CN-122018545-A - Bias differential game collaborative interception method based on area coverage

CN122018545ACN 122018545 ACN122018545 ACN 122018545ACN-122018545-A

Abstract

The invention belongs to the technical field of collaborative interception guidance, and particularly relates to a bias differential game collaborative interception method based on regional coverage. The method comprises the steps of establishing a probability distribution model of a target in an interception plane, carrying out Monte Carlo sampling, converting coverage strategy design into an optimal coverage problem of a limited central point in the interception plane, carrying out segmentation and iteration on standard maneuvers of each interceptor through a Voronoi diagram method to obtain standard maneuvers a Tsi of each interceptor, deploying the standard maneuvers a Tsi of each interceptor to corresponding optimal array positions based on the standard maneuvers a Tsi of each interceptor, carrying out bias item design of a differential game guidance law, jointly realizing the deviation of coverage range of each interceptor, and finally completing the optimal coverage and interception of the target. The method provided by the invention overcomes the limitation of the existing disc coverage model on simplifying the maneuvering distribution and the defect that only a fixed solution can be used, obviously reduces the off-target amount and overload requirement of the interceptor and improves the intercepting efficiency.

Inventors

WANG XIAO
WANG WEI
DONG CHANGHONG

Assignees

北京航空航天大学

Dates

Publication Date: 20260512
Application Date: 20250917

Claims (7)

1. A bias differential game collaborative interception method based on area coverage is characterized by comprising the following steps: s1, establishing a probability distribution model of a target in an interception plane, and carrying out Monte Carlo sampling to convert coverage strategy design into an optimal coverage problem of limited center points in the interception plane, wherein each center point corresponds to a standard maneuver of an interceptor; S2, dividing and iteratively solving the standard maneuver of each interceptor in S1 by using a Voronoi diagram method to obtain a standard maneuver a Tsi of each interceptor, namely an optimal coverage strategy; And S3, based on the standard maneuver a Tsi of each interceptor, deploying to the corresponding optimal array position and designing the bias item of the differential game guidance law, jointly realizing the offset of the coverage range of each interceptor, and finally completing the optimal coverage and interception of the target.
2. The biased differential game collaborative interception method based on area coverage according to claim 1, wherein the interception plane refers to a plane where an interceptor meets a target under the assumption of linearization, which is perpendicular to the line of sight direction, and is simplified to be in units of acceleration due to the fact that the remaining flight time t f of the interceptor and the target is the same.
3. The bias differential game collaborative interception method based on area coverage is characterized in that the specific process of the step S1 is that a target maneuvering probability distribution model is built by designing a target-based reference characteristic and a typical combat scene, any point xi in the maximum reachable area of the target is taken, and sampling is carried out on the probability distribution model of the point xi to obtain sampling points N ξ represents the total sample size, and the probability density-based integration operation is converted into the summation operation of the sampling points by means of monte carlo sampling, so that the coverage performance function of the center point a Tsj on the xi i measured by the square of the distance becomes: h(a Tsj ,ξ i )＝||a Tsj -ξ i || 2 (1) The coverage performance expression for the xi i point is: The total coverage performance function for all sample points is: Thus, the mathematical description of the area coverage problem is converted into a coordinate a Ts1 ,a Ts2 ,…,a TsN that finds N center points in the intercept plane, so that the above total coverage performance function is minimized, namely: Where a Tsj represents the coordinates of the center point a Tsj in the intercept plane and ζ i represents the coordinates of the sample point ζ i in the intercept plane.
4. The biased differential game collaborative interception method based on regional coverage according to claim 3, wherein the probability distribution model is established by the following steps that guidance law assumption a T obeys a mean value of 0 and variance of 0 Is a two-dimensional gaussian distribution independent of each other, and the specific formula is as follows: Where a Ty denotes acceleration of the target in the y-direction, a Tz denotes acceleration of the target in the z-direction, a Tmax denotes maneuver capability of the target, and a Tmax is not a hard boundary of maneuver of the target, but is used as a variance parameter.
5. The biased differential game collaborative interception method based on area coverage according to claim 4, wherein the specific process of step S2 is to define all points ζ ij ,i＝1,2,…,N ξj closest to the center point a Tsj to form an area The performance function is expressed as: consider a single optimization Then the method can split N mutually incoherent optimization problems, and further can continuously split 2N mutually incoherent optimization problems on the assumption that the coverage performance in the y and z directions are mutually independent: Taking solution J jy as an example, deriving a Tsjy to obtain a derivative of 0: And similarly, obtaining the optimization results of all the center point coordinates: Wherein: when j=0, the number of the groups, Is set to be 0, the number of the components is set to be 0, Is 0; Repeating the above process according to the new center point Constructing a new region And performing one round of optimization until the change of the coordinates of the central point is smaller than the set value, finally obtaining the corresponding standard maneuver a Tsi ,a Ts1 ,a Ts2 ,…,a TsN of each interceptor M i , wherein the standard maneuver a Tsi ,a Ts1 ,a Ts2 ,…,a TsN actually corresponds to the center of the coverage range of each interceptor, and the standard maneuver a Tsi is defined as a parameter describing the deviation of the coverage range of the interceptor.
6. The method for collaborative interception of biased differential game based on area coverage according to claim 5 wherein the specific procedure of deploying standard maneuver a Tsi based on each interceptor to corresponding optimal array in step S3 is that assuming a Tsi of each interceptor has been obtained and the remaining time of flight t f is known, the intercept plane coordinates are reconverted to units of distance, the center coordinates of each interceptor coverage are In practice, the projection of the optimal shift position in the interception plane is that the vertical distance from the optimal shift position to the interception plane is V ix t f , so the optimal shift position coordinate corresponding to the shift moment can be solved based on the circle center coordinates a Tsi and t f , and under the condition that the interception plane and the origin point coordinate are known, under the ballistic coordinate system of one interceptor at the collision moment, the optimal shift position coordinates of the rest interceptors are as follows: where a Tsiy and a Tsiz represent the coordinates in the y and z directions, respectively, in the intercept plane.
7. The area coverage-based bias differential game collaborative interception method according to claim 6, wherein the specific process of the bias item design of the differential game guidance law based on the standard maneuver a Tsi of each interceptor in the step 3 is that the interceptor and the target command acceleration of the traditional differential game guidance law are as follows, without considering the control cost and the maneuver has the upper limit: Wherein ZEM (t) represents zero control off-target quantity, a Tmax represents the maneuverability of a target, and a Mmax represents the maneuverability of an interceptor; In order to truly realize offset of the coverage range of the interceptor, the differential game guidance law is similarly processed based on the improved thought of the proportional guidance method by the existing method, wherein the similar processing is that the bias item ZEMB (t) is designed for the game guidance law on the basis of ZEM (0) provided by the coverage strategy, the actual zero control off-target quantity is biased based on the bias item ZEMB (t) of the game guidance law, and the instruction acceleration is calculated by the following formula: The coverage offset of one interceptor may be described by the parameter a Ts , called standard maneuver, ZEM (0) and ZEMB (t) set according to standard maneuver a Ts as follows: Where t f represents the remaining time of flight at the time of shift, and t go represents the remaining time of flight at the current time.

Description

Bias differential game collaborative interception method based on area coverage Technical Field The invention belongs to the technical field of collaborative interception guidance, and particularly relates to a bias differential game collaborative interception method based on regional coverage. Background The problem of collaborative interception guidance has been attracting attention in recent years, and is a hotspot problem in the aerospace field. In order to cope with the threat of a target with stronger maneuverability to defense, the interception hit rate is improved, the cooperative interception of the target is necessarily realized by adopting a mode of mutually matching a plurality of interceptors, in the cooperative interception process, the interceptor areas of each interceptor are limited, in order to ensure that the intercepting areas of a plurality of interceptors almost or completely cover the possible areas of the target, an efficient area coverage optimization method is required to be researched, and the idea of the existing optimization method is to simplify the method into a disc coverage model, namely, the ratio of a small circle to a large circle radius is determined according to the maneuvering ratio of the interceptors to the target. Under the condition of a given ratio, the determined minimum coverage circle number and the optimal space configuration scheme thereof exist, the disc coverage model can directly call the corresponding minimum interceptor number and the optimal distribution mode according to different value intervals of the ratio, and the problem is that the conditions of target maneuver distribution and the like are simplified excessively and the method is only suitable for the conditions of uniform distribution of the target maneuver circles. And the circular coverage model can only apply a few fixed solutions, and can not realize the optimization of the array coverage effect under the condition of given interceptors. The existing terminal guidance law is basically designed based on a proportional guidance method to perform bias item design, so that the directional offset of the coverage center of the interceptor can be realized. However, the interception performance of the proportional guidance method is limited, so that the requirement on the maneuverability of the interception bomb is high, and the coverage area is smaller when the interception bomb has the same maneuverability in an interception plane. Disclosure of Invention The invention solves the problem that the existing area coverage optimization method cannot realize the optimization of the array coverage effect under the condition of the given number of interceptors and the problem that the coverage area of the interceptors is small in the existing terminal guidance law design, and provides an offset differential game collaborative interception method based on area coverage. The technical scheme of the invention is as follows: a bias differential game collaborative interception method based on area coverage comprises the following steps: s1, establishing a probability distribution model of a target in an interception plane, and carrying out Monte Carlo sampling to convert coverage strategy design into an optimal coverage problem of limited center points in the interception plane, wherein each center point corresponds to a standard maneuver of an interceptor; S2, dividing and iteratively solving the standard maneuver of each interceptor in S1 by using a Voronoi diagram method to obtain a standard maneuver a Tsi of each interceptor, namely an optimal coverage strategy; And S3, based on the standard maneuver a Tsi of each interceptor, deploying to the corresponding optimal array position and designing the bias item of the differential game guidance law, jointly realizing the offset of the coverage range of each interceptor, and finally completing the optimal coverage and interception of the target. Preferably, the interception plane refers to a plane where the interceptor meets the target under the assumption of linearization, and is perpendicular to the direction of the line of sight, and the interception plane is simplified to be in units of acceleration due to the fact that the remaining flight time t f of the interceptor and the target is the same. Preferably, the specific process of the step S1 comprises the steps of designing a probability distribution model based on the reference characteristic and typical combat scene of the target, establishing the maneuvering probability distribution model of the target, sampling any point xi in the maximum reachable area of the target, and sampling the probability distribution model of the point xi to obtain a sampling pointN ξ represents the total sample size, and the probability density-based integration operation is converted into the summation operation of the sampling points by means of monte carlo sampling, so that the coverage performance function of the center