Method of attacking protected target area by unmanned surface boat based on differential game

Abstract

The present invention discloses a method for a surface unmanned boat to attack a protected target area based on differential game. Based on the motion model of the offensive surface unmanned boat, the attack point of the offensive surface unmanned boat is obtained. According to the position coordinates of the attack point of the offensive surface unmanned boat and the position coordinates of the offensive surface unmanned boat, the attack angle of the offensive surface unmanned boat, the first-order differential of the inner product between the unit vector of the attack angle of the offensive surface unmanned boat and the unit vector of the current heading angle and the state condition of the offensive surface unmanned boat are obtained; and then the heading control input of the offensive surface unmanned boat is obtained to construct the offensive strategy of the offensive surface unmanned boat. In the process of solving, it is not necessary to calculate a complex differential equation group, which greatly reduces the difficulty and time of solving the strategy, and can adapt to the highly dynamic sea battlefield form.

Description

Technical Field

[0001] The invention relates to the technical field of motion control of unmanned surface boats, and in particular to a method for an unmanned surface boat to attack a protected target area based on differential game. Background Art

[0002] The game confrontation of surface unmanned boats is a key technology for future surface warfare. In the game confrontation of surface unmanned boats, according to the different mission objectives of the two parties, they can be divided into defensive surface unmanned boats and offensive surface unmanned boats. When both parties make autonomous decisions and movements based on state information (position and heading), the confrontation will be a complex game problem.

[0003] Differential game is a theory that uses differential methods and optimal control methods to study continuous dynamic games. It is very suitable for modeling the game process of the two opposing parties. When applying this theory for quantitative analysis, most of the related studies focus on defensive surface unmanned boats, unilaterally simplifying the model establishment and strategy solution of offensive surface unmanned boats. In the specific implementation, offensive surface unmanned boats are regarded as attackers with simple linear motion or dynamic obstacle avoidance capabilities. There are few studies on offensive strategies for offensive surface unmanned boats. In addition, because the differential game solution process that satisfies the optimal control of constrained surface unmanned boats often requires solving complex differential equations, the strategy solution process is complicated, and with the increase in the number of confrontation nodes, the difficulty and time of the strategy solution are further aggravated, making it difficult to adapt to the highly dynamic sea battlefield situation. Summary of the invention

[0004] The present invention provides a method for an unmanned surface boat to attack a protected target area based on differential game, so as to overcome the above technical problems.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A method for an unmanned surface boat to attack a protected target area based on differential game theory comprises the following steps:

[0007] S1: Obtain the initial parameters of the surface unmanned boat, establish the motion model of the surface unmanned boat, and obtain the target area of ​​the surface unmanned boat game;

[0008] The initial parameters of the unmanned surface boat include: the position coordinates of the defensive unmanned surface boat, the position coordinates of the offensive unmanned surface boat, the heading angle of the defensive unmanned surface boat and the heading angle of the offensive unmanned surface boat;

[0009] S2: acquiring the attack point position coordinates of the offensive surface unmanned boat according to the initial parameters of the surface unmanned boat and the target area;

[0010] S3: acquiring an attack angle of the offensive unmanned surface boat according to the attack point position coordinates of the offensive unmanned surface boat and the position coordinates of the offensive unmanned surface boat;

[0011] S4: according to the attack angle of the offensive unmanned surface boat, obtaining the first-order differential of the inner product between the unit vector of the attack angle of the offensive unmanned surface boat and the unit vector of the current heading angle; obtaining the state condition of the offensive unmanned surface boat;

[0012] S5: Based on the first-order differential of the inner product between the unit vector of the offensive surface unmanned boat's attack angle and the unit vector of the current heading angle, the state condition of the offensive surface unmanned boat, and the heading angle of the offensive surface unmanned boat, the heading control input of the offensive surface unmanned boat is obtained to realize the surface unmanned boat's attack on the protected target area.

[0013] Beneficial effects: The method of the present invention for using a surface unmanned boat to attack a protected target area based on differential game, based on the motion model of the offensive surface unmanned boat, obtains the attack point of the offensive surface unmanned boat, obtains the attack angle of the offensive surface unmanned boat according to the position coordinates of the attack point of the offensive surface unmanned boat and the position coordinates of the offensive surface unmanned boat, the first-order differential of the inner product between the unit vector of the attack angle of the offensive surface unmanned boat and the unit vector of the current heading angle, and the state condition of the offensive surface unmanned boat; and then obtains the heading control input of the offensive surface unmanned boat to construct the offensive strategy of the offensive surface unmanned boat. In the process of solving, there is no need to calculate a complex differential equation group, which greatly reduces the difficulty and time of solving the strategy, and can adapt to the highly dynamic sea battlefield form. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0015] Figure 1 A flow chart of a differential game strategy method for an unmanned surface boat to attack a protected target area according to the present invention;

[0016] Figure 2 A two-dimensional plane schematic diagram of the unmanned surface boat confrontation area according to an embodiment of the present invention;

[0017] Figure 3 A schematic diagram of a safety area of ​​an offensive unmanned surface boat according to an embodiment of the present invention;

[0018] Figure 4It is a schematic diagram of the trajectory of the offensive strategy for adjusting the heading of an offensive unmanned surface boat according to an embodiment of the present invention. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0020] This embodiment provides a method for an unmanned surface boat to attack a protected target area based on differential game theory, such as Figure 1 As shown, the following steps are included:

[0021] S1: Obtain the initial parameters of the surface unmanned boat (including the defensive surface unmanned boat and the offensive surface unmanned boat) to establish the motion model of the surface unmanned boat; obtain the target area of ​​the surface unmanned boat game;

[0022] The initial parameters of the unmanned surface boat include: the position coordinates of the defensive unmanned surface boat, the position coordinates of the offensive unmanned surface boat, the heading angle of the defensive unmanned surface boat and the heading angle of the offensive unmanned surface boat;

[0023] Among them, surface unmanned boats include offensive surface unmanned boats and defensive surface unmanned boats. The surface unmanned boat confrontation area is considered to be a two-dimensional sea plane, which includes: the interior of the target area, the boundary of the target area and the game area.

[0024] Preferably, in S1, the motion model of the unmanned surface vehicle is established as follows:

[0025]

[0026] In the formula, is the first-order differential of the horizontal coordinate of the position coordinate of the offensive surface unmanned boat; is the first-order differential of the ordinate coordinate of the position coordinate of the offensive surface unmanned boat; is the first-order differential of the heading angle of the offensive surface unmanned vehicle; is the first-order differential of the horizontal coordinate of the position coordinate of the j-th defensive surface unmanned boat; is the first-order differential of the ordinate coordinate of the position coordinate of the j-th defensive surface unmanned boat; is the first-order differential of the heading angle of the jth defensive surface unmanned boat; K E is the heading control input of the offensive surface unmanned boat; U E is the constant speed of the offensive surface unmanned vehicle; RE is the minimum turning radius of an offensive surface unmanned vehicle; is the heading control input of the jth defensive surface unmanned vehicle; is the constant speed of the jth defensive surface unmanned vehicle; is the minimum turning radius of the jth defensive surface unmanned vehicle; is the heading angle of the jth defensive surface unmanned boat, j represents the index number of the defensive unmanned surface boat; J represents the number of the defensive unmanned surface boat;

[0027] Specifically, after integrating the first-order differential, the position coordinates of the offensive surface unmanned boat are obtained: and the heading angle φ of the position of the offensive surface unmanned boat E ∈[0,2π); the position coordinates of the jth defensive surface unmanned boat and the heading angle of the jth defensive surface unmanned boat in, It means defensive unmanned surface vessel team; represents the two-dimensional sea plane; x E ' is the horizontal coordinate of the offensive surface unmanned boat; y E ' is the ordinate of the offensive unmanned surface vessel; is the horizontal coordinate of the jth defensive surface unmanned boat; is the ordinate of the jth defensive unmanned surface vehicle;

[0028] Specifically, the target area in this embodiment is established as follows: Figure 2 As shown:

[0029] Figure 2 The game area and target area in the confrontation area are shown in the figure. The target area is the area that the attacking boat wants to reach safely; the game area Target area The two are considered to be planes in the two-dimensional sea area, and the boundary line segment of the target area of ​​the surface unmanned boat game is defined as:

[0030]

[0031] Where: g i (x b ,y b ) represents the line segment that constitutes the boundary of the target area of ​​the surface unmanned boat game, where x b The horizontal coordinate of the point on the line segment that constitutes the boundary of the target area of ​​the surface unmanned boat game; y b The vertical coordinates of the points on the line segment that constitutes the boundary of the target area of ​​the surface unmanned boat game; m i Indicates the slope of the line segment; ni represents the intercept of the line segment; i=1,...,Ι represents the number of line segments; represents a mathematical definition symbol; x and y represent the horizontal and vertical coordinates of a point in the two-dimensional sea plane, respectively. Among them, the interior of the target area is formed by connecting the i line segments that constitute the boundary of the target area of ​​the surface unmanned boat game end to end; the geometric figure formed by connecting the line segments that constitute the boundary of the target area of ​​the surface unmanned boat game end to end is the boundary of the target area, expressed as g(x b ,y b ), the boundary of the target area and the interior of the target area together form the offensive target area of ​​the offensive surface unmanned boat. Specifically:

[0032]

[0033]

[0034]

[0035] Where: g(x b ,y b ) represents a geometric figure composed of line segments; Indicates the boundary of the target area; inter(g(x b ,y b )) represents the interior of the geometric figure, Ω goal Indicates the interior of the target area; exter(g(x b ,y b )) represents the exterior of the geometric figure, Ω play Represents the outside of the target area, that is, the game area; (x, y) represents the coordinates of a point in the two-dimensional sea plane.

[0036] The offensive surface unmanned vehicle will try to enter the target area before being captured, while the defensive surface unmanned vehicle team Try to capture the target area protected by the offensive surface unmanned boat as much as possible in the game area. In this embodiment, various state quantities and confrontation area information of the surface unmanned boat are obtained through conventional sensing equipment.

[0037] S2: Obtaining the attack point of the offensive surface unmanned boat according to the initial parameters of the surface unmanned boat;

[0038] Preferably, the attack point of the offensive unmanned surface boat is obtained as follows:

[0039] S21: constructing a safety zone for the offensive unmanned surface boat according to the position coordinates of the defensive unmanned surface boat and the position coordinates of the offensive unmanned surface boat: determining the position coordinates of points within the safety zone for the offensive unmanned surface boat;

[0040]

[0041]

[0042]

[0043] In the formula, It represents the closed area formed by the safety area of ​​the offensive unmanned surface vehicle and the boundary of the safety area; Indicates the boundary of the safety area of ​​the offensive unmanned surface vehicle; Ω SRE Indicates the safety area for offensive unmanned surface vessels; represents the boundary coordinates of the safety zone for offensive surface unmanned boats, x Ea ' represents the horizontal coordinate of the safety zone boundary of the offensive surface unmanned boat; y Ea ' represents the vertical coordinate of the safety zone boundary of the offensive surface unmanned boat; t represents the time; f j (x Ea ,t) represents the geometric figure of the safety area boundary of the offensive surface unmanned boat relative to the jth defensive surface unmanned boat: Represents offensive surface unmanned boat and defensive surface unmanned boat team The intersection of the closed areas of the offensive surface unmanned boats, such as Figure 3 As shown; ||·||2 represents the Euclidean norm; represents the position coordinates of the jth defensive surface unmanned boat; Indicates the position coordinates of the offensive surface unmanned boat; represents the speed ratio of the jth defensive surface unmanned boat and the offensive surface unmanned boat;

[0044] Specifically, the closed area formed by the safety area of ​​the offensive surface unmanned boat and the safety area boundary is the union of the safety area boundary and the safety area, that is, The safety area is the area constructed by the offensive surface unmanned boat and the corresponding defensive surface unmanned boat to ensure a certain safety range for the offensive surface unmanned boat. Therefore, in this embodiment, the boundary of the safety area is not counted as the boundary of the area to ensure a certain safety range for the offensive surface unmanned boat.

[0045] Furthermore, the coordinates of the point positions within the safety zone of the offensive surface unmanned boat are determined as follows:

[0046]

[0047] In the formula, x * represents the coordinate set of points in the safety area of ​​the offensive surface unmanned boat, x IIndicates the position coordinates of any point within the safety zone of the offensive surface unmanned vehicle; [·] T Represents the transpose of a vector.

[0048] S22: Obtain the coordinates of the center point of the safety zone of the offensive unmanned surface boat:

[0049]

[0050] In the formula, represents the position coordinates of the jth defensive surface unmanned boat; Indicates the position coordinates of the offensive surface unmanned boat; x o The coordinates of the center point of the circle representing the safety zone of the offensive unmanned surface vehicle;

[0051] So we get the center point x of the safe area of ​​the offensive surface unmanned boat. o And the straight line of the line segment formula (2) perpendicular to the boundary of the target area is:

[0052]

[0053] In the formula, (x c ,y c ) is too x o The coordinates of any point on the straight line that is perpendicular to the boundary of the target area; -1 / m i For x o The slope of the line segment perpendicular to the boundary of the target area; x E ' is the horizontal coordinate of the position coordinate of the offensive surface unmanned boat; y E ' is the ordinate of the position coordinate of the offensive surface unmanned boat; is the horizontal coordinate of the position coordinate of the jth defensive surface unmanned boat; is the ordinate of the position coordinate of the jth defensive surface unmanned boat;

[0054] S23: Based on the position coordinates of the point in the safety area of ​​the offensive unmanned surface boat and the straight line passing through the center point of the safety area of ​​the offensive unmanned surface boat and perpendicular to the line segment of the target area boundary, the position coordinates of the attack point of the offensive unmanned surface boat are obtained by combining equations (6) and (8) as follows:

[0055]

[0056] In the formula, x I’ Indicates the position coordinates of the attack point of the offensive unmanned surface vehicle;

[0057] So far, the attack point position coordinates of the offensive surface unmanned boat are obtained as x I’ .

[0058] S3: Obtain the attack angle of the offensive unmanned surface boat according to the attack point position coordinates of the offensive unmanned surface boat and the heading angle of the offensive unmanned surface boat:

[0059]

[0060] In the formula, x I’ ' is the horizontal coordinate of the attack point position coordinate of the offensive surface unmanned boat; y I’ ' is the ordinate of the attack point position coordinate of the offensive surface unmanned boat; θ E is the attack angle of the offensive surface unmanned vehicle; Indicates the position coordinates of the offensive surface unmanned boat; x E ' is the horizontal coordinate of the position coordinate of the offensive surface unmanned boat; y E ' is the ordinate of the position coordinate of the offensive surface unmanned boat;

[0061] S4: Obtain the first-order differential of the inner product between the unit vector of the attack angle of the offensive unmanned surface boat and the unit vector of the current heading angle and the state condition of the offensive unmanned surface boat;

[0062] Preferably, the first-order differential of the inner product between the unit vector of the attack angle of the offensive unmanned surface vehicle and the unit vector of the current heading angle is obtained as follows:

[0063] Take the inner product of the heading angle unit vector of the offensive surface unmanned vehicle and the attack angle unit vector, and combine equations (1), (12) and (10):

[0064]

[0065] In the formula, [cosφ E ,sinφ E ] represents the unit vector of the current heading angle of the offensive surface unmanned boat; represents the transpose of the unit vector of the attack angle of the offensive surface unmanned boat; c represents the inner product between the unit vector of the attack angle of the offensive surface unmanned boat and the unit vector of the current heading angle; x I’ Indicates the position coordinates of the attack point of the offensive surface unmanned boat; U E is the constant speed of the offensive surface unmanned vehicle; Represents the first-order differential transpose of the position coordinates of the offensive surface unmanned boat;

[0066] Differentiate the inner product of the heading angle unit vector and the attack angle unit vector of the offensive surface unmanned boat to obtain:

[0067]

[0068] In the formula, is the first-order differential of the inner product between the unit vector of the attack angle of the offensive unmanned surface vehicle and the unit vector of the current heading angle; represents the first-order differential of the position coordinates of the offensive surface unmanned boat; is the second-order differential transpose of the position coordinates of the offensive surface unmanned boat; is the first-order differential of the position coordinates of the attack point of the offensive surface unmanned boat.

[0069] According to the coordinates of the points in the safety area of ​​the unmanned boat, combined with equations (1), (6) and (14), we can get

[0070]

[0071] In the formula, y I’ ' is the ordinate of the attack point position coordinate of the offensive surface unmanned boat; y E ' is the ordinate of the position coordinate of the offensive surface unmanned boat; is the heading angle of the jth defensive surface unmanned boat; K E is the heading control input of the offensive surface unmanned boat; U E is the constant speed of the offensive surface unmanned vehicle; R E is the minimum turning radius of an offensive surface unmanned vehicle; is the constant speed of the jth defensive surface unmanned vehicle; represents the speed ratio of the jth defensive surface unmanned boat and the offensive surface unmanned boat; Indicates the position coordinates of the offensive surface unmanned boat; x I’ Indicates the position coordinates of the attack point of the offensive unmanned surface vehicle; represents the position coordinates of the jth defensive surface unmanned boat; φ E represents the heading angle of the offensive surface unmanned boat; θ E is the attack angle of the offensive surface unmanned vehicle; A joint function representing the heading angle and attack angle of an offensive unmanned surface vehicle, and the heading angle and azimuth of a defensive unmanned surface vehicle;

[0072] in:

[0073]

[0074]

[0075] Where η represents the azimuth angle of the jth defensive surface unmanned boat;

[0076] According to the absolute value inequality scaling principle, equation (16) is simplified to:

[0077]

[0078] According to the range of trigonometric functions, we can get:

[0079]

[0080] Combining equation (15) and equation (18), according to the inequality scaling principle, we can obtain:

[0081]

[0082] Then according to the position coordinates of the attack point of the offensive surface unmanned boat (9), we get:

[0083]

[0084] In the formula, is the radius of the offensive unmanned surface vessel.

[0085] Substituting formula (20) into formula (19), we get:

[0086]

[0087] Preferably, the state condition of the offensive unmanned surface vehicle is obtained as follows:

[0088]

[0089] In the formula, R is the radius of the offensive surface unmanned boat. E is the minimum turning radius of an offensive surface unmanned vehicle;

[0090] S5: Based on the first-order differential of the inner product between the unit vector of the offensive surface unmanned boat's attack angle and the unit vector of the current heading angle, the state condition of the offensive surface unmanned boat, and the heading angle of the offensive surface unmanned boat, the heading control input of the offensive surface unmanned boat is obtained to construct an offensive strategy for the offensive surface unmanned boat and realize the surface unmanned boat's attack on the protected target area.

[0091] Preferably, the heading control input of the offensive surface unmanned boat is obtained as follows:

[0092] When φ E =θ E When , the heading angle of the offensive surface unmanned boat is equal to the attack angle, and the heading control input of the offensive surface unmanned boat is:

[0093] K E =0 (11)

[0094] Where: K E Represents the heading control input of the offensive surface unmanned vehicle; φ E represents the heading angle of the offensive surface unmanned boat,

[0095] When φ E ≠θ E When , the heading angle of the offensive surface unmanned boat is not equal to the attack angle. From formula (21), we can know that sin(φ E -θ E )≠0, therefore,

[0096] When the offensive unmanned surface boat satisfies: the first-order differential of the inner product between the unit vector of the offensive unmanned surface boat's attack angle and the unit vector of the current heading angle is greater than zero, and the offensive unmanned surface boat satisfies the state condition of the offensive unmanned surface boat, the heading control input of the offensive unmanned surface boat is:

[0097]

[0098] Where, sign() represents the sign function; x E ' is the horizontal coordinate of the position coordinate of the offensive surface unmanned boat; x I’ ' is the horizontal coordinate of the attack point position coordinate of the offensive surface unmanned boat; |θ E -φ E |=π means the absolute value of the difference between the heading angle and the attack angle of the offensive surface unmanned boat is π; sign(x E '-x I’ ') means when x E ' <x I’ ', K E <0, the offensive surface unmanned boat adopts the strategy of turning counterclockwise. E '>x I’ ', K E >0, E adopts a clockwise turning strategy.

[0099] Specifically, when the offensive unmanned surface boat does not satisfy the first-order differential of the inner product between the unit vector of the offensive unmanned surface boat's attack angle and the unit vector of the current heading angle is greater than zero, and the offensive unmanned surface boat satisfies the state condition of the offensive unmanned surface boat, the offensive unmanned surface boat cannot obtain heading control input.

[0100] like Figure 4 The display shows an offensive unmanned surface boat in φ E ≠θ E When x E '>x I’ ', the motion trajectory of the offensive surface unmanned boat. At this time, the offensive surface unmanned boat needs to satisfy the state condition of the offensive surface unmanned boat (22).

[0101] In this embodiment, when φ E -θ E →0, that is That is, in formula (12), c = 1, then φ E -θ E = 0, the above process shows that the offensive surface unmanned boat can adjust its course to make φ E =θ E .

[0102] S6: According to the heading control input of the offensive unmanned surface boat, the position coordinates and heading angle of the offensive unmanned surface boat are updated to determine whether the offensive unmanned surface boat has successfully attacked.

[0103] Specifically, the heading control input of the offensive surface unmanned boat is substituted into the surface unmanned boat motion model; according to the offensive strategy formula (11) and formula (23) of the offensive surface unmanned boat, the state quantity of the offensive surface unmanned boat is updated, including the position coordinates of the offensive surface unmanned boat and the heading angle φ of the offensive surface unmanned boat E .

[0104] When the updated position coordinates of the offensive unmanned surface boat are located in the target area, the offensive unmanned surface boat successfully attacks;

[0105] When the updated position coordinates of the offensive unmanned surface boat are not located in the target area, the offensive unmanned surface boat fails in its attack;

[0106] Specifically, substitute the updated position coordinates of the offensive surface unmanned boat into:

[0107]

[0108] In the formula, Flag is the flag of whether the attack is successful; x E1 Represents the updated position coordinates of the offensive surface unmanned boat; Ω goal Indicates the target area. When the updated position of the offensive surface unmanned boat is within the target area, it is determined that the offensive surface unmanned boat successfully attacks the target area; otherwise, the offensive surface unmanned boat fails to attack the target area.

[0109] The differential game strategy method for a surface unmanned boat to attack a protected target area in this embodiment mainly focuses on offensive surface unmanned boats, obtains the attack point of the offensive surface unmanned boat based on the motion model of the offensive surface unmanned boat, further combines the heading angle of the offensive surface unmanned boat, and can quickly calculate the offensive strategy that the offensive surface unmanned boat needs to meet based on the state information of the opposing parties and the geometric figures based on the state information of both parties, providing an effective reference for the offensive surface unmanned boat to implement the offensive strategy for the high-value surface area protected by multiple defensive surface unmanned boats. In the process of solving, there is no need to calculate complex differential equations, which greatly reduces the difficulty and time of strategy solution, and can adapt to the highly dynamic sea battlefield form.

[0110] 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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned 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 method for an unmanned surface boat to attack a protected target area based on differential game, characterized in that: The steps include: S1: Obtain the initial parameters of the surface unmanned boat, establish the motion model of the surface unmanned boat, and obtain the target area of ​​the surface unmanned boat game; The initial parameters of the unmanned surface boat include: the position coordinates of the defensive unmanned surface boat, the position coordinates of the offensive unmanned surface boat, the heading angle of the defensive unmanned surface boat and the heading angle of the offensive unmanned surface boat; S2: acquiring the attack point position coordinates of the offensive unmanned surface boat according to the initial parameters of the unmanned surface boat and the target area; S3: acquiring an attack angle of the offensive unmanned surface boat according to the attack point position coordinates of the offensive unmanned surface boat and the position coordinates of the offensive unmanned surface boat; S4: according to the attack angle of the offensive unmanned surface boat, obtaining the first-order differential of the inner product between the unit vector of the attack angle of the offensive unmanned surface boat and the unit vector of the current heading angle; obtaining the state condition of the offensive unmanned surface boat; S5: Based on the first-order differential of the inner product between the unit vector of the offensive surface unmanned boat's attack angle and the unit vector of the current heading angle, the state condition of the offensive surface unmanned boat, and the heading angle of the offensive surface unmanned boat, the heading control input of the offensive surface unmanned boat is obtained to realize the surface unmanned boat's attack on the protected target area.

2. According to claim 1, a method for attacking a protected target area by an unmanned surface boat based on differential game, characterized in that: In S4, the first-order differential of the inner product between the unit vector of the attack angle of the offensive unmanned surface boat and the unit vector of the current heading angle is obtained as follows: Taking the inner product of the heading angle unit vector of the offensive surface unmanned boat and the attack angle unit vector, we get In the formula, [cosφ E ,sinφ E ] represents the unit vector of the current heading angle of the offensive surface unmanned boat; represents the transpose of the unit vector of the attack angle of the offensive surface unmanned boat; c represents the inner product between the unit vector of the attack angle of the offensive surface unmanned boat and the unit vector of the current heading angle; x I’ Indicates the position coordinates of the attack point of the offensive surface unmanned boat; U E is the constant speed of the offensive surface unmanned vehicle; represents the first-order differential transpose of the position coordinates of the offensive surface unmanned boat; φ E represents the heading angle of the offensive surface unmanned boat, θ E is the attack angle of the offensive surface unmanned vehicle; Indicates the position coordinates of the offensive surface unmanned boat; represents a two-dimensional sea plane; Differentiate the inner product of the heading angle unit vector of the offensive surface unmanned vehicle and the attack angle unit vector, have to: In the formula, is the first-order differential of the inner product between the unit vector of the attack angle of the offensive unmanned surface vehicle and the unit vector of the current heading angle; represents the first-order differential of the position coordinates of the offensive surface unmanned boat; is the second-order differential transpose of the position coordinates of the offensive surface unmanned boat; is the first-order differential of the position coordinates of the attack point of the offensive surface unmanned boat; x I’ represents the position coordinates of the attack point of the offensive surface unmanned boat; ||·||2 represents the Euclidean norm; According to the coordinates of the points in the safety area of ​​the unmanned boat, we can get In the formula, y I’ ' is the ordinate of the attack point position coordinate of the offensive surface unmanned boat; y E ' is the ordinate of the position coordinate of the offensive surface unmanned boat; is the heading angle of the jth defensive surface unmanned boat; K E is the heading control input of the offensive surface unmanned boat; U E is the constant speed of the offensive surface unmanned vehicle; R E is the minimum turning radius of an offensive surface unmanned vehicle; is the constant speed of the jth defensive surface unmanned vehicle; j =U Pj / U E represents the speed ratio of the jth defensive surface unmanned boat and the offensive surface unmanned boat; Indicates the position coordinates of the offensive surface unmanned boat; x I’ Indicates the position coordinates of the attack point of the offensive unmanned surface vehicle; represents the position coordinates of the jth defensive surface unmanned boat; φ E represents the heading angle of the offensive surface unmanned boat; θ E is the attack angle of the offensive surface unmanned boat; z(θ E ,φ E ,η,ψ Pj ) represents the joint function of the heading angle and attack angle of the offensive surface unmanned boat, and the heading angle and azimuth of the defensive surface unmanned boat; x P Indicates the position coordinates of the defensive unmanned surface boat; in: Where η represents the azimuth angle of the jth defensive surface unmanned boat; The ordinate represents the position coordinate of the jth defensive unmanned surface vehicle; represents the horizontal coordinate of the position coordinate of the jth defensive surface unmanned boat; E 'The horizontal coordinate representing the position coordinate of the offensive surface unmanned boat; According to the absolute value inequality scaling principle, equation (S-4) is simplified to: According to the range of trigonometric functions, we can get: |z(θ E ,f E ,h,p Pj )|≤1+λ j +1 / min j +1=(λ j +1) 2 / l j (S-6) Combining equation (S-3) and equation (S-6), according to the inequality scaling principle, we can obtain: According to the position coordinates of the attack point of the offensive surface unmanned boat, we get: In the formula, is the radius of the offensive unmanned surface vessel; Substituting formula (S-8) into formula (S-7), we get:

3. The method for attacking a protected target area by an unmanned surface boat based on differential game according to claim 1, characterized in that: In S1, the motion model of the unmanned surface vehicle is established as follows: In the formula, is the first-order differential of the horizontal coordinate of the position coordinate of the offensive surface unmanned boat; is the first-order differential of the ordinate coordinate of the position coordinate of the offensive surface unmanned boat; is the first-order differential of the heading angle of the offensive surface unmanned vehicle; is the first-order differential of the horizontal coordinate of the position coordinate of the j-th defensive surface unmanned boat; is the first-order differential of the ordinate coordinate of the position coordinate of the jth defensive surface unmanned boat; is the first-order differential of the heading angle of the jth defensive surface unmanned boat; K E is the heading control input of the offensive surface unmanned boat; U E is the constant speed of the offensive surface unmanned vehicle; R E is the minimum turning radius of an offensive surface unmanned vehicle; is the heading control input of the jth defensive surface unmanned vehicle; is the constant speed of the jth defensive surface unmanned vehicle; is the minimum turning radius of the jth defensive surface unmanned vehicle; is the heading angle of the jth defensive surface unmanned boat, j represents the index number of the defensive surface unmanned boat; J represents the number of defensive surface unmanned boats.

4. The method for attacking a protected target area by an unmanned surface boat based on differential game according to claim 1, characterized in that: In S1, the target area of ​​the unmanned surface boat game is obtained as follows: Get the line segments that form the boundary of the target area for the surface unmanned vehicle game: Where: g i (x b ,y b ) represents the line segment that constitutes the boundary of the target area of ​​the surface unmanned boat game, where x b The horizontal coordinate of the point on the line segment that constitutes the boundary of the target area of ​​the surface unmanned boat game; y b The ordinate of a point on the line segment that represents the boundary of the target area of ​​the surface unmanned boat game; m i Indicates the slope of the line segment; n i represents the intercept of the line segment; i=1,...,Ι represents the number of line segments; Indicates mathematical definition symbols; x and y represent the horizontal and vertical coordinates of a point in a two-dimensional sea plane, respectively; Therefore, by connecting the line segments constituting the boundary of the target area of ​​the surface unmanned boat game end to end, the boundary of the target area of ​​the surface unmanned boat game can be obtained, which is recorded as g(x b ,y b ); Then the target area of ​​the surface unmanned boat game is obtained as follows: Where: Ω goal represents the target area; (x, y) represents the coordinates of a point in the two-dimensional sea plane; inter(g(x b ,y b )) represents the interior of the geometric figure formed by the boundary of the target area of ​​the surface unmanned boat game.

5. The method for attacking a protected target area by an unmanned surface boat based on differential game according to claim 1, characterized in that: In S2, the attack point of the offensive unmanned surface boat is obtained as follows: S21: constructing a safety zone for the offensive unmanned surface boat according to the position coordinates of the defensive unmanned surface boat and the position coordinates of the offensive unmanned surface boat: determining the position coordinates of points within the safety zone for the offensive unmanned surface boat; In the formula, It represents the closed area formed by the safety area of ​​the offensive unmanned surface vehicle and the boundary of the safety area; Indicates the boundary of the safety area of ​​the offensive unmanned surface vehicle; Ω SRE Indicates the safety area for offensive unmanned surface vessels; represents the boundary coordinates of the safety zone for offensive surface unmanned boats, x Ea ' represents the horizontal coordinate of the safety zone boundary of the offensive surface unmanned boat; y Ea ' represents the vertical coordinate of the safety zone boundary of the offensive surface unmanned boat; t represents the time; f j (x Ea ,t) represents the geometric figure of the safety area boundary of the offensive surface unmanned boat relative to the jth defensive surface unmanned boat: Represents offensive surface unmanned boat and defensive surface unmanned boat team The intersection of the closed areas of the offensive surface unmanned boats; ||·||2 represents the Euclidean norm; represents the position coordinates of the jth defensive surface unmanned boat; Indicates the position coordinates of the offensive surface unmanned boat; represents the speed ratio of the jth defensive surface unmanned boat and the offensive surface unmanned boat; The coordinates of the point positions within the safety zone of the offensive surface unmanned vehicle are determined as follows: In the formula, x * represents the coordinate set of points in the safety area of ​​the offensive surface unmanned boat, x I Indicates the position coordinates of any point in the safety area of ​​the offensive surface unmanned boat; Represents vector transpose; S22: Obtain the coordinates of the center point of the safety zone of the offensive unmanned surface boat: In the formula, represents the position coordinates of the jth defensive surface unmanned boat; Indicates the position coordinates of the offensive surface unmanned boat; x o The coordinates of the center point of the circle representing the safety zone of the offensive unmanned surface vehicle; Get the center point x of the circle passing through the safety area of ​​the offensive surface unmanned boat o And the straight line perpendicular to the line segment of the target area boundary is: In the formula, (x c ,y c ) is too x o The coordinates of any point on the straight line that is perpendicular to the boundary of the target area; -1 / m i For x o The slope of the line segment that is perpendicular to the boundary of the target area; x E ' is the horizontal coordinate of the position coordinate of the offensive surface unmanned boat; y E ' is the ordinate of the position coordinate of the offensive surface unmanned boat; is the horizontal coordinate of the position coordinate of the jth defensive surface unmanned boat; is the ordinate of the position coordinate of the jth defensive surface unmanned boat; S23: Based on the position coordinates of the point in the safety zone of the offensive unmanned surface boat and the straight line passing through the center point of the safety zone of the offensive unmanned surface boat and perpendicular to the line segment of the target area boundary, the position coordinates of the attack point of the offensive unmanned surface boat are obtained as follows: In the formula, x I’ Indicates the position coordinates of the attack point of the offensive surface unmanned boat.

6. The method for attacking a protected target area by an unmanned surface boat based on differential game according to claim 1, characterized in that: In S3, the attack angle of the offensive unmanned surface boat is obtained using the following formula: In the formula, x I’ ' is the horizontal coordinate of the attack point position coordinate of the offensive surface unmanned boat; y I’ ' is the ordinate of the attack point position coordinate of the offensive surface unmanned boat; θ E is the attack angle of the offensive surface unmanned vehicle; Indicates the position coordinates of the offensive surface unmanned boat; x E ' is the horizontal coordinate of the position coordinate of the offensive surface unmanned boat; y E ' is the ordinate of the position coordinates of the offensive surface unmanned boat.

7. The method for attacking a protected target area by an unmanned surface boat based on differential game according to claim 1, characterized in that: In S4, the state condition of the offensive unmanned surface boat is obtained as follows: In the formula, is the radius of the offensive surface unmanned boat; R E is the minimum turning radius of an offensive surface unmanned vehicle; Represents the speed ratio of the jth defensive surface unmanned boat and the offensive surface unmanned boat.

8. The method for attacking a protected target area by an unmanned surface boat based on differential game according to claim 1, characterized in that: In S5, the heading control input of the offensive surface unmanned boat is obtained as follows: S51: When φ E =θ E When , the heading control input of the offensive surface unmanned boat is: K E =0(S-20) Where: K E Represents the heading control input of the offensive surface unmanned vehicle; φ E represents the heading angle of the offensive surface unmanned boat, S52: When φ E ≠θ E When sin(φ E -θ E )≠0, therefore, When the offensive unmanned surface boat satisfies: the first-order differential of the inner product between the unit vector of the offensive unmanned surface boat's attack angle and the unit vector of the current heading angle is greater than zero, and the offensive unmanned surface boat satisfies the state condition of the offensive unmanned surface boat, the heading control input of the offensive unmanned surface boat is obtained as follows: Where, sign() represents the sign function; x E ' is the horizontal coordinate of the position coordinate of the offensive surface unmanned boat; x I’ ' is the horizontal coordinate of the attack point position coordinate of the offensive surface unmanned boat; |θ E -φ E |=π means the absolute value of the difference between the heading angle and the attack angle of the offensive surface unmanned boat is π; sign(x E '-x I’ ') means when x E ' <x I’ ', K E <0, the offensive surface unmanned boat adopts the strategy of turning counterclockwise. E '>x I’ ', K E >0, E adopts a clockwise turning strategy.

9. The method for attacking a protected target area by an unmanned surface boat based on differential game according to claim 1, characterized in that: The S5 also includes: S6: According to the heading control input of the offensive surface unmanned boat, the position coordinates of the offensive surface unmanned boat are updated, so as to determine whether the offensive surface unmanned boat has successfully attacked based on the updated position coordinates of the offensive surface unmanned boat and the target area.

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