Earth-moon space transfer trajectory migration method and system under high-fidelity model

Abstract

The invention provides an earth-moon space transfer trajectory migration method and system under a high-fidelity model, and relates to the technical field of aerospace. The method provided by the invention comprises the following steps: firstly, determining a plurality of transfer trajectories from an initial orbit to a target orbit based on a simplified model, and then determining an initial transfer trajectory from the plurality of transfer trajectories; then, the initial transfer trajectory is optimized, a target transfer trajectory based on the high-fidelity model is obtained, the tail end position of the target transfer trajectory is located on the target trajectory based on the high-fidelity model, and the target transfer trajectory meets shape constraint and long-term bounded constraint. Therefore, the method provided by the invention can quickly and accurately determine the earth-moon space transfer trajectory under the high-fidelity model, improves the adaptability, and meets the use requirements of users in different use scenes.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular, to a method and system for migrating the Earth-Moon space transfer trajectory under a high-fidelity model. Background Art

[0002] The design of the transfer trajectory under a high-fidelity model is an important part of the Earth-Moon space mission planning. Searching for the trajectory directly under the high-fidelity model places high demands on the accuracy and speed of the integrator, and it is impossible to reveal the general laws of orbit transfer. To reduce the complexity of the dynamic model and improve the calculation efficiency, usually, the transfer trajectory is first analyzed and calculated under a simplified model, and then converted to the high-fidelity model.

[0003] In the related art, the conversion of multiple turns of NRHO orbits under the ephemeris model is studied, and the basis for the selection of the splicing point is given. However, this method still has certain problems. This method is only applicable to periodic orbits or quasi-periodic orbits and cannot be migrated to large-scale transfer trajectories. In summary, the correction method for converting the trajectory from the simplified model to the high-fidelity model in the prior art has poor convergence and trajectory reuse ability, and requires providing the analytical Jacobian matrix information of the high-fidelity model, with poor applicability.

[0004] Therefore, there is an urgent need for a method and system for migrating the Earth-Moon space transfer trajectory under a high-fidelity model, which can quickly and accurately determine the Earth-Moon space transfer trajectory under the high-fidelity model, improve the adaptability, and meet the usage requirements of users in different usage scenarios. Summary of the Invention

[0005] Embodiments of the present invention provide a method and system for migrating the Earth-Moon space transfer trajectory under a high-fidelity model, which can quickly and accurately determine the Earth-Moon space transfer trajectory under the high-fidelity model, improve the adaptability, and meet the usage requirements of users in different usage scenarios.

[0006] To achieve the above object, the embodiments of the present invention adopt the following technical solutions: In a first aspect, a method for migrating the Earth-Moon space transfer trajectory under a high-fidelity model is provided. The method includes: constructing an Earth-Moon transfer trajectory database based on the initial orbit and the target orbit of the simplified model, where the Earth-Moon transfer trajectory database includes the orbit information of each transfer trajectory in a plurality of transfer trajectories based on the simplified model; the transfer trajectory is the trajectory transferred from the initial orbit to the target orbit; determining an initial transfer trajectory from the plurality of transfer trajectories according to the orbit information of each transfer trajectory; optimizing the initial transfer trajectory to obtain a target transfer trajectory based on the high-fidelity model, where the end position of the target transfer trajectory is located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfies the shape constraint and the long-term boundedness constraint.

[0007] In a possible implementation of the first aspect, based on the initial orbit and the target orbit of the simplified model, a lunar transfer trajectory database is constructed, including: discretizing the initial orbit to determine a plurality of discrete points located on the initial orbit; setting departure velocity increments with different directions and magnitudes for each discrete point to obtain a plurality of transfer trajectories corresponding to each discrete point; retaining the transfer trajectories with the minimum distance from the target orbit based on the simplified model less than a preset distance threshold; optimizing, through multi-step shooting correction and continuation, the transfer trajectories with the minimum distance from the target orbit based on the simplified model less than the preset distance threshold according to the terminal constraint conditions to obtain transfer trajectories with multiple terminal positions based on the simplified model located on the target orbit based on the simplified model; generating a lunar transfer trajectory database according to the transfer trajectories with multiple terminal positions based on the simplified model located on the target orbit based on the simplified model.

[0008] In a possible implementation of the first aspect, the simplified model is a circular restricted three-body model or a double-circle restricted four-body model.

[0009] In a possible implementation of the first aspect, the initial transfer trajectory is optimized to obtain a target transfer trajectory based on the high-fidelity model, including: optimizing the initial transfer trajectory according to a first optimization function, where the first optimization function is used to characterize the similarity between the initial transfer trajectory based on the simplified model and the initial transfer trajectory based on the high-fidelity model; optimizing the initial transfer trajectory according to a second optimization function to obtain a target transfer trajectory based on the high-fidelity model, where the second optimization function is used to characterize the similarity between the target orbit based on the simplified model and the target orbit based on the high-fidelity model.

[0010] In a possible implementation of the first aspect, optimizing the initial transfer trajectory according to the first optimization function includes: Constructing the first optimization function; The first optimization function is: ; ; where and are optimization variables, is the initial transfer trajectory under the simplified model; is the initial transfer trajectory under the high-fidelity model; represents the apsidal position similarity between transfer trajectory A and transfer trajectory B; is a weight coefficient; In the case where the transfer trajectory includes apsides, the position vector of the th apsis relative to the moon is ; Determine the departure velocity pulse of the initial transfer trajectory under the simplified model , with the departure position of the initial transfer trajectory under the simplified model as the starting point, apply different departure pulses for orbit extrapolation to obtain multiple transfer trajectories, where , the step interval of different departure pulses is ; Convert the multiple transfer trajectories to the Earth-Moon rotating system and perform normalization processing; determine the first optimization function value corresponding to each transfer trajectory; determine the upper and lower bounds of the first guess interval for the departure pulse corresponding to the transfer trajectory with the minimum first optimization function value adjacent to two departure pulses; when the length of the first guess interval is greater than or equal to the preset length threshold, determine the target departure pulse by the bisection method and update the departure velocity pulse to update the first guess interval; when the length of the guess interval is less than the preset length threshold, determine the target departure pulse by the bisection method, and when the end position of the transfer trajectory corresponding to the target departure pulse is on the target orbit, complete the optimization of the initial transfer trajectory.

[0011] In a possible implementation manner of the first aspect, optimize the initial transfer trajectory according to the second optimization function to obtain the target transfer trajectory based on the high-fidelity model, including: constructing the second optimization function based on the input task expected stable time; The second optimization function is: ; ; ; where is the optimization variable, is the target orbit under the simplified model; is the target orbit under the high-fidelity model; represents the Hausdorff distance between the transfer trajectory A sequence and the transfer trajectory B sequence; represents the point and the point the Euclidean distance between; Determine the injection velocity pulse of the initial transfer trajectory under the simplified model , with the end position of the initial transfer trajectory under the simplified model as the starting point, apply different velocity pulses for orbit extrapolation to obtain multiple transfer trajectories, where , the step interval of different velocity pulses is Convert multiple transfer trajectories to the Earth-Moon rotating system and perform normalization processing; determine the second optimization function value corresponding to each transfer trajectory; the velocity impulse corresponding to the transfer trajectory with the minimum second optimization function value Determine the upper and lower bounds of the second guess interval for two adjacent velocity impulses; when the length of the second guess interval is greater than or equal to the length threshold, determine the target velocity impulse by the bisection method and update the injection velocity impulse according to the target velocity impulse , so as to update the second guess interval; when the length of the second guess interval is less than the length threshold, determine the target velocity impulse by the bisection method, and when the transfer trajectory corresponding to the target departure impulse satisfies the shape constraint and the long-term boundedness constraint, migrate the transfer trajectory corresponding to the target departure impulse to the target transfer trajectory based on the high-fidelity model.

[0012] In a possible implementation manner of the first aspect, the conversion formula for converting multiple transfer trajectories to the Earth-Moon rotating system is: ; ; where represents the position vector of the Earth's center relative to the Earth-Moon barycenter in the Earth-Moon rotating system, represents the velocity vector of the Earth's center relative to the Earth-Moon barycenter in the Earth-Moon rotating system; and are the rotation matrix and derivative from the J2000 inertial system to the Earth-Moon rotating system; r J2000 is the position vector in the J2000 inertial system, v J2000 is the velocity vector in the J2000 inertial system; r EMR is the position vector in the Earth-Moon rotating system; v EMR is the velocity vector in the Earth-Moon rotating system.

[0013] In a possible implementation manner of the first aspect, the formula for normalization processing is: ; where is the trajectory sequence after normalization processing, is the trajectory sequence before normalization processing.

[0014] The beneficial effects of the present invention are as follows: The method provided by the present invention first determines multiple transfer trajectories from the initial orbit to the target orbit based on a simplified model, then determines an initial transfer trajectory from the multiple transfer trajectories, and then optimizes the initial transfer trajectory to obtain a target transfer trajectory based on a high-fidelity model. The end position of the target transfer trajectory is located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfies the shape constraint and the long-term boundedness constraint. In this way, the method provided by the present invention can quickly and accurately determine the Earth-Moon space transfer trajectory under the high-fidelity model, improve adaptability, and meet the user's usage requirements in different usage scenarios. Moreover, the method provided by the present invention can be applied to the transfer between orbits similar to the initial orbit and the target orbit under the simplified model, rather than being limited to the transfer between determined orbits; and, compared with the related art, the method provided by the present invention can effectively improve the trajectory migration efficiency and has universality under any dynamic model. That is to say, the method provided by the present invention is based on the shape similarity matching algorithm, and uses the bisection method to quickly search for a high-fidelity trajectory similar to the trajectory transfer mode of the simplified model. Through verification, it can generate an Earth-Moon space transfer trajectory whose time and fuel consumption cost meet the expectations, and has strong transferability for similar initial orbits, providing a new idea for the conversion of the simplified model trajectory to the high-fidelity model trajectory.

[0015] In a second aspect, the present invention provides an Earth-Moon space transfer trajectory migration system under a high-fidelity model. The system includes: a database construction module for constructing an Earth-Moon transfer trajectory database based on the initial orbit and the target orbit of the simplified model. The Earth-Moon transfer trajectory database includes the orbit information of each transfer trajectory in multiple transfer trajectories based on the simplified model; the transfer trajectory is the trajectory from the initial orbit to the target orbit; a trajectory migration module for determining an initial transfer trajectory from the multiple transfer trajectories according to the orbit information of each transfer trajectory; and a trajectory optimization module for optimizing the initial transfer trajectory to obtain a target transfer trajectory based on the high-fidelity model. The end position of the target transfer trajectory is located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfies the shape constraint and the long-term boundedness constraint.

[0016] 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.

[0017] In a fourth aspect, a computer-readable storage medium is provided, including computer instructions. When the computer instructions are run on the electronic device, the electronic device is caused to execute the method in any implementation manner of the first aspect.

[0018] In a fifth aspect, there is provided a computer program product which, when running on a computer, causes the computer to execute the method in any implementation manner of the first aspect.

[0019] It can be understood that for the beneficial effects that can be achieved by the system in the second aspect, the electronic device in the third aspect, the computer-readable storage medium in the fourth aspect, and the computer program product in the fifth aspect provided above, reference can be made to the beneficial effects in the first aspect and any possible design manner thereof, which will not be elaborated herein. Description of the Drawings

[0020] Figure 1 Schematic structural diagram of an electronic device provided by an embodiment of the present invention; Figure 2 Flowchart of a method for migrating a lunar-earth space transfer trajectory under a high-fidelity model provided by an embodiment of the present invention; Figure 3 Schematic diagram of a Pareto frontier of an initial orbit and a target orbit with respect to a transfer duration and a total velocity increment provided by an embodiment of the present invention; Figure 4 Schematic diagram of calculation results of a target transfer trajectory under a simplified model and a target transfer trajectory under a high-fidelity model provided by an embodiment of the present invention; Figure 5 Schematic diagram of different transfer trajectories under a simplified model and a high-fidelity model provided by an embodiment of the present invention; Figure 6 Schematic diagram of a process of optimization based on a first optimization function provided by an embodiment of the present invention; Figure 7 Schematic diagram of a process of optimization based on a second optimization function provided by an embodiment of the present invention; Figure 8 Schematic diagram of a target transfer trajectory provided by an embodiment of the present invention; Figure 9 Schematic diagram of a definition and conversion relationship between a J2000 inertial system and a lunar-earth rotation system provided by an embodiment of the present invention; Figure 10 Schematic structural diagram of a migration system provided by an embodiment of the present invention. Detailed Embodiments

[0021] 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. Among them, in the description of the present invention, unless otherwise specified, " / " means 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 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 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 (piece)" or its similar expression refers to any combination of these items, including any combination of single items (pieces) or plural items (pieces).

[0022] 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, terms such as "first" and "second" are used to distinguish identical or similar items with basically the same functions and roles. Those skilled in the art can understand that terms such as "first" and "second" do not limit the quantity and execution order, and terms such as "first" and "second" do not necessarily limit being different from each other.

[0023] Meanwhile, 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 superior or more advantageous than other embodiments or design solutions. Exactly speaking, using words such as "exemplary" or "for example" aims to present relevant concepts in a specific way for easy understanding.

[0024] The transfer trajectory design under the high-fidelity model is an important part of the Earth-Moon space mission planning. Searching for trajectories directly under the high-fidelity model places high requirements on the accuracy and speed of the integrator, and the general laws of orbit transfer cannot be revealed. To reduce the complexity of the dynamic model and improve the calculation efficiency, usually the transfer trajectory is first analyzed and calculated under the simplified model, and then converted to the high-fidelity model.

[0025] In the related art, the conversion of multi-loop NRHO orbits under the ephemeris model is studied, and the selection basis for the splicing points is given. However, this method still has certain problems. This method is only applicable to periodic orbits or quasi-periodic orbits and cannot be migrated to large-scale transfer trajectories. To sum up, the existing correction methods for converting trajectories from the simplified model to the high-fidelity model have poor convergence and trajectory reuse capabilities, and require the provision of the analytical Jacobian matrix information of the high-fidelity model, with poor applicability.

[0026] Therefore, there is an urgent need for a method and system for migrating the Earth-Moon space transfer trajectory under a high-fidelity model, which can quickly and accurately determine the Earth-Moon space transfer trajectory under the high-fidelity model, improve adaptability, and meet the user's usage requirements in different usage scenarios.

[0027] In view of this, the embodiments of the present invention provide a method and system for migrating the Earth-Moon space transfer trajectory under a high-fidelity model. The above method includes: constructing an Earth-Moon transfer trajectory database based on the initial orbit and the target orbit of the simplified model, where the Earth-Moon transfer trajectory database includes the orbit information of each transfer trajectory in multiple transfer trajectories based on the simplified model; the transfer trajectory is the trajectory transferred from the initial orbit to the target orbit; determining an initial transfer trajectory from multiple transfer trajectories according to the orbit information of each transfer trajectory; optimizing the initial transfer trajectory to obtain a target transfer trajectory based on the high-fidelity model, the end position of the target transfer trajectory is located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfies the shape constraint and the long-term boundedness constraint.

[0028] The method provided by the present invention first determines multiple transfer trajectories from the initial orbit to the target orbit based on the simplified model, then determines the initial transfer trajectory from multiple transfer trajectories, and then optimizes the initial transfer trajectory to obtain a target transfer trajectory based on the high-fidelity model. The end position of the target transfer trajectory is located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfies the shape constraint and the long-term boundedness constraint. In this way, the method provided by the present invention can quickly and accurately determine the Earth-Moon space transfer trajectory under the high-fidelity model, improve adaptability, and meet the user's usage requirements in different usage scenarios. Moreover, the method provided by the present invention can be applied to the transfer between similar orbits of the initial orbit and the target orbit under the simplified model, rather than being limited to the transfer between the determined orbits; and, compared with the related technology, the method provided by the present invention can effectively improve the trajectory migration efficiency and has universality under any dynamic model. That is to say, the method provided by the present invention is based on the shape similarity matching algorithm, uses the dichotomy method to quickly search for the high-fidelity trajectory similar to the trajectory transfer mode of the simplified model, and through verification, can generate the Earth-Moon space transfer trajectory whose time and fuel consumption cost meet the expectations, and has strong transferability for similar initial orbits, providing a new idea for the conversion of the simplified model trajectory to the high-fidelity model trajectory.

[0029] In some embodiments, a method for migrating the Earth-Moon space transfer trajectory under a high-fidelity model provided by the embodiments of the present invention can be executed by a system 100 for migrating the Earth-Moon space transfer trajectory under a high-fidelity model (hereinafter referred to as the migration system 100).

[0030] As an example, the migration 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 manner of the migration system 100 is not limited herein.

[0031] Figure 1 FIG. shows a schematic diagram of the hardware structure of the electronic device provided by an embodiment of the present invention. The electronic device 200 includes a processor 210, a memory 220, and a communication interface 230.

[0032] 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).

[0033] The memory 220 may include a random access memory (RAM), or 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, code, 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 various method embodiments, etc.

[0034] 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.

[0035] In terms of physical implementation, the above-mentioned various devices (such as the processor 210, the memory 220, and the communication interface 230) can be respectively the devices in the same device (such as a laptop computer). Alternatively, at least two of them can be arranged in the same device, that is, as different devices in a device, similar to the deployment method of devices or components in a distributed system.

[0036] 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 components shown in the figure can be implemented in hardware, software, or a combination of software and hardware.

[0037] The following will describe a method for migrating the Earth-Moon space transfer trajectory under a high-fidelity model provided by an embodiment of the present invention in conjunction with the accompanying drawings of the specification.

[0038] Figure 2 It is a flowchart of a method for migrating the Earth-Moon space transfer trajectory under a high-fidelity model 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 initial orbit and the target orbit of the simplified model, construct an Earth-Moon transfer trajectory database.

[0039] Among them, the Earth-Moon transfer trajectory database includes the orbit information of each transfer trajectory in multiple transfer trajectories based on the simplified model; the transfer trajectory is the trajectory transferred from the initial orbit to the target orbit; In a possible implementation manner, the above S1 includes: S11. Discretize the initial orbit to determine multiple discrete points located on the initial orbit; S12. Set departure velocity increments with different directions and magnitudes for each discrete point to obtain multiple transfer trajectories corresponding to each discrete point; S13. Retain the transfer trajectories whose minimum distance from the target orbit based on the simplified model is less than a preset distance threshold; S14. Based on the terminal constraint conditions, optimize the transfer trajectories whose minimum distance from the target orbit based on the simplified model is less than the preset distance threshold through multi-step shooting correction and continuation to obtain multiple transfer trajectories with the terminal positions based on the simplified model located on the target orbit based on the simplified model; S15. Generate an Earth-Moon transfer trajectory database according to the multiple transfer trajectories with the terminal positions based on the simplified model located on the target orbit based on the simplified model.

[0040] In some embodiments, the simplified model is a circular restricted three-body model or a double-circle restricted four-body model.

[0041] In one example, the above S1 includes: Give the departure orbit (initial orbit) and the target orbit under the simplified model (circular restricted three-body model or double-circle restricted four-body model); discretize the departure orbit at equal time intervals into , where is the equal-interval phase factor. For unstable orbits, the departure velocity increment is in the direction of the eigenvector corresponding to the unstable invariant manifold; for stable orbits, the departure velocity increment is along the relative tangential angle , and its magnitude can be evaluated according to the Jacobi constant, divide the grid; prune to generate an initial guess. Search for the transfer trajectory according to the above grid. If the minimum distance between the transfer trajectory and the target orbit is less than the preset distance threshold, then retain the transfer trajectory. If the minimum distance between the transfer trajectory and the target orbit is greater than or equal to the preset distance threshold, then delete the transfer trajectory. Finally, correct and extend through multi-step shooting. Use the multi-step shooting method to correct the transfer trajectory retained in the above steps so that it satisfies the terminal constraint condition, that is, the terminal position of the transfer trajectory is on the target orbit; extend the departure time and the transfer duration , and generate a global transfer trajectory solution family (Earth-Moon transfer trajectory database).

[0042] In some embodiments, the simplified model is a circular restricted three-body model or a double-circle restricted four-body model.

[0043] It should be noted that the above simplified model is only for illustrative purposes, and the specific types and implementation methods of the simplified model in the embodiments of the present invention are not particularly limited.

[0044] S2. Determine the initial transfer trajectory from multiple transfer trajectories according to the orbit information of each transfer trajectory.

[0045] In a possible implementation manner, the above S2 includes: Project all the transfer trajectories included in the Earth-Moon transfer trajectory database onto a plane, extract the Pareto front, as shown by the green dots in Figure 3 . Determine the initial transfer trajectory, as shown in (a) in Figure 4 , corresponding to the red dot in Figure 3 .

[0046] S3. Optimize the initial transfer trajectory to obtain a target transfer trajectory based on a high-fidelity model. The terminal position of the target transfer trajectory is on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfies the shape constraint and the long-term boundedness constraint.

[0047] Specifically, optimizing the initial transfer trajectory is to construct an optimization problem and solve the optimization problem. As Figure 5 shown, the position sequence of the initial orbit under the high-fidelity model is represented by a function of time ; the initial orbit of the simplified model is represented by ; the target transfer trajectory under the high-fidelity model is represented by a function of time and control variables ; the target orbit under the simplified model is represented by ; the target orbit under the high-fidelity model is represented by . The design variables are , where and represent the departure pulse and the injection pulse, respectively. The optimization problem is as follows: .

[0048] Where and represent the similarity function of the transfer trajectory and the similarity function of the target orbit, respectively.

[0049] In a possible implementation, the above S3 includes: S31. Optimize the initial transfer trajectory according to the first optimization function, where the first optimization function is used to characterize the similarity between the initial transfer trajectory based on the simplified model and the initial transfer trajectory based on the high-fidelity model.

[0050] In some embodiments, the above S31 includes: S311. Construct the first optimization function; The first optimization function is: ; ; ; ; Where and are optimization variables, is the initial transfer trajectory under the simplified model; is the initial transfer trajectory under the high-fidelity model; represents the similarity of the apsidal positions of transfer trajectory A and transfer trajectory B; is the weight coefficient; In the case where the transfer trajectory includes apsides, the position vector of the th apsis relative to the moon is ; S312. Determine the departure velocity pulse of the initial transfer trajectory under the simplified model , taking the departure position of the initial transfer trajectory under the simplified model as the starting point, apply different departure pulses for orbit extrapolation to obtain multiple transfer trajectories. Among them, , the step interval of different departure pulses is ; S313. Convert the multiple transfer trajectories to the Earth-Moon rotation system and perform normalization processing; S314. Determine the first optimization function value corresponding to each transfer trajectory; S315. Determine the upper and lower bounds of the first guess interval for the departure pulse corresponding to the transfer trajectory with the minimum first optimization function value by taking two adjacent departure pulses; S316. When the length of the first guess interval is greater than or equal to the preset length threshold, determine the target departure pulse by the bisection method, and update the departure velocity pulse according to the target departure pulse to update the first guess interval; S317. When the length of the guess interval is less than the preset length threshold, determine the target departure pulse by the bisection method. When the end position of the transfer trajectory corresponding to the target departure pulse is on the target orbit, complete the optimization of the initial transfer trajectory.

[0051] The following combines an example to explain the implementation process of S31 provided by the embodiments of the present invention. The above S31 includes: First, construct the optimization problem (the first optimization function): where and are optimization variables, is defined as: .

[0052] Among them, represents the apsidal position similarity between transfer trajectory A and transfer trajectory B. For a trajectory containing apsides, the position vector of the th apsis relative to the moon is . For transfer trajectory A and transfer trajectory B, is defined as: ; It can also be understood as: ; Among them, is the weight coefficient, and the calculation method of this weight coefficient is as follows. The two trajectories respectively represent the initial transfer trajectory under the simplified model and the target transfer trajectory under the high-fidelity model. The red dot is the apse (perilune) of the initial transfer trajectory under the simplified model, and the green dot is the apse (perilune) of the target transfer trajectory under the high-fidelity model. Figure 6 Extract the departure velocity impulse of the initial transfer trajectory under the simplified model

[0053] m / s, starting from the departure position of the initial transfer trajectory under the simplified model Apply the velocity impulse: m / s; Perform orbit extrapolation under the high-fidelity model with a step size of 1.2185 m / s; Convert the extrapolated transfer trajectory to the Earth-Moon rotating system according to the conversion method of the following embodiments and perform normalization processing: In this embodiment, .

[0054] For each transfer trajectory corresponding to each pulse Determine the first optimization function value corresponding to each transfer trajectory according to the above formula , and the weight coefficient satisfies: .

[0055] Among them, . Take the two adjacent pulses of the pulse corresponding to the minimum first optimization function value (the highest similarity) as the lower and upper bounds of the first guess interval; Based on the first guess interval [28.03, 29.24] m / s, use the bisection method to calculate the optimal pulse, and the velocity direction is the same as that under the simplified model, gradually narrowing the interval and updating the first optimization function value ; When the interval length is less than 0.001 m / s, stop the search; Extend the departure time and judge whether the target transfer trajectory meets the end position constraint; If not, locally extend the departure time , and repeat the above steps until the target transfer trajectory meets the end position constraint. A total of 11 iterations are performed, and the calculation result = 28.424 m / s, and the calculation result is as shown in Figure 4 (b)

[0056] ​S32. Optimize the initial transfer trajectory according to the second optimization function to obtain the target transfer trajectory based on the high-fidelity model. The second optimization function is used to characterize the similarity between the target orbit based on the simplified model and the target orbit based on the high-fidelity model.

[0057] In some embodiments, the above S32 includes: S321. Construct the second optimization function based on the input task expected stable time; The second optimization function is: ; ; ; where is the optimization variable, is the target orbit under the simplified model; is the target orbit under the high-fidelity model; represents the Hausdorff distance between the transfer trajectory A sequence and the transfer trajectory B sequence; represents the point and the point the Euclidean distance between; S322. Determine the injection velocity pulse of the initial transfer trajectory under the simplified model , starting from the end position of the initial transfer trajectory under the simplified model, apply different velocity pulses for orbit extrapolation to obtain multiple transfer trajectories, where , different velocity pulses the step interval of is ; S323. Convert the multiple transfer trajectories to the Earth-Moon rotating system and perform normalization processing; S324. Determine the second optimization function value corresponding to each transfer trajectory; S325. Determine the upper and lower bounds of the second guess interval as the velocity pulse corresponding to the transfer trajectory with the minimum second optimization function value and the two adjacent velocity pulses; S326. When the length of the second guess interval is greater than or equal to the length threshold, determine the target velocity pulse by the bisection method, and update the injection velocity pulse according to the target velocity pulse to update the second guess interval; S327. When the length of the second guess interval is less than the length threshold, the target speed pulse is determined by the bisection method. When the transfer trajectory corresponding to the target departure pulse satisfies the shape constraint and the long-term boundedness constraint, the transfer trajectory corresponding to the target departure pulse is migrated to the target transfer trajectory based on the high-fidelity model.

[0058] The following combines an example to explain the implementation process of S31 provided by the embodiments of the present invention.

[0059] In one example, the above S32 includes: According to the preset task expected stable time yr. According to the target transfer trajectory obtained in S31 , starting with =[-228634.2, 15799.526, -841.5244] km, construct an optimization problem (the second optimization function): ; ; Among them, is the optimization variable, represents the Hausdorff distance between two trajectory sequences; .

[0060] .

[0061] In the above formula represents the point and the point 's Euclidean distance. The calculation method of the Hausdorff distance is as Figure 7 shown; Extract the departure speed pulse of the initial transfer trajectory under the simplified model = 37.002 m / s. Starting from the end position of the initial transfer trajectory under the simplified model, apply the speed pulse [29.60, 44.40] m / s for orbit extrapolation in the high-fidelity model with a step size of 1.8501 m / s; Convert the extrapolated transfer trajectory to the Earth-Moon rotating system and perform normalization processing: For each pulse 's corresponding trajectory, calculate the second optimization function value , and take the minimum (highest similarity) corresponding pulse's adjacent two pulses as the lower and upper bounds of the second guess interval; According to the second guess interval [33.30, 35.15] m / s. The bisection method is used to calculate the optimal pulse. The velocity direction is the same as that in the simplified model. The interval is gradually reduced and the second optimization function value is updated ; when the interval length is less than 0.001 m / s, the search is stopped. A total of 11 iterations are performed, and the calculation result = 35.01 m / s; it is judged that the trajectory shape is similar to the simplified model and satisfies long-term boundedness, so it is not necessary to extend the departure time of the transfer trajectory , and the calculation result is as Figure 8 shown.

[0062] In one example, the initial orbit is a Earth-Moon 2:1 DRO, the target orbit is a 3:2 resonance orbit, and it is expected that the spacecraft will be stable for at least 2 years after entering the resonance orbit. A transfer database from the Earth-Moon 2:1 DRO to the 3:2 resonance orbit is constructed under the simplified model, including multiple transfer trajectories from the Earth-Moon 2:1 DRO to the 3:2 resonance orbit; an optimization problem is constructed from the perspective of shape similarity matching; the transfer trajectory (the first optimization function) that meets the constraints is searched based on the apse adaptive weight algorithm, and the target orbit (the second optimization function) that meets the constraints is searched based on the Hausdorff distance.

[0063] As can be seen from the above S1-S3, the method provided by the embodiment of the present invention first determines multiple transfer trajectories from the initial orbit to the target orbit based on the simplified model, then determines the initial transfer trajectory from multiple transfer trajectories, and then optimizes the initial transfer trajectory to obtain the target transfer trajectory based on the high-fidelity model. The end position of the target transfer trajectory is located on the target orbit based on the high-fidelity model, and the target transfer trajectory meets the shape constraint and the long-term boundedness constraint. In this way, the method provided by the present invention can quickly and accurately determine the Earth-Moon space transfer trajectory under the high-fidelity model, improve adaptability, and meet the usage requirements of users in different usage scenarios. Moreover, the method provided by the embodiment of the present invention can be applied to the transfer between orbits similar to the initial orbit and the target orbit under the simplified model, rather than being limited to the transfer between the determined orbits; and, compared with the related technology, the method provided by the embodiment of the present invention can effectively improve the trajectory migration efficiency and has universality under any dynamic model. That is to say, the method provided by the embodiment of the present invention is based on the shape similarity matching algorithm, and uses the bisection method to quickly search for the high-fidelity trajectory similar to the trajectory transfer mode of the simplified model. Through verification, it can generate the Earth-Moon space transfer trajectory with the time and fuel consumption cost meeting the expectations, and has strong transferability for similar initial orbits, providing a new idea for the conversion of the simplified model trajectory to the high-fidelity model trajectory.

[0064] In some embodiments, in the above S313 and S323, the conversion formula for converting multiple transfer trajectories to the Earth-Moon rotating system is: ; ; Among them, represents the position vector of the geocenter relative to the geocenter - lunar center mass in the geocentric - lunar rotational system, and represents the velocity vector of the geocenter relative to the geocenter - lunar center mass in the geocentric - lunar rotational system; and are the rotation matrix and its derivative from the J2000 inertial system to the geocentric - lunar rotational system; The following combines an example to explain the conversion process of converting multiple transfer trajectories provided in the embodiments of the present invention to the geocentric - lunar rotational system.

[0065] In an example, according to the position and velocity of the initial orbit in the J2000 coordinate system under the high - fidelity model as shown in Table 1, extrapolate the position and velocity for one period to obtain the trajectory in the J2000 coordinate system ; Table 1 Calculate the transformation matrix between the J2000 coordinate system and the geocentric - lunar rotational system. As shown in Figure 9 , in the figure represents the J2000 inertial system, represents the geocenter - lunar center mass rotational coordinate system, represents the lunar center rotational coordinate system. and respectively represent the position vector and velocity vector of the moon at the current epoch in the J2000 inertial system. The geocentric - lunar rotational system can be expressed in the J2000 inertial system as: ; The derivatives of the axes of the geocentric - lunar rotational system with respect to time in the J2000 inertial system are: Among them, is the acceleration of the moon relative to the earth. Calculate the rotation matrix and its derivative from the J2000 inertial system to the geocentric - lunar rotational system accordingly: ; The formula for converting the spacecraft state in the J2000 inertial system to the geocentric - lunar rotational system is as follows: .

[0066] Among them, represents the position vector of the geocenter relative to the geocenter - lunar center mass in the geocentric - lunar rotational system, represents the velocity vector of the geocenter relative to the geocenter - lunar center mass in the geocentric - lunar rotational system; and are the rotation matrix and its derivative from the J2000 inertial system to the geocentric - lunar rotational system; rJ2000 is the position vector in the J2000 inertial system, v J2000 is the velocity vector in the J2000 inertial system; r EMR is the position vector in the Earth-Moon rotation system; v EMR is the velocity vector in the Earth-Moon rotation system.

[0067] Transfer to the Earth-Moon rotation system trajectory , extract the departure orbit phase corresponding to the transfer trajectory under the simplified model , in the high-fidelity model, from orbit extrapolate to obtain the departure position of the transfer trajectory in the Earth-Moon rotation system ; In some embodiments, in the above S313 and S323, in the above S313 and S323, the formula for normalization processing is: ; Wherein, is the trajectory sequence after normalization processing, is the trajectory sequence before normalization processing.

[0068] 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 migration 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 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.

[0069] The embodiments of the present invention can divide the migration system 100 into functional units according to the above method examples. For example, each function of the migration system 100 can be divided into corresponding functional units, 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 function division, and there may be other division methods in actual implementation.

[0070] Exemplarily, Figure 10The figure shows a schematic hardware structure diagram of a migration system provided by an embodiment of the present invention. The migration system 100 includes: a database construction module 110, configured to construct a lunar-earth transfer trajectory database based on the initial orbit and the target orbit of a simplified model, where the lunar-earth transfer trajectory database includes the orbit information of each transfer trajectory in a plurality of transfer trajectories based on the simplified model; the transfer trajectory is a trajectory transferred from the initial orbit to the target orbit; a trajectory migration module 120, configured to determine an initial transfer trajectory from the plurality of transfer trajectories according to the orbit information of each transfer trajectory; a trajectory optimization module 130, configured to optimize the initial transfer trajectory to obtain a target transfer trajectory based on a high-fidelity model, where the end position of the target transfer trajectory is located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfies the shape constraint and the long-term boundedness constraint.

[0071] It should be understood that for the specific descriptions of the above optional manners, reference may be made to the foregoing method embodiments, and details are not described herein again. In addition, for the explanations and beneficial effects descriptions of any of the above-provided migration systems 100, reference may be made to the corresponding method embodiments above, and details are not described herein again.

[0072] An embodiment of the present invention further provides 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 in the above various embodiments. For the explanations and beneficial effects descriptions of the relevant contents in any of the above-provided computer-readable storage media, reference may be made to the corresponding embodiments above, and details are not described herein again.

[0073] An embodiment of the present invention further provides a chip. The chip integrates a control circuit for implementing the functions of the above migration system 100 and one or more ports. Optionally, the functions supported by the chip may refer to the above, and details are not described herein again.

[0074] Those of ordinary skill in the art can understand that all or part of the steps for implementing 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.

[0075] An embodiment of the present invention also provides 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 a website, a computer, a server, or a 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 available media integrated. 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.

[0076] 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.

[0077] 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 method for transferring the lunar-earth space trajectory under a high-fidelity model, characterized in that The method includes: Based on the initial orbit and the target orbit of the simplified model, constructing a lunar transfer trajectory database, where the lunar transfer trajectory database includes the orbit information of each transfer trajectory in multiple transfer trajectories based on the simplified model; the transfer trajectory is the trajectory transferred from the initial orbit to the target orbit; Determining an initial transfer trajectory from the multiple transfer trajectories according to the orbit information of each transfer trajectory; Optimizing the initial transfer trajectory to obtain a target transfer trajectory based on the high-fidelity model, where the end position of the target transfer trajectory is located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfies the shape constraint and the long-term boundedness constraint.

2. The method according to claim 1, wherein The constructing of the lunar transfer trajectory database based on the initial orbit and the target orbit of the simplified model includes: Performing discretization processing on the initial orbit to determine multiple discrete points located on the initial orbit; Setting departure speed increments with different directions and magnitudes for each of the discrete points to obtain multiple transfer trajectories corresponding to each of the discrete points; Retaining the transfer trajectories whose minimum distance from the target orbit based on the simplified model is less than a preset distance threshold; Based on the end constraint conditions, optimizing the transfer trajectories whose minimum distance from the target orbit based on the simplified model is less than the preset distance threshold through multi-step shooting correction and continuation to obtain multiple transfer trajectories based on the simplified model whose end positions are located on the target orbit based on the simplified model; Generating the lunar transfer trajectory database according to the multiple transfer trajectories based on the simplified model whose end positions are located on the target orbit based on the simplified model.

3. The method according to claim 2, characterized in that, The simplified model is a circular restricted three-body model or a double-circle restricted four-body model.

4. The method according to claim 3, characterized in that, The optimizing of the initial transfer trajectory to obtain a target transfer trajectory based on the high-fidelity model includes: Optimizing the initial transfer trajectory according to a first optimization function, where the first optimization function is used to characterize the similarity between the initial transfer trajectory based on the simplified model and the initial transfer trajectory based on the high-fidelity model; Optimizing the initial transfer trajectory according to a second optimization function to obtain a target transfer trajectory based on the high-fidelity model, where the second optimization function is used to characterize the similarity between the target orbit based on the simplified model and the target orbit based on the high-fidelity model.

5. The method according to claim 4, wherein The optimizing of the initial transfer trajectory according to the first optimization function includes: Constructing the first optimization function; The first optimization function is as follows: ； ； Among them, and are optimization variables, is the initial transfer trajectory under the simplified model; is the initial transfer trajectory under the high-fidelity model; represents the apsidal position similarity between transfer trajectory A and transfer trajectory B; is the weight coefficient; In the case where the transfer trajectory includes apogees, the position vector of the th apogee relative to the moon is ; Determine the departure velocity pulse of the initial transfer trajectory under the simplified model , starting from the departure position of the initial transfer trajectory under the simplified model , apply different departure pulses for orbit extrapolation to obtain multiple transfer trajectories, where , the step intervals of different departure pulses are ; Converting the multiple transfer trajectories to the Earth-Moon rotating system and performing normalization processing; Determining the first optimization function value corresponding to each transfer trajectory; The starting pulse corresponding to the transfer trajectory with the minimum first optimization function value Two adjacent starting pulses are determined as the upper and lower bounds of the first guess interval; When the length of the first guess interval is greater than or equal to a preset length threshold, a target departure pulse is determined by the bisection method, and the departure speed pulse is updated according to the target departure pulse to update the first guess interval; When the length of the guess interval is less than a preset length threshold, determining the target departure pulse by the bisection method, and when the end position of the transfer trajectory corresponding to the target departure pulse is located on the target orbit, completing the optimization of the initial transfer trajectory.

6. The method according to claim 5, wherein The optimizing of the initial transfer trajectory according to the second optimization function to obtain a target transfer trajectory based on the high-fidelity model includes: Constructing a second optimization function based on the input task expected stable time; The second optimization function is as follows: ； ； ； Among them is the optimization variable is the target orbit under the simplified model is the target orbit under the high-fidelity model represents the Hausdorff distance between the transfer trajectory A sequence and the transfer trajectory B sequence represents the point and the point the Euclidean distance between them Determine the injection velocity pulse of the initial transfer trajectory under the simplified model , using the end position of the initial transfer trajectory under the simplified model as the starting point, apply different velocity pulses for orbit extrapolation to obtain multiple transfer trajectories, where , the step interval of different velocity pulses is ; Converting the multiple transfer trajectories to the Earth-Moon rotating system and performing normalization processing; Determine the second optimized function value corresponding to each transfer trajectory; The speed pulse corresponding to the transfer trajectory with the smallest second optimization function value Two adjacent speed pulses are determined as the upper and lower bounds of the second guess interval; When the length of the second guess interval is greater than or equal to the length threshold, determine the target speed pulse by the bisection method, and update the in-orbit speed pulse according to the target speed pulse , so as to update the second guess interval; When the length of the second guess interval is less than the length threshold, determine the target velocity pulse by the bisection method. When the transfer trajectory corresponding to the target departure pulse satisfies the shape constraint and the long-term boundedness constraint, migrate the transfer trajectory corresponding to the target departure pulse to the target transfer trajectory based on the high-fidelity model.

7. The method according to claim 6, characterized in that The conversion formula for converting the multiple transfer trajectories to the Earth-Moon rotating system is: ； ； Among them, represents the position vector of the geocenter relative to the geocenter - lunar center of mass in the Earth - Moon rotation system, represents the velocity vector of the geocenter relative to the geocenter - lunar center of mass in the Earth - Moon rotation system; and are the rotation matrix and derivative from the J2000 inertial system to the Earth - Moon rotation system; r J2000 is the position vector in the J2000 inertial system, v J2000 is the velocity vector in the J2000 inertial system; r EMR is the position vector in the Earth - Moon rotation system; v EMR is the velocity vector in the Earth - Moon rotation system.

8. The method according to claim 7, wherein The formula for performing the normalization process is: ； Among them, is the trajectory sequence after normalization processing, is the trajectory sequence before normalization processing.

9. A lunar-earth space transfer trajectory migration system under a high-fidelity model, characterized in that The system includes: A database construction module, configured to construct an Earth-Moon transfer trajectory database based on the initial orbit and the target orbit of the simplified model. The Earth-Moon transfer trajectory database includes the orbit information of each transfer trajectory in the multiple transfer trajectories based on the simplified model; the transfer trajectory is the trajectory transferred from the initial orbit to the target orbit; A trajectory migration module, configured to determine an initial transfer trajectory from the multiple transfer trajectories according to the orbit information of each transfer trajectory; A trajectory optimization module, configured to optimize the initial transfer trajectory to obtain a target transfer trajectory based on the high-fidelity model. The end position of the target transfer trajectory is located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfies the shape constraint and the long-term boundedness constraint.

10. An electronic device, characterized in that, Includes: A processor; A memory for storing executable instructions of the processor; Wherein, the processor is configured to execute the instructions to implement the method for migrating the Earth-Moon space transfer trajectory under the high-fidelity model as described in any one of claims 1-8.

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