A system and method for planning aircraft trajectory to find weak points in defense systems

Abstract

The present invention discloses an aircraft trajectory planning system and method for finding weak points in a defense system, and establishes an aircraft motion equation. Secondly, by establishing a sensor system detection target blind area model, an interception blind area model, and a detection information to decision information conversion invalidity model, a target defense system weakness evaluation function is obtained. On the basis of satisfying the ballistic constraints of striking within the target weak protection area, an aircraft trajectory planning index function based on weakness evaluation is established. Finally, the optimization variable set is determined, and the pigeon flock algorithm is used to solve the trajectory planning model for automatically cutting into the weak area of ​​the defense system to obtain the aircraft's angle of attack and roll angle control instructions.

Description

Technical Field

[0001] The invention belongs to the field of aircraft guidance, and in particular relates to an aircraft trajectory planning system and method for finding weak points of a defense system. Background Art

[0002] With the continuous improvement of the missile defense system, the penetration capability of the aircraft has become an issue that must be considered. The aircraft faces complex and changing flight conditions and the influence of uncertain factors such as aerodynamic heat protection and overload limit during its full ballistic flight. At the same time, due to the rapid development of interception and defense systems, in order to avoid detection by the defense system as much as possible during flight, it has become a difficult problem to quickly design a penetration trajectory that meets a series of process constraints and can accurately hit the target.

[0003] There are many existing single-aircraft penetration trajectory planning methods. One is to set the aircraft's maneuver penetration program in advance and perform fixed maneuvers within a fixed time, but the trajectory penetration efficiency of this planning method is not high; while an attack and defense confrontation model is established under set conditions, and the analysis is performed with the limited available overload of both sides as a constraint to obtain the maneuver penetration area that can produce the maximum miss amount. However, this method requires full perception of the information of both sides, so the intelligence of this trajectory planning method is not high. Summary of the invention

[0004] The purpose of the present invention is to overcome the above-mentioned shortcomings of the prior art and to provide an aircraft trajectory planning system and method for finding weak points in a defense system, so as to solve the problem of trajectory planning for an aircraft to attack a target from a weak area in a defense system.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for aircraft trajectory planning for finding weak points of a defense system, comprising:

[0007] Establish the trajectory equation of the aircraft;

[0008] Establishing a target defense system weakness evaluation function based on the ballistic equation of the aircraft; the target defense system weakness evaluation function is composed of a possibility model of the defense system failing to detect the aircraft, an evaluation function of the target defense system failing to intercept, and an evaluation function of the invalidity of conversion from detection information to decision information;

[0009] The trajectory planning index function is established based on the target defense system weakness evaluation function and the aircraft landing point deviation evaluation model;

[0010] The trajectory planning index function is optimized by the pigeon flock optimization algorithm to obtain the angle of attack command function and roll angle command sequence of the trajectory penetrating the weak area of ​​the target defense system.

[0011] A further improvement of the present invention is:

[0012] Preferably, the trajectory equation of the aircraft is:

[0013]

[0014] In the formula, V is the speed of the aircraft, θ is the trajectory inclination angle, ψ is the trajectory deviation angle, and x, y, z are the position information of the aircraft;

[0015] In the formula, μ M is the earth's gravitational constant, m is the mass of the aircraft, υ is the roll angle command, which represents the angle between the lift direction and the vertical plane containing the velocity vector, S is the reference area, and ρ is the atmospheric density;

[0016] Where D and L are the drag and lift of the aircraft respectively.

[0017] Preferably, the calculation formula f of the weakness evaluation function is:

[0018] f=A1p1+A2p2+A3p3 (17)

[0019] Where A1, A2, and A3 are weight coefficients; p1 is the possibility model that the defense system cannot detect the aircraft; p2 is the evaluation function of the target defense system's interception failure; and p3 is the evaluation function of the invalidity of the conversion from detection information to decision information.

[0020] Preferably, the probability model of the defense system failing to detect the aircraft is:

[0021]

[0022] Where ξ is the angle between the projection of the line between the aircraft and the target in the longitudinal plane and the ground, ζ is the angle between the projection of the line between the aircraft and the target in the horizontal plane and the true north direction, is the mean value of the detection angle of the detection system in the longitudinal plane, ε0 is the mean value of the detection angle of the detection system in the horizontal plane; λ 11 , 12 are weight coefficients respectively;

[0023] The evaluation function of the target defense system interception failure is:

[0024]

[0025] in, is the killing radius of the aircraft, D R is the minimum distance between the aircraft and the interceptor missile,

[0026]

[0027] Among them, x(t), y(t), z(t) are the position information of the aircraft at the current moment, x M (t),y M (t),z M (t) is the position information of the interceptor missile at each moment;

[0028] The evaluation function of the ineffectiveness of the conversion from detection information to decision information is:

[0029]

[0030] In the formula, p represents the total amount of detection information, p t To effectively convert information.

[0031] Preferably, the trajectory planning index function fitness is:

[0032] fitness=B1F1-B2F2 (21)

[0033] Among them, B1 and B2 are indicator weight coefficients, F1 is the weakness evaluation function of the area where the aircraft trajectory is located, and F2 is the weakness evaluation function of the target defense system; F2 is the aircraft landing point deviation evaluation model.

[0034] Preferably, the aircraft landing point deviation evaluation model F2 is:

[0035]

[0036] Among them, x T (t f ),y T (t f ),z T (t f ) is the coordinate of the target point in the ballistic coordinate system when the aircraft lands, x(t f ),y(t f ),z(t f ) is the coordinate of the aircraft at the time of landing, is a constant used to normalize the landing point error.

[0037] Preferably, the optimization process of the pigeon flock optimization algorithm is:

[0038] Step 1, parameter setting

[0039] Step 1.1, set the objective function to be optimized fitness, population size N, the number of penetration trajectory attack angle control instruction parameters to 3, the number of roll angle control instruction parameters n, the dimension of the solution space D = 3 + n, the map and compass factor R, the number of map operator iterations N c1 , the number of iterations of the compass operator N c2 , where N is requiredc1 >N c2 ; The value range of independent variable α1, the value range of independent variable α2; independent variable V F The value range of the independent variable υ1, the value range of the independent variable υ2, ..., the value range of the independent variable υ n The value range of .

[0040] Step 2: Initialization of the i-th pigeon

[0041] Step 2.1: Assuming that the pigeons are evenly distributed in the given space, randomly initialize the pigeon's position information x i1 ;

[0042] Step 2.2, assuming that the pigeons are evenly distributed in the given space, randomly initialize the pigeon's speed information v i1 ;

[0043] Step 2.3, the pigeon position information x in step 2.1 i,1 ,x i,2 ,x i,3 Substitute the value of into formula (3) to obtain the attack angle control command of the penetration trajectory, and convert the pigeon position information x i,4 ,x i,5 ,…x i,n+3 Substitute the value of into formula (4) to obtain the roll angle control command of the penetration trajectory, substitute the angle of attack control command and the roll angle control command into formula (1), integrate to obtain the complete penetration trajectory, and record the trajectory information; substitute the penetration trajectory information into the trajectory planning index function based on weakness evaluation to obtain the fitness value fitness[i] of the i-th pigeon.

[0044] Step 2.4, initialize the individual local optimal value and set the initial position x of the i-th pigeon i1 is the individual local optimal value p i1 ;

[0045] Step 3: Compass operator update

[0046] Step 3.1, update the position and speed of each pigeon;

[0047] Step 3.2, update the individual local optimal value p id ; Compare the current fitness function value of the pigeon with the fitness value of the historical optimal position. If the current position is better, set the current position as the optimal position of the pigeon;

[0048] Step 3.3, repeat steps 3.1 to 3.2 until the maximum number of iterations of the compass operator N is reached. c2 ;

[0049] Step 4: Landmark operator update

[0050] Step 4.1: According to step 3, the optimal position p of each pigeon can be obtained. i , p i Substitute the trajectory planning index function based on weakness evaluation, calculate the fitness value of each pigeon, and rank all pigeons according to their adaptability;

[0051] Step 4.2: Repeat step 4.1 until the maximum number of iterations N of the landmark operator is reached. c2 , output the position of the ideal destination, which is the optimal control instruction.

[0052] Preferably, in step 3.1, during the fitness ranking process, the position and speed of each pigeon are updated according to formula (23);

[0053]

[0054] Preferably, in step 4.1, during the fitness ranking process, half of the pigeons with low fitness are halved according to formula (24); the center of all pigeons is found according to formula (25), and the center is the ideal destination; all pigeons will fly to the destination and adjust the flight direction according to formula (26); wherein, is the number of pigeons in the kth generation, is the center position of all pigeons in the kth generation;

[0055]

[0056]

[0057]

[0058] An aircraft trajectory planning system for finding weak points in a defense system, comprising:

[0059] The ballistic equation unit is used to establish the ballistic equation of the aircraft;

[0060] An evaluation function unit is used to establish a target defense system weakness evaluation function based on the aircraft's ballistic equation;

[0061] An index function unit, used to establish a trajectory planning index function based on a weakness evaluation function and an aircraft landing point deviation evaluation model;

[0062] The optimization unit is used to optimize the trajectory planning index function through the pigeon flock optimization algorithm to obtain the attack angle command function and the roll angle command sequence of the trajectory penetrating the weak area of ​​the target defense system.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] The present invention discloses a system and method for aircraft trajectory planning to find weak points in a defense system. The present invention first establishes an aircraft motion equation. Secondly, a sensor system detection target blind area model, an interception blind area model, and a detection information to decision information conversion invalidity model are established to obtain a target defense system weakness evaluation function. On the basis of satisfying the ballistic constraints of striking within the target weak protection area, an aircraft trajectory planning index function based on weakness evaluation is established. Finally, an optimization variable set is determined, and a pigeon flock algorithm is used to solve a trajectory planning model for automatically cutting into the weak area of ​​the defense system to obtain the aircraft's angle of attack and roll angle control instructions. The present invention establishes a target defense system weakness evaluation function, so that the aircraft strikes from the target weak protection area, solves the trajectory planning problem of the aircraft attacking the target from the weak area of ​​the defense system, improves the strike accuracy and survivability of the aircraft, can improve the intelligence level of penetration trajectory planning, and enhances the aircraft's penetration capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 is a flow chart of the calculation method of the present invention;

[0066] Figure 2 It is a flow chart of the pigeon flock optimization algorithm of the present invention; DETAILED DESCRIPTION

[0067] The present invention is further described in detail below with reference to the accompanying drawings. The present invention discloses an aircraft penetration trajectory planning system and method for automatically finding weak points in a target defense system. Figure 1 , the method comprises the following steps:

[0068] Step 1. Establish the trajectory equation of the aircraft.

[0069] Considering the earth's gravity and aerodynamic force acting on the aircraft, the motion equation of the aircraft is established in the ballistic coordinate system, which is expressed as follows:

[0070]

[0071] In the formula, there are 6 state variables, V is the speed of the aircraft, θ is the ballistic inclination angle, ψ is the ballistic deviation angle, and x, y, z are the position information of the aircraft.

[0072] In the formula, μ M is the earth's gravitational constant, m is the vehicle mass, υ is the roll angle command, which represents the angle between the lift direction and the vertical plane containing the velocity vector, S is the reference area, and ρ is the atmospheric density.

[0073] In the formula, D and L are the drag and lift of the aircraft respectively, and the calculation formula is as follows:

[0074]

[0075] Among them, C L ,C D They represent the lift coefficient and the drag coefficient respectively, and can be obtained by inputting the angle of attack command and flight speed at the current moment and querying the interpolation table.

[0076] It can be seen that the state variables of the system are V, θ, ψ, x, y, z, and the control inputs are the angle of attack command α and the roll angle command υ. By setting the initial values ​​of the state variables, inputting the angle of attack command and the roll angle command into formula (1), and integrating the system, the flight trajectory of the aircraft can be obtained.

[0077] The expression formulas for the angle of attack command α and the roll angle command υ are given below.

[0078] The angle of attack-velocity profile is set to divide the flight state of the aircraft into two sections: the initial dive section and the descending section. The function of the angle of attack changing with the velocity is shown in the following formula:

[0079]

[0080] Among them, α1 is the initial dive angle, α2 is the setting parameter, V F The segmentation basis parameter.

[0081] The given roll angle command is as follows:

[0082]

[0083] Therefore, the angle of attack control command parameters α1, α2, V and the roll angle command parameters υ1, υ2, …, υ n The choice will affect the flight trajectory of the aircraft.

[0084] Step 2. Establish a ballistic constraint model for striking from within the target’s weakly protected area.

[0085] During the flight, the aircraft must meet thermal flow constraints, overload constraints and dynamic pressure constraints.

[0086] The heat flux constraint is established as follows:

[0087]

[0088] Where Q represents the heat flux, Q max is the maximum heat flux, k Q is a constant coefficient related to the shape and appearance of the stationary point, and k is taken Q =6×10 -8 , v is the speed of the aircraft, ρ is the atmospheric density, and the simplified exponential form is expressed as follows:

[0089]

[0090] Where, ρ0 = 1.225 g / L, h s =7200m.

[0091] The dynamic pressure constraint is established as follows:

[0092]

[0093] Create a normal overload constraint as follows:

[0094]

[0095] In the formula, L and D represent the lift and drag of the aircraft respectively, α is the angle of attack, m is the mass of the aircraft, g is the gravitational acceleration, and n is ymax Indicates the maximum overload value allowed by the aircraft.

[0096] Substituting the glide phase angle of attack into equations (5), (7), and (8), the three process constraints can be transformed into the HV form as follows:

[0097]

[0098] Where H is the height, V is the speed, H Q , H q and H n Given the values ​​of α1 and α2, substitute them into formula (3) to get an angle of attack command. Set the roll angle command to 0, and substitute these two commands into formula 1 and integrate to get a trajectory. After getting the trajectory, the parameters such as V, CL, CD, etc. at each moment can be known, so the three HV curves corresponding to formula (9) can be drawn. These three lines drawn on a graph constitute the so-called "HV reentry corridor".

[0099] The above formula can determine the range of the reentry corridor. In the initial subduction stage, the reentry corridor is mainly determined by the heat flux density constraint. Given an α1, the real HV diagram of the initial subduction stage can be drawn, and the three HV curves corresponding to formula (9) can be drawn. When α1 is too small, the glide trajectory does not satisfy the heat flux density constraint. Therefore, when the glide trajectory is consistent with the reentry corridor H constrained by the heat flux Q When -V is tangent, the corresponding α1 is the minimum value α 1min ; When α1 is too large, the gliding trajectory will show obvious jumps, so the maximum value of α1 can be determined as α 1max .

[0100] Given an α2, we can draw the real HV diagram of the descent section and the three HV curves (reentry corridor) corresponding to formula (9). max -α2 corresponding to the gliding trajectory tangent to V is the maximum value of α22max ; and the lower boundary of the reentry corridor H min -α2 corresponding to the gliding trajectory tangent to V is the minimum value of α2 2min .

[0101] Therefore, the value ranges of the two parameters of the angle of attack command can be determined by the process constraints as follows:

[0102]

[0103] Step 3. Establish a vulnerability evaluation function for the target defense system.

[0104] The defense system is composed of sensor systems, interception weapon systems, combat command and communication systems. Therefore, its defense weakness is measured by the sensor system's target detection blind spots, interception blind spots, and the ineffectiveness of converting detection information into decision-making information.

[0105] ① Establish the possibility model of the defense system not being able to detect the aircraft as shown in the following formula. The larger p1 is, the better.

[0106]

[0107] Where ξ is the angle between the projection of the line between the aircraft and the target in the longitudinal plane and the ground, and ζ is the angle between the projection of the line between the aircraft and the target in the horizontal plane and the true north direction. The calculation is shown in formula (12). is the mean value of the detection angle of the detection system in the longitudinal plane, and ε0 is the mean value of the detection angle of the detection system in the horizontal plane. 11 , 12 are weight coefficients respectively, depending on the situation.

[0108]

[0109] Where (x E ,y E ,z E ) is the position of the aircraft in the geocentric coordinate system, (x TE ,y TE ,z TE ) is the position of the target in the geocentric coordinate system. By integrating formula (1), we can get the position information (x, y, z) of the aircraft in the ballistic coordinate system. Knowing the transformation matrix T from the ballistic coordinate system to the geocentric coordinate system, we can get the position of the aircraft in the geocentric coordinate system as follows:

[0110]

[0111] ② Establish the evaluation function of the target defense system interception failure as follows. The larger the result of the evaluation function, the better. That is, the greater the possibility of failure, the better.

[0112] When the aircraft is in the interception zone of the target defense system, the defense system launches an interceptor missile to intercept it. The position information of the interceptor missile at each moment (x M (t),y M (t),z M (t)), the minimum distance between the aircraft and the interceptor missile is calculated as shown below.

[0113]

[0114] Therefore, the evaluation function of the target defense system interception failure can be expressed as:

[0115]

[0116] In the formula, x(t), y(t), z(t) are the position information of the aircraft at the current moment. is the killing radius of the aircraft.

[0117] ③ Establish the invalidity evaluation function of the conversion from detection information to decision information as follows:

[0118] ④

[0119] In the formula, p represents the total amount of detection information, p t In order to effectively convert the amount of information, the larger the P3, the better, that is, the greater the ineffectiveness, the better.

[0120] Based on the above models, the target defense system weakness evaluation function is established as follows:

[0121] f=A1p1+A2p2+A3p3 (17)

[0122] In the formula, A1, A2, and A3 are weight coefficients, depending on the situation.

[0123] Step 4. Establish a trajectory planning index function based on the weakness evaluation function

[0124] The quality of trajectory planning is measured by the weakness of the target defense system in the area where the aircraft's trajectory is located and the deviation of the aircraft's landing point.

[0125] The evaluation function of the weakness of the area where the aircraft trajectory is located is established as follows:

[0126] F1=f (18)

[0127] The landing point deviation evaluation model of the aircraft is established as follows:

[0128]

[0129] Where (x T (t f ),yT (t f ),z T (t f )) is the coordinate of the target point in the ballistic coordinate system when the aircraft lands, (x(t f ),y(t f ),z(t f )) is the coordinate of the aircraft landing time, is a constant used to normalize the landing point error.

[0130] Known (x TE ,y TE ,z TE ) is the position of the target in the geocentric coordinate system, and the transformation matrix G from the geocentric coordinate system to the ballistic coordinate system can be obtained as follows:

[0131]

[0132] In the formula, θ(t f ) is the ballistic inclination angle of the aircraft at the time of landing, ψ(t f ) is the ballistic deviation angle of the aircraft at the moment of landing.

[0133] Combining the above evaluation models, the trajectory planning index function based on weakness evaluation is obtained as follows:

[0134] fitness=B1F1-B2F2 (21)

[0135] Among them, B1 and B2 are indicator weight coefficients, which depend on the situation.

[0136] Step 5. Online re-planning of the trajectory to automatically cut into the weak points of the target's defense system.

[0137] In order to optimize the attack angle command and the roll angle command to achieve the best penetration trajectory performance, the optimization variable set is U = {α1, α2, V F ,υ1,υ2,…υ n}, the performance indicator function is expressed as follows:

[0138] J = max{fitness} (22)

[0139] It is proposed to use the pigeon swarm optimization algorithm to solve the trajectory planning problem and obtain the attack angle command function and roll angle command sequence of the trajectory that penetrates the weak area of ​​the target defense system. Figure 2 , the process is as follows:

[0140] Step 1: Parameter Setting

[0141] Step 1.1: The objective function fitness to be optimized is as shown in formula (21), the population size is N, the number of penetration trajectory attack angle control instruction parameters is 3, the number of roll angle control instruction parameters is n, the dimension of the solution space is D = 3 + n, the map and compass factor is R, and the number of map operator iterations is N. c1 , the number of iterations of the compass operator N c2 , where N is required c1 >N c2 The value range of the independent variable α1 and the value range of the independent variable α2 (given according to formula (10)). F The value range of the independent variable υ1, the value range of the independent variable υ2, ..., the value range of the independent variable υ n The value range of (set by yourself).

[0142] Step 2: Initialization of the i-th pigeon

[0143] Step 2.1: Assuming that the pigeons are evenly distributed in the given space, randomly initialize the pigeon's position information [x i,1 ,x i,2 ,....,x i,n+3 ](Since the number of independent variables is 3+n, the pigeon is 3+n-dimensional)

[0144] Step 2.2: Assuming that the pigeons are uniformly distributed in the given space, randomly initialize the pigeon's speed information [v i,1 ,v i,2 ,....,v i,n+3 ]

[0145] Step 2.3: Convert the pigeon's position information x in step 2.1 to i,1 ,x i,2 ,x i,3 Substitute the value of into formula (3) to obtain the attack angle control command of the penetration trajectory, and convert the pigeon position information x i,4 ,x i,5 ,…x i,n+3 Substitute the value of into formula (4) to obtain the roll angle control command of the penetration trajectory, substitute the angle of attack control command and the roll angle control command into formula (1), integrate to obtain the complete penetration trajectory, and record the trajectory information. Substitute the penetration trajectory information into formula (21) to obtain the fitness value fitness[i] of the i-th pigeon.

[0146] Step 2.4: Initialize the individual local optimal value and set the initial position x of the i-th pigeon i1 is the individual local optimal value p i1 ;

[0147] Step 3: Compass operator update

[0148] Step 3.1: Update the position and velocity of each pigeon according to formula (23);

[0149]

[0150] Step 3.2: Update individual local optimal value p id . Compare the current fitness function value of the pigeon with the fitness value of the historical optimal position. If the fitness value of the current position is greater than the fitness value of the historical optimal position, the current position is considered to be better, and the current position is set as the optimal position of the pigeon.

[0151] Step 3.3: Repeat steps 3.1 to 3.2 until the maximum number of iterations of the compass operator N is reached. c2

[0152] Step 4: Landmark operator update

[0153] Step 4.1: According to step 3, the optimal position p of each pigeon can be obtained i , p i Substitute into formula (21), calculate the fitness value of each pigeon, and rank all the pigeons according to their fitness. Half of the pigeons with low fitness will be halved according to formula (24), and the half of the pigeons with low fitness ranking will be eliminated. Then, according to equation (25), find the center of all pigeons, which is the ideal destination. All pigeons will fly to the destination and adjust their flight direction according to formula (26). In the formula, Used to record the number of pigeons in the kth generation, is the center position of all pigeons in the kth generation

[0154]

[0155]

[0156]

[0157] Step 4.2: Repeat step 4.1 until the maximum number of iterations N of the landmark operator is reached. c2 , output the ideal destination position, which is the optimal control instruction U, specifically U={α1,α2,V F ,υ1,υ2,…υ n}, the attack angle command and the invasion angle command are obtained.

[0158] The present invention also discloses an aircraft penetration trajectory planning system for automatically finding weak points of a target defense system, the system comprising:

[0159] The ballistic equation unit is used to establish the ballistic equation of the aircraft;

[0160] An evaluation function unit is used to establish a target defense system weakness evaluation function based on the aircraft's ballistic equation;

[0161] An index function unit, used to establish a trajectory planning index function based on a weakness evaluation function and an aircraft landing point deviation evaluation model;

[0162] The optimization unit is used to optimize the trajectory planning index function through the pigeon flock optimization algorithm to obtain the attack angle command function and the roll angle command sequence of the trajectory penetrating the weak area of ​​the target defense system.

Claims

1. A method for aircraft trajectory planning for finding weak points in a defense system, characterized in that: include: Establish the trajectory equation of the aircraft; Establish the target defense system weakness evaluation function based on the aircraft's ballistic equation; The target defense system weakness evaluation function is composed of a probability model of the defense system failing to detect the aircraft, an evaluation function of the target defense system failing to intercept, and an evaluation function of the invalidity of the conversion from detection information to decision information; The calculation formula of the weakness evaluation function is f for: (17) In the formula, is the weight coefficient; Model the probability that the aircraft will not be detected by the defense system; is the evaluation function of interception failure of the target defense system, An evaluation function for the ineffectiveness of conversion from detection information to decision information; The probability model of the defense system failing to detect the aircraft is: (11) In the formula, is the angle between the projection of the line between the aircraft and the target in the longitudinal plane and the ground, is the angle between the projection of the line between the aircraft and the target in the horizontal plane and the true north direction, is the mean value of the detection angle of the detection system in the longitudinal plane, is the mean value of the detection angle of the detection system in the horizontal plane; are weight coefficients respectively; The evaluation function of the target defense system interception failure is: (15) in, is the killing radius of the interceptor missile, is the minimum distance between the aircraft and the interceptor missile, (14) in, is the position information of the aircraft at the current moment, The position information of the interceptor missile at each moment; The evaluation function of the ineffectiveness of the conversion from detection information to decision information is: (16) In the formula, Represents the total amount of detection information, To effectively convert information; The trajectory planning index function is established based on the target defense system weakness evaluation function and the aircraft landing point deviation evaluation model; The trajectory planning index function for: (21) in is the indicator weight coefficient, is the weakness evaluation function of the area where the aircraft trajectory is located, and is the weakness evaluation function of the target defense system; It is a model for evaluating the landing point deviation of the aircraft; The aircraft landing point deviation evaluation model for: (19) in, is the coordinate of the target point in the ballistic coordinate system when the aircraft lands. is the coordinate of the aircraft landing time, is a constant used to normalize the landing point error; The trajectory planning index function is optimized by the pigeon flock optimization algorithm to obtain the angle of attack command function and roll angle command sequence of the trajectory penetrating the weak area of ​​the target defense system.

2. The method for aircraft trajectory planning for finding weak points in a defense system according to claim 1, characterized in that: The trajectory equation of the aircraft is: (1) Where V is the speed of the aircraft, is the ballistic inclination angle, is the ballistic deflection angle, The position information of the aircraft; In the formula, is the Earth's gravitational constant, is the mass of the aircraft, is the roll angle command, which represents the angle between the lift direction and the vertical plane containing the velocity vector. is the reference area, is the atmospheric density; In the formula, are the drag and lift acting on the aircraft respectively.

3. The method for aircraft trajectory planning for finding weak points in a defense system according to claim 1, characterized in that: The optimization process of the pigeon flock optimization algorithm is: Step 1, parameter setting Step 1.1, set the objective function to be optimized , population size , the number of penetration trajectory attack angle control command parameters is 3, the number of roll angle control command parameters is , the dimension of the solution space , map and compass factors R , the number of map operator iterations , the number of iterations of the compass operator , which requires ; Independent variable The value range of the independent variable The value range of the independent variable The value range of the independent variable The value range of the independent variable The value range of, ..., independent variable The value range of Step 2, for Initialization of pigeons Step 2.1: Assuming that the pigeons are evenly distributed in the given space, randomly initialize the pigeons’ position information. ; Step 2.2: Assuming that the pigeons are evenly distributed in the given space, randomly initialize the speed information of the pigeons. ; Step 2.3, the location information of the pigeon in step 2.1 Substitute the value of into formula (3) to obtain the attack angle control command of the penetration trajectory, and convert the position information of the pigeon Substitute the value of into formula (4) to obtain the roll angle control command of the penetration trajectory, substitute the angle of attack control command and the roll angle control command into formula (1), integrate to obtain the complete penetration trajectory, and record the trajectory information; substitute the penetration trajectory information into the trajectory planning index function based on weakness evaluation, and obtain the first The fitness value of a pigeon ; Step 2.4, initialize the individual local optimal value and set the The initial position of the pigeons is the individual local optimum ; Step 3: Compass operator update Step 3.1, update the position and speed of each pigeon; Step 3.2, update individual local optimal value ; Compare the fitness function value of the pigeon's current position with the fitness value of the historical optimal position. If the current position is better, set the current position as the optimal position of the pigeon; Step 3.3, repeat steps 3.1 to 3.2 until the maximum number of iterations of the compass operator is reached. ; Step 4: Landmark operator update Step 4.1, according to step 3, the optimal position of each pigeon can be obtained ,Will Substitute the trajectory planning index function based on weakness evaluation, calculate the fitness value of each pigeon, and rank all pigeons according to their adaptability; Step 4.2, repeat step 4.1 until the maximum number of iterations of the landmark operator is reached , output the position of the ideal destination, which is the optimal control instruction.

4. The method for aircraft trajectory planning for finding weak points in a defense system according to claim 3, characterized in that: In step 3.1, during the fitness ranking process, the position and speed of each pigeon are updated according to formula (23); (23)。 5. The method for aircraft trajectory planning for finding weak points in a defense system according to claim 3, characterized in that: In step 4.1, during the fitness ranking process, half of the pigeons with low fitness are halved according to equation (24); the center of all pigeons is found according to equation (25), and the center is the ideal destination; all pigeons will fly to the destination and adjust the flight direction according to equation (26); where, For the The number of pigeons in the generation, For the represents the central position of all pigeons; (24) (25) (26)。 6. An aircraft trajectory planning system for finding weak points of a defense system for implementing the method of claim 1, characterized in that: include: The ballistic equation unit is used to establish the ballistic equation of the aircraft; An evaluation function unit is used to establish a target defense system weakness evaluation function based on the aircraft's ballistic equation; An index function unit, used to establish a trajectory planning index function based on a weakness evaluation function and an aircraft landing point deviation evaluation model; The optimization unit is used to optimize the trajectory planning index function through the pigeon flock optimization algorithm to obtain the attack angle command function and the roll angle command sequence of the trajectory penetrating the weak area of ​​the target defense system.

Images