Boundary grid construction method for target-attacker-defender mixed game in three-dimensional space

Abstract

The invention belongs to the technical field of game and decision, and provides a target-attacker-defender mixed game boundary grid construction method in a three-dimensional space, and the method comprises the following steps: assuming that a target, an attacker and a defender are included in the game process of the three-dimensional space; decomposing the game process into included angle sub-countermeasures by using a geometric analysis method and an explicit strategy method; solving an included angle sub-countermeasure to obtain winning conditions of an attacker and a defender-target; and when all persons in the current office adopt the optimal control strategy movement, an included angle sub-strategy and a distance strategy are fused to obtain a boundary grid expression for dividing the win area of the persons in the current office. According to the method, based on a geometric analysis method and a display strategy method, the optimal control strategy and the boundary grid expression of the person in the office in the three-dimensional space can be solved through analysis of the constructed Aboronius ball. Therefore, clearer guidance is provided for the players to realize own targets in practical application, and the working efficiency of the players is improved.

Description

Technical Field

[0001] The invention belongs to the field of target-attacker-defender (TAD) game and decision-making technology, and in particular to a boundary fence construction method for a target-attacker-defender mixed game in three-dimensional space. Background Art

[0002] TAD games in three-dimensional space have a wide range of applications in modern technology. In missile defense systems, the optimal interception time and optimal interception position of defensive missiles can be calculated to improve the protection efficiency of targets; in multi-UAV collaborative tasks, the deployment strategy of defenders can be optimized to form a dynamic defense barrier. These scenarios can be summarized as the target and the defender cooperate to reach their winning area to avoid the target being captured by the attacker. Such TAD game problems are part of differential games. To solve such problems, the traditional ISSACS method is usually used to derive the expression of the boundary fence and the optimal operation strategy of the players. However, due to the increase in dimensions and the involvement of multiple agents, it becomes very challenging to directly solve the Hamilton-Jacobi-Isaacs (HJI) equation.

[0003] At present, most of the research on TAD game is aimed at two-dimensional scenes, or only involves the game problem of the two parties in three-dimensional space. When the attacker pursues the target and avoids the interception of the defender in three-dimensional space, he often faces two problems: one is that the attacker cannot determine the position where he can successfully capture the target, and the other is that he cannot determine the optimal strategy of each party in the game. Similarly, when the target avoids the interception of the attacker, the defender cannot confirm his optimal position to ensure the victory of the target-defender team game, and cannot determine the optimal strategy of the players. Summary of the invention

[0004] To solve the above problems, the present invention provides a barrier construction method for a target-attacker-defender mixed game in a three-dimensional space. In practical applications, such as in a drone penetration, if we are the attacker (penetrating drone), we can use the speed and position information of the attacked target (the object to be hit) and the defender (interceptor) to obtain the winning conditions using the barrier construction theory provided by the present invention: within what position range our attack missiles are arranged to ensure the completion of the target capture task and during the capture process, provide a real-time optimal strategy for the attacker (penetrating drone) to complete the capture task in the shortest time. On the contrary, if we are the defender, we can deploy the corresponding defender (interceptor) according to the information of the attacker (penetrating drone) and the speed and position of the protected target (the object to be hit), and also provide the optimal real-time strategy for our target and defender during the anti-capture process.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for constructing a boundary fence for a target-attacker-defender mixed game in a three-dimensional space comprises the following steps:

[0007] Step 1: Assume that the game process in three-dimensional space includes a target, an attacker, and a defender. Use geometric analysis and explicit strategy method to decompose the game process into corner sub-strategies.

[0008] Step 2: Solve the corner game and obtain the winning conditions of the attacker and the defender-target;

[0009] Step 3: When all players in the game adopt the optimal control strategy, the corner strategy and distance strategy are integrated to obtain the boundary fence expression for dividing the winning area of ​​the players in the game;

[0010] The application of the boundary fence construction method in various fields involving three-dimensional space includes but is not limited to drone penetration, drone active defense, drone-missile coordinated interception, ball games, target search and rescue, and territorial attack and defense;

[0011] In the application of the boundary fence construction method in the UAV penetration, the target represents the object to be hit, the attacker represents the penetrating UAV, and the defender represents the interceptor.

[0012] Preferably, the mathematical model of the movement of the target, attacker and defender in three-dimensional space is as follows:

[0013]

[0014]

[0015]

[0016] Among them, x T ,x A ,x D are the positions of the target, attacker, and defender, respectively, and u T ,u A ,u D are the control input variables of the target, attacker and defender respectively. The relationship between the player’s speed and the control input variable is V i =||u i || 2 ,i=T,A,D.

[0017] Preferably, the method of decomposing the game process into corner sub-strategies by using geometric analysis and explicit strategy method comprises the following steps:

[0018] S11. Use geometric analysis to establish the pursuit-escape game model between the target, attacker and defender, and use the Apollonius sphere to construct the reachable area of ​​the target and attacker. 1 and O 2 The centers of the spheres are as follows:

[0019]

[0020]

[0021] Where α = V T / V A represents the speed ratio between the target and the attacker and α<1, β=V D / V A represents the speed ratio between the defender and the attacker and β<1.

[0022] S12. Set the attacker's pursuit strategy and obtain the attacker's parallel strategy:

[0023]

[0024] in, Represents the control input variable of the target.

[0025] Preferably, the angle sub-strategy is formed by the attacker increasing the angle θ to bypass the interception of the defender. To ensure that the attacker is not intercepted by the defender in the process of pursuing the target by adopting the parallel strategy, the angle θ needs to meet the following conditions:

[0026] θ>η+σ

[0027] Among them, θ is the angle between the target, attacker, and defender, and η is the angle between the attacker A and the Apollonius ball O. 1 The angle between the tangent line AE and the straight line AT, σ is the angle between the attacker A and the Apollonius ball O 2 The angle between the tangent line AP and the straight line AD.

[0028] Preferably, in order to achieve the winning condition of the attacker, the optimal control strategy of the attacker in the three-dimensional space is as follows:

[0029] uA=V A (c D cos(θ-θ A )+w T，D ×c D sin(θ-θ A ))

[0030] Among them, u A is the initial vector c D Rotation around the axis w T，DCounterclockwise rotation angle θ A The vector obtained after A The attacker is heading along the 3D space at an angle θ A The moving speed, c D is the attacker’s initial vector, w T,D is the rotation axis, θ A is the optimal control heading angle taken by the attacker, that is, the attacker's rotation angle.

[0031] Preferably, the optimal control heading angle taken by the attacker is:

[0032]

[0033] Where r = ||AD|| 2 Represents the distance between the attacker and the defender, R = ||AT|| 2 Indicates the distance between the attacker and the target.

[0034] Preferably, in order to achieve the winning condition of the defender-target, the optimal control strategies of the defender and the target in three-dimensional space are as follows:

[0035] u T =-V T w T,D ×c T ,

[0036] u D =V D w T,D ×c D .

[0037] Among them, u T is the initial vector c T Clockwise rotation angle Get, u D is the initial vector c D Counterclockwise rotation angle Ψ is obtained; V T and V D The target and defender should follow the heading angle on the TAD plane and the speed of movement of Ψ, c T and c D are the initial vectors of the target and defender respectively, w T,D is the rotation axis.

[0038] Preferably, in order to achieve the winning condition of the defender-target, the optimal control heading angle taken by the defender and the target is:

[0039]

[0040] Preferably, the boundary fence expression is expressed in three-dimensional space as:

[0041] d=αr+βR

[0042] Where, d = ||DT|| 2 represents the distance between the defender and the target, r = ||AD|| 2 Represents the distance between the attacker and the defender, R = ||AT|| 2 Indicates the distance between the attacker and the target.

[0043] Preferably, when everyone in the authority adopts the optimal control strategy, the impact of the movement of the three participants, the target, the attacker, and the defender, on θ can be expressed as:

[0044]

[0045] When d>αr+βR, then The attacker wins the game; when d<αr+βR, then The defender and the target win the game.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] 1. The present invention provides a method for constructing a boundary fence for a target-attacker-defender mixed game in three-dimensional space. For the scenario of target, attacker and defender in three-dimensional space, based on explicit strategy method and geometric analysis method, an analytical expression of the target-attacker-defender boundary fence in three-dimensional space is constructed, which effectively reduces the computational complexity of the traditional ISSASC method. In other words, the present invention can determine the winning area boundary between the attacker and the target-defender team in the three-party game, and improve the efficiency of the defender in protecting the target. The boundary fence analysis method proposed in the present invention can be widely used in practical applications such as drone penetration, drone active defense, aircraft-missile coordinated interception, ball games, target search and rescue, territorial attack and defense, etc. It has important practical application value and promotion prospects, and can effectively promote the development and progress of related technologies.

[0048] 2. The present invention provides a method for constructing a boundary fence for a target-attacker-defender mixed game in three-dimensional space. Based on the analytical expression of the boundary fence obtained, the position of the deployed defender can be determined to ensure that the defender can successfully protect the target and improve the winning rate of ensuring the safety of the target.

[0049] 3. The present invention provides a method for constructing a boundary fence of a target-attacker-defender mixed game in three-dimensional space. Based on the geometric analysis method and the display strategy method, the optimal control strategy of the player in three-dimensional space can be solved by analyzing the constructed Apollonius sphere. This provides clearer guidance for the players to achieve their own goals in practical applications and improves their work efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flow chart of the present invention;

[0051] Figure 2 This is a schematic diagram of the TAD game model of the present invention;

[0052] Figure 3 A schematic diagram of the TAD game process of the present invention;

[0053] Figure 4 This is a second schematic diagram of the TAD game process of the present invention;

[0054] Figure 5 The third schematic diagram of the TAD game process of the present invention;

[0055] Figure 6 This is a fourth schematic diagram of the TAD game process of the present invention;

[0056] Figure 7 This is a fifth schematic diagram of the TAD game process of the present invention;

[0057] Figure 8 Schematic diagram of the TAD game process of the present invention;

[0058] Fig. 9 Schematic diagram of the TAD game process of the present invention; Fig.10 Schematic diagram of the TAD game process of the present invention; Fig.11 Schematic diagram of the TAD game process of the present invention. DETAILED DESCRIPTION

[0059] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0060] Traditional methods face challenges in dealing with TAD game problems in three-dimensional space, and the decision-making method proposed in the present invention is better adapted to actual application scenarios. Specifically, the present invention provides a more practical and feasible solution to TAD game problems in three-dimensional space through geometric analysis methods and explicit strategy methods, enabling the system to more flexibly respond to multi-agent game situations in three-dimensional space.

[0061] Example:

[0062] A method for constructing a barrier for a target-attacker-defender hybrid game in a three-dimensional space is applied to various fields involving three-dimensional space, including drone penetration, drone active defense, drone-missile coordinated interception, ball games, target search and rescue, territorial attack and defense, etc. This embodiment is described by taking drone penetration as an example. Specifically, Figure 1 As shown, the following steps are included:

[0063] Step 1: Assume that the game process in three-dimensional space includes a target, an attacker, and a defender. Use geometric analysis and explicit strategy methods to decompose the game process into corner sub-games.

[0064] Specifically, the game process of the present invention includes a striking object (T), a penetration drone (A) and an interceptor (D), and the mathematical model of the movement in three-dimensional space is as follows (eg Figure 2 shown):

[0065]

[0066]

[0067]

[0068] Among them, x T , x A , x D They represent the spatial positions of the target, the penetration drone and the interceptor respectively, and u T ,u A ,u D represents the control input variables of the hit object, the penetration drone and the interceptor. The relationship between the player's speed and the control input variable is V i =||u i || 2 ,i=T,A,D. The distance between the penetrating UAV and the object being hit is expressed as R=||AT|| 2 , the distance between the penetration drone and the interceptor is expressed as r = ||A D || 2 , the distance between the interceptor and the target is expressed as d = ||DT|| 2 .

[0069] It can be seen that the goal of the penetration drone is to capture the object being hit while trying to avoid being intercepted by the interceptor. The object being hit and the interceptor try to cooperate to prevent the penetration drone from successfully capturing the object being hit. When the penetration drone successfully captures the object being hit and avoids interception by the interceptor, the penetration drone (attacker) is considered to have won the game; when the interceptor successfully intercepts the penetration drone to protect the object being hit or the interceptor and the object being hit converge, the target-defender team is considered to have won the game. This setting forms a complex game environment with strategic and dynamic decision-making elements, which aims to study how the penetration drone can effectively capture the object being hit when it is in the initial position, and how the interceptor can adopt strategies to avoid the capture of the object being hit when it is in the initial position.

[0070] Based on this, the present invention can use geometric analysis to establish the pursuit and escape game model between the hit object, the penetration drone and the interceptor, and use the Apollonius sphere to construct the hit object and the reachable area of ​​the penetration drone. According to the speed ratio α of the hit object and the penetration drone, we can get:

[0071]

[0072] Simplifying the above formula, we can write it as a standard expression for a sphere, so we can get the Apollonius sphere O of the object being hit and the penetration drone. 1 Expressed as:

[0073]

[0074] According to the speed ratio β between the penetration UAV and the penetration UAV, we can get:

[0075]

[0076] Similarly, simplifying the above formula, the Apollonius sphere O between the interceptor and the penetration drone 2 It is expressed as follows:

[0077]

[0078] The speed ratio between the object being hit and the penetration drone is expressed as α = V T / V A , the speed ratio between the interceptor and the penetration drone is expressed as β = V D / V A Assuming that the penetration drone has a speed advantage, the speed ratio satisfies α<1 and β<1. Apollonius sphere O 1 and O 2 The centers of the spheres are as follows:

[0079]

[0080]

[0081] like Figure 3 As shown in the figure, the pursuit strategy of the penetration drone is set, and the penetration drone will capture the hit object on or inside the Apollonius Sphere. The hit object can reach any place inside the Apollonius Sphere without being captured by the pursuer (penetration drone). If the hit object selects the control input The object being hit can move in any direction in space. The direction of motion of the object being hit is the same as the direction of the Apollonian sphere O 1 Intersect at point G 1 According to the speed ratio between the objects hit by the penetration drone, we can get In the triangle TAG 1 middle, Therefore, the penetration drone can adopt the following parallel strategies to ensure the capture of the object struck on or inside the Sphere of Apollonius:

[0082]

[0083] When the hit object and the attacking drone move simultaneously within the time interval ΔT, their new positions are T 1 and A 1 , and form an Apollonian sphere O. This new sphere is contained in the original Apollonian sphere O 1 Since the speed ratio α between the penetration drone and the object being hit is always less than 1, after a period of movement, the penetration drone will be closer to the object being hit relative to its initial position. Therefore, the radius of the newly formed sphere O will continue to decrease, and the new sphere center O will always remain within the original sphere O. 1 Inside.

[0084] If the object you hit changes direction during the evasion (such as Figure 3 As shown, the object being hit is from G 1 The penetrating drone adjusts its strategy accordingly, moves toward point G, and captures the object it hits at point G. This shows that the penetrating drone can always successfully capture the object it hits.

[0085] like Figure 4 As shown in the figure, in order to ensure that the penetration drone is not intercepted by the interceptor in the process of adopting a parallel strategy to pursue the target, the angle θ needs to satisfy the condition θ>η+σ, where θ is the angle between the target, the penetration drone, and the interceptor, and η is the angle between the penetration drone A and the Apollonius ball O. 1 The angle between the tangent line AE and the straight line AT, σ is the angle between the penetration drone A and the Apollonius sphere O 2The angle between the tangent line AP and the straight line AD. When θ>η+σ, the penetration drone will pass through the interceptor's advantage area when pursuing the target with a parallel strategy and be intercepted by the interceptor. Therefore, the penetration drone must increase the angle θ to bypass the interception of the interceptor, which forms an angle sub-strategy. The purpose of the penetration drone is to increase the angle θ, while the purpose of the interceptor and the target is to reduce θ.

[0086] Step 2: Solve the angle sub-game to obtain the winning conditions of the attacker and the defender-target, that is, when the penetration drone (attacker) meets what initial conditions, it can increase the angle θ to bypass the interception of the interceptor, and when the target hit by the interceptor meets what initial conditions, it can prevent the penetration drone from increasing the angle θ to bypass the interception of the interceptor;

[0087] The goal of the two players is to increase or decrease the angle θ. First, we analyze the relationship between the movement direction vector of the players and the angle. The specific analysis process is as follows:

[0088]

[0089] in

[0090] From the above formula, we can conclude that for the motion direction vector u A , the angle θ changes only with (x T -x A ) A and(I D -x A ) A Related. (x T -x A ) A and(I D -x A ) A Respectively represent vector u A In vector and This means that Only with u A It is related to the projection on the TAD plane.

[0091] Similarly, we use the same method to analyze the relationship between the motion direction vector and the angle θ of the object and the interceptor. T and u D , Depends on the following factors in three-dimensional space: (x T -x A ) T 、(x D -x A ) T、(x T -x A ) D and (x D -x A ) D This shows that the size of the angle θ is determined only by the components of the object being hit and the interceptor's motion direction on the TAD plane.

[0092] It can be concluded that the movement of the player in the direction perpendicular to the TAD plane will not change the angle θ, but the movement in the direction parallel to the TAD plane will change the angle θ. Therefore, in the present invention, the expression of the movement of the penetration drone and the change Δθ′ of the angle θ caused is as follows:

[0093] Δθ′=θ′-θ=θ′ 1 +θ′ 2 .

[0094] The purpose of the penetration drone is to make the included angle θ as large as possible, so the above formula is derived to obtain:

[0095]

[0096] where u AP It is the directional component of the penetration UAV's motion on the plane TAD.

[0097] In order to quickly increase the angle θ so that the penetration drone does not pass through the interceptor's winning area, it is necessary to find Therefore, the above formula is about θ A Taking the derivative and setting the result equal to zero, we can get the following optimal control heading angle for the penetration drone:

[0098]

[0099] like Figure 5 As shown in Figure 2, in order to solve the optimal strategy for the penetration UAV to move in three-dimensional space, we first establish a suitable coordinate system according to the right-hand rule. In three-dimensional space, it can be observed that only the motion direction component u of the penetration UAV on the plane TAD AP The angle θ can be changed. Therefore, in order to increase the angle as quickly as possible, there should be no component perpendicular to the TAD plane in the movement direction of the penetration drone. By synthesizing the decomposed movement direction components, it can be concluded that the penetration drone should follow the heading angle θ in three-dimensional space. A Move, its speed is V A .

[0100] The rotated vector u A can be viewed as rotating the initial vector cD around the axis w T，D Counterclockwise rotation angle θ AThat is, u A It is obtained by synthesizing its components on the x-axis and y-axis. Therefore, the optimal control strategy of the penetration UAV in three-dimensional space is as follows:

[0101] u A =V A (c D cos(θ-θ A )+w T，D ×c D sin(θ-θ A ))

[0102] From the perspective of the target-defender (TD) team, their goal is opposite to that of the penetrating drone. In this game process, the target and the interceptor try to reduce the angle θ through cooperative strategies to protect the target. Next, the strategies that the target and the interceptor team should adopt in three-dimensional space are analyzed.

[0103] The relationship between the hit object and the interceptor team's motion direction vector and the rate of change of the angle θ is as follows:

[0104]

[0105] In order to reduce the included angle θ as quickly as possible and thus achieve the goal of the TD team, it can be deduced that the object being hit and the interceptor can reduce the included angle θ as quickly as possible while moving along the following heading angles in the TAD plane:

[0106]

[0107] First, establish the coordinate system in the same way, such as Figure 6 As shown. By merging the decomposed vectors separately, the vector u in the three-dimensional space T and u D It can be converted into a calculation on a two-dimensional TAD plane, that is, the target and the interceptor should follow the heading angle on the TAD plane respectively. and Ψ move, and their speeds are V T and V D .

[0108] The moving direction vector u of the object being hit T By setting the initial vector c T Clockwise rotation angle Obtained, and the interceptor's motion direction vector u D Then by setting the initial vector c D The angle Ψ is obtained by counterclockwise rotation. Therefore, by synthesizing the components on the x-axis and y-axis, the motion direction vectors of the hit object and the interceptor in three-dimensional space can be obtained as follows:

[0109]

[0110] u D =V D (c D cosΨ+w T,D ×c D sinΨ).

[0111] The optimal heading angle between the target and the penetration drone Substituting into the above formula, we can get:

[0112] u T =-V T w T，D ×c T ,

[0113] u D =V D w T，D ×c D .

[0114] Step 3: When all players in the game adopt the optimal control strategy, the corner strategy and distance strategy are integrated to obtain the boundary fence expression for dividing the winning area of ​​the players in the game. The specific solution process is as follows:

[0115] In the present invention, the influence of the movement of the participants on θ can be divided into two parts: the influence of the movement of the penetration drone on θ, and the influence of the movement of the hit object and the interceptor team on θ. Combined with the optimal control strategy of the players, the following results can be obtained:

[0116]

[0117] When the initial condition satisfies d>αr+βR, we can get This shows that the angle θ gradually increases over time. In this case, no matter the initial angle condition is θ>η+σ or θ>η+σ, the penetration drone can take the optimal strategy to make θ reach the condition η+σ. However, when the initial condition satisfies d<αr+βR, we can get This means that the angle θ gradually decreases over time, so the penetration drone cannot increase θ to satisfy the condition θ>η+σ.

[0118] When the target, the penetration UAV, and the interceptor all adopt their own optimal heading angles, it can be concluded that when d>αr+βR, the distance R between the hit object and the penetration UAV and the distance r between the interceptor and the penetration UAV will continue to decrease over time, that is, and In addition, since R(t) and r(t) decrease proportionally with time, because

[0119]

[0120] The above equations show that R and r gradually converge to zero over time but will never be equal to zero. Combined with the conditions d>αr+βR and As well as the previous analysis of distance, it can be deduced that as long as the penetration drone adopts the optimal strategy, before r decreases to zero, θ can reach the winning condition η+σ. According to the concept of Nash equilibrium, the penetration drone will win the game regardless of the strategy adopted by the target and the interceptor. In other words, the condition d>αr+βR is the barrier condition of the angle game.

[0121] Combining the barrier conditions of the angle game with geometric analysis, it can be concluded that the condition d>αr+βR completely contains the condition {θ>η+σ, R>0}. In other words, the barrier expression of the TAD game is expressed in three-dimensional space as d=αr+βR. Figure 7 Figure 8 shown.

[0122] Here are some examples:

[0123] S1: Assume that the speed ratio of the target to the penetration drone is α=0.6, the speed ratio of the interceptor to the penetration drone is β=0.7, and the initial positions of the players are T(0, 0, 1), A(0.5, -0.8, 0.8), and D(0, 0, -1). The distances between the three are R=||AT|| 2 =0.96, r = ||AD|| 2 =2.03, d=||TD|| 2 =2. By calculation, it can be concluded that the initial state of the players satisfies the condition d>αr+βR, which indicates that the initial state is in the winning area of ​​the penetration drone. The movement trajectory of each participant is as follows Figure 8 As shown, the penetration UAV can successfully capture the target at t = 2s.

[0124] S2: Assume that the position of the penetration drone is A(0.5, 1.1, 0.6), and other conditions are the same as S1. At this time, the distance between the three participants satisfies the condition d<αr+βR, which indicates that the initial state of the players meets the winning condition of the target-defender team. Fig. 9 ), it can be concluded that at t = 1.9s, the target and the interceptor can successfully merge, preventing the penetrating UAV from capturing the target.

[0125] S3: When the other initial conditions are the same as S2, but the speed of the interceptor is reduced, specifically set to β = 0.5, the initial condition of the player satisfies d>αr+βR. This shows that the penetration drone can successfully capture the target. By reducing the speed of the interceptor, the player's initial state is transformed from the winning area of ​​the target-interceptor team to the winning area of ​​the penetration drone. The movement trajectories of each player are shown in Fig.10 As shown, the game ends at t = 1.9s.

[0126] In summary, the present invention specifically provides the optimal control strategy of the target, attacker, and defender and the boundary fence expression for dividing the boundaries of the winning area of ​​the players in the game for the scenario of the target-attacker-defender game in three-dimensional space; compared with the traditional research based on the ISSACS method, the method of the present invention is more in line with the application scenarios in real life, which makes the method more versatile. In addition to being able to be applied to drone penetration, it can also be applied to other fields involving three-dimensional space, such as drone active defense, aircraft-missile coordinated interception, ball games, target search and rescue, territorial attack and defense, etc.

[0127] Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may certainly make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for constructing a boundary fence for a target-attacker-defender mixed game in three-dimensional space, characterized in that: The following steps are involved: Step 1: Assume that the game process in three-dimensional space includes a target, an attacker, and a defender. Use geometric analysis and explicit strategy method to decompose the game process into corner sub-strategies. Step 2: Solve the corner game and obtain the winning conditions of the attacker and the defender-target; Step 3: When all players in the game adopt the optimal control strategy, the corner strategy and distance strategy are integrated to obtain the boundary fence expression for dividing the winning area of ​​the players in the game; The application of the boundary fence construction method in various fields involving three-dimensional space includes but is not limited to drone penetration, drone active defense, drone-missile coordinated interception, ball games, target search and rescue, and territorial attack and defense; In the application of the boundary fence construction method in the UAV penetration, the target represents the object to be hit, the attacker represents the penetrating UAV, and the defender represents the interceptor.

2. The method for constructing a boundary fence of a target-attacker-defender mixed game in three-dimensional space according to claim 1, characterized in that: The mathematical model of the target, attacker and defender moving in three-dimensional space is as follows: Among them, x T ,x A ,x D are the positions of the target, attacker, and defender, respectively, and u T ,u A ,u D are the control input variables of the target, attacker and defender respectively. The relationship between the player’s speed and the control input variable is V i =||u i ||2,i=T,A,D.

3. The method for constructing a boundary fence of a target-attacker-defender mixed game in three-dimensional space according to claim 2, characterized in that: The method of decomposing the game process into corner sub-games by using the geometric analysis method and the explicit strategy method comprises the following steps: S11. Use geometric analysis to establish a pursuit-escape game model between the target, attacker, and defender. Use the Apollonius sphere to construct the reachable area of ​​the target and attacker. The centers of the Apollonius spheres O1 and O2 are as follows: Where α = V T / V A represents the speed ratio between the target and the attacker and α<1, β=V D / V A represents the speed ratio between the defender and the attacker and β<1. S12. Set the attacker's pursuit strategy and obtain the attacker's parallel strategy: in, The control input variable representing the target.

4. The method for constructing a boundary fence for a target-attacker-defender mixed game in three-dimensional space according to claim 3, characterized in that: The angle sub-strategy is formed by the attacker increasing the angle θ to bypass the defender's interception. To ensure that the attacker is not intercepted by the defender in the process of pursuing the target with the parallel strategy, the angle θ needs to meet the following conditions: θ>η+σ Among them, θ is the angle between the target, attacker, and defender, η is the angle between the tangent line AE between the attacker A and the Apollonius sphere O1 and the straight line AT, and σ is the angle between the tangent line AP between the attacker A and the Apollonius sphere O2 and the straight line AD.

5. The method for constructing a boundary fence for a target-attacker-defender mixed game in a three-dimensional space according to claim 4, characterized in that: In order to achieve the attacker's winning condition, the attacker's optimal control strategy in three-dimensional space is as follows: you A =V A (c D cos(θ-θ A )+w T,D ×c D sin(θ-θ A )) Among them, u A is the initial vector c D Rotation around the axis w T，D Counterclockwise rotation angle θ A The vector obtained after A The attacker is heading along the 3D space at an angle θ A The moving speed, c D is the attacker’s initial vector, w T，D is the rotation axis, θ A is the optimal control heading angle taken by the attacker, that is, the attacker's rotation angle.

6. The method for constructing a boundary fence for a target-attacker-defender mixed game in three-dimensional space according to claim 5, characterized in that: The optimal control heading angle taken by the attacker is: Among them, r = ||AD||2 represents the distance between the attacker and the defender, and R = ||AT||2 represents the distance between the attacker and the target.

7. The method for constructing a boundary fence for a target-attacker-defender mixed game in three-dimensional space according to claim 4, characterized in that: In order to achieve the winning condition of the defender-target, the optimal control strategies of the defender and the target in three-dimensional space are as follows: U T =-V T w T,D ×C T , u D =V D w T,D ×C D . Among them, u T is the initial vector c T Clockwise rotation angle Get, u D is the initial vector c D Counterclockwise rotation angle Ψ is obtained; V T and V D The target and defender should follow the heading angle on the TAD plane and the speed of movement of Ψ, c T and c D are the initial vectors of the target and defender respectively, w T，D is the rotation axis.

8. The method for constructing a boundary fence for a target-attacker-defender mixed game in three-dimensional space according to claim 7, characterized in that: In order to achieve the winning condition of the defender-target, the optimal control heading angle taken by the defender and the target is:

9. The method for constructing a boundary fence for a target-attacker-defender mixed game in three-dimensional space according to claim 4, characterized in that: The boundary fence expression is expressed in three-dimensional space as: d=αr+βR Among them, d = ||DT||2 represents the distance between the defender and the target, r = ||AD||2 represents the distance between the attacker and the defender, and R = ||AT||2 represents the distance between the attacker and the target.

10. The method for constructing a boundary fence for a target-attacker-defender mixed game in three-dimensional space according to claim 7, characterized in that: When each person in the authority adopts the optimal control strategy, the impact of the movement of the three participants, the target, the attacker, and the defender, on θ can be expressed as: When d>αr+βR, then The attacker wins the game; when d<αr+βR, then The defender and the target win the game.

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