A multi-to-one cooperative interception method based on location coverage

Abstract

The application relates to a multi-to-one cooperative interception method based on position coverage. The application aims to solve the problem that a single interceptor cannot achieve full coverage of the reachable range of an enemy target under limited fuel. The process comprises the following steps: 1. obtaining the estimated value of the size and direction of the target's maneuvering acceleration at the current time, considering the estimation error, and solving the envelope of the reachable domain of the maneuvering target at the predicted interception time; 2. obtaining all the sampling points of the reachable domain of the maneuvering target at the predicted interception time; 3. constructing a reachable domain distribution optimization index, and solving the aiming point in the reachable domain of the maneuvering target matched with the number of interceptors by using an optimization algorithm according to the number of the interceptors; 4. obtaining the fuel-optimal corresponding relationship between the N interceptors and the N aiming points by using the Hungarian algorithm, and drawing the coverage of the reachable domain of the N interceptors on the target reachable domain. The application is used in the field of aircraft guidance.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of multi-to-one cooperative interception method, belong to the field of aircraft guidance. BACKGROUND

[0002] With the continuous development of aerospace technology, satellite as an effective detection means, play an increasingly important role in the military field.If in space power confrontation can effectively intercept or destroy enemy satellite, can greatly weaken its space power, so as to ensure our operational advantage.Therefore, various satellites have become the main research target of each country.

[0003] For space on-orbit satellite, it often has certain maneuverability, although maneuverability is poor, but can be expanded by long-time maneuvering its reachable range.In this case, single interceptor under limited fuel, often cannot realize the full coverage of enemy target reachable range, traditional one-to-one interception method is likely to face failure.Based on this, it is necessary to use multiple interceptors for cooperative interception to improve the success rate of interception task. SUMMARY

[0004] The purpose of the present application is to solve the problem that single interceptor under limited fuel often cannot realize the full coverage of enemy target reachable range, and propose a multi-to-one cooperative interception method based on position coverage.

[0005] The specific process of a multi-to-one cooperative interception method based on position coverage is as follows:

[0006] Step one, obtain the estimated value of the size and direction of target maneuvering acceleration at the current time, and consider the estimated error of the size and direction of target maneuvering acceleration, solve the maneuvering target reachable domain envelope at the predicted interception time;

[0007] Step two, sample the inside of the maneuvering target reachable domain envelope at the interception time obtained in step one, to obtain all the sampling points of the maneuvering target reachable domain at the predicted interception time;

[0008] Step three, build a reachable domain allocation optimization index, according to the number of interceptor, solve the aiming point in the maneuvering target reachable domain matched with the number of interceptor by using optimization algorithm;

[0009] Step four, obtain the fuel optimal correspondence relationship between N interceptors and N aiming points by using Hungarian algorithm, and draw the coverage of N interceptors' reachable domain to target reachable domain.

[0010] The beneficial effects of the present application are as follows:

[0011] The application provides a multi-to-one cooperative interception strategy based on position coverage. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 The flowchart of the application is shown in the figure;

[0013] Figure 2 The figure is a schematic diagram of the reachable domain of the target at the predicted interception time, and eci is the geocentric inertial coordinate system;

[0014] Figure 3 The figure is a schematic diagram of the reachable domain sampling points of the target;

[0015] Figure 4 The figure is a result diagram of the assignment based on the reachable domain of the target at the current time. DETAILED DESCRIPTION

[0016] Embodiment one: the specific process of the multi-to-one cooperative interception method based on position coverage is as follows:

[0017] The application provides a multi-to-one cooperative interception strategy based on position coverage, which quickly solves the reachable domain of the maneuvering target first, then assigns the target reachable domain by constructing a reachable domain optimization index and using an optimization algorithm, determines the aiming center of the multiple interceptors, realizes the optimal coverage of the target maneuvering reachable domain by the interceptors, and is beneficial to the smooth realization of the interception task.

[0018] In the algorithm, the target uses continuous thrust maneuvering, but the maneuvering time is relatively long, and therefore the target reachable range is relatively large;

[0019] In the algorithm, the interceptor uses pulse maneuvering, but the available fuel of a single interceptor is limited;

[0020] Step one: obtaining the estimated value of the size and direction of the target maneuvering acceleration at the current time, considering the estimated error of the size and direction of the target maneuvering acceleration, and quickly solving the reachable domain envelope of the maneuvering target at the predicted interception time by using the dynamic targeting method;

[0021] Step two, sampling inside the envelope of the reachable region of the maneuvering target at the predicted interception time obtained in step one to obtain all sampling points of the reachable region of the maneuvering target at the predicted interception time;

[0022] Step three, constructing a reachable region distribution optimization index, and solving the aiming points in the reachable region of the maneuvering target matched with the number of interceptors by using an optimization algorithm according to the number of the interceptors of the own side;

[0023] Step four, obtaining the fuel-optimal correspondence relationship between the N interceptors and the N aiming points by using the Hungarian algorithm, and drawing the coverage of the reachable region of the N interceptors on the reachable region of the target.

[0024] Specific implementation method two: the difference between the embodiment and the specific implementation method one is that the estimated value of the size and direction of the target maneuvering acceleration at the current time is obtained in the step one, and the estimated error of the size and direction of the target maneuvering acceleration is considered, and the dynamic shooting method is used to quickly solve the envelope of the reachable region of the maneuvering target at the predicted interception time; the specific process is as follows:

[0025] Defining a target orbit coordinate system: the origin of the coordinate system is the center of the target, the x-axis points to the direction of the target mass center along the center of the earth, the y-axis is perpendicular to the x-axis in the orbit plane and points to the direction of the orbit advancing, and the z-axis can be determined by the right-hand rule;

[0026] The size and direction of the target maneuvering acceleration at the current time are obtained by a corresponding estimation method (such as the existing nonlinear least square estimation method or extended Kalman filtering method), which is not the main content of the present application, and therefore will not be specifically introduced in the present application. In the present application, it is assumed that the estimated value of the size of the target maneuvering acceleration at the current time in the target orbit coordinate system has been obtained and the estimated value of the two thrust direction angles of the target and

[0027] wherein represents the estimated value of the angle between the target maneuvering acceleration and the orbit plane, represents the estimated value of the angle between the projection of the target maneuvering acceleration in the orbit plane and the x-axis of the target orbit coordinate system;

[0028] It is assumed that the estimated errors of the size and direction of the target maneuvering acceleration both obey Gaussian distribution, and the 1σ estimated error of the target maneuvering acceleration is σ u , and the 1σ estimated errors of the two thrust direction angles of the target are σ α and σ β , respectively;

[0029] The dynamic shooting method is used to quickly solve the envelope of the reachable region of the maneuvering target at the predicted interception time; the specific process is as follows:

[0030] 1), First, according to the estimated error (σ u and σ α σ β ) of the estimated maneuvering acceleration, the range in which the target real maneuvering acceleration may exist is determined, and considering the 3σ principle, the range of the target real maneuvering acceleration amplitude u is The range of the target real thrust direction angle α is The range of the target real thrust direction angle β is

[0031] 2), Considering that the target vehicle has the maximum maneuvering range when the maneuvering acceleration amplitude of the target vehicle is maximum, the maximum amplitude of the target maneuvering acceleration is set as

[0032] The traversal step of the two thrust direction angles is set as τ α ,τ β , and traversal is performed according to the step τ α ,τ β , so that the target thrust direction angle is obtained in the form of

[0033]

[0034]

[0035] Wherein C α , C β are intermediate variables, · is a multiplication sign, C α =floor(6σ α / τ α ), C β =floor(6σ β / τ β ), and floor(·) represents a floor function;

[0036] Under each set of determined target thrust direction angles (that is, after a value of k α and k β is given, the corresponding values of α and β are obtained, which are referred to as a set of determined target thrust direction angles. Then, traversal is performed on all values of k α and k β for subsequent solving.), and the maximum amplitude of the target maneuvering acceleration is combined to determine the maneuvering acceleration of the target vehicle in the target orbit coordinate system as

[0037]

[0038] 3), taking the position vector and velocity vector of the target observed by the observation equipment at the current time as initial values, performing orbit numerical integration operation on the dynamic model of the target under continuous thrust to solve the terminal position vector of the target

[0039] wherein C is the total number of terminal positions, C = (C α +1) · (C β +1) ;

[0040] Considering the maneuvering acceleration of the target described in the target orbit coordinate system, the dynamic model of the target under continuous thrust is represented as:

[0041]

[0042]

[0043] wherein u = [u x ,u y ,u z ] T is the maneuvering acceleration of the target in the target orbit coordinate system, u x is the maneuvering acceleration of the target in the x-axis of the target orbit coordinate system, u y is the maneuvering acceleration of the target in the y-axis of the target orbit coordinate system, u z is the maneuvering acceleration of the target in the z-axis of the target orbit coordinate system, T is the transpose, represents the radial direction, i z = (r x v) / ||r x v|| represents the normal direction, i y = i z x i x represents the circumferential direction; μ represents the gravitational constant of the earth, r and v represent the position vector and velocity vector of the J2000 inertial system respectively, represents the magnitude of the corresponding position vector; represents the first derivative of r, represents the first derivative of v;

[0044] 4), when the target is in the state of unpowered flight, performing orbit numerical integration operation on the dynamic model of the target under unpowered flight to solve the terminal position vector of the target

[0045] The dynamic model of the target under unpowered flight is a two-body model, represented as:

[0046]

[0047]

[0048] 5), and The combination of these elements forms the envelope of the reachable domain of the maneuvering target at the moment of interception.

[0049] The other steps and parameters are the same as in Specific Implementation Method 1.

[0050] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that, in step two, sampling is performed on the envelope of the reachable domain of the maneuvering target obtained in step one to obtain all sampling points of the reachable domain of the maneuvering target at the time of interception; the specific process is as follows:

[0051] For each terminal location Will and Make a connection;

[0052] Let L be the number of equal divisions set for the connecting line, then the sampling points inside the connecting line... The formula is:

[0053]

[0054] For each terminal location, a total of L-1 sampling points are obtained.

[0055] Thus, combined and This yields all the sampling points within the reachable domain of the target.

[0056] Other steps and parameters are the same as in specific implementation method one or two.

[0057] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that step three involves constructing an reachability domain allocation optimization index. Based on the number of friendly interceptors, an optimization algorithm is used to solve for the aiming points within the reachability domain of the maneuvering target that match the number of interceptors. The specific process is as follows:

[0058] Let the positions of all sampling points in the reachable domain of the maneuvering target obtained in step two, in the J2000 geocentric inertial coordinate system, be:

[0059]

[0060] In the formula, Let represent the position of the i-th sampling point in the target reachable domain in the J2000 geocentric inertial coordinate system, and m represent the total number of sampling points in the target reachable domain (including ). and ); RS tar This indicates the positions of all sampling points within the target reachable domain in the J2000 geocentric inertial coordinate system; the position of the i-th sampling point of the target reachable region in the x-axis of the J2000 geocentric inertial coordinate system, the position of the i-th sampling point of the target reachable region in the y-axis of the J2000 geocentric inertial coordinate system, the position of the i-th sampling point of the target reachable region in the z-axis of the J2000 geocentric inertial coordinate system;

[0061] Suppose there are N interceptors in total, so N aiming points in the target reachable region need to be determined, and the number of independent variables is 3N (because each aiming point is a position vector containing 3 components, so there are 3N in total), denoted as

[0062] X = {r1, r2, …, rN} N} = { [x1, y1, z1] T , [x2, y2, z2] T , …, [xN, yN, zN] N} N N T}

[0063] wherein X represents the positions of the N aiming points in the J2000 geocentric inertial coordinate system; r j = [x j , y j , z j ] T (j = 1, 2, …, N) represents the position of the j-th aiming point in the J2000 geocentric inertial coordinate system; x j is the position of the j-th aiming point in the x-axis of the J2000 geocentric inertial coordinate system, y j is the position of the j-th aiming point in the y-axis of the J2000 geocentric inertial coordinate system, and z j is the position of the j-th aiming point in the z-axis of the J2000 geocentric inertial coordinate system; T is the transpose;

[0064] An optimization index for reachable region allocation is constructed, and the construction process is as follows:

[0065] First, the distance between the i-th sampling point r i tar of the target reachable region and the N aiming points is solved, and the minimum distance is obtained, denoted as

[0066]

[0067] Then, all the sampling points of the target reachable region are traversed, and the minimum distance d is summed up to obtain the final index, denoted as

[0068] ​​

[0069] In order to disperse the N aiming points in the target reachable domain, the following constraint is needed:

[0070] ||r p -r q ||>d min (p≠q)

[0071] where d min represents the minimum distance between each aiming point in the target reachable domain, which can be set according to the remaining flight time, i.e. the smaller the remaining flight time, the smaller the value of d min ; r p represents the position of the pthaiming point in the J2000 geocentric inertial coordinate system, p = 1, 2, …, N; r q represents the position of the qthaiming point in the J2000 geocentric inertial coordinate system, q = 1, 2, …, N.

[0072] The above problem is optimized by using an optimization algorithm (such as the sequential quadratic programming algorithm), and the positions of the N aiming points after optimization are obtained.

[0073] The other steps and parameters are the same as one of the first to third embodiments.

[0074] The fifth embodiment is different from one of the first to fourth embodiments in that the above problem is optimized by using an optimization algorithm (such as the sequential quadratic programming algorithm), and the positions of the N aiming points after optimization are obtained; the specific process is as follows:

[0075] The positions X of the N aiming points in the J2000 geocentric inertial coordinate system are taken as independent variables;

[0076] The obj is taken as the optimization index;

[0077] ||r p -r q ||>d min (p≠q) as constraint conditions;

[0078] The optimization algorithm (such as the sequential quadratic programming algorithm) is used for optimization, and the positions of the N aiming points in the J2000 geocentric inertial coordinate system after optimization are obtained, i.e. the positions of the N aiming points.

[0079] The other steps and parameters are the same as one of the first to fourth embodiments.

[0080] The sixth embodiment is different from one of the first to fifth embodiments in that the Hungarian algorithm is used in step four to obtain the fuel-optimal correspondence relationship between the N interceptors and the N aiming points, and to draw the coverage of the target reachable domain by the reachable domain of the N interceptors; the specific process is as follows:

[0081] Step four one, the Hungarian algorithm is used to obtain the fuel optimal correspondence of multiple interceptors and multiple aiming points;

[0082] Step four two, the reachable domain envelope of the interceptor is solved;

[0083] Step four three, the coverage of the reachable domain of the N interceptors on the target reachable domain is drawn.

[0084] The other steps and parameters are the same as one of the first to fifth embodiments.

[0085] The seventh embodiment is different from one of the first to sixth embodiments in that the Hungarian algorithm is used in step four one to obtain the fuel optimal correspondence of multiple interceptors and multiple aiming points; the specific process is as follows:

[0086] Since the positions and velocities of the N interceptors in the J2000 geocentric inertial coordinate system at the current time are known (obtained through observation equipment), and the positions of the N aiming points at the predicted interception time have been obtained through step three.

[0087] After the initial position and velocity of an interceptor and the position of the aiming point that the interceptor needs to reach are given, the transfer time is the length of time from the current time to the predicted interception time, and then a standard Lambert problem is formed;

[0088] The size of the velocity increment required for the N interceptors to respectively go to the N aiming points is solved through the Lambert algorithm (that is, for each interceptor, the fuel required to go to the N aiming points is solved. For example, the number of interceptors is 3, numbered 1, 2, and 3; the number of aiming points is also 3, numbered a, b, and c. Here, the required velocity increments for 1 to go to a, b, and c respectively, 2 to go to a, b, and c respectively, and 3 to go to a, b, and c respectively are required);

[0089] After obtaining the velocity increments required for the N interceptors to respectively go to the N aiming points, the correspondence of the N interceptors and the N aiming points is obtained by using the Hungarian algorithm with fuel optimization as the index (the correspondence of the interceptor and the aiming point is the independent variable), and the task allocation of the N interceptors is completed (the correspondence of each interceptor and each aiming point is determined with fuel optimization as the index, for example, it is finally determined that 1 aims at c, 2 aims at a, and 3 aims at b, which is the fuel optimal scheme).

[0090] The other steps and parameters are the same as one of the first to sixth embodiments.

[0091] The eighth embodiment is different from one of the first to seventh embodiments in that the reachable domain envelope of the interceptor is solved in step four two; the specific process is as follows:

[0092] Assume that the available fuel of each interceptor at the current time is Δv max , based on the task assignment result of N interceptors (i.e. the correspondence between N interceptors and N aiming points obtained by using the Hungarian algorithm), the pulse thrust Δv j (j = 1, 2, …, N) is applied to each interceptor respectively after aiming at the corresponding aiming point (contained in the task assignment result), and the residual fuel size of each interceptor is obtained as wherein represents the modulus of the pulse;

[0093] wherein, represents the residual fuel size of each interceptor (scalar);

[0094] Since the time length to the predicted interception time is known, only the direction of the pulse needs to be traversed to obtain the reachable domain of the interceptor;

[0095] Assume that in the J2000 geocentric inertial system, the two thrust direction angles of the pulse thrust are and γ;

[0096] wherein represents the angle between the projection of the pulse thrust in the X-Y plane and the X axis in the J2000 geocentric inertial system;

[0097] γ ∈ [-90°, 90°] represents the angle between the pulse thrust and the X-Y plane in the J2000 geocentric inertial system;

[0098] Considering that the traversal step lengths of and γ are and τ γ , for each set of and γ (i.e. taking a value in the range of and taking a value in the range of γ ∈ [-90°, 90°], which is called a set of and γ), the corresponding pulse thrust can be obtained as

[0099]

[0100] wherein, Δv left,j represents the pulse thrust (vector) provided by the residual fuel of each interceptor;

[0101] After applying the corresponding pulse thrust to the interceptor, the position vector of the interceptor at the predicted interception time can be obtained by performing orbit numerical integration operation on the dynamics model of the interceptor under no power;

[0102] Traverse the two thrust direction angles of the pulse thrust and γ, the set of all position vectors of the interceptor at the predicted intercept time is obtained, which constitutes the envelope of the interceptor reachable domain (for a single interceptor) ;

[0103] 1. The pulse thrust is applied to the interceptor, which instantaneously changes the current velocity vector, and the position vector remains the original position vector; 2. Numerical integration is performed, which requires the initial position vector of the interceptor (the initial position of the interceptor, which is known by default) and the velocity vector (after the corresponding pulse thrust is obtained, the velocity vector of the interceptor after the pulse thrust is applied can be obtained) as input; 3. After the numerical integration is performed, the position vector of the interceptor at the predicted intercept time (a point in space) is obtained. 4. The direction angle of the pulse thrust is traversed, and 123 is repeated, so that the set of all terminal position vectors (a set of points) is obtained.

[0104] The other steps and parameters are the same as one of the first to seventh embodiments.

[0105] The ninth embodiment is different from one of the first to eighth embodiments in that the dynamics model of the interceptor under no power is a two-body model, which is represented as:

[0106]

[0107]

[0108] wherein μ represents the gravitational constant of the earth, r and v represent the position vector and the velocity vector of the J2000 inertial system respectively, represents the magnitude of the corresponding position vector; represents the first derivative of r, represents the first derivative of v.

[0109] The other steps and parameters are the same as one of the first to eighth embodiments.

[0110] The beneficial effects of the present application are verified by the following embodiments:

[0111] Embodiment one:

[0112] In this embodiment, the number of interceptors is given as N = 3, and the time 3000s away from the predicted intercept time is set as the current time t0. At the time t0, the position and velocity of the target and each interceptor in the J2000 geocentric inertial coordinate system are shown in Table 1:

[0113] Table 1 Position and velocity of the target and each interceptor in the J2000 geocentric inertial coordinate system at the current time

[0114]

[0115] Assume that the target vehicle continues to perform an escape maneuver with the maximum maneuvering acceleration for the last 3000s. In addition, at the current time t0, the available fuel of each interceptor is Δv max = 0.4 km / s.

[0116] The maneuvering acceleration estimation module estimates the maneuvering acceleration amplitude and two maneuvering direction angles of the target vehicle at the current time as

[0117]

[0118] where g = 9.80665 m / s 2 , and the 1σ value of the estimation error of the corresponding estimation module is

[0119] σ u = 0.0025g, σ α = 10°, and σ β = 10°

[0120] The sampling step of the two thrust direction angles is set as τ α = τ β = 10°. According to the specific process in step one, the reachable region of the target vehicle at the terminal time is obtained as shown in Figure 2

[0121] L is set as 5, and the reachable region of the target vehicle is sampled according to the process in step two. The schematic diagram of all the sampling points is shown in Figure 3

[0122] Then, the aiming point positions that need to be aimed at by each interceptor and the pulse thrusts that need to be applied are obtained by using the processes in steps three and four, as shown in Table 2:

[0123] Table 2 Multi-interceptor allocation result based on target reachable region

[0124]

[0125]

[0126] At the same time, after the pulse thrust is applied, the remaining fuel of the interceptor 1 is the remaining fuel of the interceptor 2 is and the remaining fuel of the interceptor 3 is On this basis, L is set as According to the remaining fuel of each interceptor, the reachable region of the interceptor at the predicted interception time is drawn, and is compared with the reachable region of the target. The result is shown in Figure 4 The figure shows that the reachable regions of the interceptors basically achieve full coverage of the reachable region of the maneuvering target, which indicates that the multi-to-one cooperative interception strategy based on position coverage proposed in the present application is feasible and effective.​​

[0127] The application also can have other various embodiments, and those skilled in the art can make various corresponding changes and modifications according to the application without departing from the spirit and essence of the application, and these corresponding changes and modifications should all belong to the protection scope of the claims attached to the application.

Claims

1. A many-to-one collaborative interception method based on location coverage, characterized in that: The specific process of the method is as follows: Step 1: Obtain the estimated values ​​of the magnitude and direction of the target's maneuvering acceleration at the current moment, and considering the estimation error of the magnitude and direction of the target's maneuvering acceleration, solve for the envelope of the reachable domain of the maneuvering target at the time of interception; Step 2: Sample the envelope of the maneuvering target reachable at the predicted interception time obtained in Step 1 to obtain all sampling points of the maneuvering target reachable at the predicted interception time. Step 3: Construct an optimization index for reachability domain allocation. Based on the number of friendly interceptors, use an optimization algorithm to solve for the aiming points within the reachability domain of maneuvering targets that match the number of interceptors. Step 4: Obtain the results using the Hungarian algorithm. One interceptor and The optimal fuel correspondence for each aiming point is plotted. The coverage of the reachable domain of an interceptor with the reachable domain of the target.

2. The many-to-one collaborative interception method based on location coverage according to claim 1, characterized in that: In step one, the estimated values ​​of the magnitude and direction of the target's maneuvering acceleration at the current moment are obtained, and considering the estimation errors of the target's maneuvering acceleration, the reachability envelope of the maneuvering target at the predicted interception moment is solved; the specific process is as follows: Define the target orbit coordinate system: the origin of the coordinate system is the center of the target. The axis points from the Earth's center to the target's center of mass. The axis is perpendicular to the orbital plane. The axis points in the direction of the track's movement. The axis can be determined by the right-hand rule; Obtain an estimate of the magnitude of the target's maneuvering acceleration in the target's orbital coordinate system at the current moment. Estimates of the two thrust direction angles of the target and the target and ; in This represents an estimated angle between the target's maneuvering acceleration and the orbital plane. Represents the projection of the target's maneuvering acceleration onto the orbital plane and the target's orbital coordinate system. The estimated value of the included angle of the axis; Assume that the estimation errors of the magnitude and direction of the target's maneuvering acceleration both follow a Gaussian distribution, and that the target's maneuvering acceleration... The estimation error is The two thrust direction angles of the target The estimation errors are respectively and ; The process of solving for the reachable envelope of the maneuvering target at the interception time is as follows: 1) Consider In principle, the target's true acceleration amplitude The range is The true thrust direction angle of the target The range is The true thrust direction angle of the target The range is ; 2) Set the maximum amplitude of the target's maneuvering acceleration to be [value missing]. ; The traversal step size for the two thrust direction angles is set to... Then according to step size By iterating through the data, the target thrust direction angle can be obtained in the following form. in , As an intermediate variable, It is a multiplication sign. , This represents the floor function; Under each set of determined target thrust direction angles, combined with the maximum amplitude of the target maneuvering acceleration... The target's maneuvering acceleration in the target orbital coordinate system is determined as follows: 3) Using the target's position and velocity vectors observed by the observation equipment at the current moment as initial values, perform numerical integration calculations on the target's dynamic model under continuous thrust to solve for the target's terminal position vector. ; in This represents the total number of terminal locations. ; The dynamic model of the target under continuous thrust is expressed as follows: in, The acceleration of the target in the target orbit coordinate system is the maneuvering acceleration. For the target in the target orbit coordinate system Under-axis acceleration For the target in the target orbit coordinate system Under-axis acceleration For the target in the target orbit coordinate system The under-axis acceleration, where T is the transpose. Indicates radial direction, Indicates the normal direction. Indicates circumference; The gravitational constant representing the Earth. and Let these represent the position vector and velocity vector of the J2000 inertial frame, respectively. Indicates the magnitude of the corresponding position vector; express The first derivative, express The first derivative; Represents the norm; 4) When the target is in unpowered flight, perform numerical integration calculations on the target's dynamic model under unpowered conditions to solve for the target's terminal position vector. ; The dynamic model of the target device under no-power conditions is a two-body model, expressed as follows: 5) and The combination of these elements forms the envelope of the reachable domain of the maneuvering target at the moment of interception.

3. The many-to-one collaborative interception method based on location coverage according to claim 2, characterized in that: In step two, the envelope of the maneuvering target reachable at the predicted interception time obtained in step one is sampled to obtain all sampling points of the maneuvering target reachable at the predicted interception time; the specific process is as follows: For each terminal position vector ,Will and Make a connection; Let the number of equal divisions be . Then connect the internal sampling points The formula is: For each terminal position vector, we obtain: sampling points ; Thus, combined and This yields all the sampling points within the reachable domain of the target.

4. The many-to-one cooperative interception method based on location coverage according to claim 3, characterized in that: In step three, an optimization index for reachability domain allocation is constructed. Based on the number of friendly interceptors, an optimization algorithm is used to solve for the aiming points within the reachability domain of the maneuvering target that match the number of interceptors. The specific process is as follows: Let the positions of all sampling points in the reachable domain of the maneuvering target obtained in step two, in the J2000 geocentric inertial coordinate system, be: In the formula, The first domain of the target reachable region The positions of the sampling points in the J2000 geocentric inertial coordinate system. This represents the total number of sampling points within the reachable domain of the target. This indicates the positions of all sampling points within the target reachable domain in the J2000 geocentric inertial coordinate system; The first domain of the target reachable region Each sampling point is located in the J2000 geocentric inertial coordinate system. The position below the axis, The first domain of the target reachable region Each sampling point is located in the J2000 geocentric inertial coordinate system. The position below the axis, The first domain of the target reachable region Each sampling point is located in the J2000 geocentric inertial coordinate system. Position below the axis; Assume there are a total of There are several interceptors, so it is necessary to determine the target's reachability domain. If there are _ ... , recorded as in express The position of the aiming point in the J2000 geocentric inertial coordinate system; Indicates the first The position of the aiming point in the J2000 geocentric inertial coordinate system; For the first The aiming point is in the J2000 geocentric inertial coordinate system. The position below the axis, For the first The aiming point is in the J2000 geocentric inertial coordinate system. The position below the axis, For the first The aiming point is in the J2000 geocentric inertial coordinate system. Position below the axis; T is for transpose; The optimization metrics for reachability domain allocation are constructed as follows: First, solve for the reachable domain of the objective. sampling points Distances The distance between each aiming point is calculated, and the minimum distance is obtained, expressed as: Then, traverse all sampling points in the reachable region of the target and calculate the minimum distance. The final index is obtained by summing the results, and is expressed as follows: Furthermore, in order to The aiming points are distributed within the target's reachability region, and the following constraints need to be set: in This represents the minimum distance between all aiming points within the target's reachability domain; Indicates the first The position of the aiming point in the J2000 geocentric inertial coordinate system. ; Indicates the first The position of the aiming point in the J2000 geocentric inertial coordinate system. ; By using an optimization algorithm to optimize the above problem, an optimized solution can be obtained. The position of the aiming point.

5. A many-to-one cooperative interception method based on location coverage according to claim 4, characterized in that: By employing an optimization algorithm to optimize the above problem, an optimized solution can be obtained. The location of each aiming point; the specific process is as follows: by The position of the aiming point in the J2000 geocentric inertial coordinate system As the independent variable; by To optimize the indicators; As a constraint; Optimization is performed using an optimization algorithm to obtain the optimized result. The position of the aiming point in the J2000 geocentric inertial coordinate system is... The position of the aiming point.

6. The many-to-one cooperative interception method based on location coverage according to claim 5, characterized in that: In step four, the Hungarian algorithm is used to obtain... One interceptor and The optimal fuel correspondence for each aiming point is plotted. The coverage of the reachable domain of each interceptor with the reachable domain of the target; the specific process is as follows: Step 41: Use the Hungarian algorithm to obtain the optimal fuel correspondence between multiple interceptors and multiple aiming points; Step 42: Solve for the reachability envelope of the interceptor; Step 43: Drawing The coverage of the reachable domain of an interceptor with the reachable domain of the target.

7. A many-to-one cooperative interception method based on location coverage according to claim 6, characterized in that: In step four, the Hungarian algorithm is used to obtain the optimal fuel correspondence between multiple interceptors and multiple aiming points; the specific process is as follows: Given the initial position and velocity of an interceptor and the target point that the interceptor needs to reach, the transition time is the time from the current moment to the predicted interception moment. Solve using the Lambert algorithm respectively Each interceptor went to The magnitude of the velocity increment required for each aiming point; In obtaining Each interceptor went to After determining the required velocity increment for each aiming point, and using optimal fuel efficiency as an indicator, the Hungarian algorithm is employed to obtain... One interceptor and The correspondence between each aiming point is completed. Task allocation for each interceptor.

8. A many-to-one cooperative interception method based on location coverage according to claim 7, characterized in that: In step four-two, the reachability envelope of the interceptor is solved; the specific process is as follows: Assume that at the current moment, all interceptors have available fuel. ,based on The task allocation results for each interceptor apply pulse thrust to each interceptor. After aligning with their respective aiming points, the remaining fuel of each interceptor is calculated as follows: ,in Indicates the magnitude of the applied pulse; in, Indicates the remaining fuel level of each interceptor; Assuming that in the J2000 geocentric inertial frame, the two thrust direction angles of the pulse thrust are respectively and ; in This indicates that in the J2000 geocentric inertial frame, the pulse thrust is... Projection in the plane and The included angle of the axis; This indicates that in the J2000 geocentric inertial frame, the pulse thrust and Angle between planes; consider and The traversal step sizes are respectively and Then for each group of traversals, the obtained and The corresponding pulse thrust can be obtained as follows: in, This indicates the pulse thrust provided by the remaining fuel of each interceptor; After applying the corresponding pulse thrust to the interceptor, the position vector of the interceptor at the predicted interception time can be obtained by performing orbital numerical integration on the dynamic model of the interceptor under no-power conditions. Traversing the two thrust direction angles of the pulse thrust and The set of all position vectors of the interceptor at the predicted interception time constitutes the envelope of the reachable domain of the interceptor.

9. A many-to-one cooperative interception method based on location coverage according to claim 8, characterized in that: The dynamic model of the interceptor under no-power conditions is a two-body model, expressed as: in, The gravitational constant of the Earth, and Let these represent the position vector and velocity vector of the J2000 inertial frame, respectively. Indicates the magnitude of the corresponding position vector; express The first derivative, express The first derivative.

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