A method and system for migrating Earth-Moon space transfer trajectories under a high-fidelity model

Abstract

The present invention provides a method and system for migrating Earth-Moon space transfer trajectories based on a high-fidelity model, relating to the field of aerospace technology. The method first determines multiple transfer trajectories from an initial orbit to a target orbit based on a simplified model. The method then determines an initial transfer trajectory from the multiple transfer trajectories. The initial transfer trajectory is then optimized to obtain a target transfer trajectory based on the high-fidelity model. The target transfer trajectory's end position is located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfies shape constraints and long-term boundedness constraints. This method can quickly and accurately determine Earth-Moon space transfer trajectories based on a high-fidelity model, improving adaptability and meeting user needs in different scenarios.

Description

Technical Field

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

[0002] Designing transfer trajectories using a high-fidelity model is a crucial component of cis-lunar space mission planning. Directly searching for trajectories using a high-fidelity model places high demands on integrator accuracy and speed, and fails to reveal the general patterns of orbital transfer. To reduce the complexity of the dynamics model and improve computational efficiency, transfer trajectories are typically first analyzed and calculated using a simplified model, then converted to a high-fidelity model.

[0003] Related research has investigated the conversion of multi-loop NRHO orbits under the ephemeris model and provided a basis for selecting splicing points. However, this approach still has certain issues. It is only applicable to periodic or quasi-periodic orbits and cannot be transferred to large-scale transfer trajectories. In summary, existing correction methods for converting trajectories from simplified models to high-fidelity models suffer from poor convergence and trajectory reuse capabilities, and require the analytical Jacobian matrix of the high-fidelity model, making them less applicable.

[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 a high-fidelity model, improve adaptability, and meet the user's usage needs in different usage scenarios. Summary of the Invention

[0005] Embodiments of the present invention provide a method and system for migrating Earth-Moon space transfer trajectories under a high-fidelity model, which can achieve rapid and accurate determination of Earth-Moon space transfer trajectories under a high-fidelity model, improve adaptability, and meet user needs in different usage scenarios.

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

[0007] In a first aspect, a method for migrating Earth-Moon space transfer trajectories under a high-fidelity model is provided, the method comprising: constructing an Earth-Moon transfer trajectory database based on an initial orbit and a target orbit of a simplified model, the Earth-Moon transfer trajectory database comprising orbital information of each transfer trajectory in a plurality of transfer trajectories based on the simplified model; a transfer trajectory being a trajectory from an initial orbit to a target orbit; determining an initial transfer trajectory from a plurality of transfer trajectories based on the orbital information of each transfer trajectory; and 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 being located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfying shape constraints and long-term boundedness constraints.

[0008] In a possible implementation of the first aspect, an Earth-Moon transfer trajectory database is constructed based on the initial orbit and target orbit of a simplified model, including: discretizing the initial orbit to determine multiple discrete points on the initial orbit; setting departure velocity increments of different directions and sizes for each discrete point to obtain multiple transfer trajectories corresponding to each discrete point; retaining transfer trajectories whose minimum distance from the target orbit based on the simplified model is less than a preset distance threshold; optimizing transfer trajectories whose minimum distance from the target orbit based on the simplified model is less than a preset distance threshold through multi-step target correction and extension based on terminal constraints to obtain transfer trajectories based on the simplified model whose multiple terminal positions are located in the target orbit based on the simplified model; and generating an Earth-Moon transfer trajectory database based on transfer trajectories whose multiple terminal positions are located in the target orbit based on the simplified model.

[0009] In a possible implementation manner of the first aspect, the simplified model is a circular restricted three-body model or a double-circular restricted four-body model.

[0010] In a possible implementation of the first aspect, optimizing 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, the first optimization function being 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; and optimizing the initial transfer trajectory according to a second optimization function to obtain the target transfer trajectory based on the high-fidelity model, the second optimization function being used to characterize the similarity between the target trajectory based on the simplified model and the target trajectory based on the high-fidelity model.

[0011] In a possible implementation of the first aspect, optimizing the initial transfer trajectory according to the first optimization function includes:

[0012] Constructing the first optimization function;

[0013] The first optimization function for:

[0014] ;

[0015] ;

[0016] in, and To optimize the variables, To simplify the initial transfer trajectory under the model; is the initial transfer trajectory under the high-fidelity model; Indicates the similarity of the apses positions between transfer trajectories A and B; is the weight coefficient;

[0017] The transfer trajectory includes In the case of apses, The position vector of the apses relative to the moon is ; Determine the starting velocity pulse of the initial transfer trajectory under the simplified model , to simplify the starting position of the initial transfer trajectory under the model As the starting point, apply different starting pulses Perform orbital extrapolation to obtain multiple transfer trajectories, among which, , different starting pulses The step interval is ; Convert multiple transfer trajectories to the Earth-Moon rotation system and perform normalization processing; Determine the first optimization function value corresponding to each transfer trajectory; The starting pulse corresponding to the transfer trajectory with the smallest first optimization function value The 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 the preset length threshold, the target starting pulse is determined by dichotomy, and the starting speed pulse is updated according to the target starting pulse. , to update the first guess interval; when the length of the guess interval is less than the preset length threshold, the target starting pulse is determined by bisection, and when the end position of the transfer trajectory corresponding to the target starting pulse is located on the target orbit, the optimization of the initial transfer trajectory is completed.

[0018] In a possible implementation of the first aspect, optimizing the initial transfer trajectory according to the second optimization function to obtain a target transfer trajectory based on the high-fidelity model includes: constructing the second optimization function based on an input expected stabilization time of the task;

[0019] Second optimization function for:

[0020] ;

[0021] ;

[0022] ;

[0023] in To optimize the variables, To simplify the target trajectory under the model; is the target orbit under the high-fidelity model; Represents the Hausdorff distance between the transfer trajectory sequence A and the transfer trajectory sequence B; Indicates a point and point The Euclidean distance between

[0024] Determine the orbital velocity pulse of the initial transfer trajectory under the simplified model , to simplify the end position of the initial transfer trajectory under the model As the starting point, apply different speed pulses Perform orbital extrapolation to obtain multiple transfer trajectories, among which, , different speed pulses The step interval is ; Convert multiple transfer trajectories to the Earth-Moon rotation system and perform normalization processing; Determine the second optimization function value corresponding to each transfer trajectory; The velocity pulse corresponding to the transfer trajectory with the smallest second optimization function value The 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, the target speed pulse is determined by dichotomy, and the orbital speed pulse is updated according to the target speed pulse. , to update the second guess interval; when the length of the second guess interval is less than the length threshold, the target velocity pulse is determined by bisection, and when the transfer trajectory corresponding to the target departure pulse satisfies the shape constraint and 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.

[0025] In a possible implementation of the first aspect, a conversion formula for converting multiple transfer trajectories to the Earth-Moon rotation system is:

[0026] ;

[0027] ;

[0028] in, represents the position vector of the Earth's center relative to the Earth-Moon mass center in the Earth-Moon rotation system, It represents the velocity vector of the Earth's center relative to the Earth-Moon's mass center in the Earth-Moon rotation system; and is 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.

[0029] In a possible implementation of the first aspect, a formula for performing normalization processing is:

[0030] ;

[0031] in, is the normalized trajectory sequence, is the trajectory sequence before normalization.

[0032] 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 the simplified model, then determines the initial transfer trajectory from the 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 satisfies the shape constraint and the long-term boundedness constraint. In this way, the method provided by the present invention can achieve rapid and accurate determination of the Earth-Moon space transfer trajectory under the high-fidelity model, improve adaptability, and meet the user's usage needs in different usage scenarios. In addition, the method provided by the present invention can be applied to transfers between orbits similar to the initial orbit and the target orbit under the simplified model, and is not limited to determining transfers between orbits; and, compared with related technologies, the method provided by the present invention can effectively improve the efficiency of trajectory migration and can be universal under any dynamic model. In other words, the method provided by the present invention is based on a shape similarity matching algorithm and uses a binary search method to quickly search for high-fidelity trajectories that are similar to the simplified model trajectory transfer mode. It has been verified that it can generate Earth-Moon space transfer trajectories that meet the expected time and fuel costs, and has strong transferability for similar initial orbits, providing a new idea for the conversion of simplified model trajectories to high-fidelity model trajectories.

[0033] In second aspect, the present invention provides an Earth-Moon space transfer trajectory migration system under a high-fidelity model, the system comprising: a database construction module for constructing an Earth-Moon transfer trajectory database based on the initial orbit and target orbit of a simplified model, the Earth-Moon transfer trajectory database comprising orbital information of each transfer trajectory in a plurality of transfer trajectories based on the simplified model; a transfer trajectory being a trajectory from an initial orbit to a target orbit; a trajectory migration module for determining an initial transfer trajectory from a plurality of transfer trajectories based on the orbital information of each transfer trajectory; a trajectory optimization module for optimizing the initial transfer trajectory to obtain a target transfer trajectory based on a high-fidelity model, the end position of the target transfer trajectory being located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfying shape constraints and long-term boundedness constraints.

[0034] 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.

[0035] 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.

[0036] 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.

[0037] 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

[0038] Figure 1 A schematic structural diagram of an electronic device provided by an embodiment of the present invention;

[0039] Figure 2 A flowchart of a method for migrating Earth-Moon space transfer trajectories under a high-fidelity model provided by an embodiment of the present invention;

[0040] Figure 3 A schematic diagram of the Pareto front of an initial trajectory and a target trajectory with respect to transfer duration and total velocity increment provided by an embodiment of the present invention;

[0041] Figure 4 A 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;

[0042] Figure 5 Schematic diagram of different transfer trajectories under a simplified model and a high-fidelity model according to an embodiment of the present invention;

[0043] Figure 6 A schematic diagram of an optimization process based on a first optimization function according to an embodiment of the present invention;

[0044] Figure 7 A schematic diagram of an optimization process based on a second optimization function according to an embodiment of the present invention;

[0045] Figure 8 A schematic diagram of a target transfer trajectory shown in an embodiment of the present invention;

[0046] Figure 9 A schematic diagram illustrating the definition and conversion relationship between the J2000 inertial system and the Earth-Moon rotational system according to an embodiment of the present invention;

[0047] Figure 10A schematic diagram of the structure of a migration system provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0048] 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.

[0049] 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.

[0050] 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.

[0051] Designing transfer trajectories using a high-fidelity model is a crucial component of cis-lunar space mission planning. Directly searching for trajectories using a high-fidelity model places high demands on integrator accuracy and speed, and fails to reveal the general patterns of orbital transfer. To reduce the complexity of the dynamics model and improve computational efficiency, transfer trajectories are typically first analyzed and calculated using a simplified model, then converted to a high-fidelity model.

[0052] Related research has investigated the conversion of multi-loop NRHO orbits under the ephemeris model and provided a basis for selecting splicing points. However, this approach still has certain issues. It is only applicable to periodic or quasi-periodic orbits and cannot be transferred to large-scale transfer trajectories. In summary, existing correction methods for converting trajectories from simplified models to high-fidelity models suffer from poor convergence and trajectory reuse capabilities, and require the analytical Jacobian matrix of the high-fidelity model, making them less applicable.

[0053] 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 a high-fidelity model, improve adaptability, and meet the user's usage needs in different usage scenarios.

[0054] In view of this, an embodiment of the present invention provides a method and system for migrating Earth-Moon space transfer trajectories under a high-fidelity model. The method includes: constructing an Earth-Moon transfer trajectory database based on the initial orbit and target orbit of a simplified model, wherein the Earth-Moon transfer trajectory database includes orbital information of each transfer trajectory in multiple transfer trajectories based on the simplified model; the transfer trajectory is a trajectory that transfers from the initial orbit to the target orbit; determining the initial transfer trajectory from the multiple transfer trajectories based on the orbital information of each transfer trajectory; optimizing the initial transfer trajectory to obtain a target transfer trajectory based on the high-fidelity model, wherein 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 shape constraints and long-term boundedness constraints.

[0055] 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 the initial transfer trajectory from the 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 satisfies the shape constraint and the long-term boundedness constraint. In this way, the method provided by the present invention can achieve rapid and accurate determination of the Earth-Moon space transfer trajectory under the high-fidelity model, improve adaptability, and meet the user's usage needs in different usage scenarios. In addition, the method provided by the present invention can be applied to transfers between orbits similar to the initial orbit and the target orbit under the simplified model, and is not limited to determining transfers between orbits; and, compared with related technologies, the method provided by the present invention can effectively improve the efficiency of trajectory migration and can be universal under any dynamic model. In other words, the method provided by the present invention is based on a shape similarity matching algorithm and uses a binary search method to quickly search for high-fidelity trajectories that are similar to the simplified model trajectory transfer mode. It has been verified that it can generate Earth-Moon space transfer trajectories that meet the expected time and fuel costs, and has strong transferability for similar initial orbits, providing a new idea for the conversion of simplified model trajectories to high-fidelity model trajectories.

[0056] In some embodiments, an Earth-Moon space transfer trajectory migration method under a high-fidelity model provided by an embodiment of the present invention can be executed by an Earth-Moon space transfer trajectory migration system 100 under a high-fidelity model (hereinafter referred to as migration system 100 ).

[0057] As an example, the migration system 100 may be any electronic device 200 with data processing capabilities, such as a general-purpose computer, a personal computer, a laptop, a switch, or a tablet computer. The specific implementation of the migration system 100 is not limited here.

[0058] Figure 1 The electronic device 200 includes a processor 210 , a memory 220 , and a communication interface 230 .

[0059] 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).

[0060] 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.

[0061] 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.

[0062] 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.

[0063] 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.

[0064] The following describes a method for migrating Earth-Moon space transfer trajectories under a high-fidelity model provided by an embodiment of the present invention in conjunction with the accompanying drawings.

[0065] Figure 2 This is a flow chart of a method for migrating Earth-Moon space transfer trajectories under a high-fidelity model provided by an embodiment of the present invention. Figure 1 The electronic device 200 shown in FIG. 10 is executed. The method may include the following steps:

[0066] S1. Construct an Earth-Moon transfer trajectory database based on the initial and target orbits of the simplified model.

[0067] The Earth-Moon transfer trajectory database includes orbital information of each transfer trajectory in multiple transfer trajectories based on a simplified model; a transfer trajectory is a trajectory from an initial orbit to a target orbit;

[0068] In a possible implementation, the above S1 includes:

[0069] S11, discretizing the initial trajectory to determine a plurality of discrete points on the initial trajectory;

[0070] S12, setting a starting speed increment of different directions and sizes for each discrete point to obtain multiple transfer trajectories corresponding to each discrete point;

[0071] S13, retaining the transfer trajectory whose minimum distance to the target trajectory based on the simplified model is less than a preset distance threshold;

[0072] S14. Based on the terminal constraint, the transfer trajectory whose minimum distance from the target trajectory based on the simplified model is less than a preset distance threshold is optimized through multi-step target correction and extension to obtain transfer trajectories whose terminal positions based on the simplified model are located on the target trajectory based on the simplified model;

[0073] S15. Generate an Earth-Moon transfer trajectory database based on the transfer trajectories whose end positions are located in the target orbit based on the simplified model.

[0074] In some embodiments, the simplified model is a circularly restricted three-body model or a double-circle restricted four-body model.

[0075] In one example, the above S1 includes:

[0076] Given the starting orbit (initial orbit) and target orbit under the simplified model (circular restricted three-body model or double circular restricted four-body model); discretize the starting orbit into equal time intervals. ,in is an equally spaced phase factor. For unstable orbits, the departure velocity increment The direction is along the eigenvector corresponding to the unstable invariant manifold; for a stable orbit, the departure velocity increment Along the relative tangential angle , the size can be evaluated according to the Jacobi constant and divided into grids; pruning generates initial guesses. According to the above grid search transfer trajectory, if the minimum distance between the transfer trajectory and the target track is less than the preset distance threshold, the transfer trajectory is retained; if the minimum distance between the transfer trajectory and the target track is greater than or equal to the preset distance threshold, the transfer trajectory is deleted. Finally, multi-step shooting correction and extension are performed. The multi-step shooting method is used to correct the transfer trajectory retained in the above steps so that it meets the terminal constraint condition, that is, the terminal position of the transfer trajectory is located on the target track; the departure time is extended. and transfer duration , generating a global transfer trajectory solution family (Earth-Moon transfer trajectory database).

[0077] In some embodiments, the simplified model is a circularly restricted three-body model or a double-circle restricted four-body model.

[0078] It should be noted that the above simplified model is only for illustrative purposes, and the embodiments of the present invention do not impose any particular restrictions on the specific type and implementation of the simplified model.

[0079] S2. Determine an initial transfer trajectory from multiple transfer trajectories according to the orbit information of each transfer trajectory.

[0080] In a possible implementation, the above S2 includes:

[0081] Project all transfer trajectories included in the Earth-Moon transfer trajectory database onto the plane and extract the Pareto front, such as Figure 3 The green dot in the middle shows the initial transfer trajectory. Figure 4 As shown in (a), the corresponding Figure 3 The red dot in .

[0082] S3. 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 track based on the high-fidelity model, and the target transfer trajectory satisfies shape constraints and long-term boundedness constraints.

[0083] Specifically, the optimization of the initial transfer trajectory is a construction optimization problem, and the optimization problem is solved, such as Figure 5 As shown, the position sequence of the initial track under the high-fidelity model adopts a function of time Represents; the initial orbit of the simplified model adopts Representation; the target transfer trajectory under the high-fidelity model adopts a function of time and control variables Indicates that the target orbit under the simplified model adopts Indicates that the target trajectory under the high-fidelity model adopts The design variables are ,in and represents the departure pulse and the orbit entry pulse, and the optimization problem is as follows:

[0084] .

[0085] in and denote the similarity functions of transfer trajectories and target trajectories respectively.

[0086] In a possible implementation, the above S3 includes:

[0087] S31 . 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.

[0088] In some embodiments, the above S31 includes:

[0089] S311, constructing a first optimization function;

[0090] The first optimization function for:

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] in, and To optimize the variables, To simplify the initial transfer trajectory under the model; is the initial transfer trajectory under the high-fidelity model; Indicates the similarity of the apses positions between transfer trajectories A and B; is the weight coefficient;

[0096] The transfer trajectory includes In the case of apses, The position vector of the apses relative to the moon is ;

[0097] S312: Determine the starting speed pulse of the initial transfer trajectory under the simplified model , to simplify the starting position of the initial transfer trajectory under the model As the starting point, apply different starting pulses Perform orbital extrapolation to obtain multiple transfer trajectories, among which, , different starting pulses The step interval is ;

[0098] S313, converting the multiple transfer trajectories into the Earth-Moon rotation system and performing normalization processing;

[0099] S314, determining a first optimization function value corresponding to each transfer trajectory;

[0100] S315, the starting pulse corresponding to the transfer trajectory with the minimum value of the first optimization function Two adjacent starting pulses are determined as the upper and lower bounds of the first guess interval;

[0101] S316: If the length of the first guess interval is greater than or equal to the preset length threshold, determine the target starting pulse by dichotomy, and update the starting speed pulse according to the target starting pulse. , to update the first guess interval;

[0102] S317. When the length of the guessed interval is less than a preset length threshold, determine the target starting pulse by bisection, and when the end position of the transfer trajectory corresponding to the target starting pulse is located on the target trajectory, complete the optimization of the initial transfer trajectory.

[0103] The following is an example to explain the implementation process of S31 provided in the embodiment of the present invention. The above S31 includes:

[0104] First build Optimization problem (first optimization function):

[0105]

[0106] in and To optimize the variables, Defined as:

[0107] .

[0108] in, Indicates the similarity between the apses of transfer trajectory A and transfer trajectory B. The trajectory of the apses, The position vector of the apses relative to the moon is , for transfer trajectory A and transfer trajectory B, Defined as:

[0109] ;

[0110] It can also be understood as:

[0111] ;

[0112] in, is the weight coefficient, the weight coefficient The calculation method is as follows Figure 6 As shown, the two trajectories represent the initial transfer trajectory under the simplified model and the target transfer trajectory under the high-fidelity model, respectively. The red dot is the apside (perilunary point) of the initial transfer trajectory under the simplified model, and the green dot is the anti-apsis (perilunary point) of the target transfer trajectory under the high-fidelity model.

[0113] Extract the starting velocity pulse of the initial transfer trajectory under the simplified model m / s, to simplify the starting position of the initial transfer trajectory under the model As the starting point, apply a velocity pulse: m / s;

[0114] The orbit was extrapolated under the high-fidelity model with a step size of 1.2185 m / s;

[0115] The extrapolated transfer trajectory The conversion method of the following embodiment is used to convert to the Earth-Moon rotation system and perform normalization processing:

[0116] In this embodiment, .

[0117] For each pulse The corresponding transfer trajectory is determined according to the above formula to determine the first optimization function value corresponding to each transfer trajectory , the weight coefficient satisfies:

[0118] .

[0119] in, . Take the first optimization function value The two adjacent pulses of the minimum (highest similarity) corresponding pulse are used as the lower and upper bounds of the first guess interval; based on the first guess interval [28.03, 29.24] m / s, using the bisection method to calculate the optimal pulse, the speed direction is consistent with the simplified model, the interval is narrowed and the first optimization function value is updated in each round ; When the interval length is less than 0.001 m / s, stop searching; extend the departure time to determine whether the target transfer trajectory meets the terminal 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, the calculation results =28.424 m / s, the calculation result is as follows Figure 4 As shown in (b) in .

[0120] S32. Optimize the initial transfer trajectory according to a second optimization function to obtain a target transfer trajectory based on the high-fidelity model. The second optimization function is used to characterize the similarity between the target trajectory based on the simplified model and the target trajectory based on the high-fidelity model.

[0121] In some embodiments, the above S32 includes:

[0122] S321. Construct a second optimization function based on the input expected stabilization time of the task;

[0123] Second optimization function for:

[0124] ;

[0125] ;

[0126] ;

[0127] in To optimize the variables, To simplify the target trajectory under the model; is the target orbit under the high-fidelity model; Represents the Hausdorff distance between the transfer trajectory sequence A and the transfer trajectory sequence B; Indicates a point and point The Euclidean distance between

[0128] S322: Determine the orbital velocity pulse of the initial transfer trajectory under the simplified model , to simplify the end position of the initial transfer trajectory under the model As the starting point, apply different speed pulses Perform orbital extrapolation to obtain multiple transfer trajectories, among which, , different speed pulses The step interval is ;

[0129] S323, converting the multiple transfer trajectories into the Earth-Moon rotation system and performing normalization processing;

[0130] S324, determining a second optimization function value corresponding to each transfer trajectory;

[0131] S325, the speed pulse corresponding to the transfer trajectory with the minimum value of the second optimization function The two adjacent speed pulses are determined as the upper and lower bounds of the second guess interval;

[0132] S326: If the length of the second guess interval is greater than or equal to the length threshold, determine the target speed pulse by dichotomy, and update the orbital speed pulse according to the target speed pulse. , to update the second guess interval;

[0133] S327. When the length of the second guess interval is less than the length threshold, determine the target velocity pulse by bisection, and 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.

[0134] The following is an example to explain the implementation process of S31 provided by the embodiment of the present invention.

[0135] In one example, the above S32 includes:

[0136] Expected stabilization time based on preset tasks yr. According to the target transfer trajectory obtained in S31 ,by =[-228634.2, 15799.526, -841.5244] km as the starting point, Construct the optimization problem (second optimization function):

[0137] ;

[0138] ;

[0139] in, To optimize the variables, Represents the Hausdorff distance between two trajectory sequences;

[0140] .

[0141] .

[0142] In the above formula Indicates a point and point The Euclidean distance and Hausdorff distance are calculated as follows Figure 7 As shown;

[0143] Extract the starting velocity pulse of the initial transfer trajectory under the simplified model =37.002 m / s to simplify the end position of the initial transfer trajectory under the model As the starting point, apply speed pulse [29.60, 44.40] m / s Orbital extrapolation is performed under the high-fidelity model with a step size of 1.8501 m / s;

[0144] The extrapolated transfer trajectory Convert to the Earth-Moon rotation system and perform normalization:

[0145] For each pulse Calculate the second optimization function value by taking the corresponding trajectory ,Pick The two adjacent pulses of the minimum (highest similarity) corresponding pulse are used as the lower and upper bounds of the second guess interval; according to the second guess interval [33.30, 35.15] m / s, using the bisection method to calculate the optimal pulse, the speed direction is consistent with the simplified model, the interval is narrowed and the second optimization function value is updated in each round ; When the interval length is less than 0.001 m / s, stop searching, iterate 11 times in total, and calculate the result =35.01 m / s; the trajectory shape is similar to the simplified model and satisfies the long-term boundedness, so there is no need to extend the transfer trajectory departure time , the calculation results are as follows Figure 8 shown.

[0146] In one example, the initial orbit is a 2:1 DRO Earth-Moon orbit, and the target orbit is a 3:2 resonant orbit. The spacecraft is expected to maintain stability for at least two years after entering the resonant orbit. A simplified Earth-Moon 2:1 DRO to 3:2 resonant orbit transfer database is constructed, including multiple transfer trajectories from the 2:1 DRO to 3:2 resonant orbit. An optimization problem is formulated from the perspective of shape similarity matching. A transfer trajectory that satisfies the constraints is searched using an apsidal adaptive weighting algorithm (the first optimization function), and a target orbit that satisfies the constraints is searched using the Hausdoff distance (the second optimization function).

[0147] As can be seen from S1-S3 above, 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 the 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 satisfies the shape constraint and the long-term boundedness constraint. In this way, the method provided by the present invention can realize the rapid and accurate determination of the Earth-Moon space transfer trajectory under the high-fidelity model, improve adaptability, and meet the user's usage needs in different usage scenarios. In addition, the method provided by the embodiment of the present invention can be applied to transfers between orbits similar to the initial orbit and the target orbit under the simplified model, and is not limited to determining transfers between orbits; and, compared with related technologies, the method provided by the embodiment of the present invention can effectively improve the efficiency of trajectory migration and can be universal under any dynamic model. In other words, the method provided by the embodiment of the present invention is based on a shape similarity matching algorithm and uses a binary search method to quickly search for high-fidelity trajectories that are similar to the simplified model trajectory transfer pattern. It has been verified that it can generate Earth-Moon space transfer trajectories that meet the expected time and fuel costs, and has strong transferability for similar initial orbits, providing a new idea for the conversion of simplified model trajectories to high-fidelity model trajectories.

[0148] In some embodiments, in S313 and S323 above, the conversion formula for converting the multiple transfer trajectories to the Earth-Moon rotation system is:

[0149] ;

[0150] ;

[0151] in, represents the position vector of the Earth's center relative to the Earth-Moon mass center in the Earth-Moon rotation system, It represents the velocity vector of the Earth's center relative to the Earth-Moon's mass center in the Earth-Moon rotation system; and is the rotation matrix and derivative from the J2000 inertial system to the Earth-Moon rotation system;

[0152] The following uses an example to explain the conversion process of multiple transfer trajectories provided by an embodiment of the present invention into the Earth-Moon rotation system.

[0153] In one example, the position and velocity of the initial trajectory in the J2000 coordinate system under the high-fidelity model are shown in Table 1. The position and velocity are extrapolated for one cycle to obtain the trajectory in the J2000 coordinate system. ;

[0154] Table 1

[0155]

[0156] Calculate the transformation matrix between the J2000 coordinate system and the Earth-Moon rotation system, such as Figure 9 As shown in the figure represents the J2000 inertial system, represents the Earth-Moon mass center rotating coordinate system, Represents the lunar-centered rotation coordinate system. and They represent the position vector and velocity vector of the moon in the current epoch in the J2000 inertial system. The Earth-Moon rotation system can be expressed in the J2000 inertial system as follows:

[0157] ;

[0158] The time derivatives of the axes of the Earth-Moon rotation system in the J2000 inertial system are:

[0159]

[0160] in, is the acceleration of the moon relative to the earth. Based on this, the rotation matrix and its derivative from the J2000 inertial system to the earth-moon rotation system are calculated:

[0161] ;

[0162] The formula for converting the spacecraft state from the J2000 inertial system to the Earth-Moon rotation system is as follows:

[0163] .

[0164] in, represents the position vector of the Earth's center relative to the Earth-Moon mass center in the Earth-Moon rotation system, It represents the velocity vector of the Earth's center relative to the Earth-Moon's mass center in the Earth-Moon rotation system; and is 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.

[0165] Will Transformation to the Earth-Moon rotation system trajectory , extract the departure orbit phase corresponding to the transfer trajectory under the simplified model , under the high-fidelity model Extrapolate the track to Obtain the starting position of the transfer trajectory in the lunar center Earth-Moon rotation system ;

[0166] In some embodiments, in the above S313 and S323, the formula for normalization processing in the above S313 and S323 is:

[0167] ;

[0168] in, is the normalized trajectory sequence, is the trajectory sequence before normalization.

[0169] 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 migration system 100 includes at least one of the hardware structures and software modules corresponding to the execution of each function. Those skilled in the art should easily 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.

[0170] In embodiments of the present invention, migration system 100 can be divided into functional units based on the above-described method examples. For example, migration system 100 can be divided into functional units corresponding to respective functions, or two or more functions can be integrated into a single processing unit. These integrated units can be implemented as either hardware or software functional units. It should be noted that the division of units in the embodiments of the present invention is illustrative and represents only one logical functional division. In actual implementation, other division methods may be employed.

[0171] For example, Figure 10A schematic diagram of the hardware structure of a migration system provided by an embodiment of the present invention is shown. The migration system 100 includes: a database construction module 110, configured to construct an Earth-Moon transfer trajectory database based on the initial and target orbits of a simplified model. The Earth-Moon transfer trajectory database includes orbital information for each of multiple transfer trajectories based on the simplified model; a transfer trajectory is a trajectory that transfers from an initial orbit to a target orbit; a trajectory migration module 120, configured to determine an initial transfer trajectory from the multiple transfer trajectories based on the orbital information of each transfer trajectory; and a trajectory optimization module 130, configured to optimize the initial transfer trajectory to obtain a target transfer trajectory based on a high-fidelity model. The target transfer trajectory has its end position located on the target orbit based on the high-fidelity model, and the target transfer trajectory satisfies shape constraints and long-term boundedness constraints.

[0172] It should be understood that the detailed description of the above optional methods can be found in the above method embodiments, which will not be repeated here. In addition, the explanation and description of the beneficial effects of any migration system 100 provided above can refer to the above corresponding method embodiments, which will not be repeated here.

[0173] 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.

[0174] 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 migration system 100. Optionally, the functions supported by the chip can be referred to above and will not be described in detail here.

[0175] 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.

[0176] 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).

[0177] 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.

[0178] 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 method for migrating Earth-Moon space transfer trajectories under a high-fidelity model, characterized in that: The method comprises: constructing an Earth-Moon transfer trajectory database based on the initial orbit and the target orbit of the simplified model, wherein the Earth-Moon transfer trajectory database includes orbital information of each of a plurality of transfer trajectories based on the simplified model; the transfer trajectory is a trajectory from the initial orbit to the target orbit; determining an initial transfer trajectory from the plurality of transfer trajectories according to the trajectory information of each transfer trajectory; Optimizing the initial transfer trajectory to obtain a target transfer trajectory based on a high-fidelity model, wherein an end position of the target transfer trajectory is located on the target track based on the high-fidelity model, and the target transfer trajectory satisfies shape constraints and long-term boundedness constraints; The initial orbit and target orbit based on the simplified model are used to construct an Earth-Moon transfer trajectory database, including: performing discretization processing on the initial trajectory to determine a plurality of discrete points located on the initial trajectory; Setting a starting speed increment of different directions and sizes for each discrete point to obtain multiple transfer trajectories corresponding to each discrete point; Retain the transfer trajectories whose minimum distance to the target trajectory based on the simplified model is less than a preset distance threshold; Based on the terminal constraint condition, the transfer trajectory whose minimum distance from the target trajectory based on the simplified model is less than a preset distance threshold is optimized through multi-step target correction and extension to obtain transfer trajectories based on the simplified model whose terminal positions are located on the target trajectory based on the simplified model; The Earth-Moon transfer trajectory database is generated according to the transfer trajectories based on the simplified model with multiple end positions located in the target orbit based on the simplified model.

2. The method according to claim 1, characterized in that The simplified model is a circular restricted three-body model or a double-circle restricted four-body model.

3. The method according to claim 2, characterized in that Optimizing the initial transfer trajectory to obtain a target transfer trajectory based on a 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; The initial transfer trajectory is optimized according to a second optimization function to obtain a target transfer trajectory based on the high-fidelity model, wherein the second optimization function is used to characterize the similarity between the target trajectory based on the simplified model and the target trajectory based on the high-fidelity model.

4. The method according to claim 3, characterized in that Optimizing the initial transfer trajectory according to the first optimization function includes: Constructing the first optimization function; The first optimization function for: ； ； in, and To optimize the variables, To simplify the initial transfer trajectory under the model; is the initial transfer trajectory under the high-fidelity model; Indicates the similarity of the apses positions between transfer trajectories A and B; is the weight coefficient; The transfer trajectory includes In the case of apses, The position vector of the apses relative to the moon is ; Determine the starting velocity pulse of the initial transfer trajectory under the simplified model , to simplify the starting position of the initial transfer trajectory under the model As the starting point, apply different starting pulses Perform orbital extrapolation to obtain multiple transfer trajectories, among which, , different starting pulses The step interval is ; Converting the multiple transfer trajectories to the Earth-Moon rotation system and performing normalization processing; Determining a first optimization function value corresponding to each transfer trajectory; The starting pulse corresponding to the transfer trajectory with the minimum value of the first optimization function 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 the preset length threshold, the target starting pulse is determined by dichotomy, and the starting speed pulse is updated according to the target starting pulse. , to update the first guess interval; When the length of the guessed interval is less than a preset length threshold, the target starting pulse is determined by bisection, and when the end position of the transfer trajectory corresponding to the target starting pulse is located at the target trajectory, the optimization of the initial transfer trajectory is completed.

5. The method according to claim 4, characterized in that Optimizing the initial transfer trajectory according to the second optimization function to obtain a target transfer trajectory based on a high-fidelity model includes: Constructing a second optimization function based on the input task expected stabilization time; The second optimization function for: ； ； ； in To optimize the variables, To simplify the target trajectory under the model; is the target orbit under the high-fidelity model; Represents the Hausdorff distance between the transfer trajectory sequence A and the transfer trajectory sequence B; Indicates a point and point The Euclidean distance between Determine the orbital velocity pulse of the initial transfer trajectory under the simplified model , to simplify the end position of the initial transfer trajectory under the model As the starting point, apply different speed pulses Perform orbital extrapolation to obtain multiple transfer trajectories, among which, , different speed pulses The step interval is ; Converting the multiple transfer trajectories to the Earth-Moon rotation system and performing normalization processing; Determining a second optimization function value corresponding to each transfer trajectory; The velocity pulse corresponding to the transfer trajectory with the minimum value of the second optimization function The 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, the target speed pulse is determined by dichotomy, and the orbital speed pulse is updated according to the target speed pulse. , to update the second guess interval; When the length of the second guess interval is less than a length threshold, the target velocity pulse is determined by a bisection method. When the transfer trajectory corresponding to the target departure pulse satisfies shape constraints and long-term boundedness constraints, the transfer trajectory corresponding to the target departure pulse is migrated to the target transfer trajectory based on the high-fidelity model.

6. The method according to claim 5, characterized in that The conversion formula for converting the multiple transfer trajectories to the Earth-Moon rotation system is: ； ； in, represents the position vector of the Earth's center relative to the Earth-Moon mass center in the Earth-Moon rotation system, It represents the velocity vector of the Earth's center relative to the Earth-Moon's mass center in the Earth-Moon rotation system; and is 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.

7. The method according to claim 6, characterized in that The formula for normalization is: ； in, is the normalized trajectory sequence, is the trajectory sequence before normalization.

8. A high-fidelity Earth-Moon space transfer trajectory migration system, characterized by: The system comprises: 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, wherein the Earth-Moon transfer trajectory database includes orbital information of each of a plurality of transfer trajectories based on the simplified model; the transfer trajectory is a trajectory from the initial orbit to the target orbit; a trajectory migration module, 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, configured to optimize the initial transfer trajectory to obtain a target transfer trajectory based on a high-fidelity model, wherein the end position of the target transfer trajectory is located on the target track based on the high-fidelity model, and the target transfer trajectory satisfies shape constraints and long-term boundedness constraints; The database construction module is specifically used to: performing discretization processing on the initial trajectory to determine a plurality of discrete points located on the initial trajectory; Setting a starting speed increment of different directions and sizes for each discrete point to obtain multiple transfer trajectories corresponding to each discrete point; Retain the transfer trajectories whose minimum distance to the target trajectory based on the simplified model is less than a preset distance threshold; Based on the terminal constraint condition, the transfer trajectory whose minimum distance from the target trajectory based on the simplified model is less than a preset distance threshold is optimized through multi-step target correction and extension to obtain transfer trajectories based on the simplified model whose terminal positions are located on the target trajectory based on the simplified model; The Earth-Moon transfer trajectory database is generated according to the transfer trajectories based on the simplified model with multiple end positions located in the target orbit based on the simplified model.

9. 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 Earth-Moon space transfer trajectory migration method under the high-fidelity model as described in any one of claims 1-7.

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