A small-thrust trajectory analytical planning method for baseline adjustment of side-by-side four-star formation

Abstract

The application discloses a small-thrust trajectory analytic planning method for baseline adjustment of a side-by-side four-star formation, and comprises the following steps: according to the formation characteristics of the side-by-side four-star formation, a baseline adjustment control target decoupling description model is established for the four-star formation; according to the baseline adjustment control target decoupling description model, a multi-orbit transfer method for the baseline adjustment of the side-by-side four-star formation is constructed, and a multi-orbit adjustment sequence planning model is obtained; and according to the obtained multi-orbit adjustment sequence planning model, a continuous thrust control strategy for near-earth control points and far-earth control points is constructed. The application provides a rapid planning method for the small-thrust trajectory maneuvering strategy of the baseline adjustment of the side-by-side four-star formation.

Description

Technical Field

[0001] This invention relates to a low-thrust trajectory analytical planning method for baseline adjustment of a four-satellite formation, belonging to the field of space technology. Background Technology

[0002] In high-precision 3D imaging, side-by-side multi-satellite formations require adjustments to inter-satellite measurement baselines to alter imaging results. Low-thrust systems, characterized by small thrust amplitude, high specific impulse, and long lifespan, can effectively extend the lifespan of low-Earth orbit 3D imaging satellite formations and are suitable for small-scale orbital maneuvers. However, existing analytical trajectory planning methods for side-by-side four-satellite formations do not consider maintaining consistency in the semi-major axis, orbital inclination, right ascension of the ascending node, perigee distance, and mean perigee difference before and after baseline adjustment. Furthermore, numerical trajectory planning methods for low-thrust systems require trajectory optimization based on the initial and final states of baseline adjustment, resulting in lower trajectory planning efficiency. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a low-thrust trajectory analytical planning method for baseline adjustment of a four-star formation alongside each other, providing a fast planning method for low-thrust trajectory maneuvering strategies for baseline adjustment of a four-star formation alongside each other.

[0004] The technical solution of this invention is: a finite thrust maneuver planning method for baseline adjustment of a side-by-side four-star formation, comprising:

[0005] Based on the characteristics of the side-by-side four-star formation configuration, a decoupling description model for baseline adjustment control objectives oriented towards four-star formations is established.

[0006] Based on the decoupled description model of baseline adjustment control target, a multi-cycle transfer method for baseline adjustment of parallel four-star formation is constructed to obtain a multi-cycle adjustment sequence planning model.

[0007] Based on the obtained multi-cycle adjustment sequence planning model, a continuous thrust control strategy for near-ground control points and far-ground control points is constructed.

[0008] The establishment of a baseline adjustment control target decoupling description model for four-star formations includes:

[0009] The four satellites will conduct formation flight missions, establishing a side-by-side four-satellite formation configuration based on a master-slave satellite architecture;

[0010] Let the initial baseline length of the four-star formation be l. u Then, the initial orbital elements of the four slave stars based on the virtual primary star are:

[0011]

[0012] In the formula, variables a, e, i, Ω, ω, and M represent the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, angular distance from perigee, and mean perigee angle, respectively; subscript c represents the orbital elements of the virtual primary star; subscripts I, II, III, and IIII represent the four secondary stars in the four-star formation; and subscript u represents the orbital elements of the four secondary stars in the initial formation configuration.

[0013] Let the baseline length after the adjustment of the four-star formation be l. v The baseline adjustment control target decoupling description model for a 4-star formation is as follows:

[0014]

[0015] In the formula, the subscript v represents the orbital elements of each star in the formation after baseline adjustment.

[0016] The method for constructing a multi-lap transfer method for baseline adjustment of a side-by-side four-star formation, based on the decoupled description model of the baseline adjustment control target, includes:

[0017] The multi-round transfer strategy for baseline adjustment of a four-star formation includes: setting the total number of rounds to m; each star starts from perigee, applies orbital maneuvers to adjust apogee altitude; after reaching apogee, applies orbital maneuvers to adjust perigee altitude; after returning to perigee, applies thrust again to adjust apogee altitude, and applies the best maneuver to the target orbit after reaching perigee on the last round; by adjusting the perigee and apogee altitudes of each round, the orbital period of each round is ensured to be consistent with the orbital period of the virtual primary star; at this time, the baseline adjustment maneuver sequence of each slave star in the four-star formation includes m+1 perigee maneuvers and m apogee maneuvers;

[0018] The obtained multi-cycle adjustment sequence planning model includes a multi-cycle transfer track control point sequence and track altitude adjustment amounts, including:

[0019] Each satellite in the formation performs an orbital maneuver at its apogee to adjust its perigee altitude, and calculates the perigee altitude adjustment amount and apogee altitude control sequence for each maneuver.

[0020] Each satellite in the formation performs an orbital maneuver at perigee to adjust its apogee altitude, and calculates the apogee orbital altitude adjustment amount and perigee altitude control sequence for each maneuver.

[0021] Based on the baseline adjustment perigee orbit altitude control sequence and apogee orbit altitude control sequence of the satellite, the multi-cycle transfer orbit altitude adjustment amount of each satellite, i.e., the altitude control point sequence, is obtained, which is the multi-cycle adjustment sequence planning model.

[0022] The calculation yields the perigee altitude adjustment and apogee altitude control sequence for each maneuver, including:

[0023] The apogee altitude control sequence for a four-star formation maneuvering from the star baseline is as follows:

[0024] r a =[r 1,a ,r 2,a ,,r m,a ]

[0025] In the formula, r represents the orbital altitude; the subscript a represents the apogee.

[0026] When a satellite passes a distant control point, the corresponding perigee altitude adjustment target is:

[0027]

[0028] In the formula, the subscript k∈[1,m] represents the number of cycles in the multi-cycle transfer; the subscript p represents the perigee;

[0029] The perigee orbital altitude adjustment amount is:

[0030] Δr k,p =r k+1,p -r k,p .

[0031] The calculation yields the apogee orbital altitude adjustment and perigee altitude control sequence for each maneuver, including:

[0032] The perigee altitude control sequence for a four-star formation maneuvering from the star baseline is as follows:

[0033] r p =[r 1,p ,r 2,p ,,r m,p ,r v,p ];

[0034] The apogee orbital altitude adjustment is:

[0035]

[0036] In the formula, r k,a This is the target for adjusting the apogee altitude when the satellite passes the near-Earth control point. This target is calculated based on the apogee altitude constraint model adjusted from the satellite baseline. The apogee altitude constraint model is...

[0037]

[0038] By solving the apogee height constraint model using Newton's iterative method, the apogee height adjustment target r can be obtained. k,a .

[0039] The sequence of multiple transfer orbit altitude control points for each satellite, based on the perigee altitude adjustment sequence and apogee altitude control sequence from the satellite baseline, is as follows:

[0040] r S =[r 1,p ,r 1,a ,r 2,p ,r 2,a ,,r k,p ,r k,a ,r v,p ];

[0041] The perigee and apogee altitude adjustments for each maneuver in the multi-loop transfer orbit control point sequence are:

[0042]

[0043] In the formula, This indicates the apogee altitude adjustment amount corresponding to each near-ground control point; This represents the perigee altitude adjustment amount corresponding to each far-ground control point; this multi-cycle transfer orbit control point sequence and the corresponding orbit altitude adjustment amount constitute the multi-cycle transfer strategy for side-by-side multi-satellite formations.

[0044] The step of constructing a continuous thrust control strategy for near-ground control points and far-ground control points based on the obtained multi-cycle adjustment sequence planning model includes:

[0045] Establish a virtual primary star RTN coordinate system for a four-star parallel formation;

[0046] Based on the RTN coordinate system and the obtained multi-cycle adjustment sequence planning model, a continuous thrust control strategy for near-ground and far-ground control points is constructed, including thrust direction, thruster start-up time and start-up duration.

[0047] The establishment of the parallel four-star formation virtual primary star RTN coordinate system includes:

[0048] The origin of the RTN coordinate system is the virtual primary star, the R vector is the unit vector pointing from the Earth's center of mass to the primary star, the N direction is the unit vector of the virtual primary star's angular momentum axis, and the T vector is the direction of motion of the virtual primary star, forming a right-handed relationship with the N and R vectors.

[0049] Based on the obtained multi-cycle adjustment sequence programming model, a continuous thrust control strategy for near-ground control points is constructed, including:

[0050] When the satellite reaches its perigee, it applies continuous thrust in the T-vector direction to adjust its apogee altitude. The thruster is activated for a duration T. thrust,a for:

[0051]

[0052] In the formula, n is the average angular velocity of the virtual primary star's orbit. μ is the Earth's gravitational constant; m k For the current mass of the star; e k F represents the current eccentricity. thrust This represents the thrust amplitude of the orbital-controlled engine; when the thruster is activated for a negative duration, it indicates that the thrust direction is opposite to the T vector.

[0053] Thrust start-up time T start,p for:

[0054]

[0055] In the formula, T p This refers to the moment when the virtual primary star reaches its perigee.

[0056] Based on the obtained multi-cycle adjustment sequence programming model, a continuous thrust control strategy for remote control points is constructed, including:

[0057] When the satellite reaches its apogee, it applies continuous thrust in the T-vector direction to adjust its perigee altitude. The thruster activation duration is:

[0058]

[0059] When the thruster's start-up duration is negative, it indicates that the thrust direction is the opposite of the T vector.

[0060] Thrust start-up time T start,a for:

[0061]

[0062] In the formula, T a This refers to the moment when the virtual primary star reaches its apogee.

[0063] The advantages of this invention compared to the prior art are:

[0064] 1. This invention addresses the baseline adjustment requirements of a four-star formation alongside another star by proposing a decoupled initial and final state description model to ensure that the semi-major axis, inclination angle, right ascension of the ascending node, perigee distance, and mean perigee angle difference remain unchanged during the baseline adjustment process of the four-star formation alongside another star.

[0065] 2. This invention addresses the need for multi-cycle transfer trajectory planning in parallel four-star formation baseline adjustments by proposing an analytical multi-cycle transfer sequence planning model. This model adjusts the orbital altitudes at perigee and apogee, respectively, thereby improving the efficiency of low-thrust transfer trajectory planning.

[0066] 3. This invention addresses the need for low-thrust transfer trajectory planning in parallel four-star formation baseline adjustment. It proposes an analytical low-thrust trajectory planning model, which analytically solves the lateral low-thrust start-up time and duration at perigee and apogee, while ensuring the semi-major axis, inclination angle, right ascension of the ascending node, perigee angular distance, and mean perigee angular difference, thus achieving rapid analytical planning of low-thrust trajectories. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of the low-thrust baseline adjustment trajectory in the geocentric J2000 inertial frame.

[0068] Figure 2 This is a schematic diagram of the small thrust baseline adjustment trajectory in the RTN coordinate system.

[0069] Figure 3 This is a schematic diagram showing the changes in orbital altitude at apogee and perigee.

[0070] Figure 4 This is a schematic diagram of the baseline distance variation.

[0071] Figure 5 This is a schematic diagram showing the start-up time of the thruster. Detailed Implementation

[0072] This invention provides a finite thrust maneuver planning method for baseline adjustment in a side-by-side four-star formation, comprising the following steps:

[0073] 1) Based on the characteristics of the side-by-side four-star formation configuration, establish a decoupling description model for baseline adjustment control objectives oriented towards four-star formations;

[0074] 2) Based on the decoupled description model of the baseline adjustment control target, a multi-cycle transfer method for baseline adjustment of a parallel four-star formation is constructed to obtain a multi-cycle adjustment sequence planning model;

[0075] 3) Based on the obtained multi-cycle adjustment sequence planning model, construct a continuous thrust control strategy for near-ground control points and far-ground control points.

[0076] Further, step 1) specifically includes:

[0077] The four satellites will conduct formation flight missions, establishing a side-by-side four-satellite formation configuration based on a master-slave satellite architecture;

[0078] Let the initial baseline length of the four-star formation be l. u Then, the initial orbital elements of the four slave stars based on the virtual primary star are:

[0079]

[0080] In the formula, variables a, e, i, Ω, ω, and M represent the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, angular distance from perigee, and mean perigee angle, respectively; subscript c represents the orbital elements of the virtual primary star; subscripts I, II, III, and IIII represent the four secondary stars in the four-star formation; and subscript u represents the orbital elements of the four secondary stars in the initial formation configuration.

[0081] Considering an initial maximum baseline distance of 500m, the orbital elements of the four-star formation are shown in Table 1.

[0082] Table 1. Orbital elements of a 500m side-by-side four-star formation

[0083]

[0084] Let the baseline length after the adjustment of the four-star formation be l. v The baseline adjustment control target decoupling description model for a 4-star formation is as follows:

[0085]

[0086] In the formula, the subscript v represents the orbital elements of each star in the formation after baseline adjustment.

[0087] The orbital elements of the four slave stars in the formation after baseline adjustment are as follows:

[0088]

[0089] In the formula, the subscript f represents the number of orbital elements after baseline adjustment.

[0090] Considering the adjusted longest baseline distance of 1000m, the orbital elements of the four-star formation are shown in Table 2.

[0091] Table 2. Orbital elements of a 1000m side-by-side four-star formation

[0092]

[0093] Furthermore, step 2) specifically includes:

[0094] The four-satellite formation employs a decoupled adjustment method for continuous thrust orbital maneuvers, with the orbital transfers of the four satellites occurring independently. Each satellite uses a multi-orbit transfer method to achieve limited thrust baseline adjustment. Let the total number of orbits be m. Each satellite starts from perigee, applies orbital maneuvers to adjust its apogee altitude; upon reaching apogee, it applies another orbital maneuver to adjust its perigee altitude; upon returning to perigee, it applies thrust again to adjust its apogee altitude, and finally, upon reaching perigee on the last orbit, it applies the final maneuver to its target orbit. By adjusting the perigee and apogee altitudes on each orbit, the orbital period of each orbit is ensured to be consistent with the orbital period of the virtual primary satellite. Therefore, the baseline adjustment maneuver sequence for each satellite in the four-satellite formation includes m+1 perigee maneuvers and m apogee maneuvers.

[0095] The obtained multi-cycle adjustment sequence planning model includes a multi-cycle transfer track control point sequence and track altitude adjustment amounts, including:

[0096] Each satellite in the formation performs an orbital maneuver at its apogee to adjust its perigee altitude, and calculates the perigee altitude adjustment amount and apogee altitude control sequence for each maneuver.

[0097] Each satellite in the formation performs an orbital maneuver at perigee to adjust its apogee altitude, and calculates the apogee orbital altitude adjustment amount and perigee altitude control sequence for each maneuver.

[0098] Based on the baseline adjustment perigee orbit altitude control sequence and apogee orbit altitude control sequence of the satellite, the multi-cycle transfer orbit altitude adjustment amount of each satellite, i.e., the altitude control point sequence, is obtained, which is the multi-cycle adjustment sequence planning model.

[0099] The calculation yields the perigee altitude adjustment and apogee altitude control sequence for each maneuver, including:

[0100] The apogee altitude control sequence for a four-star formation maneuvering from the star baseline is as follows:

[0101] r a =[r 1,a ,r 2,a ,…,r m,a ]

[0102] In the formula, r represents the orbital altitude; the subscript a represents the apogee.

[0103] When a satellite passes a distant control point, the corresponding perigee altitude adjustment target is:

[0104]

[0105] In the formula, the subscript k∈[1,m] represents the number of cycles in the multi-cycle transfer; the subscript p represents the perigee;

[0106] The perigee orbital altitude adjustment amount is:

[0107] Δr k,p =r k+1,p -r k,p .

[0108] The calculation yields the apogee orbital altitude adjustment and perigee altitude control sequence for each maneuver, including:

[0109] The perigee altitude control sequence for a four-star formation maneuvering from the star baseline is as follows:

[0110] r p =[r 1,p ,r 2,p ,…,r m,p ,r v,p ];

[0111] The apogee orbital altitude adjustment is:

[0112]

[0113] In the formula, r k,a This is the target for adjusting the apogee altitude when the satellite passes the near-Earth control point. This target is calculated based on the apogee altitude constraint model adjusted from the satellite baseline. The apogee altitude constraint model is...

[0114]

[0115] By solving the apogee height constraint model using Newton's iterative method, the apogee height adjustment target r can be obtained. k,a .

[0116] The sequence of multiple transfer orbit altitude control points for each satellite, based on the perigee altitude adjustment sequence and apogee altitude control sequence from the satellite baseline, is as follows:

[0117] r S =[r 1,p ,r 1,a ,r 2,p ,r 2,a ,,r k,p ,r k,a ,r v,p ];

[0118] The perigee and apogee altitude adjustments for each maneuver in the multi-loop transfer orbit control point sequence are:

[0119]

[0120] In the formula, This indicates the apogee altitude adjustment amount corresponding to each near-ground control point; This represents the perigee altitude adjustment amount corresponding to each far-ground control point; this multi-cycle transfer orbit control point sequence and the corresponding orbit altitude adjustment amount constitute the multi-cycle transfer strategy for side-by-side multi-satellite formations.

[0121] Taking the baseline adjustment of small thrust trajectory planning from Star 1 as an example, its initial and expected terminal perigee and apogee orbital altitudes are shown in Table 3.

[0122] Table 3 Initial and Expected Terminal Perigeogeometry Orbital Altitudes

[0123] initial 6873.5133 6873.8467 end 6873.3467 6874.0133

[0124] Assuming the baseline adjustment maneuver count is 5, the orbital maneuver sequence from Star 1 is shown in Table 4.

[0125] Table 4 Track Maneuver Sequence

[0126] 1 Nearest point 1 <![CDATA[r 1,a =6873.8633km]]> 16.67m 2 apogee 1 <![CDATA[r 1,p =6873.4800km]]> 33.33m 3 Nearest point 2 <![CDATA[r 2,a =6873.8967km]]> 33.33m 4 apogee 2 <![CDATA[r 2,p =6873.4467km]]> 33.33m 5 Perimeter 3 <![CDATA[r 3,a =6873.9300km]]> 33.33m 6 apogee 3 <![CDATA[r 3,p =6873.4133km]]> 33.33m 7 Perimeter 4 <![CDATA[r 4,a =6873.9633km]]> 33.33m 8 apogee 4 <![CDATA[r 4,p =6873.3800km]]> 33.33m 9 Perimeter 5 <![CDATA[r 5,a =6873.9967km]]> 33.33m 10 apogee 5 <![CDATA[r 5,p =6873.3467km]]> 33.33m 11 Perimeter 6 <![CDATA[r 6,a =6874.0133km]]> 16.67m

[0127] Step 3) specifically includes:

[0128] Establish a virtual primary star RTN coordinate system for a four-star parallel formation;

[0129] Based on the RTN coordinate system and the obtained multi-cycle adjustment sequence planning model, a continuous thrust control strategy for near-ground and far-ground control points is constructed, including thrust direction, thruster start-up time and start-up duration.

[0130] The establishment of the parallel four-star formation virtual primary star RTN coordinate system includes:

[0131] The origin of the RTN coordinate system is the virtual primary star, the R vector is the unit vector pointing from the Earth's center of mass to the primary star, the N direction is the unit vector of the virtual primary star's angular momentum axis, and the T vector is the direction of motion of the virtual primary star, forming a right-handed relationship with the N and R vectors.

[0132] Based on the obtained multi-cycle adjustment sequence programming model, a continuous thrust control strategy for near-ground control points is constructed, including:

[0133] When the satellite reaches its perigee, it applies continuous thrust in the T-vector direction to adjust its apogee altitude. The thruster is activated for a duration T. thrust,a for:

[0134]

[0135] In the formula, n is the average angular velocity of the virtual primary star's orbit. μ is the Earth's gravitational constant; m k For the current mass of the star; e k F represents the current eccentricity. thrustThis represents the thrust amplitude of the orbital-controlled engine; when the thruster is activated for a negative duration, it indicates that the thrust direction is opposite to the T vector.

[0136] Thrust start-up time T start,p for:

[0137]

[0138] In the formula, T p This refers to the moment when the virtual primary star reaches its perigee.

[0139] Based on the obtained multi-cycle adjustment sequence programming model, a continuous thrust control strategy for remote control points is constructed, including:

[0140] When the satellite reaches its apogee, it applies continuous thrust in the T-vector direction to adjust its perigee altitude. The thruster activation duration is:

[0141]

[0142] When the thruster's start-up duration is negative, it indicates that the thrust direction is the opposite of the T vector.

[0143] Thrust start-up time T start,a for:

[0144]

[0145] In the formula, T a This refers to the moment when the virtual primary star reaches its apogee.

[0146] This simulation assumes that Satellite 1 has a mass of 1000 kg and a thrust amplitude of 80 mN. Steps 33)-34) calculate the start-up time and duration of the thruster transition from the small thrust trajectory of Satellite 1. The thruster start-up duration is shown below. Figure 5 The trajectory of low-thrust baseline adjustment in the geocentric J2000 inertial frame and RTN coordinate system is shown below. Figure 1 and Figure 2 The orbital altitude and baseline changes at perigee and apogee are shown as follows: Figure 3 and Figure 4 .

[0147] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention based on the above-disclosed technical content without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A low-thrust trajectory analytical planning method for baseline adjustment of a four-star formation alongside each other, characterized in that, include: Based on the characteristics of the side-by-side four-star formation configuration, a decoupling description model for baseline adjustment control objectives oriented towards four-star formations is established. Based on the decoupled description model of baseline adjustment control target, a multi-cycle transfer method for baseline adjustment of parallel four-star formation is constructed to obtain a multi-cycle adjustment sequence planning model. Based on the obtained multi-cycle adjustment sequence planning model, a continuous thrust control strategy for near-ground control points and far-ground control points is constructed. The establishment of a baseline adjustment control target decoupling description model for four-star formations includes: The four satellites will conduct formation flight missions, establishing a side-by-side four-satellite formation configuration based on a master-slave satellite architecture; Let the initial baseline length of the four-star formation be... l u Then, the initial orbital elements of the four slave stars based on the virtual primary star are: In the formula, variables a , e i, Ω ω , M These represent the semi-major axis, eccentricity, orbital inclination, right ascension of the ascending node, perigee distance, and mean perigee angle, respectively; the subscript c represents the orbital elements of the virtual primary star; the subscripts I, II, III, and IIII represent the four secondary stars in the four-star formation; the subscript u represents the orbital elements of the four secondary stars in the initial formation configuration. Let the baseline length of the side-by-side four-star formation after adjustment be... l v The baseline adjustment control target decoupling description model for a 4-star formation is as follows: In the formula, the subscript v represents the orbital elements of each star in the formation after baseline adjustment; The method for constructing a multi-lap transfer method for baseline adjustment of a side-by-side four-star formation, based on the decoupled description model of the baseline adjustment control target, includes: The multi-round transfer strategy for baseline adjustment of a four-star formation includes: setting the total number of rounds to m; each star starts from perigee, applies orbital maneuvers, and adjusts its apogee altitude; after reaching apogee, applies orbital maneuvers and adjusts its perigee altitude; after returning to perigee, applies thrust again to adjust its apogee altitude, and applies the best maneuver to the target orbit after reaching perigee on the last round; by adjusting the perigee and apogee altitudes of each round, the orbital period of each round is ensured to be consistent with the orbital period of the virtual primary star; at this time, the baseline adjustment maneuver sequence of each slave star in the four-star formation includes m+1 perigee maneuvers and m apogee maneuvers.

2. The low-thrust trajectory analytical planning method for baseline adjustment of a side-by-side four-star formation according to claim 1, characterized in that, The obtained multi-cycle adjustment sequence planning model includes a multi-cycle transfer track control point sequence and track altitude adjustment amounts, including: Each satellite in the formation performs an orbital maneuver at its apogee to adjust its perigee altitude, and calculates the perigee altitude adjustment amount and apogee altitude control sequence for each maneuver. Each satellite in the formation performs an orbital maneuver at perigee to adjust its apogee altitude, and calculates the apogee orbital altitude adjustment amount and perigee altitude control sequence for each maneuver; Based on the baseline adjustment perigee orbit altitude control sequence and apogee orbit altitude control sequence of the satellite, the multi-cycle transfer orbit altitude adjustment amount of each satellite, i.e., the altitude control point sequence, is obtained, which is the multi-cycle adjustment sequence planning model.

3. The low-thrust trajectory analytical planning method for baseline adjustment of a side-by-side four-star formation according to claim 2, characterized in that, The calculation yields the perigee altitude adjustment and apogee altitude control sequence for each maneuver, including: The apogee altitude control sequence for a four-star formation maneuvering from the star baseline is as follows: In the formula, r represents the orbital altitude; the subscript a represents the apogee. When the satellite passes the remote control point, the corresponding perigee altitude adjustment target is: In the formula, the subscript Indicates the number of orbits in a multi-orbit transfer; the subscript p represents the perigee; The perigee orbital altitude adjustment amount is: 。 4. The low-thrust trajectory analytical planning method for baseline adjustment of a side-by-side four-star formation according to claim 3, characterized in that, The calculation yields the apogee orbital altitude adjustment and perigee altitude control sequence for each maneuver, including: The perigee altitude control sequence for a four-star formation maneuvering from the star baseline is as follows: ； The apogee orbital altitude adjustment is: ； In the formula, r k,a This is the target for adjusting the apogee altitude when the satellite passes the near-Earth control point. This target is calculated based on the apogee altitude constraint model adjusted from the satellite baseline. The apogee altitude constraint model is... By solving the apogee height constraint model using Newton's iterative method, the apogee height adjustment target r can be obtained. k,a .

5. The low-thrust trajectory analytical planning method for baseline adjustment of a side-by-side four-star formation according to claim 4, characterized in that, The sequence of multiple transfer orbit altitude control points for each slave satellite, based on the perigee altitude adjustment sequence and apogee altitude control sequence from the satellite baseline, is as follows: ； The perigee and apogee altitude adjustments for each maneuver in the multi-loop transfer orbit control point sequence are: In the formula, This indicates the apogee altitude adjustment amount corresponding to each near-ground control point; This represents the perigee altitude adjustment amount corresponding to each far-ground control point; this multi-cycle transfer orbit control point sequence and the corresponding orbit altitude adjustment amount constitute the multi-cycle transfer strategy for side-by-side multi-satellite formations.

6. The low-thrust trajectory analytical planning method for baseline adjustment of a side-by-side four-star formation according to claim 5, characterized in that, The step of constructing a continuous thrust control strategy for near-ground control points and far-ground control points based on the obtained multi-cycle adjustment sequence planning model includes: Establish a virtual primary star RTN coordinate system for a four-star parallel formation; Based on the RTN coordinate system and the obtained multi-cycle adjustment sequence planning model, a continuous thrust control strategy for near-ground and far-ground control points is constructed, including thrust direction, thruster start-up time and start-up duration.

7. The low-thrust trajectory analytical planning method for baseline adjustment of a side-by-side four-star formation according to claim 6, characterized in that, The establishment of the parallel four-star formation virtual primary star RTN coordinate system includes: The origin of the RTN coordinate system is the virtual primary star. R The vector is the unit vector pointing from the Earth's center of mass to the primary star; N The direction is the unit vector of the virtual principal star's angular momentum axis; T The vector represents the direction of motion of the virtual primary star, and... N , R Vector composition is a right-handed relation.

8. The low-thrust trajectory analytical planning method for baseline adjustment of a side-by-side four-star formation according to claim 7, characterized in that, Based on the obtained multi-cycle adjustment sequence programming model, a continuous thrust control strategy for near-ground control points is constructed, including: When the star reaches its perigee, the star is at T Continuous thrust is applied in the vector direction to adjust the apogee altitude; thruster activation duration. T thrust,p for: In the formula, n The average angular velocity of the hypothetical primary star's orbit. , μ The gravitational constant of Earth; m k The current mass of the star; e k The current eccentricity; F thrust This refers to the thrust amplitude of the orbital-controlled engine; when the thruster's activation duration is negative, it indicates that the thrust direction is... T The opposite direction of the vector; Thrust start-up time T start,p for: In the formula, T p This refers to the moment when the virtual primary star reaches its perigee.

9. The low-thrust trajectory analytical planning method for baseline adjustment of a side-by-side four-star formation according to claim 8, characterized in that, Based on the obtained multi-cycle adjustment sequence programming model, a continuous thrust control strategy for remote control points is constructed, including: When the star reaches its apogee, the star is at... T Continuous thrust is applied in the vector direction to adjust the perigee altitude. The thruster activation duration is: When the thruster's start-up duration is negative, it indicates that the thrust direction is... T The opposite direction of the vector; Thrust start-up time T start,a for: In the formula, T a This refers to the moment when the virtual primary star reaches its apogee.

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