A multiple-to-multiple task allocation method based on minimizing zero-control miss distance
By establishing a three-dimensional relative motion equation between the missile and the target and improving the Hungarian algorithm, combined with generalized differential geometry guidance, an improved real-proportional guidance law was designed, which solved the problem of low interception efficiency of multiple incoming targets in the existing technology and realized efficient many-to-many task allocation and interception.
Patent Information
- Application Number
- CN202510131588.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-06
- Publication Date
- 2026-02-24
- Estimated Expiration
- 2045-02-06
AI Technical Summary
Existing technologies suffer from the problem of two-dimensional linear assumptions in intercepting multiple incoming targets, resulting in inefficient computation, the need for a large amount of data for learning, poor environmental adaptability, low interception efficiency, and insufficient projection of the interception guidance law in the line-of-sight direction.
A three-dimensional relative motion equation between the projectile and the target is established, the analytical and dynamic equations of the zero-control miss distance are derived, the Hungarian algorithm is improved, and the generalized differential geometry guidance law is combined with the improved real-world proportional guidance law. Through the combination of improved real-world technologies, an effective guidance method to suppress the zero-control miss distance is designed, and the improved real-world true proportional guidance law is used for many-to-many task allocation.
It improves the solution speed of many-to-many task allocation, reduces the zero-control miss rate, increases the interception success rate, and achieves a highly efficient three-dimensional interception effect.
Smart Images
Figure CN119960472B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of aircraft control technology, and in particular to a many-to-many task allocation method based on minimizing zero-control miss distance. Background Technology
[0002] With the continuous development of collaborative technologies, saturation strikes against ground targets are an effective means to enhance lethality and improve penetration. However, from the defender's perspective, achieving effective task allocation and interception of multiple incoming targets faces significant challenges. Current methods suffer from the problem of two-dimensional linear assumptions in modeling, and allocation methods are mostly based on intelligent means, including genetics, particle swarm optimization, deep learning, and reinforcement learning. These methods suffer from problems such as low computational efficiency, the need for large amounts of data for learning, and poor environmental adaptability. Furthermore, the interception guidance law suffers from insufficient projection in the line-of-sight direction, leading to low interception efficiency. Therefore, there is an urgent need to propose an efficient three-dimensional interception many-to-many task allocation method and a guidance law that effectively eliminates zero-control misses. Summary of the Invention
[0003] Therefore, it is necessary to provide a many-to-many task allocation method based on minimizing the zero-control miss rate to address the above-mentioned technical problems.
[0004] A many-to-many task allocation method based on minimizing zero-control misses, the method comprising:
[0005] Establish the three-dimensional relative motion equations between the projectile and the target, and derive the analytical and dynamic equations for the zero-control miss distance.
[0006] Based on the initial conditions of terminal guidance and the analytical formula for zero-control miss distance, calculate the zero-control miss distance between each interceptor missile and the target;
[0007] Based on the pre-set interception task, an intermediate matrix is constructed, and the cost matrix of the Hungarian algorithm is used as a matrix element to fill the intermediate matrix to obtain a unified cost matrix;
[0008] Substitute the zero-control miss value into the unified cost matrix, and generate a many-to-many task allocation scheme based on the Hungarian algorithm;
[0009] An improved real-proportional guidance law is designed to eliminate zero-control miss distance, and the improved real-proportional guidance law is used to implement the many-to-many task allocation scheme.
[0010] In one embodiment, the method further includes: constructing the three-dimensional relative motion equations of the projectile and the target as follows:
[0011]
[0012] Among them, a ir a iq a iωi = t and m represent the accelerations of the target and the interceptor missile at time e, respectively. r e q e ω Projection of direction, ω s With Ω s These represent the angular velocities of rotation of the line of sight and the plane, respectively.
[0013] In one embodiment, the method further includes: constructing a k-row, l-column intermediate matrix according to a pre-set interception task; where k represents that each target requires k interceptor missiles to intercept, and l represents that each interceptor missile needs to intercept l targets;
[0014] Construct the cost matrix J = [J] of the Hungarian algorithm ij The cost matrix of the Hungarian algorithm is used as matrix element to fill the intermediate matrix. After zeroing, 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] Where, n m For velocity normal;
[0018] Based on the generalized differential geometry guidance, the improved real true proportional guidance law is as follows:
[0019]
[0020] Select the command application direction as a three-dimensional pure proportional guidance direction:
[0021]
[0022] The aforementioned multi-to-multi task allocation method based on minimizing zero-control miss distance first establishes a three-dimensional missile-target relative motion equation, derives the analytical and dynamic equations of the zero-control miss distance, and analyzes the relationship between the zero-control miss distance and the components of the guidance command. Second, it calculates the zero-control miss distance between each interceptor missile and the target based on the initial conditions of terminal guidance. Then, it improves the cost matrix form of the Hungarian algorithm to adapt it to multi-to-multi task target allocation. Next, it substitutes the calculated zero-control miss distance between the missile and the target into the improved cost matrix, generating a multi-to-multi task allocation scheme based on the Hungarian algorithm. Furthermore, it designs an improved realistic true proportional guidance law to effectively suppress the zero-control miss distance. Finally, it uses the improved realistic true proportional guidance for the interceptor missile and intercepts the allocated targets according to the allocation scheme. Compared to 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 improved Hungarian algorithm has a much faster solution speed than the intelligent algorithm, and the solution results can minimize the zero-control miss distance during interception. The designed guidance law adopts an advanced generalized differential geometry guidance form, which can effectively eliminate the zero-control miss distance and increase the interception success rate. Attached Figure Description
[0023] Figure 1 This is a flowchart illustrating a many-to-many task allocation method based on minimizing zero-control misses in one embodiment;
[0024] Figure 2 This is a schematic diagram of the missile's flight trajectory during the interception process in one embodiment;
[0025] Figure 3 This is a schematic diagram of the guidance acceleration curves of six interceptor missiles in one embodiment;
[0026] Figure 4 This is a schematic diagram of the zero-control miss distance curves of six interceptor missiles in one embodiment. Detailed Implementation
[0027] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0028] In one embodiment, such as Figure 1 As shown, a many-to-many task allocation method based on minimizing zero-control misses is provided, including the following steps:
[0029] Step 102: Establish the three-dimensional relative motion equations of the projectile and the target, and derive the analytical and dynamic equations of the zero-control miss distance.
[0030] Step 104: Calculate the zero-control miss distance between each interceptor missile and the target based on the initial terminal guidance conditions and the analytical formula for zero-control miss distance.
[0031] Step 106: Based on the pre-set interception task, construct an intermediate matrix and fill the intermediate matrix with the cost matrix of the Hungarian algorithm as matrix elements to obtain a unified cost matrix.
[0032] Step 108: Substitute the zero-control miss value into the unified cost matrix and generate a many-to-many task allocation scheme based on the Hungarian algorithm.
[0033] Step 110: Design an improved real-proportional guidance law to control the zero-control miss distance, and use the improved real-proportional guidance law to realize a many-to-many task allocation scheme.
[0034] In the aforementioned multi-to-multi task allocation method based on minimizing zero-control miss, the following steps are taken: First, a three-dimensional relative motion equation between the missile and the target is established, and the analytical and dynamic equations of the zero-control miss are derived. The relationship between the zero-control miss and the components of the guidance command is analyzed. Second, the zero-control miss values between each interceptor missile and the target are calculated based on the initial conditions of terminal guidance. Then, the cost matrix form of the Hungarian algorithm is improved to adapt to multi-to-multi task target allocation. Next, the calculated zero-control miss values between the missile and the target are substituted into the improved cost matrix, and a multi-to-multi task allocation scheme is generated based on the Hungarian algorithm. Furthermore, an improved real-proportional guidance law is designed to effectively suppress the zero-control miss. Finally, the interceptor missile is guided using the improved real-proportional guidance, and the allocated target is intercepted according to the allocation scheme.
[0035] In one embodiment, the three-dimensional relative motion equations of the projectile and the target are constructed as follows:
[0036]
[0037] Among them, a ir a iq a iω i = t and m represent the accelerations of the target and the interceptor missile at time e, respectively. r e q e ω Projection of direction, ω s With Ω s These represent the angular velocities of rotation of the line of sight and the plane, respectively.
[0038] In another embodiment, the zero-efffort miss (ZEM) represents the nominal miss distance between the missile and the target in an uncontrolled state (with zero guidance acceleration). Ideally, without considering the effects of aerodynamic forces and gravity, the formula for calculating the zero-efffort miss is as follows:
[0039]
[0040] Where ZEM represents the zero-control miss distance, r = r T -r M r is the relative distance vector between the projectile and the target. M With r T Let v = v0 and v0 represent the position vectors of the interceptor missile and the target in the inertial frame, respectively. T -v M Let v be the relative velocity vector between the projectile and the target. M With v T Let t represent the velocity vectors of the interceptor missile and the target in the inertial frame, respectively. go =t f –t represents the remaining flight time of the interceptor missile, t f The terminal guidance moment, also known as the collision moment, is δ, which represents the pointing error.
[0041] Choosing the sine value of the pointing error δ as an intermediate variable, an equation is established:
[0042]
[0043] Among them, v q The relative velocity vector between the projectile and the target along e q Projection of direction.
[0044] Based on the expression for the line-of-sight rotation rate in the plane, the expression for calculating the zero-control miss distance is as follows:
[0045]
[0046] Taking the time derivative of the expression for calculating the zero-control miss distance, we obtain the time derivative expression as follows:
[0047]
[0048] Based on the time derivative expression and the three-dimensional projectile-target relative motion equation, the kinematic equation for zero-control miss distance is obtained as follows:
[0049]
[0050] As shown in the above formula, ZEM is actually determined by the difference between the commanded acceleration of the interceptor and the target along the line-of-sight direction, and the difference between their commanded accelerations along the line-of-sight normal. Further observation of the coefficients of the two commanded acceleration terms reveals that they represent the approach velocities along the line-of-sight direction of the interceptor and the target. Relative velocity v to the line of sight in the plane q =ω s r.
[0051] Considering the high-speed interception scenario and the relatively long correction time during the interceptor missile's guidance, the interceptor missile has initially formed a good interception geometry. Therefore, in the terminal guidance phase, it has a high missile-target approach velocity, while its relative velocity along the line-of-sight normal is relatively small. On the other hand, in order to achieve their respective objectives—successful interception and timely escape—both the interceptor missile and the incoming target will maximize the projection of the command acceleration along the line-of-sight normal. Therefore, the value in parentheses in the second term is considered to be a small quantity. Thus, according to the analysis, it can be concluded that... a mq The command is more efficient at controlling ZEM.
[0052] In one embodiment, assuming there are m interceptor missiles and n incoming targets, the position vectors in the inertial frame are respectively represented as r Mi With r Tj The velocity vectors are respectively expressed as v Mi With v Tj Where i = 1, 2, ..., m, j = 1, 2, ..., n. Calculate the relative position vector and relative velocity vector as follows:
[0053] r ij =r Tj -r Mi ,v ij =v Tj -v Mi
[0054] Then, substituting into the ZEM analytical formula, we obtain...
[0055]
[0056] In one embodiment, since the traditional Hungarian algorithm can only handle binary allocation problems and cannot handle target allocation problems in many-to-many interception tasks, it needs to be improved. Based on the pre-set interception task, a k-row, l-column intermediate matrix is constructed; where k represents that each target requires k interceptor missiles to intercept, and l represents that each interceptor missile needs to intercept l targets; the cost matrix J = [J...] of the Hungarian algorithm is then constructed. ij The cost matrix of the Hungarian algorithm is used as matrix element to fill the intermediate matrix. After zeroing, a unified cost matrix of km×ln is obtained.
[0057] In one embodiment, the generalized differential geometry guidance is obtained as follows:
[0058]
[0059] Where, n m This is the velocity normal; that is, the direction in which the guidance command is applied. It can be seen that the above guidance law form applies to the line-of-sight normal e. q Directional projection of the newspaper and the design to be used. mqConsistent. Therefore, based on generalized differential geometry guidance, the improved real true proportional guidance law is:
[0060]
[0061] Select the command application direction as a three-dimensional pure proportional guidance direction:
[0062]
[0063] Specifically, simulation software was used to verify the correctness of the proposed many-to-many task allocation method. The scenario was set as nine missiles intercepting three incoming targets, with r... mc =(x mc ,y mc ,z mc Centered on (10,10,0)km, 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, where the velocities 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 incoming target has a velocity of 2000m / s, with position vectors of (60,30,60)km, (50,32,62)km, and (62,28,50)km, all with velocity inclination angles of 0° and velocity azimuth angles of 135°, 130°, and 140°, respectively. The target performs constant maneuvers along the normal to the plane formed by the positive y-axis and the velocity direction, with maneuver accelerations of 3g, -3g, and -3g, respectively. The target allocation is as follows: 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 in the simulation is designed as N=3.
[0064] Based on the allocation results, an interception simulation is performed, and the simulation results are as follows: Figures 2 to 4 As shown. Figure 3 The diagram shows the guidance acceleration curves of nine interceptor missiles. The reason for the sudden decrease in terminal acceleration is that a guidance blind zone was added to the interceptor missiles in the simulation. When the interceptor missiles enter the blind zone, their acceleration is set to zero. Figure 2 The diagram shows the trajectory of the missile during the interception process. Figure 4 The diagram shows the zero-control miss distance curves of nine interceptor missiles. It can be seen that, based on the allocation results and the proposed guidance law, the zero-control miss distance was effectively eliminated, and all nine interceptor missiles successfully intercepted the target, verifying the effectiveness of the proposed method and guidance law.
[0065] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, 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. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.
[0066] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0067] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.
Claims
1. A many-to-many task allocation method based on minimizing zero-control miss distance, characterized in that, The method includes: Establish the three-dimensional relative motion equations between the projectile and the target, and derive the analytical and dynamic equations for the zero-control miss distance. Based on the initial conditions of terminal guidance and the analytical formula for zero-control miss distance, calculate the zero-control miss distance between each interceptor missile and the target; Based on the pre-set interception task, an intermediate matrix is constructed, and the cost matrix of the Hungarian algorithm is used as a matrix element to fill the intermediate matrix to obtain a unified cost matrix; Substitute the zero-control miss value into the unified cost matrix, and generate a many-to-many task allocation scheme based on the Hungarian algorithm; An improved real-proportional guidance law is designed to eliminate zero-control miss distance, and the improved real-proportional guidance law is used to implement the many-to-many task allocation scheme.
2. The method according to claim 1, characterized in that, The construction of the three-dimensional relative motion equations between the projectile and the target includes: The three-dimensional equations of relative motion between the projectile and the target are as follows: ； in, , These represent the accelerations of the target and the interceptor missile, respectively. Projection of direction and These represent the angular velocities of rotation of the line of sight and the plane, respectively.
3. The method according to claim 2, characterized in that, Deriving the analytical expression for the zero-control miss distance, and deriving the dynamic equation for the zero-control miss distance based on the relative motion equation, including: The formula for calculating the zero-control miss distance is as follows: ； ZEM represents the zero-control miss distance. The relative distance vector between the projectile and the target. and Let represent the position vectors of the interceptor missile and the target in the inertial frame, respectively. The relative velocity vector between the projectile and the target. and Let these represent the velocity vectors of the interceptor missile and the target in the inertial frame, respectively. The remaining flight time of the interceptor missile, The terminal guidance moment, also known as the collision moment, is the moment when the guidance system terminates. Indicates pointing error; Select the pointing error Using the sine value as an intermediate variable, establish an equation: ； in, The relative velocity vector of the projectile and the target along Projection of direction; Based on the expression for the line-of-sight rotation rate in the plane, the expression for calculating the zero-control miss distance is as follows: ； Taking the time derivative of the expression for calculating the zero-control miss distance, we obtain the time derivative expression as follows: ； Based on 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 step of constructing an intermediate matrix according to a pre-set interception task, and filling the intermediate matrix with the cost matrix of the Hungarian algorithm as matrix elements to obtain a unified cost matrix includes: Based on the pre-set interception task, build k OK l The middle matrix of the columns; where, k This indicates that each objective requires k One interceptor missile intercepts it. l This indicates that each interceptor missile needs to be intercepted. l One goal; Constructing the cost matrix of the Hungarian algorithm The cost matrix of the Hungarian algorithm is used as matrix elements to fill the intermediate matrix. After padding with zeros, the following is obtained: km × ln The unified cost matrix.
5. The method according to claim 2, characterized in that, Design an improved real proportional guidance law to control the zero-control miss distance, including: The generalized differential geometry guidance form is obtained as follows: ； in, For velocity normal, This represents the acceleration vector of the interceptor missile; Based on the generalized differential geometry guidance, the improved real true proportional guidance law is as follows: ； in, N These are guidance parameters; Select the command application direction as a three-dimensional pure proportional guidance direction: 。