A rapid design method and system for low-energy transfer window for Earth-Moon DRO

Abstract

The present invention provides a method and system for rapid design of a low-energy transfer window for an Earth-Moon DRO (Dro-orbital orbiting resonator), relating to the field of aerospace technology. Based on a two-circle restricted four-body model, the present invention constructs an Earth-Moon transfer orbit database, which includes multiple transfer orbits from a target low-Earth orbit to a target long-range retrograde orbit. Based on an orbital distribution diagram of the orbital information of each transfer orbit, the target trajectory point is determined from the orbital distribution diagram corresponding to each orbital leverage category based on the input low-Earth orbit information and epoch time of the target spacecraft. The orbital 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 achieve rapid and accurate planning of the Earth-Moon DRO low-energy transfer window, reducing processing time and improving planning efficiency.

Description

Technical Field

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

[0002] Current research on low-energy transfers in distant retrograde orbits (DROs) for the Earth-Moon system focuses primarily on trajectory optimization and energy analysis. However, in actual mission planning, the ability to quickly plan transfer windows remains insufficient.

[0003] Related technologies usually rely on complex numerical optimization and trajectory integration. The calculation process is time-consuming and lacks intuitive and visual explanations, making it difficult to meet the needs of rapid evaluation and real-time mission adjustment. For example, Related Technology 1 performs low-energy transfer window planning based on numerical optimization of leverage and initial value correction. By combining the initial value screening of the perilunar point Poincaré map with a multi-step shooting method, a high-precision transfer trajectory library is constructed under the ephemeris model. However, it only completes the orbit design and lacks regularity analysis 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 spacecraft's low-energy Earth-Moon transfer window. However, Related Technology 2 needs to recalculate the invariant manifold corresponding to the Sun-Earth Halo orbit at different launch times for different launch times, which has the problems of long planning time and low planning efficiency.

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

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

[0006] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0007] In the first aspect, a method for rapid design of a low-energy transfer window for an Earth-Moon DRO is provided. The method comprises: constructing an Earth-Moon transfer orbit database based on a double-circle restricted four-body model, wherein the Earth-Moon transfer orbit database includes orbit information and orbit leverage categories of each transfer orbit in a plurality of transfer orbits, wherein the orbit information includes the initial state , initial epoch time , the phase of the sun at the reference point in the Earth-Moon rotation system and transfer duration The orbital leverage categories include backward departure leverage, backward return leverage, or departure without lunar leverage; the apsidal angle of each transfer orbit in the Sun-Earth rotation system is determined based on the orbital information of each transfer orbit. and the lunar phase angle ; According to the apsidal angle of each transfer orbit in the Sun-Earth rotation system and the lunar phase angle Generate a track distribution map corresponding to each track leverage category. The track distribution map includes track points corresponding to each transfer track, where the horizontal coordinate of the track point is the arch angle. , the vertical axis is the lunar phase angle ; Determine the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system based on the input target spacecraft's near-Earth orbit information and epoch time and the lunar phase angle ; According to the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system and the lunar phase angle The target trajectory point is determined from the orbit distribution map corresponding to each orbit leveraging 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 takes the trajectory point corresponding to the low-Earth orbit of the target spacecraft in the orbit distribution map as the starting point and moves along the target ray. In the positive direction, the slope is 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, the orbital information of the transfer orbit corresponding to the target trajectory point is corrected to obtain the target transfer orbit of the target spacecraft.

[0008] In a possible implementation of the first aspect, based on the double-circle restricted four-body model, constructing an Earth-Moon transfer orbit database includes: determining the phase factor of the target low-Earth orbit based on the double-circle restricted four-body model; Phase factor of the target's long-distance retrograde orbit , the phase of the sun at the reference point in the Earth-Moon rotation system and deorbit velocity pulse ; According to the phase factor of the target's long-range retrograde orbit , the phase of the sun at the reference point in the Earth-Moon rotation system and deorbit velocity pulse Determine the orbital status of the target's long-range retrograde orbit , is the mission end time; according to the inverse dynamics model, according to the target long-range retrograde orbit entry state and the phase factor of the target low Earth orbit Determine the two perigee states included in the transfer trajectory integration process, select the transfer orbit according to the latter perigee state, and take the orbit with a perigee height less than 40,000 kilometers as the feasible solution of the transfer orbit; based on the weak stability boundary constraint condition, according to the orbital state of the target long-range retrograde orbit Multiple orbital families are determined based on the perigee state corresponding to the target low-Earth orbit, and each orbital family includes multiple transfer orbits. Based on the preset long-distance retrograde orbit insertion pulse, the pseudo-arc length method is used for numerical extension to determine the transfer orbit with the minimum total pulse in each orbital family. The orbital leverage category of the transfer orbit with the minimum total pulse in each orbital family is determined. An Earth-Moon transfer orbit database is constructed based on the orbital information with the minimum total pulse in each orbital family and the orbital leverage category of backward departure leverage, backward return leverage, or no lunar leverage in the departure phase.

[0009] In a possible implementation of the first aspect, the apsidal angle of each transfer orbit in the Sun-Earth rotation system is determined based on the orbital information of each transfer orbit. and the lunar phase angle , including: determining the departure phase angle of each transfer orbit in the Earth-Moon rotation system based on the orbital information of each transfer orbit and the solar phase angle at departure time ; According to the phase angle of each transfer orbit in the Earth-Moon rotation system and the solar phase angle at departure time Determine the apsidal angle of each transfer orbit in the Sun-Earth rotation system and the lunar phase angle ;

[0010] Low Earth orbit departure phase angle The formula for determining is:

[0011] ;

[0012] is a 6-dimensional state vector, express The x-direction component of express y-direction component.

[0013] Solar phase angle at departure time The formula for determining is:

[0014] ;

[0015] ;

[0016] in, is the dimensionless gravitational constant, TU is the dimensionless unit of time, 1TU is equal to 4.35 days, is the angular velocity of the sun in the Earth-Moon rotation system;

[0017] The angle of the apses in the Sun-Earth rotation system The formula for determining is:

[0018] ;

[0019] lunar phase angle The formula for determining is:

[0020] .

[0021] In a possible implementation of the first aspect, the apsidal angle of the target spacecraft's low-Earth orbit in the Sun-Earth rotation system is The formula for determining is:

[0022] ;

[0023] The lunar phase angle of the target spacecraft's low-Earth orbit in the Sun-Earth rotation system The formula for determining is:

[0024] ;

[0025] in, ;

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] 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 perigee, is the true anomaly angle.

[0031] In a possible implementation of the first aspect, according to the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system and the lunar phase angle The target trajectory point is determined from the orbit distribution map corresponding to each orbit leveraging category, including: taking the trajectory point corresponding to the low-Earth orbit of the target spacecraft in the orbit distribution map as the starting point, presetting the slope k as the slope, and Determine the target ray in the track distribution map in the positive direction; determine the first track point that meets the preset conditions among the multiple track points included in the track distribution map through which the target ray passes as the target track point;

[0032] The default conditions are:

[0033] and ;

[0034] ;

[0035] in, is the starting point interval time, is the Earth's gravitational constant, The corresponding track point in the track distribution diagram .

[0036] In a possible implementation of the first aspect, the above method also includes: when the target ray reaches the top point of the trajectory distribution map and does not pass through any trajectory point that meets the preset conditions, setting the starting point to the bottom endpoint 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 trajectory distribution map; wherein the bottom endpoint corresponding to the top point has the same horizontal coordinate as the top point, and the vertical coordinate of the bottom endpoint is 0.

[0037] In a possible implementation of the first aspect, the orbital 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, including: determining all the perigees in the transfer orbit corresponding to the target trajectory point; discretizing the trajectory segment between each two perigees to obtain multiple discrete points; using the state information of each discrete point in the multiple discrete points as the initial value for multi-step targeting based on the ephemeris model, and correcting the transfer orbit corresponding to the target trajectory point according to the initial value for multi-step targeting to obtain the target transfer orbit of the target spacecraft.

[0038] The beneficial effects of the present invention are as follows: the method provided by the present invention is based on a two-circle restricted four-body model to construct an Earth-Moon transfer orbit database, and according to the orbital information of each transfer orbit, an orbital distribution map is obtained, and then the target trajectory point is determined from the orbital distribution map corresponding to each orbital leverage category according to the input near-Earth orbit information and epoch time of the target spacecraft, and the orbital 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 achieve rapid and accurate planning of the low-energy transfer window of the Earth-Moon DRO, reduce processing time, and improve planning efficiency. In other words, the method provided by the present invention constructs an Earth-Moon transfer orbit database under a two-circle restricted four-body model through grid search and multi-step shooting, and provides a reasonable characterization method for the database, and adopts a graphical method to achieve rapid and accurate search of the transfer orbit from the near-Earth orbit to the DRO at any time under the ephemeris, and optimizes and corrects it under the ephemeris. On the other hand, the method provided by the present invention can quickly and accurately determine the transfer orbit from low-Earth orbit to long-distance retrograde orbit. Compared with the method of determining the transfer orbit from low-Earth orbit to long-distance retrograde orbit in related technologies, the method provided by the present invention can be applied to rapid emergency response in abnormal orbit entry situations, meeting the user's usage needs in different usage scenarios.

[0039] In the second aspect, the present invention provides a low-energy transfer window rapid design system for Earth-Moon DRO, the system comprising: a database construction module for constructing an Earth-Moon transfer orbit database based on a double-circle restricted four-body model, the Earth-Moon transfer orbit database comprising orbital information and orbital leverage categories for each of a plurality of transfer orbits, the transfer orbit being an orbit from a target near-Earth orbit to a target long-range retrograde orbit, wherein the orbital information includes an initial state , initial epoch time , the phase of the sun at the reference point in the Earth-Moon rotation system and transfer duration The orbital leverage categories include backward departure leverage, backward return leverage, or departure without lunar leverage; the first determination module is used to determine the apsidal angle of each transfer orbit in the Sun-Earth rotation system based on the orbital information of each transfer orbit. and the lunar phase angle ; Generate a module for the apsidal angle of each transfer orbit in the Sun-Earth rotation system and the lunar phase angle Generate a track distribution map corresponding to each track leverage category. The track distribution map includes track points corresponding to each transfer track, where the horizontal coordinate of the track point is the arch angle. , the vertical axis is the lunar phase angle The second determination module is used to determine the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system based on the input near-Earth orbit information and epoch time of the target spacecraft. and the lunar phase angle The third determination module is used to determine the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system. and the lunar phase angle The target trajectory point is determined from the orbit distribution map corresponding to each orbit leveraging 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 takes the trajectory point corresponding to the low-Earth orbit of the target spacecraft in the orbit distribution map as the starting point and moves along the target ray. In the positive direction, the slope is a preset slope k, and the preset condition is associated with the starting point interval time and the equivalent velocity increment; the trajectory correction module is used 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.

[0040] In a possible implementation of the second aspect, the third determination module is specifically configured to: take the trajectory point corresponding to the low-Earth orbit of the target spacecraft in the orbit distribution map as the starting point, preset the slope k as the slope, and Determine the target ray in the track distribution map in the positive direction; determine the first track point that meets the preset conditions among the multiple track points included in the track distribution map through which the target ray passes as the target track point;

[0041] The default conditions are:

[0042] and ;

[0043] ;

[0044] in, is the starting point interval time, is the Earth's gravitational constant, The corresponding track point in the track distribution diagram .

[0045] In a third aspect, an electronic device is provided, comprising 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 comprises computer instructions, and when the computer instructions are executed by the processor, the electronic device executes a method as in any implementation of the first aspect.

[0046] In a fourth aspect, a computer-readable storage medium is provided, comprising computer instructions. When the computer instructions are executed on an electronic device, the electronic device executes the method in any implementation of the first aspect.

[0047] According to a fifth aspect, a computer program product is provided. When the computer program product is run on a computer, the computer is caused to execute the method in any implementation of the first aspect.

[0048] It can be understood that the beneficial effects that can be achieved by the system of the second aspect, the electronic device of the third aspect, the computer-readable storage medium of the fourth aspect, and the computer program product of the fifth aspect provided above can be referred to the beneficial effects in the first aspect and any possible design method thereof, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A schematic structural diagram of an electronic device provided by an embodiment of the present invention;

[0050] Figure 2 A flowchart of a method for rapidly designing a low-energy transfer window for a Earth-Moon DRO provided in an embodiment of the present invention;

[0051] Figure 3 A schematic diagram of a track leveraging type provided by an embodiment of the present invention;

[0052] Figure 4 The apsidal angle of a transfer orbit in the Sun-Earth rotation system is shown in an embodiment of the present invention. and the lunar phase angle Schematic diagram of;

[0053] Figure 5 This is a flow chart illustrating another method for rapidly designing a low-energy transfer window for a Earth-Moon DRO according to an embodiment of the present invention;

[0054] Figure 6 The starting phase angle of a transfer orbit in the Earth-Moon rotation system in the embodiment of the present invention is shown as follows: and the solar phase angle at departure time Schematic diagram of;

[0055] Figure 7 A schematic diagram of a track distribution diagram according to an embodiment of the present invention;

[0056] Figure 8 A schematic diagram of a target trajectory point determination process according to an embodiment of the present invention;

[0057] Figure 9 A schematic diagram of a transfer orbit correction process according to an embodiment of the present invention;

[0058] Figure 10 A schematic diagram of the structure of a design system provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0059] The technical solutions in the embodiments of the present invention will be described below with reference to the accompanying drawings in the embodiments of the present invention. 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 can represent A or B. The "or" in the present invention is only a description of the association relationship of the associated objects, indicating that there can be three relationships. For example, A or B can represent: A exists alone, A and B exist at the same time, and B exists alone. A and B can be singular or plural. In addition, in the description of the present invention, unless otherwise specified, "multiple" refers to two or more than two. "At least one of the following items" or similar expressions refers to any combination of these items, including any combination of single or plural items.

[0060] In addition, to facilitate a clear description of the technical solutions of the embodiments of the present invention, in the embodiments of the present invention, the words "first" and "second" are used to distinguish between identical or similar items with substantially the same functions and effects. Those skilled in the art will understand that the words "first" and "second" do not limit the quantity or execution order, and the words "first" and "second" do not necessarily mean different.

[0061] In the embodiments of the present invention, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present invention should not be construed as superior or more advantageous than other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner to facilitate understanding.

[0062] Current research on low-energy transfers in distant retrograde orbits (DROs) for the Earth-Moon system focuses primarily on trajectory optimization and energy analysis. However, in actual mission planning, the ability to quickly plan transfer windows remains insufficient.

[0063] Related technologies usually rely on complex numerical optimization and trajectory integration. The calculation process is time-consuming and lacks intuitive and visual explanations, making it difficult to meet the needs of rapid evaluation and real-time mission adjustment. For example, Related Technology 1 performs low-energy transfer window planning based on numerical optimization of leverage and initial value correction. By combining the initial value screening of the perilunar point Poincaré map with a multi-step shooting method, a high-precision transfer trajectory library is constructed under the ephemeris model. However, it only completes the orbit design and lacks regularity analysis 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 spacecraft's low-energy Earth-Moon transfer window. However, Related Technology 2 needs to recalculate the invariant manifold corresponding to the Sun-Earth Halo orbit at different launch times for different launch times, which has the problems of long planning time and low planning efficiency.

[0064] Therefore, there is an urgent need for a rapid design method and system for the low-energy transfer window of the Earth-Moon DRO, which can realize rapid and accurate planning of the low-energy transfer window of the Earth-Moon DRO, reduce processing time, and improve planning efficiency.

[0065] It should be noted that the rapid design of the low-energy transfer window of the Earth-Moon DRO can also be understood as the design of a transfer orbit from the target low-Earth orbit to the target long-range retrograde orbit.

[0066] In view of this, an embodiment of the present invention provides a method for rapid design of a low-energy transfer window for an Earth-Moon DRO. The method includes: constructing an 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 leverage categories of each transfer orbit in a plurality of transfer orbits. The transfer orbit is an orbit from a target low-Earth orbit to a target long-distance retrograde orbit. The orbit information includes the initial state , initial epoch time , the phase of the sun at the reference point in the Earth-Moon rotation system and transfer duration The orbital leverage categories include backward departure leverage, backward return leverage, or departure without lunar leverage. Based on the orbital information of each transfer orbit, the apsidal angle of each transfer orbit in the Sun-Earth rotation system is determined. and the lunar phase angle According to the apsidal angle of each transfer orbit in the Sun-Earth rotation system and the lunar phase angle Generate a track distribution map corresponding to each track leverage category. The track distribution map includes track points corresponding to each transfer track, where the horizontal coordinate of the track point is the arch angle. , the vertical axis is the lunar phase angle Determine the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system based on the input target spacecraft's near-Earth orbit information and epoch time. and the lunar phase angle According to the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system and the lunar phase angle The target trajectory point is determined from the orbit distribution map corresponding to each orbit leveraging 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 takes the trajectory point corresponding to the low-Earth orbit of the target spacecraft in the orbit distribution map as the starting point and moves along the target ray. In the positive direction, the slope is a preset slope k, and the preset condition is related to the starting point interval time and the equivalent velocity increment. 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.

[0067] The method provided by the present invention is based on a dual-circle restricted four-body model to construct an Earth-Moon transfer orbit database. According to the orbital information of each transfer orbit, an orbital distribution map is obtained. Then, according to the input low-Earth orbit information and epoch time of the target spacecraft, the target trajectory point is determined from the orbital distribution map corresponding to each orbital leverage category. The orbital 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 achieve rapid and accurate planning of the low-energy transfer window of the Earth-Moon DRO, reduce processing time, and improve planning efficiency. In other words, the method provided by the present invention constructs an Earth-Moon transfer orbit database under the dual-circle restricted four-body model through grid search and multi-step shooting, and provides a reasonable characterization method for the database. A graphical method is used to achieve rapid and accurate search of the transfer orbit from the low-Earth orbit to the DRO at any time under the ephemeris, and optimize and correct it under the ephemeris. On the other hand, the method provided by the present invention can quickly and accurately determine the transfer orbit from low-Earth orbit to long-distance retrograde orbit. Compared with the method of determining the transfer orbit from low-Earth orbit to long-distance retrograde orbit in related technologies, the method provided by the present invention can be applied to rapid emergency response in abnormal orbit entry situations, meeting the user's usage needs in different usage scenarios.

[0068] In some embodiments, a method for rapid design of a low-energy transfer window for a cis-lunar DRO provided by an embodiment of the present invention may be executed by a system 100 for rapid design of a low-energy transfer window for a cis-lunar DRO (hereinafter referred to as the design system 100 ).

[0069] As an example, the design system 100 can be any electronic device 200 with data processing capabilities, such as a general-purpose computer, a personal computer, a laptop computer, a switch, or a tablet computer, etc. The specific implementation method of the design system 100 is not limited here.

[0070] Figure 1 The electronic device 200 includes a processor 210 , a memory 220 , and a communication interface 230 .

[0071] The processor 210 may include one or more processing cores. The processor 210 connects to various components within the electronic device 200 using various interfaces and circuits. It executes instructions, programs, code sets, or instruction sets stored in the memory 220, and calls data stored in the memory 220 to perform various functions of the electronic device 200 and process data. Optionally, the processor 210 may be implemented in the form of at least one of a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processing unit (DSP), a field-programmable gate array (FPGA), and a programmable logic array (PLA).

[0072] The memory 220 may include random access memory (RAM) or read-only memory (ROL). Optionally, the memory 220 includes non-transitory computer-readable storage media (NTS). The memory 220 may be used to store instructions, programs, code, a code set, or an instruction set. The memory 220 may include a program storage area. The program storage area may store instructions for implementing an operating system, instructions for implementing at least one function, and instructions for implementing each of the aforementioned method embodiments.

[0073] The communication interface 230 is used to communicate with other devices, equipment or communication networks, such as data storage devices, image processing equipment or Ethernet, radio access network (RAN), wireless local area network (WLAN), etc.

[0074] In physical implementation, the aforementioned components (e.g., processor 210, memory 220, and communication interface 230) may be components within the same device (e.g., a laptop). Alternatively, at least two of these components may be provided within the same device, i.e., as different components within the same device, similar to the deployment of devices or components in a distributed system.

[0075] It should 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 shown, or may combine or separate certain components, or arrange the components differently. The illustrated components may be implemented in hardware, software, or a combination of software and hardware.

[0076] The following describes a method for rapidly designing a low-energy transfer window for an Earth-Moon DRO, provided by an embodiment of the present invention, in conjunction with the accompanying drawings.

[0077] Figure 2 A flowchart of a method for rapidly designing a low-energy transfer window for a Earth-Moon DRO provided in an embodiment of the present invention. Optionally, the method may be Figure 1 The electronic device 200 shown in FIG. 10 is executed. The method may include the following steps:

[0078] S1. Construct an Earth-Moon transfer orbit database based on the double-circle restricted four-body model.

[0079] The Earth-Moon transfer orbit database includes the orbit information and orbit leverage category of each transfer orbit in multiple transfer orbits. The transfer orbit is the orbit from the target low-Earth orbit to the target long-distance retrograde orbit. The orbit information includes the initial state , initial epoch time , the phase of the sun at the reference point in the Earth-Moon rotation system and transfer duration The orbital leverage categories include backward departure leverage, backward return leverage, or no lunar leverage in the departure phase.

[0080] Specifically, the process of constructing the Earth-Moon transfer orbit database described above is based on grid search and multi-step shooting. Grid search is a numerical method that discretizes the parameter space and traverses all possible parameter combinations to find the optimal solution. In orbit design, it is primarily used to systematically scan high-dimensional parameters (such as phase factors, solar phases, and pulse velocities). Multi-step shooting is a numerical method used in orbit optimization. It divides long-term orbits into multiple short time periods, imposes continuity constraints at the time boundaries of each segment, and ultimately satisfies the overall dynamic equations through iterative corrections.

[0081] In some embodiments, the above S1 includes:

[0082] S11. Determine the phase factor of the target low-Earth orbit based on the two-circle restricted four-body model Phase factor of the target's long-distance retrograde orbit , the phase of the sun at the reference point in the Earth-Moon rotation system and deorbit velocity pulse .

[0083] S12, according to the phase factor of the target's long-range retrograde orbit , the phase of the sun at the reference point in the Earth-Moon rotation system and deorbit velocity pulse Determine the orbital status of the target's long-range retrograde orbit , The mission ends.

[0084] S13. According to the inverse dynamics model, the target long-range retrograde orbit is placed into 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 orbit based on the latter perigee state, and take the orbit with a perigee altitude less than 40,000 kilometers as the feasible solution of the transfer orbit.

[0085] S14. Based on the weak stability boundary constraint condition, according to the target long-distance retrograde orbit entry state A plurality of orbital families are determined based on the perigee state corresponding to the target low-Earth orbit, and each orbital family includes a plurality of transfer orbits.

[0086] S15. Based on the preset long-distance retrograde orbit insertion pulse, use the pseudo-arc length method for numerical extension to determine the transfer orbit with the minimum total pulse in each orbit family.

[0087] S16. Determine the orbital borrowing category of the transfer orbit with the smallest total pulse in each orbital family.

[0088] S17. Construct an Earth-Moon transfer orbit database based on the orbit information with the smallest total pulse in each orbit family, and the orbit leverage type is backward departure leverage, backward return leverage, or no lunar leverage in the departure phase.

[0089] To facilitate understanding of this solution, the following explains the process of constructing the Earth-Moon transfer orbit database included in the embodiment of the present invention with reference to an example.

[0090] In one example, the above S1 specifically includes:

[0091] Input the starting LEO (target LEO) and the Earth-Moon 2:1 DRO orbit (target long-range retrograde orbit) under the two-circle restricted four-body model. The phase factor of the gridded target LEO is Phase factor of the target's long-distance retrograde orbit , the phase of the sun at the reference point in the Earth-Moon rotation system and deorbit velocity pulse , obtain different long-distance retrograde orbit entry states ,in The task ends at Start the reverse integral dynamics equation to make the spacecraft reach perigee , save the states of the first two perigees during the flight. Use multi-step shooting correction to obtain the transfer orbit of the long-distance retrograde orbit based on the weak stability boundary. Fix the orbital entry pulse of the long-distance retrograde orbit, use the pseudo-arc length method to numerically extend the transfer orbit, and determine the transfer orbit with the smallest departure pulse in each orbit family. Then fix the departure pulse and determine the transfer orbit with the smallest total pulse through numerical extension. Discretize into 100 phase values, classify the transfer orbits according to the discretized long-distance retrograde orbit entry position, select the transfer orbit with the lowest total pulse at each phase, use these transfer orbits as the initial value of the extension, use the pseudo arc length method to numerically extend the transfer orbit, and obtain the orbit family starting from different low-Earth orbit phases. The orbit information of the generated transfer trajectory is stored in the form of a database, and the orbit information includes the initial state , initial epoch time , the phase of the sun at the reference point in the Earth-Moon rotation system and transfer duration .

[0092] For further information, see Figure 3 , Figure 3 A schematic diagram of an orbital leverage category provided for an embodiment of the present invention includes forward departure leverage, forward return leverage, backward departure leverage and backward return leverage. Classification based on the lunar leverage method: According to the relative position relationship between the spacecraft and the moon at the time of leverage and whether it reaches the apogee first before leveraging, it can be divided into forward departure leverage, forward return leverage, backward departure leverage, backward return leverage and no lunar leverage in the departure stage. Delete the orbits with the orbital leverage category of forward departure leverage and forward return leverage. Among them, Figure 3 The solid black orbit in the figure is the 2:1 DRO orbit, the dashed red orbit is the Moon's SOI orbit, the green dot is Earth, the black dot is the Moon's state at LGA, the gray dot is the Moon's initial state, and the red dot is the perilunar point. S2. Based on the orbital information for each transfer orbit, determine the apsidal angle and lunar phase angle for each transfer orbit in the Sun-Earth rotation system.

[0093] For example, see Figure 4 , Figure 4 The apsidal angle of a transfer orbit in the Sun-Earth rotation system is shown in an embodiment of the present invention. and the lunar phase angle Schematic diagram of .

[0094] In one possible implementation, see Figure 5 , the above S2, including:

[0095] S21. Determine the low-Earth orbit departure phase angle and the solar phase angle at the departure time of each transfer orbit in the Earth-Moon rotation system based on the orbital information of each transfer orbit.

[0096] S22. Determine the apsidal angle and lunar phase angle of each transfer orbit in the Sun-Earth rotation system based on the near-Earth orbit departure phase angle of each transfer orbit in the Earth-Moon rotation system and the solar phase angle at the departure time.

[0097] Low Earth orbit departure phase angle The formula for determining is:

[0098] ;

[0099] is a 6-dimensional state vector, express The x-direction component of express y-direction component.

[0100] In one example, =0.012150585.

[0101] Solar phase angle at departure time The formula for determining is:

[0102] ;

[0103] ;

[0104] in, is the dimensionless gravitational constant, TU is the dimensionless unit of time, 1TU is equal to 4.35 days, is the angular velocity of the Sun in the Earth-Moon rotation system.

[0105] See also Figure 6 , Figure 6 The starting phase angle of a transfer orbit in the Earth-Moon rotation system in the embodiment of the present invention is shown as follows: and the solar phase angle at departure time Schematic diagram of .

[0106] The angle of the apses in the Sun-Earth rotation system The formula for determining is:

[0107] ;

[0108] lunar phase angle The formula for determining is:

[0109] ;

[0110] S3. Generate an orbital distribution diagram corresponding to each orbital leverage category based on the apsidal angle of each transfer orbit in the Sun-Earth rotation system and the lunar phase angle.

[0111] Specifically, the orbit distribution diagram includes the trajectory points corresponding to each transfer orbit, where the horizontal coordinate of the trajectory point is the apsidal angle , the vertical axis is the lunar phase angle .

[0112] The track distribution diagram is Distribution map, see Figure 7 , Figure 7 A schematic diagram of a track distribution diagram according to an embodiment of the present invention. Figure 7 The orbital distribution diagram includes the following types of orbital leverage: backward departure leverage, backward return leverage, and no departure leverage. The horizontal axis is the apsidal angle of the transfer orbit in the Sun-Earth rotation system. , the vertical axis is the lunar phase angle Different colors are used to represent the equivalent velocity increments corresponding to different transfer trajectories.

[0113] S4. Determine the apsidal angle and lunar phase angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system based on the input near-Earth orbit information and epoch time of the target spacecraft.

[0114] Specifically, the near-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. ,in 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 perigee, Indicates the true anomaly angle.

[0115] For example, see Table 1, which is a data table of near-Earth orbit information and epoch time of a target spacecraft according to an embodiment of the present invention.

[0116] Table 1

[0117]

[0118] In some embodiments, the apsidal angle of the target spacecraft's low-Earth orbit in the Sun-Earth rotation system is The formula for determining is:

[0119] ;

[0120] The lunar phase angle of the target spacecraft's low-Earth orbit in the Sun-Earth rotation system The formula for determining is:

[0121] ;

[0122] in, ;

[0123] ;

[0124] ;

[0125] ;

[0126] ;

[0127] 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 perigee, is the true anomaly angle.

[0128] The following is an example of the embodiment of the present invention showing the apsidal angle of the target spacecraft's low-Earth orbit in the Sun-Earth rotation system. and the lunar phase angle Specifically, the position vector corresponding to the perigee is calculated based on the input target spacecraft's near-Earth orbit information and epoch time. .

[0129] The calculation formula is:

[0130] ;

[0131] ;

[0132] ;

[0133] The orbital perigee and lunar positions in the J2000 coordinate system are then converted to the Sun-Earth system. The lunar position vector can be read from the ephemeris at the time of perigee. The origin of the Sun-Earth system is fixed at the center of the Earth, with the X-axis pointing toward the Earth along the Sun and the Z-axis pointing toward the ecliptic. The coordinate conversion formula is as follows:

[0134] ;

[0135] ;

[0136] Finally, determine the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system. and the lunar phase angle :

[0137] ;

[0138] ;

[0139] It should be noted that the apsidal angle of the above target spacecraft's near-Earth orbit in the Sun-Earth rotation system is and the lunar phase angle The determination process is only an example. Other methods can also be used to determine the apsidal angle of the target spacecraft's low-Earth orbit in the Sun-Earth rotation system. and the lunar phase angle , the embodiment of the present invention does not impose any special restrictions on this.

[0140] S5. Determine the target trajectory point from the orbit distribution map corresponding to each orbit leverage category based on the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system and the lunar phase angle.

[0141] Specifically, 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 takes the trajectory point corresponding to the low-Earth orbit of the target spacecraft in the orbit distribution map as the starting point and moves along the trajectory point. In the positive direction, the slope is the preset slope k, and the preset condition is associated with the starting point interval time and the equivalent speed increment.

[0142] In one example, the formula for determining the preset slope k is:

[0143] ;

[0144] In some embodiments, the above S5 includes:

[0145] The target spacecraft’s low-Earth orbit corresponds to the trajectory point in the orbit distribution map as the starting point, the preset slope k is the slope, and along The positive direction identifies the target ray in the track distribution diagram.

[0146] The first trajectory point that meets a preset condition among the multiple trajectory points included in the trajectory distribution diagram through which the target ray passes is determined as the target trajectory point.

[0147] The default conditions are:

[0148] and ;

[0149] ;

[0150] in, is the starting point interval time, is the Earth's gravitational constant, The corresponding track point in the track distribution diagram .

[0151] Furthermore, the method provided in the embodiment of the present invention further includes the following steps:

[0152] If the target ray reaches the top point of the trajectory distribution map and does not pass through any trajectory point that meets the preset conditions, the starting point is set to the bottom endpoint 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 trajectory distribution map. The bottom endpoint corresponding to the top point has the same abscissa as the top point, and the ordinate of the bottom endpoint is 0.

[0153] The following is an example, for example, see Figure 8 , the process of determining the target trajectory point provided by the embodiment of the present invention is explained. and As the starting point, Upper edge of the distribution map Draw a straight line in the positive direction with a slope of:

[0154] ;

[0155] When the line reaches the bottom of the distribution ( ), the starting point is reset to the top of the distribution graph ( ), and continue drawing along the slope, repeating this process until the first trajectory point is reached.

[0156] Extract the first trajectory point arrived at , the time interval with the starting point is:

[0157] .

[0158] Determine whether the preset conditions are met, if:

[0159] and ;

[0160] in, is the Earth's gravitational constant, is the equivalent velocity increment from low Earth orbit, that is, Figure 7 The color column in corresponds to the axis. If the above conditions are met, the current transfer trajectory is feasible. Otherwise, the above steps are repeated until the first trajectory point that meets the preset conditions is found and this trajectory point is determined as the target trajectory point.

[0161] It should be noted that in the above steps, the first trajectory point that meets the preset conditions is determined in the trajectory distribution maps corresponding to different trajectory leveraging categories. When there is a first trajectory point that meets the preset conditions in the trajectory distribution maps corresponding to multiple trajectory leveraging categories, the trajectory point with the smallest starting point interval time is determined as the target trajectory point.

[0162] Specific, combined Figure 8 , Figure 8 (a), (b) and (c) are the orbital distribution maps corresponding to different orbital leveraging categories. The three orbital distribution maps share the same coordinates, so it is necessary to superimpose the orbital distribution maps corresponding to the three different orbital leveraging categories before analyzing them. Starting from the green starting point, move along the target ray to reach all the trajectory points in the three figures. and The closest trajectory point is red point ①. However, the time interval between the starting points of red point ① does not meet the preset time interval condition, so it is excluded. Continuing along the ray, we reach red point ②, which meets the preset time interval condition. However, red point ② does not meet the preset velocity increment condition, so it is also excluded. In Figure (c), there are multiple intersections between the ray and the trajectory points (colored areas). Since they all conflict with the preset conditions, they are not listed here one by one. Only red points ① and ② are shown as examples. Continuing along the green ray, we reach red point ③ in Figure (a). Red point ③ well meets the preset conditions, so red point ③ is selected as the target trajectory point.

[0163] It should be noted that in the above steps, the first trajectory point that meets the preset conditions is determined in the trajectory distribution maps corresponding to different trajectory leveraging categories. When there is a first trajectory point that meets the preset conditions in the trajectory distribution maps corresponding to multiple trajectory leveraging categories, the trajectory point with the smallest starting point interval time is determined as the target trajectory point.

[0164] S6. 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.

[0165] In a possible implementation, the above S6 specifically includes the following steps:

[0166] S61. Determine all perigees in the transfer orbit corresponding to the target trajectory point.

[0167] S62. Discretize the trajectory segment between each two perigees to obtain multiple discrete points.

[0168] S63. Using the state information of each discrete point among the multiple discrete points as an initial value for multi-step shooting.

[0169] S64. Based on the ephemeris model, the transfer orbit corresponding to the target trajectory point is corrected according to the initial value of the multi-step shooting to obtain the target transfer orbit of the target spacecraft.

[0170] In one example, the above S6 includes:

[0171] According to the orbit information of the transfer orbit corresponding to the target trajectory point under the double-circle restricted four-body model, all perigees in the transfer trajectory are extracted. For each trajectory segment between two perigees, the trajectory segment is discretized into 20 points, and the state information is extracted as the initial value of the multi-step shooting. The transfer trajectory is corrected by multi-step shooting under the ephemeris model to obtain the continuous transfer trajectory under the ephemeris model, as shown in the figure below. Figure 9 As 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 dual-circle restricted four-body model to construct an Earth-Moon transfer orbit database, and according to the orbital information of each transfer orbit, the orbital distribution map is used, and then the target trajectory point is determined from the orbital distribution map corresponding to each orbital leverage category according to the input near-Earth orbit information and epoch time of the target spacecraft, and the orbital 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 the Earth-Moon transfer orbit database under the dual-circle restricted four-body model through grid search and multi-step shooting, and provides a reasonable characterization method of the database, and adopts a graphical method to realize the rapid and accurate search of the transfer orbit from the near-Earth orbit to the DRO at any time under the ephemeris, and optimizes and corrects it under the ephemeris. On the other hand, the method provided by the present invention can quickly and accurately determine the transfer orbit from low-Earth orbit to long-distance retrograde orbit. Compared with the method of determining the transfer orbit from low-Earth orbit to long-distance retrograde orbit in related technologies, the method provided by the present invention can be applied to rapid emergency response in abnormal orbit entry situations, meeting the user's usage needs in different usage scenarios.

[0172] The above mainly introduces the solution of the embodiment of the present invention from the perspective of method. It can be understood that in order to realize the above functions, the design system 100 includes at least one of the hardware structure and software modules corresponding to the execution of each function. It should be easy for those skilled in the art to realize that, in combination with the units and algorithm steps of each example described in the embodiment disclosed herein, the embodiment of the present invention can be implemented in the form of hardware or a combination of hardware and computer software. Whether a function is executed in the form of hardware or computer software driving hardware depends on the specific application and design constraints of the technical solution. Professional and technical personnel 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 embodiment of the present invention.

[0173] In an embodiment of the present invention, the design system 100 can be divided into functional units according to the above-mentioned method example. For example, the design system 100 can be divided into functional units corresponding to each function, or two or more functions can be integrated into a single processing unit. The above-mentioned integrated units can be implemented in the form of hardware or software functional units. It should be noted that the division of units in the embodiment of the present invention is schematic and is only a logical functional division. In actual implementation, other division methods may be used.

[0174] For example, Figure 10 The hardware structure diagram of a design system provided by an embodiment of the present invention is shown. The design system 100 includes: a database construction module 110, which is used to construct an Earth-Moon transfer orbit database based on a two-circle restricted four-body model. The Earth-Moon transfer orbit database includes orbit information and orbit leverage categories for 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 long-distance retrograde orbit, wherein the orbit information includes the initial state , initial epoch time , the phase of the sun at the reference point in the Earth-Moon rotation system and transfer duration The orbital leverage categories include backward departure leverage, backward return leverage, or no lunar leverage in the departure phase.

[0175] The first determination module 120 is used to determine the apsidal angle of each transfer orbit in the Sun-Earth rotation system based on the orbital information of each transfer orbit. and the lunar phase angle The generating module 130 is used to generate the apsidal angle of each transfer orbit in the Sun-Earth rotation system. and the lunar phase angle Generate a track distribution map corresponding to each track leverage category. The track distribution map includes track points corresponding to each transfer track, where the horizontal coordinate of the track point is the arch angle. , the vertical axis is the lunar phase angle The second determination module 140 is used to determine the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system based on the input near-Earth orbit information and epoch time of the target spacecraft. and the lunar phase angle The third determining module 150 is used to determine the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system. and the lunar phase angle The target trajectory point is determined from the orbit distribution map corresponding to each orbit leveraging 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 takes the trajectory point corresponding to the low-Earth orbit of the target spacecraft in the orbit distribution map as the starting point and moves along the target ray. In the positive direction, the slope is a preset slope k, and the preset condition is associated with the starting point interval time and the equivalent velocity increment. The trajectory correction module 160 is used 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.

[0176] Optionally, the third determination module 150 is specifically configured to: take the trajectory point corresponding to the low-Earth orbit of the target spacecraft in the orbit distribution map as the starting point, preset the slope k as the slope, and The target ray is determined in the track distribution map in the positive direction, and the first track point that meets a preset condition among the multiple track points included in the track distribution map through which the target ray passes is determined as the target track point.

[0177] The default conditions are:

[0178] and ;

[0179] ;

[0180] in, is the dimensionless gravitational constant, TU is the dimensionless unit of time, 1TU is equal to 4.35 days, is the angular velocity of the Sun in the Earth-Moon rotation system.

[0181] It should be understood that the specific description of the above optional methods can be found in the above method embodiments, which will not be repeated here. In addition, the explanation of any design system 100 provided above and the description of its beneficial effects can refer to the above corresponding method embodiments, which will not be repeated here.

[0182] An embodiment of the present invention further provides a computer-readable storage medium storing at least one computer instruction, which is loaded and executed by a processor to implement the methods of each of the above embodiments. For explanations of the relevant contents and descriptions of the beneficial effects of any of the above-mentioned computer-readable storage media, reference can be made to the corresponding embodiments described above and will not be repeated here.

[0183] The embodiment of the present invention further provides a chip. The chip integrates a control circuit and one or more ports for implementing the functions of the above-mentioned design system 100. Optionally, the functions supported by the chip can be referred to above and will not be repeated here.

[0184] Those skilled in the art will appreciate that all or part of the steps of the above-described embodiments can be implemented by a program that instructs the relevant hardware to perform the program, which can be stored in a computer-readable storage medium. The aforementioned storage medium can be a read-only memory, a random access memory, or the like. The aforementioned processing unit or processor can be a central processing unit, a general-purpose processor, an application-specific integrated circuit (ASIC), a microprocessor (digital signal processor, DSP), a field programmable gate array (FPGA), or other programmable logic device, transistor logic device, hardware component, or any combination thereof.

[0185] An embodiment of the present invention further provides a computer program product comprising instructions that, when executed on a computer, cause the computer to perform any of the methods described in the above embodiments. The computer program product comprises 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 fully or partially performed. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. 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 via wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium accessible by a computer or a data storage device such as a server or data center that integrates one or more available media. Available media may include magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives).

[0186] 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 memories, computer-readable storage media, and communication chips, are all non-transitory. Those skilled in the art should appreciate that in one or more of the above examples, the functions described in the embodiments of the present invention can be implemented using hardware, software, firmware, or any combination thereof. When implemented using software, these functions can be stored in a computer-readable storage medium or transmitted as one or more instructions or codes on a computer-readable storage medium. Computer-readable storage media include computer storage media and communication media, where communication media includes any medium that facilitates the transmission of computer programs from one location to another. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0187] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A rapid design method for low-energy transfer window for Earth-Moon DRO, characterized by: The method comprises: Based on the double-circle restricted four-body model, a Earth-Moon transfer orbit database is constructed. The Earth-Moon transfer orbit database includes the orbit information and orbit leverage category of each transfer orbit in multiple transfer orbits. The transfer orbit is the orbit from the target low-Earth orbit to the target long-distance retrograde orbit, wherein the orbit information includes the initial state , initial epoch time , the phase of the sun at the reference point in the Earth-Moon rotation system and transfer duration The orbital leverage categories include backward departure leverage, backward return leverage, or no lunar leverage in the departure phase; Determine the apsidal angle of each transfer orbit in the Sun-Earth rotation system based on the orbital information of each transfer orbit and the lunar phase angle ; According to the apsidal angle of each transfer orbit in the Sun-Earth rotation system and the lunar phase angle Generate a track distribution map corresponding to each track leveraging category, the track distribution map includes the track points corresponding to each transfer track, wherein the horizontal coordinate of the track point is the arch line angle , the vertical axis is the lunar phase angle ; Determine the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system based on the input near-Earth orbit information and epoch time of the target spacecraft and the lunar phase angle ; 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 The target trajectory point is determined from the orbital distribution map corresponding to each orbital leverage category. The target trajectory point is the first trajectory point that meets the preset conditions reached by the target ray in the orbital distribution map. The target ray takes the trajectory point corresponding to the low-Earth orbit of the target spacecraft in the orbital distribution map as the starting point and travels along the target trajectory point. In the positive direction, the slope is a preset slope k, and the preset condition is associated with the starting point interval time and the equivalent speed increment; 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; The apsidal angle of the near-Earth orbit of the target spacecraft in the Sun-Earth rotation system and the lunar phase angle Determining a target track point from a track distribution map corresponding to each track leveraging category includes: The target spacecraft's near-Earth orbit corresponds to the trajectory point in the orbit distribution map as the starting point, the preset slope k is the slope, and along The positive direction determines the target ray in the track distribution map; Determining a first trajectory point that meets a preset condition among a plurality of trajectory points included in the trajectory distribution diagram through which the target ray passes as a target trajectory point; The preset conditions are: and ; ； in, is the starting point interval time, is the Earth's gravitational constant, The corresponding track point in the track distribution diagram .

2. The method according to claim 1, characterized in that The method of constructing an Earth-Moon transfer orbit database based on a two-circle restricted four-body model includes: Determine the phase factor of the target low-Earth orbit based on the two-circle restricted four-body model Phase factor of the target's long-distance retrograde orbit , the phase of the sun at the reference point in the Earth-Moon rotation system and deorbit velocity pulse ; According to the phase factor of the target's long-range retrograde orbit , the phase of the sun at the reference point in the Earth-Moon rotation system and deorbit velocity pulse Determine the orbital status of the target long-range retrograde orbit , The task ends at this time; According to the inverse dynamics model, the target long-range retrograde orbit is placed into orbit and the phase factor of the target low Earth orbit Determine the two perigee states included in the transfer trajectory integration process, select the transfer orbit based on the latter perigee state, and take the orbit with a perigee altitude less than 40,000 kilometers as the feasible solution of the transfer orbit; Based on the weak stability boundary constraint condition, according to the orbital state of the target long-range retrograde orbit Determining a plurality of orbital clusters according to a perigee state corresponding to the target low-Earth orbit, each of the orbital clusters including a plurality of transfer orbits; Based on the preset long-distance retrograde orbit insertion pulse, the pseudo-arc length method is used for numerical extension to determine the transfer orbit with the minimum total pulse in each orbit family; determining the orbital borrowing category of the transfer orbit with the minimum total pulse in each orbital family; An Earth-Moon transfer orbit database is constructed based on the orbit information with the smallest total pulse in each orbit family and whose orbit leverage category is backward departure leverage, backward return leverage, or no lunar leverage in the departure phase.

3. The method according to claim 2, characterized in that The apsidal angle of each transfer orbit in the Sun-Earth rotation system is determined based on the orbital information of each transfer orbit. and the lunar phase angle ,include: Determine the departure phase angle of each transfer orbit in the Earth-Moon rotation system based on the orbital information of each transfer orbit and the solar phase angle at departure time ; According to the phase angle of each transfer orbit in the Earth-Moon rotation system and the solar phase angle at departure time Determine the apsidal angle of each transfer orbit in the Sun-Earth rotation system and the lunar phase angle ; Low Earth orbit departure phase angle The formula for determining is: ； is a 6-dimensional state vector, express The x-direction component of express y-direction component; Solar phase angle at departure time The formula for determining is: ； ； in, is the dimensionless gravitational constant, TU is the dimensionless unit of time, 1TU is equal to 4.35 days, is the angular velocity of the sun in the Earth-Moon rotation system; The angle of the apses in the Sun-Earth rotation system The formula for determining is: ； lunar phase angle The formula for determining is: 。 4. The method according to claim 3, characterized in that The apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system The formula for determining is: ； The lunar phase angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system The formula for determining is: ； in, ; ； ； ； ； 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 perigee, is the true anomaly angle.

5. The method according to claim 1, wherein The method further comprises: When the target ray reaches the top point of the trajectory distribution diagram and does not pass through any trajectory point that meets the preset conditions, the starting point is set to the bottom endpoint 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 trajectory distribution diagram; wherein the bottom endpoint corresponding to the top point has the same abscissa as the top point, and the ordinate of the bottom endpoint is 0.

6. The method according to claim 5, characterized in that The step of 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 perigees in the transfer orbit corresponding to the target trajectory point; Discretize the trajectory segment between each two perigees to obtain multiple discrete points; The state information of each discrete point in the plurality of discrete points is used as the initial value of the multi-step shooting Based on the ephemeris model, the transfer orbit corresponding to the target trajectory point is corrected according to the multi-step target shooting initial value to obtain the target transfer orbit of the target spacecraft.

7. A low-energy transfer window rapid design system for Earth-Moon DRO, characterized by: The system comprises: A database construction module is used to construct an Earth-Moon transfer orbit database based on a two-circle restricted four-body model. The Earth-Moon transfer orbit database includes orbit information and orbit leverage categories for each of a plurality of transfer orbits. The transfer orbit is an orbit from a target low-Earth orbit to a target long-distance retrograde orbit. The orbit information includes the initial state , initial epoch time , the phase of the sun at the reference point in the Earth-Moon rotation system and transfer duration The orbital leverage categories include backward departure leverage, backward return leverage, or no lunar leverage in the departure phase; The first determination module is used to determine the apsidal angle of each transfer orbit in the Sun-Earth rotation system based on the orbital information of each transfer orbit. and the lunar phase angle ; The generation module is used to generate the angle of the apses of each transfer orbit in the Sun-Earth rotation system. and the lunar phase angle Generate a track distribution map corresponding to each track leveraging category, the track distribution map includes the track points corresponding to each transfer track, wherein the horizontal coordinate of the track point is the arch line angle , the vertical axis is the lunar phase angle ; The second determination module is used to determine the apsidal angle of the target spacecraft's near-Earth orbit in the Sun-Earth rotation system based on the input near-Earth orbit information and epoch time of the target spacecraft. and the lunar phase angle ; The third determination module is used to determine the apsidal angle of the near-Earth orbit of the target spacecraft in the Sun-Earth rotation system. and the lunar phase angle The target trajectory point is determined from the orbital distribution map corresponding to each orbital leverage category. The target trajectory point is the first trajectory point that meets the preset conditions reached by the target ray in the orbital distribution map. The target ray takes the trajectory point corresponding to the low-Earth orbit of the target spacecraft in the orbital distribution map as the starting point and travels along the target trajectory point. In the positive direction, the slope is a preset slope k, and the preset condition is associated with the starting point interval time and the equivalent speed increment; a trajectory correction module, configured to correct the orbit information of the transfer orbit corresponding to the target trajectory point based on an ephemeris model to obtain a target transfer orbit of the target spacecraft; The third determination module is specifically configured to: The target spacecraft's near-Earth orbit corresponds to the trajectory point in the orbit distribution map as the starting point, the preset slope k is the slope, and along The positive direction determines the target ray in the track distribution map; Determining a first trajectory point that meets a preset condition among a plurality of trajectory points included in the trajectory distribution diagram through which the target ray passes as a target trajectory point; The preset conditions are: and ; ； in, is the starting point interval time, is the Earth's gravitational constant, The corresponding track point in the track distribution diagram .

8. An electronic device, characterized in that: include: processor; a memory for storing instructions executable by the processor; The processor is configured to execute the instructions to implement the low-energy transfer window rapid design method for the Earth-Moon DRO according to any one of claims 1 to 6.

Images