Cluster optimal coverage cooperative guidance method for intercepting high maneuvering target

Abstract

The invention discloses a cluster optimal coverage cooperative guidance method for intercepting a high maneuvering target. The method comprises the following steps: setting an interceptor control instruction; setting an optimization function by taking the minimum total overload of the interceptor as a target; according to the optimization function, obtaining a coverage mode with the minimum overload at the current moment; based on the coverage mode, setting the number of interceptors and the initial coverage upper limit of each interceptor; according to the initial coverage upper limit of the interceptor, the initial speed direction of the interceptor is obtained, the interceptor flies in the initial speed direction by adopting the set control instruction, and target interception is achieved. According to the cluster optimal coverage cooperative guidance method for intercepting the high maneuvering target, the target can be effectively intercepted under the condition that the maneuvering capability of the target is higher than that of the interceptor, and the total overload consumption and the energy consumption of the interceptor are small.

Description

Technical Field

[0001] The present invention relates to a cluster optimal coverage cooperative guidance method for intercepting highly maneuverable targets, belonging to the technical field of flight control. Background Art

[0002] In the face of highly maneuverable targets, the existing interception strategies can be roughly divided into two modes: saturation interception and estimating the target acceleration. The former essentially completes the interception by virtue of an obvious numerical advantage, and through the cooperative positioning of multiple interceptors, completes the cooperative encirclement of the target. However, this method is only applicable to interception with an advantage in overload. For targets with a maneuverability superior to that of the interceptors, it is difficult to complete the interception with high guidance accuracy at the end; the latter, due to the lack of sensors directly perceiving the target maneuverability, mainly relies on Kalman filter estimation for obtaining the target acceleration information. However, this method is difficult to accurately predict the magnitude of the target acceleration and cannot be directly applied to engineering practice.

[0003] In addition, to solve the problem of low interception probability of highly maneuverable targets, the prior art has also proposed a multi-to-one interception strategy based on the coverage theory. This method makes the interception domain of the interceptors cover the reachable domain of the target by changing the magnitudes of the bias terms of multiple interceptors. However, most of the above methods keep the division and coverage method of the target maneuver domain fixed and evenly distribute them according to the number of interceptors, resulting in a relatively high overall overload consumption and greatly increasing the energy cost.

[0004] Due to the above reasons, it is necessary to conduct in-depth research on the existing methods for intercepting highly maneuverable targets to solve the above problems. Summary of the Invention

[0005] In order to overcome the above problems, in-depth research has been carried out and a cluster optimal coverage cooperative guidance method for intercepting highly maneuverable targets is proposed, including the following steps:

[0006] S1. Set the control command of the interceptor;

[0007] S2. Set an optimization function with the minimum total overload of the interceptors as the goal;

[0008] S3. According to the optimization function, obtain the coverage method with the minimum overload at the current moment;

[0009] S4. Based on the coverage method, set the number of interceptors and the initial coverage upper limit of each interceptor;

[0010] S5. According to the initial coverage upper limit of the interceptors, obtain the initial velocity direction of the interceptors. The interceptors fly with the set control command in this initial velocity direction to achieve the interception of the target.

[0011] In a preferred embodiment, in S1, the interceptor control command is set as:

[0012]

[0013] where a i represents the acceleration of the i-th interceptor, N is the proportional navigation coefficient, and t go,i is the remaining flight time of the i-th interceptor, ZEM i is the zero-effort miss of the i-th interceptor, and B i is the proportional navigation bias term of the i-th interceptor.

[0014] In a preferred embodiment, in S2, the objective function of the optimization function is set as:

[0015] f(A1,A2…A n ) = u1 2 + u2 2 + … + u n 2

[0016]

[0017] where A i represents the upper limit of the interception domain coverage of the i-th interceptor, a m,max represents the upper limit of the maneuverability of the interceptor, q i0 represents the initial line-of-sight angle of the i-th interceptor

[0018] u i represents the overload consumption of the i-th interceptor and is in the form of the upper limit of the interception domain coverage of the interceptor used.

[0019] In a preferred embodiment, in S2, the constraints of the optimization function are expressed as:

[0020]

[0021] where a Tmax represents the maximum acceleration of the target, C i represents the size of the interception domain of the i-th interceptor, q i0 represents the initial line-of-sight angle of the i-th interceptor, and n represents the total number of interceptors.

[0022] In a preferred embodiment, in S4, the number of interceptors satisfies the constraint:

[0023]

[0024] c min = min(c1,c n )

[0025] where NUM represents the number of interceptors, cmin represents the smaller value of c1 and c n in it.

[0026] In a preferred embodiment, in S4, the initial coverage upper limit of each interceptor is expressed as:

[0027]

[0028] where n = NUM, A i,0 represents the initial coverage upper limit of the i-th interceptor, A 1,0 represents the initial coverage upper limit of the 1st interceptor

[0029] In a preferred embodiment, in S5, based on the relationship between the velocity direction and the coverage upper limit and the initial coverage upper limit of the interceptor, the initial velocity direction of the interceptor is obtained through the relationship between the velocity direction and the coverage upper limit.

[0030] The relationship between the velocity direction and the coverage upper limit is expressed as:

[0031]

[0032] K T = cos(θ t + q i0 ), K Mi = cos(θ i - q i0 )

[0033] where K T , K Mi are intermediate variables.

[0034] The beneficial effects of the present invention include:

[0035] (1) It can effectively intercept the target when the target's maneuverability is higher than that of the interceptor;

[0036] (2) The overall overload consumption of the interceptor is small, saving energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Shows a schematic flow chart of the cluster optimal coverage cooperative guidance method for intercepting a highly maneuverable target according to a preferred embodiment of the present invention;

[0038] Figure 2 Shows the trajectory diagrams of the interceptor and the target under the fixed coverage method in Example 1 and Comparative Example 1;

[0039] Figure 3 Shows the comparison diagram of the acceleration control commands of the interceptor under the fixed coverage method in Example 1 and Comparative Example 1;

[0040] Figure 4Show the comparison chart of the total overload consumption of the interceptor under the fixed coverage method in Embodiment 1 and Comparative Example 1;

[0041] Figure 5 Show the trajectory charts of the interceptor and the target under the optimal array position guidance method with overload constraint in Embodiment 1 and Comparative Example 1;

[0042] Figure 6 Show the comparison chart of the acceleration control commands of the interceptor under the optimal array position guidance method with overload constraint in Embodiment 1 and Comparative Example 1;

[0043] Figure 7 Show the comparison chart of the total overload consumption of the interceptor under the optimal array position guidance method with overload constraint in Embodiment 1 and Comparative Example 1. Detailed implementation manners

[0044] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become more clearly defined.

[0045] The special term "exemplary" herein means "serving as an example, an embodiment or an illustration". Any embodiment described herein as "exemplary" does not necessarily have to be construed as superior to or better than other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings do not have to be drawn to scale unless otherwise specified.

[0046] A cluster optimal coverage cooperative guidance method for intercepting a highly maneuverable target provided by the present invention, as Figure 1 shown, includes the following steps:

[0047] S1. Set the control commands of the interceptor;

[0048] S2. Set the optimization function with the goal of minimizing the total overload of the interceptor;

[0049] S3. Obtain the coverage mode with the minimum overload at the current moment according to the optimization function;

[0050] S4. Based on the coverage mode, set the number of interceptors and the initial coverage upper limit of each interceptor;

[0051] S5. According to the initial coverage upper limit of the interceptor, obtain the initial velocity direction of the interceptor. The interceptor flies with the initial velocity direction and uses the set control commands to intercept the target.

[0052] In the present invention, the kinematic equation is satisfied between the target and the interceptor, which is expressed as:

[0053]

[0054] where, r iDenotes the distance between the $i$-th interceptor and the target, $q$ i Denotes the line-of-sight angle of the $i$-th interceptor, $\theta$ i Denotes the velocity direction angle of the $i$-th interceptor, $v$ i Denotes the velocity of the $i$-th interceptor, $a$ i Denotes the acceleration of the $i$-th interceptor, $v$ t Denotes the velocity of the target, $\theta$ t Denotes the velocity direction angle of the target, $a$ t Denotes the velocity of the target, and the superscript $\cdot$ represents the first derivative.

[0055] In $S1$, the interceptor control command is set as:

[0056]

[0057] where $a$ i Denotes the acceleration of the $i$-th interceptor, $N$ is the proportional navigation coefficient, $t$ go,i is the remaining flight time of the $i$-th interceptor, $ZEM$ i is the zero-effort miss of the $i$-th interceptor, $B$ i is the proportional navigation bias term of the $i$-th interceptor.

[0058] In $S2$, based on the set interceptor control command, the initial zero-effort miss constraint and the interceptable target maneuver range under this control command are:

[0059]

[0060] where $a$ m,max denotes the upper limit of the interceptor's maneuverability, $t$ f,i denotes the total flight time of the $i$-th interceptor's guidance phase, $ZEM$ 0,i denotes the zero-effort miss of the $i$-th interceptor at the initial moment, $q$ i0 denotes the initial line-of-sight angle of the $i$-th interceptor.

[0061] Then the size of the interceptor's intercept domain is independent of the bias, and the bias can only translate the intercept domain. The upper limit of the interceptor's intercept domain coverage is:

[0062]

[0063] where $A$ i denotes the upper limit of the intercept domain coverage of the $i$-th interceptor.

[0064] In $S2$, the objective function of the optimization function is set as:

[0065] $f(A1,A2…A$ n ) = u1 2 +u22 +…+u n 2

[0066]

[0067] Among them, A i represents the upper limit of the interception area coverage of the i-th interceptor, and a m,max represents the upper limit of the maneuverability of the interceptor, and q i0 represents the initial line-of-sight angle of the i-th interceptor

[0068] u i represents the overload consumption of the i-th interceptor, and is in the form of representing the upper limit of the interception area coverage of the adopted interceptor.

[0069] In S2, the constraints of the optimization function are expressed as:

[0070]

[0071] Among them, a Tmax represents the maximum acceleration of the target, C i represents the size of the interception area of the i-th interceptor, q i0 represents the initial line-of-sight angle of the i-th interceptor, and n represents the total number of interceptors.

[0072] In S3, the optimization problem is solved by the Lagrange function.

[0073] The Lagrange function is expressed as:

[0074]

[0075] Among them, λ0, λ1…λ n represents the Lagrange multiplier.

[0076] Then the necessary and sufficient conditions for the optimization problem are:

[0077]

[0078] For different Lagrange multipliers, the analytical solution of A i is as follows:

[0079] 1) λ i-1 = 0, λ i = 0

[0080]

[0081] 2) λ i-1 = 0, λ i ≠ 0

[0082]

[0083] 3) λ i-1 ≠0, λ i When λ = 0

[0084]

[0085] 4) λ i-1 ≠0, λ i When λ ≠ 0, λ ≠ 0

[0086]

[0087] where d i = NZEM i / t go,i 2 - a max (K Mi N - 2) / 2, K T = cos(θ t + q i0 ),K Mi = cos(θ i - q i0 )。

[0088] According to the analytical solution, A1 has 4 forms of analytical solutions, A i (i = 2 ···· n - 1) has 5 forms of analytical solutions, A n has 4 forms of analytical solutions. Through the KKT conditions of the original problem, only one set of A i (i = 1, 2 ···· n) meets all the inequality constraints, and this set of solutions is the coverage method with the minimum overload at the current moment. In the present invention, the method for judging the specific solution values will not be elaborated, and those skilled in the art can make judgments according to experience.

[0089] In S4, the number of interceptors satisfies the constraint:

[0090]

[0091] c min = min(c1, c n )

[0092] where NUM represents the number of interceptors, and min(c1, c n ) represents the smaller value between c1 and c n , that is, c min represents the smaller value in the interception areas of the 1st and the nth interceptors.

[0093] In the present invention, according to the above-mentioned number constraint of interceptors, those skilled in the art can select the specific number of interceptors according to actual needs.

[0094] Furthermore, the initial coverage upper limit of each interceptor is expressed as:

[0095]

[0096] where n = NUM, A i,0 represents the initial coverage upper limit of the i-th interceptor, and A 1,0 represents the initial coverage upper limit of the 1st interceptor.

[0097] In S5, on the premise that the initial velocity direction of the interceptor is controllable at the initial moment, the target velocity, relative distance, etc. should be determined by the incoming posture of the target. There should be a combination of the initial interceptor velocity and coverage method such that the overload at the initial moment is 0. Then the relationship between the velocity direction and the coverage upper limit is:

[0098]

[0099] K T = cos(θ t + q i0 ) =, K Mi = cos(θ i - q i0 )

[0100] where K T , K Mi are intermediate variables.

[0101] Through the above formula, taking A i,0 as A i , the initial velocity direction of the interceptor can be obtained.

[0102] Embodiment

[0103] Embodiment 1

[0104] A simulation experiment is carried out to intercept a highly maneuverable target. In the simulation experiment, the interceptor and the target are set as:

[0105] <![CDATA[Interceptor M1]]> <![CDATA[Interceptor M2]]> <![CDATA[Interceptor M3]]> Target Initial position (m) (0,0) (0,0) (0,0) (50000,0) Speed (m / s) 7Ma 7Ma 7Ma 6Ma Initial velocity direction (°) 4.4 0 -4.4 180 <![CDATA[Mobility (m / s 2 )]]> 3.3g 3.3g 3.3g 4g

[0106] The simulation process includes the following steps:

[0107] S1. Set the control command of the interceptor;

[0108] S2. Set the optimization function with the goal of minimizing the total overload of the interceptor;

[0109] S3. Obtain the coverage method with the minimum overload at the current moment according to the optimization function;

[0110] S4. Based on the coverage method, set the number of interceptors and the initial coverage upper limit of each interceptor;

[0111] S5. Obtain the initial velocity direction of the interceptor according to the initial coverage upper limit of the interceptor. The interceptor flies with the set control command in this initial velocity direction to achieve the interception of the target.

[0112] In S1, the interceptor control command is set as:

[0113]

[0114] In S2, the objective function of the optimization function is set as:

[0115] f(A1,A2…A n )=u1 2 +u2 2 +…+u n 2

[0116]

[0117] The constraint of the optimization function is expressed as:

[0118]

[0119] In S4, the number of interceptors satisfies the constraint:

[0120]

[0121] c min =min(c1,c n )

[0122] The initial coverage upper limit of each interceptor is expressed as:

[0123]

[0124] In S5, based on the initial coverage upper limit of the interceptor, obtain the initial velocity direction of the interceptor through the relationship between the velocity direction and the coverage upper limit.

[0125] The relationship between the velocity direction and the coverage upper limit is expressed as:

[0126]

[0127] Comparative example

[0128] Comparative example 1

[0129] Perform the same simulation experiment as in Embodiment 1, except that the fixed coverage method (CBCGS) and the optimal array position guidance (CGS) method under overload constraint are used respectively.

[0130] Among them, for the fixed coverage guidance method (CBCGS), refer to the literature: Wenshan, Su, Kebo, et al. Coverage-based cooperative guidance strategy against highly maneuvering target [J]. Aerospace Science & Technology, 2017. DOI: 10.1016 / j.ast.2017.09.021.

[0131] For the optimal array position guidance (CGS) method under overload constraint, refer to the literature: Chen Z, Yu J, Dong X, et al. Three-dimensional cooperative guidance strategy and guidance law for intercepting highly maneuvering target [J]. Chinese Journal of Aeronautics, 2021, 34(3). DOI: 10.1016 / j.cja.2020.12.014.

[0132] Compare the simulation results of Example 1 and Comparative Example 1, as Figure 2 - 7 shown.

[0133] Among them, Figure 2 - 4 is the comparison result of the fixed coverage guidance method (CBCGS) in Example 1 and Comparative Example 1, Figure 2 is the trajectory diagram of the interceptor and the target, Figure 3 is the comparison diagram of the acceleration control commands of the interceptor, Figure 4 is the comparison of the total overload consumption of the interceptor.

[0134] From Figure 2 it can be seen that both Example 1 and Comparative Example 1 can ensure that at least one interceptor can successfully intercept the target; from Figure 3 it can be seen that since the target maneuvers with its maximum maneuvering ability and is greater than the maneuvering ability of the interceptor, as the target velocity direction changes, the interceptor needs to intercept with its maximum maneuver, but the acceleration commands in Example 1 are smaller in the initial stage of guidance; from Figure 4 it can be seen that the total overload consumption of all interceptors in the method of Example 1 is smaller, and the energy consumption is reduced by 2.04×10 3 .

[0135] Among them, Figure 5 - 7 is the comparison result of the optimal array position guidance (CGS) under overload constraint in Example 1 and Comparative Example 1, Figure 5 is the trajectory diagram of the interceptor and the target, Figure 6It is a comparison diagram of the interceptor acceleration control instructions. Figure 7 It is a comparison of the total overload consumption of the interceptor.

[0136] From Figure 5 it can be seen that both Example 1 and Comparative Example 1 can ensure that at least one interceptor can successfully intercept the target; from Figure 6 it can be seen that in the initial stage of guidance of the interceptor, the acceleration instructions of different interceptors in Example 1 are all smaller; from Figure 7 it can be seen that the total overload consumption of all interceptors in Example 1 is smaller, and the energy consumption is reduced by 1.95×10 3 .

[0137] The present invention has been described above in combination with preferred embodiments, but these embodiments are only exemplary and only play an illustrative role. On this basis, various substitutions and improvements can be made to the present invention, and these all fall within the protection scope of the present invention.

Claims

1. A cluster optimal coverage cooperative guidance method for intercepting highly maneuverable targets, characterized in that, It includes the following steps: S1. Set the interceptor control instruction; S2. Set the optimization function with the goal of minimizing the total overload of the interceptor; S3. Obtain the coverage method with the minimum overload at the current moment according to the optimization function; S4. Based on the coverage method, set the number of interceptors and the initial coverage upper limit of each interceptor; S5. According to the initial coverage upper limit of the interceptor, obtain the initial velocity direction of the interceptor. The interceptor flies with the set control instruction in this initial velocity direction to achieve the interception of the target.

2. The optimal coverage cooperative guidance method for intercepting high-maneuver targets by a cluster according to claim 1, wherein in S1, the interceptor control instruction is set as: Among them, a i represents the acceleration of the i-th interceptor, N is the proportional navigation coefficient, t go,i is the remaining flight time of the i-th interceptor, ZEM i is the zero-effort miss of the i-th interceptor, B i is the proportional navigation bias term of the i-th interceptor.

3. The optimal coverage cooperative guidance method for intercepting high-maneuver targets by a cluster according to claim 1, wherein in S2, the objective function of the optimization function is set as: f(A1,A2…A n ) = u1 2 + u2 2 + … + u n 2 Among them, A i represents the upper limit of the interception domain coverage of the i-th interceptor, a m,max represents the upper limit of the maneuverability of the interceptor, q i0 represents the initial line-of-sight angle of the i-th interceptor, θ i represents the velocity direction angle of the i-th interceptor, θ t represents the velocity direction angle of the target u i It represents the overload consumption of the i-th interceptor and is in the form of representing the upper limit of the coverage of the interception area of the adopted interceptor.

4. The optimal coverage cooperative guidance method for intercepting high-maneuver targets by a cluster according to claim 1, wherein in S2, the constraint of the optimization function is expressed as: Among them, a Tmax represents the target maximum acceleration, C i represents the interception range size of the i-th interceptor, q i0 represents the initial line-of-sight angle of the i-th interceptor, and n represents the total number of interceptors.

5. The optimal coverage cooperative guidance method for intercepting high-maneuver targets by a cluster according to claim 1, wherein in S4, the number of interceptors satisfies the constraint: c min = min(c1, c n ) where NUM represents the number of interceptors, and c min represents the smaller value between c1 and c n in 6. The optimal coverage cooperative guidance method for intercepting high-maneuver targets by a cluster according to claim 1, wherein in S4, the initial coverage upper limit of each interceptor is expressed as: where n = NUM, A i,0 represents the initial coverage upper limit of the i-th interceptor, A 1,0 represents the initial coverage upper limit of the first interceptor.

7. The optimal coverage cooperative guidance method for intercepting high-maneuver targets by a cluster according to claim 1, wherein in S5, through the relationship between the velocity direction and the coverage upper limit, based on the initial coverage upper limit of the interceptor, obtain the initial velocity direction of the interceptor, the relationship between the velocity direction and the coverage upper limit is expressed as: K T = cos(θ t + q i0 ), K Mi = cos(θ i - q i0 ) Among them, K T , K Mi are intermediate variables, r i represents the distance between the i-th interceptor and the target, v i represents the speed of the i-th interceptor, q i represents the line-of-sight angle of the i-th interceptor, v t represents the speed of the target.

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