[0069] By combining the mathematical model of ship motion, the bow motion dynamics error is obtained, and its expression is r ei ,r ei =β ri -r i ;

[0070] S63: constructing a fourth performance indicator function for describing the bow motion disturbance according to the bow motion dynamics error, and obtaining the ship bow motion disturbance in combination with the constructed second optimal value function;

[0071] The expression of the fourth performance indicator function is:

[0072]

[0073] Where: J dri Denotes the performance index describing the disturbance of bow motion; d i With t i are constants greater than 0 that respectively represent the magnitude of the yaw motion disturbance and the yaw motion control input;

[0074] The expression of the second optimal value function is:

[0075]

[0076] Where: represents the worst-case bow motion disturbance, which is d in the fourth performance indicator function. wri Input quantity; Indicates that it is used for the negative gradient form of the second optimal value function to be evaluated; and are the estimated values ​​of the critic and actor neural network weights for the bow motion disturbance; S dri Neural network activation function representing the bow motion disturbance.

[0077] Furthermore, the step S7 specifically includes the following steps:

[0078] S71: Design the fifth performance index function for stabilizing the ship bow motion dynamics error, and its expression is:

[0079]

[0080] S72: Obtaining an optimal robust controller that minimizes the fifth performance indicator function under the disturbance of the ship's bow motion, so as to achieve robust control of the coordinated obstacle avoidance of the ship formation;

[0081] The expression of the optimal robust controller is:

[0082]

[0083] Where: represents the optimal bowing controller, i.e. the optimal robust controller; k rei Indicates the yaw motion control parameters; and are the estimated weights of the neural network for the ship's reorganized bow motion and the estimated weights of the critic-only neural network for the bow motion, respectively; S fri With S ri Represent the estimated values ​​of neural network weights and The activation function of C i represents the intermediate parameter and C i =1 / m ri -t i / d i ;

[0084] in and The update law is:

[0085]

[0086] and

[0087] ΔS ri (t) = S ri (r ei (t))-S ri (r ei (th))

[0088]

[0089] Where: and Respectively and The update law of Γ fri With Γ ri Respectively and The update rate of σ ri Indicates that it is used to control The matrix of the change range of and greater than 0; e ri V represents the Bellman error of the fifth performance index function; 2i Represents the value function of the fifth performance indicator function.

[0090] Compared with the prior art, the ship obstacle avoidance and robust control method based on differential game in the present invention has the following beneficial effects:

[0091] (1) Aiming at the problem of ship formation coordination and obstacle avoidance, the ship obstacle avoidance function is constructed and combined with the first performance index function to design the optimal virtual control law. That is, according to the ship detection distance, safety zone range, and the position coordinates of the ship and the obstacle, an obstacle avoidance function is constructed to describe the ship collision risk situation. Based on the cooperative differential game theory, a performance index function is established to describe the coordinated movement and obstacle avoidance of the ship formation, thereby obtaining the optimal virtual control law that can minimize the error and the obstacle avoidance function value, that is, ensure both the ship control accuracy and the effectiveness of obstacle avoidance.

[0092] (2) In order to solve the problem of marine environment disturbance to ship motion control, we first construct a second performance index function for stabilizing the ship position dynamics error, and combine it with the constructed first optimal value function to obtain the ship ocean state disturbance, aiming to obtain the disturbance that makes the control error the worst. Then, based on this disturbance, we establish a performance index function for stabilizing the ship state dynamics error, so as to obtain the optimal robust controller under the disturbance of ship bow motion, and further obtain the optimal control input that can compensate for the disturbance in the worst case. By directly compensating the control input with the disturbance in the worst case, the control input is greatly increased, the response of the ship propeller and rudder to the external environment is accelerated, and the control error is quickly stabilized. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to 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.

[0094] Figure 1This is a flow chart of the ship formation cooperative obstacle avoidance and robust control method based on differential game of the present invention;

[0095] Figure 2 Schematic diagram of the wind field and wind-generated waves under wind condition level 3 in this embodiment;

[0096] Figure 3 Schematic diagram of the obstacle avoidance results of the ship formation in this embodiment under wind conditions of level 3;

[0097] Figure 4 : This is a curve diagram of the ship trajectory tracking error in this embodiment;

[0098] Figure 5 This is a curve diagram of ship control input in this embodiment;

[0099] Figure 6 This is a curve diagram of the ship formation obstacle avoidance distance simulation in this embodiment;

[0100] Figure 7 : is a comparative simulation curve diagram of the ship trajectory in this embodiment;

[0101] Figure 8 This is a simulation curve diagram of ship position error comparison in this embodiment;

[0102] Figure 9 This is a comparison simulation curve diagram of ship interference compensation in this embodiment;

[0103] Figure 10 This is the core block diagram of the ship formation collaborative obstacle avoidance and robust control method based on differential game in this embodiment. DETAILED DESCRIPTION

[0104] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of 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. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0105] This embodiment provides a method for coordinated obstacle avoidance and robust control of a fleet of ships based on differential game theory. Figure 1 and Figure 10 As shown, the specific steps include:

[0106] S1: Obtaining a mathematical model of ship motion of the ships in the ship formation;

[0107] Specifically, assuming that the fleet consists of N ships, the mathematical model of the three-degree-of-freedom plane motion of the i-th ship, that is, the expression of the mathematical model of the ship motion is

[0108]

[0109] Where: P i =[x i ,y i ] T Indicates the position status of the i-th ship; P i rate of change; express The derivative of x i ,y i They represent the x-axis coordinate and y-axis coordinate of the ship in the geodetic coordinate system respectively; Represents x i ,y i The rate of change of ψ i represents the heading angle of the i-th ship; v i =[u i ,v i ,r i ] T represents the i-th ship speed matrix, which is the ship's forward speed, drift speed and bow speed respectively; F i =[f ui (v i ),f vi (v i )] T represents the nonlinear matrix of the state of i ships; f ui (v i ),f vi (v i ),f ri (v i ) represent the nonlinear terms of ship's forward, drift and pitching degrees of freedom that can be approximated online by radial basis function neural network; M i =[m ui ,m vi ] T represents the displacement matrix of the i-th ship; m ui ,m vi ,m ri Respectively represent the displacement of the ship in forward, drifting and pitching degrees of freedom; d wi =[d wui ,d wvi ] T represents the state interference matrix of the i-th ship; d wui ,d wvi ,dwri They represent the interference of the ocean environment on the ship's forward movement, drift and bow rolling directions respectively; τ ui ,τ ri They represent the propulsion force provided by the propeller of the i-th ship and the turning torque generated by the rudder blade, and serve as the control input of the ship motion control system; τ xi ,τ yi Respectively represent τ ui The decomposition amount along the x-axis and y-axis of the geodetic coordinate system; τ i =[τ xi ,τ yi ] T represents the input matrix of the ship and τ xi =τ ui cos(ψ i ),τ yi =τ ui sin(ψ i );R i represents the rotation matrix of the i-th ship and R i =[cos(ψ i ),-sin(ψ i ); sin(ψ i ),cos(ψ i )]; represents the additional matrix of the i-th ship;

[0110] S2: A reference path is obtained by the set virtual ship, and the distributed kinematic error of the ship is obtained according to the mathematical model of ship motion, so as to construct a first performance indicator function for describing the coordinated obstacle avoidance of ships based on differential game theory;

[0111] The specific steps include:

[0112] S21: Assume that the reference trajectory of the ship is generated by real-time planning of the virtual ship, that is, the reference path is obtained by the set virtual ship. The expression of the reference path is:

[0113]

[0114] Where: x r ,y r ,ψ r They represent the x-axis coordinate, y-axis coordinate and heading angle of the virtual ship in the geodetic coordinate system respectively; u r ,r r They represent the forward speed and bow rolling speed of the virtual ship respectively; Represents x r ,y r ,ψ r The first derivative of

[0115] S22: Based on the reference path, the distributed kinematic error of the ship is obtained according to the mathematical model of ship motion, and its expression is:

[0116]

[0117] Where: P ei =[x ei ,y ei ] T represents the distributed kinematic error of the i-th ship; x ei ,y ei Represents the coordinate errors along the x-axis and y-axis respectively; P j =[x j ,y j ] T represents the state of the j-th ship, x j ,y j They represent the x-axis coordinate and y-axis coordinate of the j-th ship in the geodetic coordinate system; P r =[x r ,y r ] T Indicates the state of the virtual ship; Δ i With Δ j Represents the fleet structure configuration of ship i and ship j respectively; a ij Indicates the communication status between the i-th ship and the j-th ship. If there is communication, then a ij =1, if there is no communication then a ij =0;g i Indicates the communication status between the i-th ship and the virtual ship. If there is communication, g i =1, if there is no communication then g i =0;

[0118] S23: Based on differential game theory, the first performance index function for describing the coordinated obstacle avoidance of ships is constructed, and its expression is:

[0119]

[0120] In this embodiment, in order to ensure that the first performance indicator function of coordination and obstacle avoidance is the minimum value, the variables related to the obstacle avoidance function are designed as follows:

[0121]

[0122] Where: Indicates P j The rate of change, specifically, Represents x j ,y j rate of change; represents the dynamic form of the j-th ship; They are The derivative of h i Represents variables related to the obstacle avoidance function; and denote the kinematic critic neural network weight estimates for the i-th ship and the j-th ship respectively;

[0123] S3: Construct a ship obstacle avoidance function and design an optimal virtual control law based on the first performance index function; specifically, the following steps are included:

[0124] S31: In order to measure the navigation safety of the ship and help the ship make autonomous obstacle avoidance decisions in this embodiment, the following ship obstacle avoidance function is constructed to substitute the ship's distributed kinematic error. Its expression is:

[0125]

[0126] Where: K i =diag{k oxi ,k oyi} represents the obstacle avoidance parameter of the i-th ship; k oxi ,k oyi represent the obstacle avoidance parameters controlling the x-axis and y-axis obstacle avoidance respectively; O represents the number of obstacles considered, then k∈{N,O} and k≠i; P k =[x k ,y k ] T represents the state of the target obstacle k, x k ,y k x k ,y k They represent the x-axis coordinate and y-axis coordinate of the target obstacle k in the geodetic coordinate system; R k represents the detection radius of the target obstacle k by the i-th ship; r k represents the safety zone radius between target obstacle k and the i-th ship; With A i Denote the obstacle function and obstacle avoidance function of the i-th ship, respectively, so that all ships are outside the safety domain;

[0127] S32: Based on the ship's distributed kinematic error and the first performance index function introduced in step S31, an optimal virtual control law is designed to minimize the first performance index function. That is, there exists an optimal virtual control law such that J pi Reaching the minimum value, the expression of the optimal virtual control law is:

[0128]

[0129] Where: and They represent the inputs of the optimal virtual control of the i-th ship and the j-th ship, which are the first performance index function and Input quantity; K pi With K pj denote the virtual control parameters of the i-th ship and the j-th ship respectively; and denotes the inter-ship communication topology of ship i and ship j respectively; d j represents the communication mode between the jth ship and the virtual ship; P ej is the distributed kinematic error of the jth ship; A j is the obstacle avoidance function of the j-th ship; and are the kinematic actor neural network weight estimates for the i-th ship and the j-th ship respectively; S pi With S pj represent the kinematic neural network activation functions of the i-th ship and the j-th ship respectively;

[0130] S4: Reduce the order of the derivative of the optimal virtual control law and define the ship position dynamics error in combination with the ship motion mathematical model; construct a second performance indicator function for stabilizing the ship position dynamics error and obtain the ship ocean state disturbance in combination with the constructed first optimal value function;

[0131] The specific steps include:

[0132] S41: Optimal Virtual Control Law This will cause a large computational load problem in the subsequent derivation, so the dynamic surface technology is introduced to reduce the order of the derivative of the optimal virtual control law, and its expression is:

[0133]

[0134] In the formula: i express The filter time constant; β i Indicates that The dynamic reference signal obtained after filtering; β i (0), Represents β i , The initial value of

[0135] S42: Based on step S41 and combined with the ship motion mathematical model, define the ship position dynamics error Its expression is

[0136]

[0137] According to the mathematical model of ship motion and the ship position dynamics error, the derivative of the ship dynamics control error is obtained, and its expression is:

[0138]

[0139] S43: constructing a second performance indicator function for stabilizing the ship position dynamics error according to the ship dynamics control error, and obtaining the ship ocean state disturbance by combining the first optimal value function constructed to minimize the second performance indicator function;

[0140] The expression of the second performance indicator function is:

[0141]

[0142] Where: J di Denotes the performance index describing the ship status interference; D i With T i The symmetric matrices representing the size of the control interference and the control performance index in describing the ship state interference are respectively; in actual engineering use, adjusting D i and T i The size depends on the ocean environment. When the ocean conditions are good, a smaller D i and larger T i When the sea conditions are bad or extreme, a larger D i and smaller T i ;

[0143] For the second performance indicator function, there is a worst-case ocean state disturbance that makes J di Reach the minimum value, that is, obtain the expected ship ocean state interference through the constructed first optimal value function; the expression of the first optimal value function is

[0144]

[0145] Where: represents the worst-case ocean state disturbance obtained by the i-th ship; Indicates that it is used for Performance indicators for evaluation J di The negative gradient of the optimal value function; and They represent the actor and critic neural network estimates of the ship state disturbance respectively; S di The activation function of the neural network representing the disturbance of the ship state;

[0146] S5: Design a third performance index function for stabilizing the ship state dynamics error to obtain the optimal response controller under the ship sea state disturbance;

[0147] The specific steps include:

[0148] S51: Design the third performance index function for stabilizing the ship state dynamics error, expressed as

[0149]

[0150] Where: represents a performance indicator describing the dynamics of the state;

[0151] S52: Obtain the optimal response controller that minimizes the third performance index function under the disturbance of the ship's ocean state, and its expression is:

[0152]

[0153] Where: is the input of the optimal controller, which is τ in the third performance index function i The input amount; They represent the optimal controllers for controlling the x-axis and y-axis motion of the ship respectively; Control parameters representing the state dynamics; and They represent the estimated weights of the neural network for the ship reorganization state nonlinearity and state dynamics critic-only; S fi and Respectively and The activation function L i represents the intermediate parameter quantity and

[0154] in and The update law is:

[0155]

[0156] and

[0157] and Represent the estimated values ​​of neural network weights and The update law of Γ fi and Respectively and The update rate of σ fi Indicates that it is used to control The matrix of the change amplitude and greater than 0; h represents the time interval of each update; V represents the Bellman error of the third performance indicator function obtained in the reinforcement learning algorithm; 1i represents the value function of the third performance indicator function; wherein the method for obtaining the Bellman error of the third performance indicator function and the value function is a well-known technical means and will not be elaborated on here;

[0158] S6: Obtaining a heading virtual control law based on the optimal response controller; performing order reduction processing on the derivative of the heading virtual control law to obtain the heading motion dynamics error;

[0159] Constructing a fourth performance index function for describing the bow motion disturbance, and obtaining the ship bow motion disturbance in combination with the constructed second optimal value function;

[0160] The specific steps include:

[0161] S61: Obtain the reference heading angle according to the optimal response controller: And define the heading kinematic error as ψ ei =ψ di -ψ i , to obtain the heading virtual control law, which is expressed as

[0162]

[0163] Where: α ri represents the virtual control law of heading; Indicates the heading virtual control parameter; Represents ψ di The first derivative of i Indicates the actual heading angle;

[0164] S62: Heading virtual control law α ri This will cause a large computational load problem in the subsequent derivation, so the dynamic surface technology is introduced to reduce the order of the derivative of the heading virtual control law, and its expression is:

[0165] α ri (0) = β ri (0)

[0166] Where: ∈ ri Represents α ri α ri The filter time constant; β ri β ri Indicates that α ri α ri The heading dynamics reference signal obtained after filtering; α ri (0),β ri (0) represents α ri ,β riThe initial value of

[0167] By combining the mathematical model of ship motion, the bow motion dynamics error is obtained, and its expression is r ei , r ei =β ri -r i ;

[0168] S63: constructing a fourth performance indicator function for describing the bow motion disturbance according to the bow motion dynamics error, and obtaining the ship bow motion disturbance in combination with the constructed second optimal value function;

[0169] The expression of the fourth performance indicator function is:

[0170]

[0171] Where: J dri It represents the performance index describing the bow motion disturbance, which is d in the fourth performance index function. wri Input quantity; d i With t i are constants greater than 0 that respectively represent the magnitude of the yaw motion disturbance and yaw motion control input;

[0172] For the fourth performance index function, there is a worst-case bow motion interference, which makes the fourth performance index function take the minimum value, that is, the expected ship bow motion interference is obtained by constructing the second optimal value function. The expression of the second optimal value function is:

[0173]

[0174] Where: represents the worst-case bow motion disturbance; Indicates that it is used for the negative gradient form of the second optimal value function to be evaluated; and are the estimated values ​​of the critic and actor neural network weights for the bow motion disturbance; S dri The neural network activation function representing the bow motion disturbance;

[0175] S7: Design a fifth performance index function for stabilizing the ship's bow motion dynamics error to obtain the optimal robust controller under the ship's bow motion disturbance, so as to achieve robust control of coordinated obstacle avoidance in the ship formation;

[0176] The specific steps include:

[0177] S71: Design the fifth performance index function for stabilizing the ship bow motion dynamics error, and its expression is:

[0178]

[0179] S72: Obtaining an optimal robust controller that minimizes the fifth performance indicator function under the disturbance of the ship's bow motion, so as to achieve robust control of the coordinated obstacle avoidance of the ship formation;

[0180] The expression of the optimal robust controller is:

[0181]

[0182] Where: represents the optimal bowing controller, i.e. the optimal robust controller; k rei Indicates the yaw motion control parameters; and are the estimated weights of the neural network for the ship's reorganized bow motion and the estimated weights of the critic-only neural network for the bow motion, respectively; S fri With S ri Represent the estimated values ​​of neural network weights and The activation function of C i represents the intermediate parameter and C i =1 / m ri -t i / d i ;

[0183] in and The update law is:

[0184]

[0185] and

[0186] ΔS ri (t) = S ri (r ei (t))-S ri (r ei (th))

[0187]

[0188] Where: and Respectively and The update law of Γ fri With Γ ri Respectively and The update rate of σ ri Indicates that it is used to control The matrix of the change range of and greater than 0; eri V represents the Bellman error of the fifth performance index function; 2i Represents the value function of the fifth performance indicator function.

[0189] In this embodiment as well as Real-time updates are required according to the following update rules:

[0190]

[0191] Where: σ li Represents a constant greater than 0, intended to control and The change range of I represents the unit matrix; k lci With k lai Respectively and Update rate; and Respectively and The update law of .

[0192] In this example, in order to verify the effectiveness of the proposed ship formation cooperative obstacle avoidance and robust control based on differential game in terms of obstacle avoidance and robustness, computer simulation experiments were carried out using MATLAB and compared with existing algorithms.

[0193] Experiment 1: Using the inland waterway environment as the experimental background, the initial state of the virtual ship is set to [x r (0),y r (0),ψ r (0)] = [0m, 0m, 67deg], and its speed is set to u r =3m / s,r r = 0deg / s. The ship formation structure is set to Δ1 = [0; 0]; The main parameters are selected as follows K i =diag{50,50},K pi =diag{2,2},K pi =diag{2,2}, k rei = 10, i = 1, 2, 3. The ship formation will encounter the moving obstacle a, and the static obstacles b, c, d, and e at the 200th, 400th, 600th, and 800th seconds, respectively, and form a collision situation. It is hoped that the control method proposed in this invention can avoid various collisions of the ship formation.

[0194] like Figures 2 to 6The following are the simulation results of ship formation obstacle avoidance under level 3 wind conditions simulated on the Matlab simulation platform; Figure 2 This is the simulation environment used on the Matlab simulation platform, namely the wind field plane view and wave three-dimensional view under level 3 wind conditions, where Figure 2 (a) is a schematic diagram of the wind field at a 150° wind direction. Figure 2 (b) is a three-dimensional diagram of wind-induced waves; Figure 3 The trajectory of the ship formation shows that the ship formation can maintain coordinated navigation and has the ability to avoid collisions autonomously. The ship formation and the moving obstacle a collided at time t1, crossing each other. According to the International Regulations for Preventing Collisions at Sea, the ship formation should pass by the stern of the moving obstacle a to avoid collision. However, the actual distance between ships 1 and 2 and moving obstacle a is relatively far, while ship 3 is relatively close. In this case, ship 3 has sufficient time and maneuvering space to pass by the stern of moving obstacle a, while ships 1 and 2 should pass by as quickly as possible when they are relatively far away from moving obstacle a. Figure 4 is the position coordinate error of the ship formation. It can be seen that when the ship performs collision avoidance maneuvers, the position error of the ship will become larger, but after avoiding the obstacle, the ship formation will restore the formation and the error will return to near 0. Figure 4 (a) Position error. Figure 4 (b) attitude error; Figure 5 This is the curve of the control input provided by the ship in this embodiment. When the ship needs to avoid collision, more control input is required. In order to more intuitively show the obstacle avoidance effect of the ship formation, Figure 5 (a) is the propeller thrust diagram. Figure 5 (b) is the rudder turning moment diagram; Figure 6 The distances between ships in the fleet and the distances between each ship and each obstacle are given, and it can be seen that all ships are outside the collision distance. Figure 6 (a) is the distance between ships in the fleet. Figure 6 (b) is the distance diagram between each ship and the moving obstacle a. Figure 6 (c) is the distance diagram between each ship and the static obstacle b. Figure 6 (d) Distance diagram between each ship and static obstacle c. Figure 6 (e) Distance d between each ship and static obstacles. Figure 6 (f) Distance diagram between each ship and static obstacle e.

[0195] Experiment 2. This experiment compares the method of this embodiment with the control algorithm of reference [5] to verify the superiority of the control algorithm of the present invention in terms of interference compensation and robustness.

[0196] In this experiment, the forward speed of the virtual ship is u r=3m / s, the bow speed is 18π / 5deg. The initial state of the virtual ship is [x r (0),y r (0),ψ r (0)] = [0m, 0m, 45deg], the initial state of the ship is [x(0), y(0), ψ(0), u(0), v(0), r(0)] = [-20m, 0m, 0deg, 0m / s, 0m / s, 0deg / s]. The main parameters are selected as follows:

[0197] D=diag{0.07,0.07}, T=diag{1,1}, d=0.08, t=1.

[0198] like Figures 7 to 9 Shown are the experimental results of this experiment; Figure 7 For ship trajectory, both the algorithm proposed in this invention and the algorithm in the literature [1] can realize ship trajectory tracking, but the ship using the algorithm proposed in this invention is closer to the virtual ship and has better trajectory tracking performance; Figure 8 is the control error, where Figure 8 (a) is the comparison of x-axis errors. Figure 8 (b) is a comparison of the y-axis error. It can be seen from the figure that the algorithm proposed in the present invention has a smaller control error and a smaller range of jitter, which indicates that the control algorithm responds to interference more quickly and effectively. Figure 9 The comparison between the worst-case interference calculated by the algorithm of the present invention and the actual interference is shown. Figure 9 (a) is a comparison diagram of forward degree of freedom interference. Figure 9 (b) is a comparison diagram of the interference of the lateral drift freedom. Figure 9 (c) is a comparison diagram of the bow freedom interference. The worst-case interference calculated by the algorithm of the present invention, d wu ,d wv ,d wr For actual interference.

[0199] Combined with the above verification test and compared with the existing technology, the use of the present invention can bring the following two beneficial effects:

[0200] (1) The method of this embodiment solves the problem of ship formation cooperation and autonomous obstacle avoidance. The established ship formation cooperative differential game relationship can not only realize the cooperative navigation of the ship formation, but also make autonomous ship formation obstacle avoidance decisions, which is of great significance to the autonomous and safe navigation of the ship formation.

[0201] (2) The ocean disturbance compensation method based on the master-slave differential game proposed in this embodiment takes into account the relationship between ocean environmental disturbance, dynamic control error and control input, and has the ability to resist ocean environmental disturbance. The ship controller designed in this way has strong robustness and is of great significance to ship engineering with high navigation accuracy requirements.

[0202] The relevant documents involved in this embodiment are as follows:

[0203] [1]Guoqing Zhang, Shang Liu, Xianku Zhang and Weidong Zhang. Event-triggered cooperative formation control for autonomous surface vehicles under the maritime search operation. IEEE Transactions on Intelligent TransportationSystems, 2022, 23(11):21392–21404.

[0204] [2] Nan Gu, Dan Wang, Zhouhua Peng and Lu liu. Observer-based finite-timecontrol for distributed path maneuvering of underactuated unmanned surfacevehicles with collision avoidance and connectivitypreservation. IEEE Transactions on Systems, man, and cybernetics: systems, 2021, 51 (8): 5105-5115.

[0205] [3]Yu Lu,Guoqing Zhang,Zhijian Sun and Weidong Zhang.Robust adaptiveformation control of underactuated autonomous surface vessels based on MLPand DOB.Nonlinear Dynamics.2018,94:503–519.

[0206] [4]Xiao Liang,Xingru Qu,Ning Wang,Ye Li and Rubo Zhang.Swarm controlwith collision avoidance for multiple underactuated surface vehicles.2019,191:106516.

[0207] [5]Guoxing Wen, Shuzhi Sam Ge, CLPhilip Chen, Fangwen Tu and ShengnanWang. Adaptive tracking control of surface vessel using optimized backsteppingtechnique. IEEE Transactions on Cybernetics, 2019, 49(9): 3420-3431.

[0208] 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. A ship formation coordinated obstacle avoidance and robust control method based on differential game, characterized by: The specific steps include: S1: Obtaining a mathematical model of ship motion of the ships in the ship formation; S2: A reference path is obtained by the set virtual ship, and the distributed kinematic error of the ship is obtained according to the mathematical model of ship motion, so as to construct a first performance indicator function for describing the coordinated obstacle avoidance of ships based on differential game theory; S3: Construct a ship obstacle avoidance function and design an optimal virtual control law based on the first performance index function; S4: Reduce the order of the derivative of the optimal virtual control law and define the ship position dynamics error in combination with the ship motion mathematical model; construct a second performance indicator function for stabilizing the ship position dynamics error and obtain the ship ocean state disturbance in combination with the constructed first optimal value function; S5: Design a third performance index function for stabilizing the ship state dynamics error to obtain the optimal response controller under the ship sea state disturbance; S6: Obtaining a heading virtual control law based on the optimal response controller; performing order reduction processing on the derivative of the heading virtual control law to obtain the heading motion dynamics error; Constructing a fourth performance index function for describing the bow motion disturbance, and obtaining the ship bow motion disturbance in combination with the constructed second optimal value function; S7: Design a fifth performance index function for stabilizing the ship bow motion dynamics error to obtain the optimal robust controller under the ship bow motion disturbance, so as to achieve robust control of coordinated obstacle avoidance of ship formation.

2. The method for coordinated obstacle avoidance and robust control of a ship formation based on differential game according to claim 1, characterized in that: The expression of the mathematical model of ship motion is: Where: P i =[x i ,y i ] T Indicates the position status of the i-th ship; P i rate of change; express The derivative of x i ,y i They represent the x-axis coordinate and y-axis coordinate of the ship in the geodetic coordinate system respectively; Represents x i ,y i The rate of change of ψ i represents the heading angle of the i-th ship; v i =[u i ,v i ,r i ] T represents the i-th ship speed matrix, which is the ship's forward speed, drift speed and bow speed respectively; F i =[f ui (v i ),f vi (v i )] T represents the nonlinear matrix of the state of i ships; f ui (v i ),f vi (v i ),f ri (v i ) represent the nonlinear terms of ship's forward, drift and pitching degrees of freedom that can be approximated online by radial basis function neural network; M i =[m ui ,m vi ] T represents the displacement matrix of the i-th ship; m ui ,m vi ,m ri Respectively represent the displacement of the ship in forward, drifting and pitching degrees of freedom; d wi =[d wui ,d wvi ] T represents the state interference matrix of the i-th ship; d wui ,d wvi ,d wri They represent the interference of the ocean environment on the ship's forward movement, drift and bow rolling directions respectively; τ ui ,τ ri They represent the propulsion force provided by the propeller of the i-th ship and the turning torque generated by the rudder blade, and serve as the control input of the ship motion control system; τ xi ,τ yi Respectively represent τ ui The decomposition amount along the x-axis and y-axis of the geodetic coordinate system; τ i =[τ xi ,τ yi ] T represents the input matrix of the ship and τ xi =τ ui cos(ψ i ),τ yi =τ ui sin(ψ i );R i represents the rotation matrix of the i-th ship and R i =[cos(ψ i ),-sin(ψ i ); sin(ψ i ),cos(ψ i )]; Represents the additional matrix of the i-th ship.

3. The method for coordinated obstacle avoidance and robust control of a ship formation based on differential game according to claim 2, characterized in that: The S2 specifically includes the following steps: S21: Obtain a reference path from the set virtual ship. The expression of the reference path is: Where: x r ,y r ,ψ r They represent the x-axis coordinate, y-axis coordinate and heading angle of the virtual ship in the geodetic coordinate system respectively; u r ,r r They represent the forward speed and bow rolling speed of the virtual ship respectively; Represents x r ,y r ,ψ r The first derivative of S22: Based on the reference path, the distributed kinematic error of the ship is obtained according to the mathematical model of ship motion, and its expression is: Where: P ei =[x ei ,y ei ] T represents the distributed kinematic error of the i-th ship; x ei ,y ei Represents the coordinate errors along the x-axis and y-axis respectively; P j =[x j ,y j ] T represents the state of the j-th ship, x j ,y j They represent the x-axis coordinate and y-axis coordinate of the j-th ship in the geodetic coordinate system; P r =[x r ,y r ] T Indicates the state of the virtual ship; Δ i With Δ j Represents the fleet structure configuration of ship i and ship j respectively; a ij represents the communication status between the i-th ship and the j-th ship; g i represents the communication status between the i-th ship and the virtual ship; S23: Based on differential game theory, the first performance index function for describing the coordinated obstacle avoidance of ships is constructed, and its expression is: Where: Indicates P j The rate of change, specifically, Represents x j ,y j rate of change; represents the dynamic form of the j-th ship; They are The derivative of h i Represents variables related to the obstacle avoidance function; and They represent the kinematic critic neural network weight estimates for the i-th ship and the j-th ship respectively.

4. The method for coordinated obstacle avoidance and robust control of a ship formation based on differential game according to claim 3 is characterized in that: The S3 specifically includes the following steps: S31: Construct the ship obstacle avoidance function and substitute it into the ship's distributed kinematic error. The expression is: Where: K i =diag{k oxi ,k oyi } represents the obstacle avoidance parameter of the i-th ship; k oxi ,k oyi They represent the obstacle avoidance parameters for controlling the x-axis and y-axis obstacle avoidance respectively; O represents the number of obstacles; P k =[x k ,y k ] T represents the state of the target obstacle k, x k ,y k They represent the x-axis coordinate and y-axis coordinate of the target obstacle k in the geodetic coordinate system; R k represents the detection radius of the target obstacle k by the i-th ship; r k represents the safety zone radius between target obstacle k and the i-th ship; With A i represent the obstacle function and obstacle avoidance function of the i-th ship respectively; S32: Based on the distributed kinematic error of the ship and the first performance index function substituted in step S31, an optimal virtual control law is designed to minimize the first performance index function. The expression of the optimal virtual control law is: Where: and They represent the inputs of the optimal virtual control of the i-th ship and the j-th ship, which are the first performance index function and Input quantity; K pi With K pj denote the virtual control parameters of the i-th ship and the j-th ship respectively; and denotes the inter-ship communication topology of ship i and ship j respectively; d j represents the communication mode between the jth ship and the virtual ship; P ej is the distributed kinematic error of the jth ship; A j is the obstacle avoidance function of the j-th ship; and are the kinematic actor neural network weight estimates for the i-th ship and the j-th ship respectively; S pi With S pj represent the kinematic neural network activation functions of the i-th ship and the j-th ship respectively.

5. The method for coordinated obstacle avoidance and robust control of a ship formation based on differential game according to claim 4 is characterized in that: The S4 specifically includes the following steps: S41: The derivative of the optimal virtual control law is reduced to the order, and its expression is In the formula: i express The filter time constant; β i Indicates that The dynamic reference signal obtained after filtering; Represents β i , The initial value of S42: Based on step S41 and combined with the ship motion mathematical model, define the ship position dynamics error Its expression is According to the mathematical model of ship motion and the ship position dynamics error, the derivative of the ship dynamics control error is obtained, and its expression is: S43: constructing a second performance indicator function for stabilizing the ship position dynamics error according to the ship dynamics control error, and obtaining the ship ocean state disturbance by combining the first optimal value function constructed to minimize the second performance indicator function; The expression of the second performance indicator function is: Where: J di Denotes the performance index describing the ship status interference; D i With T i are symmetric matrices representing the magnitude of control disturbance and control performance in describing ship state disturbance; The expression of the first optimal value function is: Where: represents the worst-case ocean state disturbance obtained by the i-th ship; Indicates that it is used for Performance indicators for evaluation J di The negative gradient of the optimal value function; and They represent the actor and critic neural network estimates of the ship state disturbance respectively; S di Activation function of the neural network representing the disturbance of the ship state.

6. The method for coordinated obstacle avoidance and robust control of a ship formation based on differential game according to claim 5, characterized in that: The S5 specifically includes the following steps: S51: Design the third performance index function for stabilizing the ship state dynamics error, expressed as Where: represents a performance indicator describing the dynamics of the state; S52: Obtain the optimal response controller that minimizes the third performance index function under the disturbance of the ship's ocean state, and its expression is: Where: is the input of the optimal controller, which is τ in the third performance index function i The input amount; They represent the optimal controllers for controlling the x-axis and y-axis motion of the ship respectively; Control parameters representing the state dynamics; and They represent the estimated weights of the neural network for the ship reorganization state nonlinearity and state dynamics critic-only; S fi and Respectively and The activation function L i represents the intermediate parameter quantity and in and The update law is: and and Represent the estimated values ​​of neural network weights and The update law of Γ fi and Respectively and The update rate of σ fi Indicates that it is used to control The matrix of the change amplitude and greater than 0; h represents the time interval of each update; represents the Bellman error of the third performance index function; V 1i A value function representing the third performance indicator function.

7. The method for coordinated obstacle avoidance and robust control of a ship formation based on differential game according to claim 6, characterized in that: The S6 specifically includes the following steps: S61: Obtain the reference heading angle according to the optimal response controller: And define the heading kinematic error as ψ ei =ψ di -ψ i , to obtain the heading virtual control law, which is expressed as Where: α ri represents the virtual control law of heading; Indicates the heading virtual control parameter; Represents ψ di The first derivative of i Indicates the actual heading angle; S62: The derivative of the heading virtual control law is reduced to the following expression: Where: ∈ ri Represents α ri The filter time constant; β ri Indicates that α ri The heading dynamics reference signal obtained after filtering; α ri (0),β ri (0) represents α ri ,β ri The initial value of By combining the mathematical model of ship motion, the bow motion dynamics error is obtained, and its expression is r ei , r ei =β ri -r i ; S63: constructing a fourth performance indicator function for describing the bow motion disturbance according to the bow motion dynamics error, and obtaining the ship bow motion disturbance in combination with the constructed second optimal value function; The expression of the fourth performance indicator function is: Where: J dri Denotes the performance index describing the disturbance of bow motion; d i With t i are constants greater than 0 that respectively represent the magnitude of the yaw motion disturbance and the yaw motion control input; The expression of the second optimal value function is: Where: represents the worst-case bow motion disturbance, which is d in the fourth performance index function. wri Input quantity; Indicates that it is used for the negative gradient form of the second optimal value function to be evaluated; and are the estimated values ​​of the critic and actor neural network weights for the bow motion disturbance; S dri Neural network activation function representing the bow motion disturbance.

8. The method for coordinated obstacle avoidance and robust control of a ship formation based on differential game according to claim 7, characterized in that: The S7 specifically includes the following steps: S71: Design the fifth performance index function for stabilizing the ship bow motion dynamics error, and its expression is: S72: Obtaining an optimal robust controller that minimizes the fifth performance indicator function under the disturbance of the ship's bow motion, so as to achieve robust control of the coordinated obstacle avoidance of the ship formation; The expression of the optimal robust controller is: Where: represents the optimal bowing controller, i.e. the optimal robust controller; k rei Indicates the yaw motion control parameters; and are the estimated weights of the neural network for the ship's reorganized bow motion and the estimated weights of the critic-only neural network for the bow motion, respectively; S fri With S ri Represent the estimated values ​​of neural network weights and The activation function of C i represents the intermediate parameter and C i =1 / m ri -t i / d i ; in and The update law is: and ΔS ri (t)=S ri (r ei (t))-S ri (r ei (t-h)) Where: and Respectively and The update law of Γ fri With Γ ri Respectively and The update rate of σ ri Indicates that it is used to control The matrix of the change range of and greater than 0; e ri V represents the Bellman error of the fifth performance index function; 2i Represents the value function of the fifth performance indicator function.

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