An optimization method and system for cooperative position occupation of two aircrafts of our side in a typical borrow field scene

Abstract

The application discloses a method and system for optimizing double-aircraft cooperative occupation in a typical borrowed missile scene, and relates to the technical field of aerospace. The method comprises the following steps: constructing a borrowed missile air combat scene and defining double-aircraft role tasks; constructing a three-degree-of-freedom dynamics and kinematics model of a combat aircraft, a weapon combat zone and an inescapable zone model and an over-the-horizon air combat situation reward and punishment situation function; performing multi-step enemy track prediction by using an LSTM model to determine enemy state information at each time step; solving an optimal occupation route by using an improved particle swarm algorithm according to the enemy state information at each time step; and controlling the double aircraft to reach a specified position by using an improved track planning algorithm according to the optimal occupation route. The application can realize double-aircraft cooperative occupation optimization in a typical borrowed missile scene, and provide theoretical support for multi-UCAV cooperative operation in over-the-horizon air combat.

Description

Technical Field

[0001] This application relates to the field of aerospace technology, and in particular to an optimization method and system for our dual-aircraft coordinated positioning in a typical missile borrowing scenario. Background Technology

[0002] With the development of airborne radar and missile technology, beyond-visual-range (BVR) air combat has become the core form of modern air warfare. Multiple unmanned combat aerial vehicles (UCAVs) have demonstrated significant effectiveness in cooperative air combat due to their advantages such as low cost, high maneuverability, and zero casualties.

[0003] However, there are three major limitations in the existing technology:

[0004] 1) Singularity of scenarios: Most air combat decision models focus on single-aircraft combat (one-to-one) and lack multi-UCAV collaborative positioning methods.

[0005] 2) Lack of coordination mechanism: Existing research on multi-machine coordination focuses on in-line-of-sight (WVR) dogfights or target allocation, neglecting the key link of coordinated seizure of attack positions.

[0006] 3) Insufficient dynamic modeling: Traditional methods (such as matrix game theory) do not incorporate the geometric constraints of the weapon engagement zone (WEZ), resulting in the selection of the occupancy area being detached from the actual dynamic characteristics of air combat (such as the coupling effect of range, azimuth, and entry angle).

[0007] In summary, there is an urgent need to provide an optimized method and system for dual-aircraft collaborative positioning to achieve optimized dual-aircraft collaborative positioning in typical bomb-borrowing scenarios. This would address the problems of scenario uniformity, lack of collaborative mechanisms, and insufficient dynamic modeling in existing technologies, and provide theoretical support for multi-UCAV collaborative operations in beyond-visual-range air combat. Summary of the Invention

[0008] The purpose of this application is to provide an optimization method and system for the coordinated positioning of two aircraft in a typical bomb-borrowing scenario. This method can optimize the coordinated positioning of two aircraft in a typical bomb-borrowing scenario and provide theoretical support for multi-UCAV cooperative operations in beyond-visual-range air combat.

[0009] To achieve the above objectives, this application provides the following solution.

[0010] Firstly, this application provides an optimization method for our dual-aircraft coordinated positioning in a typical bomb-borrowing scenario, which includes the following steps.

[0011] Construct a missile-borrowing air combat scenario and define the dual-aircraft roles and tasks; the dual-aircraft include a detection and guidance aircraft and a weapon launcher. The task of the detection and guidance aircraft is to keep the enemy within a detectable range at all times, and the task of the weapon launcher is to safely reach the designated position and status within a specified time to complete the missile launch.

[0012] Based on the aforementioned missile-borrowing air combat scenario and the dual-aircraft role mission, a three-degree-of-freedom dynamics and kinematics model of the fighter jet, a weapon engagement zone and no-escape zone model, and a beyond-visual-range (BVR) air combat situation reward and punishment function are constructed respectively. The three-degree-of-freedom dynamics and kinematics model of the fighter jet includes a particle kinematic equation and a dynamic equation. The state variables of the particle kinematic equation and the dynamic equation include position, velocity components, and track angle parameters in the inertial coordinate system. The control variables include tangential overload, normal overload, and roll angle. The weapon engagement zone and no-escape zone model is a simulation model based on the weapon engagement zone and no-escape zone. The BVR air combat situation reward and punishment function includes an off-axis launch angle reward and a relative position reward based on the missile attack zone, and the weights of the off-axis launch angle reward and the relative position reward based on the missile attack zone are balanced by adjustment coefficients.

[0013] Based on the three-degree-of-freedom dynamics and kinematics model of the fighter jet, the weapon engagement zone and no-escape zone model, and the beyond-visual-range air combat situation reward and punishment function, the LSTM model is used to predict the enemy's multi-step trajectory and determine the enemy's state information at each time step; the enemy's state information includes the enemy's position information and velocity information.

[0014] Based on the enemy's state information at each time step, an improved particle swarm optimization algorithm is used to solve for the optimal occupancy route.

[0015] Based on the optimal positioning route, an improved trajectory planning algorithm is used to control the two aircraft to reach the designated position.

[0016] Optionally, the expression for the three-degree-of-freedom dynamics and kinematics model of the fighter jet is as follows.

[0017] ;

[0018] in, This indicates the position of the aircraft in the inertial coordinate system, where the aircraft includes detection and guidance systems and weapon launchers; This represents the components of the aircraft's velocity along the three coordinate axes of the inertial coordinate system. These represent the track inclination angle, track deviation angle, and roll angle, respectively. and These represent tangential overload along the velocity direction and normal overload perpendicular to the velocity direction, respectively. Indicates the speed of the aircraft; Represents gravitational acceleration; These represent the first derivatives of the aircraft's speed, track inclination, and track deviation with respect to time, respectively.

[0019] Optionally, the constraint condition of the control quantity is the following formula.

[0020] ;

[0021] in, , These represent the minimum values ​​of tangential overload and normal overload, respectively. , These represent the maximum values ​​of tangential overload and normal overload, respectively; , These represent the maximum and minimum roll angles, respectively.

[0022] Optionally, the expression for the beyond-visual-range air combat situation reward and punishment situation function is as follows.

[0023] ;

[0024] ;

[0025] ;

[0026] in, The reward and punishment situation function represents the situational awareness of beyond-visual-range air combat. Off-axis launch angle, For the maximum off-axis launch angle, This indicates the bonus for the off-axis launch angle. This indicates a reward based on the relative position of the missile's attack zone. , They are respectively , Adjustment coefficient, Indicates the distance between the weapon launcher and the weapon engagement zone. Indicates the distance from which one cannot escape. Indicates the attack range.

[0027] Optionally, in the weapon engagement zone and no-escape zone model, the weapon engagement zone is a spatial region centered on the enemy. The weapon engagement zone satisfies the rule that if the enemy moves in a straight line at a constant speed after the attacking side launches a missile, the missile can hit it. The boundary of the weapon engagement zone is calculated using a pattern search algorithm, and the range of the weapon engagement zone changes dynamically with the enemy's azimuth and entry angle.

[0028] The no-escape zone is a sub-region of the weapon engagement zone. The no-escape zone satisfies the rule that the attacking side can destroy the missile regardless of the enemy's maneuvering evasion after launching it. The no-escape zone is the area in which the enemy cannot escape the missile's kill envelope due to energy constraints or time constraints.

[0029] Optionally, based on the enemy state information at each time step, an improved particle swarm optimization algorithm is used to solve for the optimal occupancy route, specifically including the following steps.

[0030] Based on the enemy state information at each time step, a multi-constraint optimization problem is constructed. The constraints of the multi-constraint optimization problem include: the enemy is always in the front hemisphere region of our dual aircraft, our detection and guidance aircraft are always observing the enemy, and our weapon launchers do not remain in the enemy's weapon engagement zone for a long time and do not enter the enemy's no-escape zone. The objective function of the multi-constraint optimization problem is to maximize the sum of the differences between the reward and the penalty at each time step.

[0031] Based on the aforementioned multi-constraint optimization problem, an improved particle swarm optimization algorithm is adopted to discretize the continuous problem by using a space grid. Particles are defined as pairs of position and orientation matrices, and a three-subgroup cooperative mechanism is constructed to iteratively update the individual optimal solution and the group optimal solution to obtain the optimal placement route.

[0032] Optionally, the expression for the multi-constraint optimization problem is as follows.

[0033] ;

[0034] in, This means maximizing the sum of the differences between the reward and penalty at each moment. This indicates the maximum time required to solve the problem. This indicates that the enemy is always in the front hemisphere area of ​​our two aircraft. This indicates that our detection and guidance systems are constantly observing the enemy. This indicates that our weapon launchers will not remain in the enemy's weapon engagement zone for extended periods and will not enter the enemy's no-escape zone.

[0035] Optionally, based on the optimal positioning route, an improved trajectory planning algorithm is used to control the two aircraft to reach the designated position, specifically including the following steps.

[0036] Based on the optimal positioning route, a relative position description matrix is ​​constructed, and a mapping function is used to discretize the continuous relative distance between the two machines into direction labels, generating the current formation matrix and the target formation matrix.

[0037] A similarity matrix is ​​constructed based on the current formation matrix and the target formation matrix.

[0038] Based on the similarity matrix, a position allocation optimization model is constructed, and the position allocation optimization model is solved to obtain the optimal fighter-target position mapping relationship; the optimal fighter-target position mapping relationship is the fighter-target position mapping relationship with the highest matching degree.

[0039] Based on the optimal fighter-target position mapping relationship, and combined with the tangential overload, normal overload, and roll angle output by the three-degree-of-freedom dynamics and kinematics model of the fighter jet as the control variables, the two aircraft are controlled to reach the designated position, thereby achieving time coordination and collision avoidance between the two aircraft.

[0040] Optionally, the expression for the mapping function is as follows.

[0041] ;

[0042] in, Represents a mapping function. This indicates the front-to-back or left-to-right distance between the two machines.

[0043] The expression for the location allocation optimization model is as follows.

[0044] ;

[0045] ;

[0046] in, and Representing the target location respectively and target location , Indicates the target location and target location Similarity between them For selection function, This indicates that a location has been assigned to each detection guidance device or weapon launcher. This means that a detection guidance device or weapon launcher is assigned to each location.

[0047] Secondly, this application provides an optimization system for our dual-machine collaborative positioning in a typical ammunition borrowing scenario. The optimization system for our dual-machine collaborative positioning in a typical ammunition borrowing scenario applies the optimization method for our dual-machine collaborative positioning in a typical ammunition borrowing scenario. The optimization system for our dual-machine collaborative positioning in a typical ammunition borrowing scenario includes the following functional modules.

[0048] The scenario construction and role task definition module is used to construct the air combat scenario of borrowing missiles and define the dual-aircraft role tasks. The dual-aircraft includes a detection and guidance aircraft and a weapon launcher. The task of the detection and guidance aircraft is to keep the enemy within the detection range at all times, and the task of the weapon launcher is to safely reach the designated position and status within a specified time to complete the missile launch.

[0049] The model and function construction module is used to construct, based on the missile-borrowing air combat scenario and the dual-aircraft role mission, a three-degree-of-freedom dynamics and kinematics model of the fighter jet, a weapon engagement zone and no-escape zone model, and a beyond-visual-range air combat situation reward and punishment function. The three-degree-of-freedom dynamics and kinematics model of the fighter jet includes a particle kinematic equation and a dynamic equation. The state variables of the particle kinematic equation and the dynamic equation include position, velocity components, and track angle parameters in the inertial coordinate system. The control variables include tangential overload, normal overload, and roll angle. The weapon engagement zone and no-escape zone model is a simulation model based on the weapon engagement zone and no-escape zone. The beyond-visual-range air combat situation reward and punishment function includes an off-axis launch angle reward and a relative position reward based on the missile attack zone, and the weights of the off-axis launch angle reward and the relative position reward based on the missile attack zone are balanced by adjustment coefficients.

[0050] The enemy state prediction module is used to predict the enemy's multi-step trajectory using an LSTM model based on the three-degree-of-freedom dynamics and kinematics model of the fighter jet, the weapon engagement zone and no escape zone model, and the beyond-visual-range air combat situation reward and punishment function, and to determine the enemy state information at each time step; the enemy state information includes the enemy's position information and velocity information.

[0051] The optimal positioning route solution module is used to solve for the optimal positioning route based on the enemy's state information at each time step using an improved particle swarm optimization algorithm.

[0052] The trajectory planning module is used to control the two aircraft to reach the designated position based on the optimal positioning route and an improved trajectory planning algorithm.

[0053] According to the specific embodiments provided in this application, this application has the following technical effects:

[0054] This application provides an optimization method and system for the coordinated positioning of two friendly aircraft in a typical missile-borrowing scenario. By constructing a missile-borrowing air combat scenario and defining the roles and tasks of the two aircraft, a three-degree-of-freedom dynamics and kinematics model of the fighter jet, a weapon engagement zone and no-escape zone model, and a beyond-visual-range air combat situation reward and punishment function are constructed. The three-degree-of-freedom dynamics and kinematics model of the fighter jet includes the kinematic equations of a particle and the dynamic equations. The state variables involve the position, velocity components, and track angle parameters in the inertial coordinate system. The control variables involve tangential overload, normal overload, and roll angle. The weapon engagement zone and no-escape zone model is a simulation model based on the weapon engagement zone and no-escape zone. The beyond-visual-range air combat situation reward and punishment function includes off-axis launch angle reward and relative position reward based on the missile attack zone. The weights of the two rewards are balanced by adjusting the coefficients. Based on the construction of a three-degree-of-freedom dynamics and kinematics model of the fighter jet, a weapon engagement zone and no-escape zone model, and a beyond-visual-range (BVR) air combat situation reward and punishment function, this application utilizes an LSTM model to predict the enemy's multi-step trajectory, then employs an improved particle swarm optimization algorithm to solve for the optimal positioning route, and combines this with an improved trajectory planning algorithm to control the two aircraft to reach the designated position. This application combines dynamics and kinematics modeling techniques, neural network technology, particle swarm optimization technology, and trajectory planning technology to achieve autonomous collaborative positioning optimization decision-making between two aircraft in BVR air combat under a typical bomb-borrowing scenario. It overcomes the limitations of traditional single-aircraft decision-making and solves the problems of scenario uniformity, lack of collaborative mechanisms, and insufficient dynamic modeling in existing technologies, providing theoretical support for multi-UCAV cooperative operations in BVR air combat. Attached Figure Description

[0055] 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.

[0056] Figure 1 This is a flowchart illustrating an optimized method for dual-machine collaborative positioning in a typical bomb-borrowing scenario, as provided in an embodiment of this application.

[0057] Figure 2 This is a schematic diagram illustrating the principle of an optimization method for our dual-machine collaborative positioning in a typical bomb-borrowing scenario, provided as an embodiment of this application.

[0058] Figure 3 This is a schematic diagram illustrating the application scenario of an optimized method for dual-machine collaborative positioning in a typical bomb-borrowing scenario, as provided in an embodiment of this application.

[0059] Figure 4 This is a schematic diagram of an LSTM network structure provided in an embodiment of this application.

[0060] Figure 5 This is a schematic diagram of the LSTM trajectory prediction process provided in an embodiment of this application.

[0061] Figure 6 This is a schematic diagram of the particle swarm algorithm provided in an embodiment of this application.

[0062] Figure 7 This is a schematic diagram of a trajectory planning algorithm provided in an embodiment of this application.

[0063] Figure 8 This is a schematic diagram of the structure of an optimized system for dual-machine collaborative positioning in a typical bomb-borrowing scenario, provided as an embodiment of this application. Detailed Implementation

[0064] 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.

[0065] 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.

[0066] like Figure 1 As shown, an optimization method for coordinated positioning of two friendly aircraft in a typical bomb-borrowing scenario is presented. This method is mainly applied to the optimization of coordinated positioning and collision avoidance between at least two fighter jets (e.g., a detection and guidance aircraft and a weapon launcher) in typical bomb-borrowing scenarios. The optimization method for coordinated positioning of two friendly aircraft in this typical bomb-borrowing scenario specifically includes the following steps.

[0067] S1: Construct a missile-borrowing air combat scenario and define the dual-aircraft role missions.

[0068] In this embodiment, the dual-machine system includes a detection and guidance machine and a weapon launcher. The task of the detection and guidance machine is to keep the enemy within a detectable range at all times, and the task of the weapon launcher is to safely reach the designated position and status within a specified time to complete the missile launch.

[0069] S2: Based on the aforementioned air combat scenario involving borrowed missiles and the dual-aircraft role mission, construct the three-degree-of-freedom dynamics and kinematics model of the fighter jet, the weapon engagement zone and no escape zone model, and the beyond-visual-range air combat situation reward and punishment function, respectively.

[0070] In this embodiment, the three-degree-of-freedom dynamics and kinematics model of the fighter jet includes a particle kinematic equation and a dynamic equation. The state variables of the particle kinematic equation and the dynamic equation include position, velocity components and track angle parameters in the inertial coordinate system. The control variables include tangential overload, normal overload and roll angle. The weapon engagement zone and no-escape zone model is a simulation model based on the weapon engagement zone and no-escape zone. The beyond-visual-range air combat situation reward and punishment situation function includes off-axis launch angle reward and relative position reward based on the missile attack zone, and the weights of the off-axis launch angle reward and the relative position reward based on the missile attack zone are balanced by adjustment coefficients.

[0071] S3: Based on the three-degree-of-freedom dynamics and kinematics model of the fighter jet, the weapon engagement zone and no-escape zone model, and the beyond-visual-range air combat situation reward and punishment function, the LSTM model is used to predict the enemy's multi-step trajectory and determine the enemy's state information at each time step; the enemy's state information includes the enemy's position information and velocity information.

[0072] S4: Based on the enemy state information at each time step, the optimal positioning route is obtained by using an improved particle swarm optimization algorithm.

[0073] S5: Based on the optimal positioning route, an improved trajectory planning algorithm is used to control the two aircraft to reach the designated position.

[0074] In this embodiment, in the weapon engagement zone and no-escape zone model constructed in step S2, the weapon engagement zone is a spatial region centered on the enemy. The weapon engagement zone satisfies the rule that if the enemy moves in a uniform straight line after the attacker launches a missile, the missile can hit them. The boundary of the weapon engagement zone is calculated using a pattern search algorithm, and the range of the weapon engagement zone dynamically changes with the enemy's azimuth and entry angle. The no-escape zone is a sub-region of the weapon engagement zone. The no-escape zone satisfies the rule that the missile launched by the attacker can destroy the enemy regardless of their maneuvering evasion. The no-escape zone is the region where the enemy cannot escape the missile's kill envelope due to energy or time constraints.

[0075] In this embodiment, step S4 uses an improved particle swarm optimization algorithm to solve for the optimal positioning route based on the enemy's state information at each time step, specifically including the following steps.

[0076] S41: Based on the enemy state information at each time step, construct a multi-constraint optimization problem; the constraints of the multi-constraint optimization problem include: the enemy is always in the front hemisphere region of our dual aircraft, our detection and guidance aircraft is always observing the enemy, our weapon launcher does not stay in the enemy's weapon engagement zone for a long time and does not enter the enemy's no-escape zone; the objective function of the multi-constraint optimization problem is to maximize the sum of the differences between the reward and the penalty at each time step.

[0077] S42: Based on the aforementioned multi-constraint optimization problem, an improved particle swarm optimization algorithm is used to discretize the continuous problem in a space-based grid manner. Particles are defined as pairs of position and orientation matrices, and a three-subgroup cooperative mechanism is constructed to iteratively update the individual optimal solution and the group optimal solution to obtain the optimal placement route.

[0078] In this embodiment, step S5 uses an improved trajectory planning algorithm based on the optimal positioning route to control the two aircraft to reach the designated position, specifically including the following steps.

[0079] S51: Based on the optimal positioning route, construct a relative position description matrix, use a mapping function to discretize the continuous relative distance between the two machines into direction labels, and generate the current formation matrix and the target formation matrix.

[0080] S52: Construct a similarity matrix based on the current formation matrix and the target formation matrix.

[0081] S53: Construct a position allocation optimization model based on the similarity matrix, and solve the position allocation optimization model to obtain the optimal fighter-target position mapping relationship; the optimal fighter-target position mapping relationship is the fighter-target position mapping relationship with the highest matching degree.

[0082] S54: Based on the optimal fighter-target position mapping relationship, and combined with the tangential overload, normal overload, and roll angle output by the three-degree-of-freedom dynamics and kinematics model of the fighter jet as the control variables, the two aircraft are controlled to reach the designated position, thereby achieving time coordination and collision avoidance between the two aircraft.

[0083] To make the technical solution of this application clearer, the specific implementation process of the technical solution of this application will be explained in detail below with examples.

[0084] Figure 2This paper illustrates the principle of the optimized method for coordinated positioning of two friendly aircraft in a typical missile-borrowing scenario. Assuming the two friendly aircraft are designated UCAV1 (detection and guidance aircraft) and UCAV2 (weapon launcher), the method first determines the target position and heading using a coordinated positioning algorithm. Then, a formation switching algorithm obtains the current positions (x1, y1) of UCAV1 and (x2, y2) of UCAV2, respectively, and calculates control variables. Target position 1 and target position 2 are then assigned to UCAV1 and UCAV2, respectively. Real-time control is then used to guide UCAV1 and UCAV2 to their designated positions, achieving time-coordinated operation and collision avoidance. Under defined tactics, this significantly enhances the autonomous decision-making capability of the friendly forces in air combat, enabling the implementation of a complete set of tactics as needed. Simultaneously, it maximizes the avoidance of enemy threats, significantly improving the friendly forces' strike and survivability under tactical coordination in autonomous operations. The method specifically includes the following implementation steps.

[0085] S1: Construct a missile-borrowing air combat scenario and define the dual-aircraft role missions.

[0086] In this embodiment, the missile-borrowing air combat scenario constructed in step S1 is a typical missile-borrowing attack scenario, involving fighter jets. One fighter jet acts as a detection and guidance aircraft, whose goal is to keep the enemy within our detection range at all times; the other fighter jet acts as a weapon launcher, whose goal is to safely reach the designated position and state within a specified time to launch the missile.

[0087] Figure 3 The application scenario of the optimized method of our dual-aircraft coordinated positioning in a typical bomb borrowing scenario is shown. The spatial position of the dual-aircraft coordinated positioning and the arrival at the designated position according to the positioning route are demonstrated.

[0088] S2: Based on the aforementioned missile-borrowing air combat scenario and the aforementioned dual-aircraft role mission, construct a three-degree-of-freedom dynamics and kinematics model for the fighter jet, a weapon engagement zone and no-escape zone model, and a beyond-visual-range (BVR) air combat situation reward and punishment function, respectively. The three-degree-of-freedom dynamics and kinematics model includes a particle kinematic equation and a dynamic equation. The state variables of the particle kinematic equation and the dynamic equation include position, velocity components, and track angle parameters in the inertial coordinate system. The control variables include tangential overload, normal overload, and roll angle. The weapon engagement zone and no-escape zone model is a simulation model based on the weapon engagement zone and no-escape zone. The BVR air combat situation reward and punishment function includes an off-axis launch angle reward and a relative position reward based on the missile attack zone, and the weights of the off-axis launch angle reward and the relative position reward based on the missile attack zone are balanced by adjustment coefficients.

[0089] In this embodiment, step S2 is implemented as follows: First, the three-degree-of-freedom dynamics and kinematics model of the fighter jet is performed, that is, a three-degree-of-freedom dynamics and kinematics model of the fighter jet is established. When studying the air combat maneuver decision-making of an aircraft, in order to accurately describe the trajectory and maneuver characteristics of the aircraft, a three-degree-of-freedom point mass kinematics model of the aircraft is performed in three-dimensional space.

[0090] In order to focus the research on air combat maneuver decision-making, this embodiment establishes a model based on the following conditions.

[0091] (1) During the flight of the aircraft, the influence of airflow speed on the flight of the aircraft is not considered.

[0092] (2) The gravitational acceleration g remains constant, and the influence of environmental factors such as altitude and air density on acceleration is not considered.

[0093] (3) The size of the aircraft has negligible effect on the motion, and the aircraft is regarded as a movable point mass.

[0094] (4) The aircraft does not experience sideslip during its movement.

[0095] (5) During the flight of the aircraft, the ground reference frame remains stationary and the Earth’s rotation is not considered.

[0096] Based on the above conditions, the dynamic equation of a three-degree-of-freedom particle in three-dimensional space can be expressed as follows.

[0097] (1)

[0098] in, This indicates the position of the aircraft in the inertial coordinate system; Indicates the speed of the aircraft Components on the three coordinate axes; These represent the track inclination angle, track deviation angle, and roll angle, respectively. and These represent tangential overload along the velocity direction and normal overload perpendicular to the velocity direction, respectively. Let $\mathbf$ and $\mathbf$ represent the first derivatives of the aircraft's velocity, trajectory inclination angle, and trajectory deviation angle with respect to time, respectively. In equation (1), the first three terms represent the kinematic model of the aircraft's particle, and the last three terms represent the dynamic model of the aircraft; the state variables include... and Control quantities include and .

[0099] In this embodiment, it can be seen from the three-degree-of-freedom particle dynamics equations of the aircraft in three-dimensional space that the aircraft's maneuvering actions can be derived from... and Three variables are used to control the aircraft's maneuvers. To ensure the effectiveness of the research and to make the maneuver decisions made by reinforcement learning conform to the characteristics of a real maneuver model, factors such as the strength of the aircraft's internal structure and the normal operating conditions of various sensors need to be considered during the design phase. Constraints need to be placed on the control variables, as shown in the following equation.

[0100] (2)

[0101] in, , These represent the minimum values ​​of tangential overload and normal overload, respectively. , These represent the maximum values ​​of tangential overload and normal overload, respectively; , These represent the maximum and minimum roll angles, respectively. Considering the aircraft's physical limits (i.e., the maximum overload during aircraft design), this embodiment sets... , , , , , .

[0102] In this embodiment, it is necessary to construct a model of the fighter jet's weapon engagement zone and no escape zone, as detailed below.

[0103] In beyond-visual-range (BVR) air combat decision-making models, the weapon engagement zone (WEZ) refers to the attackable zone, defined as the spatial area centered on the target. When the attacker launches a missile from this zone, if the target maintains uniform linear motion, the missile can effectively hit the target. The WEZ boundary is precisely calculated using a pattern search algorithm, and its range varies with the target azimuth angle (i.e., off-axis launch angle). and entry angle Dynamic changes: when and WEZ's range is largest during a head-on attack, and Approaching maximum off-axis launch angle At this time, the WEZ range is significantly reduced. The no-escape zone (NEZ) is a sub-region within the WEZ. When the attacker launches a missile from within the NEZ, the missile is guaranteed to destroy the target regardless of its maneuvering or evasion. The physical essence of the NEZ is that the target cannot escape the core area of ​​the missile's kill envelope due to energy or time constraints, and its range is significantly smaller than the WEZ.

[0104] In this embodiment, the beyond-visual-range air combat situation reward and punishment function constructed in step S2 includes off-axis launch angle reward and relative position reward based on the missile attack zone, as shown in the following formula.

[0105] (3)

[0106] (4)

[0107] (5)

[0108] in, The reward and punishment situation function represents the situational awareness of beyond-visual-range air combat. Off-axis launch angle, For the maximum off-axis launch angle, This indicates the bonus for the off-axis launch angle. This indicates a reward based on the relative position of the missile's attack zone. , They are respectively , The adjustment coefficients for both depend on whether the reward is more biased towards off-axis launch angle or distance. Indicates the distance between the weapon launcher and the weapon engagement zone. Indicates the distance from which one cannot escape. Indicates the attack range.

[0109] S3: Based on the three-degree-of-freedom dynamics and kinematics model of the fighter jet, the weapon engagement zone and no-escape zone model, and the beyond-visual-range air combat situation reward and punishment function, the LSTM model is used to predict the enemy's multi-step trajectory and determine the enemy's state information at each time step; the enemy's state information includes the enemy's position information and velocity information.

[0110] In this embodiment, step S3 is implemented as follows.

[0111] Assuming the plane is currently in At any time, for and Historical position before the moment Speed ​​information and control quantity Training is performed using LSTM. The target position state at different prediction times is obtained by using position and velocity information. .

[0112] In this embodiment, the LSTM network structure is as follows: Figure 4 As shown, in At any given moment, a single layer of a network consists of two information flows, one above the other. From... arrive The information flow represents the transmission of cell states, and the entire line interacts linearly with the information flow below through three gating structures. The gating structures allow information to flow selectively, flowing upwards... arrive The information flow deletes or adds information about the cell state. In the gating structure... Activation function layer and The activation function layer transforms the input into the ranges (0, 1) and (-1, 1) respectively, generating weights for the input data and thus filtering it. Each LSTM network layer has three gate structures to control the cell state.

[0113] (1) The Gate of Oblivion.

[0114] The expression for the forget gate is shown below.

[0115] (6)

[0116] in, The layer uses the hidden state from the previous time step. and Input of time A value between 0 and 1 is obtained as the probability that the cell state of the previous layer is forgotten, and is considered as... The decay coefficient of memory, denoted as . It is a two-dimensional matrix that represents the parameters that the LSTM model needs to learn. This matrix contains the knowledge learned by the model and is used to determine which information should be forgotten based on past hidden states and the current input. It defines the importance weights of the input information combinations. This is a vector, and also a parameter that the LSTM model needs to learn, adding an offset (constant term) to the calculation of the forget gate. This allows the LSTM model to still output a non-zero value when the weighted sum of the inputs is zero (e.g., by default, it tends to retain or forget some information), thus increasing the model's flexibility.

[0117] (2) Input gate.

[0118] Input gate part will Hidden state from the previous moment After linear combination, through Layer activation is obtained This part determines which information needs to be updated; this information is the part selected to be forgotten through the forgetting gate. The other part will... and Through a The layer generates a vector This refers to the alternative content to be updated. Then, the two parts will be combined to update the state. Updated to The formula for the input gate update process is as follows.

[0119] (7)

[0120] (8)

[0121] (9)

[0122] in, The input gate vector is used to control the degree to which new information is retained (0~1). The input gate weight matrix is ​​used to learn how to combine historical information and the current input; This is the input gate bias vector, used to increase the flexibility of the model; This is the candidate state weight matrix, used to learn how to combine new information; These are candidate state bias vectors, used to increase the flexibility of the model; This represents convolution.

[0123] (3) Output gate.

[0124] (10)

[0125] (11)

[0126] in, This is the output gate vector, used to control the degree of output of cell state; This is the output gate weight matrix, used to output weights; This is the output gate bias vector; This represents the current hidden state, which is the final output of the LSTM model and also the input for the next step. Additionally, and , , These represent the output weights and bias matrices, respectively, which are also parameters that need to be learned during training. Since each iteration uses information from the previous iteration... and Each output state is influenced by the previous state, so the LSTM model has the ability to remember long-term historical information.

[0127] Figure 5 The flowchart illustrates the LSTM trajectory prediction process. First, the dataset is acquired, then partitioned and normalized. Next, the network structure parameters (initial parameters) are checked for fit. If fit, the accuracy is checked. If fit is achieved, the network model is saved, input into the test set, and the output is predicted. If not fit, the network structure parameters are adjusted and optimized, and the fit is checked again until a fit is achieved. If accuracy is not met, the network structure parameters are adjusted and optimized again, and the fit and accuracy checks are checked again until a fit is achieved and the accuracy is met.

[0128] S4: Based on the enemy state information at each time step, the optimal positioning route is obtained by using an improved particle swarm optimization algorithm.

[0129] In this embodiment, step S4 is implemented as follows.

[0130] The target point is calculated using an improved Particle Swarm Optimization (PSO) algorithm. PSO is a swarm intelligence-based optimization algorithm inspired by the foraging behavior of birds. Each particle represents a candidate solution in the solution space, and particles dynamically adjust their flight direction and speed based on their own historical best solution (pbest) and the swarm's historical best solution (gbest). Figure 6 The basic framework flowchart of the particle swarm optimization algorithm is shown. First, the particle swarm is initialized and the particle fitness is calculated. Then, it is determined whether the termination condition is met. If it is, the optimal solution is output. Otherwise, the individual optimal solution and the swarm optimal solution are updated. Then, the particle velocity and position are updated, and the particle fitness is recalculated based on the updated particle velocity and position, so as to achieve the purpose of dynamically adjusting the flight direction and speed.

[0131] This embodiment focuses on dual-machine collaborative positioning in a typical bomb-borrowing scenario. The core steps of the improved particle swarm algorithm are as follows.

[0132] First, the occupancy space is divided into a grid, facilitating the transformation of the continuous position space into a discrete combinatorial problem that is easier to solve, namely a multi-constraint optimization problem. This allows for the simultaneous optimization of discrete variables (occupancy grid positions) and continuous variables (UCAV orientation angles), while satisfying the constraints of avoiding missile attack zones. The constraints of this multi-constraint optimization problem include: the enemy is always located in the forward hemisphere region of our dual aircraft; our detection and guidance aircraft are always observing the enemy; and our weapon launchers do not remain in the enemy's weapon engagement zone for extended periods and do not enter the enemy's no-escape zone. The objective function of the multi-constraint optimization problem is to maximize the sum of the differences between the reward and penalty at each time step.

[0133] Through the position matrix and orientation matrix The particle swarm is defined as follows.

[0134] (12)

[0135] (13)

[0136] in, Orientation matrix The i-th element in the array, with its superscript This indicates transpose.

[0137] A three-subgroup cooperative mechanism is employed. Specifically, in the improved particle swarm optimization algorithm, the three-subgroup cooperative mechanism achieves global optimization through functional complementarity, and the exploration subgroup generates new particles (position matrix) completely randomly in each generation. Randomly set to 1, heading exist Uniform sampling (accounting for 30% of the total number of particles) ensures the diversity of the solution space and avoids premature convergence; the empirical inheritance subgroup is based on the previous generation of particles and subjected to bounded perturbation, as shown below.

[0138] (14)

[0139] in, The grid coordinates (row and column indices) represent the current position of the particle, and the values ​​are based on the positions of non-zero elements in the position matrix of the previous generation of particles; This represents the new grid coordinates after the perturbation, and the values ​​are based on the new position matrix. index; This is a function to generate random integers within a range; This indicates the maximum positional perturbation step size (grid unit).

[0140] In this embodiment, the heading is... Adjust and truncate to It only accepts updates that improve fitness to preserve historical experience. Among these, This represents the original heading angle, and its value is based on the heading matrix of the previous generation of particles. The value in; Indicates the new heading angle after the disturbance; This represents the maximum heading disturbance amplitude (in degrees). The elite development subgroup focuses on the global optimum and samples locally within its grid neighborhood (neighborhood radius). ,in, The neighborhood radius, (for grid width), and finely adjust the heading ( The range is completely reset in each generation to new particles in the neighborhood to achieve in-depth development. The three subgroups unify the synchronization direction, and the low-fitness particles in the experience inheritance subgroup are replaced by high-fitness random particles in the exploration subgroup to prevent stagnation. The three subgroups work together in a 1:1:1 resource ratio to break through the local optimum of the MINLP (Mixed Integer Nonlinear Programming) problem.

[0141] S5: Based on the optimal positioning route, an improved trajectory planning algorithm is used to control the two aircraft to reach the designated position.

[0142] In this embodiment, step S5 is implemented as follows.

[0143] Formation switching is the first step in the trajectory planning algorithm. In this algorithm, the relative position description matrix is ​​the core tool; its essence is to quantify the formation structure by discretizing directional relationships, effectively reducing the computational complexity of trajectory planning. First, a mapping function is defined. As shown in the following formula.

[0144] (15)

[0145] in, Represents a mapping function. This indicates the front-to-back or left-to-right distance between the two machines, including the front-to-back distance. and left and right distance The output of this mapping function is 1 for a positive direction, 0 for coincidence, and -1 for a negative direction. It maps the relative positions of aircraft in continuous space (e.g.,...) Indicates the distance between front and back. The left and right distances are compressed into discrete direction labels. The current formation matrix is ​​then constructed based on these labels. Current formation matrix It is A matrix, where each off-diagonal element By binary Composition, complete record of the first The fighter jets relative to the first The directional relationship of the fighter jets, for example express exist The front right side, while the diagonal elements are always 0. Simultaneously construct the target formation matrix Its structure and The same but ideal geometric relationship calculation based on the target occupancy points forms a mathematical abstract expression of the formation structure.

[0146] Figure 7 The flowchart illustrates the trajectory planning algorithm. First, the current formation matrix and the target formation matrix are calculated based on the input data. Then, a similarity matrix is ​​constructed, and the position allocation problem is solved. Finally, a consistency control protocol is applied to ensure that the UCAVs arrive at the target position synchronously. The position allocation problem is solved using the similarity matrix. Transform it into an optimization task. Calculate. and similarity between At that time, extract the current formation matrix. The Line (describing the directional relationship between the detection guidance device and the weapon launcher) and target formation matrix The line (target location) (Required directional relationship), count the number of pairs that perfectly match as Therefore, a location allocation optimization model is constructed, as follows.

[0147] (16)

[0148] (17)

[0149] in, and Representing the target location respectively and target location , Indicates the target location and target location Similarity between them Let be a selection function that takes either 0 or 1 from (0, 1). This indicates that a location has been assigned to each detection guidance device or weapon launcher. This means that a detection guidance device or weapon launcher is assigned to each location.

[0150] Its essence is to seek the optimal aircraft-target position mapping relationship, and its discretization process significantly reduces computational complexity.

[0151] (18)

[0152] in, This represents the output control quantity. and It is a constant. Indicates the target's heading requirements. Indicates the location requirements of the target.

[0153] After completing the position allocation, based on the previously constrained heading requirements and the target's position requirements, constants are set. and It can output control quantity By combining the three-degree-of-freedom dynamics and kinematics model of the fighter jet mentioned above, we can control our two aircraft to reach the designated position and achieve coordinated positioning and collision avoidance.

[0154] Based on the same inventive concept, this application also provides an optimization system for the collaborative positioning of two friendly aircraft in a typical ammunition borrowing scenario, used to implement the optimization method for the collaborative positioning of two friendly aircraft in the typical ammunition borrowing scenario described above. The solution provided by this system is similar to the implementation scheme described in the above method. Therefore, the specific limitations in the following embodiments of the optimization system for the collaborative positioning of two friendly aircraft in a typical ammunition borrowing scenario can be found in the limitations of the optimization method for the collaborative positioning of two friendly aircraft in a typical ammunition borrowing scenario described above, and will not be repeated here.

[0155] In one exemplary embodiment, such as Figure 8 As shown, an optimized system for our dual-machine collaborative positioning in a typical bomb-borrowing scenario is provided, which includes the following functional modules.

[0156] The scenario construction and role task definition module is used to construct the air combat scenario of borrowing missiles and define the dual-aircraft role tasks. The dual-aircraft includes a detection and guidance aircraft and a weapon launcher. The task of the detection and guidance aircraft is to keep the enemy within the detection range at all times, and the task of the weapon launcher is to safely reach the designated position and status within a specified time to complete the missile launch.

[0157] The model and function construction module is used to construct, based on the missile-borrowing air combat scenario and the dual-aircraft role mission, a three-degree-of-freedom dynamics and kinematics model of the fighter jet, a weapon engagement zone and no-escape zone model, and a beyond-visual-range air combat situation reward and punishment function. The three-degree-of-freedom dynamics and kinematics model of the fighter jet includes a particle kinematic equation and a dynamic equation. The state variables of the particle kinematic equation and the dynamic equation include position, velocity components, and track angle parameters in the inertial coordinate system. The control variables include tangential overload, normal overload, and roll angle. The weapon engagement zone and no-escape zone model is a simulation model based on the weapon engagement zone and no-escape zone. The beyond-visual-range air combat situation reward and punishment function includes an off-axis launch angle reward and a relative position reward based on the missile attack zone, and the weights of the off-axis launch angle reward and the relative position reward based on the missile attack zone are balanced by adjustment coefficients.

[0158] The enemy state prediction module is used to predict the enemy's multi-step trajectory using an LSTM model based on the three-degree-of-freedom dynamics and kinematics model of the fighter jet, the weapon engagement zone and no escape zone model, and the beyond-visual-range air combat situation reward and punishment function, and to determine the enemy state information at each time step; the enemy state information includes the enemy's position information and velocity information.

[0159] The optimal positioning route solution module is used to solve for the optimal positioning route based on the enemy's state information at each time step using an improved particle swarm optimization algorithm.

[0160] The trajectory planning module is used to control the two aircraft to reach the designated position based on the optimal positioning route and an improved trajectory planning algorithm.

[0161] 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.

[0162] This embodiment uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this application; at the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. In summary, the content of this specification should not be construed as a limitation of this application.

Claims

1. An optimized method for coordinated positioning of two friendly aircraft in a typical bomb-borrowing scenario, characterized in that, The optimization method for our dual-aircraft coordinated positioning in the typical bomb-borrowing scenario includes: Construct a missile-borrowing air combat scenario and define the dual-aircraft roles and tasks; the dual-aircraft include a detection and guidance aircraft and a weapon launcher. The task of the detection and guidance aircraft is to keep the enemy within a detectable range at all times, and the task of the weapon launcher is to safely reach the designated position and status within a specified time to complete the missile launch. Based on the aforementioned missile-assisted air combat scenario and the dual-aircraft role mission, a three-degree-of-freedom dynamics and kinematics model of the fighter jet, a weapon engagement zone and no-escape zone model, and a beyond-visual-range (BVR) air combat situation reward and punishment function are constructed respectively. The three-degree-of-freedom dynamics and kinematics model of the fighter jet includes a particle kinematic equation and a dynamic equation. The state variables of the particle kinematic equation and the dynamic equation include position, velocity components, and track angle parameters in the inertial coordinate system. The control variables include tangential overload, normal overload, and roll angle. The weapon engagement zone and no-escape zone model is a simulation model based on the weapon engagement zone and no-escape zone. The BVR air combat situation reward and punishment function includes an off-axis launch angle reward and a relative position reward based on the missile attack zone, and the weights of the off-axis launch angle reward and the relative position reward based on the missile attack zone are balanced by adjustment coefficients. Based on the aforementioned three-degree-of-freedom dynamics and kinematics model of the fighter jet, the aforementioned weapon engagement zone and no-escape zone model, and the aforementioned beyond-visual-range air combat situation reward and punishment function, an LSTM model is used to predict the enemy's multi-step trajectory and determine the enemy's state information at each time step; the enemy's state information includes the enemy's position information and velocity information. Based on the enemy's state information at each time step, the optimal occupancy route is obtained by using an improved particle swarm optimization algorithm. Based on the optimal positioning route, an improved trajectory planning algorithm is used to control the two aircraft to reach the designated position.

2. The optimized method for our dual-aircraft coordinated positioning in a typical bomb-borrowing scenario as described in claim 1, characterized in that, The expression for the three-degree-of-freedom dynamics and kinematics model of the fighter jet is as follows: ； in, This indicates the position of the aircraft in the inertial coordinate system, where the aircraft includes detection and guidance systems and weapon launchers; This represents the components of the aircraft's velocity along the three coordinate axes of the inertial coordinate system. These represent the track inclination angle, track deviation angle, and roll angle, respectively. and These represent tangential overload along the velocity direction and normal overload perpendicular to the velocity direction, respectively. Indicates the speed of the aircraft; Represents gravitational acceleration; These represent the first derivatives of the aircraft's speed, track inclination, and track deviation with respect to time, respectively.

3. The optimized method for our dual-aircraft coordinated positioning in a typical bomb-borrowing scenario as described in claim 2, characterized in that, The constraint condition for the control quantity is: ； in, , These represent the minimum values ​​of tangential overload and normal overload, respectively. , These represent the maximum values ​​of tangential overload and normal overload, respectively; , These represent the maximum and minimum roll angles, respectively.

4. The optimized method for our dual-aircraft coordinated positioning in a typical bomb-borrowing scenario as described in claim 1, characterized in that, The expression for the beyond-visual-range air combat situation reward and punishment function is as follows: ； ； ； in, The reward and punishment situation function represents the situational awareness of beyond-visual-range air combat. Off-axis launch angle, For the maximum off-axis launch angle, This indicates the bonus for the off-axis launch angle. This indicates a reward based on the relative position of the missile's attack zone. , They are respectively , Adjustment coefficient, Indicates the distance between the weapon launcher and the weapon engagement zone. Indicates the distance from which one cannot escape. Indicates the attack range.

5. The optimized method for our dual-aircraft coordinated positioning in a typical bomb-borrowing scenario as described in claim 1, characterized in that, In the weapon engagement zone and no escape zone model, the weapon engagement zone is a spatial region centered on the enemy. The weapon engagement zone satisfies the rule that if the enemy moves in a straight line at a constant speed after the attacker launches a missile, the missile can hit the target. The boundary of the weapon engagement zone is calculated using a pattern search algorithm, and the range of the weapon engagement zone changes dynamically with the enemy's azimuth and entry angle. The no-escape zone is a sub-region of the weapon engagement zone. The no-escape zone satisfies the rule that the attacking side can destroy the missile regardless of the enemy's maneuvering evasion after launching it. The no-escape zone is the area in which the enemy cannot escape the missile's kill envelope due to energy constraints or time constraints.

6. The optimized method for our dual-aircraft coordinated positioning in a typical bomb-borrowing scenario as described in claim 1, characterized in that, Based on the enemy state information at each time step, an improved particle swarm optimization algorithm is used to solve for the optimal positioning route, specifically including: Based on the enemy's state information at each time step, a multi-constraint optimization problem is constructed. The constraints of the multi-constraint optimization problem include: the enemy is always in the front hemisphere region of our dual aircraft; our detection and guidance aircraft are always observing the enemy; our weapon launchers do not remain in the enemy's weapon engagement zone for extended periods and do not enter the enemy's no-escape zone. The objective function of the multi-constraint optimization problem is to maximize the sum of the differences between the reward and the penalty at each time step. Based on the aforementioned multi-constraint optimization problem, an improved particle swarm optimization algorithm is adopted to discretize the continuous problem by using a space grid. Particles are defined as pairs of position and orientation matrices, and a three-subgroup cooperative mechanism is constructed to iteratively update the individual optimal solution and the group optimal solution to obtain the optimal placement route.

7. The optimized method for our dual-aircraft coordinated positioning in a typical bomb-borrowing scenario as described in claim 6, characterized in that, The expression for the multi-constraint optimization problem is: ； in, This means maximizing the sum of the differences between the reward and penalty at each moment. This indicates the maximum time required to solve the problem. This indicates that the enemy is always in the front hemisphere area of ​​our two aircraft. This indicates that our detection and guidance systems are constantly observing the enemy. This indicates that our weapon launchers will not remain in the enemy's weapon engagement zone for extended periods and will not enter the enemy's no-escape zone.

8. The optimized method for our dual-aircraft coordinated positioning in a typical bomb-borrowing scenario as described in claim 1, characterized in that, Based on the optimal positioning route, an improved trajectory planning algorithm is used to control the two aircraft to reach the designated position, specifically including: Based on the optimal positioning route, a relative position description matrix is ​​constructed, and a mapping function is used to discretize the continuous relative distance between the two machines into direction labels to generate the current formation matrix and the target formation matrix. Construct a similarity matrix based on the current formation matrix and the target formation matrix; A position allocation optimization model is constructed based on the similarity matrix, and the optimal fighter-target position mapping relationship is obtained by solving the optimization model; the optimal fighter-target position mapping relationship is the fighter-target position mapping relationship with the highest matching degree. Based on the optimal fighter-target position mapping relationship, and combined with the tangential overload, normal overload, and roll angle output by the three-degree-of-freedom dynamics and kinematics model of the fighter jet as the control variables, the two aircraft are controlled to reach the designated position, thereby achieving time coordination and collision avoidance between the two aircraft.

9. The optimized method for our dual-aircraft coordinated positioning in a typical bomb-borrowing scenario as described in claim 8, characterized in that, The expression for the mapping function is: ； in, Represents a mapping function. Indicates the front-to-back or left-to-right distance between the two machines; The expression for the location allocation optimization model is: ； ； in, and Representing the target location respectively and target location , Indicates the target location and target location Similarity between them For selection function, This indicates that a location has been assigned to each detection guidance device or weapon launcher. This means that a detection guidance device or weapon launcher is assigned to each location.

10. An optimized system for coordinated positioning of two friendly aircraft in a typical bomb-borrowing scenario, characterized in that: The optimized system for our dual-aircraft coordinated positioning in the typical ammunition borrowing scenario applies the optimized method for our dual-aircraft coordinated positioning in the typical ammunition borrowing scenario as described in any one of claims 1-9. The optimized system for our dual-aircraft coordinated positioning in the typical ammunition borrowing scenario includes: The scenario construction and role task definition module is used to construct the air combat scenario of borrowing missiles and define the dual-aircraft role tasks; the dual-aircraft includes a detection and guidance aircraft and a weapon launcher. The task of the detection and guidance aircraft is to keep the enemy within the detection range at all times, and the task of the weapon launcher is to safely reach the designated position and status within a specified time to complete the missile launch. The model and function construction module is used to construct, based on the missile-borrowing air combat scenario and the dual-aircraft role mission, a three-degree-of-freedom dynamics and kinematics model of the fighter jet, a weapon engagement zone and no-escape zone model, and a beyond-visual-range air combat situation reward and punishment function. The three-degree-of-freedom dynamics and kinematics model of the fighter jet includes a particle kinematic equation and a dynamic equation. The state variables of the particle kinematic equation and the dynamic equation include position, velocity components, and track angle parameters in the inertial coordinate system. The control variables include tangential overload, normal overload, and roll angle. The weapon engagement zone and no-escape zone model is a simulation model based on the weapon engagement zone and no-escape zone. The beyond-visual-range air combat situation reward and punishment function includes an off-axis launch angle reward and a relative position reward based on the missile attack zone, and the weights of the off-axis launch angle reward and the relative position reward based on the missile attack zone are balanced by adjustment coefficients. The enemy state prediction module is used to predict the enemy's multi-step trajectory using an LSTM model based on the three-degree-of-freedom dynamics and kinematics model of the fighter jet, the weapon engagement zone and no escape zone model, and the beyond-visual-range air combat situation reward and punishment function, and to determine the enemy state information at each time step; the enemy state information includes the enemy's position information and velocity information. The optimal positioning route solution module is used to solve for the optimal positioning route based on the enemy's state information at each time step using an improved particle swarm optimization algorithm. The trajectory planning module is used to control the two aircraft to reach the designated position based on the optimal positioning route and an improved trajectory planning algorithm.

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