An optimization method for multi-plane batch deployment time of continuous low-thrust satellites

Abstract

The present invention provides a method for optimizing the multi-plane batch deployment time of continuous low-thrust satellites, which solves the technical problem of long deployment time in a one-shot multi-satellite mode, including: determining the deployment time consumed by each group of continuous low-thrust satellites according to the orbital inclination difference, orbital semi-major axis difference and ascending node right ascension difference between the relay orbit and multiple target orbits to be formed by multiple groups of continuous low-thrust satellites; the deployment time includes relay time and transfer time; changing the orbital inclination and orbital semi-major axis at the same time, accumulating the time difference of the precession amount of the ascending node of the relay orbit and the target orbit to form the ascending node right ascension difference of the orbital plane, and reducing the relay time; using Hamiltonian function and Euler-Lagrange equation to control the thrust yaw angle, reducing the transfer time; by reducing the relay time and transfer time, the optimization of deployment time is completed. The present invention can deploy satellites faster and more energy-saving, and the deployment effect of high-inclination satellite constellations is more obvious.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite deployment, and in particular relates to a method for optimizing the multi-plane batch deployment time of continuous low-thrust satellites. Background Art

[0002] The deployment of large-scale satellite constellations usually involves dozens to thirty circular orbital planes. The traditional method of directly launching into orbit and releasing satellites in orbit by rockets is very costly. Currently, when deploying constellations of large quantities of continuous small-thrust satellites, they mostly use the method of launching multiple satellites with one rocket to send satellites into near-Earth space, which greatly reduces construction costs.

[0003] After the satellites separate from the rocket, they enter the initial parking orbit. According to the grouping order determined by the constellation configuration, the first group of satellites use their small thrust devices to maneuver in one direction to raise their orbits to the target orbit. The remaining satellites raise their orbits in time according to the grouping order and are finally deployed on different orbital planes. In the non-spherical perturbation of the Earth, the semi-major axis of the orbit and the orbital inclination have a greater impact on the precession of the ascending node. The different amounts of precession of the ascending node generated by the different semi-major axes of the orbit are used to achieve the separation of the right ascension of the ascending nodes between different satellites through time accumulation, and finally all satellites are deployed on different orbital planes.

[0004] During the research, the inventors found that in the method of launching multiple satellites with one rocket, the initial orbit and the target orbit have different orbital semi-major axes and the same orbital inclination, which requires a longer deployment time. Using different orbital semi-major axes to achieve the separation of the right ascension of the ascending node between different satellites, when multi-plane deployment is involved, multiple groups of satellites will spend too long in the initial parking orbit, extending the time period for constellation construction. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a method for optimizing the multi-plane batch deployment time of continuous low-thrust satellites, in which the semi-major axis and orbital inclination of the initial orbit and the target orbit are different, and the two parameters of the semi-major axis and orbital inclination are used to accumulate the time difference of the ascending node precession of different orbits. During the maneuvering process of the satellite from the initial orbit to the target orbit, the Hamiltonian function and the Euler-Lagrange equation are used to optimize the control of the tangential direction and normal direction of the satellite thrust, rather than applying thrust in a single direction, so that the satellite can be deployed faster and more energy-saving. After calculation, this method has a more obvious deployment effect on high-inclination satellite constellations.

[0006] To achieve the above object, the present invention provides a method for optimizing the multi-plane batch deployment time of continuous low-thrust satellites, comprising the following steps:

[0007] Determine the deployment time consumed by each group of continuous low-thrust satellites according to the orbital inclination difference, orbital semi-major axis difference and ascending node right ascension difference between the relay orbit and multiple target orbits to be formed by multiple groups of continuous low-thrust satellites; the deployment time includes relay time and transfer time; and optimize the multi-plane batch deployment time of continuous low-thrust satellites by reducing the relay time and the transfer time;

[0008] The method for optimizing the relay time includes: simultaneously changing the orbital inclination and the orbital semi-major axis, accumulating the difference in the precession amount of the ascending node of the relay orbit and the target orbit over time to form the right ascension difference of the ascending node of the orbital plane, thereby reducing the relay time;

[0009] The method for optimizing the transfer time includes: controlling the thrust yaw angle by using the Hamiltonian function and the Euler-Lagrange equation, thereby reducing the transfer time.

[0010] Furthermore, the calculation method of the minimum relay time consumed by each group of continuous low-thrust satellites is specifically as follows:

[0011]

[0012] Where T1 is the relay time between groups; ΔΩ is the change in right ascension of the ascending node; is the rate of change of right ascension of ascending node; a0 is the semi-major axis of relay orbit; i0 is the inclination of relay orbit; a f is the semi-major axis of the target orbit; i f is the target orbit inclination.

[0013] Furthermore, the calculation method of the minimum transfer time consumed by each group of continuous low-thrust satellites is specifically as follows:

[0014]

[0015] Where β0 is the initial yaw angle of thrust; Δi f The target change of orbital inclination; v0 is the relay orbit speed; v f is the target orbital velocity; β is the thrust yaw angle; f is the thrust acceleration; t is the duration of thrust application; Δi is the change in orbital inclination during the transfer process; v is the satellite velocity during the transfer process; Δv is the change in satellite velocity during the transfer process; and T2 is the transfer time.

[0016] The thrust yaw angle is the angle between the thrust in the tangential direction and the normal direction.

[0017] Furthermore, the method also includes: a method for calculating the mathematical limit of the high and low orbital inclinations during the continuous low-thrust satellite batch deployment time, including:

[0018]

[0019] Where Δv a The velocity increment required to change the semi-major axis of the orbit; Δv i is the velocity increment required to change the orbital inclination; i is the orbital inclination.

[0020] Furthermore, the method also includes: the critical value of the mathematical limit for distinguishing high and low orbital inclinations during the continuous low-thrust satellite batch deployment time is:

[0021] When the orbital inclination is 0≤i<81.8699 or 98.1301°<i≤180°, adjusting the orbital semi-major axis to achieve the separation of the ascending node right ascension requires a smaller velocity increment; when 81.8699<i<98.1301, adjusting the orbital inclination to complete the deployment of continuous low-thrust satellite orbital planes can save more fuel.

[0022] The present invention has the following beneficial effects:

[0023] 1. Simultaneously changing the orbital inclination and the orbital semi-major axis to accumulate the ascending node precession momentum over time, shortening the satellite relay time;

[0024] 2. A dynamic model of orbital semi-major axis and orbital inclination transfer based on Hamiltonian function and Euler-Lagrange equation was established, and the transfer time of the satellite from the relay orbit to the target orbit was solved as the objective function to obtain the most time-saving thrust direction control method;

[0025] 3. Calculating the difference between high and low orbital inclinations requires clear mathematical boundaries. The method of this application is more effective for the deployment of high-inclination constellations.

[0026] The method provided by the present invention has the following advantages in the multi-plane batch deployment of satellite constellations:

[0027] 1. The relay time is significantly shortened compared with the existing deployment strategy. The more track surfaces there are, the more obvious this effect is.

[0028] 2. The Hamiltonian function and the Euler-Lagrange equation are used to optimize the control of the tangential and normal directions of the thrust, and a more energy-saving control method can be obtained on the basis of time optimization;

[0029] 3. During the satellite transfer process, the thrust yaw angle changes in a small range, reducing the difficulty of spacecraft attitude control;

[0030] 4. Solve the mathematical boundaries of orbital inclination in continuous low-thrust satellite deployment. In engineering practice, the orbital semi-major axis difference and orbital inclination difference between the relay orbit and the target orbit can be adjusted according to mission requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1It is a schematic diagram of a method for optimizing the multi-plane batch deployment time of continuous low-thrust satellites of the present invention. DETAILED DESCRIPTION

[0032] like Figure 1 As shown, in an embodiment of the present invention, a method for optimizing the multi-plane batch deployment time of continuous low-thrust satellites is provided, comprising the following steps:

[0033] Determining the deployment time consumed by each group of continuous low-thrust satellites according to the orbital inclination difference, orbital semi-major axis difference and ascending node right ascension difference between the relay orbit and the multiple target orbits to be formed by the multiple groups of continuous low-thrust satellites; the deployment time includes the relay time and the transfer time;

[0034] At the same time, the orbital inclination and orbital semi-major axis are changed, and the difference in the precession of the ascending node of the relay orbit and the target orbit is accumulated over time to form the right ascension difference of the ascending node of the orbital plane, thereby reducing the relay time;

[0035] The Hamiltonian function and Euler-Lagrange equations are used to control the thrust yaw angle, thereby reducing the transfer time;

[0036] The multi-plane batch deployment time of continuous low-thrust satellites is optimized by reducing the relay time and transfer time.

[0037] Furthermore, the calculation method of the minimum relay time consumed by each group of continuous low-thrust satellites is specifically as follows:

[0038]

[0039] Where T1 is the relay time between groups; ΔΩ is the change in right ascension of the ascending node; is the rate of change of right ascension of ascending node; a0 is the semi-major axis of relay orbit; i0 is the inclination of relay orbit; a f is the semi-major axis of the target orbit; i f is the target orbit inclination.

[0040] Furthermore, the calculation method of the minimum transfer time consumed by each group of continuous low-thrust satellites is specifically as follows:

[0041]

[0042] Where β0 is the initial yaw angle of thrust; Δi f The target change of orbital inclination; v0 is the relay orbit speed; v f is the target orbital velocity; β is the thrust yaw angle; f is the thrust acceleration; t is the duration of thrust application; Δi is the change in orbital inclination during the transfer process; v is the satellite velocity during the transfer process; Δv is the change in satellite velocity during the transfer process; and T2 is the transfer time.

[0043] The thrust yaw angle is the angle between the thrust in the tangential direction and the normal direction.

[0044] The Hamiltonian function and the Euler-Lagrange equation are used to control the thrust yaw angle (the angle between the tangential and normal thrusts). The specific control law is related to the initial orbital velocity, the initial thrust yaw angle, the thrust magnitude, and the transfer time. In this process, the orbital inclination and orbital semi-major axis can be changed more efficiently.

[0045] Furthermore, the method also includes: a method for calculating the mathematical limit of the high and low orbital inclinations in the continuous low-thrust satellite batch deployment time, including:

[0046]

[0047] Where Δv a The velocity increment required to change the semi-major axis of the orbit; Δv i is the velocity increment required to change the orbital inclination; i is the orbital inclination.

[0048] Furthermore, the method also includes: the critical value of the mathematical limit for distinguishing high and low orbital inclinations during the continuous low-thrust satellite batch deployment time is:

[0049] When the orbital inclination is 0≤i<81.8699 or 98.1301°<i≤180°, adjusting the orbital semi-major axis to achieve the separation of the ascending node right ascension requires a smaller velocity increment; when 81.8699<i<98.1301, adjusting the orbital inclination to complete the deployment of continuous low-thrust satellite orbital planes can save more fuel.

[0050] Preferably, a first embodiment of the present invention provides a multi-plane batch deployment method for continuous low-thrust satellites, and the multi-plane batch deployment method applies a multi-plane batch deployment time optimization method for continuous low-thrust satellites provided by the present invention, and comprises the following steps:

[0051] Step 1: Multiple continuous low-thrust satellites simultaneously carry a carrier into near-Earth space, and after separating from the carrier, the multiple continuous low-thrust satellites enter the initial orbit to form a relay orbit; the continuous low-thrust satellites are grouped according to the group order determined by the constellation configuration;

[0052] Specifically, N satellites simultaneously carry a carrier into near-Earth space. After the satellites are separated from the carrier, all satellites are controlled to enter the initial orbit to form a relay orbit (RO); according to the group order determined by the constellation configuration, the N satellites are divided into K groups, each with M satellites; among them, 2≤K<N, K*M=N, K, M, N are positive integers.

[0053] Step 2: Determine the deployment time consumed by each group of continuous low-thrust satellites according to the orbital inclination difference, orbital semi-major axis difference and ascending node right ascension difference between the relay orbit and multiple target orbits to be formed by multiple groups of continuous low-thrust satellites; the deployment time includes relay time and transfer time; change the orbital inclination and orbital semi-major axis at the same time, accumulate the difference in the precession amount of the ascending node between the relay orbit and the target orbit over time to form the ascending node right ascension difference of the orbital plane, thereby reducing the relay time; use the Hamiltonian function and the Euler-Lagrange equation to optimize the thrust yaw angle, thereby reducing the transfer time; and optimize the multi-plane batch deployment time of continuous low-thrust satellites by reducing the relay time and the transfer time.

[0054] Step 3: Transfer the continuous low-thrust satellites from the relay orbit to the target orbit in a grouped order with an optimized deployment time, so that all the continuous low-thrust satellites are finally deployed on the target orbital plane.

[0055] Specifically, the continuous low-thrust satellites are maneuvered and transferred in time according to the order of the first group to the Kth group. After the first group of continuous low-thrust satellites is transferred to the first target orbit, the second to the Kth groups of continuous low-thrust satellites are still operating in the relay orbit. After a certain period of time, the second group of continuous low-thrust satellites are maneuvered and transferred to the second target orbit, and so on, until all continuous low-thrust satellites are finally deployed on the target orbital plane.

[0056] In the step 2, the ascending node precession is the continuous low-thrust satellite in the motion around the earth. Under the influence of the non-spherical perturbation of the earth, the right ascension of the orbital ascending node will drift, which is called the precession of the ascending node. The degree of the drift of the right ascension of the ascending node is called the precession of the ascending node.

[0057] In the step 2, the relay time is the time that each group of continuous low-thrust satellites stays in the relay orbit, and the right ascension difference of the ascending node of each group of continuous low-thrust satellites comes from the difference in the length of time that the continuous low-thrust satellites between the groups stay in the relay orbit.

[0058] In the step 2, the transfer time is the time consumed by the continuous low-thrust satellite to transfer from the relay orbit to the target orbit.

[0059] In step 2, the calculation method for reducing the relay time is specifically as follows:

[0060]

[0061] Where T1 is the relay time between groups; ΔΩ is the change in right ascension of the ascending node; is the rate of change of right ascension of ascending node; a0 is the semi-major axis of relay orbit; i0 is the inclination of relay orbit; a f is the semi-major axis of the target orbit; i f is the target orbit inclination.

[0062] The technical principles for reducing relay time are as follows:

[0063] Each target orbit has the same height, eccentricity, orbital inclination, and different right ascension of the ascending node; the relay orbit of each group of satellites has a different height, eccentricity, orbital inclination, and right ascension of the ascending node from its target orbit. The length of time each group of satellites stays in the relay orbit is different, that is, the relay time is different; but the transfer time of each group of satellites is the same, that is, the change in orbital parameters required for the transfer process is the same.

[0064] Calculation of inter-group relay time T1:

[0065] The rate of change of the ascending node right ascension under the action of the main perturbation term gravitational field J2 can be expressed as:

[0066]

[0067] In the formula, the J2 term of the non-spherical earth is 1.0826×10 -3 , μ=3.986005×10 14 m 3 / s 2 is the Earth’s gravitational constant, a is the semi-major axis of the orbit, and i is the orbital inclination.

[0068] The ascending node precession is accumulated over time using the orbital semi-major axis and the orbital inclination difference to form the ascending node right ascension difference of the orbital plane. Combined with formula (1), the relay time is:

[0069]

[0070] In step 2, the calculation method for reducing the transfer time is specifically as follows:

[0071]

[0072] Where β0 is the initial yaw angle of thrust; Δi f The target change of orbital inclination; v0 is the relay orbit speed; v f is the target orbital velocity; β is the thrust yaw angle; f is the thrust acceleration; t is the duration of thrust application; Δi is the change in orbital inclination during the transfer process; v is the satellite velocity during the transfer process; Δv is the change in satellite velocity during the transfer process; and T2 is the transfer time.

[0073] The technical principles for reducing transfer time are as follows:

[0074] When both the initial and final orbits are circular orbits (e=0), the perturbation motion equation represented by the classical orbital elements (a, e, i, Ω, ω, M) will have singularities, so the non-singular variable is introduced

[0075] a,i,Ω,ξ=ecosω; η=esinω; ψ=M+ω (4)

[0076] The perturbation motion equation is described by the orbital elements without singular points as follows:

[0077]

[0078] Where: n is the average angular velocity; f t 、f n 、f h are the thrust acceleration components in the orbital tangent, principal normal (perpendicular to the tangent and pointing to the center of the earth, i.e. radial) and secondary normal (normal to the orbital plane) directions respectively. The above formula has simplified the Gaussian perturbation motion equation according to the characteristics of the near-circular orbit, but when i = 0 and i = π, the equation still has singularity, so this formula is not applicable to the case where the orbital plane is in the equatorial plane.

[0079] Assume that the thrust acceleration vector f has no radial component, that is, f n = 0, the tangential component and subnormal component of f are given by f t =fcosβ and f h =fsinβ, the acceleration value f = |f|, so the simplified equation of motion can be written as

[0080]

[0081] During the maneuver that satisfies equation (6), the orbit will remain a circular orbit. Let f represent the magnitude of the thrust acceleration, and β represent the thrust yaw angle (the angle between the thrust acceleration vector and the current orbital plane). Then,

[0082] f t =fcosβ,f h =fsinβ(7)

[0083] Eliminate the cosψ term in the second equation of (6) and divide the second equation of (6) by the fourth equation to obtain

[0084]

[0085] Using the orbital averaging method, β The time-varying sign and the change in inclination angle are

[0086]

[0087] One orbital period is Δt = 2πa / v, and v = na, so we have

[0088]

[0089] For circular orbits, r = a, so the energy formula becomes

[0090]

[0091] Differentiate the above equation and substitute (6) and (11) into it to obtain

[0092]

[0093] Right now

[0094]

[0095] The orbital maneuver control equation under continuous low thrust is as follows

[0096]

[0097] The first and second equations of (14) are used as the state equations to describe the velocity and inclination transfer problem under continuous small thrust. The two state variables are v and i, respectively. Time t is the independent variable, and the thrust yaw angle β is the control variable. Given the radius r0 of the initial orbit, the inclination i0, and the radius r of the target orbit, f 、Inclination angle i f Since both the initial and final orbits are circular orbits, it is equivalent to giving v0 and v f The satellite is required to transfer from the initial orbit to the target orbit in the shortest time, and the performance index is

[0098]

[0099] According to the minimum principle, the Hamiltonian function is

[0100]

[0101] λ i , V For the covariate variable, the Euler-Lagrange equation is given by:

[0102]

[0103] It can be seen that λ i is a constant, and the extreme value condition is

[0104]

[0105] The optimal control law can be obtained as

[0106]

[0107] Since the Hamiltonian function does not explicitly contain time t, the function is a constant on the optimal control trajectory.f Free, so the end transversality condition H f = 0. So we can get

[0108]

[0109] therefore

[0110]

[0111] When the thrust acceleration f is constant, according to the first formula in the above formula, we can get

[0112] vsinβ=v0sinβ0 (22)

[0113] It can be seen that the optimal control law β is related to the speed v and the initial yaw angle β0. Differentiating (19), we can get

[0114]

[0115] Substituting (22) into (22) we get

[0116]

[0117] Therefore

[0118]

[0119] Integrating the above formula, we can get

[0120]

[0121] The optimal control law is

[0122]

[0123] It can be seen that in order to obtain the optimal control law, it is only necessary to determine the initial yaw angle β0.

[0124] In order to find β0, we need to first analyze the changing laws of velocity and orbital inclination. From formula (13), we can get

[0125]

[0126] Integrating the above formula, we can get

[0127]

[0128] The law of velocity variation with time can be obtained as

[0129]

[0130] Next, we analyze the variation law of orbital inclination change Δi with time t. By integrating equation (10), we can get

[0131]

[0132] In this process, there are

[0133]

[0134] Using trigonometric formulas, we can get

[0135]

[0136] The transfer time T2 is:

[0137]

[0138] Based on the above derivation, let’s find β0

[0139]

[0140] Finally, a dynamic model of orbital semi-major axis and orbital inclination transfer based on Hamiltonian function and Euler-Lagrange equation was established. The dynamic model process of velocity and inclination transfer is described as follows:

[0141]

[0142] Furthermore, the method also includes: a method for calculating a mathematical limit for distinguishing high and low orbital inclinations, including:

[0143]

[0144] Where Δv a The velocity increment required to change the semi-major axis of the orbit; Δv i is the velocity increment required to change the orbital inclination; i is the orbital inclination.

[0145] Specifically, the technical principle is as follows:

[0146] In engineering problems, it is necessary to distinguish between high and low orbital inclinations. The electric propulsion medium carried by small satellites is an important condition that constrains their on-orbit life. The following is the optimal solution under the condition of saving the most energy. Formula (1) shows that the rate of change of the right ascension of the ascending node is related to the semi-major axis and the orbital inclination. The total differential of formula (1) is:

[0147]

[0148] For a given rate of change of right ascension of the ascending node, the required change to correct the semi-major axis or orbital inclination can be calculated using equation (2):

[0149]

[0150] Under the condition of continuous small thrust, the velocity increment required to adjust the orbit semi-major axis and orbit inclination is:

[0151]

[0152] Substituting equation (40) into equation (39), and comparing the velocity increment required to achieve the separation of the ascending node right ascension by changing the semi-major axis and orbit inclination, we have

[0153]

[0154] Furthermore, the method further includes: the critical value of the mathematical boundary for distinguishing high and low orbital inclination is:

[0155] Let equation (41) be equal to 1, then i = 81.8699° or i = 98.1301°. When the orbital inclination is 0≤i<81.8699 or 98.1301<i≤180°, adjusting the orbital semi-major axis to achieve the separation of the ascending node right ascension requires a smaller velocity increment. When 81.8699<i<98.1301, adjusting the orbital inclination to complete the deployment of the continuous low-thrust satellite orbital plane can save more fuel.

[0156] The first embodiment of the present invention has the following beneficial effects:

[0157] 1. Simultaneously changing the orbital inclination and the orbital semi-major axis to accumulate the ascending node precession momentum over time, shortening the satellite relay time;

[0158] 2. A dynamic model of the transfer of orbital semi-major axis and orbital inclination based on the Hamiltonian function and Euler-Lagrange equations was established, and the transfer time of the satellite from the relay orbit to the target orbit was solved as the objective function to obtain the most time-saving thrust direction control method.

[0159] 3. Calculating the difference between high and low orbital inclinations requires clear mathematical boundaries. The method of this application is more effective for the deployment of high-inclination constellations.

[0160] The method provided by the present invention has the following advantages in the multi-plane batch deployment of satellite constellations:

[0161] 1. The relay time is significantly shortened compared with the existing deployment strategy. The more track surfaces there are, the more obvious this effect is.

[0162] 2. The Hamiltonian function is used to optimize the thrust direction and obtain a more energy-saving control method based on the optimal time.

[0163] 3. During the satellite transfer process, the thrust yaw angle changes in a small range, reducing the difficulty of spacecraft attitude control;

[0164] 4. Solve the mathematical boundaries of orbital inclination in continuous low-thrust satellite deployment. In engineering practice, the orbital semi-major axis difference and orbital inclination difference between the relay orbit and the target orbit can be adjusted according to mission requirements.

[0165] In order to explain the technical solution of the present invention more clearly, a preferred embodiment is now provided as follows:

[0166] Satellite multi-plane batch deployment method based on multi-element transfer

[0167] Referring to a batch of satellites launched by the OneWeb constellation in October 2021, a batch of 36 satellites were carried by the same carrier into the initial orbit (orbital semi-major axis 6978km, orbital altitude 600km, orbital inclination 87.1°), and then the ground measurement and control system controlled the satellites, distributing them in three orbital planes with an interval of 15°, an orbital semi-major axis of 7578km, an orbital altitude of 1200km, and an orbital inclination of 87.9°, with 12 satellites deployed in each orbital plane. The Hamiltonian function is used to optimize the satellite transfer process, and the dynamic model of the continuous low-thrust spacecraft in this paper is used. The satellite parameters are shown in Table 1.

[0168] Table 1

[0169]

[0170]

[0171] The satellite is deployed from the parking orbit (6978km, 87.1°) to the target orbit (7578km, 87.9°). The specific control strategy is as follows:

[0172] (1) The first batch of 12 satellites will directly transfer from the parking orbit after entering orbit, and stop maneuvering after reaching the target orbit about 63.5 days later.

[0173] (2) The second batch of satellites remained in the parking orbit for 89 days. After the orbital plane deviated by 15° from the first target orbital plane, they underwent orbit transfer and reached the target orbit after 63.5 days.

[0174] (3) The third batch of satellites remained in the parking orbit for 178 days, with a difference of 15° from the second target orbital plane and 30° from the first target orbital plane. They then underwent orbit transfer and reached the target orbit after 63.5 days.

[0175] The 36 satellites launched on one rocket were divided into three batches for mobile deployment, distributed on three orbital planes with a 15° difference in the right ascension of the ascending node. The entire deployment process includes three satellite maneuvers and two right ascension separation processes of the ascending node, but there is an overlap in time between each process, so the total duration is less than the sum of all durations, totaling 241.5 days.

[0176] Three methods are used for simulation comparison during the transfer process:

[0177] Strategy 1: First change the orbital inclination on the relay orbit, then change the orbital semi-major axis, and maneuver to the target orbit;

[0178] Strategy 2: First change the semi-major axis of the orbit on the relay orbit, then change the orbital inclination, and maneuver to the target orbit;

[0179] Strategy 3: Use the control method in this article to change the inclination and altitude simultaneously and maneuver to the target orbit.

[0180] The results are shown in Table 2:

[0181] Table 2

[0182] Strategy 1 Strategy 2 Strategy Three Time (day) 75.4277 74.6450 63.4871 Speed ​​increment (m / s) 410.8994 406.6355 345.8521

[0183] It can be seen from the table that the dynamic model solved by the Hamiltonian function in this application can significantly reduce the deployment time and speed increment, thereby improving the deployment efficiency and reducing the deployment cost.

[0184] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for optimizing the multi-plane batch deployment time of continuous low-thrust satellites, characterized in that: The following steps are involved: Determining the deployment time consumed by each group of continuous low-thrust satellites according to the orbital inclination difference, orbital semi-major axis difference and ascending node right ascension difference between the relay orbit and the multiple target orbits to be formed by the multiple groups of continuous low-thrust satellites; the deployment time includes the relay time and the transfer time; By reducing the relay time and transfer time, the multi-plane batch deployment time of continuous low-thrust satellites is optimized; The method for optimizing the relay time includes: simultaneously changing the orbital inclination and the orbital semi-major axis, accumulating the difference in the precession amount of the ascending node of the relay orbit and the target orbit over time to form the right ascension difference of the ascending node of the orbital plane, thereby reducing the relay time; The transfer time optimization method includes: using Hamiltonian function and Euler-Lagrange equation to control the thrust yaw angle, thereby reducing the transfer time; The specific calculation method of the minimum relay time consumed by each group of continuous low-thrust satellites is: Where T1 is the relay time between groups; ΔΩ is the change in right ascension of the ascending node; is the rate of change of right ascension of ascending node; a0 is the semi-major axis of relay orbit; i0 is the inclination of relay orbit; a f is the semi-major axis of the target orbit; i f is the target orbit inclination.

2. The method according to claim 1, characterized in that The specific calculation method of the minimum transfer time consumed by each group of continuous low-thrust satellites is: Where β0 is the initial yaw angle of thrust; Δi f The target change of orbital inclination; v0 is the relay orbit speed; v f is the target orbital velocity; β is the thrust yaw angle; f is the thrust acceleration; t is the duration of thrust application; Δi is the change in orbital inclination during the transfer process; v is the satellite velocity during the transfer process; Δv is the change in satellite velocity during the transfer process; and T2 is the transfer time.

3. The method according to claim 1 or 2, characterized in that The thrust yaw angle is the angle between the thrust in the tangential direction and the normal direction.

4. The method according to claim 1, characterized in that The method also includes: a method for calculating the mathematical limit of the high and low orbital inclinations during the continuous low-thrust satellite batch deployment time, including: Where Δv a The velocity increment required to change the semi-major axis of the orbit; Δv i is the velocity increment required to change the orbital inclination; i is the orbital inclination.

5. The method according to claim 1 or 4, characterized in that The method also includes: the critical value of the mathematical limit for distinguishing high and low orbital inclinations during the continuous low-thrust satellite batch deployment time is: When the orbital inclination is 0≤i<81.8699° or 98.1301°<i≤180°, adjusting the orbital semi-major axis to achieve the separation of the ascending node right ascension requires a smaller velocity increment; when 81.8699°<i<98.1301°, adjusting the orbital inclination to complete the deployment of continuous low-thrust satellite orbital planes can save more fuel.

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