A space-based interception guidance control method and system for a satellite group on the same orbit

Abstract

The present invention provides a space-based interception guidance control method and system for a co-orbital satellite group, belonging to the field of space target interception guidance technology. In order to solve the problem of poor stability and low interception accuracy caused by J2 perturbation during orbit design of a co-orbital satellite group in a complex space environment in the existing interception guidance method. After two-body motion modeling of the interception satellite and the target satellite is performed respectively, the orbit of the interception satellite under J2 perturbation is solved and relevant analysis is performed, and an orbit correction algorithm is established in combination with the influence of J2 perturbation to correct the orbit of the interception satellite. After obtaining the corrected interception satellite orbit, a proportional guidance law is designed to control the interceptor to further approach the target satellite, so as to intercept and strike the co-orbital satellite group of the space target. The present invention ensures that the interceptor can accurately approach and destroy the target satellite in a complex space environment, ensures the interception success rate and stability of the system, and improves the guidance accuracy and response speed to achieve precision strikes.

Description

Technical Field

[0001] The present invention relates to the technical field of space target interception guidance, and in particular to a space-based interception guidance control method and system for a co-orbital satellite group. Background Art

[0002] The advantages of low-orbit giant star constellation, such as low launch cost, wide coverage, low latency and low power consumption, have become the future of space technology development. The satellite group in the same orbit is an important part of the low-orbit giant star constellation. Through dense layout, it realizes global interoperability and plays an important role in reconnaissance and communication. It also brings potential risks to my country's network, data and military security.

[0003] In order to achieve the interception and guidance of non-cooperative co-orbital satellite cluster targets, it is urgent to develop corresponding approach technology. At present, through reasonable orbit design, the interceptor can periodically revisit each sub-satellite of the co-orbital satellite cluster, so as to carry out space security tasks such as interception. However, in the orbit design for the co-orbital satellite cluster, affected by the non-spherical gravitational field of the earth, the J2 perturbation affects the orbit stability and interception accuracy. Especially in complex space environments, it is difficult for the interceptor to accurately approach and destroy the target satellite, resulting in a low interception success rate and poor stability. Summary of the invention

[0004] The technical problems to be solved by the present invention are:

[0005] In order to solve the problems that the existing interception guidance method lacks guidance for the same-orbit satellite group in a complex space environment, and the interception satellite is affected by J2 perturbation, resulting in poor stability and low interception accuracy.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] The present invention provides a space-based interception guidance control method for a satellite group on the same orbit, comprising the following steps:

[0008] S100, modeling the target satellite orbit and solving the intercept satellite orbit under the two-body motion problem,

[0009] This includes deriving the relationship between the target satellite position and its velocity over time based on the basic dynamic equations under the two-body problem and the Kepler equation, and determining the initial state of the target star cluster based on the design parameters of the co-orbital satellite cluster, and then completing the dynamic modeling of the target satellite; deriving the relationship between the orbital parameters of the target satellite and the interceptor satellite based on the interception plan, and solving to obtain the initial interceptor satellite orbit;

[0010] S200, model the interceptor satellite and target satellite under J2 perturbation and analyze the impact of J2 perturbation,

[0011] The first-order perturbation model of the earth's gravitational field considering J2 perturbation is obtained by describing the earth's gravitational field with potential function. Then, the analytical form of the perturbation force component in the geocentric inertial system is obtained by taking the negative partial derivative of the potential function with respect to the x-axis, y-axis and z-axis of the geocentric inertial system. The differential equations solved by ode45 are used to obtain the position of the target satellite and the interceptor satellite under J2 perturbation and the relationship between the change of their velocities with time. Then, the modeling and simulation of the orbits of the interceptor satellite and the target satellite under J2 perturbation are completed, and the influence of J2 perturbation on the orbit of the interceptor satellite is analyzed.

[0012] S300, re-correct the orbital parameters of the interceptor satellite according to the J2 perturbation effect,

[0013] The method includes an orbit correction scheme that uses orbit maneuvers as a means according to the influence of the J2 perturbation obtained in step S220 on the orbits of the interceptor satellite and the target satellite, and performs multiple pulse orbit changes so that the distance between the interceptor satellite orbit and the target satellite near the interception point meets a threshold value, thereby completing the orbit correction; then a differential correction algorithm is used as the orbit correction algorithm, and the small velocity pulse Δv is solved by the required correction amount δr to obtain the corrected orbit and then the process is repeated continuously; after n iterations, at the rendezvous moment, when the position difference between the target satellite and the interceptor satellite is within a preset accuracy range, the orbit correction of the interceptor satellite under the J2 perturbation is achieved;

[0014] S400, through the true proportional guidance law, the interceptor satellite approaches the target satellite.

[0015] Including establishing a relative motion coordinate system in three-dimensional space and fixing it to the interceptor, designing the command acceleration a M According to the geometric relationship, the kinematic modeling of the true proportional guidance law in three-dimensional space is carried out, and the relative position vector R and the relative velocity vector V in the geocentric inertial system are used. r Complete the design and simulation of the true proportional guidance rate; based on the orbit correction in step S300, take the moment of the preset time ahead of the expected interception time, the interception satellite releases the sub-interceptor, and starts proportional guidance for the sub-interceptor; analyze the trajectory, distance and command acceleration change of the interception satellite and the target satellite obtained by simulation over time, and realize the true proportional guidance law to control the interception satellite to further approach the target satellite.

[0016] Furthermore, in step S100, it includes:

[0017] S110, modeling the two-body motion of the target satellite.

[0018] In the geocentric inertial system, the motion of the target satellite around the earth is simplified to the motion of a particle around the central gravitational body; the basic dynamic equation under this two-body problem is:

[0019]

[0020] Among them, r is the position vector from the center of the earth to the target satellite at the current moment; μ is the gravitational constant of the central celestial body; is the acceleration vector from the center of the earth to the target satellite at the current moment; f is the resultant external force on the target satellite except the gravitational force;

[0021] For the target satellite, the resultant external force f is zero, and the motion of the target satellite satisfies Kepler's equation:

[0022]

[0023] Among them, t p is the flight time of the target satellite; α is the semi-major axis of the target satellite orbit; e is the eccentricity of the target satellite; Ψ is the anomaly angle of the target satellite;

[0024] There is a relationship between the target satellite's eccentric anomaly angle Ψ and true anomaly angle θ:

[0025]

[0026] The flight time t with perigee as time zero is obtained p Relationship with the true anomaly θ;

[0027] The relationship between the six orbital numbers and the position vector r and velocity vector v from the center of the Earth to the target satellite is:

[0028]

[0029] Where i is the target satellite orbit inclination; Ω is the target satellite ascending node longitude; ω is the target satellite perigee argument; θ is the target satellite true anomaly;

[0030] According to the relationship between the position and velocity of the target satellite and time, the orbit model of the target satellite under the two-body problem is established;

[0031] S120, determining the initial state of the target star cluster according to the orbital parameters of the target co-orbital star cluster, wherein the orbital parameters include the semi-major axis, eccentricity, orbital inclination, ascending node longitude, perigee argument and true anomaly of the intercepting satellite;

[0032] S130, solving the interception satellite orbit, solving the parameters of the interception satellite orbit obtained in step S120 according to the model of the target satellite orbit under the two-body problem obtained in step S110,

[0033] According to Kepler's third law:

[0034]

[0035] According to the interception plan that the interception satellite can meet the next satellite in the orbit of the target co-orbital satellite group at the perigee every time it runs one week, the orbital period T of the interception satellite is obtained. m is N+1 / N or N-1 / N of the target satellite, where N is the number of low-orbit satellites on the orbital plane; take the case where the intercepting satellite has a longer orbital period:

[0036]

[0037] Using the transformed form of Kepler's third law, the semi-major axis a of the interceptor satellite orbit is obtained: m ; According to the coincidence of the perigee of the intercepting satellite orbit and the perigee of the target satellite orbit, the two orbits have the same perigee radius vector:

[0038] a1-c1=a m -c m

[0039] Among them, c1, c m are the orbital semi-focal lengths of the target satellite and the interceptor satellite, respectively;

[0040] Get the orbital eccentricity of the intercepting satellite:

[0041]

[0042] The eccentricity vector is expressed using the six orbital elements other than the true anomaly:

[0043]

[0044] The direction of the interceptor satellite eccentricity vector Equal to the target satellite eccentricity vector direction

[0045] cosω m cosΩ m -sinω m cosi m sinΩ m =cosω1cosΩ1-sinω1cosi1 sinΩ1

[0046] cosω m sinΩ m +sinω m cosi m cosΩ m =cosω1sinΩ1+sinω1cosi1 cosΩ1

[0047] sinω m sini m =sinω1sini1

[0048] Given the additional constraint i m ,ω m ,Ω m After finding one of the values ​​in , the other two parameters of the intercepting satellite orbit are obtained according to the equation group; then the intercepting satellite orbit and the target satellite orbit are solved for the two cases of being coplanar and non-planar to obtain i m ,ω m ,Ω m , and then solve the true anomaly to get the intercept satellite orbit;

[0049] In order for the interceptor satellite to rendezvous with the target satellite at perigee, the time when the interceptor satellite and the first target satellite first pass the perigee should satisfy:

[0050]

[0051] Among them, k is the condition for the intercept satellite to rendezvous with the k+1 satellite first;

[0052] Take k = 0, t m = t1, according to t m The true anomaly angle of the satellite intercepted at the moment is zero, and the true anomaly angle of the satellite intercepted at the initial moment is obtained.

[0053] Furthermore, in step S200, it includes:

[0054] Orbital solution under S210 and J2 perturbations,

[0055] The earth's gravitational field is described by the potential function U, and the earth's gravity F is the negative gradient of the potential function:

[0056]

[0057] Among them, i is the unit vector in the x-axis direction in the geocentric inertial system; j is the unit vector in the y-axis direction in the geocentric inertial system; k is the unit vector in the z-axis direction in the geocentric inertial system;

[0058] For the first-order perturbation model of the earth's gravitational field considering the J2 term, we have:

[0059]

[0060] in, is the latitude of the subsatellite point; R e is the equatorial radius of the Earth; J2 = -1.08264×10 -3 ;

[0061] The first term below is the central gravitational potential function, and the second term is the Earth flattening perturbation term that causes the interference force:

[0062]

[0063] Right now:

[0064]

[0065] The kinetic equation In component form:

[0066]

[0067] Potential function U p Calculate the negative partial derivatives of x, y, and z respectively, and obtain the perturbation force component f in the geocentric inertial system x 、f y 、f z The analytical form of the differential equations can be directly obtained by using the Cowell method and the ode45 solver.

[0068] S220, analyze the influence of J2 perturbation, and expand the simulation time range to the orbit period T of the interceptor satellite under the two-body motion. m , use step S210 to solve the state vector of the intercepted satellite, set the point at the interval constant time as the sampling point, calculate the satellite orbit at the corresponding time, and thus calculate the corresponding six orbital numbers:

[0069]

[0070] Among them, r is the position vector of the earth's center to the satellite at the current moment; v is the velocity vector of the satellite at the current moment; z i is the z-axis basis of the geocentric inertial system; x i is the x-axis basis of the geocentric inertial system; h = r × v is the satellite angular momentum vector; n = z i ×j is the ascending node vector; e is the eccentricity vector; n i is the direction vector of the ascending node vector;

[0071] The satellite state of the interceptor satellite co-orbiting with the target satellite is selected for calculation to obtain the relationship between the six orbital elements and time, and the influence of the J2 perturbation on the orbit is used as the basis for correcting the orbit in step S300.

[0072] Further, in step S300, it includes: using a differential correction algorithm to transform the state (t1, r1, v1) of the intercepting satellite at time t1 under the J2 model and the position vector at time t2 The corresponding relationship between them is expressed as a functional relationship:

[0073]

[0074] At time t1, a velocity pulse Δv1 is added to the intercepting satellite:

[0075]

[0076] When Δv1 is small enough, it can be regarded as a partial derivative relationship:

[0077]

[0078] make Then there is Right now Take Δv1 as Δv 1x =[0.001,0,0] T , Δv 1y =[0,0.001,0] T , Δv 1z =[0,0,0.001] T , substituted into the J2 model for calculation, and the corresponding three position changes are obtained Then the matrix M1 can be:

[0079]

[0080] Use the M1 matrix obtained and the required position correction δr (1) Calculate the required velocity pulse Δv1:

[0081]

[0082] The corrected trajectory is calculated from the velocity pulse Δv1, and the difference between the corrected trajectory and the target position at time t2 is taken as the new required position correction δr (2) , recalculate the above process to obtain the new matrix M2;

[0083] The speed pulse is:

[0084]

[0085] Recalculate the corrected trajectory and the new required position correction δr based on the obtained velocity pulse Δv2 (3) ;

[0086] Repeat the correction process, then we have:

[0087]

[0088] After n iterations, the position difference between the intercept satellite and the target satellite at time t2 is δr (n+1) Within the required accuracy range, the speed pulses of each iteration are accumulated to obtain the final speed pulse Δv required for this correction:

[0089]

[0090] Furthermore, in step S400, it includes:

[0091] Establish a relative motion coordinate system to connect the interceptor satellite to the interceptor, where the origin of the relative motion coordinate system is O r Located at the interceptor center of mass, x r The y axis is parallel to the intersection of the instantaneous line of sight transfer plane and the equatorial plane, and its positive direction points to the target satellite; r The axis is located in the instantaneous line of sight transfer plane and is perpendicular to x r Axis, the positive direction is toward the North Pole of the Earth; z r Axis and x r Axis, y r The axes are vertical and form a right-hand system; the relative speed V between the line of sight and the interceptor and the target satellite r Always at x r O r y r In the plane, the angular velocity of the line of sight Ω is related to z r Axis parallel; V r Decomposed into the approaching speed V along the line of sight c and the component V perpendicular to the line of sight n :

[0092] |V c |=|R·V r | / |R|

[0093] |V n |=|R×V r | / |R|

[0094] Where R is the relative position vector in the Earth-centered inertial system;

[0095] Command acceleration a M Applied in the direction perpendicular to the line of sight, its magnitude is proportional to the product of the approach velocity and the line of sight angular velocity:

[0096] |a M |=N|V c |(dλ / dt)

[0097] Where λ is the instantaneous sight angle, located at x r O r y r In the plane; N is the proportionality factor;

[0098] Because M Parallel to V n , a M Perpendicular to V c , Ω is perpendicular to a M , so a M With Vc ×Ω are parallel, then:

[0099] |V c ×Ω|=|V c ||Ω|=|V c |(dλ / dt)

[0100] The vector form of the true proportional guidance law is obtained:

[0101] a M =NV c ×Ω

[0102] Since Ω=R×V r / R 2 , so:

[0103]

[0104] After the kinematic modeling of the true proportional guidance law in three-dimensional space is completed, according to the relative position vector R and relative velocity vector V in the geocentric inertial system r Complete the design and simulation of the true proportional guidance law, and then achieve the precise approach of the interception target to the co-orbital satellite group target.

[0105] The present invention provides a space-based interception guidance control system for a satellite group on the same orbit. The system has a program module corresponding to the above steps, and executes the steps in the above space-based interception guidance control method for a satellite group on the same orbit when running.

[0106] The present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of a space-based interception guidance control method for a co-orbital satellite group when called by a processor.

[0107] Compared with the prior art, the present invention has the following beneficial effects:

[0108] (1) Comprehensive summary of the impact of J2 perturbations on orbits

[0109] J2 perturbation is caused by the non-spherical gravitational field of the earth, which produces periodic and long-term cumulative effects on the six elements of the satellite orbit, affecting the orbit stability and interception accuracy. The present invention summarizes the influence of J2 perturbation on the orbit of the intercepted satellite through orbit modeling and simulation of the target satellite and the intercepted satellite under the J2 model under the two-body dynamics model. The J2 perturbation has a short-term periodic fluctuation effect on the semi-major axis a, eccentricity e, and orbit inclination i of the intercepted satellite orbit, but no long-term cumulative effect. The J2 perturbation has both a short-term periodic fluctuation effect and a long-term cumulative effect on the right ascension Ω of the ascending node and the perigee argument ω of the intercepted satellite orbit, providing guidance for orbit correction under J2 perturbation.

[0110] (2) Effective J2 perturbation orbit correction

[0111] Combined with the analysis of the influence of J2 perturbation on the orbits of both parties, the present invention adopts a differential correction algorithm to design a correction scheme, which reduces the influence of J2 perturbation on the interceptor's interception and braking of non-co-orbit satellites, and effectively corrects the minimum rendezvous distance with each target satellite to within 20 kilometers, ensuring that the target co-orbital satellite group can be accurately intercepted in the space environment under J2 perturbation, filling the technical gap in the guidance of the co-orbital satellite group;

[0112] (3) Precise proportional guidance control

[0113] By deriving the true proportional guidance law in three-dimensional space and completing the kinematic modeling using vector cross multiplication, the true proportional guidance law was applied to the terminal guidance of the interceptor in low earth orbit. By gradually approaching the target satellite with continuous small thrust, the final interception and strike was completed accurately and efficiently, and the relative distance during the rendezvous was greatly shortened, ensuring the effectiveness of the space-based interceptor's anti-co-orbital satellite group technical solution and the corresponding guidance and control method.

[0114] (4) Test performance

[0115] According to the test experiments after correcting the orbit by considering the influence of J2 perturbation and adding true proportional guidance law, the space-based interception guidance control method designed by the present invention for the co-orbital satellite cluster realizes the on-orbit interception of the co-orbital satellite cluster. The data simulation performed by simulation software shows that the shortest distance between the interceptor and the target satellite during the interception process is 0.4km, which shows the high accuracy and stability of the method in space-based interception guidance. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] Figure 1 It is a flow chart of a space-based interception guidance control method for a co-orbital satellite group in an embodiment of the present invention;

[0117] Figure 2 3D schematic diagram of the interception orbit under STK simulation J2 perturbation in an embodiment of the present invention, wherein the red line is the interception satellite orbit and the blue line is the target satellite group orbit;

[0118] Figure 3 2D schematic diagram of the interception orbit under STK simulation J2 perturbation in an embodiment of the present invention, wherein the red line is the sub-satellite point trajectory of the intercepting satellite, and the blue line is the sub-satellite point trajectory of the target satellite group;

[0119] Figure 4 A diagram showing the distance variation between the intercepting satellite and a certain satellite in the target constellation under the J2 perturbation in an embodiment of the present invention;

[0120] Figure 5A diagram showing the distance variation between the intercepting satellite and a certain satellite in the target constellation after J2 perturbation correction in an embodiment of the present invention;

[0121] Figure 6 This is a diagram showing the distance variation between the sub-interceptor and a satellite in the target constellation according to the true proportional guidance law in the final guidance stage in an embodiment of the present invention. DETAILED DESCRIPTION

[0122] In the description of the present invention, it should be noted that the terms "first", "second", and "third" mentioned in the embodiments of the present invention are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first", "second", and "third" may explicitly or implicitly include one or more of the features.

[0123] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0124] Specific implementation plan 1: Combine Figures 1 to 6 As shown, the present invention provides a space-based interception guidance control method for a satellite group on the same orbit, comprising the following steps:

[0125] S100, modeling the orbit of the target satellite and solving the orbit of the intercepting satellite under the two-body motion problem, including analyzing and constructing the dynamic model of the target satellite under the two-body problem, and solving the orbit of the intercepting satellite according to the designed interception plan;

[0126] First, the relationship between the position and velocity of the target satellite and time is derived based on the basic dynamic equations under the two-body problem and the Kepler equation, and the design parameters of the satellite group on the same orbit are referred to. This implementation plan takes the Starlink satellite as an example to determine the initial state of the target star group, and then completes the dynamic modeling of the target satellite; the relationship between the orbital parameters of the target satellite and the intercepting satellite is obtained according to the designed interception scheme, and the initial intercepting satellite orbit is obtained by solving;

[0127] Specifically include:

[0128] S110, firstly, a two-body motion model is constructed for the target satellite.

[0129] In the geocentric inertial system, the motion of the target satellite around the earth is simplified to the motion of a particle around the central gravitational body; the basic dynamic equation under this two-body problem is:

[0130]

[0131] Among them, r is the position vector from the center of the earth to the target satellite at the current moment; μ is the gravitational constant of the central celestial body; is the acceleration vector from the center of the earth to the target satellite at the current moment; f is the resultant external force on the target satellite except the gravitational force;

[0132] For the target satellite, the resultant external force f is zero, and the motion of the target satellite satisfies Kepler's equation:

[0133]

[0134] Among them, t p is the flight time of the target satellite; α is the semi-major axis of the target satellite orbit; e is the eccentricity of the target satellite; Ψ is the anomaly angle of the target satellite;

[0135] There is a relationship between the eccentric anomaly angle Ψ and the true anomaly angle θ:

[0136]

[0137] In the two-body problem, except for the true anomaly θ, the six orbital elements do not change with time t. Therefore, when the other five of the six orbital elements are also known, the change of the target satellite's motion state with time can be completely determined.

[0138] The relationship between the six orbital numbers and the position vector r and velocity vector v from the center of the Earth to the target satellite is:

[0139]

[0140] Where i is the target satellite orbit inclination; Ω is the target satellite ascending node longitude; ω is the target satellite perigee argument; θ is the target satellite true anomaly;

[0141] After sorting, we can get the relationship between the position of the target satellite and its speed and time, so as to establish the orbit model of the target satellite under the two-body problem;

[0142] S120, determining the initial state of the target star cluster according to the orbital parameters of the target co-orbital star cluster,

[0143] The present invention selects a group of satellites on a certain orbital plane in the Starlink plan as the interception target. It is known that in the first phase of the Starlink plan, 1584 satellites are deployed on 72 circular orbits with different right ascensions of ascending nodes, and 22 satellites are evenly distributed on each orbit; for each orbit, its orbital inclination i=53°, orbital altitude 550km, eccentricity e=0, then the orbital semi-major axis a=6921.004km; since the 72 orbits only differ in the right ascension of the ascending node, and all the orbits are approximately evenly distributed on the equatorial plane, the present invention assumes that the orbits of these 72 orbits are The right ascension Ω of the ascending node is 5°, 10°, ..., 360°. To be similar to the actual target situation, an orbital plane with the right ascension Ω of the ascending node being 30° is selected for research; when the eccentricity e is 0, the perigee argument ω of the orbit has no physical meaning and is a circular orbit; for the convenience of definition and simulation research, it is assumed that e=0.00010; in addition, ω=20° is selected, and the point on the target satellite orbit corresponding to 20° rotation from the ascending node along the satellite movement direction is called the target satellite orbit perigee, and the intercept satellite orbit and the target satellite orbit will intersect at this point;

[0144] Combination Figure 3 As shown, the 22 target satellites located on the same orbital plane are numbered according to the true anomaly. Since the orbital inclination i = 53°, the angle between the orbital plane and the equatorial plane is an acute angle, which is a prograde orbit. Therefore, the running direction of the target satellite is the same as the rotation direction of the earth. Assume that at the initial moment there is a target satellite exactly at the perigee, that is, the initial true anomaly θ of the satellite is 0°. Let this satellite be target satellite No. 1, and the next target satellite passing the perigee be target satellite No. 2. Then the initial true anomaly of each satellite can be obtained.

[0145] S130, solving the interception satellite orbit, solving the parameters of the interception satellite orbit according to the model of the target satellite orbit under the two-body problem,

[0146] According to Kepler's third law:

[0147]

[0148] In a co-orbital satellite group with 22 low-orbit satellites in the orbital plane, according to the interception scheme of the present invention that "the interception satellite can meet the next satellite on the orbit of the target co-orbital satellite group exactly at the perigee every time it runs one circle", the orbital period T of the interception satellite is obtained. m It is 23 / 22 or 21 / 22 of the target satellite. For the convenience of expression, the present invention only selects the case where the interception satellite orbit period is longer for subsequent research:

[0149]

[0150] Using the transformed form of Kepler's third law, the semi-major axis a of the intercepting satellite orbit can be obtained:m ; According to the design plan that "the perigee of the intercept satellite orbit coincides with the perigee of the target satellite orbit", the two orbits have the same perigee radius vector:

[0151] a1-c1=a m -c m

[0152] Among them, c1, c m are the orbital semi-focal lengths of the target satellite and the interceptor satellite, respectively;

[0153] After sorting, the orbital eccentricity of the intercepting satellite is:

[0154]

[0155] The eccentricity vector is expressed using the six orbital elements other than the true anomaly:

[0156]

[0157] Since the direction of the perigee radius vector is the same as the direction of the orbital eccentricity vector, the directions of the eccentricity vectors of the target satellite orbit and the interceptor satellite orbit are also the same; then the direction of the interceptor satellite eccentricity vector is Equal to the target satellite eccentricity vector direction

[0158] cosω m cosΩ m -sinω m cosi m sinΩ m =cosω1cosΩ1-sinω1cosi1 sinΩ1

[0159] cosω m sinΩ m +sinω m cosi m cosΩ m =cosω1sinΩ1+sinω1cosi1 cosΩ1

[0160] sinω m sini m =sinω1sini1

[0161] In the obtained three-equation system consisting of three equations, only two equations are independent, so the system has countless sets of solutions; the additional constraint is given by i m ,ω m ,Ω mAfter a certain value in is found, the other two parameters of the intercept satellite orbit are obtained according to the equation group; since the perigee argument ranges from 0° to 180°, the equation has one and only one set of solutions in the range of 0° to 360°; the intercept satellite orbit and the target satellite orbit are solved and analyzed for the two situations of being coplanar and out of plane:

[0162] 1) Coplanar situation: i m =i1=53°,ω m =ω1=20°,Ω m =Ω1=30°;

[0163] 2) Out-of-plane situation: Take any interception satellite orbit inclination i m =60°, find ω m ≈18.39°,Ω m ≈32.92°;

[0164] Among the six numbers of the intercept satellite orbit, except the true anomaly angle θ m The remaining five parameters have been determined, and the intercept satellite orbit can be obtained by solving the true anomaly angle;

[0165] In order to make the interceptor satellite rendezvous with the target satellite at perigee, the time when the interceptor satellite and target satellite No. 1 pass the perigee for the first time should satisfy:

[0166]

[0167] Among them, k is the condition for the intercept satellite to rendezvous with the k+1 satellite first, which only affects the order in which the intercept satellite rendezvous with each target satellite. Therefore, to simplify the simulation, k=0, t m = t1, at which time the interceptor satellite first intersects with target satellite No. 1; according to t m The true anomaly angle of the satellite intercepted at the moment is zero, so the true anomaly angle of the satellite intercepted at the initial moment can be obtained;

[0168] S200, modeling of interceptor satellite and target satellite under J2 perturbation and analysis of J2 perturbation influence. The present invention models and simulates interceptor satellite and target satellite under J2 perturbation, and analyzes the influence of J2 perturbation on the orbits of interceptor satellite and target satellite; the first-order perturbation model of the earth's gravitational field considering the J2 term is obtained by describing the earth's gravitational field with a potential function, and then the analytical form of the perturbation force component under the earth's center inertial system is obtained by taking the negative partial derivative of the potential function with respect to the x-axis, y-axis and z-axis of the earth's center inertial system. The differential equation obtained by solving ode45 can be used to obtain the relationship between the position and velocity of the target satellite and the interceptor satellite under J2 perturbation and the time, thereby completing the modeling and simulation of the orbits of the interceptor satellite and the target satellite under J2 perturbation;

[0169] After completing the modeling simulation under J2 perturbation, the simulation time range is expanded to 110 times the orbital period of the intercepting satellite under two-body motion. Every 100 seconds is used as a sampling point to calculate the state vector of the satellite at that moment to obtain the corresponding six orbital numbers. By observing and analyzing the calculation results, the influence of J2 perturbation on the six orbital numbers of the satellite can be obtained.

[0170] Specifically include:

[0171] Orbital solution under S210 and J2 perturbations,

[0172] The earth's gravitational field is described by the potential function U, and the earth's gravity F is the negative gradient of the potential function:

[0173]

[0174] Among them, i is the unit vector in the x-axis direction in the geocentric inertial system; j is the unit vector in the y-axis direction in the geocentric inertial system; k is the unit vector in the z-axis direction in the geocentric inertial system;

[0175] For the first-order perturbation model of the earth's gravitational field considering the J2 term, we have:

[0176]

[0177] in, is the latitude of the subsatellite point; R e is the equatorial radius of the Earth; J2 = -1.08264×10 -3 ;

[0178] The first term below is the central gravitational potential function, and the second term is the Earth flattening perturbation term that causes the interference force:

[0179]

[0180] Right now

[0181]

[0182] The kinetic equation In component form:

[0183]

[0184] Potential function U p Calculate the negative partial derivatives of x, y, and z respectively, and obtain the perturbation force component f in the geocentric inertial system x 、f y 、f zThe analytical form of the differential equations is obtained by using the Cowell method and the ode45 solver. In order to make the initial motion state of the interceptor satellite and the target satellite under the J2 perturbation the same as that under the two-body motion problem, the components of the initial position and initial velocity in the x, y, and z directions obtained under the two-body motion are input into the ode45 solver as the initial values ​​of the differential equations, and the relationship between the position and velocity of the target satellite and the interceptor satellite over time is obtained.

[0185] S220, analyze the impact of J2 perturbation,

[0186] In step S210, the modeling and simulation of the interceptor satellite and the target satellite under the J2 perturbation have been completed, and the influence of the J2 perturbation will now be analyzed;

[0187] In order to facilitate the observation of the simulation results, the simulation time range is expanded to 110 times the orbital period T of the interceptor satellite under the two-body motion. m , to ensure that the simulation time range is an integer multiple of both the intercept satellite operation period and the target satellite operation period; the satellite state vector is solved using the method in the previous steps, and every 100 seconds is a sampling point to ensure the simulation speed while ensuring the simulation accuracy; the satellite orbit at the corresponding time is calculated, and the corresponding six orbital numbers are calculated accordingly:

[0188]

[0189] Where r is the satellite’s current position vector; v is the satellite’s current velocity vector; z i is the z-axis basis of the geocentric inertial system; x i is the x-axis basis of the geocentric inertial system; h = r × v is the satellite angular momentum vector; n = z i ×h is the ascending node vector; e is the eccentricity vector; n i is the direction vector of the ascending node vector;

[0190] The satellite state of the interceptor satellite in the same orbit as the target satellite is selected for calculation, and the relationship between the six orbital elements and time is obtained. The influence of J2 perturbation on the orbit is summarized as follows: J2 perturbation has a short-term periodic fluctuation effect on the semi-major axis a, eccentricity e, and orbital inclination i of the interceptor satellite orbit, but no long-term cumulative effect; it has both a short-term periodic fluctuation effect and a long-term cumulative effect on the right ascension Ω and perigee argument ω of the interceptor satellite orbit;

[0191] S300, re-correct orbital parameters according to the J2 perturbation effect,

[0192] This step designs an orbit correction scheme that relies on orbit maneuvers based on the influence of the J2 perturbation obtained in step S220 on the six elements of the satellite orbit. Through multiple pulse orbit changes, the intercepting satellite orbit is made close enough to the target satellite near the interception point, thereby completing the orbit correction. Then, a differential correction algorithm is used as the orbit correction algorithm, and the small velocity pulse Δv is solved by the required correction amount δr to obtain the corrected orbit and repeat this process. After n iterations, the difference between the position of the target satellite and the intercepting satellite at the rendezvous moment is within a certain accuracy range, thereby achieving orbit correction under J2 perturbation, so that the intercepting satellite and the target satellite are close enough at the time of rendezvous. The accumulation of velocity pulses from all iterations is the pulse required for this correction.

[0193] Specifically include:

[0194] The present invention uses pulse maneuvers as an orbit correction scheme, and applies a certain size of speed pulse to the interception satellite to change the speed of the interception satellite, thereby changing the orbit. By relying on multiple pulse orbit changes, the distance between the interception satellite orbit and the target satellite orbit at the interception point is within a sufficiently close range, thereby achieving the purpose of orbit correction.

[0195] Design an orbit correction scheme: when intercepting a target satellite in a satellite group on the same orbit, take the time corresponding to the minimum intersection distance obtained in step S200 as the interception time t2, and predict its position r2 at this time through the established model of the target satellite under the J2 perturbation. By correcting the position of the intercepting satellite at time t2, make its position reach r2 at this time, and thus complete the interception mission. During each correction, record the position r1 of the intercepting satellite at time t1, and find the orbit that can make the intercepting satellite reach the position r1 at time t1 and the position r2 at time t2. This orbit is the corrected interception orbit, and the speed difference before and after the correction is the required speed pulse. Consider other factors, such as the perturbation of the orbit by solar pressure and the perturbation of the orbit by atmospheric drag, and take the same process to correct the orbit at regular intervals until the interception mission is completed.

[0196] This step uses the differential correction algorithm to design the orbit correction algorithm, which transforms the state (t1, r1, v1) of the interceptor satellite at time t1 under the J2 model and the position vector at time t2 The corresponding relationship between them is expressed as a functional relationship:

[0197]

[0198] At time t1, a tiny velocity pulse Δv1 is added to the intercepting satellite:

[0199]

[0200] When Δv1 is small enough, it can be regarded as a partial derivative relationship:

[0201]

[0202] make Then there is Right now Take Δv1 as Δv 1x =[0.001,0,0] T , Δv 1y =[0,0.001,0] T , Δv 1z =[0,0,0.001] T , substituted into the J2 model for calculation, and the corresponding three position changes are obtained Then the matrix M1 can be:

[0203]

[0204] Use the M1 matrix obtained and the required position correction δr (1) Calculate the required velocity pulse Δv1:

[0205]

[0206] The corrected orbit is calculated from the velocity pulse Δv1, and the difference between the corrected orbit and the position of the target satellite at time t2 is taken as the new required position correction δr (2) , recalculate the above process to obtain the new matrix M2;

[0207] The required speed pulse is:

[0208]

[0209] Recalculate the corrected trajectory and the new required position correction δr based on the obtained velocity pulse Δv2 (3) ; Repeat the correction process, then we have:

[0210]

[0211] After n iterations, the position difference between the intercept satellite and the target satellite at time t2 is δr (n+1) Within the required accuracy range, the speed pulses of each iteration are accumulated to obtain the final speed pulse Δv required for this correction:

[0212]

[0213] S400, achieves approach to the target satellite through true proportional guidance law,

[0214] Due to the influence of various other uncertain factors in reality, the corrected minimum interception distance still has a large error. Therefore, the present invention adopts a proportional guidance law to control the interceptor to further approach the target satellite; a relative motion coordinate system is established in three-dimensional space and fixedly connected to the interceptor, and the command acceleration a is designed. M According to the geometric relationship, the kinematic modeling of the true proportional guidance law in three-dimensional space is carried out, and the relative position vector R and the relative velocity vector V in the geocentric inertial system are used. r Complete the design and simulation of the true proportional guidance rate; based on the orbit correction in step S300, take the time 300s in advance of the expected interception time, release the sub-interceptor from the interception satellite, and start proportional guidance for the sub-interceptor; analyze the trajectory, distance and command acceleration change diagram of the interception satellite and the target satellite obtained by simulation over time, and realize the true proportional guidance law to control the interception satellite to further approach the target satellite;

[0215] Specifically include:

[0216] In actual situations, the influence of various other perturbations and uncertain factors cannot be ignored, so it is necessary to design a proportional guidance law to guide the interceptor to approach the target satellite and complete a more accurate interception and strike.

[0217] First, a relative motion coordinate system is established, in which the interceptor satellite is fixedly connected to the interceptor, and the origin O r Located at the interceptor center of mass, x r The y axis is parallel to the intersection of the instantaneous line of sight transfer plane and the equatorial plane, and its positive direction points to the target satellite; r The axis is located in the instantaneous line of sight transfer plane and is perpendicular to x r Axis, the positive direction is toward the North Pole of the Earth; z r Axis and x r Axis, y r The axes are vertical and form a right-hand system; the relative speed V between the line of sight and the interceptor and the target satellite r Always at x r O r y r In the plane, the angular velocity of the line of sight Ω is related to z r Axis parallel; V r Decomposed into the approaching speed V along the line of sight c and the component V perpendicular to the line of sight n :

[0218] |V c |=|R·V r | / |R|

[0219] |V n |=|R×V r | / |R|

[0220] Where R is the relative position vector in the Earth-centered inertial system;

[0221] Command acceleration a M Applied in the direction perpendicular to the line of sight, its magnitude is proportional to the product of the approach velocity and the line of sight angular velocity:

[0222] |a M |=N|V c |(dλ / dt)

[0223] Where λ is the instantaneous sight angle, located at x r O r y r In the plane; N is the proportionality factor;

[0224] Command acceleration a M The role of is to eliminate the line of sight angular velocity, so a M The interceptor should be made to generate V n The interceptor satellite and the target satellite are of equal speed, so that the distance between them is only the closing speed V c Approach and hit the target; therefore a M Parallel to V n , perpendicular to V c ; and because Ω is perpendicular to V n , Ω is perpendicular to a M , so a M With V c ×Ω are parallel, then:

[0225] |V c ×Ω|=|V c ||Ω|=|V c |(dλ / dt)

[0226] After sorting, the vector form of the true proportional guidance law is obtained:

[0227] a M =NV c ×Ω

[0228] Since Ω=R×V r / R 2 , so:

[0229]

[0230] The kinematic modeling of the true proportional guidance law in three-dimensional space is completed. According to the relative position vector R and relative velocity vector V in the geocentric inertial system, r The design and simulation of the true proportional guidance law can be completed, thereby achieving the precise approach of the interception target to the co-orbital satellite group target.

[0231] Specific implementation scheme 2: The present invention provides a space-based interception guidance and control system for a co-orbital satellite cluster. The system has a program module corresponding to the above steps, and executes the steps in the above-mentioned space-based interception guidance and control method for a co-orbital satellite cluster during operation.

[0232] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0233] Specific implementation scheme three: The present invention provides a computer-readable storage medium, which stores a computer program. The computer program is configured to implement the steps of a space-based interception guidance control method for a co-orbital satellite group when called by a processor.

[0234] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0235] Simulation experiment

[0236] Experimental steps:

[0237] 1. First, the six initial orbital numbers of the interceptor satellite are calculated based on the orbital parameters of the Starlink satellite, and input into the STK simulation software to generate 3D and 2D schematic diagrams with J2 perturbation, so as to intuitively reflect the feasibility of interception. The built-in analysis tool of the STK software is used to generate the relative distance diagram between the interceptor and the satellite group on the same orbit (taking the interceptor and the target satellite No. 22 as an example);

[0238] 2. Use the differential correction algorithm to calculate the pulse velocity vector required for satellite orbit correction, add Maneuver under the orbit setting Astrogator module of STK simulation software, so that the interceptor satellite can obtain the expected pulse velocity 1500s before reaching the minimum rendezvous distance, and use the built-in analysis tool of STK software to generate the relative distance diagram between the interceptor satellite and the satellite group on the same orbit (take the interceptor satellite and target satellite No. 22 as an example);

[0239] 3. Use the Simulink function in the MATLAB simulation software to generate a control program for the true proportional guidance law. The initial value of the simulation is set according to the orbit correction algorithm in the previous article. After the orbit correction, when the interceptor satellite and the target satellite reach the minimum rendezvous distance, the positions and velocities of the two are generated. Use the built-in analysis tools in the MATLAB software to generate a relative distance diagram between the interceptor and the satellite group on the same orbit (taking the interceptor satellite and the target satellite No. 22 as an example).

[0240] The present invention is used for co-orbit satellite guidance, combined with Figure 2 As shown, the red line represents the intercepting satellite orbit, and the blue line represents the target satellite group orbit, which intuitively reflects the feasibility of interception. Figure 3As shown in the figure, the red line represents the sub-satellite trajectory of the intercepting satellite, and the blue line represents the sub-satellite trajectory of the target satellite group, which also intuitively reflects the feasibility of interception; combined with Figure 4 As shown in the figure, under J2 perturbation, the minimum distance between the interceptor satellite and the target satellite can reach about 200 km without introducing orbit correction. Figure 5 As shown in Figure 2, under J2 perturbation, the minimum distance between the interceptor satellite and the target satellite can be within 20 km when the orbit correction is introduced. Figure 6 As shown in the figure, under J2 perturbation, the orbit correction and true proportional guidance law are introduced, and the minimum distance between the interceptor and the target satellite can reach 0.4km. The comparison of the three clearly shows that the use of the present invention can effectively shorten the distance between the interceptor satellite and the target satellite, proving that the guidance effect of the present invention is better.

[0241] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A space-based interception guidance and control method for a satellite group in the same orbit, It is characterized in that The following steps are involved: S100, modeling the target satellite orbit and solving the intercept satellite orbit under the two-body motion problem, This includes deriving the relationship between the position and velocity of the target satellite and time based on the basic dynamic equations of the two-body problem and the Kepler equation, and determining the initial state of the target star cluster based on the design parameters of the co-orbital satellite cluster, thereby completing the dynamic modeling of the target satellite. According to the interception plan, the relationship between the orbital parameters of the target satellite and the intercepting satellite is obtained, and the initial orbit of the intercepting satellite is obtained by solving; S200, model the interceptor satellite and target satellite under J2 perturbation and analyze the impact of J2 perturbation, The first-order perturbation model of the earth's gravitational field considering J2 perturbation is obtained by describing the earth's gravitational field with potential function. Then, the analytical form of the perturbation force component in the geocentric inertial system is obtained by taking the negative partial derivative of the potential function with respect to the x-axis, y-axis and z-axis of the geocentric inertial system. The differential equations solved by ode45 are used to obtain the position of the target satellite and the interceptor satellite under J2 perturbation and the relationship between the change of their velocities with time. Then, the modeling and simulation of the orbits of the interceptor satellite and the target satellite under J2 perturbation are completed, and the influence of J2 perturbation on the orbit of the interceptor satellite is analyzed. include: Orbital solution under S210 and J2 perturbations, The earth's gravitational field is described by the potential function U, and the earth's gravity F is the negative gradient of the potential function: Among them, i is the unit vector in the x-axis direction in the geocentric inertial system; j is the unit vector in the y-axis direction in the geocentric inertial system; k is the unit vector in the z-axis direction in the geocentric inertial system; For considering J 2 The first-order perturbation model of the earth's gravitational field is: in, is the latitude of the subsatellite point; R e is the equatorial radius of the Earth; J 2 =-1.08264×10 -3 ; The first term below is the central gravitational potential function, and the second term is the Earth flattening perturbation term that causes the interference force: Right now: The kinetic equation In component form: Potential function U p Calculate the negative partial derivatives of x, y, and z respectively, and obtain the perturbation force component f in the geocentric inertial system x 、f y 、f z The analytical form of the differential equations can be directly obtained by using the Cowell method and the ode45 solver. S220, analyze the influence of J2 perturbation, and expand the simulation time range to the orbit period T of the interceptor satellite under the two-body motion. m , use step S210 to solve the state vector of the intercepted satellite, set the point at the interval constant time as the sampling point, calculate the satellite orbit at the corresponding time, and thus calculate the corresponding six orbital numbers: Among them, r is the position vector of the earth's center to the satellite at the current moment; v is the velocity vector of the satellite at the current moment; z i is the z-axis basis of the geocentric inertial system; x i is the x-axis basis of the geocentric inertial system; h = r × v is the satellite angular momentum vector; n = z i ×h is the ascending node vector; e is the eccentricity vector; n i is the direction vector of the ascending node vector; Select the satellite state of the interceptor satellite in the same orbit as the target satellite to start calculation, obtain the relationship between the six orbit elements and time, and then obtain the influence of the J2 perturbation on the orbit as the basis for correcting the orbit in step S300; S300, re-correct the orbital parameters of the interceptor satellite according to the J2 perturbation effect, The method includes an orbit correction scheme that uses orbit maneuvers as a means according to the influence of the J2 perturbation obtained in step S220 on the orbits of the interceptor satellite and the target satellite, and performs multiple pulse orbit changes so that the distance between the interceptor satellite orbit and the target satellite near the interception point meets a threshold value, thereby completing the orbit correction; then a differential correction algorithm is used as the orbit correction algorithm, and the small velocity pulse Δv is solved by the required correction amount δr to obtain the corrected orbit and then the process is repeated continuously; after n iterations, at the rendezvous moment, when the position difference between the target satellite and the interceptor satellite is within a preset accuracy range, the orbit correction of the interceptor satellite under the J2 perturbation is achieved; S400, through the true proportional guidance law, the interceptor satellite approaches the target satellite. Including establishing a relative motion coordinate system in three-dimensional space and fixing it to the interceptor, designing the command acceleration a M According to the geometric relationship, the kinematic modeling of the true proportional guidance law in three-dimensional space is carried out, and the relative position vector R and the relative velocity vector V in the geocentric inertial system are used. r Complete the design and simulation of the true proportional guidance rate; based on the orbit correction in step S300, take the moment of the preset time ahead of the expected interception time, the interception satellite releases the sub-interceptor, and starts proportional guidance for the sub-interceptor; analyze the trajectory, distance and command acceleration change of the interception satellite and the target satellite obtained by simulation over time, and realize the true proportional guidance law to control the interception satellite to further approach the target satellite.

2. A space-based interception guidance control method for a satellite group on the same orbit according to claim 1, It is characterized in that In step S100, it includes: S110, modeling the two-body motion of the target satellite. In the geocentric inertial system, the motion of the target satellite around the earth is simplified to the motion of a particle around the central gravitational body; the basic dynamic equation under this two-body problem is: Among them, r is the position vector from the center of the earth to the target satellite at the current moment; μ is the gravitational constant of the central celestial body; is the acceleration vector from the center of the earth to the target satellite at the current moment; f is the resultant external force on the target satellite except the gravitational force; For the target satellite, the resultant external force f is zero, and the motion of the target satellite satisfies Kepler's equation: Among them, t p is the flight time of the target satellite; α is the semi-major axis of the target satellite orbit; e is the eccentricity of the target satellite; Ψ is the anomaly angle of the target satellite; There is a relationship between the target satellite's eccentric anomaly angle Ψ and true anomaly angle θ: The flight time t with perigee as time zero is obtained p Relationship with the true anomaly θ; The relationship between the six orbital numbers and the position vector r and velocity vector v from the center of the Earth to the target satellite is: Where i is the target satellite orbit inclination; Ω is the target satellite ascending node longitude; ω is the target satellite perigee argument; θ is the target satellite true anomaly; According to the relationship between the position and velocity of the target satellite and time, the orbit model of the target satellite under the two-body problem is established; S120, determining the initial state of the target star cluster according to the orbital parameters of the target co-orbital star cluster, wherein the orbital parameters include the semi-major axis, eccentricity, orbital inclination, ascending node longitude, perigee argument and true anomaly of the intercepting satellite; S130, solving the interception satellite orbit, solving the parameters of the interception satellite orbit obtained in step S120 according to the model of the target satellite orbit under the two-body problem obtained in step S110, According to Kepler's third law: According to the interception plan that the interception satellite can meet the next satellite in the orbit of the target co-orbital satellite group at the perigee every time it runs one week, the orbital period T of the interception satellite is obtained. m is N+1 / N or N-1 / N of the target satellite, where N is the number of low-orbit satellites on the orbital plane; take the case where the intercepting satellite has a longer orbital period: Using the transformed form of Kepler's third law, the semi-major axis a of the interceptor satellite orbit is obtained: m ; According to the coincidence of the perigee of the intercepting satellite orbit and the perigee of the target satellite orbit, the two orbits have the same perigee radius vector: a 1 -c 1 =a m -c m Among them, c 1 、c m are the orbital semi-focal lengths of the target satellite and the interceptor satellite, respectively; Get the orbital eccentricity of the intercepting satellite: The eccentricity vector is expressed using the six orbital elements other than the true anomaly: The direction of the interceptor satellite eccentricity vector Equal to the target satellite eccentricity vector direction what is it m what is it m -sinω m Like this m sinΩ m =whatsω 1 what is it 1 -sinω 1 Like this 1 sinΩ 1 what is it m sinΩ m +sinω m Like this m what is it m =whatsω 1 sinΩ 1 +sinω 1 Like this 1 what is it 1 here m here m =sinω 1 here 1 Given the additional constraint i m ,ω m ,Ω m After finding one of the values ​​in , the other two parameters of the intercepting satellite orbit are obtained according to the equation group; then the intercepting satellite orbit and the target satellite orbit are solved for the two cases of being coplanar and non-planar to obtain i m ,ω m ,Ω m , and then solve the true anomaly to get the intercept satellite orbit; In order for the interceptor satellite to rendezvous with the target satellite at perigee, the time when the interceptor satellite and the first target satellite first pass the perigee should satisfy: Among them, k is the condition for the intercept satellite to rendezvous with the k+1 satellite first; Take k = 0, t m =t 1 , according to t m The true anomaly angle of the satellite intercepted at the moment is zero, and the true anomaly angle of the satellite intercepted at the initial moment is obtained.

3. A space-based interception guidance control method for a satellite group on the same orbit according to claim 2, It is characterized in that In step S300, it includes: using a differential correction algorithm to adjust the interception satellite under the J2 model 1 The state at the moment (t 1 ,r 1 ,v 1 ) and t 2 Position vector at time The corresponding relationship between them is expressed as a functional relationship: In t 1 Add a velocity pulse Δv to the intercepting satellite at any time 1 : When Δv 1 When it is small enough, it can be considered as a partial derivative relationship: make Then there is Right now Take Δv respectively 1 is Δv 1x =[0.001,0,0] T , Δv 1y =[0,0.001,0] T , Δv 1z =[0,0,0.001] T , substituted into the J2 model for calculation, and the corresponding three position changes are obtained Then we can let the matrix M 1 for: Using the M obtained in this way 1 Matrix and required position correction δr (1) Calculate the required velocity pulse Δv 1 : The velocity pulse Δv obtained by 1 Calculate the corrected orbit and obtain the corrected orbit at t 2 The difference between the time and the target position is taken as the new required position correction δr (2) , recalculate the new matrix M using the above process 2 ; The speed pulse is: The velocity pulse Δv obtained by 2 Recalculate the corrected orbit and the new required position correction δr (3) ; Repeat the correction process, then we have: After n iterations, let t 2 The position difference between the intercept satellite and the target satellite at the moment δr (n+1) Within the required accuracy range, the speed pulses of each iteration are accumulated to obtain the final speed pulse Δv required for this correction:

4. A space-based interception guidance control method for a satellite group on the same orbit according to claim 3, It is characterized in that In step S400, it includes: Establish a relative motion coordinate system to connect the interceptor satellite to the interceptor, where the origin of the relative motion coordinate system is O r Located at the interceptor center of mass, x r The y axis is parallel to the intersection of the instantaneous line of sight transfer plane and the equatorial plane, and its positive direction points to the target satellite; r The axis is located in the instantaneous line of sight transfer plane and is perpendicular to x r Axis, the positive direction is toward the North Pole of the Earth; z r Axis and x r Axis, y r The axes are vertical and form a right-hand system; the relative speed V between the line of sight and the interceptor and the target satellite r Always at x r O r y r In the plane, the angular velocity of the line of sight Ω is related to z r Axis parallel; V r Decomposed into the approaching speed V along the line of sight c and the component V perpendicular to the line of sight n : |V c |=|R·V r | / |R| |V n |=|R×V r | / |R| Where R is the relative position vector in the Earth-centered inertial system; Command acceleration a M Applied in the direction perpendicular to the line of sight, its magnitude is proportional to the product of the approach velocity and the line of sight angular velocity: |a M |=N|V c |(dλ / dt) Where λ is the instantaneous sight angle, located at x r O r y r In the plane; N is the proportionality factor; Because M Parallel to V n , a M Perpendicular to V c , Ω is perpendicular to a M , so a M With V c ×Ω are parallel, then: |V c ×Ω|=|V c ‖Ω|=|V c |(dλ / dt) The vector form of the true proportional guidance law is obtained: a M =NV c ×Ω Since Ω=R×V r / R 2 , so: After the kinematic modeling of the true proportional guidance law in three-dimensional space is completed, according to the relative position vector R and relative velocity vector V in the geocentric inertial system r Complete the design and simulation of the true proportional guidance law, and then achieve the precise approach of the interception target to the co-orbital satellite group target.

5. A space-based interception guidance and control system for a group of satellites in the same orbit, Features: The system has a program module corresponding to the steps of any one of claims 1 to 4 above, and executes the steps in the above-mentioned space-based interception guidance control method for a co-orbital satellite group when running.

6. A computer-readable storage medium, Features: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the space-based interception guidance control method for a co-orbital satellite group described in any one of claims 1 to 4 when called by a processor.

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