Many-to-many task allocation method based on minimum zero-control miss distance

Abstract

The invention relates to a many-to-many task allocation method based on a minimum zero control miss distance. The method comprises the following steps: establishing a three-dimensional missile-target relative motion equation, and deducing an analytic expression and a kinetic equation of the zero-control miss distance; according to terminal guidance initial conditions and the zero-control miss distance analytic expression, calculating a zero-control miss distance value between each interception missile and the target; constructing an intermediate matrix according to a preset interception task, and filling the intermediate matrix with the cost matrix of the Hungary algorithm as a matrix element to obtain a unified cost matrix; substituting the zero-control miss distance value into the unified cost matrix, and generating a many-to-many task allocation scheme based on a Hungary algorithm; and designing an improved reality true proportion guidance law for controlling the zero control miss distance, and adopting the improved reality true proportion guidance law to realize the many-to-many task allocation scheme. The method can effectively eliminate the zero-control miss distance and increase the interception success rate.

Description

Technical Field

[0001] The present application relates to the field of aircraft control technology, and in particular to a multi-to-multi task allocation method based on minimizing zero-control miss amount. Background Art

[0002] With the continuous development of collaborative technology, saturation strikes on the ground are an effective means to enhance lethality and improve penetration. From the perspective of the defender, achieving effective task allocation and interception of multiple incoming targets faces huge challenges. The existing modeling methods have two-dimensional linear assumptions, and the allocation methods are mostly based on intelligent means, including genetics, particle swarms, deep learning, and reinforcement learning. There are problems such as time-consuming and inefficient calculations, the need for a large amount of data learning, and poor environmental adaptability. The interception guidance law is not projected in the line of sight, resulting in low interception efficiency. Therefore, it is urgent to propose an efficient three-dimensional interception multi-to-multi task allocation method and a guidance law that effectively eliminates zero-control misses. Summary of the invention

[0003] Based on this, it is necessary to provide a many-to-many task allocation method based on minimizing the zero-control miss amount to address the above technical problems.

[0004] A multi-to-multi task allocation method based on minimizing zero-control miss amount, the method comprising:

[0005] Establish the three-dimensional relative motion equation of projectile and target, and derive the analytical expression and dynamic equation of zero-control miss distance;

[0006] Calculating the zero-control miss distance value between each interceptor missile and the target according to the initial conditions of terminal guidance and the zero-control miss distance analytical formula;

[0007] According to the preset interception task, an intermediate matrix is ​​constructed, and the cost matrix of the Hungarian algorithm is filled into the intermediate matrix as a matrix element to obtain a unified cost matrix;

[0008] Substituting the zero-control miss value into the unified cost matrix, and generating a many-to-many task allocation scheme based on the Hungarian algorithm;

[0009] An improved realistic true proportional guidance law for eliminating zero-control miss amount is designed, and the improved realistic true proportional guidance law is adopted to realize the many-to-many task allocation scheme.

[0010] In one embodiment, the method further includes: constructing a three-dimensional relative motion equation of the projectile as follows:

[0011]

[0012] Among them, a ir 、a iq 、a iω, i = t, m represents the acceleration of the target and the interceptor respectively r 、e q 、e ω Projection of direction, ω s With Ω s represent the angular rates of rotation of the line of sight and the plane respectively.

[0013] In one embodiment, the method further includes: constructing an intermediate matrix of k rows and l columns according to a preset interception task; wherein k means that each target needs k interceptor missiles to intercept, and l means that each interceptor missile needs to intercept l targets;

[0014] Construct the cost matrix J of the Hungarian algorithm = [J ij ], the cost matrix of the Hungarian algorithm is used as a matrix element to fill the intermediate matrix, and after zero filling, a unified cost matrix of km×ln is obtained.

[0015] In one embodiment, the method further includes: obtaining the generalized differential geometry guidance as:

[0016]

[0017] Among them, n m is the velocity normal;

[0018] According to the generalized differential geometry guidance, the improved real proportional guidance law is:

[0019]

[0020] Select the command application direction as the three-dimensional pure proportional guidance direction:

[0021]

[0022] The above-mentioned multi-to-multi task allocation method based on minimizing the zero-control miss amount first establishes a three-dimensional missile-target relative motion equation, derives the analytical expression of the zero-control miss amount and the dynamic equation, and analyzes the relationship between the zero-control miss amount and the components of the guidance instruction; secondly, the zero-control miss amount value between each interceptor missile and the target is calculated according to the initial conditions of the terminal guidance; then, the cost matrix form of the Hungarian algorithm is improved to adapt to the multi-to-multi task target allocation task; then, the calculated value of the zero-control miss amount between the missile and the target is substituted into the improved cost matrix, and a multi-to-multi task allocation scheme is generated based on the Hungarian algorithm; then, an improved realistic true proportional guidance law that effectively suppresses the zero-control miss amount is designed; finally, the interceptor missile is guided using the improved realistic true proportional guidance, and the allocated target is intercepted according to the allocation scheme. Compared with the multi-target allocation and interception methods based on two-dimensional linearization, complex intelligent algorithms and traditional guidance laws, the proposed method adopts a three-dimensional nonlinear model. The allocation result of the improved Hungarian algorithm is solved much faster than the intelligent algorithm. The solution result can minimize the zero-control miss amount of the interception. The designed guidance law adopts the advanced generalized differential geometry guidance form, which can effectively eliminate the zero-control miss amount and increase the interception success rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A schematic flow chart of a multi-to-multi task allocation method based on minimizing zero-control miss distance in one embodiment;

[0024] Figure 2 A schematic diagram of the flight trajectory of a missile and a target during an interception process in one embodiment;

[0025] Figure 3 A schematic diagram of the guidance acceleration curves of six interceptor missiles in one embodiment;

[0026] Figure 4 It is a schematic diagram of the zero-control miss amount curve of six interceptor missiles in one embodiment. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0028] In one embodiment, Figure 1 As shown, a multi-to-multi task allocation method based on minimizing the zero-control miss amount is provided, comprising the following steps:

[0029] Step 102, establish a three-dimensional projectile-target relative motion equation, and derive an analytical expression and a dynamic equation for the zero-control miss distance.

[0030] Step 104, calculating the zero-control miss distance value between each interceptor missile and the target according to the terminal guidance initial condition and the zero-control miss distance analytical formula.

[0031] Step 106, constructing an intermediate matrix according to the preset interception task, and filling the cost matrix of the Hungarian algorithm as a matrix element into the intermediate matrix to obtain a unified cost matrix.

[0032] Step 108, substituting the zero-control miss value into the unified cost matrix, and generating a many-to-many task allocation scheme based on the Hungarian algorithm.

[0033] Step 110, designing an improved realistic true proportional guidance law for controlling the zero control miss amount, and using the improved realistic true proportional guidance law to implement a multi-to-multi task allocation scheme.

[0034] In the above-mentioned many-to-many task allocation method based on minimizing the zero-control miss amount, firstly, the three-dimensional missile-target relative motion equation is established, the analytical expression of the zero-control miss amount and the dynamic equation are derived, and the relationship between the zero-control miss amount and the components of the guidance instruction is analyzed; secondly, the zero-control miss amount value between each interceptor missile and the target is calculated according to the initial conditions of the terminal guidance; then, the cost matrix form of the Hungarian algorithm is improved to adapt to the many-to-many task target allocation task; then, the calculated value of the zero-control miss amount between the missile and the target is substituted into the improved cost matrix, and a many-to-many task allocation scheme is generated based on the Hungarian algorithm; then, an improved realistic true proportional guidance law that effectively suppresses the zero-control miss amount is designed; finally, the interceptor missile is guided by the improved realistic true proportional guidance, and the allocated target is intercepted according to the allocation scheme.

[0035] In one embodiment, the three-dimensional projectile-target relative motion equation is constructed as:

[0036]

[0037] Among them, a ir 、a iq 、a iω , i = t, m represents the acceleration of the target and the interceptor respectively r 、e q 、e ω Projection of direction, ω s With Ω s represent the angular rates of rotation of the line of sight and the plane respectively.

[0038] In another embodiment, the zero-effort miss (ZEM) represents the nominal miss distance between the missile and the target in an uncontrolled state (the guidance acceleration is zero). In an ideal state, without considering the influence of aerodynamic force and gravity, the calculation formula for constructing the zero-effort miss is:

[0039]

[0040] Where ZEM represents the zero control miss distance, r = r T –r M is the relative distance vector between the projectile and the target, r M With r T They represent the position vectors of the interceptor missile and the target in the inertial system, v = v T –v M is the relative velocity vector of the projectile and target, v M With v T They represent the velocity vectors of the interceptor missile and the target in the inertial system, t go =t f –t is the remaining flight time of the interceptor missile, t f is the final guidance terminal moment or the collision moment, and δ represents the pointing error.

[0041] Select the sine value of the pointing error δ as the intermediate variable and establish the equation relationship:

[0042]

[0043] Among them, v q is the relative velocity vector of the projectile and the target along e q Direction projection.

[0044] According to the expression of the line of sight rotation rate in the plane, the calculation expression of the zero control miss value is obtained as follows:

[0045]

[0046] The time derivative of the zero-control miss value calculation expression is obtained as follows:

[0047]

[0048] According to the time derivative expression and the three-dimensional projectile-target relative motion equation, the kinematic equation of zero-control miss distance is obtained as follows:

[0049]

[0050] From the above formula, we can see that ZEM is actually determined by the difference between the command acceleration of the interceptor and the target along the line of sight and the difference between the command acceleration of the two along the line of sight normal. Further observation of the two command acceleration coefficients are: Relative velocity v to the line of sight in the plane q =ω s r.

[0051] Considering the high-speed interception scenario and the long-term correction of the interceptor missile's guidance, the interceptor missile has initially formed a good interception geometry, so the terminal guidance stage has a higher missile-target approach speed, and the relative speed along the normal direction of the line of sight is small; on the other hand, in order to achieve their respective goals as much as possible, namely successful interception and timely escape, the interceptor missile and the incoming target will maximize the projection of the command acceleration in the normal direction of the line of sight, so the value in the brackets of the second term is considered to be a small amount; therefore, according to the analysis, it can be known that a mq Instructions are more efficient in controlling ZEM.

[0052] In one embodiment, assuming that there are m interceptor missiles and n incoming targets, the position vectors in the inertial system are represented by r Mi With r Tj , the velocity vectors are represented as v Mi With v Tj , where i = 1, 2, ..., m, j = 1, 2, ..., n. The relative position vector and relative velocity vector are calculated as

[0053] r ij =r Tj –r Mi ,v ij =v Tj –v Mi

[0054] Then substitute it into the ZEM analytical formula to get

[0055]

[0056] In one embodiment, the traditional Hungarian algorithm can only deal with the binary allocation problem and cannot handle the many-to-many interception task target allocation problem, so it needs to be improved. According to the preset interception task, an intermediate matrix with k rows and l columns is constructed; k means that each target needs k interceptors to intercept, and l means that each interceptor needs to intercept l targets; the cost matrix J of the Hungarian algorithm is constructed = [J ij ], the cost matrix of the Hungarian algorithm is used as a matrix element to fill the intermediate matrix. After zero filling, a unified cost matrix of km×ln is obtained.

[0057] In one embodiment, the generalized differential geometry guidance is obtained as:

[0058]

[0059] Among them, n m is the velocity normal direction; that is, the direction in which the guidance command is applied. It can be seen that the above guidance law form is in the line of sight normal direction e q Projection newspaper in the direction and a to be designed mqTherefore, according to the generalized differential geometry guidance, the improved real proportional guidance law is:

[0060]

[0061] Select the command application direction as the three-dimensional pure proportional guidance direction:

[0062]

[0063] Specifically, simulation software is used to verify the correctness of the proposed many-to-many task allocation method. The scenario is set as 9 missiles intercepting 3 incoming targets, with r mc =(x mc ,y mc ,z mc )=(10,10,0)km as the center, and the positions of the 9 interceptor missiles are r mc +(1,0,0)km,r mc +(0,1,0)km,r mc +(0,0,1)km,r mc -(1,0,0)km,r mc -(0,1,0)km,r mc -(0,0,1)km,r mc +(2,0,0)km,r mc +(0,2,0)km,r mc +(0,0,2)km, design v mc =1800*(cos(45°)cos(-45°),sin(45°),-cos(45°)sin(-45°))m / s, the speeds of the 9 interceptor missiles are v mc +(100,0,0)m / s,v mc +(0,100,0)m / s,v mc +(0,0,100)m / s,v mc -(100,0,0)m / s,v mc -(0,100,0)m / s,v mc -(0,0,100)m / s,v mc +(200,0,0)m / s,v mc +(0,200,0)m / s,v mc+(0,0,200)m / s. The speed of the incoming target is 2000m / s, and the position vectors are (60,30,60)km, (50,32,62)km, (62,28,50)km, respectively. The speed inclination is 0°, and the speed azimuth is 135°, 130°, 140°, respectively. The target makes a constant maneuver along the normal of the plane formed by the positive y-axis and the speed direction, and the maneuvering acceleration is 3g, -3g, -3g, respectively. The target allocation result is that target 1 is intercepted by interceptor missiles 3, 5, and 9, target 2 is intercepted by interceptor missiles 2, 4, and 8, and target 3 is intercepted by interceptor missiles 1, 6, and 7. The guidance parameter design in the simulation is N=3.

[0064] According to the allocation results, interception simulation is performed. The simulation results are as follows: Figures 2 to 4 shown. Figure 3 The figure is a schematic diagram of the guidance acceleration curves of 9 interceptor missiles. The reason for the sudden drop in terminal acceleration is that a guidance blind zone is added to the interceptor missile in the simulation. When the interceptor missile enters the blind zone, its acceleration is set to zero. Figure 2 The schematic diagram of the missile-target flight trajectory during the interception process is shown. Figure 4 A schematic diagram of the zero-control miss-value curves of 9 interceptor missiles is shown. It can be seen that according to the allocation results and the proposed guidance law, the zero-control miss-value has been effectively eliminated, and all 9 interceptor missiles successfully intercepted the targets, verifying the effectiveness of the proposed method and guidance law.

[0065] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0066] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0067] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A multi-to-multi task allocation method based on minimizing zero-control miss distance, characterized in that: The method comprises: Establish the three-dimensional relative motion equation of projectile and target, and derive the analytical expression and dynamic equation of zero-control miss distance; Calculating the zero-control miss distance value between each interceptor missile and the target according to the initial conditions of terminal guidance and the zero-control miss distance analytical formula; According to the preset interception task, an intermediate matrix is ​​constructed, and the cost matrix of the Hungarian algorithm is filled into the intermediate matrix as a matrix element to obtain a unified cost matrix; Substituting the zero-control miss value into the unified cost matrix, and generating a many-to-many task allocation scheme based on the Hungarian algorithm; An improved realistic true proportional guidance law for eliminating zero-control miss amount is designed, and the improved realistic true proportional guidance law is adopted to realize the many-to-many task allocation scheme.

2. The method according to claim 1, characterized in that The construction of the three-dimensional projectile-target relative motion equation comprises: The three-dimensional relative motion equation of projectile and target is constructed as: Among them, a ir 、a iq 、a iω , i = t, m represents the acceleration of the target and the interceptor respectively r 、e q 、e ω Projection of direction, ω s With Ω s represent the angular rates of rotation of the line of sight and the plane respectively.

3. The method according to claim 2, characterized in that The analytical formula of the zero-control miss amount is derived, and the dynamic equation of the zero-control miss amount is derived according to the relative motion equation, including: The calculation formula for constructing the zero-control miss amount is: Where ZEM represents the zero control miss distance, r = r T –r M is the relative distance vector between the projectile and the target, r M With r T They represent the position vectors of the interceptor missile and the target in the inertial system, v = v T –v M is the relative velocity vector of the projectile and target, v M With v T They represent the velocity vectors of the interceptor missile and the target in the inertial system, t go =t f –t is the remaining flight time of the interceptor missile, t f is the final guidance terminal moment or collision moment, δ represents the pointing error; The sine value of the pointing error δ is selected as the intermediate variable, and the equation relationship is established: Among them, v q is the relative velocity vector of the projectile and the target along e q Directional projection; According to the expression of the line of sight rotation rate in the plane, the calculation expression of the zero control miss value is obtained as follows: The time derivative of the zero-control miss value calculation expression is performed to obtain the time derivative expression: According to the time derivative expression and the three-dimensional projectile-target relative motion equation, the zero-control miss distance dynamic equation is obtained as follows:

4. The method according to claim 1, characterized in that: The method constructs an intermediate matrix according to the preset interception task, and fills the cost matrix of the Hungarian algorithm as a matrix element into the intermediate matrix to obtain a unified cost matrix, including: According to the preset interception mission, an intermediate matrix with k rows and l columns is constructed; k means that each target needs k interceptor missiles to intercept, and l means that each interceptor missile needs to intercept l targets; Construct the cost matrix J of the Hungarian algorithm = [J ij ], the cost matrix of the Hungarian algorithm is used as a matrix element to fill the intermediate matrix, and after zero filling, a unified cost matrix of km×ln is obtained.

5. The method according to claim 2, characterized in that: Design an improved realistic proportional guidance law to control zero miss distance, including: The generalized differential geometry guidance form is obtained as: Among them, n m is the velocity normal; According to the generalized differential geometry guidance, the improved real proportional guidance law is: Select the command application direction as the three-dimensional pure proportional guidance direction:

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