Satellite formation autonomous control method based on relative motion fitting

Abstract

The invention discloses a satellite formation autonomous control method based on relative motion fitting, belongs to the technical field of spacecraft control, and aims to solve the problem that a traditional formation control method cannot meet formation control requirements in an environment with navigation signal deficiency. The method comprises the following steps: step 1, when a main satellite passes through an ascending node, performing relative motion fitting by utilizing inter-satellite spacing and direction of a plurality of discretely distributed sub-satellites relative to the main satellite observed in a previous orbital period so as to obtain coefficients of relative motion functions of the sub-satellites; step 2, obtaining orbit parameter deviation of the child satellites relative to the primary satellite according to the coefficient of the relative motion function of the child satellites; step 3, acquiring a control vector and a control duration required by the formation adjustment of the child satellites according to the orbit parameter deviation; and step 4, each sub-satellite performs autonomous control according to the control vector and the control duration obtained in the step 3. The method is used for satellite formation autonomous control.

Description

Technical Field

[0001] The present invention relates to a method for autonomous control of satellite formation based on relative motion fitting, belonging to the technical field of spacecraft control. Background Art

[0002] Satellite formation flying is a space technology that accomplishes specific tasks through the cooperation of multiple satellites. Compared with traditional single large satellites, satellite formations with distributed layouts of multiple small satellites can improve the resolution, coverage, and redundancy of tasks, and can demonstrate higher flexibility, lower cost, and stronger fault tolerance when completing complex tasks. Formation flying technology is widely applied in fields such as Earth observation, space science, deep space exploration, and communication enhancement. For example, in Earth observation tasks and deep space exploration tasks, it can achieve scientific goals such as multi-angle observation and interferometry, and can also optimize data relay and communication efficiency.

[0003] However, in an environment where navigation signals are missing, satellite formation flying faces significant challenges. Especially in specific scenarios such as deep space exploration, polar observation, or severe electronic interference, traditional positioning and time synchronization methods based on the Global Navigation Satellite System (GNSS) are difficult to apply. Most traditional satellite formation control methods use the CW equation to control using the relative position and velocity obtained by navigation, or calculate and control the control quantity using the deviation orbit parameters obtained by navigation. However, using the CW equation for formation control has errors caused by linearization at relatively long formation distances, and for multi-satellite formation tasks under deep space conditions or navigation-limited conditions, traditional formation control methods cannot meet the formation control requirements. Summary of the Invention

[0004] In order to solve the problem that traditional formation control methods cannot meet the formation control requirements in an environment where navigation signals are missing, the present invention provides a method for autonomous control of satellite formation based on relative motion fitting.

[0005] The method for autonomous control of satellite formation based on relative motion fitting according to the present invention includes the following steps: Step 1: Whenever the main satellite passes through the ascending node, use the inter-satellite spacings and directions of multiple discretely distributed sub-satellites relative to the main satellite observed in the previous orbital period for relative motion fitting, and then obtain the coefficients of the relative motion function of the sub-satellites. Step 2: Obtain the orbital parameter deviations of the sub-satellites relative to the main satellite according to the coefficients of the relative motion function of the sub-satellites. Step 3: Obtain the control vectors and control durations required for sub-satellite formation adjustment according to the orbital parameter deviations. Step 4: Each sub-satellite performs autonomous control according to the control vectors and control durations obtained in Step 3.

[0006] Preferably, the relative motion function of the neutron star in step one is: In the LVHV coordinate system, the relative motion function of the sub-star is fitted separately along the X, Y, and Z axes; where x, y, and z are the inter-star distances between the sub-star and the primary star along the X, Y, and Z axes in the LVLH coordinate system, is the latitude argument of the primary star, , is the argument of pericenter, is the true anomaly, is the time; are the coefficients to be solved, is the amplitude of the oscillation of the relative motion along the X axis, is the phase of the oscillation of the relative motion along the X axis relative to the latitude argument, is the rate of change of the drift distance of the relative motion along the Y axis, is the drift distance of the relative motion along the Y axis, is the amplitude of the oscillation of the relative motion along the Y axis, is the phase of the oscillation of the relative motion along the Y axis relative to the true anomaly, is the amplitude of the oscillation of the relative motion along the Z axis, is the phase of the oscillation of the relative motion along the Z axis relative to the latitude argument.

[0007] Preferably, the motion fitting in step one uses the non-linear least squares method.

[0008] Preferably, the orbital parameter deviations of the sub-star relative to the primary star in step two , , , , , are obtained according to the following formula: where is the deviation of the semi-major axis of the orbit, is the deviation of the orbital inclination, is the deviation of the right ascension of the ascending node, , are the non-singular orbital parameter deviations, is the deviation of the latitude argument; is the orbital inclination of the primary star, is the geocentric distance between the primary star and the central celestial body, T is the orbital period of the primary star, and n is the orbital angular velocity of the primary star; is the semi-latus rectum of the primary star, , is the semi-major axis of the primary star's orbit, is the eccentricity of the primary star's orbit; is the non-singular orbital parameter of the primary star, , , is the argument of perigee of the primary star; is calculated when the primary star passes through the ascending node for the (k + 1)-th time , is calculated when the primary star passes through the ascending node for the first time .

[0009] Preferably, the control vector in step three includes a control quantity and the latitude argument for applying the control quantity; The control quantity , , is obtained according to the following formula: In the formula is an intermediate parameter, , is the gravitational constant of the central celestial body; is the tangential impulse control quantity along the orbit, , is the orbital angular momentum of the primary star, ; is the total deviation of the semi-major axis to be adjusted, , is the additional control quantity of the semi-major axis, , is the given adjustment required total duration; This control quantity is applied at both the perifocal point and the apofocal point of the central celestial body , and the latitude argument for applying this control quantity at the perifocal point of the central celestial body , and the latitude argument for applying this control quantity at the apofocal point of the central celestial body ; is the normal impulse control quantity along the orbit, , and the latitude argument for applying this control quantity ; is the radial impulse control quantity along the orbit; , and the latitude argument for applying this control quantity .

[0010] Preferably, the process of autonomous control of each sub - satellite according to the control vector obtained in Step 3 in Step 4 is as follows: normal control, radial control, and tangential control are sequentially performed within three consecutive orbital periods. One type of control is executed in each orbital period. After each type of control is completed, return to execute Steps 1 to 3, recalculate the deviation, control vector, and control duration, and then perform the next type of control, so as to realize the formation adjustment of the sub - satellite with the latitude argument of the main star as the reference value in the case where it is impossible to obtain the relevant orbital information of the sub - satellite due to navigation constraints.

[0011] Preferably, the start time and end time of the normal control are respectively , ; the start time and end time of the radial control are respectively , ; the start time and end time of the tangential control at the point near the central celestial body are respectively , , and the start time and end time of the tangential control at the point far from the central celestial body are respectively , ; is the latitude argument of the main star when the predicted control amount is applied , , , corresponding times, , , are respectively the control durations required for normal control, radial control, and tangential control.

[0012] Preferably, the control duration required for normal control is: In the formula, is the thrust of the sub - satellite thruster, is the mass of the sub - satellite.

[0013] Preferably, the control duration required for radial control is: In the formula, is the thrust of the sub - satellite thruster, is the mass of the sub - satellite.

[0014] Preferably, the control duration required for tangential control is: In the formula, is the thrust of the sub - satellite thruster, is the mass of the sub - satellite.

[0015] The beneficial effects of the present invention: The present invention proposes a satellite formation autonomous control method based on relative motion fitting, which is applicable to the multi-satellite autonomous formation control tasks under deep space conditions or navigation restricted conditions. When each formation satellite passes through the ascending node, the relative motion fitting is carried out by using the discrete ranging and direction finding information (including the inter-satellite distance and direction) of the formation satellites in the previous orbital period. Through the function correlation coefficient obtained by fitting, the corresponding orbital parameter deviation of the formation satellites can be directly calculated, and the required control quantity and the latitude argument of the applied control quantity can be calculated accordingly. The effect of autonomous formation control is achieved through two adjustment means: phase drift control and in-plane and out-of-plane flying-around control.

[0016] Compared with the formation control using GNSS navigation results, it has the advantages of good autonomy, no need for ground navigation support, and high control accuracy in the case of relatively long distances. Brief Description of the Drawings

[0017] Figure 1 is the flowchart of a satellite formation autonomous control method based on relative motion fitting according to the present invention; Figure 2 is the schematic diagram of the LVLH coordinate system; Figure 3 is the fitting result of the X-axis, where Figure 3 (a) is the position curve of the LVLH system relative to the X-axis, Figure 3 (b) is the fitting error curve of the LVLH system relative to the X-axis; Figure 4 is the fitting result of the Y-axis, where Figure 4 (a) is the position curve of the LVLH system relative to the Y-axis, Figure 4 (b) is the fitting error curve of the LVLH system relative to the Y-axis; Figure 5 is the fitting result of the Z-axis, where Figure 5 (a) is the position curve of the LVLH system relative to the Z-axis, Figure 5 (b) is the fitting error curve of the LVLH system relative to the Z-axis; Figure 6 is the schematic diagram of autonomous control according to the control quantity obtained by the method of the present invention; Figure 7 is the relative motion relationship diagram of the master and slave satellites, where Figure 7 (a) is the global view, Figure 7 (b) is the Y-Z plane view for normal control, where the red dot is the position where the normal control is applied, Figure 7 (c) is the X-Y plane view for radial control, where the red dot is the position where the radial control is applied, Figure 7 (d) is the X-Z plane view; Figure 8 is the schematic diagram of the slave satellite applying thrust control; Figure 9is the deviation curve of the semi-major axis of the orbit; Figure 10 is the deviation curve of the orbital eccentricity; Figure 11 is the deviation curve of the orbital inclination; Figure 12 is the deviation curve of the right ascension of the ascending node; Figure 13 is the deviation curve of the argument of the pericenter. Detailed implementation manners

[0018] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0019] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments may be combined with each other.

[0020] Next, the present invention will be further described in conjunction with the accompanying drawings and specific embodiments, but it is not a limitation of the present invention.

[0021] Detailed implementation manner 1: Next, in conjunction with Figures 1 to 13 this implementation manner will be described. The described satellite formation autonomous control method based on relative motion fitting includes the following steps: Step 1. Whenever the main satellite passes through the ascending node, use the inter-satellite spacings and directions of multiple discretely distributed sub-satellites relative to the main satellite observed in the previous orbital period for relative motion fitting, and then obtain the coefficients of the relative motion function of the sub-satellites. Step 2. Obtain the orbital parameter deviations of the sub-satellites relative to the main satellite according to the coefficients of the relative motion function of the sub-satellites. Step 3. Obtain the control vectors and control durations required for sub-satellite formation adjustment according to the orbital parameter deviations. Step 4. Each sub-satellite performs autonomous control according to the control vectors and control durations obtained in Step 3.

[0022] The present invention considers the formation control idea, completes the phase drift control by controlling the semi-major axis of the orbit, and completes the oscillation control of the in-plane and out-of-plane quantities by controlling the eccentricity vector, orbital inclination, and right ascension of the ascending node. See Figure 3 as shown.

[0023] The LVLH coordinate system is shown in Figure 2As shown, the main satellite and each sub-satellite fly in formation around the central celestial body. In specific scenarios such as deep space exploration, polar observation, or severe electronic interference, traditional positioning and time synchronization methods based on the Global Navigation Satellite System (GNSS) are difficult to apply. The present invention uses a non-linear method for analysis.

[0024] In the LVLH coordinate system, the relative motion law can be expressed by non-singular relative orbital element deviations as the following equation: (1) In the formula, x, y, and z are the inter-satellite distances between the sub-satellite and the main satellite on the X, Y, and Z axes in the LVLH coordinate system, is the geocentric distance between the main satellite and the central celestial body, is the semi-major axis of the main satellite's orbit, is the eccentricity of the main satellite's orbit, is the inclination of the main satellite's orbit, is the right ascension of the ascending node of the main satellite, is the argument of perigee of the main satellite, is the true anomaly of the main satellite, is the semi-latus rectum of the main satellite, , is the argument of latitude of the main satellite, . To avoid the singular problem caused by near-circular orbits, non-singular orbital parameters are used, is the non-singular orbital parameter of the main satellite, , . The above symbols are all parameters related to the main satellite, represents the deviation of the parameters related to the sub-satellite and the main satellite, where is the deviation of the semi-major axis of the orbit, is the deviation of the inclination of the orbit, is the deviation of the right ascension of the ascending node, is the deviation of the argument of latitude, , are the deviations of the non-singular orbital parameters, , are used to characterize the deviation of the eccentricity vector.

[0025] For the near-circular small deviation assumption, equation (1) can be simplified to the following form: (2) As a function of the relative motion of the sub-satellite, in the LVHV coordinate system, the relative motion function of the sub-satellite is fitted separately along the X, Y, and Z axes; that is, three relative motion functions with a total of 8 coefficients. The inter-satellite distances (x, y, z) of the sub-satellite relative to the main satellite observed in the previous orbit period are used to solve by sampling at least 5 discrete sampling points of the sub-satellite within the orbit period (one circle).

[0026] In the formula, is the time; is the coefficient to be solved is the amplitude of the oscillation of the relative motion on the X-axis is the phase of the oscillation of the relative motion on the X-axis with respect to the latitude argument is the rate of change of the drift distance of the relative motion on the Y-axis is the drift distance of the relative motion on the Y-axis is the amplitude of the oscillation of the relative motion on the Y-axis is the phase of the oscillation of the relative motion on the Y-axis with respect to the true anomaly is the amplitude of the oscillation of the relative motion on the Z-axis is the phase of the oscillation of the relative motion on the Z-axis with respect to the latitude argument

[0027] In step 1, the motion fitting adopts the nonlinear least squares method

[0028] The parameters related to the deviation estimation in Equation (2) are as follows (3) In the formula is the relative deviation orbital angular velocity of the primary star and the secondary star, n is the orbital angular velocity of the primary star , is the gravitational constant of the central celestial body. Therefore, the relative distance of the Y-axis (phase) of the LVLH system can be controlled by controlling the semi-major axis

[0029] From the above relative motion analysis, it can be seen that in the LVLH coordinate system, the relative motion of the formation can be fitted into the above form, where the above is the coefficient to be solved. Therefore, the relative motion fitting method can be considered to obtain the above undetermined parameters and then obtain the orbital deviation of the primary star and the secondary star

[0030] In step 2, the orbital parameter deviation of the secondary star relative to the primary star , , , , , is obtained according to the following formula (4) Equation (4) is derived from Equation (3)

[0031] In the formula T is the orbital period of the primary star Calculated when the primary star passes through the ascending node for the (k + 1)-th time , Calculated when the primary star passes through the ascending node for the first time .

[0032] The control vector in step three includes a control quantity and the latitude argument for applying the control quantity; The control quantity , , is obtained according to the following formula: where is an intermediate parameter, ; is the tangential pulse control quantity along the orbit, , is the orbital angular momentum of the primary star, ; is the total deviation of the semi-major axis to be adjusted, , is the additional control quantity of the semi-major axis, , is the given adjustment required total duration; This control quantity is applied at both the pericenter and apocenter of the central body . The latitude argument for applying this control quantity at the pericenter is , and the latitude argument for applying this control quantity at the apocenter is ; is the normal pulse control quantity along the orbit, , and the latitude argument for applying this control quantity is ; is the radial pulse control quantity along the orbit; , and the latitude argument for applying this control quantity is .

[0033] For the control of the deviation adjustment of the latitude argument, it can be indirectly achieved by controlling the semi-major axis. The specific formula is as follows: After calculating the latitude argument deviation of the secondary star relative to the primary star , given the adjustment required total duration , the additional control quantity of the semi-major axis required can be calculated by the following formula Combined with the obtained in step two, the total deviation of the semi-major axis to be actually controlled is obtained .

[0034] The process of autonomous control of each sub-satellite according to the control vector obtained in Step 3 in Step 4 is as follows: normal control, radial control, and tangential control are sequentially performed within three consecutive orbital periods. One type of control is executed in each orbital period. After each type of control is completed, Steps 1 to 3 are returned to, and the deviation, control vector, and control duration are recalculated before the next type of control is performed, so as to achieve the formation adjustment of the sub-satellites with the latitude argument of the main satellite as the reference value in the case where relevant orbital information of the sub-satellites cannot be obtained due to navigation limitations.

[0035] The start time and end time of the normal control are respectively , ; the start time and end time of the radial control are respectively , ; the start time and end time of the tangential control at the near central body point are respectively , , and the start time and end time of the tangential control at the far central body point are respectively , ; is the latitude argument of the main satellite when the predicted control amount is applied , , , corresponding time, , , are the control durations required for normal control, radial control, and tangential control respectively.

[0036] The normal control is to eliminate the deviation of the right ascension of the ascending node and the deviation of the orbital inclination , and the control is performed by applying the normal pulse control amount at the latitude argument .

[0037] The control duration required for normal control is: In the formula, is the thrust of the sub-satellite thruster, is the mass of the sub-satellite.

[0038] The radial control is used to eliminate the deviation of the eccentricity vector, and the control is performed by applying the normal pulse control amount at the latitude argument .

[0039] The control duration required for radial control is: Tangential control is used to eliminate the deviation of the orbital semi-major axis , during the operation within the orbital period, the neutron star and the primary star will continue to generate deviations, and the additional control amount of the semi-major axis , the total deviation of the semi-major axis that needs to be eliminated , by eliminating the deviation of the semi-major axis, the deviation of the latitude argument is further eliminated , by applying a tangential pulse control amount at the near central body point ( ), the far central body point ( ) with a phase interval of 180° respectively for control.

[0040] The required control duration for tangential control is: Normal control, radial control, and tangential control are carried out in different orbital periods. First, normal control is applied; after completing normal control, return to execute steps one to three to recalculate the deviation, control amount, and control duration, and then perform radial control; after completing radial control, return to execute steps one to three to recalculate the deviation, control amount, and control duration to perform tangential control.

[0041] The following gives a specific example.

[0042] Taking the formation control problem of a certain satellite flying along the track around the moon as a simulation example to verify the feasibility of the method. The orbital parameters of the primary star are selected as follows: The orbital parameters of the secondary star are selected as follows: The control target is the Y direction in the LVLH coordinate system. After 14 days, the secondary star is controlled 10 km in front of the primary star. The mass of the secondary star is set to 100 kg, and a thruster with a thrust of 80 mN is used for small thrust control, with a thrust error of 5%. The maximum working time of the thruster for a single time is 600 s, the orbit determination error of the primary star is 1 km@1 m / s, the ranging and direction finding error between the primary star and the secondary star is 3 m@one arc minute, and the thrust direction error is 2°.

[0043] Step 1, through the observed discrete sampling points, the relative motion fitting result obtained by using non-linear least squares curve fitting Figures 3 to 5 is shown as follows.

[0044] Step 2, obtain the orbital parameter deviation of the secondary star relative to the primary star according to the coefficients of the relative motion function of the secondary star; Based on the fitting result in step 1, the deviation of the primary star is estimated, as shown in Figures 9 to 13 the following figure.

[0045] Step 3, obtain the control vector and control duration required for the formation adjustment of the secondary star according to the orbital parameter deviation; Step 4: Each sub - satellite performs autonomous control according to the control vector and control duration obtained in Step 3. Refer to Figure 7 and Figure 8 .

[0046] Through normal, radial, and tangential controls, autonomous control of the sub - satellite formation can be completed. Tangential control realizes phase drift control, and normal and radial controls realize in - plane and out - of - plane flying - around control. The oscillation of the sub - satellite relative to the mother satellite is effectively reduced, and the relative distance in the Y - direction can be controlled at 10 km. The autonomous formation control algorithm is effective.

[0047] Although the present invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed, as long as they do not depart from the spirit and scope of the present invention as defined by the appended claims. It should be understood that different dependent claims and the features described herein can be combined in a manner different from that described in the original claims. It should also be understood that the features described in connection with a single embodiment can be used in other described embodiments.

Claims

1. An autonomous control method for satellite formation based on relative motion fitting, characterized in that, The method comprises the following steps: Step 1: Whenever the primary star passes through the ascending node, perform relative motion fitting on the inter-satellite spacings and directions of multiple discretely distributed secondary stars relative to the primary star observed in the previous orbital period, and then obtain the coefficients of the relative motion function of the secondary stars; Step 2: Obtain the orbital parameter deviations of the secondary stars relative to the primary star according to the coefficients of the relative motion function of the secondary stars; Step 3: Obtain the control vectors and control durations required for the formation adjustment of the secondary stars according to the orbital parameter deviations; Step 4: Each secondary star performs autonomous control according to the control vectors and control durations obtained in Step 3.

2. The satellite formation autonomous control method based on relative motion fitting according to claim 1, characterized in that, The relative motion function of the secondary stars in Step 1 is: In the LVHV coordinate system, the relative motion function of the secondary stars is fitted respectively along the X, Y, and Z axes; Where x, y, and z are the inter-satellite distances between the deputy satellite and the primary satellite along the X, Y, and Z axes in the LVLH coordinate system, is the latitude argument of the primary satellite, , is the argument of perigee, is the true anomaly, is the time; is the coefficient to be solved is the amplitude of the oscillation of the relative motion on the X-axis is the phase of the oscillation of the relative motion on the X-axis relative to the latitude argument is the rate of change of the drift distance of the relative motion on the Y-axis is the drift distance of the relative motion on the Y-axis is the amplitude of the oscillation of the relative motion on the Y-axis is the phase of the oscillation of the relative motion on the Y-axis relative to the true anomaly is the amplitude of the oscillation of the relative motion on the Z-axis is the phase of the oscillation of the relative motion on the Z-axis relative to the latitude argument 3. The autonomous control method for satellite formation based on relative motion fitting according to claim 1 or 2, characterized in that, Nonlinear least squares method is adopted for the motion fitting in Step 1.

4. The satellite formation autonomous control method based on relative motion fitting according to claim 2, characterized in that The orbital parameter deviation of the sub-star relative to the main star in Step 2 , , , , , Obtained according to the following formula: wherein, is the deviation of the semi-major axis of the orbit, is the deviation of the orbital inclination, is the deviation of the right ascension of the ascending node, , are the deviations of the non-singular orbital parameters, is the deviation of the argument of latitude; is the orbital inclination of the primary star, is the distance between the primary star and the geocenter of the central celestial body, T is the orbital period of the primary star, and n is the orbital angular velocity of the primary star; is the semi-latus rectum of the primary star, , is the semi-major axis of the primary star's orbit, is the eccentricity of the primary star's orbit; are the non-singular orbital parameters of the primary star, , , is the argument of perigee of the primary star; Calculated when the primary star passes through the ascending node for the (k + 1)-th time , Calculated when the primary star passes through the ascending node for the first time .

5. The satellite formation autonomous control method based on relative motion fitting according to claim 4, characterized in that The control vectors in Step 3 include the control quantities and the latitude argument for applying the control quantities; Control quantity , , Obtained according to the following formula: In the formula, is an intermediate parameter, , is the gravitational constant of the central celestial body; is the tangential pulse control quantity along the orbit, , is the orbital angular momentum of the primary star, ; is the total deviation of the semi-major axis to be adjusted, , is the additional control quantity of the semi-major axis, , is the given adjustment required total duration; Apply this control quantity at both the perifocal point and the apofocal point , the latitude argument of applying this control quantity at the perifocal point , the latitude argument of applying this control quantity at the apofocal point ; is the pulsed control quantity along the orbital normal, , and the latitude argument of application of this control quantity ; is the radial pulse control quantity along the orbit; , and the latitude argument of application of this control quantity .

6. The autonomous control method for satellite formation based on relative motion fitting according to claim 5, characterized in that, The process of each secondary star performing autonomous control according to the control vectors obtained in Step 3 in Step 4 is as follows: normal control, radial control, and tangential control are sequentially performed within three consecutive orbital periods. One type of control is executed in each orbital period. After each type of control is executed, return to execute Steps 1 to 3, recalculate the deviations, control vectors, and control durations, and then perform the next type of control, so as to realize the formation adjustment of the secondary stars with the latitude argument of the primary star as the reference value in the case where it is impossible to obtain the relevant orbital information of the secondary stars due to navigation limitations.

7. The satellite formation autonomous control method based on relative motion fitting according to claim 6, characterized in that The start and end times of the normal control are , respectively; the start and end times of the radial control are , respectively; the start and end times of the tangential control at the near central celestial body point are , respectively, and the start and end times of the tangential control at the far central celestial body point are , respectively; For the argument of latitude of the main star when applying the predicted control quantity and and and at the corresponding moments, and and are the required control durations for normal control, radial control, and tangential control, respectively.

8. The satellite formation autonomous control method based on relative motion fitting according to claim 7, characterized in that, The control duration required for normal control is: In the formula, is the thrust of the sub-satellite thruster, is the mass of the sub-satellite.

9. The autonomous control method for satellite formation based on relative motion fitting according to claim 7, characterized in that The control duration required for radial control is: In the formula, is the thrust of the sub - satellite thruster, is the mass of the sub - satellite.

10. The satellite formation autonomous control method based on relative motion fitting according to claim 7, characterized in that The control duration required for tangential control is: In the formula, is the thrust of the sub - satellite thruster, is the mass of the sub - satellite.

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