A multi-unmanned aerial vehicle cooperative trajectory optimization method for complex dynamic scenes

Abstract

The application discloses a kind of multi-unmanned aerial vehicle cooperative trajectory optimization methods for complex dynamic scene, it is related to unmanned aerial vehicle cluster cooperative control and trajectory planning technical field, comprising: the establishment of multi-unmanned aerial vehicle flight dynamics and air combat environment constraint model;Fusion angle, tail pursuit, distance and height four-dimensional subfunction constructs single machine advantage function, and superimposes anti-encirclement, cooperative encirclement and collision penalty term, constitutes multi-machine cooperative air combat objective function;With distributed model prediction control as framework, real-time solution is carried out to local finite time domain optimization problem using improved grey wolf optimization algorithm;Finally, based on the closed-loop iteration of rolling horizon strategy completes optimal control quantity to exert.The application unifies multi-dimensional air combat advantage and multi-machine cooperative tactical intention into optimization framework, and combines with the improved solver with neighborhood learning mechanism, effectively solve the defects that trajectory lacks tactical cooperation and online solution real-time is difficult to guarantee in prior art.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) swarm cooperative control and trajectory planning technology, and in particular to a method for optimizing the online cooperative trajectory of multiple UAVs based on nonlinear model predictive control. Background Technology

[0002] In real-world UAV combat, UAVs need to perform trajectory planning and tactical decisions in real time within highly dynamic and complex environments, directly relying on the real-time performance and global optimality of the trajectory planning system. Therefore, multi-UAV trajectory optimization has always been a research hotspot in the field of intelligent control, and various planning schemes have been developed, including graph search-based global planning methods, model predictive control-based online optimization methods, and reinforcement learning-based autonomous decision-making methods. However, due to the high uncertainty of the environment and the complex coupling of multi-UAV cooperative constraints, achieving high real-time performance and high tactical effectiveness in collaborative trajectory planning remains a significant challenge.

[0003] Model predictive control (MMDC), as an effective online optimization method, has been widely applied to solve UAV trajectory planning problems under complex constraints. Existing research combines nonlinear MMDC with various intelligent optimization algorithms to address the impact of nonlinear dynamic constraints and multi-objective optimization, while also introducing advantage functions or threat assessment models to characterize air combat situations. However, due to the imperfections in existing advantage function modeling, these solutions typically only consider a single or a few dimensions of situation assessment, making it difficult to comprehensively reflect the combined effects of multi-dimensional air combat advantages such as angle, altitude, and tail-chase azimuth. In actual multi-aircraft air combat scenarios, the limitations of single-aircraft situation assessment may lead to a lack of tactical-level coordination in trajectory planning, or even unfavorable situations such as friendly forces being surrounded or attacked. Although some studies have theoretically demonstrated the feasibility of multi-aircraft cooperative planning, extending these methods to highly coupled, highly adversarial multi-aircraft air combat scenarios still faces many challenges.

[0004] At the solution method level, existing online trajectory planning mainly relies on two types of solvers: gradient-based algorithms and traditional swarm intelligence algorithms. Gradient-based methods, such as sequential quadratic programming, have strict requirements for the differentiability of the objective function. Once mode-switching logic or non-smooth structures are introduced into the dominant function, the solver is prone to numerical divergence or getting trapped in local maxima. Although traditional swarm intelligence algorithms have a certain robustness to non-convex problems, basic particle swarm optimization and genetic algorithms have slow convergence speeds in high-dimensional decision spaces, and population diversity is rapidly lost in the middle of the iteration, making it difficult to stably output high-quality solutions within the extremely short control step size required for air combat. The Grey Wolf Optimization Algorithm, as a novel swarm intelligence method proposed in recent years, has fewer parameters and a simpler structure, and has good global search capabilities for non-convex problems. However, its basic form still has shortcomings in maintaining population diversity, dynamic balance between exploration and development, and late-stage convergence accuracy, which is particularly prominent in multi-machine, high-dimensional, strongly coupled optimization scenarios.

[0005] In summary, existing technologies have significant shortcomings in multi-dimensional advantage modeling and real-time online solution in multi-UAV air combat trajectory planning. Summary of the Invention

[0006] This invention provides an online trajectory optimization method for multiple unmanned aerial vehicles (UAVs) based on nonlinear model predictive control (NMPC) to solve the aforementioned technical problems. This method can integrate the multi-dimensional advantages of single-UAV air combat with the tactical intent of multi-UAV cooperation into the online optimization framework, and achieve efficient real-time solution of complex non-convex problems through systematic improvement of the Grey Wolf optimization algorithm. This meets the actual needs of multi-UAV cooperative air combat in dynamic confrontation environments and provides a theoretical basis and technical support for future intelligent unmanned combat.

[0007] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0008] A method for cooperative trajectory optimization of multiple UAVs in complex dynamic scenarios includes the following steps:

[0009] S1: Based on the kinematic model of the center of mass, establish the flight dynamics equations of multiple UAVs, define the state vector and control input vector, and discretize them by the forward Euler method to obtain the discrete state transition equations;

[0010] S2: Construct an air combat environment model, including a flight altitude constraint model and an inter-aircraft collision avoidance model;

[0011] S3: Construct a single-aircraft air combat advantage sub-function from four dimensions: angle, tail chase, distance and altitude, and combine it into a single-aircraft comprehensive advantage function through adaptive weighting. Then, add anti-encirclement term, cooperative encirclement term and collision penalty term to form a multi-aircraft cooperative air combat objective function.

[0012] S4: Using distributed nonlinear model predictive control as the online optimization framework, each UAV solves the local finite-time domain optimization problem in real time at each control moment based on the discrete state transition equation and the multi-aircraft cooperative air combat objective function, and realizes multi-aircraft cooperative tactical optimization through inter-aircraft information interaction;

[0013] S5: An improved gray wolf optimization algorithm is used to solve the local finite-time domain optimization problem online. The population diversity and solution quality are improved by a hunting neighborhood learning search strategy based on multi-dimensional learning, and the optimal control sequence is output.

[0014] S6: Based on the rolling time-domain strategy, the optimal control quantity at the current moment is extracted from the optimal control sequence and applied to each UAV, completing the closed-loop iteration of state perception, optimization solution and control quantity application, and realizing the full-process online real-time optimization of the air combat trajectory of multiple UAVs.

[0015] Compared with the prior art, the beneficial effects of the present invention are:

[0016] (1) This invention comprehensively enhances the tactical level and situational advantage of multi-aircraft cooperative air combat: Existing methods only consider advantages in a single or a few dimensions and are difficult to reflect the intention of multi-aircraft cooperation. This invention constructs a multi-dimensional single-aircraft comprehensive advantage function that includes angle, tail chase, distance and altitude, and explicitly introduces anti-encirclement and cooperative encirclement terms. It directly quantifies and characterizes the tactical intention of multi-aircraft cooperation at the objective function level. This mechanism enables our UAV swarm to not only adaptively switch between approach and escape modes in actual combat, but also actively cooperate to form a pincer encirclement formation, while avoiding the disadvantage of being pincered by the enemy. It effectively overcomes the shortcomings of traditional methods in expressing multi-aircraft cooperative tactics and being prone to falling into unfavorable situations.

[0017] (2) This invention effectively improves the real-time performance and global optimization capability of online solution for high-dimensional non-convex optimization problems. In view of the shortcomings of traditional swarm intelligence algorithms under the NMPC framework, such as slow convergence and easy getting trapped in local optima, this invention adopts an improved gray wolf optimization algorithm (IGWO): by introducing a hunting (DLH) neighborhood search strategy based on multi-dimensional learning, it breaks the limitation that the basic GWO only relies on three alpha wolves for guidance. Each gray wolf generates candidate positions through neighborhood learning and compares them with the GWO search results in a greedy manner to select the best one. This effectively maintains the diversity of the population, enhances the global search capability, and ensures that a high-quality optimal control sequence is stably output within a very short control step.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, embodiments of the present invention are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a diagram illustrating the overall technical framework of the method of the present invention;

[0021] Figure 2 Comparison of three-dimensional trajectories in a two-on-two air combat simulation

[0022] Figure 3 The curve showing the change of the comprehensive air combat superiority function over time;

[0023] Figure 4 This is a three-dimensional situational awareness graph that changes over time.

[0024] Figure 5 This is a graph showing the changes in weights. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0026] like Figure 1 As shown, this invention discloses a multi-UAV online trajectory optimization method based on NMPC, specifically including the following steps S1 to S6:

[0027] S1: Based on the point centroid kinematic model, establish the flight dynamics equations of multiple UAVs, define the state vector and control input vector, and discretize them using the forward Euler method to obtain the discrete state transition equations.

[0028] This invention uses a point-centrifuge kinematic model to describe the flight dynamics of an unmanned aerial vehicle (UAV). For the first... The drone is defined as follows:

[0029] (1)

[0030] In the formula, These are respectively the climb angle, yaw angle, and roll angle; These are three-dimensional spatial coordinates; For speed; This is a normal overload.

[0031] The control input vector is defined as follows:

[0032] (2)

[0033] In the formula, This refers to the rate of change of roll angular velocity; The normal overload rate of change; This is the tangential overload control variable.

[0034] Based on the forward Euler method with time step Discretize the dynamic equations of the centroid, and the specific state equations of each core are as follows:

[0035] (3)

[0036] (4)

[0037] (5)

[0038] (6)

[0039] (7)

[0040] (8)

[0041] (9)

[0042] (10)

[0043] The above discrete dynamic equations can be uniformly written as: This serves as an equality constraint in the NMPC optimization model, namely the discrete state transition equation.

[0044] S2: Construct an air combat environment model, including a flight altitude constraint model and an inter-aircraft collision avoidance model.

[0045] (1) Flight altitude constraint model

[0046] To ensure the flight safety of the UAV, upper and lower bound constraints are imposed on the flight altitude at any control time s:

[0047] (11)

[0048] in and These are the lower and upper limits of flight altitude, respectively.

[0049] Individuals that violate the constraints are penalized with large values ​​in the fitness calculation of the improved gray wolf optimization algorithm:

[0050] (12)

[0051] In the formula For example, take the penalty weight coefficient. =1×10 6 .

[0052] (2) Inter-machine collision avoidance model

[0053] For any two machines k and k', when their distance is less than the safety radius... At this time, the collision penalty terms, which will be detailed below, are used to calculate the cost. The collision weight of friendly aircraft against enemy aircraft is higher than that of friendly aircraft against each other, so as to maintain close-range suppression of enemy aircraft while ensuring safety.

[0054] S3: Construct a single-aircraft air combat advantage sub-function from four dimensions: angle, tail chase, distance, and altitude. Then, combine them into a single-aircraft comprehensive advantage function through adaptive weighting. On this basis, add anti-encirclement term, cooperative encirclement term, and collision penalty term to form a multi-aircraft cooperative air combat objective function.

[0055] (1) The specific construction of the four-dimensional single-aircraft air combat advantage sub-function is as follows:

[0056] Angle advantage This characterizes the degree to which our aircraft's velocity vector points towards the enemy aircraft. Define our aircraft's velocity vector V. r The angle between the vector d and the line connecting friend and foe is φ1, and a Gaussian function is used for modeling:

[0057] (13)

[0058] when hour That is, the maximum value is taken when our aircraft's nose is directly facing the enemy aircraft.

[0059] Tail-end advantage The degree to which the enemy aircraft is facing away from our aircraft is represented by the enemy aircraft's velocity vector V. b Modeling the angle cosine (q) between the line connecting the enemy and friendly aircraft, where the direction of the line is defined as from the enemy aircraft to the friendly aircraft:

[0060] (14)

[0061] When the enemy aircraft completely turns away from our aircraft =1 represents the maximum value, indicating the most advantageous tail-chasing and positioning posture.

[0062] Distance advantage The system adaptively switches based on the current mission mode of our machine. In close-range mode, the excitation distance approaches the optimal engagement distance. In escape mode, the stimulation increases the distance to the enemy aircraft.

[0063] Closer:

[0064] (15)

[0065] escape:

[0066] (16)

[0067] In the formula, This represents the three-dimensional relative spatial distance between our aircraft and the main target enemy aircraft; constants 800 and 6000 are the corresponding distance width scaling parameters.

[0068] height advantage To incentivize our aircraft to maintain the optimal altitude difference relative to the enemy aircraft, a Gaussian function model is used:

[0069] (17)

[0070] In the formula, This represents the current actual altitude difference between our aircraft and the enemy aircraft. The desired height difference; These are the height and width scaling parameters.

[0071] The single-machine comprehensive advantage function is composed of a weighted sum of sub-functions from the above four dimensions:

[0072] (18)

[0073] In the formula ~ The weighting coefficient is adjustable and can be adjusted online based on enemy-ally distance, altitude difference, and angle of attack; it can be used to adjust the weighting coefficient. The positive and negative values ​​adaptively switch the task mode. When corresponding to the tracking mode, when This corresponds to the escape mode.

[0074] (2) Based on this, anti-encirclement term, cooperative encirclement term, and collision penalty term are introduced:

[0075] Anti-surround item By exciting the machine using the hyperbolic tangent function, it stays outside the geometric center of the enemy's two machines, thus avoiding the disadvantageous situation of being sandwiched.

[0076] (19)

[0077] In the formula, This represents the distance from the machine to the three-dimensional geometric centers of the two enemy aircraft. This represents the distance between the two enemy aircraft.

[0078] when At that time, the aircraft was positioned on the outer edge of the enemy formation. The value approaches 1 and is taken as high as possible; when the machine is trapped inside the enemy's encirclement. Approaching zero will result in penalties.

[0079] Cooperative Enclosing Items This incentivizes our two aircraft to flank the enemy formation from both sides, using the difference in azimuth angle to approximate the value of pi. To optimize the objective:

[0080] (20)

[0081] In the formula, The absolute value of the difference between the azimuth angles formed by our two aircraft and the enemy's three-dimensional geometric center can be calculated using the following formula:

[0082] (twenty one)

[0083] (twenty two)

[0084] (twenty three)

[0085] The three-dimensional geometric center of the two enemy aircraft. , These are the positions of our aircraft and another friendly aircraft, respectively. and These are the azimuth angles of the aircraft and friendly aircraft relative to the geometric center of the enemy aircraft, respectively; when At that time, the two aircraft were positioned on opposite sides of the enemy. Take the maximum value to achieve the best coordinated encirclement posture.

[0086] Collision Penalty The specific expression is:

[0087] (twenty four)

[0088] In the formula, Represents the target set, including friendly machines. Enemy aircraft ; For the local machine and the target The Euclidean distance between them; The preset safe collision radius; These are weighting coefficients used to differentiate collision avoidance priorities for targets of different natures.

[0089] S4: Using distributed nonlinear model predictive control as the online optimization framework, each UAV solves the local finite-time domain optimization problem in real time at each control moment based on the discrete state transition equation and the multi-aircraft cooperative air combat objective function, and realizes multi-aircraft cooperative tactical optimization through inter-aircraft information interaction.

[0090] When solving the local finite-time optimization problem, the constraints are set as follows:

[0091] Flight altitude constraints: ;

[0092] Speed ​​constraints: ;

[0093] Machine room safety distance constraints: ,in and For any two machines at control time s and The position vector;

[0094] In a two-on-two air combat scenario, the advantages of a single aircraft and the tactical penalties of multiple aircraft are integrated into the NMPC (Non-Machine Computation). The overall objective function used in the local finite-time domain optimization problem is defined as:

[0095] (25)

[0096] In the formula, The overall objective function value; Representing two of our drones; This represents the term that maximizes the combined single-machine advantage of both of our aircraft throughout the entire prediction time domain; To predict the length of the time domain; , , These are the weight coefficients for the anti-encirclement term, the cooperative encirclement term, and the collision penalty term, respectively.

[0097] S5: Use IGWO to solve the local finite-time optimization problem online.

[0098] The improved gray wolf optimization algorithm encodes the sequence of decision variables composed of control input vectors into population individual position vectors with fitness F, where F = -J, and improves the solution efficiency through the following strategies:

[0099] (1) Basic GWO search strategy:

[0100] Calculate the distances between the top three alpha wolves (α, β, δ) in the population based on their fitness and calculate candidate positions:

[0101] (26)

[0102] (27)

[0103] In the formula, n is the current iteration number; These represent the positions of the three alpha wolves, which are the optimal positions of the top three fittest wolves in the current population. This indicates the current position of the Grey Wolves. , , This is the vector of synergistic coefficients used to simulate the effects of obstacles; , , The convergence factor vector used to determine whether the algorithm leans towards exploration or development.

[0104] The average of the above three factors is used to generate basic candidate positions. :

[0105] (28)

[0106] (2) DLH neighborhood learning search strategy:

[0107] Calculate the Euclidean distance between the current position and the basic candidate positions, and use this distance as the neighborhood radius. :

[0108] (29)

[0109] Construct the first within the neighborhood radius A gray wolf's neighboring population :

[0110] (30)

[0111] In the formula, For the current gray wolf population; For the neighborhood individuals in the current population that satisfy the distance constraint; For the first The current location of the gray wolf.

[0112] For each spatial dimension From neighboring populations Randomly selected individuals and randomly selecting individuals from the current population. Generate neighborhood learning candidate positions :

[0113] (31)

[0114] In the formula, This represents the current position of the gray wolf in dimension d. and For each selected individual in the dimension Location; A random number between 0 and 1.

[0115] (3) Candidate position selection and update strategy:

[0116] Compare the basic candidate positions Learn candidate positions with the neighborhood The fitness value is used to select the candidate position with the better fitness value as the update position for this iteration:

[0117]

[0118] In the formula, The fitness function is used to determine the optimal solution; a higher fitness value indicates a lower objective function cost and a better solution quality. If the fitness of the selected candidate position is better than that of the current position... If the candidate position is found, the current population position of the gray wolves will be updated accordingly; otherwise, the current position will remain unchanged.

[0119] S6: Based on the rolling time-domain strategy, the optimal control quantity at the current moment is extracted from the optimal control sequence and applied to each UAV, completing the closed-loop iteration of state perception, optimization solution, and control quantity application, realizing the full-process online real-time optimization of multi-UAV air combat trajectories. The control moment is moved forward one step, returning to step 1, and the environment model is re-acquired with new state information, and the optimization problem is solved in a rolling manner.

[0120] We are based on the above A simulation of a 2v2 multi-UAV cooperative trajectory planning method was performed. The simulation process included:

[0121] 1) Input simulation parameters , Rolling optimization time domain , number of walks Control the number of segments Initial states of both red and blue teams, upper and lower bounds of control variables, and IGWO algorithm parameters;

[0122] 2) At time Based on the current states of our two drones (red) and the enemy's two drones (blue), construct the state vector:

[0123]

[0124] and control input

[0125]

[0126] 3) The enemy drone uses a weak rule-based maneuvering model to generate its trajectory in the current time domain. It only maintains distance, avoids collisions, and strives for ascent, and does not participate in the optimization solution.

[0127] 4) Based on the relative distance, attack range, and altitude difference between our aircraft and the primary target enemy aircraft, determine the weights of the advantage function using fuzzy weighting rules:

[0128]

[0129] 5) Using the 2v2 integrated combat advantage function as the function to be optimized, rewrite the control sequence of our aircraft as follows: Dimensional decision variables, and utilize Search for the optimal control sequence within the current rolling time domain.

[0130] 6) Substituting the optimal control sequence into the centroid dynamics model, the results are recursively obtained for our UAV in... Internal state

[0131] 7) Record the trajectory data of Red 1, Red 2, Blue 1, and Blue 2, and determine whether the combat termination condition is met. If not, then... Repeat the above process until the simulation ends.

[0132] In this simulation experiment, the initial states of both sides are set as follows:

[0133]

[0134]

[0135]

[0136]

[0137] The state variables are, in order: heading angle, climb angle, three-dimensional position coordinates, velocity, roll angle, and normal overload. The simulation employs a rolling time-domain optimization method, with each optimization time domain being [missing information]. The number of walks is The time step is The number of control segments is The red machine control input is ,in The normal overload rate of change, The rate of change of roll angle, This is the tangential overload control variable.

[0138] The upper and lower bounds of the control variable are set as follows:

[0139]

[0140] The drone state constraints are set as follows:

[0141]

[0142] And limit the climb angular velocity and the rate of change of velocity to:

[0143]

[0144] Algorithm parameters are set as follows: population size Maximum number of iterations penalty function coefficient The algorithm initializes the gray wolf population within the upper and lower bounds of the control variables, uses a comprehensive advantage function with constraints and penalties as the fitness function, and then... , and Individual-guided search, combined with The candidate position update mechanism obtains the optimal control sequence in the current rolling time domain.

[0145] The collision avoidance start distance is The starting distance for collision avoidance between members of the same faction is... .

[0146] Analysis of experimental results: such as Figure 2 As shown, a 3D trajectory comparison diagram of a 2-on-2 air combat simulation is displayed. It can be seen that our side (the red aircraft) was able to effectively coordinate and proactively form a pincer encirclement formation against the two enemy drones, demonstrating good tactical coordination capabilities. Figure 3 As shown, the graph illustrates the variation of the comprehensive air combat advantage function R over time, verifying the stable convergence and high-yield output of the improved solver of this invention throughout the entire high-dynamic air combat process. Figure 4 As shown, the three-dimensional situational awareness changes over time, demonstrating the evolution of multi-dimensional air combat advantages such as range advantage, altitude advantage, angle, and tail-chase during the simulation. This intuitively confirms the effective constraint and characterization capability of the multi-dimensional single-aircraft air combat advantage sub-function. Figure 5 As shown, the weight changes are dynamically adjusted, which intuitively reflects the changes in the air combat situation. The algorithm can intelligently adjust the weights online and achieve adaptive and flexible switching between close-range mode, escape mode, and different local advantage emphases.

[0147] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for multi-UAV cooperative trajectory optimization in complex dynamic scenarios, characterized in that, Includes the following steps: S1: Based on the kinematic model of the center of mass, establish the flight dynamics equations of multiple UAVs, define the state vector and control input vector, and discretize them by the forward Euler method to obtain the discrete state transition equations; S2: Construct an air combat environment model, including a flight altitude constraint model and an inter-aircraft collision avoidance model; S3: Construct a single-aircraft air combat advantage sub-function from four dimensions: angle, tail chase, distance and altitude, and combine it into a single-aircraft comprehensive advantage function through adaptive weighting. Then, add anti-encirclement term, cooperative encirclement term and collision penalty term to form a multi-aircraft cooperative air combat objective function. S4: Using distributed nonlinear model predictive control as the online optimization framework, each UAV solves the local finite-time domain optimization problem in real time at each control moment based on the discrete state transition equation and the multi-aircraft cooperative air combat objective function, and realizes multi-aircraft cooperative tactical optimization through inter-aircraft information interaction; S5: An improved gray wolf optimization algorithm is used to solve the local finite-time domain optimization problem online. The population diversity and solution quality are improved by a hunting neighborhood learning search strategy based on multi-dimensional learning, and the optimal control sequence is output. S6: Based on the rolling time-domain strategy, the optimal control quantity at the current moment is extracted from the optimal control sequence and applied to each UAV, completing the closed-loop iteration of state perception, optimization solution and control quantity application, and realizing the full-process online real-time optimization of the air combat trajectory of multiple UAVs.

2. The multi-UAV cooperative trajectory optimization method for complex dynamic scenarios according to claim 1, characterized in that, In step S1, for the first The drone is defined with the following state vector: In the formula, These are respectively the climb angle, yaw angle, and roll angle; These are three-dimensional spatial coordinates; For speed; This is a normal overload. Define the control input vector as follows: In the formula, This refers to the rate of change of roll angular velocity; The normal overload rate of change; This is the tangential overload control variable.

3. The multi-UAV cooperative trajectory optimization method for complex dynamic scenarios according to claim 1, characterized in that, In step S3, the single-aircraft comprehensive advantage function is composed of a weighted average of the four dimensions of the single-aircraft air combat advantage sub-functions, expressed as: In the formula, For the first Our drones were under control at the time The single-machine comprehensive advantage function, Advantage of the angle; This provides an advantage in tail-chase maneuvers. Advantage of distance; For the advantage of height; , , , These are adjustable weighting coefficients, where Supports positive and negative switching to achieve adaptive switching of task modes. When corresponding to the tracking mode, when This corresponds to the escape mode.

4. The multi-UAV cooperative trajectory optimization method for complex dynamic scenarios according to claim 3, characterized in that, In step S3, the anti-surrounding item By exciting the local aircraft to be outside the geometric centers of the enemy's two aircraft using the hyperbolic tangent function, the expression is: In the formula, This represents the distance from the machine to the three-dimensional geometric centers of the two enemy aircraft. This represents the distance between two enemy aircraft. Cooperative Enclosing Items The difference in azimuth angles formed by our two aircraft and the enemy's three-dimensional geometric center. Approaching pi To optimize the objective, the expression is: Collision Penalty The specific expression is: In the formula, Represents the target set, including friendly machines. Enemy aircraft ; For the local machine and the target The Euclidean distance between them; The preset safe collision radius; These are weighting coefficients used to distinguish the collision avoidance priorities of targets with different properties.

5. The multi-UAV cooperative trajectory optimization method for complex dynamic scenarios according to claim 4, characterized in that, In step S4, when solving the local finite-time optimization problem, the constraints include flight altitude constraints, speed constraints, and inter-aircraft safety distance constraints. The flight altitude constraint is as follows: ,in and These are the lower and upper limits of flight altitude, respectively. The speed constraint is: ,in and These are the lower and upper bounds of flight speed, respectively. The inter-machine safety distance constraint is: ,in and Let be the position vectors of any two machines. For the safety radius; In a two-on-two air combat scenario, the overall objective function used in the local finite-time domain optimization problem is defined as: In the formula, The overall objective function value; Representing two of our drones; To predict the length of the time domain; , , These are the weight coefficients for the anti-encirclement term, the cooperative encirclement term, and the collision penalty term, respectively.

6. The multi-UAV cooperative trajectory optimization method for complex dynamic scenarios according to claim 1, characterized in that, In step S5, the improved gray wolf optimization algorithm encodes the decision variable sequence composed of the control input vector into population individual position vectors and constructs a fitness function. ; Hunting neighborhood learning search methods based on multi-dimensional learning specifically include: Basic candidate positions are generated using the basic gray wolf search strategy. Calculate the first The current location of the gray wolf With the basic candidate positions The Euclidean distance between them is used as the neighborhood radius. : In the formula, This represents the current iteration number. The distance is Euclidean. Construct the first within the neighborhood radius A gray wolf's neighboring population : In the formula, For the current population; For each spatial dimension, the neighborhood individuals in the current population that satisfy the distance constraint are considered; From neighboring populations Randomly selected individuals and randomly selecting individuals from the current population. Generate neighborhood learning candidate positions : In the formula, For the first A gray wolf in the dimension Location; for In dimensions Location; for In dimensions Location; A random number between 0 and 1; Compare the basic candidate positions Learn candidate positions with the neighborhood The fitness value is used to select the candidate position with the better fitness value as the update position for this iteration; if the fitness of the selected candidate position is better than the current position... If the current population position of the gray wolves is updated, then the current population position of the gray wolves will be updated; otherwise, it will remain unchanged.

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