Low-energy transfer window rapid design method and system for earth-moon DRO

Abstract

The invention provides a low-energy transfer window rapid design method and system for earth-moon DRO, and relates to the technical field of aerospace. Based on a double-circle restrictive four-body model, an earth-moon transfer orbit database is constructed, the earth-moon transfer orbit database comprises a plurality of transfer orbits from a target near-earth orbit to a target long-distance retrograde orbit; determining a target track point from the track distribution diagram corresponding to each track leveraging category according to the track information track distribution diagram of each transfer track and the input near-earth track information and epoch time of the target spacecraft, and correcting the track information of the transfer track corresponding to the target track point based on an ephemeris model, and obtaining a target transfer orbit of the target spacecraft. According to the method provided by the invention, rapid and accurate planning of the earth-moon DRO low-energy transfer window can be realized, the processing time is reduced, and the planning efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and particularly to a method and system for rapidly designing a low-energy transfer window for Earth-Moon DRO. Background Art

[0002] Current research on low-energy transfer of the Distant Retrograde Orbit (DRO) in the Earth-Moon system mainly focuses on the fields of trajectory optimization and energy analysis. However, in actual mission planning, the ability to rapidly plan the transfer window is still insufficient.

[0003] In related technologies, it usually relies on complex numerical optimization and trajectory integration. The calculation process is time-consuming and lacks intuitive visual explanations, making it difficult to meet the requirements of rapid evaluation and real-time mission adjustment. For example, related technology 1 conducts low-energy transfer window planning based on numerical optimization of leveraging and initial value correction. By screening the initial values of the Poincaré map at the perilune and combining the multi-step shooting method, a high-precision transfer trajectory library is constructed under the ephemeris model, but only the orbit design is completed without the analysis of the regularity of the launch / arrival window. Related technology 2 solves the manifold splicing problem through a two-layer optimization algorithm to achieve the planning of the low-energy Earth-Moon transfer window for spacecraft. However, for different launch times, related technology 2 needs to recalculate the invariant manifolds corresponding to the Sun-Earth Halo orbits at different times, resulting in a long planning time and low planning efficiency.

[0004] Therefore, there is an urgent need for a method and system for rapidly designing a low-energy transfer window for Earth-Moon DRO, which can achieve rapid and accurate planning of the low-energy transfer window for Earth-Moon DRO, reduce the processing time, and improve the planning efficiency. Summary of the Invention

[0005] Embodiments of the present invention provide a method and system for rapidly designing a low-energy transfer window for Earth-Moon DRO, which can achieve rapid and accurate planning of the low-energy transfer window for Earth-Moon DRO, reduce the processing time, and improve the planning efficiency.

[0006] To achieve the above object, the embodiments of the present invention adopt the following technical solutions: In a first aspect, a method for rapidly designing a low-energy transfer window for Earth-Moon DRO is provided. The method includes: based on the double-circle restricted four-body model, constructing an Earth-Moon transfer orbit database, where the Earth-Moon transfer orbit database includes the orbit information and orbit leveraging categories of each transfer orbit in multiple transfer orbits, and the orbit information includes the initial state , the initial epoch , the solar phase of the reference point in the Earth-Moon rotating system , and the transfer duration , the orbit gravity assist categories include backward departure gravity assist, backward return gravity assist, or no lunar gravity assist in the departure phase; determine the apsidal angle of each transfer orbit in the Earth-Sun rotating system according to the orbit information of each transfer orbit and the lunar phase angle ; according to the apsidal angle of each transfer orbit in the Earth-Sun rotating system and the lunar phase angle generate an orbit distribution map corresponding to each orbit gravity assist category, the orbit distribution map includes the trajectory points corresponding to each transfer orbit, wherein, the abscissa of the trajectory point is the apsidal angle , and the ordinate is the lunar phase angle ; determine the apsidal angle of the target spacecraft's low-Earth orbit in the Earth-Sun rotating system according to the input low-Earth orbit information of the target spacecraft and the epoch and the lunar phase angle ; according to the apsidal angle of the target spacecraft's low-Earth orbit in the Earth-Sun rotating system and the lunar phase angle determine the target trajectory point from the orbit distribution map corresponding to each orbit gravity assist category, the target trajectory point is the first trajectory point that satisfies the preset conditions reached by the target ray in the orbit distribution map, the target ray starts from the trajectory point corresponding to the target spacecraft's low-Earth orbit in the orbit distribution map, and along the positive direction, and the slope is the preset slope k, and the preset conditions are associated with the starting point interval time and the equivalent velocity increment; correct the orbit information of the transfer orbit corresponding to the target trajectory point based on the ephemeris model to obtain the target transfer orbit of the target spacecraft.

[0007] In a possible implementation manner of the first aspect, based on the double-circle restricted four-body model, construct a Earth-Moon transfer orbit database, including: based on the double-circle restricted four-body model, determine the phase factor of the target low-Earth orbit and the phase factor of the target distant retrograde orbit , the reference point solar phase in the Earth-Moon rotating system and the deorbit velocity pulse ; according to the phase factor of the target distant retrograde orbit , the reference point solar phase in the Earth-Moon rotating system and the deorbit velocity pulse determine the injection state of the target distant retrograde orbit , is the mission end time; according to the inverse dynamics model, according to the injection state of the target distant retrograde orbit and the phase factor of the target low-Earth orbit Determine the two perigee states included in the transfer trajectory integration process, screen the transfer orbits according to the latter perigee state, and take the orbits with a perigee altitude less than 40,000 km as the feasible solutions of the transfer orbits; based on the weak stable boundary constraint conditions, determine multiple orbit families according to the injection state of the target distant retrograde orbit and the perigee state corresponding to the target low Earth orbit. Each orbit family includes multiple transfer orbits; based on the preset injection pulse of the distant retrograde orbit, use the pseudo-arc length method for numerical continuation to determine the transfer orbit with the minimum total pulse in each orbit family; determine the orbit boost category of the transfer orbit with the minimum total pulse in each orbit family; construct a Earth-Moon transfer orbit database according to the orbit information of the transfer orbit with the minimum total pulse in each orbit family and the orbit boost category being backward departure boost, backward return boost or no lunar boost in the departure section.

[0008] In a possible implementation manner of the first aspect, determine the apsidal angle of each transfer orbit in the heliocentric- Earth coordinate system according to the orbit information of each transfer orbit and the lunar phase angle , including: determining the perigee departure phase angle of each transfer orbit in the Earth-Moon coordinate system and the solar phase angle at the departure time according to the orbit information of each transfer orbit ; determining the apsidal angle of each transfer orbit in the heliocentric- Earth coordinate system and the lunar phase angle according to the perigee departure phase angle of each transfer orbit in the Earth-Moon coordinate system and the solar phase angle at the departure time ; The determination formula of the perigee departure phase angle is: ; is a 6D state vector, represents the x-direction component of and the y-direction component of

[0009] The determination formula of the solar phase angle at the departure time is: ; ; wherein, is the dimensionless gravitational constant, TU is the dimensionless time unit, 1 TU is equal to 4.35 days, is the solar rotation angular velocity in the Earth-Moon coordinate system; The determination formula of the apsidal angle in the heliocentric- Earth coordinate system is:​ ; Determination formula for the lunar phase angle is: .

[0010] In a possible implementation of the first aspect, the apsidal angle of the target spacecraft's low-Earth orbit in the heliocentric-Earth-rotating frame is determined by the formula: ; The lunar phase angle of the target spacecraft's low-Earth orbit in the heliocentric-Earth-rotating frame is determined by the formula: ; where ; ; ; ; ; is the semi-major axis of the orbit, represents the eccentricity, is the orbital inclination, is the right ascension of the ascending node, is the argument of periapsis, is the true anomaly.

[0011] In a possible implementation of the first aspect, based on the apsidal angle of the target spacecraft's low-Earth orbit in the heliocentric-Earth-rotating frame and the lunar phase angle to determine the target trajectory point from the orbit distribution diagram corresponding to each orbit boosting category, including: taking the trajectory point corresponding to the target spacecraft's low-Earth orbit in the orbit distribution diagram as the starting point, with the preset slope k as the slope, and along the positive direction to determine the target ray in the orbit distribution diagram; determining the first trajectory point among the multiple trajectory points included in the orbit distribution diagram passed by the target ray that satisfies the preset conditions as the target trajectory point; The preset conditions are: and ; ; where is the starting point interval time, is the Earth's gravitational constant, is the corresponding to the trajectory point in the orbit distribution diagram.

[0012] In a possible implementation of the first aspect, the above method further includes: when the target ray reaches the top point of the orbit distribution diagram and has not passed through any trajectory point that meets the preset conditions, setting the starting point as the bottom point corresponding to the top point until the target ray passes through the first trajectory point that meets the preset conditions among the multiple trajectory points included in the orbit distribution diagram; wherein, the bottom point corresponding to the top point has the same abscissa as the top point, and the ordinate of the bottom point is 0.

[0013] In a possible implementation of the first aspect, correcting the orbit information of the transfer orbit corresponding to the target trajectory point based on the ephemeris model to obtain the target transfer orbit of the target spacecraft, including: determining all the perigees in the transfer orbit corresponding to the target trajectory point; discretizing the trajectory segments between every two perigees to obtain a plurality of discrete points; using the state information of each discrete point among the plurality of discrete points as the multi-step shooting initial value based on the ephemeris model, and correcting the transfer orbit corresponding to the target trajectory point according to the multi-step shooting initial value to obtain the target transfer orbit of the target spacecraft.

[0014] The beneficial effects of the present invention are as follows: The method provided by the present invention is based on the double-circle restricted four-body model, constructs a database of Earth-Moon transfer orbits, and according to the orbit information orbit distribution diagram of each transfer orbit, and then determines the target trajectory point from the orbit distribution diagrams corresponding to each orbit boost category based on the input near-Earth orbit information of the target spacecraft and the epoch moment. The orbit information of the transfer orbit corresponding to the target trajectory point is corrected based on the ephemeris model to obtain the target transfer orbit of the target spacecraft. The method provided by the present invention can realize the rapid and accurate planning of the low-energy transfer window of the Earth-Moon DRO, reduce the processing time, and improve the planning efficiency. That is to say, the method provided by the present invention constructs a database of Earth-Moon transfer orbits under the double-circle restricted four-body model through grid search and multi-step shooting, and gives a reasonable representation method of the database, and uses the graphical method to realize the rapid and accurate search of the transfer orbit from the near-Earth orbit to the DRO at any moment under the ephemeris, and optimizes and corrects it under the ephemeris. On the other hand, since the method provided by the present invention can quickly and accurately determine the transfer orbit from the near-Earth orbit to the long-distance retrograde orbit, compared with the method for determining the transfer orbit from the near-Earth orbit to the long-distance retrograde orbit in the related art, the method provided by the present invention can be applied to the rapid emergency disposal in the case of abnormal orbital injection, and meet the user's usage requirements in different usage scenarios.

[0015] Second aspect, the present invention provides a low-energy transfer window rapid design system for Earth-Moon DRO. The system includes: a database construction module for constructing an Earth-Moon transfer orbit database based on the double-circle restricted four-body model. The Earth-Moon transfer orbit database includes the orbit information and orbit boost category of each transfer orbit in multiple transfer orbits. The transfer orbit is an orbit that transfers from a target low Earth orbit to a target distant retrograde orbit. Among them, the orbit information includes the initial state , the initial epoch , the solar phase of the reference point in the Earth-Moon rotation system and the transfer duration . The orbit boost category includes backward departure boost, backward return boost, or no lunar boost in the departure section; a first determination module for determining the apsidal angle and the lunar phase angle of each transfer orbit in the Sun-Earth rotation system according to the orbit information of each transfer orbit; a generation module for generating an orbit distribution map corresponding to each orbit boost category according to the apsidal angle and the lunar phase angle of each transfer orbit in the Sun-Earth rotation system. The orbit distribution map includes the trajectory points corresponding to each transfer orbit. Among them, the abscissa of the trajectory point is the apsidal angle , and the ordinate is the lunar phase angle ; a second determination module for determining the apsidal angle and the lunar phase angle of the target spacecraft's low Earth orbit in the Sun-Earth rotation system according to the input low Earth orbit information and epoch of the target spacecraft; a third determination module for determining the target trajectory point from the orbit distribution map corresponding to each orbit boost category according to the apsidal angle and the lunar phase angle of the target spacecraft's low Earth orbit in the Sun-Earth rotation system. The target trajectory point is the first trajectory point that satisfies the preset conditions reached by the target ray in the orbit distribution map. The target ray starts from the trajectory point corresponding to the target spacecraft's low Earth orbit in the orbit distribution map and is along the positive direction with a slope of the preset slope k. The preset conditions are associated with the starting point interval time and the equivalent velocity increment; a trajectory correction module for correcting the orbit information of the transfer orbit corresponding to the target trajectory point based on the ephemeris model to obtain the target transfer orbit of the target spacecraft.

[0016] In a possible implementation manner of the second aspect, the third determination module is specifically used for: taking the trajectory point corresponding to the target spacecraft's low Earth orbit in the orbit distribution map as the starting point, with the preset slope k as the slope, and along Determine the target ray in the orbital distribution diagram in the positive direction; determine the target trajectory point as the first trajectory point among the multiple trajectory points included in the orbital distribution diagram passed by the target ray that satisfies the preset condition; The preset condition is: and ; ; Wherein, is the starting point interval time, is the earth's gravitational constant, is the corresponding to the trajectory point in the orbital distribution diagram.

[0017] In a third aspect, an electronic device is provided. The electronic device includes a memory and one or more processors; the memory is coupled to the processor; wherein, computer program code is stored in the memory, and the computer program code includes computer instructions. When the computer instructions are executed by the processor, the electronic device is caused to execute the method in any implementation manner of the first aspect.

[0018] In a fourth aspect, a computer-readable storage medium is provided, including computer instructions. When the computer instructions run on an electronic device, the electronic device is caused to execute the method in any implementation manner of the first aspect.

[0019] In a fifth aspect, a computer program product is provided. When the computer program product runs on a computer, the computer is caused to execute the method in any implementation manner of the first aspect.

[0020] It can be understood that the beneficial effects that can be achieved by the system provided in the second aspect, the electronic device provided in the third aspect, the computer-readable storage medium provided in the fourth aspect, and the computer program product provided in the fifth aspect can refer to the beneficial effects in the first aspect and any possible design manner thereof, and will not be elaborated herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a schematic structural diagram of an electronic device provided by an embodiment of the present invention; Figure 2 is a flowchart of a method for quickly designing a low-energy transfer window for Earth-Moon DRO provided by an embodiment of the present invention; Figure 3 is a schematic diagram of a type of orbital boost provided by an embodiment of the present invention; Figure 4 is an illustration of the apsidal angle and the lunar phase angle of a transfer orbit in the heliocentric-rotating system provided by an embodiment of the present invention; Figure 5Flowchart of another rapid design method for low-energy transfer windows for Earth-Moon DRO shown in the embodiments of the present invention; Figure 6 Departure phase angle of a transfer orbit in the Earth-Moon rotating system for the embodiments of the present invention and departure moment solar phase angle Schematic diagram; Figure 7 Schematic diagram of an orbit distribution map shown in the embodiments of the present invention; Figure 8 Schematic diagram of the determination process of a target trajectory point shown in the embodiments of the present invention; Figure 9 Schematic diagram of a transfer orbit correction process shown in the embodiments of the present invention; Figure 10 Schematic diagram of the structure of a design system provided by the embodiments of the present invention. Detailed implementation manners

[0022] Next, the technical solutions in the embodiments of the present invention will be described with reference to the accompanying drawings in the embodiments of the present invention. Among them, in the description of the present invention, unless otherwise specified, " / " indicates that the objects associated before and after are in an "or" relationship. For example, A / B may represent A or B; the "or" in the present invention is merely a description of the association relationship of the associated objects, indicating that there can be three relationships. For example, A or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. Among them, A and B can be singular or plural. And, in the description of the present invention, unless otherwise specified, "a plurality of" means two or more than two. "At least one (item)" or its similar expression refers to any combination of these items, including any combination of a single item (item) or plural items (items).

[0023] In addition, in order to facilitate a clear description of the technical solutions in the embodiments of the present invention, in the embodiments of the present invention, words such as "first" and "second" are used to distinguish the same items or similar items with basically the same functions and roles. Those skilled in the art can understand that the words "first" and "second" do not limit the quantity and execution order, and the words "first" and "second" do not necessarily limit being different.

[0024] At the same time, in the embodiments of the present invention, words such as "exemplary" or "for example" are used to represent examples, illustrations or explanations. Any embodiment or design solution described as "exemplary" or "for example" in the embodiments of the present invention should not be construed as being more excellent or having more advantages than other embodiments or design solutions. Exactly speaking, using words such as "exemplary" or "for example" aims to present relevant concepts in a specific manner for easy understanding.

[0025] Current research on low-energy transfers in the Earth-Moon system's Distant Retrograde Orbit (DRO) mainly focuses on trajectory optimization and energy analysis. However, in actual mission planning, the ability to quickly plan transfer windows is still insufficient.

[0026] In related technologies, it usually relies on complex numerical optimization and trajectory integration. The calculation process is time-consuming and lacks intuitive visual explanations, making it difficult to meet the requirements of rapid evaluation and real-time mission adjustment. For example, Related Technology 1 plans low-energy transfer windows based on numerical optimization of gravity assist and initial value correction. By screening initial values through the Poincaré map at the perilune and combining multi-step shooting methods, a high-precision transfer trajectory library is constructed under the ephemeris model, but only the orbit design is completed without regular analysis of the launch / arrival windows. Related Technology 2 solves the manifold splicing problem through a two-layer optimization algorithm to achieve the planning of the low-energy Earth-Moon transfer window for spacecraft. However, for different launch times, Related Technology 2 needs to recalculate the invariant manifolds corresponding to the Sun-Earth Halo orbits at different times, resulting in long planning times and low planning efficiency.

[0027] Therefore, there is an urgent need for a method and system for quickly designing low-energy transfer windows for Earth-Moon DRO, which can achieve rapid and accurate planning of low-energy transfer windows for Earth-Moon DRO, reduce processing time, and improve planning efficiency.

[0028] It should be noted that the rapid design of low-energy transfer windows for Earth-Moon DRO can also be understood as designing a transfer orbit from a target low-Earth orbit to a target distant retrograde orbit.

[0029] In view of this, an embodiment of the present invention provides a method for quickly designing low-energy transfer windows for Earth-Moon DRO. The above method includes: based on the double-circle restricted four-body model, constructing an Earth-Moon transfer orbit database. The Earth-Moon transfer orbit database includes the orbit information and orbit gravity assist categories of each transfer orbit in multiple transfer orbits. The transfer orbit is an orbit from a target low-Earth orbit to a target distant retrograde orbit. Among them, the orbit information includes the initial state , the initial epoch , the solar phase of the reference point in the Earth-Moon rotation system , and the transfer duration . The orbit gravity assist categories include backward departure gravity assist, backward return gravity assist, or no lunar gravity assist in the departure section. Determine the apsidal angle and the lunar phase angle of each transfer orbit in the Sun-Earth rotation system according to the orbit information of each transfer orbit. According to the apsidal angle and the lunar phase angle of each transfer orbit in the Sun-Earth rotation systemGenerate an orbit distribution map corresponding to each orbit gravity assist category. The orbit distribution map includes trajectory points corresponding to each transfer orbit. Among them, the abscissa of the trajectory point is the apsidal angle , and the ordinate is the lunar phase angle . Determine the apsidal angle of the target spacecraft's low Earth orbit in the heliocentric - Earth - rotating coordinate system according to the input low Earth orbit information of the target spacecraft and the epoch and the lunar phase angle . According to the apsidal angle of the target spacecraft's low Earth orbit in the heliocentric - Earth - rotating coordinate system and the lunar phase angle , determine the target trajectory point from the orbit distribution maps corresponding to each orbit gravity assist category. The target trajectory point is the first trajectory point that meets the preset conditions reached by the target ray in the orbit distribution map. The target ray starts from the trajectory point corresponding to the target spacecraft's low Earth orbit in the orbit distribution map and is along the positive direction with a preset slope k. The preset conditions are associated with the start - point interval time and the equivalent velocity increment. Based on the ephemeris model, correct the orbit information of the transfer orbit corresponding to the target trajectory point to obtain the target transfer orbit of the target spacecraft.

[0030] The method provided by the present invention is based on the double - circle restricted four - body model, constructs a database of Earth - Moon transfer orbits, and according to the orbit information of each transfer orbit, an orbit distribution map. Then, according to the input low Earth orbit information of the target spacecraft and the epoch, determine the target trajectory point from the orbit distribution maps corresponding to each orbit gravity assist category, and based on the ephemeris model, correct the orbit information of the transfer orbit corresponding to the target trajectory point to obtain the target transfer orbit of the target spacecraft. The method provided by the present invention can achieve rapid and accurate planning of the low - energy transfer window for Earth - Moon DRO, reduce the processing time, and improve the planning efficiency. That is to say, the method provided by the present invention constructs a database of Earth - Moon transfer orbits under the double - circle restricted four - body model through grid search and multi - step shooting, and gives a reasonable representation method of the database, uses the graphical method to achieve rapid and accurate search for the transfer orbit from the low Earth orbit to DRO at any time under the ephemeris, and optimizes and corrects it under the ephemeris. On the other hand, since the method provided by the present invention can quickly and accurately determine the transfer orbit from the low Earth orbit to the distant retrograde orbit, compared with the method for determining the transfer orbit from the low Earth orbit to the distant retrograde orbit in the related technology, the method provided by the present invention can be applied to rapid emergency disposal in case of abnormal orbital injection and meet the user's usage requirements in different usage scenarios.

[0031] In some embodiments, a method for rapid design of a low - energy transfer window for Earth - Moon DRO provided by an embodiment of the present invention can be executed by a rapid design system 100 for a low - energy transfer window for Earth - Moon DRO (hereinafter referred to as the design system 100).

[0032] As an example, the design system 100 can be any electronic device 200 with data processing capabilities, such as a general computer, a personal computer, a laptop, a switch, or a tablet computer, etc. The specific implementation manner of the design system 100 is not limited herein.

[0033] Figure 1 The schematic diagram of the hardware structure of the electronic device provided by the embodiment of the present invention is shown. The electronic device 200 includes a processor 210, a memory 220, and a communication interface 230.

[0034] The processor 210 may include one or more processing cores. The processor 210 connects various parts within the electronic device 200 through various interfaces and lines, and executes various functions of the electronic device 200 and processes data by running or executing instructions, programs, code sets, or instruction sets stored in the memory 220, and by calling data stored in the memory 220. Optionally, the processor 210 may be implemented in at least one hardware form of a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processing (DSP), a field-programmable gate array (FPGA), or a programmable logic array (PLA).

[0035] The memory 220 may include a random access memory (RAM), and may also include a read-only memory (ROM). Optionally, the memory 220 includes a non-transitory computer-readable medium. The memory 220 can be used to store instructions, programs, codes, code sets, or instruction sets. The memory 220 may include a storage program area. Among them, the storage program area may store instructions for implementing an operating system, instructions for implementing at least one function, instructions for implementing the above-mentioned various method embodiments, etc.

[0036] The communication interface 230 is used to communicate with other devices, equipment, or communication networks, such as a data storage device, an image processing device, or an Ethernet, a radio access network (RAN), a wireless local area network (WLAN), etc.

[0037] In terms of physical implementation, the above-mentioned devices (such as the processor 210, the memory 220, and the communication interface 230) can be components of the same device (such as a laptop computer) respectively. Alternatively, at least two of them can be arranged in the same device, that is, as different components in a device, similar to the deployment method of devices or components in a distributed system.

[0038] It can be understood that the structure illustrated in this embodiment does not constitute a specific limitation on the electronic device 200. In other embodiments of the present invention, the electronic device 200 may include more or fewer components than those shown in the figure, or combine certain components, or split certain components, or have different component arrangements. The illustrated components can be implemented in hardware, software, or a combination of software and hardware.

[0039] The following will describe a method for quickly designing a low-energy transfer window for Earth-Moon DRO provided by an embodiment of the present invention with reference to the accompanying drawings of the specification.

[0040] Figure 2 It is a flowchart of a method for quickly designing a low-energy transfer window for Earth-Moon DRO provided by an embodiment of the present invention. Optionally, this method can be executed by Figure 1 the illustrated electronic device 200. This method may include the following steps: S1. Based on the double-circle restricted four-body model, construct an Earth-Moon transfer orbit database.

[0041] The Earth-Moon transfer orbit database includes the orbit information and orbit assist category of each transfer orbit in a plurality of transfer orbits. The transfer orbit is an orbit that transfers from a target low Earth orbit to a target distant retrograde orbit. Among them, the orbit information includes the initial state , the initial epoch , the solar phase of the reference point in the Earth-Moon rotating system , and the transfer duration . The orbit assist category includes backward departure assist, backward return assist, or no lunar assist in the departure section.

[0042] Specifically, the process of constructing the Earth-Moon transfer orbit database is implemented based on grid search and multi-step shooting method. Among them, grid search is a numerical method that searches for the optimal solution by discretizing the parameter space and traversing all possible parameter combinations. In orbit design, it is mainly used for systematic scanning of high-dimensional parameters (such as phase factor, solar phase, impulse velocity, etc.). The multi-step shooting method is a numerical method in orbit optimization. By dividing the long-duration orbit into multiple short time segments and imposing continuity constraints at the time boundaries of each segment, the overall dynamic equation is finally satisfied through iterative correction.

[0043] In some embodiments, the above S1 includes: S11. Determine the phase factor of the target low Earth orbit and the phase factor of the target distant retrograde orbit based on the double-circle restricted four-body model and the reference point solar phase in the Earth-Moon rotating system and the deorbit velocity pulse . .

[0044] S12. Determine the injection state of the target distant retrograde orbit according to the phase factor of the target distant retrograde orbit , the reference point solar phase in the Earth-Moon rotating system and the deorbit velocity pulse , where is the mission end time . is the mission end time

[0045] S13. According to the inverse dynamics model, determine the states of two perigees included in the transfer trajectory integration process according to the injection state of the target distant retrograde orbit and the phase factor of the target low Earth orbit . Screen the transfer orbits according to the state of the latter perigee, and take the orbit with a perigee altitude less than 40,000 km as the feasible solution of the transfer orbit

[0046] S14. Based on the weak stable boundary constraint conditions, determine multiple orbit families according to the injection state of the target distant retrograde orbit and the perigee state corresponding to the target low Earth orbit. Each orbit family includes multiple transfer orbits

[0047] S15. Based on the preset injection pulse for the distant retrograde orbit, use the pseudo arc-length continuation method for numerical continuation to determine the transfer orbit with the minimum total pulse in each orbit family

[0048] S16. Determine the orbit boost category of the transfer orbit with the minimum total pulse in each orbit family

[0049] S17. Construct an Earth-Moon transfer orbit database according to the orbit information of the transfer orbit with the minimum total pulse in each orbit family and the orbit boost category being backward departure boost, backward return boost, or no lunar boost in the departure section

[0050] For the convenience of understanding this solution, the following uses an example to explain the construction process of the Earth-Moon transfer orbit database included in the embodiments of the present invention

[0051] In an example, the above S1 specifically includes Input the low Earth orbit (target low Earth orbit) at departure and the Earth-Moon 2:1 DRO orbit (target distant retrograde orbit) under the double-circle restricted four-body model. Grid the phase factor of the target low Earth orbit and the phase factor of the target distant retrograde orbit , the solar phase of the reference point in the Earth-Moon rotation system and the out-of-orbit velocity pulse to obtain the injection states of different distant retrograde orbits , where is the mission end time. Starting from and integrating the dynamics equation backward, the spacecraft reaches the perigee , and the states of the first two perigees during the flight are saved. Using multi-step shooting correction, the transfer orbit of the distant retrograde orbit based on the weak stability boundary is obtained. Fix the injection pulse of the distant retrograde orbit, and use the pseudo arc-length method to numerically continue the transfer orbit to determine the transfer orbit with the minimum departure pulse in each orbit family. Then fix the departure pulse and determine the transfer orbit with the minimum total pulse through numerical continuation. Discretize the injection phase of the distant retrograde orbit into 100 phase values, classify the transfer orbits according to the injection positions of the discretized distant retrograde orbits, select the transfer orbit with the lowest total pulse at each phase, use these transfer orbits as the initial values for continuation, and use the pseudo arc-length method to numerically continue the transfer orbits to obtain the orbit families starting from different geocentric orbit phases. Store the orbit information of the generated transfer trajectories in the form of a database, and the orbit information includes the initial state , the initial epoch time , the solar phase of the reference point in the Earth-Moon rotation system and the transfer duration .

[0052] Furthermore, referring to Figure 3 , Figure 3 is a schematic diagram of an orbit gravity assist category provided by an embodiment of the present invention, including forward departure gravity assist, forward return gravity assist, backward departure gravity assist, and backward return gravity assist. Classify according to the lunar gravity assist method: According to the relative position relationship between the spacecraft and the moon at the gravity assist moment and whether it first reaches the apogee before the gravity assist, it can be divided into forward departure gravity assist, forward return gravity assist, backward departure gravity assist, backward return gravity assist, and no lunar gravity assist in the departure section. Delete the orbits with the orbit gravity assist categories of forward departure gravity assist and forward return gravity assist. Among them, Figure 3 the black solid line orbit in is the 2:1 DRO orbit, the red dashed line orbit is the SOI orbit of the moon, the green dot is the earth, the black dot is the state of the moon at LGA (Moon’s state at LGA), the gray dot is the initial state of the moon (Initial state of Moon), and the red dot is the pernlune. S2. Determine the apsidal angle and lunar phase angle of each transfer orbit in the heliocentric rotation system according to the orbit information of each transfer orbit

[0053] Exemplarily, referring toFigure 4 , Figure 4 is the schematic diagram of the apsidal angle of a transfer orbit in the Earth - Sun rotating system and the lunar phase angle .

[0054] In a possible implementation, referring to Figure 5 , the above - mentioned S2 includes: S21. Determine the departure phase angle of the near - Earth orbit and the solar phase angle at the departure time of each transfer orbit in the Earth - Moon rotating system according to the orbit information of each transfer orbit.

[0055] S22. Determine the apsidal angle and the lunar phase angle of each transfer orbit in the Earth - Sun rotating system according to the departure phase angle of the near - Earth orbit and the solar phase angle at the departure time of each transfer orbit in the Earth - Moon rotating system.

[0056] The determination formula of the departure phase angle of the near - Earth orbit is: ; is a 6 - dimensional state vector, represents the x - direction component of represents the y - direction component of

[0057] In an example, = 0.012150585.

[0058] The determination formula of the solar phase angle at the departure time is: ; ; where, is the dimensionless gravitational constant, TU is the dimensionless time unit, 1TU is equal to 4.35 days, is the solar angular velocity of rotation in the Earth - Moon rotating system.

[0059] Referring to Figure 6 , Figure 6 is the schematic diagram of the departure phase angle of the near - Earth orbit and the solar phase angle at the departure time of a transfer orbit in the Earth - Moon rotating system and .

[0060] The determination formula of the apsidal angle in the Earth - Sun rotating system is: ; The determination formula of the lunar phase angle is: ; S3. Generate an orbital distribution map corresponding to each orbit assist category according to the apsidal angle and lunar phase angle of each transfer orbit in the sun-earth rotation system.

[0061] Specifically, the orbital distribution map includes the trajectory points corresponding to each transfer orbit. Among them, the abscissa of the trajectory point is the apsidal angle , and the ordinate is the lunar phase angle .

[0062] Among them, the orbital distribution map is a distribution map. See Figure 7 , Figure 7 which is a schematic diagram of an orbital distribution map shown in an embodiment of the present invention. Figure 7 It includes orbital distribution maps with orbit assist categories of backward departure assist, backward return assist, and no departure assist. Among them, the abscissa is the apsidal angle of the transfer orbit in the sun-earth rotation system , and the ordinate is the lunar phase angle . Different colors are used to represent the equivalent velocity increments corresponding to different transfer orbits.

[0063] S4. Determine the apsidal angle and lunar phase angle of the target spacecraft's low-earth orbit in the sun-earth rotation system according to the input low-earth orbit information of the target spacecraft and the epoch time.

[0064] Specifically, the low-earth orbit information and epoch time of the target spacecraft include the orbital elements of the spacecraft in the J2000 geocentric inertial system at the current epoch time , among which represents the semi-major axis of the orbit, represents the eccentricity, represents the orbital inclination, represents the right ascension of the ascending node, represents the argument of periapsis, represents the true anomaly.

[0065] Exemplarily, see Table 1. Table 1 is a data table of the low-earth orbit information and epoch time of a target spacecraft in an embodiment of the present invention.

[0066] Table 1 In some embodiments, the formula for determining the apsidal angle of the target spacecraft's low-earth orbit in the sun-earth rotation system is: ; The formula for determining the lunar phase angle of the target spacecraft's low-earth orbit in the sun-earth rotation system is: ; Among them, ; ; ; ; ; is the semi-major axis of the orbit, represents the eccentricity, is the inclination of the orbit, is the right ascension of the ascending node, is the argument of perigee, is the true anomaly.

[0067] The following combines an example to explain the determination process of the apsidal angle and the lunar phase angle of the low Earth orbit of the target spacecraft shown in the embodiments of the present invention. Specifically, according to the input low Earth orbit information of the target spacecraft and the epoch time, the position vector corresponding to the perigee is calculated.

[0068] The calculation formula is: ; ; ; Then, the positions of the perigee of the orbit and the moon in the J2000 coordinate system are converted to the heliocentric-rotating frame. The lunar position vector can be read from the ephemeris at the perigee time. The origin of the heliocentric-rotating frame is fixed at the center of the Earth, the X-axis points from the sun to the Earth, and the Z-axis points to the normal of the ecliptic plane. The coordinate transformation formulas are as follows: ; ; Finally, determine the apsidal angle and the lunar phase angle of the low Earth orbit of the target spacecraft in the heliocentric-rotating frame: ; ; It should be noted that the above determination process of the apsidal angle and the lunar phase angle of the low Earth orbit of the target spacecraft is only an exemplary explanation, and the apsidal angle and the lunar phase angle of the low Earth orbit of the target spacecraft in the heliocentric-rotating frame can also be determined by other means., the embodiments of the present invention do not make special restrictions on this.

[0069] S5. Determine the target trajectory point from the orbital distribution diagrams corresponding to each orbital boost category according to the apsidal angle of the target spacecraft's low Earth orbit in the heliocentric - geocentric rotating coordinate system and the lunar phase angle.

[0070] Specifically, the target trajectory point is the first trajectory point that meets the preset conditions reached by the target ray in the orbital distribution diagram. The target ray starts from the trajectory point corresponding to the low Earth orbit of the target spacecraft in the orbital distribution diagram and is along the positive direction, with a preset slope k. The preset conditions are associated with the starting - point interval time and the equivalent velocity increment.

[0071] In one example, the determination formula for the preset slope k is: ; In some embodiments, the above - mentioned S5 includes: Taking the trajectory point corresponding to the low Earth orbit of the target spacecraft in the orbital distribution diagram as the starting point, with the preset slope k as the slope, and along the positive direction to determine the target ray in the orbital distribution diagram.

[0072] Determine the first trajectory point that meets the preset conditions among the multiple trajectory points included in the orbital distribution diagram passed by the target ray as the target trajectory point.

[0073] The preset conditions are: and ; ; wherein, is the starting - point interval time, is the Earth's gravitational constant, is the corresponding to the trajectory point in the orbital distribution diagram.

[0074] Furthermore, the method provided by the embodiments of the present invention further includes the following steps: In the case where the target ray reaches the top - endpoint of the orbital distribution diagram and does not pass through any trajectory point that meets the preset conditions, set the starting point as the bottom - endpoint corresponding to the top - endpoint until the target ray passes through the first trajectory point that meets the preset conditions among the multiple trajectory points included in the orbital distribution diagram. Wherein, the bottom - endpoint corresponding to the top - endpoint has the same abscissa as the top - endpoint, and the ordinate of the bottom - endpoint is 0.

[0075] The following combines an example. Exemplarily, refer to Figure 8 , to explain the determination process of the target trajectory point provided by the embodiments of the present invention. Taking and Starting from draw a straight line along the positive direction on the distribution map, with a slope of: ; When the straight line reaches the bottom end of the distribution map ( ), the starting point is reset to the top end of the distribution map ( ), and continue to draw along the slope, repeating this process until the first trajectory point is reached.

[0076] Extract the corresponding to the first trajectory point reached, and the time interval from the starting point is: .

[0077] Judge whether the preset conditions are met. If: and ; Among them, is the gravitational constant of the earth, is the equivalent velocity increment starting from the low earth orbit, that is, the axis corresponding to the color column in the above Figure 7 . If the above conditions are met, the current transfer orbit is feasible; otherwise, continue to repeat the above steps until the first trajectory point that meets the preset conditions is found, and this trajectory point is determined as the target trajectory point.

[0078] It should be noted that in the above steps, the first trajectory point that meets the preset conditions is determined in the orbit distribution maps corresponding to different orbit boosting categories respectively. In the case where there is a first trajectory point that meets the preset conditions in the orbit distribution maps corresponding to multiple orbit boosting categories, the trajectory point with the smallest starting point interval time is determined as the target trajectory point.

[0079] Specifically, combined with Figure 8 , Figure 8 in (a), (b) and (c) are the orbit distribution maps corresponding to different orbit boosting categories respectively. The three orbit distribution maps share the same coordinate system. Therefore, it is necessary to stack the 3 orbit distribution maps corresponding to different orbit boosting categories together for analysis. Starting from the green starting point, move along the target ray and reach the among all the trajectory points in the three maps The closest trajectory point, i.e., the red point ①. However, the starting point interval time of the red point ① does not meet the time interval condition in the preset conditions, so it is excluded. Continuing to move along the ray, reaching the red point ② that can meet the time interval condition in the preset conditions. However, the red point ② does not meet the speed increment condition in the preset conditions, so it is also excluded. There are multiple intersections between the ray and the trajectory points (colored area) in Figure (c). Since all of them conflict with the preset conditions, they are not listed one by one here, and only the red points ① and ② are given as examples. Then continue to extend along the green ray to reach the red point ③ in Figure (a), and the red point ③ can well meet the preset conditions. Therefore, the red point ③ is selected as the target trajectory point.

[0080] It should be noted that in the above steps, the first trajectory point that meets the preset conditions is determined in the orbital distribution diagrams corresponding to different orbital boost categories respectively. In the case where there is a first trajectory point that meets the preset conditions in the orbital distribution diagrams corresponding to multiple orbital boost categories, the trajectory point with the smallest starting point interval time is determined as the target trajectory point.

[0081] S6. Based on the ephemeris model, correct the orbital information of the transfer orbit corresponding to the target trajectory point to obtain the target transfer orbit of the target spacecraft.

[0082] In a possible implementation manner, the above S6 specifically includes the following steps: S61. Determine all the perigees in the transfer orbit corresponding to the target trajectory point.

[0083] S62. Discretize the trajectory segments between every two perigees to obtain a plurality of discrete points.

[0084] S63. Use the state information of each discrete point among the plurality of discrete points as the multi-step shooting initial value.

[0085] S64. Based on the ephemeris model, correct the transfer orbit corresponding to the target trajectory point according to the multi-step shooting initial value to obtain the target transfer orbit of the target spacecraft.

[0086] In an example, the above S6 includes: According to the orbital information of the transfer orbit corresponding to the target trajectory point under the double-circle restricted four-body model, extract all the perigees in the transfer trajectory. For the trajectory segments between every two perigees, discretize the trajectory segments into 20 points, and extract the state information as the multi-step shooting initial value. Under the ephemeris model, perform multi-step shooting correction on the transfer trajectory to obtain the continuous transfer trajectory under the ephemeris model, such as Figure 9As shown. From the above S1 - S6, it can be seen that the method provided by the embodiment of the present invention is based on the double - circle restricted four - body model, constructs a database of Earth - moon transfer orbits, and according to the orbit information of each transfer orbit, an orbit distribution map is obtained. Then, based on the input near - Earth orbit information of the target spacecraft and the epoch time, the target trajectory point is determined from the orbit distribution maps corresponding to each orbit assist category. Based on the ephemeris model, the orbit information of the transfer orbit corresponding to the target trajectory point is corrected to obtain the target transfer orbit of the target spacecraft. The method provided by the present invention can achieve fast and accurate planning of the low - energy transfer window for Earth - moon DRO, reduce the processing time, and improve the planning efficiency. That is to say, the method provided by the present invention constructs a database of Earth - moon transfer orbits under the double - circle restricted four - body model through grid search and multi - step shooting, and gives a reasonable representation method for the database. The graphical method is used to achieve fast and accurate search for the transfer orbit from the near - Earth orbit to DRO at any time under the ephemeris, and optimize and correct it under the ephemeris. On the other hand, since the method provided by the present invention can quickly and accurately determine the transfer orbit from the near - Earth orbit to the long - distance retrograde orbit, compared with the method for determining the transfer orbit from the near - Earth orbit to the long - distance retrograde orbit in the related technology, the method provided by the present invention can be applied to the fast emergency disposal in case of abnormal orbit injection, and meet the user's usage requirements in different usage scenarios.

[0087] The above mainly introduces the solution of the embodiment of the present invention from the perspective of the method. It can be understood that in order to implement the above functions, the design system 100 includes at least one of the corresponding hardware structures and software modules for executing each function. Those skilled in the art should easily realize that, combining the units and algorithm steps of each example described in the embodiments disclosed herein, the embodiments of the present invention can be implemented in the form of hardware or a combination of hardware and computer software. Whether a certain function is executed in the form of hardware or computer software driving the hardware depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the embodiments of the present invention.

[0088] The embodiments of the present invention can divide the design system 100 into functional units according to the above - mentioned method examples. For example, each function of the design system 100 can be corresponding to each functional unit, or two or more functions can be integrated into one processing unit. The above - integrated unit can be implemented in the form of hardware or in the form of a software functional unit. It should be noted that the division of units in the embodiments of the present invention is illustrative, only a logical functional division, and there may be other division methods in actual implementation.

[0089] Exemplarily, Figure 10The figure shows a schematic diagram of the hardware structure of a design system provided by an embodiment of the present invention. The design system 100 includes: a database construction module 110, configured to construct a Earth-Moon transfer orbit database based on a double-circle restricted four-body model. The Earth-Moon transfer orbit database includes orbit information and orbit boost categories of each transfer orbit among a plurality of transfer orbits. The transfer orbit is an orbit transferred from a target low-Earth orbit to a target distant retrograde orbit. Among them, the orbit information includes the initial state , the initial epoch , the solar phase of the reference point in the Earth-Moon rotation system and the transfer duration . The orbit boost categories include backward departure boost, backward return boost, or no lunar boost in the departure section.

[0090] A first determination module 120, configured to determine the apsidal angle and the lunar phase angle of each transfer orbit in the Sun-Earth rotation system according to the orbit information of each transfer orbit. A generation module 130, configured to generate an orbit distribution map corresponding to each orbit boost category according to the apsidal angle and the lunar phase angle of each transfer orbit in the Sun-Earth rotation system. The orbit distribution map includes trajectory points corresponding to each transfer orbit. Among them, the abscissa of the trajectory point is the apsidal angle , and the ordinate is the lunar phase angle . A second determination module 140, configured to determine the apsidal angle and the lunar phase angle of the target spacecraft's low-Earth orbit in the Sun-Earth rotation system according to the input low-Earth orbit information and epoch of the target spacecraft. A third determination module 150, configured to determine a target trajectory point from the orbit distribution map corresponding to each orbit boost category according to the apsidal angle and the lunar phase angle of the target spacecraft's low-Earth orbit in the Sun-Earth rotation system. The target trajectory point is the first trajectory point that satisfies a preset condition reached by the target ray in the orbit distribution map. The target ray starts from the trajectory point corresponding to the target spacecraft's low-Earth orbit in the orbit distribution map and is along the positive direction with a preset slope k. The preset condition is associated with the start point interval time and the equivalent velocity increment. A trajectory correction module 160, configured to correct the orbit information of the transfer orbit corresponding to the target trajectory point based on the ephemeris model to obtain the target transfer orbit of the target spacecraft.

[0091] Optionally, the third determination module 150 is specifically configured to: start from the trajectory point corresponding to the target spacecraft's low-Earth orbit in the orbit distribution map, with the preset slope k as the slope, and along Determine the target ray in the orbital distribution diagram in the positive direction. Determine the target trajectory point as the first trajectory point among the multiple trajectory points included in the orbital distribution diagram passed by the target ray that satisfies the preset condition.

[0092] The preset condition is: and ; ; Among them, is the dimensionless gravitational constant, TU is the dimensionless time unit, 1 TU is equal to 4.35 days, is the solar rotation angular velocity in the Earth-Moon rotation system.

[0093] It should be understood that for the specific descriptions of the above optional methods, reference can be made to the foregoing method embodiments, which will not be elaborated here. In addition, the explanations and beneficial effects descriptions of any of the above-provided design systems 100 can refer to the corresponding method embodiments above and will not be elaborated.

[0094] The embodiments of the present invention further provide a computer-readable storage medium, in which at least one computer instruction is stored, and the at least one computer instruction is loaded and executed by a processor to implement the methods of the above various embodiments. For the explanations and beneficial effects descriptions of any of the above-provided computer-readable storage media, reference can be made to the corresponding embodiments above, which will not be elaborated here.

[0095] The embodiments of the present invention further provide a chip. The chip integrates a control circuit for implementing the functions of the above design system 100 and one or more ports. Optionally, the functions supported by the chip can refer to the above, which will not be elaborated here.

[0096] Those of ordinary skill in the art can understand that all or part of the steps to implement the above embodiments can be completed by a program instructing relevant hardware. The program can be stored in a computer-readable storage medium. The above-mentioned storage medium can be a read-only memory, a random access memory, etc. The above-mentioned processing unit or processor can be a central processing unit, a general-purpose processor, an application specific integrated circuit (ASIC), a digital signal processor (DSP), a field programmable gate array (FPGA), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof.

[0097] Embodiments of the present invention also provide a computer program product containing instructions. When the instructions run on a computer, the computer is caused to execute any one of the methods in the above embodiments. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the processes or functions according to the embodiments of the present invention are generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wire (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wirelessly (such as infrared, wireless, microwave, etc.). The computer-readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that includes one or more integrated available media. The available medium may be a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as an SSD), etc.

[0098] It should be noted that the devices for storing computer instructions or computer programs provided in the embodiments of the present invention, such as but not limited to, the above-mentioned memory, computer-readable storage medium, and communication chip, etc., are all non-transitory. Those skilled in the art should be able to realize that in the above one or more examples, the functions described in the embodiments of the present invention can be implemented by hardware, software, firmware, or any combination thereof. When implemented using software, these functions may be stored in a computer-readable storage medium or transmitted as one or more instructions or codes on a computer-readable storage medium. The computer-readable storage medium includes a computer storage medium and a communication medium, where the communication medium includes any medium that facilitates the transmission of a computer program from one place to another. The storage medium may be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0099] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A fast design method for low-energy transfer windows for Earth-Moon DRO, characterized in that The method includes: Based on the double-circle restricted four-body model, a database of Earth-Moon transfer orbits is constructed. The database of Earth-Moon transfer orbits includes the orbit information and the orbit boosting category of each of multiple transfer orbits. The transfer orbit is an orbit for transferring from a target low Earth orbit to a target distant retrograde orbit. Among them, the orbit information includes the initial state , the initial epoch , the solar phase of the reference point in the Earth-Moon rotation system and the transfer duration . The orbit boosting category includes backward departure boosting, backward return boosting, or no lunar boosting in the departure section; Determine the apsidal angle of each transfer orbit in the sun-earth rotation system based on the orbit information of each transfer orbit and the lunar phase angle ; According to the apsidal angle of each transfer orbit in the Earth-Sun rotating system and the lunar phase angle generate an orbit distribution map corresponding to each orbit gravity assist category, where the orbit distribution map includes the trajectory points corresponding to each transfer orbit. Among them, the abscissa of the trajectory point is the apsidal angle , and the ordinate is the lunar phase angle ; Determine the apsidal angle of the near-Earth orbit of the target spacecraft in the heliocentric-rotating coordinate system based on the near-Earth orbit information of the target spacecraft input and the epoch time and the lunar phase angle ; According to the apsidal angle of the low Earth orbit of the target spacecraft in the heliocentric rotating coordinate system and the lunar phase angle Determine a target trajectory point from the orbit distribution diagrams corresponding to each orbit assist category, where the target trajectory point is the first trajectory point that satisfies a preset condition reached by a target ray in the orbit distribution diagram. The target ray starts from the trajectory point corresponding to the low Earth orbit of the target spacecraft in the orbit distribution diagram and is along the positive direction with a preset slope k, and the preset condition is associated with the starting point interval time and the equivalent velocity increment; Based on the ephemeris model, correcting the orbital information of the transfer orbit corresponding to the target trajectory point to obtain the target transfer orbit of the target spacecraft.

2. The method according to claim 1, wherein Based on the double-circle restricted four-body model, constructing a database of Earth-Moon transfer orbits, including: Determine the phase factors of the target low Earth orbit and the target distant retrograde orbit based on the double-circle restricted four-body model and the phase factor of the target distant retrograde orbit , the reference point solar phase in the Earth-Moon rotating system and the deorbit velocity pulse ; According to the phase factor of the target distant retrograde orbit , the reference point solar phase in the Earth-Moon rotation system and the deorbit velocity pulse to determine the orbit insertion state of the target distant retrograde orbit , which is the mission end time; According to the inverse dynamics model, based on the orbital injection state of the target long-distance retrograde orbit and the phase factor of the target low Earth orbit Determine the states of two perigees included in the transfer trajectory integration process. Screen the transfer orbits according to the state of the latter perigee, and take the orbit with a perigee altitude less than 40,000 km as the feasible solution of the transfer orbit; Based on the weak stable boundary constraint conditions, according to the injection state of the target distant retrograde orbit and the perigee state corresponding to the target low Earth orbit, multiple orbit families are determined, and each of the orbit families includes multiple transfer orbits; Based on a preset impulsive injection for a distant retrograde orbit, using the pseudo-arc length continuation method for numerical continuation to determine the transfer orbit with the minimum total impulse in each orbit family; Determining the orbital swing-by category of the transfer orbit with the minimum total impulse in each orbit family; Constructing a database of Earth-Moon transfer orbits according to the orbital information of the transfer orbit with the minimum total impulse in each orbit family and with the orbital swing-by category being backward departure swing-by, backward return swing-by, or no lunar swing-by in the departure section.

3. The method according to claim 2, wherein Determining the apsidal angle of each transfer orbit in the sun-earth rotation system according to the orbit information of each transfer orbit and the lunar phase angle , including: Determine the departure phase angle of each transfer orbit in the near-Earth orbit under the Earth-Moon rotation system according to the orbit information of each transfer orbit and the solar phase angle at the departure time ; According to the departure phase angle of the near-Earth orbit in the Earth-Moon rotation system for each transfer orbit and the solar phase angle at the departure time determine the apsidal angle and the lunar phase angle ; Determination formula for the departure phase angle in a low Earth orbit is as follows: ； is a 6-dimensional state vector, denotes the x-direction component of denotes the y-direction component of; The determination formula for the solar phase angle at the departure time is as follows: ； ； Among them, is the dimensionless gravitational constant, TU is the dimensionless unit of time, and 1 TU is equal to 4.35 days. is the angular velocity of the sun's rotation in the earth-moon rotation system; The apsidal angle in the heliocentric-rotating coordinate system The determination formula is as follows: ； Lunar phase angle The determination formula is as follows: 。 4. The method according to claim 3, characterized in that, The formula for determining the apsidal angle of the near-Earth orbit of the target spacecraft in the heliocentric rotating coordinate system is as follows: ； The determination formula for the lunar phase angle of the near-Earth orbit of the target spacecraft in the heliocentric Earth-fixed coordinate system is as follows: ； Among them, ; ； ； ； ； is the semi-major axis of the orbit, represents the eccentricity, is the inclination of the orbit, is the right ascension of the ascending node, is the argument of perigee, is the true anomaly.

5. The method according to claim 4, characterized in that, the apsidal angle of the near-Earth orbit of the target spacecraft in the heliocentric-rotating coordinate system and the lunar phase angle determining a target trajectory point from the orbital distribution diagrams corresponding to each of the orbit boost categories, including: Taking the trajectory point corresponding to the low-Earth orbit of the target spacecraft in the orbit distribution diagram as the starting point, with a preset slope k as the slope, and along the positive direction to determine the target ray in the orbit distribution diagram; Determining the first trajectory point that satisfies a preset condition among the multiple trajectory points included in the orbit distribution map passed by the target ray as the target trajectory point; The preset condition is: and ; ； Among them, is the starting point interval time, is the earth's gravitational constant, corresponds to the trajectory point in the orbital distribution diagram .

6. The method according to claim 5, wherein The method further includes: In the case where the target ray reaches the top point of the orbit distribution map and does not pass through any trajectory point that satisfies the preset condition, setting the starting point as the bottom point corresponding to the top point until the target ray passes through the first trajectory point that satisfies the preset condition among the multiple trajectory points included in the orbit distribution map; wherein, the bottom point corresponding to the top point has the same abscissa as the top point, and the ordinate of the bottom point is 0.

7. The method according to claim 6, characterized in that, The correcting the orbital information of the transfer orbit corresponding to the target trajectory point based on the ephemeris model to obtain the target transfer orbit of the target spacecraft includes: Determining all the perigees in the transfer orbit corresponding to the target trajectory point; Performing discretization processing on the trajectory segments between every two perigees to obtain a plurality of discrete points; Using the state information of each discrete point among the plurality of discrete points as the multi-step shooting initial value Based on the ephemeris model, correcting the transfer orbit corresponding to the target trajectory point according to the multi-step shooting initial value to obtain the target transfer orbit of the target spacecraft.

8. A fast design system for low-energy transfer windows for Earth-Moon DRO, characterized in that, The system includes: A database construction module is used to construct a Earth-Moon transfer orbit database based on the double-circle restricted four-body model. The Earth-Moon transfer orbit database includes the orbit information and orbit boost categories of each of multiple transfer orbits. The transfer orbit is an orbit that transfers from a target low Earth orbit to a target distant retrograde orbit. Among them, the orbit information includes the initial state , the initial epoch , the solar phase of the reference point in the Earth-Moon rotation system and the transfer duration . The orbit boost categories include backward departure boost, backward return boost, or no lunar boost in the departure section; A first determination module, configured to determine the apsidal angle of each transfer orbit in the sun-earth rotation system and the lunar phase angle according to the orbit information of each transfer orbit and the lunar phase angle ; A generation module, configured to generate, according to the apsidal angle of each transfer orbit in the Earth-Sun rotation system and the lunar phase angle an orbit distribution diagram corresponding to each orbit assist category, where the orbit distribution diagram includes the trajectory points corresponding to each transfer orbit, and the abscissa of the trajectory point is the apsidal angle , and the ordinate is the lunar phase angle ; A second determination module, configured to determine an apsidal angle of the near-Earth orbit of the target spacecraft in the sun-Earth rotation system and a lunar phase angle according to the input near-Earth orbit information of the target spacecraft and the epoch time and the lunar phase angle ; A third determination module, configured to determine, according to the apsidal angle of the near-Earth orbit of the target spacecraft in the sun-earth rotation system and the lunar phase angle a target trajectory point from the trajectory distribution diagram corresponding to each orbit boost category, where the target trajectory point is the first trajectory point that satisfies a preset condition reached by a target ray in the trajectory distribution diagram, the target ray starts from the trajectory point corresponding to the near-Earth orbit of the target spacecraft in the trajectory distribution diagram, and is along the positive direction, with a preset slope k, and the preset condition is associated with the start point interval time and the equivalent velocity increment; A trajectory correction module, configured to correct the orbital information of the transfer orbit corresponding to the target trajectory point based on the ephemeris model to obtain the target transfer orbit of the target spacecraft.

9. The system according to claim 8, wherein A third determination module, specifically configured to: Taking the trajectory point corresponding to the low Earth orbit of the target spacecraft in the orbit distribution diagram as the starting point, with a preset slope k as the slope, and along the positive direction to determine the target ray in the orbit distribution diagram; Determine the first trajectory point that satisfies a preset condition among the multiple trajectory points included in the orbit distribution map passed by the target ray as the target trajectory point; The preset condition is: and ; ； Among them, is the starting point interval time, is the earth's gravitational constant, is the corresponding to the trajectory point in the orbit distribution map.

10. An electronic device, characterized in that, Including: A processor; A memory for storing instructions executable by the processor; Wherein, the processor is configured to execute the instructions to implement the method for rapid design of a low-energy transfer window for Earth-Moon DRO according to any one of claims 1-7.

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