Attack and defense game method and device for second-order damping aircraft aiming at unknown strategy opposite side, medium and product

Abstract

The invention discloses a second-order damping aircraft attack and defense game method and device for an unknown strategy opposite party, a medium and a product, and relates to the technical field of aircrafts, and the method comprises the steps: obtaining the state information of a defender; acquiring an attacker corresponding to the defender, state information of the attacker and a target area; constructing a second-order damping aircraft attack and defense game dynamics model; determining a game state based on the state information of the defender and the state information of the attacker; determining an interception point based on the game state and the target area; determining whether the game state satisfies a set state; if the game state meets the set state, the game state is a predicted defense winning state, and an interception point tracking strategy is adopted to capture an attacker; if the game state does not meet the set state, the game state is a non-predicted defense winning state, and a course and speed combined adjustment strategy is adopted to control the defenders until the game state meets the set state. According to the invention, the problem of intelligent attack and defense game of many-to-many second-order damping aircrafts can be solved.

Description

Technical Field

[0001] This application relates to the field of aircraft technology, and in particular to a method, device, medium and product for second-order damped aircraft attack and defense game against an unknown strategy opponent. Background Technology

[0002] In recent years, with the development of unmanned technology, manufacturing technology, information technology, and artificial intelligence technology, as well as the significant improvement in airborne hardware, drone swarm countermeasures technology has received high attention and vigorous development. Advances in drone swarm game technology have made multi-drone interception technology an important research topic. Intercepting multiple drones attacking multiple defense zones is the most common combat scenario in swarm warfare. Due to their dispersed, intelligent, and flexible nature, opposing drone swarms possess more efficient reconnaissance and strike capabilities, making it difficult for traditional defense systems to detect and detect enemy targets. Even if targets are detected, the sheer number of drones increases the burden on air defense systems during countermeasures, ultimately leading to system failure. Therefore, adopting a "swarm-against-swarm" combat approach outside of existing air defense systems, and weaving a dense aerial perception, reconnaissance, and denial-of-defense network, has significant application value.

[0003] Currently, much work focuses on simple dynamic models using first-order integrators. However, in real-world air combat scenarios, aircraft velocities are continuous, and thrust is constrained by magnitude and direction, making simplification to a first-order integrator model difficult. Given the current state of research on aircraft game theory, designing offensive and defensive game strategies for second-order damped aircraft is a challenging problem. Some researchers have combined geometric analysis methods and differential game theory to propose a pursuit-escape game strategy for second-order damped dynamic models, proving its optimality using the Hamilton-Jacobi-Issacs equations. However, this method is difficult to solve under complex dynamic constraints. Other researchers have used second-order Dubins vehicle dynamic models as their research object, proposing winning strategies and sufficient conditions for the defender under the constraint of a minimum turning radius for the Dubins vehicle. However, drones and other aircraft in real-world environments have velocity damping terms and thrust constraints. It is evident that the relevant technical solutions lack consideration for velocity damping terms and thrust constraints. Therefore, there is an urgent need for a second-order damped aircraft attack and defense game method against an unknown strategy opponent to solve the intelligent attack and defense game problem of second-order damped aircraft in many-to-many situations. Summary of the Invention

[0004] The purpose of this application is to provide a method, device, medium, and product for attack and defense game of second-order damped aircraft against an unknown strategy opponent, which can solve the intelligent attack and defense game problem of second-order damped aircraft in many-to-many situations.

[0005] To achieve the above objectives, this application provides the following solution: Firstly, this application provides a second-order damped aircraft attack and defense game method against an unknown strategy opponent, applicable to each aircraft in a cluster system; the method includes: Obtain the defender's status information; the status information includes position and speed. Obtain the status information and target area of ​​the attacker corresponding to the defender; the attacker is a drone in the opposing cluster system. Construct a dynamic model of offensive and defensive game theory for a second-order damped aircraft; The game state is determined based on the defender's and attacker's state information; the interception point is determined based on the game state and the target area. Based on the second-order damped aircraft attack-defense game dynamics model and the location of the interception point, an interception point tracking strategy and a heading and speed joint adjustment strategy are constructed respectively; the interception point tracking strategy and the heading and speed joint adjustment strategy correspond to different control inputs and constraints. Determine whether the game state satisfies the set state; If the game state satisfies the set state, then the game state is the expected defensive victory state, and the interception point tracking strategy is used to capture the attacker. If the game state does not meet the set state, then the game state is an unexpected defensive victory state, and a course and speed joint adjustment strategy is adopted to control the defender until the game state meets the set state.

[0006] In one embodiment, the second-order damped aircraft attack-defense game dynamics model is expressed as: ; In the formula, Indicates the defender. Indicates attacker, and The defenders Position and velocity, and attackers Position and velocity; and They are respectively and Control input; function Used for calculation The acceleration; This is a crucial moment for strategic maneuvering. in, The control input and speed respectively satisfy the constraints and ,and , for Damping coefficient; Speed ​​satisfies ,and .

[0007] In one embodiment, when the Euclidean distance between the defender and the attacker is less than a set threshold, the attacker is successfully captured by the defender.

[0008] In one embodiment, determining whether the game state satisfies a set state includes: Gain control speed from the defender; Determine whether the game state simultaneously satisfies the separation state, interception direction, and interception speed based on the location of the target area, the interception point, and the defender's constrained speed. When the game state When the separation state, interception direction, and interception speed are simultaneously satisfied, the game state satisfies the set state; when the game state does not satisfy at least one of the separation state, interception direction, and interception speed, the game state does not satisfy the set state.

[0009] In one embodiment, the process of constructing the interception point tracking strategy includes: Based on the second-order damped aircraft attack-defense game dynamics model and the location of the interception point, a first control input is determined to maintain the expected defensive victory state in the game state; the first control input satisfies a first constraint condition; the first constraint condition includes boundary constraints and azimuth angle constraints.

[0010] In one embodiment, the process of constructing the combined heading and speed adjustment strategy includes: Based on the second-order damped aircraft attack-defense game dynamics model and the location of the interception point, a second control input is determined to maintain the expected defensive victory state in the game state; the second control input satisfies the second constraint condition; the second constraint condition includes parameter constraints and time constraints.

[0011] In one embodiment, the process of determining the interception point based on the game state and the target area includes: The attacker's offensive advantage domain is determined based on the game state. Construct a convex optimization problem based on the offensive advantage domain and the target region; The interception point is obtained by solving the convex optimization problem.

[0012] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the second-order damped aircraft attack and defense game method against an unknown strategy opponent as described above.

[0013] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the second-order damped aircraft attack and defense game method against an unknown strategy opponent as described above.

[0014] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the second-order damped aircraft attack and defense game method against an unknown strategy opponent as described above.

[0015] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a method, device, medium, and product for attack-defense game theory of second-order damped aircraft against an opponent with an unknown strategy. The game state is determined by acquiring the state information of the defender and the attacker, and an interception point is determined based on the game state and the acquired target area. For the expected defensive victory state when the game state meets the set conditions, an interception point tracking strategy is used to capture the attacker. For the unexpected defensive victory state when the game state does not meet the set conditions, a combined heading and speed adjustment strategy is used to control the defender to make the game state meet the set conditions, and then the interception point tracking strategy is used to capture the attacker. Ultimately, this enables the defender in the cluster system to intercept the corresponding attacker in the opponent's cluster system, solving the intelligent attack-defense game theory problem of second-order damped aircraft in many-to-many situations. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart of a second-order damped aircraft attack and defense game method against an unknown strategy opponent in one embodiment of this application. Figure 2 A schematic diagram of an offensive and defensive game scenario in a two-dimensional plane where a single defender intercepts a single attacker, provided in an embodiment of this application; Figure 3 A schematic diagram illustrating the implementation process of the interception point following strategy under the expected defensive victory state, provided in an embodiment of this application; Figure 4 A schematic diagram illustrating the implementation process of the joint course and speed adjustment strategy under an unexpected defensive victory state, provided in an embodiment of this application; Figure 5 This is a schematic diagram of the game result provided in an embodiment of this application; Figure 6 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0018] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] In one exemplary embodiment, such as Figure 1 As shown, a second-order damped aircraft attack-defense game method against an opponent with an unknown strategy is provided. This method is applied to each aircraft in a swarm system. The second-order damped aircraft attack-defense game method against an opponent with an unknown strategy includes: S1: Obtain the defender's status information. Status information includes position and speed.

[0021] S2 retrieves the attacker's status information and target area corresponding to the defender. The attacker is a drone within the opposing cluster system.

[0022] S3, construct a dynamic model of attack and defense game of second-order damped aircraft.

[0023] S4 determines the game state based on the defender's and attacker's state information. The interception point is then determined based on the game state and the target area.

[0024] S5, based on the dynamics of a second-order damped aircraft's offensive and defensive game and the location of the interception point, constructs an interception point tracking strategy and a joint course and speed adjustment strategy. The interception point tracking strategy and the joint course and speed adjustment strategy correspond to different control inputs and constraints.

[0025] S6. Determine if the game state meets the set conditions. If the game state meets the set conditions, the game state is the expected defensive victory state, and the interception point tracking strategy is used to capture the attacker. If the game state does not meet the set conditions, the game state is the unexpected defensive victory state, and the course and speed joint adjustment strategy is used to control the defender until the game state meets the set conditions.

[0026] By implementing steps S1 to S6 above, this application can solve the intelligent offensive and defensive game problem of second-order damped aircraft in a many-to-many scenario. Here, many-to-many refers to the offensive and defensive game between a cluster system containing multiple defenders and an opposing cluster system containing multiple attackers.

[0027] In one implementation, a target allocation method can be used to assign defenders in a cluster system to aircraft (i.e., attackers) in the opposing cluster system. This creates pairs of defenders and attackers, and the goal is to find the match that maximizes the number of captures, thus simplifying the attack-defense game between cluster systems into a one-to-one game. To address this, a central control system (or console, etc.) can be set up in the cluster system. This system can assign corresponding attackers to all defenders and transmit the attacker's relevant information (e.g., ID, status information) to the defenders, enabling them to engage in one-to-one attack-defense games with attackers according to the matching relationships. Since cooperation among defenders in the cluster system is not considered at the strategy level, and attackers may not necessarily execute the optimal attack strategy, better matching relationships may emerge as the game progresses. Therefore, as the game state dynamically changes, the allocation relationship between defenders and attackers needs to be dynamically adjusted; that is, the target allocation method's matching is dynamically adjusted. Furthermore, surplus defenders can be assigned to the nearest attacker, and the defenders can cooperate to intercept that attacker.

[0028] In one implementation, for a scenario where a single defender intercepts a single attacker in a two-dimensional plane, the attack-defense game model is as follows: Figure 2 As shown. Assume the defender and attacker are point masses, and use... and This indicates that the defender moves based on a damped double integrator dynamics model, ensuring that the velocity is bounded. The attacker's motion has more general dynamic characteristics, and its acceleration is nonlinear in terms of position, velocity, and control input. The dynamic equations of the defender and attacker in the two-dimensional plane (i.e., the dynamics model of the second-order damped aircraft attack and defense game) are shown in Equation (1).

[0029] (1) In the formula, and The defenders Position and velocity, and The defenders Position and velocity, and They are respectively and Control input (decision) and (acceleration). and All meet . This represents the feasible set of control inputs. Indicates control input (for) or ), express . This refers to a game-playing moment. In the description of subsequent embodiments, for the sake of simplicity, game-playing moments will be omitted unless absolutely necessary. .

[0030] The control input and speed respectively satisfy the constraints and , , ,and , yes The damping coefficient. Speed ​​satisfies ,and . This indicates the defender's maximum speed (i.e., the constraint speed). Indicates the attacker's maximum speed. This indicates the defender's maximum control input.

[0031] function Used for calculation acceleration; function about It can be non-linear. The initial positions and velocities of the players (including defenders and attackers) are respectively... , , and .make and For speed and The unit vector.

[0032] make As the speed ratio between the defender and the attacker. In this embodiment, the defender is considered to be faster, that is... .make As The capture radius. If the attacker... and defenders The Euclidean distance between them is less than a set threshold. At that time, it was considered able to be Successful capture. For a defender with the dynamics of formula (1), The control input is derived from the linear damping of the velocity. The thrust originates from the defender's controller. Simultaneously, the thrust is subject to an angular constraint, namely... and The included angle satisfies ,in .

[0033] In game theory scenarios, such as Figure 2 As shown, the straight line plane It is divided into two parts, namely the game area and the target area, as shown in formula (2).

[0034] (2) The attacker was initially located in the game area. In order to reach the target area Furthermore, the goal was not to be captured by the defending side, while the defenders aimed to protect the target area. The purpose is to avoid being attacked by the attacker.

[0035] The information available to players plays a crucial role in determining the game's outcome. This application considers a state feedback information structure. Defenders and attackers can utilize each other's current position and velocity information to determine their current control inputs. Furthermore, the maximum speeds of all aircraft, the capture radii and damping coefficients of all defenders, and the game area are also considered. and target area The information is known to both parties.

[0036] As an optional implementation, step S5, which involves determining the interception point based on the game state and the target area, includes: determining the attacker's offensive advantage domain based on the game state; constructing a convex optimization problem based on the offensive advantage domain and the target area; and solving the convex optimization problem to obtain the interception point.

[0037] For example, in a game, the states adjusted by both the defender and the attacker according to their respective strategies will affect the game state. Therefore, to reduce the difficulty of solving the problem, a series of game states are introduced. For the attacker... and defenders The offensive and defensive game between them, defined Represents the state of a game. Definition attackers Not The set of location states of the capture A simple dynamic model is defined based on the dynamic model of the second-order damped aircraft attack and defense game, as shown in formula (3).

[0038] (3) The potential energy function is defined as shown in formula (4).

[0039] (4) Based on this, the attacker's offensive advantage domain is determined. The offensive advantage domain is determined under simple excitation... Able to precede Or with The area reached at the same time, i.e. Let the boundary of the offensive advantage domain be... This is about and The Apollonius circle, its center and radius It can be expressed as formula (5).

[0040] (5) Based on this, the interception point is defined as a convex optimization problem as shown in equation (6). The solution.

[0041] (6) in, It refers to the point To the target area The distance.

[0042] The interception point is obtained by solving the convex optimization problem shown in formula (6). As shown in formula (7).

[0043] (7) In one embodiment, determining whether the game state satisfies a set state includes: obtaining the defender's constraint speed; determining whether the game state simultaneously satisfies the separation state, the interception direction, and the interception speed based on the target area, the location of the interception point, and the defender's constraint speed; when the game state simultaneously satisfies the separation state, the interception direction, and the interception speed, the game state satisfies the set state; when the game state does not satisfy at least one of the separation state, the interception direction, and the interception speed, the game state does not satisfy the set state.

[0044] Specifically, the settings include the separation state, the interception direction, and the interception speed. For the game state... 1) If the distance from the offensive advantage zone to the target area is greater than zero, i.e. Then the game state satisfies the separation state. Wherein, It refers to the point To the target area 1) The distance. 2) If the defender's speed direction is the same as the interception direction, that is... Then the game state satisfies the interception direction. Wherein, , Indicates defender speed unit vector, Indicates the direction of interception. Indicates the interception point. Indicates the defender's position. 3) If the defender reaches maximum speed, that is... Then the game state satisfies the interception speed. Wherein, Indicates defender speed, This indicates the defender's maximum speed.

[0045] In addition, definition It is a set of states that simultaneously satisfy the interception direction and interception speed, as shown in formula (8).

[0046] (8) In the formula, This represents the set of all possible game states before the game ends. .

[0047] As an optional implementation, the process of constructing the interception point tracking strategy includes: determining the first control input to maintain the expected defensive victory state based on the dynamics model of a second-order damped aircraft attack-defense game and the location of the interception point. The first control input satisfies the first constraint conditions. The first constraint conditions include boundary constraints and azimuth constraints. Based on this, in practical applications, the defender's winning strategy (i.e., the interception point tracking strategy) under the expected defensive victory state is designed. Figure 3 As shown ( Figure 3 Parts a and b demonstrate the process of capturing attackers using an interception point tracking strategy. The interception point tracking strategy can be further described as follows: Before designing, first let This is the solution to the optimization problem as shown in Equation (9).

[0048] (9) In the formula, Used to find the minimum value. This indicates the speed ratio between the defender and the attacker. These are the first and second optimization variables, respectively. (Subsequent...) The winning conditions will be used in the analysis of formulas (19)-(20).

[0049] Assume the game state Initially, the expected defensive victory is assumed. If the dynamics model of the second-order damped aircraft's offensive and defensive game satisfies formula (10), then... Will be before reaching the target area Capture. Therefore, a suitable control law needs to be designed to ensure... .

[0050] (10) In the formula, express .

[0051] The derivative is shown in formula (11).

[0052] (11) Then, from formula (11), we can obtain: In Under these conditions, the velocity derivative should satisfy formula (12).

[0053] (12) in: (13) In the formula, Represents the identity matrix. Represents a 1×2 zero matrix. express, express The vector after rotating 90° clockwise For the first intermediate matrix variable, This indicates the defender's maximum speed.

[0054] Therefore, the game state The control inputs required to maintain the expected defensive victory (i.e., the first control input). As shown in formula (14).

[0055] (14) in, Represents the second intermediate matrix variable. , Represents the identity matrix.

[0056] After obtaining the first control input, the first constraint condition is further determined. First, consider the upper bound of the control input: Further, formula (15) is obtained from geometric relationships.

[0057] (15) In the formula, As the first intermediate variable, As the second intermediate variable, It is the third intermediate variable. As shown in formula (16).

[0058] (16) For simplicity, some parameters in formula (16) are simplified, and the first optimization variable is used. Second optimization variable It is represented as shown in formula (17).

[0059] (17) but It can be represented as: (18) Under constraints and Next, consider Upper bound: (19) Because in Before being arrested, .therefore, The upper bound satisfies formula (20).

[0060] (20) If inequalities If true, then during the tracking process, the upper bound of the control input meets the requirements (i.e., boundary constraints).

[0061] Secondly, consider controlling the orientation of the input. It can be calculated as: (twenty one) Therefore, the angle between the control input and the velocity direction is: (twenty two) If inequalities If true, then during the tracking process, the direction angle of the control input meets the requirements (i.e., direction angle constraint).

[0062] In summary, if the game state To anticipate a defensive victory, and and The game between them, from the game state At the beginning, when Execute interception point tracking strategy (i.e., Formula 14) In this case, the game state will remain the expected defensive victory state, regardless of What strategy to adopt? This can ensure the capture The first constraint condition is satisfied if and only if the parameter satisfies formula (23).

[0063] (twenty three) because The solution is difficult, therefore a sufficient condition that is easy to verify can be given: (twenty four) When formula (24) is true, formula (23) must be true.

[0064] As an optional implementation, the process of constructing a joint course and speed adjustment strategy includes: determining a second control input based on a second-order damped aircraft attack-defense game dynamics model and the location of the interception point to maintain the expected defensive victory state. The second control input satisfies a second constraint condition, which includes parameter constraints and time constraints. Based on this, in practical applications, a defender's winning strategy (i.e., a joint course and speed adjustment strategy) is designed for unexpected defensive victory states, ensuring the game state reaches the expected defensive victory state within a finite time, subsequently executing an interception point following strategy to capture (or intercept) the attacker. For example... Figure 4 As shown ( Figure 4 Parts a and b demonstrate the process of capturing attackers using a combined course and speed adjustment strategy. The construction method of the combined course and speed adjustment strategy can be further described as follows: To focus on course and speed, assume and The distance between them is sufficiently large. From this, we can obtain formula (25).

[0065] (25) Furthermore, combined with Formula (26) can be obtained.

[0066] (26) Combining formulas (25) and (26), we can obtain formula (27).

[0067] (27) For ease of calculation, let's consider the game state that simultaneously satisfies the interception direction and interception speed in an unpredictable defensive victory state. ,make They are vectors The direction vector, i.e. Define two new state variables: , And let the control input (i.e., the second control input) in this embodiment be: (28) in: (29) and It satisfies formula (30).

[0068] (30) in, As the third intermediate variable, .make Then there is It holds true. That is, when the parameters satisfy formula (31) (i.e., parameter constraints), It has the ability to execute the above control law (such as the control input shown in formula (28)).

[0069] (31) when When adopting the above strategies, The derivative satisfies . The derivative can be expressed as: (32) Similarly, The derivative can be expressed as: (33) Therefore, when When adopting the above strategies, The derivative can be expressed as: (34) consider and The game between them Moment State Begin, let The state at time is denoted as .

[0070] First consideration When, arrive The required time is It satisfies formula (35).

[0071] (35) Secondly, consider hour, pass Messenger The required time is It satisfies formula (36).

[0072] (36) Therefore, the time required for the adjustment process can be determined by formula (37).

[0073] (37) From formula (25), we can obtain formula (38): (38) So, in the initial state, When formula (39) (i.e., time constraint) is satisfied, regardless of What strategy to adopt? It can ensure that within a limited time Intragame state Once the expected defensive victory state is achieved (i.e., the game state satisfies the set conditions), the interception point tracking strategy in the above embodiment is then used to achieve [the desired outcome]. The arrest.

[0074] (39) In an exemplary embodiment, the effectiveness of the second-order damped aircraft attack-defense game method against an opponent with an unknown strategy is verified by using a specific example of a defensive aircraft (i.e., the defender) intercepting an attacking aircraft (i.e., the attacker) in the above embodiments. This embodiment does not include the target allocation process described in the above embodiments (i.e., this embodiment describes a one-to-one attack-defense game after target allocation).

[0075] Consider a defensive aircraft intercepting an offensive aircraft. The initial positions and velocities of the attacker and defender satisfy Table 1.

[0076] Table 1 Initial State Information of Both Players

[0077] The dynamic parameters of the defensive aircraft all satisfy formulas (24) and (31). Under initial conditions, the game state is an unexpected defensive victory state, satisfying formula (39). Based on the capture method in the unexpected defensive victory state described in the above embodiments, it can be seen that... A combined course and speed adjustment strategy can be adopted to achieve the expected defensive victory state within a limited time, and then... The interception point tracking strategy is implemented to ultimately capture the attacker.

[0078] The outcome of the game is as follows Figure 5 As shown, Figure 5The diagram shows the red defender intercepting the attacker using a combined heading and speed adjustment strategy. The red hollow circles represent the defender's initial position, and the blue hollow circles represent the attacker's initial position. Red dots represent the defender's movement trajectory, with lighter-colored path points indicating later movement. The defender can obtain the opponent's position and speed information. By employing the method proposed in this application, it can be seen that the defender effectively intercepts the attacker; the red asterisks mark the interception points. This demonstrates that the defensive aircraft can intercept the attacking aircraft, and the second-order damped aircraft intelligent attack-defense game method proposed in this application is effective.

[0079] In combination with the above embodiments, this application has the following advantages: This application establishes a two-dimensional plane attack-defense game model (i.e., a second-order damped aircraft attack-defense game dynamics model) for a defender's interception of an attacking aircraft. For the expected defensive victory state, it provides the defender's interception point following strategy and the first constraint condition required for victory. For the unexpected defensive victory state, it provides a joint course and speed adjustment strategy for the defender, solves for the time required to adjust to the expected defensive victory state, and finally obtains the state required for the defender's victory under any initial state and sufficient conditions for parameters (i.e., the second constraint condition, including parameter constraints and time constraints). Applying the designed strategy to a many-to-many attack-defense game enables multiple defenders to intercept multiple attacking aircraft, solving the problem of intelligent attack-defense game of second-order damped aircraft in many-to-many scenarios.

[0080] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 6 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media. The database stores data related to a second-order damped aircraft attack-defense game method against an unknown strategy opponent. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a second-order damped aircraft attack-defense game method against an unknown strategy opponent.

[0081] Those skilled in the art will understand that Figure 6 The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0082] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0083] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0084] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0085] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0086] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, etc., and are not limited to these.

[0087] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0088] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A second-order damped aircraft attack and defense game method against an opponent with an unknown strategy, characterized in that, The method is applied to each aircraft in the swarm system; the method includes: Obtain the defender's status information; the status information includes position and speed. Obtain the status information and target area of ​​the attacker corresponding to the defender; the attacker is a drone in the opposing cluster system. Construct a dynamic model of offensive and defensive game theory for a second-order damped aircraft; The game state is determined based on the defender's and attacker's state information; the interception point is determined based on the game state and the target area. Based on the second-order damped aircraft attack-defense game dynamics model and the location of the interception point, an interception point tracking strategy and a heading and speed joint adjustment strategy are constructed respectively; the interception point tracking strategy and the heading and speed joint adjustment strategy correspond to different control inputs and constraints. Determine whether the game state satisfies the set state; If the game state satisfies the set state, then the game state is the expected defensive victory state, and the interception point tracking strategy is used to capture the attacker. If the game state does not meet the set state, then the game state is an unexpected defensive victory state, and a course and speed joint adjustment strategy is adopted to control the defender until the game state meets the set state.

2. The second-order damped aircraft attack and defense game method against an unknown strategy opponent as described in claim 1, characterized in that, The dynamics model of the attack and defense game of the second-order damped aircraft is expressed as follows: ； In the formula, Indicates the defender. Indicates attacker, and The defenders Position and velocity, and attackers Position and velocity; and They are respectively and Control input; function Used for calculation The acceleration; This is a crucial moment for strategic maneuvering. in, The control input and speed respectively satisfy the constraints and ,and , for Damping coefficient; Speed ​​satisfies ,and .

3. The second-order damped aircraft attack and defense game method against an opponent with an unknown strategy as described in claim 1, characterized in that, When the Euclidean distance between the defender and the attacker is less than a set threshold, the attacker is successfully captured by the defender.

4. The second-order damped aircraft attack and defense game method against an opponent with an unknown strategy as described in claim 1, characterized in that, Determining whether the game state satisfies the set state includes: Gain control speed from the defender; Determine whether the game state simultaneously satisfies the separation state, interception direction, and interception speed based on the location of the target area, the interception point, and the defender's constrained speed. When the game state simultaneously satisfies the separation state, interception direction, and interception speed, the game state satisfies the set state; when the game state does not satisfy at least one of the separation state, interception direction, and interception speed, the game state does not satisfy the set state.

5. The second-order damped aircraft attack and defense game method against an opponent with an unknown strategy as described in claim 1, characterized in that, The process of constructing the interception point tracking strategy includes: Based on the second-order damped aircraft attack-defense game dynamics model and the location of the interception point, a first control input is determined to maintain the expected defensive victory state in the game state; the first control input satisfies a first constraint condition; the first constraint condition includes boundary constraints and azimuth angle constraints.

6. The second-order damped aircraft attack and defense game method against an opponent with an unknown strategy as described in claim 1, characterized in that, The process of constructing the aforementioned joint course and speed adjustment strategy includes: Based on the second-order damped aircraft attack-defense game dynamics model and the location of the interception point, a second control input is determined to maintain the expected defensive victory state in the game state; the second control input satisfies the second constraint condition; the second constraint condition includes parameter constraints and time constraints.

7. The second-order damped aircraft attack and defense game method against an opponent with an unknown strategy as described in claim 1, characterized in that, The process of determining the interception point based on the game state and the target area includes: The attacker's offensive advantage domain is determined based on the game state. Construct a convex optimization problem based on the offensive advantage domain and the target region; The interception point is obtained by solving the convex optimization problem.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the second-order damped aircraft attack and defense game method against an unknown strategy opponent as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the second-order damped aircraft attack and defense game method against an unknown strategy opponent as described in any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the second-order damped aircraft attack and defense game method against an unknown strategy opponent as described in any one of claims 1-7.

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