An autonomous penetration method for unmanned aerial vehicles based on individual similarity pigeon flock optimization

Abstract

The present invention discloses an autonomous penetration method for unmanned aerial vehicles based on individual similarity pigeon flock optimization. Step one: establish a six-degree-of-freedom model for both penetration parties; step two: design a two-loop sideslip turn overload control law; step three: establish a three-degree-of-freedom simplified model for both penetration parties and a library of unmanned aerial vehicle maneuvering actions; step four: generate an air situation assessment function; step five: establish a payoff matrix and design a fitness function; step six: design a pigeon flock optimization method based on individual similarity; step seven: apply the individual similarity pigeon flock optimization method to solve the optimal strategy. The present invention can realize automatic sensing of enemy actions and real-time selection of the optimal maneuvering strategy; it can complete dynamic avoidance of intercepting enemy unmanned aerial vehicles and effectively improve the battlefield survivability of unmanned aerial vehicles; the use of the individual similarity pigeon flock optimization method can improve the global search capability of the system and improve the accuracy when solving the optimal strategy fitness function.

Description

Technical Field

[0001] The invention discloses an autonomous penetration method for an unmanned aerial vehicle based on individual similarity pigeon flock optimization, belonging to the field of autonomous control of unmanned aerial vehicles. Background Art

[0002] Unmanned aerial vehicles (UAVs) are mobile strike weapons that boast high accuracy, strong concealment, and superior maneuverability. In recent years, with the rapid development of information technology, UAVs have become a crucial component of integrated, information-based strike systems across land, sea, and air. The increasingly complex battlefield environment requires UAVs to possess enhanced decision-making capabilities, including situational awareness, assessment of their own status, and decision-making regarding offensive and defensive maneuvers. However, due to limitations in system computing power and communication latency, UAVs in combat mode cannot fully receive commands from the control terminal. This necessitates a degree of autonomous decision-making capability. To improve this capability, research into close-range autonomous penetration technology for UAVs is essential.

[0003] Close-range penetration technology for UAVs can be defined as the techniques used by UAVs to circumvent enemy anti-missile defenses. When a UAV enters the interception zone of its target, it triggers a counterattack from the enemy's anti-missile defenses. If the UAV lacks the ability to autonomously evade long-range fire, the attack can be thwarted by methods such as signal jamming or induced detonation if our own aircraft approaches the enemy. Conventional defense systems typically use early warning radar to lock onto the UAV, predict its path, and then intercept it. However, with the advancement of weapon systems, autonomously guided interception defense systems have rapidly developed, transforming close-range penetration by UAVs into a two-way game.

[0004] Game-based penetration technology has a long history, but in most research scenarios, unmanned aerial vehicles (UAVs) are simplified as three-degree-of-freedom models, which do not accurately reflect real-world combat maneuvers. This approach establishes a six-degree-of-freedom nonlinear model for the UAV and designs an overload autopilot. Using overload as a control factor, a library of UAV maneuvers is constructed. Then, situational observations from both sides are incorporated to construct a game-based optimal decision-making system. This system uses a three-degree-of-freedom model to determine the motion of a six-degree-of-freedom model, thereby reducing the complexity of the solution and improving decision accuracy.

[0005] Furthermore, the current game-based penetration problem is often described as a two-way pursuit-and-escape situation during a maneuver. The success of the attacking team's penetration is measured by the miss rate of the defending UAV, and strategies such as matrix games are used to determine the optimal penetration strategy. However, traditional matrix game strategies, such as the maximum-minimum search method, only yield a unique solution under the same conditions, lacking intelligence and creating the risk of the enemy predicting the strategy. By introducing intelligent optimization methods, the intelligence of the system can be significantly improved, while the resulting conclusions are variable and difficult to predict.

[0006] The Pigeon Inspired Optimization (PIO) method is a classic intelligent optimization method designed to simulate the behavior of pigeons during their homing process. By incorporating information about solar altitude, the geomagnetic field, and landmarks, the pigeons' homing behavior is summarized as a compass operator and a landmark operator. This method seeks a global optimal solution in a high-dimensional space, effectively solving many problems in parameter optimization and optimal control. It is also useful for numerically solving the optimal fitness function for close-range penetration. However, when faced with a fitness function under complex constraints, the PIO method can sometimes become trapped in a local optimum, leading to interruptions in the strategy search. Therefore, building on the classic PIO method, the concept of individual similarity is introduced to improve the map and compass operator. This improved method is then applied to the close-range penetration problem of unmanned aerial vehicles.

[0007] In summary, this paper proposes an autonomous UAV penetration method based on individual similarity pigeon flock optimization. Its purpose is to enable an attacking UAV to automatically sense the enemy's movements when it encounters a defending UAV in a close-range penetration scenario, select the optimal maneuver strategy in real time, and dynamically avoid the enemy UAV, thereby improving battlefield survivability. Summary of the Invention

[0008] 1. Purpose of the invention:

[0009] This paper proposes an autonomous UAV penetration method based on individual similarity pigeon flock optimization. Its purpose is to enable an attacking UAV to automatically sense the enemy's movements when it encounters a defending UAV in a close-range penetration scenario, select the optimal maneuver strategy in real time, and dynamically avoid the enemy UAV, thereby improving battlefield survivability.

[0010] 2. Technical solution:

[0011] Aiming at the problem of close-range penetration of unmanned aerial vehicles, the present invention proposes an autonomous penetration method for unmanned aerial vehicles based on individual similarity pigeon flock optimization. The specific steps of the method are as follows:

[0012] Step 1: Establish a six-degree-of-freedom model for both sides of the penetration

[0013] Assuming that both sides have the same aerodynamic shape and actuators, the model of the six-degree-of-freedom unmanned aerial vehicle can be described as follows:

[0014]

[0015]

[0016]

[0017]

[0018] Where, is the rate of change of the center of mass position of the UAV; are the components of the aircraft body rotation acceleration vector on each axis of the body coordinate system; are the pitch, yaw and bank angle change rates of the UAV respectively; They are the scalar value of the airspeed vector V, the trajectory inclination angle and the rate of change of the trajectory deviation angle respectively.

[0019] M x ,M y ,M z are the components of the moment of all external forces (including thrust) acting on the UAV on the center of mass on each axis of the body coordinate system. X, Y, and Z are the components of all external forces except thrust projected onto the ballistic coordinate system. x ,I y ,I z is the UAV momentum constant. P is the engine thrust scalar value. α is the UAV attack angle, β is the UAV sideslip angle, γ V is the velocity tilt angle. m is the mass of the UAV, g is the acceleration due to gravity, and is taken as 9.8m / s 2 .

[0020] Step 2: Design a two-loop sideslip turning overload control law

[0021] Assume that all forces except gravity on a 6DOF UAV are controllable, including aerodynamics and thrust. Overload is introduced to describe the magnitude of the controllable force and is defined as follows:

[0022]

[0023] Among them, n is the overload vector, which represents the ratio of the resultant force vector N of all external forces on the UAV except gravity to the weight of the UAV, and its direction is consistent with the direction of the control force vector N. N can be decomposed into components in the body coordinate system (n x ,n y ,n z ), which are respectively represented as follows:

[0024]

[0025] Where n x It is called tangential overload, n y ,n z It is called normal overload, n y is the vertical overload, n z is the lateral overload. Substituting the above formula into the six-degree-of-freedom model of the unmanned aerial vehicle established in step 1, the overload can be expressed as follows:

[0026]

[0027] Assume the UAV speed V is constant, then the tangential overload n x Therefore, the overload can be used to construct a classic two-loop skid to turn (STT) overload autopilot, and its flight control law is expressed as follows:

[0028]

[0029] Where, δ x ,δ y ,δ z They represent the actuator input around the x-axis, y-axis, and z-axis in the body coordinate system, respectively. c is the desired tilt angle. Since STT control is adopted, γ≡0. yc ,n zc are the expected normal overload in the y direction and the expected normal overload in the z direction respectively. pp ,K dg ,K pf ,K df ,K dp are the control coefficients of each channel respectively. Based on this, the UAV overload closed-loop control system can be constructed, and its control flow chart is as follows: Figure 1 shown.

[0030] Step 3: Establish a simplified three-degree-of-freedom model of both sides and a basic operation action library for the UAV

[0031] Based on the definition of overload in step 2, the six-degree-of-freedom closed-loop control process can be simplified and expressed as the following six-state model:

[0032]

[0033] Based on the game theory, the overall framework of penetration tactical planning can be obtained as follows: Figure 2 When the initial states and overloads are consistent, the trajectory of the six-DOF model can be predicted using the trajectory of the three-DOF model.

[0034] Based on this simplified model, the velocity V can be kept constant and the equation n can be established. z ,n y It is the basic operation action library of the control quantity. By changing the size of the overload, the relationship between the overload control quantity and the flight attitude of the unmanned aerial vehicle can be obtained, that is, the basic operation action library, as shown in Table 1:

[0035] Table 1

[0036]

[0037] Step 4: Generate air situation assessment function

[0038] Step 3 has obtained the basic operation action library. In order to select the appropriate tactical action from the action library, it is necessary to design a maneuver action selection function, namely the air situation assessment function, to score and evaluate each maneuver of the UAV and select the best one for execution; its structure is as follows: Figure 3 As shown. Among them, V R is the airspeed vector of the Red UAV, V B θ is the airspeed vector of the blue UAV. R is the angle between the red UAV and the target line, θ B is the angle between the blue UAV and the target line.

[0039] According to the angle between the airspeed vectors of the two UAVs, the air situation assessment function can be described as two components: the angle situation assessment index f θ and distance situation assessment function f R , which are defined as follows:

[0040]

[0041] f R =Le -(R-r) / K (11)

[0042] Where L is a constant coefficient, R is the Euclidean distance between the two sides, r is the effective interception distance of the enemy UAV, and K is the sensitivity coefficient. red +r blue ) / 2, r red =r blue = 800m, which is the average distance between the two sides. Multiply the two exponents and get f = f θ ×f R The larger the value of the air situation assessment function, the more obvious the red side's advantage; conversely, the smaller the value, the more obvious the blue side's advantage.

[0043] Step 5: Profit matrix establishment and fitness function design

[0044] S51. Establishing a Profit Matrix

[0045] Assuming that both parties can observe each other's states at any time, then at t s At the simulation moment, obtain the state quantity from the six-degree-of-freedom model

[0046] Assuming that both the red and blue teams have the same basic operation action library, the basic operation action library can be generated according to step 3. Set n zi ,n yj t s The horizontal overload value and the vertical overload value at the moment. zi ∈[n z1 ,n z2 ,...,n zk ], k is the number of strategies in the basic operation action library of lateral overload; n yj ∈[n y1 ,n y2 ,...,n yw ], w is the number of strategies in the basic operation action library of vertical overload. From this, we can get the prediction results under the action of the values ​​in the basic operation action library. Taking the blue side as an example, if the overload n is selected zi and n yj is the input quantity, then the blue side at time t p Predicted motion state after It can be expressed as follows:

[0047]

[0048] In the above formula, f 3dof The simplified model of the three degrees of freedom of the UAV is shown in the following figure. Similarly, the red square can be obtained. The predicted motion state. Because the red and blue sides have the same basic operation action library, the total number of red and blue strategy sets is the same, which is represented by m = n = k × w. At this time, the red strategy is R = {r1, r2, ..., r m}, the blue strategy is B={b1,b2,...,b n}, according to step 4, the scoring matrix H can be obtained as follows:

[0049]

[0050] For example, if the red side chooses r m strategy, while the blue side chooses b n strategy, the corresponding score can be expressed as h mn .

[0051] S52, Obtaining the fitness function of both red and blue

[0052] The fitness function of the red and blue teams is designed using the mixed strategy method, and the red team's mixed strategy is set to The blue team's mixed strategy is Against Blue's strategy Q bmx , when the red team selects row i, the fitness function can be obtained as follows:

[0053]

[0054] The higher the function, the more favorable it is for the red team. For the blue team, the blue team will choose the minimum benefit corresponding to the red team's maximum benefit set, which corresponds to the blue team's optimal strategy Q bmx *, this obtains the blue square fitness function:

[0055]

[0056] When the blue team chooses the optimal strategy, the red team will also choose a mixed strategy to maximize benefits, thus obtaining the red team's fitness function:

[0057]

[0058] Step 6: Optimal design of pigeon flock based on individual similarity

[0059] S61. Initialization of pigeon flock optimization method

[0060] The pigeon flock optimization method is designed by simulating the behavior of pigeons during their homing process. By incorporating information about solar altitude, the geomagnetic field, and landmarks, the staged behavior of the pigeons during homing is summarized as compass and landmark operators. This allows the search for a global optimal solution in a high-dimensional space. This method effectively solves many problems in parameter optimization and optimal control, and is also useful for numerically solving the optimal fitness function for close-range penetration. However, when faced with a fitness function under complex constraints, the pigeon flock optimization method can sometimes become trapped in a local optimum, leading to interruptions in the strategy search. Therefore, building on the classic pigeon flock optimization method, the concept of individual similarity is introduced to improve the map and compass operator, and the classic pigeon flock optimization method is used to find the optimal strategy function in step four.

[0061] Assume that the number of pigeons is N, and the position and speed of each pigeon are expressed as follows:

[0062]

[0063] Where, X i ,V i They represent the position and speed of the i-th pigeon respectively, and d represents the dimension of the search space.

[0064] S62. Design of map and compass operators based on individual similarity

[0065] At the beginning of the loop, a pigeon is randomly selected as the global optimal individual. In the tth loop, the Euclidean distance of each pigeon to the global optimal pigeon is calculated as follows:

[0066]

[0067] Among them, dist t (i, G) represents the position vector of the i-th individual in the t-th cycle and the position vector X of the global optimal individual. G The distance between them.

[0068] A clustering index C is set to measure the degree of clustering of pigeons. A higher C value indicates a higher density of pigeons at the global optimal location. Conversely, a lower density of pigeons at the global optimal location. The change in the clustering index is related to an adaptive threshold. In t cycles, if the value of the i-th pigeon is less than the adaptive threshold, the clustering index C will increase as follows:

[0069]

[0070] Where β is the threshold coefficient. The product of the average Euclidean distance in the previous cycle and β constitutes the adaptive threshold for the current cycle. By adjusting the value of β, the constraint strength can be adjusted. The adaptive threshold changes with the density of pigeons. As iterations increase, the distance between pigeons decreases, and the adaptive threshold decreases accordingly.

[0071] S63. Individual similarity calculation

[0072] Use aggregation to reflect the concept of individual similarity. When C is greater than the upper limit C max When , it means that the individual aggregation is too large. At this time, the individual similarity is calculated and the concept of individual similarity is defined as follows:

[0073]

[0074] Individual similarity S t (i,j) is a piecewise function controlled by a constant M. Its structure can be found in Figure 4 In the above formula, dist t (i,j) represents the Euclidean distance between individuals i and j in t cycles, dist t max Represents the maximum Euclidean distance between individuals in the t-cycle population. If the distance between two individuals is less than th1, the individuals are highly similar. Conversely, if the distance between two individuals is greater than th2, the individuals are less similar.

[0075] S64, Random Mutation Strategy

[0076] Based on the definition of individual similarity, the individual similarity S between the global optimal position G and the i-th individual in t cycles can be calculated t (i, G). Use random mutation method to update high individual similarity pigeons as follows:

[0077]

[0078] is the mutation constant, rand is a random number between (0,1), T1 is the maximum number of iterations of the map and compass operators, L d ,U d are vectors of the maximum and minimum search space ranges respectively. Randomly generated (L d ,U d ) The random numbers of each component between the two vector search space ranges can be used to re-send high similarity individuals into the search space.

[0079] S65, Map and Compass Operator Iteration

[0080] After completing the similarity processing above, the map and compass operators of the classic pigeon flock optimization are used to update the position and velocity of the entire group as follows:

[0081]

[0082] F is the map coefficient, and the above process is repeated until the maximum number of cycles T1 is reached.

[0083] S66, Landmark Operator Iteration

[0084] After the map and compass operators reach the maximum iteration, the landmark operator iteration is performed, and the formula is as follows:

[0085]

[0086] The maximum number of iterations of the landmark operator is T2, and the population size will be halved in each iteration. It represents the geometric center of the remaining pigeon group at time t. Fitness() is the objective function, which uses the calculation results to evaluate the position information.

[0087] Step 7: Apply the individual similarity pigeon flock optimization method to solve the optimal strategy

[0088] S71. Use classic pigeon flock optimization to calculate the blue team's fitness function (15) to obtain the blue team's optimal strategy

[0089] Assume t s The time is the starting time of a round. According to the state quantity returned by the six-degree-of-freedom model of the red and blue sides, the air situation assessment function f and the basic operation action library are used to predict the situation of the next round, that is, after time t pThe profit matrix H is obtained. Then the classic pigeon flock optimization method is used, that is, the content described in steps S65 and S66 to calculate the blue team's fitness function (15). After the optimization search, the blue team's optimal strategy set can be obtained. The component values ​​in this strategy set can be used as the preference weight for selecting the corresponding strategy; the larger the weight, the more inclined to choose this strategy.

[0090] S72, at the same time, obtain the optimal strategy set Q of the blue team bmx * Finally, the individual similarity pigeon group optimization method designed by strategy six is ​​used to calculate the red team’s fitness function (16). After the optimization search, the optimal strategy set of the red team can be obtained. Similarly, each component value in this strategy set represents the weight of the tendency to choose the corresponding strategy; the larger the weight, the more inclined to choose this strategy.

[0091] S73. After determining the optimal strategy set of both parties, the strategy corresponding to the maximum weighted item in the optimal strategy set of both parties is selected as the control strategy of both parties in the next round, and then output to the controllers of both parties, thereby controlling the next round time t p Repeat S71-S73 until the simulation time ends.

[0092] Overall method framework diagram reference Figure 5 .

[0093] Step 8: Comparison diagram of the output maximum and minimum method and the individual similarity pigeon flock optimization method

[0094] Determine whether to use the maximum and minimum method or the individual similarity pigeon flock optimization decision-making method.

[0095] If it is the maximum minimum method, determine whether the simulation time reaches the final simulation result. If so, output the fitness function Figure 6 , 3D trajectory simulation Figure 7 , 2D horizontal trajectory simulation Figure 8 , 2D vertical simulation trajectory Figure 9 ; Otherwise, go to step 4.

[0096] If it is the decision method of individual similarity pigeon flock optimization, determine whether the simulation time reaches the final simulation result. If so, output the fitness function Figure 10 , 3D trajectory simulation Figure 11 , 2D horizontal trajectory simulation Figure 12 , 2D vertical simulation trajectory Figure 13 ; Otherwise, go to step 4.

[0097] The advantages and effects of the unmanned aerial vehicle autonomous penetration method based on the individual similarity pigeon flock optimization method of the present invention are: First, it provides a game method for realizing short-range autonomous penetration of unmanned aerial vehicles, realizing short-range dynamic obstacle avoidance of unmanned aerial vehicles, and having strong robustness. Second, it proposes a six-degree-of-freedom nonlinear model game implementation method, which adopts a three-degree-of-freedom model to predict the six-degree-of-freedom model, with high simulation accuracy and fits the actual scene. Third, it proposes an improved optimization method for game strategy selection, which has strong global optimization ability and can improve the accuracy of strategy selection. Fourth, it compares the decision-making effects of the individual similarity pigeon flock optimization decision-making method and the basic maximum and minimum decision-making method. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 Unmanned aerial vehicle six-degree-of-freedom model and two-loop overload pilot control flow chart

[0099] Figure 2 Unmanned aerial vehicle penetration tactical planning flow chart

[0100] Figure 3 Schematic diagram of the game-playing air defense situation Schematic diagram of the similarity function structure

[0101] Figure 4 Schematic diagram of similarity function structure

[0102] Figure 5 Overall method framework diagram

[0103] Figure 6 Schematic diagram of the maximum and minimum method output fitness function

[0104] Figure 7 Schematic diagram of the three-dimensional motion trajectory of the red and blue sides using the maximum and minimum method

[0105] Figure 8 Schematic diagram of the movement trajectory of the red and blue sides using the maximum and minimum method (horizontal direction)

[0106] Figure 9 Schematic diagram of the movement trajectory of the red and blue sides using the maximum and minimum method (vertical direction)

[0107] Figure 10 Schematic diagram of the output fitness function of the similarity pigeon flock optimization method

[0108] Figure 11 Schematic diagram of the three-dimensional motion trajectory of the red and blue parties using the similarity pigeon flock optimization method

[0109] Figure 12 Schematic diagram of the movement trajectories of the red and blue pigeons using the similarity pigeon flock optimization method (horizontal direction)

[0110] Figure 13 Schematic diagram of the movement trajectories of the red and blue parties using the similarity pigeon flock optimization method (vertical direction)

[0111] The numbers and symbols in the figure are explained as follows:

[0112] γ——tilt angle

[0113] δ xc ,δ yc ,δ zc ——Actuator control quantity

[0114] P T ——Trim thrust output

[0115] δ x ,δ y ,δ z ——Actual output of the actuator

[0116] X——UAV status

[0117] T——Actuator time constant

[0118] ω x ,ω y ,ω z ——Angular velocity of each axis

[0119] n y ——Vertical overload

[0120] n z ——Overload in the lateral direction

[0121] X r ——The state quantity of the red team at a certain moment

[0122] X b ——The state of the blue team at a certain moment

[0123] S t (i,j)——the individual similarity of two individuals i and j in t cycles

[0124] M——control constant

[0125] dist t max ——The maximum Euclidean distance in the t-cycle population

[0126] dist t (i,j)——Euclidean distance between individuals i and j in t cycles

[0127] t——t rounds of cycles

[0128] rand——random number between (0,1)

[0129] V B ——Blue airspeed

[0130] V R——Red Air Speed

[0131] θ R ——Angle between the Red Army’s UAV and the target line

[0132] θ B ——The angle between the blue UAV and the target line

[0133] x——horizontal position

[0134] y——vertical position

[0135] z——lateral position DETAILED DESCRIPTION

[0136] The following example illustrates the effectiveness of the proposed method using a specific example of an autonomous UAV penetration using individual similarity pigeon flock optimization. The experimental computer configuration is an Intel Core i7-12700 processor with a 2.30 GHz clock speed, 32 GB of memory, and MATLAB 2020a. The specific steps of the autonomous UAV penetration method based on individual similarity pigeon flock optimization are as follows:

[0137] Step 1: Establish a six-degree-of-freedom model for both sides of the penetration

[0138] Set the red team as the attacker and the blue team as the defender. Given the initial states of the red and blue UAVs, the red team [x R ,y R ,z R ]=[0,350000,0],blue side[x B ,y B ,z B ]=[25000,350000,-500]. The Red team's speed is constant at 600m / s, and the Blue team's speed is constant at 400m / s. The Red team's initial trajectory inclination is 0 degrees, and the trajectory deviation is 0 degrees. The Blue team's initial trajectory inclination is 0.07 degrees, and the trajectory deviation is -10 degrees. x ,w y ,w z ) are all 0, the angle of attack is 0.07 degrees, and the sideslip angle is 0 degrees. The simulation compensation is 0.01s, and the maximum simulation threshold is 100s.

[0139] Step 2: Design a two-loop sideslip turning overload control law

[0140] For the six-degree-of-freedom model two-loop overload autopilot in step 1, set the parameters as follows:

[0141] K pp =0.53,K dg =0.08,K pf =0.1059,K df=2.3012,K dp =0.76

[0142] Set the control range limit to n y ∈[0.8,1.2], n z ∈[-0.1,0.1], construct a two-loop sideslip turning closed-loop control law.

[0143] Step 3: Establish a simplified three-degree-of-freedom model of both sides and a basic operation action library for the UAV

[0144] According to step 2, the six-degree-of-freedom model of the UAV is simplified to a three-degree-of-freedom overload model by overload. Set the red and blue sides' candidate maneuver instruction library as:

[0145] n y =[0.8,0.9,1,1.1,1.2]

[0146] n z =[-0.1,0,0.1]

[0147] At this time, k=3, w=5, and the number of strategies for both the red and blue sides is 3×5=15, that is, m=n=15.

[0148] Step 4: Generate air situation assessment function

[0149] The state quantities of the red and blue sides obtained by steps one and two and The angle situation index and distance situation index are calculated using formula (10) and formula (11). θ and f R By multiplying, we can calculate the value of the situation evaluation function at the current moment.

[0150] Step 5: Profit matrix establishment and fitness function design

[0151] S51. Establishing a Profit Matrix

[0152] Based on the instructions in the basic action library, there are a total of m × n = 225 possible instruction results for both the red and blue teams. Setting the prediction time to 8 seconds, use formula (12) to calculate the situation function for the next 8 seconds under the 225 strategies, generating a 15 × 15 payoff matrix.

[0153] S52, red and blue fitness function design

[0154] According to the obtained payoff matrix, the fitness function of both red and blue parties can be obtained:

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161] The fitness function can be used to optimize the strategy.

[0162] Step 6: Design of pigeon flock optimization method based on individual similarity

[0163] S61. Initialize the pigeon flock optimization model

[0164] Initialize the individual similarity method and set the pigeon flock size to 10. The maximum number of iterations for the map and compass operators is 80, and the maximum number of iterations for the landmark operator is 10. The number of pigeon dimensions is 15, and the position range of each pigeon is set to [0,1], ensuring that the sum of all dimensions is 1, and taking the normalized value to meet the constraints. Randomly generate pigeon position and speed information, and it can be seen that the position is Speed ​​is

[0165] S62. Aggregation evaluation

[0166] Set the maximum upper limit of the aggregation index C max =10, and then use formula (18) to calculate the Euclidean distance between all individuals and the global optimal position. When the Euclidean distance is less than the adaptive threshold, the aggregation index is increased by 1. When the aggregation index is greater than the maximum upper limit, the group aggregation is considered to be large, and individual similarity calculation is performed. If it is less than the maximum upper limit, the group aggregation is considered to be small, and the map and compass operators are directly updated. Otherwise, individual similarity calculation is performed.

[0167] S63. Individual similarity calculation

[0168] Under high aggregation conditions, individual similarity is calculated, and the individual similarity constant M is 3.5. The individual similarity between each individual and the global optimal point is calculated using formula (21), and the individual similarity is calculated using formula (21).

[0169] S64, Random Mutation Strategy

[0170] The mutation constant is set to 0.5, and the random mutation strategy (21) is used to determine whether each individual needs to mutate. When the mutation threshold is greater than the random number rand, the spatial and positional information of the individual is randomly assigned.

[0171] S65, map and compass operator

[0172] Run the map and compass operators (22), and set the map operator value to 0.3, so that the initial iteration has a strong global search capability, and the later iteration has a strong local search capability, with e -Ft When the operator reaches the maximum number of iterations, 80, the map and compass operator calculations are completed and the landmark operator calculation begins.

[0173] S66, Landmark Operator Iteration

[0174] At the beginning of each iteration, the landmark operator ranks the pigeon swarm optimization method by fitness, selecting the half with the lowest fitness and then calculating the center of the flock. Based on the center's location, it updates the position of each pigeon within the flock and records the resulting global optimal point. This process is repeated until the landmark operator reaches its maximum number of iterations, 10, at which point the global optimal position is output as the strategy selection result.

[0175] Step 7: Apply the individual similarity pigeon flock optimization method to solve the optimal strategy

[0176] The optimal strategy set for the blue team is calculated using the classic pigeon flock optimization method (15). Based on the blue team's optimal strategy, the optimal strategy set for the red team is calculated using the individual similarity pigeon flock optimization method (16). The strategy with the maximum weight in both strategy sets is input into the corresponding six-degree-of-freedom model controller to proceed to the next round of the game. Repeat these steps until the simulation time ends.

[0177] Step 8: Comparison diagram of the output maximum and minimum method and the individual similarity pigeon flock optimization method

[0178] For comparison, under the same initial conditions, the simulation results of the individual similarity pigeon flock optimization method of the classic maximum and minimum search method are compared. The simulation time is set to 400s, and each prediction time is 8s, so the number of simulation rounds is 50 rounds. If it is the maximum and minimum method, determine whether the simulation time reaches the final simulation result. If so, output the fitness function Figure 6 , 3D trajectory simulation Figure 7 , 2D horizontal trajectory simulation Figure 8 , 2D vertical simulation trajectory Figure 9 ; Otherwise, go to step 4.

[0179] If it is the decision method of individual similarity pigeon flock optimization, determine whether the simulation time reaches the final simulation result. If so, output the fitness function Figure 10 , 3D trajectory simulation Figure 11 , 2D horizontal trajectory simulation Figure 12 , 2D vertical simulation trajectory Figure 13 ; Otherwise, go to step 4.

[0180] This invention uses two unmanned aerial vehicles (UAVs) with identical performance, uses normal overload as the control variable, and uses a three-degree-of-freedom UAV model to predict the future state of a six-degree-of-freedom model. It also designs an air situation assessment index. Based on the situation assessment index, a payoff matrix is ​​generated, which is used to construct fitness functions for both the red and blue teams. This fitness function is then solved using a pigeon flock optimization method based on individual similarity, resulting in the optimal strategy for the next control cycle. The superiority of the improved method is demonstrated using a maximum-minimum search method as a comparison method.

Claims

1. A method for autonomous penetration of unmanned aerial vehicles based on individual similarity pigeon flock optimization, characterized by: The specific steps of this method are as follows: Step 1: Establish a six-degree-of-freedom model for both sides of the penetration Step 2: Design a two-loop sideslip turning overload control law Step 3: Establish a simplified three-degree-of-freedom model of both sides and a basic operation action library for the UAV Step 4: Generate an air situation assessment function, which is described as two components: angle situation assessment index f θ and distance situation assessment function f R , multiply the two exponentials and take f = f θ ×f R As an air situation assessment function; the larger the function value, the more obvious the red side's advantage; conversely, if the value is smaller, the more obvious the blue side's advantage; Step 5: Profit matrix establishment and fitness function design S51. Establishing a benefit matrix: Based on the instructions in the basic operation action library and the output state of the six-degree-of-freedom model, the corresponding situation function is calculated to generate a benefit matrix; S52. Obtain the fitness function of both red and blue parties according to the obtained payoff matrix; Step 6: Design of pigeon flock optimization method based on individual similarity S61, initializing the pigeon flock optimization model; S62, Aggregation Degree Assessment: When the aggregation index is greater than the maximum upper limit, the group aggregation is considered to be large, and individual similarity calculation is performed at this time; if it is less than the maximum upper limit, the group aggregation is considered to be small, and the map and compass operators are directly updated; S63, individual similarity calculation; S64, random mutation strategy: Use the random mutation strategy to determine whether each individual needs to mutate; S65, map and compass operator iteration, which enables strong global search capabilities in the early stages of iteration and strong local search capabilities in the later stages; S66, Landmark Operator Iteration: At the beginning of each iteration, the landmark operator ranks the pigeon swarm optimization methods by fitness, then calculates the center position of the pigeon swarm; based on the center position of the pigeon swarm, updates the position of each pigeon in the swarm and records the global optimal point; repeats the above process until the landmark operator reaches the maximum number of iterations, and outputs the global optimal position as the strategy selection result; Step 7: Apply the individual similarity pigeon flock optimization method to solve the optimal strategy S71. Use the classic pigeon flock optimization algorithm to calculate the blue team's fitness function and obtain the blue team's optimal strategy set; S72. Based on the optimal strategy set of the blue team, the individual similarity pigeon flock optimization algorithm designed in step 6 is used to calculate the fitness function of the red team to obtain the optimal strategy set of the red team; S73. Output the strategies of both sides for the next round until the simulation time ends, and repeat the above steps S71-S73 continuously.

2. The method for autonomous penetration of unmanned aerial vehicles based on individual similarity pigeon flock optimization according to claim 1, characterized in that: The specific process of establishing the payoff matrix in step S51 is as follows: Assuming that both parties in the game can observe each other's status at any time, then at t s At the simulation moment, obtain the state quantity from the six-degree-of-freedom model Where (x, y, z) is the center of mass of the UAV; V is the scalar value of the UAV airspeed vector, θ is the ballistic inclination angle of the UAV, ψ V is the trajectory angle of the UAV; Assuming that both the red and blue sides have the same basic operation action library, generate the action library according to step 3; set n z ,n y Represents the lateral overload and vertical overload respectively, n zi ,n yj t s Horizontal overload at any moment n z and vertical overload n y Get values ​​from the basic operation action library; in, n zi ∈[n z1 ,n z2 ,...,n zk ], k is the number of strategies in the basic operation action library of lateral overload; n yj ∈[n y1 ,n y2 ,...,n yw ], w is the number of strategies in the basic operation action library of vertical overload; thus, the prediction results under the action of the values ​​in the basic operation action library are obtained; Taking the blue team as an example, if the overload value n is selected zi and n yj is the input quantity, then the blue side at time t p Predicted motion state after It is expressed as follows: In the above formula, f 3dof Simplify the three-degree-of-freedom model of the unmanned aerial vehicle; similarly, get the red square The predicted motion state; because the red and blue sides have the same basic operation action library, the total number of strategies of the red and blue sides is the same, which is expressed by m = n = k × w; at this time, the red side's strategy is R = {r1, r2, ..., r m }, the blue strategy is B={b1,b2,...,b n }, according to step 4, the profit matrix H is as follows:

3. The method for autonomous penetration of unmanned aerial vehicles based on individual similarity pigeon flock optimization according to claim 1, characterized in that: The specific process of the aggregation degree evaluation in step S62 is as follows: at the beginning of the loop, a pigeon is randomly selected as the global optimal individual; in the t-th loop, the Euclidean distance between each pigeon and the global optimal pigeon is calculated, which is expressed as follows: In the formula, the position and velocity of the i-th individual are represented by X i =[x i1 ,x i2 ,...,x id ],V i =[v i1 ,v i2 ,...,v id ], d is the individual dimension, N is the number of pigeons in the population; dist t (i, G) represents the position vector of the i-th individual in the t-th cycle and the position vector X of the global optimal individual. G the distance between them; The aggregation index C is set to measure the degree of aggregation of pigeons. The higher the C value, the higher the density of pigeons at the global optimal position. Conversely, the density of pigeons at the global optimal position is lower. The change of the aggregation index is related to an adaptive threshold. In the t-th cycle, if the value of the i-th pigeon is less than the adaptive threshold, the aggregation index C will increase as follows: Then C=C+1 Where β is the threshold coefficient; the product of the average Euclidean distance of the previous cycle and β constitutes the adaptive threshold of this cycle; by adjusting the value of β, the strength of the constraint can be adjusted.

4. The method for autonomous penetration of unmanned aerial vehicles based on individual similarity pigeon flock optimization according to claim 3, characterized in that: The adaptive threshold will change along with the change of the average density of pigeons. As the number of iterations increases, the distance between pigeons becomes closer and closer, and the adaptive threshold decreases accordingly.

5. The method for autonomous penetration of unmanned aerial vehicles based on individual similarity pigeon flock optimization according to claim 3, characterized in that: The specific process of the individual similarity evaluation in step S63 is as follows: the concept of individual similarity is reflected by the degree of aggregation. When C is greater than the upper limit C max When , it means that the individual aggregation is too large. At this time, the individual similarity is calculated and the concept of individual similarity is defined as follows: Individual similarity S t (i, j) is a piecewise function controlled by a constant M; in the above formula, dist t (i,j) represents the Euclidean distance between individuals i and j in t cycles, dist t max It represents the maximum Euclidean distance between individuals in the t-cycle population. If the distance between two individuals is less than th1, the individual similarity is high. Conversely, if the distance between two individuals is greater than th2, the individual similarity is low.

6. The method for autonomous penetration of unmanned aerial vehicles based on individual similarity pigeon flock optimization according to claim 1, characterized in that: The specific representation of the random mutation strategy in step S64 is as follows: Based on the definition of individual similarity, the individual similarity S between the global optimal position G and the i-th individual in t cycles is calculated. t (i, G); Use random mutation method to update high individual similarity pigeons as follows: is the mutation constant, rand is a random number between (0,1), T1 is the maximum number of iterations of the map and compass operators, L d ,U d are vectors of the maximum and minimum search space ranges respectively; randomly generated (L d ,U d ) The random numbers of each component between the two vector search space ranges are used to re-enter the high similarity individuals into the search space.

7. The method for autonomous penetration of unmanned aerial vehicles based on individual similarity pigeon flock optimization according to claim 1, characterized in that: Step 7: Apply the individual similarity pigeon flock optimization algorithm to obtain the optimal strategy. The specific process is as follows: Assume that at t s Time is the start time of a round. According to the state quantity returned by the six-degree-of-freedom model of the red and blue sides, the air situation assessment function f and the basic operation action library are used to predict the situation of the next round, that is, after time t p The profit matrix H after the optimization is obtained; then the classic pigeon flock optimization method is used, that is, the content of steps S65 and S66 is used to calculate the fitness function of the blue team; after the optimization search, the optimal strategy set of the blue team is obtained The component values ​​in this strategy set serve as the tendency weight for selecting the corresponding strategy; The larger the weight, the more likely it is to choose this strategy; at the same time, when obtaining the optimal strategy set Q for the blue team bmx * Finally, the individual similarity pigeon flock optimization algorithm designed in step 6 is used to calculate the red team's fitness function; after optimization search, the optimal strategy set of the red team is obtained. Similarly, each component value in this strategy set represents the weight of the tendency to choose the corresponding strategy; The larger the weight, the more likely this strategy is to be chosen. After determining the optimal strategy set for both parties, the strategy corresponding to the maximum weight in the optimal strategy set is selected as the control strategy for both parties in the next round, and then output to the controllers of both parties to control the next round time t p Repeat step 7 until the simulation time ends.

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