A fast solution method for the capture criterion of spatial adversarial non-cooperative target clusters

Abstract

The present invention discloses a method for quickly solving the criterion of cluster capture of space adversarial non-cooperative targets. The method can quickly calculate the reachable range of the target and the spacecraft cluster through the differential algebraic method, and proposes the criterion of the spacecraft cluster for the capture of the non-cooperative target. It can analyze whether the spacecraft cluster has sufficient conditions for capturing the non-cooperative target and quickly verify the effectiveness of the cluster capture configuration.

Description

Technical Field

[0001] The invention relates to the field of aerospace, and in particular to a method for quickly solving a space adversarial non-cooperative target cluster capture criterion. Background Art

[0002] Cluster capture of adversarial non-cooperative targets in space is a new concept in recent research. Cluster capture of a adversarial non-cooperative target by spacecraft is a development trend of space adversarial games. In the field of spacecraft pursuit and escape game confrontation, some researchers and scholars have used differential game strategy methods to study various situations. However, this method often transforms the problem into a two-point boundary value problem in optimal control theory. Faced with some complex nonlinear dynamic systems, the numerical solution process is complicated and sometimes even infeasible. In addition, the terminal conditions are not always met. In many cases of pursuit and escape, the pursuer does not actually have the ability to pursue the escapee. However, within the framework of optimal control theory, it is difficult to judge whether the pursuer does not have the ability to successfully pursue or the pursuit strategy is not mature enough.

[0003] Haoran Gong et al. proposed a sufficient discrimination condition for one-to-one spacecraft pursuit based on the reachable range method. The reachable ranges of the pursuer and the escaper at fixed times are obtained by the target shooting method and the traditional numerical integration method. The success or failure of the pursuit is determined by judging whether the reachable range of the pursuer can completely envelop the reachable range of the escaper. However, the calculation time of the traditional numerical integration method is related to the number of target shootings, and the time cost required to obtain accurate analysis is relatively high. Summary of the invention

[0004] The present invention aims to provide a method for quickly solving the criterion of spatial adversarial non-cooperative target cluster capture, so as to overcome the problems existing in the prior art.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for quickly solving the spatial adversarial non-cooperative target cluster capture criterion includes the following steps:

[0007] S1: Establish the dynamic model of cluster spacecraft members and target spacecraft in the non-inertial reference frame, and design the formation configuration of the spacecraft cluster; propose the criterion of many-to-one capture of non-cooperative targets in space based on the reachable range method;

[0008] S2: Based on the dynamics model of the spacecraft cluster members and the target spacecraft in S1, the optimal control method is combined to obtain the analytical form of the boundary points of the reachable range of the spacecraft cluster members and the target spacecraft, and generate the direction set of the terminal positions of the spacecraft cluster members and the target spacecraft;

[0009] S3: Based on the dynamic model of the cluster spacecraft members and the target spacecraft established in S1 and the direction set of the terminal positions of the spacecraft cluster members and the target spacecraft, an analytical form containing variable time is established, and then a genetic algorithm is used to find the optimal terminal time for the spacecraft cluster members to capture the target spacecraft. The individual terminal time in the population satisfies the requirement of being greater than 0 and less than the longest pursuit time. When the genetic generation number is less than or equal to the maximum genetic generation number, S4 is executed. Otherwise, it is determined that the spacecraft cluster does not have the conditions to capture the target.

[0010] S4: Perform Taylor polynomial approximation on the analytical form of the reachable range boundary points of the spacecraft cluster members and the target spacecraft in S2, set the evolution time to the terminal moment, integrate the dynamic model under the polynomial framework, obtain a polynomial with the terminal position direction as a variable, and then substitute it into the direction set of the terminal position in S2 to obtain the reachable range of the spacecraft cluster members and the target spacecraft, and then execute S5;

[0011] S5: Based on the reachable range of the spacecraft cluster members and the target spacecraft in S4 and the many-to-one criterion for capturing non-cooperative targets in space in S1, determine whether the capture is effective. If the capture is effective, it proves that the cluster has the conditions to capture the target. Otherwise, re-execute S3.

[0012] Preferably, the dynamic model of the target spacecraft in S1 is specifically:

[0013]

[0014] where [x E ,y E ,z E ] indicates the position status of the target spacecraft, represents the target spacecraft velocity state, represents the acceleration state of the target spacecraft, and n is the orbital angular velocity.

[0015] Preferably, in S1

[0016] Dynamical model of spacecraft cluster members:

[0017]

[0018] where [x P ,y P ,z P ] represents the position status of the cluster spacecraft members, represents the velocity state of the cluster spacecraft members, represents the acceleration state of the spacecraft cluster members, [a x ,a y ,a z ] represent the acceleration components in the x, y, and z axes respectively, and n is the orbital angular velocity.

[0019] Preferably, in S1, the criterion for capturing non-cooperative targets in space is specifically: when the reachable range of the spacecraft cluster members at a certain moment fully covers the reachable range of the target spacecraft, it proves that the spacecraft cluster members must have a maneuvering strategy to successfully capture the target; otherwise, when the reachable range of the spacecraft cluster members at any moment cannot fully cover the reachable range of the target, it proves that the target spacecraft must have a maneuvering strategy to escape the capture range of the cluster spacecraft members, that is, the capture fails.

[0020] Preferably, the mathematical expression of the criterion for many-to-one capture of spatial non-cooperative targets is:

[0021]

[0022] in is the reachable range of the target spacecraft, is the reachable range of the i-th spacecraft cluster member, and N is the number of spacecraft cluster members.

[0023] Preferably, in S2, the terminal position direction set of the spacecraft cluster members and the target spacecraft is:

[0024]

[0025] Where δ represents the terminal position direction, It represents the angle between the projection of the terminal position direction on the plane and the positive direction of the x-axis, and θ represents the angle between the terminal position direction and the positive direction of the z-axis.

[0026] Preferably, in S2, the boundary point analysis form of the reachable range of the target spacecraft is:

[0027] maxφ(x f )=δ·(x f -x0)

[0028]

[0029] where x f Indicates that the target passes through t f The terminal position reached by applying optimal control at time; x0 represents the initial position of the target; T represents the acceleration vector;

[0030] Preferably, in S2,

[0031] The analytical form of the reachable range boundary points of spacecraft cluster members is:

[0032] maxφ(x f )=δ·(x f -x0)

[0033]

[0034] where x f The spacecraft passes through t f The terminal position reached by applying optimal control over time; x0 represents the initial position of the spacecraft; x Pi represents the initial position of the i-th spacecraft; T represents the acceleration vector.

[0035] Preferably, in S4, the Taylor polynomial approximation is an approximate description of the terminal position direction angle increments of the target and the spacecraft in polynomial form, and an ordinary differential equation describing the law of their spatial motion is obtained.

[0036] Preferably, the polynomial with the terminal position direction as a variable obtained in S4 is,

[0037]

[0038] In the formula, and Δθ represent the direction δ and the nominal direction respectively Two angular deviations, nominal direction is the positive direction of the x-axis of the Hill coordinate system, j=j1+j2 represents the order of each term of the polynomial approximate solution, d represents the index value of the state vector, and x f Indicates that at t f The fragment state at the time corresponding to the initial standard orbit state x0, [x f ] represents the solution of the polynomial, represents the corresponding Taylor series expansion coefficients.

[0039] Compared with the prior art, the present invention has the following beneficial effects: the present invention provides a method for quickly solving the cluster capture criteria of space adversarial non-cooperative targets. The reachable range of the target and the spacecraft cluster can be quickly calculated through differential algebraic methods, and the capture criteria of the spacecraft cluster for the non-cooperative target are proposed. It can analyze whether the spacecraft cluster has sufficient conditions to pursue the non-cooperative target and quickly verify the effectiveness of the cluster capture configuration. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flow chart of the present invention;

[0041] Figure 2 is the position and direction of the Hill coordinate system Oxyz.

[0042] Figure 3 A schematic diagram of the spacecraft cluster flying together is shown.

[0043] FIG4 is a schematic diagram showing three situations in which the capture criteria determine the success or failure of a cluster in capturing a target. Figure 4-aA schematic diagram of a successful roundup is shown, satisfying the two constraints in the roundup criterion; Figure 4-b A schematic diagram of a failed roundup is shown, which does not satisfy the first constraint in the roundup criterion; Figure 4-c A schematic diagram of a failed roundup is shown, where the second constraint in the roundup criterion is not met. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below in conjunction with specific embodiments, which are intended to explain the present invention rather than to limit it.

[0045] like Figure 1 -4, the present invention provides a method for quickly solving the spatial adversarial non-cooperative target cluster capture criterion,

[0046] A method for quickly solving spatial adversarial non-cooperative target cluster capture criteria, characterized by comprising the following steps:

[0047] S1: Establish the dynamic model of cluster spacecraft members and target spacecraft in the non-inertial reference frame, and design the formation configuration of the spacecraft cluster; propose the criterion of many-to-one capture of non-cooperative targets in space based on the reachable range method;

[0048] S2: Based on the dynamics model of the spacecraft cluster members and the target spacecraft in S1, the optimal control method is combined to obtain the analytical form of the boundary points of the reachable range of the spacecraft cluster members and the target spacecraft, and generate the direction set of the terminal positions of the spacecraft cluster members and the target spacecraft;

[0049] S3: Based on the dynamic model of the cluster spacecraft members and the target spacecraft established in S1 and the direction set of the terminal positions of the spacecraft cluster members and the target spacecraft, an analytical form containing variable time is established, and then a genetic algorithm is used to find the optimal terminal time for the spacecraft cluster members to capture the target spacecraft. The individual terminal time in the population satisfies the requirement of being greater than 0 and less than the longest pursuit time. When the genetic generation number is less than or equal to the maximum genetic generation number, S4 is executed. Otherwise, it is determined that the spacecraft cluster does not have the conditions to capture the target.

[0050] S4: Perform Taylor polynomial approximation on the analytical form of the reachable range boundary points of the spacecraft cluster members and the target spacecraft in S2, set the evolution time to the terminal moment, integrate the dynamic model under the polynomial framework, obtain a polynomial with the terminal position direction as a variable, and then substitute it into the direction set of the terminal position in S2 to obtain the reachable range of the spacecraft cluster members and the target spacecraft, and then execute S5;

[0051] S5: Based on the reachable range of the spacecraft cluster members and the target spacecraft in S4 and the many-to-one criterion for capturing non-cooperative targets in space in S1, determine whether the capture is effective. If the capture is effective, it proves that the cluster has the conditions to capture the target. Otherwise, re-execute S3.

[0052] The dynamic model of the target spacecraft in S1 is as follows:

[0053]

[0054] where [x E ,y E ,z E ] indicates the position status of the target spacecraft, represents the target spacecraft velocity state, represents the acceleration state of the target spacecraft, and n is the orbital angular velocity.

[0055] Dynamical model of spacecraft cluster members in S1:

[0056]

[0057] where [x P ,y P ,z P ] represents the position status of the cluster spacecraft members, represents the velocity state of the cluster spacecraft members, represents the acceleration state of the spacecraft cluster members, [a x ,a y ,a z ] represent the acceleration components in the x, y, and z axes respectively, and n is the orbital angular velocity.

[0058] In S1, the specific criteria for capturing non-cooperative targets in space are: if the reachable range of the spacecraft cluster members at a certain moment fully covers the reachable range of the target spacecraft, it proves that the spacecraft cluster members must have a maneuvering strategy to successfully capture the target; otherwise, if the reachable range of the spacecraft cluster members at any moment cannot fully cover the reachable range of the target, it proves that the target spacecraft must have a maneuvering strategy to escape the capture range of the cluster spacecraft members, and the capture fails.

[0059] The mathematical expression of the criterion for many-to-one capture of spatial non-cooperative targets is:

[0060]

[0061] in is the reachable range of the target spacecraft, is the reachable range of the i-th spacecraft cluster member, and N is the number of spacecraft cluster members.

[0062] In S2, the terminal position direction set of the spacecraft cluster members and the target spacecraft is:

[0063]

[0064] Where δ represents the terminal position direction, It represents the angle between the projection of the terminal position direction on the plane and the positive direction of the x-axis, and θ represents the angle between the terminal position direction and the positive direction of the z-axis.

[0065] In S2, the boundary point analysis form of the reachable range of the target spacecraft is:

[0066] maxφ(x f )=δ·(x f -x0)

[0067]

[0068] where x f Indicates that the target passes through t f The terminal position reached by applying optimal control at time; x0 represents the initial position of the target; T represents the acceleration vector;

[0069] In S2, the boundary point analysis form of the reachable range of spacecraft cluster members is:

[0070] maxφ(x f )=δ·(x f -x0)

[0071]

[0072] where x f The spacecraft passes through t f The terminal position reached by applying optimal control over time; x0 represents the initial position of the spacecraft; x Pi represents the initial position of the i-th spacecraft; T represents the acceleration vector.

[0073] In S4, the Taylor polynomial approximation is an approximate description of the terminal position direction angle increments of the target and the spacecraft in polynomial form, and the ordinary differential equation describing the law of their spatial motion is obtained.

[0074] The polynomial with the terminal position direction as the variable obtained in S4 is:

[0075]

[0076] In the formula, and Δθ represent the direction δ and the nominal direction respectively Two angular deviations, nominal direction is the positive direction of the x-axis of the Hill coordinate system, j=j1+j2 represents the order of each term of the polynomial approximate solution, d represents the index value of the state vector, and x f Indicates that at t f The fragment state at the time corresponding to the initial standard orbit state x0, [x f ] represents the solution of the polynomial, represents the corresponding Taylor series expansion coefficients.

[0077] Example:

[0078] Step 1: Establish a non-inertial reference coordinate system (Hill coordinate system), and based on this coordinate system, establish the dynamic model of the cluster spacecraft and the target spacecraft, and design the formation configuration of the spacecraft cluster.

[0079] Assume that the adversarial non-cooperative target E first moves in a circular motion around the earth, with an orbital height of R and an orbital angular velocity of n. Assume that the spacecraft cluster P has N members, and that they are flying in a circular orbit around the adversarial non-cooperative target, with a circular orbit radius of r. p and the accompanying orbital angular velocity n p , the cluster spacecraft are evenly distributed on the circular orbit.

[0080] Based on the initial orbit and initial state of the non-cooperative target, a non-inertial reference system Oxyz is established with O as the center of the coordinate system coinciding with the center of mass of the satellite in orbit, the x-axis along the satellite orbit radius vector, the z-axis along the satellite orbit angular momentum vector, and the y-axis completing the right-hand coordinate system. The companion flight motion of the spacecraft cluster can be described as a circular orbit companion flight on the XOY plane in the Hill coordinate system, and control needs to be applied to maintain the configuration.

[0081] Dynamic model of the target:

[0082]

[0083] where [x E ,y E ,z E ] indicates the position status of the target spacecraft, represents the target spacecraft velocity state, Indicates the acceleration state of the target spacecraft.

[0084] Dynamics model of swarm spacecraft:

[0085]

[0086] where [x P ,y P ,z P ] represents the position status of the cluster spacecraft, represents the velocity state of the cluster spacecraft, represents the acceleration state of the cluster spacecraft, [a x ,a y ,a z ] represent the acceleration components in the x, y, and z axes respectively.

[0087] Step 2: Based on the reach method, a “many-to-one” criterion for capturing non-cooperative targets in space is proposed.

[0088] The definition of the encirclement and capture criterion is: if the reachable range of the spacecraft cluster at a certain moment fully covers the reachable range of the target, it proves that the spacecraft cluster must have a certain maneuvering strategy that can successfully capture the target, that is, the target cannot escape the encirclement and capture of the cluster no matter what maneuvering strategy it uses; otherwise, when the reachable range of the spacecraft cluster at any moment cannot fully cover the reachable range of the target, it proves that the target must have a certain maneuvering strategy to escape the capture range of the cluster spacecraft, that is, the encirclement and capture fails.

[0089] The mathematical expression of the round-up criterion is: in is the reachable range of the target spacecraft, is the reachable range of the i-th cluster spacecraft. This mathematical expression is also equivalent to the following two constraints: 1) The boundaries of the target reachable range are all within the reachable range of the spacecraft cluster, that is, 2) The intersection of the reachable ranges of all spacecraft in the cluster cannot be an empty set

[0090] Step 3: Combine the optimal control method with the CW equation to describe the problem of solving the boundary points of the reachable range of cluster spacecraft and targets. Use polynomials to model all reachable directions of cluster spacecraft and targets, obtain the analytical form of the boundary points of the reachable range, and generate a set of terminal position directions of cluster spacecraft and target spacecraft.

[0091] The terminal position direction set of the cluster spacecraft and the target spacecraft is:

[0092]

[0093] In the formula It represents the angle between the projection of the terminal position direction on the xoy plane and the positive direction of the x-axis, and θ represents the angle between the terminal position direction and the positive direction of the z-axis.

[0094] The problem of solving the boundary points of the reachable range can be described as an optimal control problem with the farthest displacement in the δ direction.

[0095] The reachability problem of non-cooperative targets can be described as:

[0096] maxφ(x f )=δ·(x f-x0)

[0097]

[0098] where x f Indicates that the target passes through t f time to achieve the terminal position of optimal control; x0 represents the initial position of the target; T represents the acceleration.

[0099]

[0100] The reachability problem of cluster spacecraft can be described as:

[0101] maxφ(x f )=δ·(x f -x0)

[0102]

[0103] where x f The spacecraft passes through t f The terminal position reached by applying optimal control over time; x0 represents the initial position of the spacecraft; x Pi represents the initial position of the i-th spacecraft; T represents the acceleration vector.

[0104] The dynamic models of the target and cluster spacecraft are established by combining the optimal control theory and the CW equation:

[0105] 1) Dynamic model of target terminal position:

[0106]

[0107] 2) Dynamic model of cluster spacecraft terminal position:

[0108]

[0109] Among them, v Pi represents the initial velocity of the i-th spacecraft, T Emax represents the maximum maneuverability of the target, T Pmax represents the maximum maneuverability of the cluster spacecraft, δ is the terminal position direction vector, C1, C2, C3, and C4 are all 3rd-order matrices.

[0110]

[0111] Step 4: Use genetic algorithm to find the optimal terminal time t f , when the genetic generation number is less than or equal to N GA And the individual terminal time in the population all satisfies 0s <t f <t maxs, execute step 5. Otherwise, it is determined that the spacecraft cluster does not have the conditions to capture the target. GA is the maximum genetic generation, t max The longest pursuit time.

[0112] Step 5: Based on the differential algebra method, the Taylor polynomial approximation is performed on the analytical form of the reachable range boundary points of the cluster spacecraft and the target in step 3, and the evolution time is set to the terminal time t f , integrate the dynamic model under the polynomial framework, obtain the polynomial with the terminal position direction as the variable, substitute it into the position direction set in step three, obtain the reachable range of the cluster spacecraft and the target, and then execute step six;

[0113] The specific operation is to start from the terminal position direction set of the cluster spacecraft and the target spacecraft, use the polynomial framework to perform polynomial integration on the dynamic equation and obtain the approximate solution in polynomial form. The approximate solution in polynomial form is:

[0114]

[0115] In the formula, j = j1 + j2 represents the order of each term of the polynomial approximate solution, d represents the index value of the state vector, and x f Indicates that at t f The fragment state at the time corresponding to the initial standard orbit state x0, [x f ] represents the solution of the polynomial, represents the corresponding Taylor expansion coefficient.

[0116] Taylor polynomial approximation is to describe the terminal position direction angle increment of the target and the spacecraft in polynomial form, obtain the ordinary differential equation describing the law of their spatial motion, and perform Taylor polynomial approximation on the vector field of the ordinary differential equation. Polynomial integration is to perform polynomial integration of the ordinary differential equation along time to obtain the state solution in polynomial form at a certain moment.

[0117] Step 6: Based on the reachable range of the cluster spacecraft and the target in step 5 and the capture criteria proposed in step 2, determine whether the capture is effective. If the capture is effective, it proves that the cluster has the conditions to capture the target, otherwise, start again from step 4.

[0118] Although the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments and application fields, and the above-mentioned specific embodiments are only illustrative and instructive, rather than restrictive. Under the guidance of the specification, a person skilled in the art can also make many forms without departing from the scope of protection of the claims of the present invention, all of which belong to the scope of protection of the present invention.

Claims

1. A method for quickly solving the criterion of spatial adversarial non-cooperative target cluster capture, characterized in that: The following steps are involved: S1: Establish the dynamic model of cluster spacecraft members and target spacecraft in the non-inertial reference frame, and design the formation configuration of the spacecraft cluster; Based on the reach method, a criterion for many-to-one capture of non-cooperative targets in space is proposed. S2: Based on the dynamics model of the spacecraft cluster members and the target spacecraft in S1, the optimal control method is combined to obtain the analytical form of the boundary points of the reachable range of the spacecraft cluster members and the target spacecraft, and generate the direction set of the terminal positions of the spacecraft cluster members and the target spacecraft; S3: Based on the dynamic model of the cluster spacecraft members and the target spacecraft established in S1 and the direction set of the terminal positions of the spacecraft cluster members and the target spacecraft, an analytical form containing variable time is established, and then a genetic algorithm is used to find the optimal terminal time for the spacecraft cluster members to capture the target spacecraft. The individual terminal time in the population satisfies the requirement of being greater than 0 and less than the longest pursuit time. When the genetic generation number is less than or equal to the maximum genetic generation number, S4 is executed. Otherwise, it is determined that the spacecraft cluster does not have the conditions to capture the target. S4: Perform Taylor polynomial approximation on the analytical form of the reachable range boundary points of the spacecraft cluster members and the target spacecraft in S2, set the evolution time to the terminal moment, integrate the dynamic model under the polynomial framework, obtain a polynomial with the terminal position direction as a variable, and then substitute it into the direction set of the terminal position in S2 to obtain the reachable range of the spacecraft cluster members and the target spacecraft, and then execute S5; S5: Based on the reachable range of the spacecraft cluster members and the target spacecraft in S4 and the many-to-one criterion for capturing non-cooperative targets in space in S1, determine whether the capture is effective. If the capture is effective, it proves that the cluster has the conditions to capture the target. Otherwise, re-execute S3.

2. According to claim 1, a method for quickly solving the spatial adversarial non-cooperative target cluster capture criterion is characterized in that: The dynamic model of the target spacecraft in S1 is as follows: where [x E ,y E ,z E ] indicates the position status of the target spacecraft, represents the target spacecraft velocity state, represents the acceleration state of the target spacecraft, and n is the orbital angular velocity.

3. According to claim 1, a method for quickly solving the spatial adversarial non-cooperative target cluster capture criterion is characterized in that: S1 Dynamical model of spacecraft cluster members: where [x P ,y P ,z P ] represents the position status of the cluster spacecraft members, represents the velocity state of the cluster spacecraft members, represents the acceleration state of the spacecraft cluster members, [a x ,a y ,a z ] represent the acceleration components in the x, y, and z axes respectively, and n is the orbital angular velocity.

4. The method for quickly solving the spatial adversarial non-cooperative target cluster capture criterion according to claim 1 is characterized in that: In S1, the criteria for capturing non-cooperative targets in space are as follows: if the reachable range of the spacecraft cluster members at a certain moment fully covers the reachable range of the target spacecraft, it proves that the spacecraft cluster members must have a maneuvering strategy to successfully capture the target; otherwise, if the reachable range of the spacecraft cluster members at any moment cannot fully cover the reachable range of the target, it proves that the target spacecraft must have a maneuvering strategy to escape the capture range of the cluster spacecraft members, and the capture fails.

5. The method for quickly solving the spatial adversarial non-cooperative target cluster capture criterion according to claim 1 is characterized in that: The mathematical expression of the criterion for many-to-one capture of spatial non-cooperative targets is: in is the reachable range of the target spacecraft, is the reachable range of the i-th spacecraft cluster member, and N is the number of spacecraft cluster members.

6. The method for quickly solving the spatial adversarial non-cooperative target cluster capture criterion according to claim 1 is characterized in that: In S2, the terminal position direction set of the spacecraft cluster members and the target spacecraft is: Where δ represents the terminal position direction, It represents the angle between the projection of the terminal position direction on the plane and the positive direction of the x-axis, and θ represents the angle between the terminal position direction and the positive direction of the z-axis.

7. The method for quickly solving the spatial adversarial non-cooperative target cluster capture criterion according to claim 1 is characterized in that: In S2, the boundary point analysis form of the reachable range of the target spacecraft is: maxφ(x f )=δ·(x f -x0) where x f Indicates that the target passes through t f time to achieve the terminal position after optimal control is applied; x0 represents the initial position of the target; T represents the acceleration vector.

8. The method for quickly solving the spatial adversarial non-cooperative target cluster capture criterion according to claim 1 is characterized in that: In S2, The analytical form of the reachable range boundary points of spacecraft cluster members is: maxφ(x f )=δ·(x f -x0) where x f The spacecraft passes through t f The terminal position reached by applying optimal control over time; x0 represents the initial position of the spacecraft; x Pi represents the initial position of the i-th spacecraft; T represents the acceleration vector.

9. The method for quickly solving the spatial adversarial non-cooperative target cluster capture criterion according to claim 1 is characterized in that: In S4, the Taylor polynomial approximation is an approximate description of the terminal position direction angle increments of the target and the spacecraft in polynomial form, and the ordinary differential equation describing the law of their spatial motion is obtained.

10. The method for quickly solving the spatial adversarial non-cooperative target cluster capture criterion according to claim 1, characterized in that: The polynomial with the terminal position direction as the variable obtained in S4 is: In the formula, and Δθ represent the direction δ and the nominal direction respectively Two angular deviations, nominal direction is the positive direction of the x-axis of the Hill coordinate system, j=j1+j2 represents the order of each term of the polynomial approximate solution, d represents the index value of the state vector, and x f Indicates that at t f The fragment state at the time corresponding to the initial standard orbit state x0, [x f ] represents the solution of the polynomial, represents the corresponding Taylor series expansion coefficients.

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