The orbit design method for DRO orbit vehicle to land on the moon at given angle and coordinate

Abstract

The application relates to a DRO orbit aircraft orbit design method for falling on the moon at a given angle and coordinates. The method comprises the following steps: DRO initial position and speed value integration, output of L2 coordinate system positions of the moon at different moments in a period, and mapping of the moon falling speed and transfer orbit and white plane intersection position. The mapping and DRO period position are combined to reversely coarsely calculate the moon falling moment, initial speed and transfer time length. The three are taken as iteration initial values and constraints are set to reversely accurately calculate the integral end moment, speed and orbit flight time length. The end moment is taken as the orbit transfer moment initial value, the end speed and the DRO speed difference value are taken as the orbit transfer speed increment initial value, the orbit flight time length is taken as the transfer time length initial value, the forward accurate calculation is carried out by setting the terminal constraint and the integral termination condition, and finally the transfer orbit transfer moment and speed increment projection are obtained. The method can be suitable for different task times and different DRO orbit sizes, the calculation result is high in precision, and the iteration is fast and reliable.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of space orbit design, in particular to an orbit design method for a DRO orbit spacecraft to land on the moon according to a given angle and coordinates. BACKGROUND

[0002] DRO (Distant Retrograde Orbit) is a periodic orbit under the assumption of a circular restricted three-body model. In the coordinate system rotating around the center of mass of the Earth-moon system, the shape is approximately an elliptical orbit with the direction of revolution opposite to the direction of the moon's revolution. Although the force on the DRO orbit spacecraft in the actual problem is much more complex than the force model of the circular restricted three-body problem, its periodicity and stability can still be maintained to a certain extent by control with little energy consumption. Its unique orbit characteristics can facilitate the combination of lunar surface missions and deep space missions, and therefore have unique application value in Earth-moon space and deep space exploration beyond the moon. The transfer of a spacecraft from a DRO orbit to a given lunar landing point according to a given landing angle is an important application.

[0003] Earth-moon transfer orbits are usually designed based on a circular restricted three-body model, an elliptical restricted three-body model, or a restricted four-body model. Although such analysis and design can obtain relatively simple theoretical results and can perform qualitative feature analysis, the force model is quite different from the actual force, and the spacecraft orbit near the libration point of the Earth-moon system is sensitive to initial values. In actual engineering calculations, the error of the calculation results cannot meet the precision requirements of the iterative initial values. Numerical integration based on high-precision force models can effectively improve the calculation precision, and intelligent algorithms can be used for search iteration to obtain high-precision calculation results in the global range. However, due to the sensitivity of the spacecraft orbit near the libration point to the initial values, such intelligent search algorithms often have slow convergence speed and long solution time, and the convergence reliability is difficult to guarantee. According to the current public information, there is still a lack of a design method for the orbit design problem of a spacecraft transferring from a DRO orbit to a given lunar landing point according to a given angle, which is suitable for engineering applications, has high calculation precision, and has fast and reliable iterative convergence. SUMMARY

[0004] Therefore, it is necessary to provide an orbit design method for a DRO orbit spacecraft to land on the moon according to a given angle and coordinates, which can adapt to different mission times and different DRO orbit sizes, has high calculation precision, and has fast and reliable iterative convergence.

[0005] An orbit design method for a DRO orbit spacecraft to land on the moon according to a given angle and coordinates, the method comprising:

[0006] Obtain the input parameters for orbit design; the input parameters for orbit design include the initial time of the DRO orbit, the initial position and velocity of the DRO orbit, the longitude of the landing point, the latitude of the landing point, and the landing velocity;

[0007] Based on the initial position and velocity of the DRO orbit, the position in the Earth-Moon L2 coordinate system at different times within a complete DRO cycle is output through numerical integration; a mapping between the lunar landing velocity and the position coordinates of the intersection point of the transfer orbit and the lunar orbit plane is constructed based on inverse integration;

[0008] Based on the mapping of the lunar landing velocity and the position coordinates of the intersection point of the transfer trajectory and the lunar orbit plane, and the position in the Earth-Moon L2 coordinate system at different times within a complete DRO cycle, a rough calculation is performed by inverse integration to obtain the lunar landing time, initial velocity magnitude, and transfer flight duration.

[0009] Using the lunar landing time, initial velocity magnitude, and transfer flight duration as initial values ​​for iteration and setting constraints, the inverse integration endpoint time, velocity at the inverse integration endpoint time, and inverse integration orbital flight duration are obtained through iterative inverse integration calculation.

[0010] Using the endpoint of the inverse integration as the initial value for the transfer orbit change timing iteration, the velocity at the endpoint of the inverse integration minus the velocity of the DRO spacecraft at the endpoint of the inverse integration is the initial value for the projection of the transfer orbit change velocity increment in the Earth-Moon L2 coordinate system. The inverse integration orbit flight duration is the initial value for the transfer flight duration iteration. Terminal constraints and integration termination conditions are set for forward integration precision calculation to obtain the transfer orbit change timing and the projection of the transfer orbit change velocity increment in the Earth-Moon L2 coordinate system.

[0011] The orbit design method of the DRO orbit vehicle according to the given angle and coordinate landing on the moon first takes the DRO orbit initial time, position and velocity, and the longitude and latitude of the landing point on the moon and the landing velocity as core parameters, without fixing the task time and the size limit of the DRO orbit, and then adaptively outputs the position of different DRO periods through numerical integration, which naturally has scene adaptability; in terms of accuracy, high-precision force models are used for numerical integration throughout the process, which not only accurately restores the position of the complete period of the DRO orbit, but also avoids the deviation of the simplified force model from the actual force, thereby ensuring the accuracy of the calculation results. In view of the initial value sensitivity and convergence difficulty, the multi-iteration strategy of rough calculation range determination and fine calculation interval reduction is used to break through, the wide speed range is traversed in the rough calculation stage, the position of the DRO period is combined, the landing time, the initial velocity and the transfer time close to the optimal solution are obtained, and high-quality initial values are provided for iteration; the rough calculation result is taken as the initial value in the fine calculation stage, the speed sampling range is narrowed, the interval is encrypted, and the correction direction is adjusted through the landing time deviation constraint and the terminal constraint, so as to avoid the slow convergence problem of the intelligent algorithm, and finally the rapid and stable convergence is realized. The multi-iteration method provided in the application can improve the adaptability of different working conditions while gradually improving the solving accuracy, and can realize reliable convergence for different initial conditions. The high-precision force model used can obtain high-precision calculation results, and the iterative solution is fast, reliable and stable, thereby solving the problems of low accuracy of the method based on the simplified force model and the insufficient convergence speed and stability of the intelligent search algorithm due to the initial value sensitivity of the problem itself. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 FIG. 1 is a flowchart of a DRO orbit vehicle orbit design method according to a given angle and coordinate landing on the moon in an embodiment. DETAILED DESCRIPTION

[0013] In order to make the purpose, technical scheme and advantages of the application more clear, the application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the application and not to limit the application.

[0014] In an embodiment, as shown in FIG. 1, a DRO orbit vehicle orbit design method according to a given angle and coordinate landing on the moon is provided, which comprises the following steps: Figure 1

[0015] Step 102, obtaining the input parameters of the orbit design; the input parameters of the orbit design include the DRO orbit initial time, the DRO orbit initial time position and velocity, the longitude of the landing point on the moon, the latitude of the landing point on the moon and the landing velocity.

[0016] ​The geolunar L2 coordinate system is defined as follows: the coordinate origin o is the L2 point of the geolunar system, the ox axis points to the moon from the earth, the oz axis is perpendicular to the ecliptic plane and points to the north celestial pole, and the oy axis forms a right-hand system. The falling moon velocity azimuth is defined as the angle between the projection of the falling moon velocity (in the geolunar L2 coordinate system) on the horizontal plane of the landing point and the north direction, and is calculated clockwise from the north direction. The falling moon velocity elevation is defined as the angle between the falling moon velocity (in the geolunar L2 coordinate system) and the horizontal plane of the landing point, and is calculated from the horizontal plane, with a positive value below the horizontal plane. The phase angle is defined as the angle between the projection of the direction of the moon center pointing to the spacecraft in the ecliptic plane and the direction of the earth center pointing to the moon center, and is calculated clockwise from the direction of the earth center pointing to the moon center in the north celestial sphere.

[0017] The orbit design input parameters include DRO orbit initial time, DRO orbit initial time position and velocity parameters, falling moon point longitude, falling moon point latitude, falling moon velocity azimuth, and falling moon velocity elevation.

[0018] In step 104, the position coordinates in the geolunar L2 coordinate system at different times within a complete DRO period are output by numerical integration according to the DRO orbit initial time position and velocity; and the mapping of the falling moon velocity and the position coordinates of the intersection of the transfer orbit and the ecliptic plane is constructed based on reverse integration.

[0019] According to the given DRO orbit spacecraft initial time position and velocity, the position coordinates in the geolunar L2 coordinate system at different times within a complete DRO period are output by numerical integration, and the output data step is 60 seconds. Taking the given falling moon point (described by the falling moon point longitude and latitude) as the initial position and the opposite direction of the given falling moon velocity direction (described by the falling moon azimuth and elevation) as the initial velocity direction, for any falling moon velocity, the reverse integration is first performed for 1 day, and then the reverse integration is continued until the orbit intersects with the ecliptic plane, to obtain the geolunar L2 coordinate position coordinates of the intersection point, thereby establishing the mapping of the falling moon velocity and the position coordinates of the intersection of the transfer orbit and the ecliptic plane. If the orbit does not intersect with the ecliptic plane after 30 days of reverse integration, the integration is terminated, and the integration end position replaces the intersection position.

[0020] In step 106, the falling moon time, initial velocity, and transfer flight time are obtained by reverse integration calculation according to the mapping of the falling moon velocity and the position coordinates of the intersection of the transfer orbit and the ecliptic plane and the position in the geolunar L2 coordinate system at different times within a complete DRO period.

[0021] Let the initial time be , and let be the falling moon time (in days, relative to the number of days as the time value). Take 20 days as the iteration initial value of the moon-falling time, take the given moon-falling point as the initial position, take the opposite direction of the given moon-falling direction as the initial speed direction, and traverse the initial speed size in the range of 2320 m / s to 2500 m / s at a sampling interval of 1 m / s. After one day of reverse integration, continue to integrate until the orbit intersects with the moon-falling plane or the integration is terminated, to obtain the position coordinates of the moon-falling plane in the L2 coordinate system at the integration end point.

[0022] For each sampling point corresponding to the integration end point position, calculate the relative distance between the end point position and the position of the DRO vehicle in the Earth's gravitational field within one orbit period, and find the minimum value of the relative distance. The initial speed size corresponding to the minimum value of the relative distance is denoted as . The reverse integration time length can be obtained from the reverse integration orbit corresponding to the minimum value of the relative distance, and the time length is the transfer flight time length (in days) denoted as . The reverse integration end point position can be obtained from the reverse integration orbit corresponding to the minimum value of the relative distance, and the phase angle corresponding to the position in the L2 coordinate system can be calculated from the coordinates of the position in the L2 coordinate system, and the phase angle is denoted as . According to the position coordinates of the DRO vehicle in the Earth's gravitational field at different times within one period in the L2 coordinate system, the phase angles corresponding to the times (in days) can be calculated. The phase angle corresponding to the time (in days) is denoted as The time (in days) at which the phase angle of the DRO vehicle is equal to can be obtained by interpolation, and the time is denoted as . The new calculated value of the moon-falling time (in days) is denoted as , and the deviation between the new calculated value and the original value is calculated. When the deviation is greater than 0.1 days, the new calculated value of the moon-falling time is used instead of the original value, and the above calculation process is repeated until the deviation is less than 0.1 days. From the second iteration calculation, the value range and sampling interval of the initial speed size are changed to , and the sampling interval is 0.2 m / s.

[0023] The integration based on the initial position and speed of the DRO can accurately restore the complete period of the orbit position, providing a reliable reference for subsequent matching. The reverse integration coarse calculation and fine calculation, as well as the forward integration fine calculation, are all based on high-precision force models, which avoids the deviation between the simplified force model and the actual force, and fundamentally improves the accuracy of the calculation results.

[0024] In step 108, the moon-falling time, the initial speed size, and the transfer flight time length are used as the iteration initial values and the constraint conditions are set to obtain the reverse integration end point time, the speed at the reverse integration end point time, and the reverse integration orbit flight time length through iterative reverse integration fine calculation.

[0025] Using the lunar landing time, initial velocity magnitude, and transfer flight duration as initial values ​​for iteration, and with the following three constraints—the relative positions of the reverse integral spacecraft and the DRO spacecraft along the track direction being zero at the endpoint of the reverse integration, the radial relative positions of the reverse integral spacecraft and the DRO spacecraft being zero at the endpoint of the reverse integration, and the normal relative positions of the reverse integral spacecraft and the DRO spacecraft being zero at the endpoint of the reverse integration—the reverse integral trajectory is further calculated iteratively. The endpoint of the reverse integration is equal to the lunar landing time minus the transfer flight duration.

[0026] Step 110: Using the endpoint of the inverse integration as the initial value for the transfer orbit change time iteration, the velocity at the endpoint of the inverse integration minus the velocity of the DRO spacecraft at the endpoint of the inverse integration is the initial value for the projection of the transfer orbit change velocity increment in the Earth-Moon L2 coordinate system, and the inverse integration orbit flight duration is the initial value for the transfer flight duration iteration. Set terminal constraints and integration termination conditions to perform forward integration precision calculation, and obtain the transfer orbit change time and the projection of the transfer orbit change velocity increment in the Earth-Moon L2 coordinate system.

[0027] Forward integration is employed. The parameters to be solved and the constraints are as follows, including the parameters to be solved: the transfer orbit change time, the projection of the transfer orbit change velocity increment in the Earth-Moon L2 coordinate system (x), the projection of the transfer orbit change velocity increment in the Earth-Moon L2 coordinate system (y), and the projection of the transfer orbit change velocity increment in the Earth-Moon L2 coordinate system (z). Terminal constraints: the longitude, latitude, azimuth, elevation angle, and lunar altitude at the integration endpoint are all given values. The integration termination conditions include the lunar landing time (transfer orbit change time + transfer flight duration) and a lunar altitude of zero. When the lunar elevation angle is 90°, the constraint on the azimuth angle must be removed; when the latitude of the landing point is 90°, the constraints on the longitude and azimuth angle must be removed.

[0028] In the rough calculation stage of the inverse integration, this application first traverses a relatively wide speed range (2320m / s~2500m / s), and finds the one with the smallest relative distance by combining the DRO period position. The lunar landing time and transfer duration are used to provide initial values ​​close to the optimal solution for subsequent iterations, avoiding the slow convergence problem caused by random initial values ​​in intelligent algorithms; after entering the fine calculation stage, both inverse integration and forward integration are based on the rough calculation results as initial values, and the velocity sampling range is reduced from the second iteration onwards. ~ The encryption interval further reduces the deviation between the initial value and the optimal solution. At the same time, by setting constraints such as the lunar landing time deviation < 0.1 days, terminal constraints, and integration termination conditions, the iteration direction is continuously corrected to ensure that each iteration approaches the optimal solution, and finally achieves fast and stable convergence, effectively solving the convergence reliability problem caused by the sensitivity of the initial value of the orbit near the translation point.

[0029] The aforementioned DRO orbiter's lunar landing trajectory design method, based on a given angle and coordinates, first uses the initial DRO trajectory time, position velocity, lunar landing point latitude and longitude, and landing velocity as core parameters. It does not impose fixed mission time or DRO trajectory size limitations. Subsequently, it adaptively outputs different DRO cycle positions through numerical integration, naturally possessing scenario adaptability. In terms of accuracy, it employs a high-precision force model for numerical integration throughout the process, accurately reproducing the complete DRO cycle trajectory position while avoiding deviations between simplified force models and actual forces, ensuring the accuracy of the calculation results. To address the challenges of initial value sensitivity and convergence, this paper proposes a multi-round iterative strategy that combines coarse calculation to define the range and fine calculation to narrow the interval. In the coarse calculation stage, a wide velocity range is traversed in conjunction with the DRO cycle position to obtain near-optimal lunar landing time, initial velocity, and transition time, providing high-quality initial values ​​for iteration. In the fine calculation stage, the coarse calculation results are used as initial values ​​to narrow the velocity sampling range and increase the interval. The direction is corrected through lunar landing time deviation constraints and terminal constraints to avoid the slow convergence problem of intelligent algorithms, ultimately achieving fast and stable convergence. The multi-round iterative method presented in this application significantly improves adaptability to different working conditions while progressively increasing solution accuracy. It can achieve reliable convergence under different initial conditions. Furthermore, the high-precision force model used yields high-precision calculation results, and the iterative solution is fast and the convergence is reliable and stable. This solves the problems of low accuracy in previous methods based on simplified force models and insufficient convergence speed and stability of intelligent search algorithms due to the initial value sensitivity of the problem itself.

[0030] In one embodiment, the mapping between the lunar landing velocity and the position coordinates of the intersection point of the transfer orbit and the lunar orbit plane is constructed based on inverse integration, including:

[0031] Using the latitude and longitude of the given lunar landing point as the initial position and the opposite direction of the given lunar landing velocity as the initial velocity direction, for any magnitude of the lunar landing velocity, based on the initial position and initial velocity direction, first integrate backwards for 1 day, and then continue to integrate backwards until the orbit intersects with the ecliptic plane, obtaining the Earth-Moon L2 coordinates of the intersection point, thus establishing a mapping between the lunar landing velocity and the position coordinates of the intersection point of the transfer orbit and the ecliptic plane. If the orbit still does not intersect with the ecliptic plane after 30 days of backward integration, the integration terminates, and the position of the integration endpoint replaces the position of the intersection point.

[0032] In one embodiment, a rough inverse integral orbit calculation is performed based on the mapping of the lunar landing velocity and the position coordinates of the intersection point of the transfer orbit and the lunar orbit plane, and the position in the Earth-Moon L2 coordinate system at different times within a complete DRO cycle, to obtain the lunar landing time, initial velocity magnitude, and transfer flight duration, including:

[0033] Set the basic time setting and the velocity traversal and integration rules for the first iteration, and obtain the Earth-Moon L2 coordinate system position of the integration endpoint, i.e., the integration endpoint position;

[0034] The integral end position corresponding to each sampling point is obtained based on the mapping of the falling moon speed and the position coordinates of the intersection point of the transfer orbit and the white orbit plane, the relative distance between the integral end position and the position in the lunar L2 coordinate system at different time within a complete DRO period is calculated, and the initial speed size and the transfer flight time are determined according to the relative distance;

[0035] The phase angle corresponding to the point is calculated according to the reverse integral orbit corresponding to the minimum value of the relative distance, the phase angle at each time is calculated according to the position in the lunar L2 coordinate system at different time within a complete DRO period, and the time when the DRO phase is equal to the phase angle corresponding to the minimum value of the relative distance is found through interpolation.

[0036] The falling moon time is calculated by using the time when the DRO phase is equal to the phase angle corresponding to the minimum value of the relative distance and the transfer flight time.

[0037] In one of the embodiments, the base time setting and the speed traversal and integral rule of the first iteration are set to obtain the lunar L2 coordinate system position of the integral end point, including:

[0038] The initial time is set as , The falling moon time is set as t0, the falling moon time iteration initial value is set as t0, the given falling moon point is set as the initial position, the opposite direction of the given falling moon direction is set as the initial speed direction, the initial speed size is set to traverse in the pre-set speed range according to the sampling interval of 1 m / s, the reverse integral is continued to the integral end point after 1 day, and the integral end point position coordinates in the lunar L2 coordinate system are obtained.

[0039] In one of the embodiments, the transfer flight time is determined according to the relative distance, including:

[0040] The minimum value is found from all the relative distances, the initial speed size corresponding to the minimum value is recorded as ;

[0041] The reverse integral time is obtained from the reverse integral orbit corresponding to the minimum value of the relative distance, and the reverse integral time is the transfer flight time recorded as .

[0042] In one of the embodiments, the phase angle corresponding to the point is calculated according to the reverse integral orbit corresponding to the minimum value of the relative distance, the phase angle at each time is calculated according to the position in the lunar L2 coordinate system at different time within a complete DRO period, and the time when the DRO phase is equal to the phase angle corresponding to the minimum value of the relative distance is found through interpolation.

[0043] The reverse integral end position is obtained from the reverse integral orbit corresponding to the minimum value of the relative distance, and the phase angle corresponding to the point is calculated according to the position in the lunar L2 coordinate system of the position, recorded as ;

[0044] According to the position in the L2 coordinate system at different time points in a complete DRO period, the phase angle corresponding to each time point is calculated; and By interpolation, the time point at which the phase of the DRO spacecraft is equal to is obtained, denoted as .

[0045] In one of the embodiments, the time point of the moon landing is calculated by using the time point at which the DRO phase is equal to the phase angle corresponding to the minimum relative distance and the transfer flight time, comprising:

[0046] The new calculated value of the moon landing time is , and the deviation between the new calculated value and the original value is calculated. When the deviation is greater than 0.1 day, the original value is replaced by the new calculated value of the moon landing time, and the above calculation process is repeated until the deviation is less than 0.1 day; wherein, from the second iteration calculation, the value range and sampling interval of the initial speed are changed to ~ , and the sampling interval is 0.2 m / s.

[0047] In one of the embodiments, the constraint conditions include that the relative position of the reverse integration spacecraft to the DRO spacecraft along the trace is zero at the reverse integration end point time, the relative position of the reverse integration spacecraft to the DRO spacecraft in the radial direction is zero at the reverse integration end point time, and the relative position of the reverse integration spacecraft to the DRO spacecraft in the normal direction is zero at the reverse integration end point time; wherein, the reverse integration end point time is equal to the moon landing time minus the transfer flight time.

[0048] In one of the embodiments, the terminal constraints include that the integral end point longitude is equal to a given value, the integral end point latitude is equal to a given value, the integral end point speed azimuth angle is equal to a given value, the integral end point speed elevation angle is equal to a given value, and the integral end point lunar surface height is zero.

[0049] In one of the embodiments, the integral termination conditions include the moon landing time and the lunar surface height being zero.

[0050] In specific embodiments, during the integration process, the moon landing time is equal to the transfer orbit time plus the transfer flight time, and the value of the above two quantities is directly added to obtain the moon landing time. Both quantities are to-be-solved parameters, and the initial values of the iteration have been described. The numerical value in the iteration process will also be constantly corrected and changed, and the moon landing time value will change accordingly.

[0051] It should be understood that, although each step in the flowchart of Figure 1 is displayed in sequence according to the arrow indication, these steps are not necessarily executed in the order indicated by the arrow. Unless explicitly stated in this article, the execution of these steps has no strict order limitation, and these steps can be executed in other orders. Moreover,Figure 1 At least one of the steps in the above embodiments can include a plurality of sub-steps or a plurality of stages, which are not necessarily performed at the same time, but can be performed at different times, and the order of the execution of the sub-steps or stages is not necessarily sequential, but can be performed in rotation or alternation with other steps or at least a part of the sub-steps or stages of other steps.

[0052] The technical features of the above embodiments can be combined in any manner. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described, however, as long as the combinations of the technical features do not contradict each other, they should be considered to be within the scope of the present disclosure.

[0053] The above embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the application. It should be pointed out that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A method for designing the lunar orbit of a DRO orbiter at a given angle and coordinates, characterized in that, The method includes: Obtain the input parameters for the orbit design; the input parameters for the orbit design include the initial time of the DRO orbit, the initial position and velocity of the DRO orbit, the longitude of the landing point, the latitude of the landing point, and the landing velocity. Based on the initial position and velocity of the DRO orbit, the position in the Earth-Moon L2 coordinate system at different times within a complete DRO cycle is output through numerical integration; a mapping between the lunar landing velocity and the position coordinates of the intersection point of the transfer orbit and the lunar orbit plane is constructed based on inverse integration; Based on the mapping of the lunar landing velocity and the position coordinates of the intersection point of the transfer trajectory and the lunar orbit plane, and the position in the Earth-Moon L2 coordinate system at different times within a complete DRO cycle, a rough calculation is performed by inverse integration to obtain the lunar landing time, initial velocity magnitude, and transfer flight duration. Using the lunar landing time, initial velocity magnitude, and transfer flight duration as initial values ​​for iteration and setting constraints, the inverse integration endpoint time, velocity at the inverse integration endpoint time, and inverse integration orbital flight duration are obtained through iterative inverse integration calculation. Using the endpoint of the inverse integration as the initial value for the transfer orbit change timing iteration, the velocity at the endpoint of the inverse integration minus the velocity of the DRO spacecraft at the endpoint of the inverse integration is the initial value for the projection of the transfer orbit change velocity increment in the Earth-Moon L2 coordinate system. The inverse integration orbit flight duration is the initial value for the transfer flight duration iteration. Terminal constraints and integration termination conditions are set for forward integration precision calculation to obtain the transfer orbit change timing and the projection of the transfer orbit change velocity increment in the Earth-Moon L2 coordinate system.

2. The method according to claim 1, characterized in that, The mapping between the lunar landing velocity and the position coordinates of the intersection point of the transfer orbit and the lunar orbit plane is constructed based on inverse integration, including: Using the latitude and longitude of the given lunar landing point as the initial position and the opposite direction of the given lunar landing velocity as the initial velocity direction, for any magnitude of the lunar landing velocity based on the initial position and initial velocity direction, first integrate backwards for 1 day, and then continue to integrate backwards until the orbit intersects with the lunar orbit plane, obtaining the Earth-Moon L2 coordinates of the intersection point, thus establishing a mapping between the lunar landing velocity and the position coordinates of the intersection point of the transfer orbit and the lunar orbit plane. If the orbit still does not intersect with the lunar orbit plane after 30 days of backward integration, the integration terminates, and the position of the integration endpoint replaces the position of the intersection point.

3. The method according to claim 1, characterized in that, Based on the mapping of the lunar landing velocity and the position coordinates of the intersection point of the transfer trajectory and the lunar orbit plane, and the position in the Earth-Moon L2 coordinate system at different times within a complete DRO cycle, a rough calculation of the trajectory is performed using inverse integration to obtain the lunar landing time, initial velocity magnitude, and transfer flight duration, including: Set the basic time setting and the velocity traversal and integration rules for the first iteration, and obtain the Earth-Moon L2 coordinate system position of the integration endpoint, i.e., the integration endpoint position; The integral endpoint position corresponding to each sampling point is obtained by mapping the lunar landing velocity and the position coordinates of the intersection of the transfer trajectory and the lunar orbit plane. The relative distance between the integral endpoint position and the position in the Earth-Moon L2 coordinate system at different times within a complete DRO cycle is calculated. The initial velocity magnitude and transfer flight duration are determined based on the relative distance. The phase angle corresponding to the point on the inverse integral orbit is calculated based on the inverse integral orbit corresponding to the minimum relative distance. The phase angle at each moment is calculated based on the position in the Earth-Moon L2 coordinate system at different moments within a complete DRO cycle. The moment when the DRO phase is equal to the phase angle corresponding to the minimum relative distance is found by interpolation. The lunar landing time is calculated using the moment when the DRO phase equals the phase angle corresponding to the minimum relative distance and the transfer flight duration.

4. The method according to claim 3, characterized in that, Set the basic time settings and the velocity traversal and integration rules for the first iteration, and obtain the Earth-Moon L2 coordinate system position of the integration endpoint, including: Let the initial time be , The landing time is set, and 20 days is used as the initial value for the landing time iteration. The given landing point is used as the initial position, and the opposite direction of the given landing direction is used as the initial velocity direction. The initial velocity magnitude is traversed within the pre-set velocity range at a sampling interval of 1 m / s. After inverse integration for 1 day, integration continues until the orbit intersects with the lunar orbit plane or the integration terminates, and the Earth-Moon L2 coordinates of the integration endpoint are obtained.

5. The method according to claim 3, characterized in that, Determining the transfer flight duration based on the relative distance includes: Find the minimum value among all relative distances; the initial velocity corresponding to this minimum value is denoted as . ; The inverse integration time is obtained from the inverse integration trajectory corresponding to the minimum relative distance. This inverse integration time is the transfer flight time, denoted as [missing information]. .

6. The method according to claim 5, characterized in that, The phase angle corresponding to the point on the inverse integral orbit is calculated based on the inverse integral orbit corresponding to the minimum relative distance. The phase angle at each moment is calculated based on the position in the Earth-Moon L2 coordinate system at different times within a complete DRO cycle, and the moment when the DRO phase equals the phase angle corresponding to the minimum relative distance is found through interpolation. This includes: The position of the inverse integration endpoint is obtained from the inverse integration trajectory corresponding to the minimum relative distance. The phase angle corresponding to the endpoint is calculated from the position of the inverse integration endpoint in the Earth-Moon L2 coordinate system, denoted as [equation missing]. ; Calculate the phase angle at each moment based on the Earth-Moon L2 coordinate system position at different times within a complete DRO cycle; By interpolation, the phase of the DRO spacecraft is obtained as equal to... The moment is recorded as .

7. The method according to claim 6, characterized in that, The lunar landing time is calculated using the moment when the DRO phase equals the phase angle corresponding to the minimum relative distance and the transfer flight duration, including: use This is the new calculated value at the moment of lunar landing. The deviation between the new calculated value and the original value is calculated. When the deviation is greater than 0.1 days, the new calculated value at the moment of lunar landing replaces the original value, and the above calculation process is repeated until the deviation is less than 0.1 days. Starting from the second iteration, the range of initial velocity magnitude and the sampling interval are changed to... ~ .

8. The method according to claim 1, characterized in that, The constraints include the following: at the end of the reverse integration, the relative position of the reverse integrator and the DRO along the track is zero; at the end of the reverse integration, the relative position of the reverse integrator and the DRO radially is zero; and at the end of the reverse integration, the relative position of the reverse integrator and the DRO normal is zero. The end of the reverse integration is equal to the lunar landing time minus the transfer flight duration.

9. The method according to claim 1, characterized in that, The terminal constraints include the integration endpoint longitude being equal to a given value, the integration endpoint latitude being equal to a given value, the integration endpoint velocity azimuth being equal to a given value, the integration endpoint velocity elevation angle being equal to a given value, and the integration endpoint lunar altitude being zero.

10. The method according to claim 1, characterized in that, The integration termination conditions include the moment of lunar landing and the lunar altitude being zero.

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