Design method for transfer orbit of HALO orbiter to fly over a given ground point

Abstract

The present application relates to a method for designing a transfer orbit for a HALO orbiter to fly over a given ground point. The method includes: finding the moment when the lunar declination value is equal to the latitude value of the given ground point within the given mission time range, and selecting the time point closest to the initial moment as the initial value of the iteration for the orbit transfer moment; calculating the flight duration of the orbit transfer point relative to the starting point using the starting time and the initial value of the iteration for the orbit transfer moment; calculating the normalized time by dividing the flight duration by the HALO orbit period; calculating the magnitude of the orbit transfer velocity increment based on the normalized time using the polynomial fitting coefficients; establishing a mapping relationship between the magnitude of the orbit transfer velocity increment and the initial value of the iteration for the orbit transfer moment through numerical integration based on a high-precision force model; and completing the solution of the parameter to be solved using the Newton iteration method based on the mapping relationship. The method adopted has a short response time, high calculation result accuracy, and fast iteration convergence.

Description

Technical Field

[0001] This application relates to the technical field of orbit design, and particularly to a method for designing a transfer orbit for a HALO orbit vehicle to fly over a given ground point. Background Art

[0002] The HALO orbit at the Earth-Moon L2 point is a periodic orbit at the collinear libration point L2 of the Earth-Moon system under the assumption of the circular restricted three-body model. In practical problems, although the force acting on the HALO orbit vehicle 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 through control with very small energy consumption. Therefore, it has unique application value in the exploration applications in the Earth-Moon space and the deep space far from the Moon.

[0003] The Earth-Moon space transfer orbit is usually designed based on the circular restricted three-body model, the elliptical restricted three-body model, or the restricted four-body model. Although such analysis and design can obtain relatively simple theoretical results and can also conduct qualitative characteristic analysis, due to the large difference between the force model and the actual force situation, and the sensitivity of the spacecraft orbit near the libration point of the Earth-Moon system to the initial value, in actual engineering calculations, the error of the calculation result often cannot meet the accuracy requirement of the iterative initial value. Adopting a numerical integration method based on a high-precision force model can effectively improve the calculation accuracy. By performing search iteration through an intelligent algorithm, high-precision calculation results within the global range can be obtained. However, due to the sensitivity of the spacecraft orbit near the libration point to the initial value, such intelligent search algorithms often have a slow convergence speed and a long solution time, and it is difficult to guarantee the convergence reliability. In addition, the traditional Earth-Moon system transfer orbit is usually designed based on the invariant manifold of the HALO orbit at the libration point. Although the energy consumption is low, due to the long transfer flight time, it is not suitable for the rapid response requirement in the near-Earth support application in the Earth-Moon space. From the currently available public information, for the problem of designing an orbit for a HALO orbit vehicle at the Moon's L2 point to fly over a given ground point, there is still a lack of a design method suitable for engineering applications, which does not pursue the optimal energy consumption but requires a short response time, high calculation result accuracy, and fast and reliable iterative convergence. Summary of the Invention

[0004] Based on this, in view of the above technical problems, it is necessary to provide a method for designing a transfer orbit for a HALO orbit vehicle to fly over a given ground point, which has a short response time, high calculation result accuracy, and fast iterative convergence.

[0005] A method for designing a transfer orbit for a HALO orbit vehicle to fly over a given ground point, the method comprising:

[0006] Obtain relevant information of the HALO orbiter; the relevant information includes the initial position, initial velocity, ground point longitude, latitude altitude, and flyby altitude; calculate the starting time of the orbiter based on the relevant information;

[0007] Find the moment when the lunar declination value is equal to the given ground point latitude value within the given mission time range, and select the time point closest to the initial moment as the initial value of the orbit transfer moment iteration;

[0008] Calculate the flight duration of the orbit transfer point relative to the starting point using the starting time and the initial value of the orbit transfer moment iteration; calculate the normalized time by dividing the flight duration by the HALO orbit period;

[0009] Calculate the magnitude of the orbit transfer velocity increment based on the normalized time according to the polynomial fitting coefficients; establish the mapping relationship between the magnitude of the orbit transfer velocity increment and the initial value of the orbit transfer moment iteration through numerical integration based on the high-precision force model;

[0010] Complete the solution of the parameter to be solved using the Newton iteration method based on the mapping relationship.

[0011] The above transfer orbit design method for the HALO orbiter to fly over a given ground point. First, in terms of obtaining high-precision calculation results, this application is based on a high-precision force model and uses numerical integration to establish a mapping relationship between the orbit transfer velocity increment and the initial iteration value of the orbit transfer time. Different from the traditional method that relies on a simplified force model, the high-precision force model can accurately reflect the actual force on the aircraft, avoiding calculation errors caused by the distortion of the force model and laying a foundation for accurate calculation. In terms of rapid convergence and stability, by searching for the moment when the lunar declination matches the latitude of the ground point within the mission time and selecting the point closest to the initial moment as the initial iteration value of the orbit transfer time. The correlation between the lunar declination and the latitude of the ground point is fully utilized to set an initial value closer to the true solution for the iteration, greatly reducing the search range, overcoming the drawback of blind search in traditional intelligent search algorithms, and improving the convergence speed and stability. Secondly, normalized time is introduced, and the flight duration at the orbit transfer point is divided by the HALO orbit period. This operation unifies the time scale, facilitating the calculation of the orbit transfer velocity increment in combination with the polynomial fitting coefficients, making the calculation process more stable and creating conditions for the efficient convergence of the iteration. Finally, the Newton iteration method is used to solve the parameters to be solved. Based on the established mapping relationship, it can quickly approach the optimal solution, further ensuring the rapidity and stability of the iteration. In terms of response time, this application breaks through the limitations of the traditional design based on the invariant manifold of the libration point HALO orbit. Although the traditional design has low energy consumption, the transfer flight time is long and it is difficult to meet the requirements of rapid response. However, this application does not overly pursue the optimal energy consumption, focuses on rapid response, and by virtue of reasonable selection of the initial iteration value and efficient iteration algorithm, greatly shortens the response time from the HALO orbit to over the given ground point. Through the optimization of the force model, the initial iteration value, the calculation process, and the algorithm, this application effectively solves the problems existing in the traditional orbit design method and achieves the goals of short response time, high precision of calculation results, and rapid, reliable iteration convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a schematic flowchart of a transfer orbit design method for a HALO orbiter to fly over a given ground point in an embodiment;

[0013] Figure 2 It is an internal structure diagram of a computer device in an embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0014] In order to make the objectives, technical solutions, and advantages of this application clearer, the following further elaborates on this application in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not used to limit this application.

[0015] In one embodiment, as Figure 1As shown, a method for designing a transfer orbit for a HALO orbiter to fly over a given ground point is provided, including the following steps:

[0016] Step 102, obtain relevant information of the HALO orbiter; the relevant information includes the initial position, initial velocity, longitude of the ground point, latitude altitude, and flyover altitude; calculate the starting time of the aircraft based on the relevant information.

[0017] Define the L2 coordinate system as: the coordinate origin is the L2 point of the Earth-Moon system, the axis is in the direction from the Earth's center to the Moon's center, the axis is perpendicular to the lunar orbit plane and points to the north celestial pole direction, and the axis forms a right-handed system. Define the normalized time as: the starting point is the point closest to the Earth, and the flight duration starting from the starting point, divided by the HALO orbit period. Given the parameters, the initial time , the initial position and velocity of the HALO orbiter, the longitude of the ground point , the latitude altitude , and the flyover altitude . According to the position and velocity of the HALO orbiter at the initial time, perform reverse numerical integration to the starting point to obtain the time (in ephemeris days) when the aircraft is at the starting point, denoted as .

[0018] Step 104, find the moment when the lunar declination value is equal to the given ground point latitude value according to the lunar declination value within the given mission time range, and select the time point closest to the initial time as the initial value for the iteration of the orbit transfer moment.

[0019] According to the lunar declination value (calculated according to the lunar ephemeris) within the given mission time range, find the moment when the lunar declination value is equal to the given ground point latitude value, and select the time point closest to the initial time as the initial value for the iteration of the orbit transfer moment .

[0020] Find the moment when the lunar declination value is equal to the given ground point latitude value according to the lunar declination value within the given mission time range, and select the time point closest to the initial time as the initial value for the iteration of the orbit transfer moment. This selection method utilizes the relationship between the lunar declination and the ground point latitude, combines the actual situation of the mission, provides an initial value relatively close to the true solution for the iteration, narrows the search range, and avoids the blind search of traditional intelligent search algorithms in the global range, thereby improving the convergence speed and stability.

[0021] Step 106, calculate the flight duration of the orbit transfer point relative to the starting point using the starting time and the initial value of the iteration of the orbit transfer moment; calculate the normalized time by dividing the flight duration by the HALO orbit period.

[0022] According to the initial value of the orbit transfer time iteration and the starting time , calculate the flight duration of the orbit transfer point relative to the starting point by taking the difference (in units of epoch days), that is:

[0023] ;

[0024] Denote the HALO orbit period as , divide by the orbit period as the unit to calculate the normalized time, denoted as , that is:

[0025] .

[0026] By calculating the flight duration of the orbit transfer point relative to the starting point, and taking the quotient according to the flight duration and the HALO orbit period to obtain the normalized time. The normalized time unifies different time scales into a relatively fixed range, which is convenient for subsequent calculation of the magnitude of the orbit transfer velocity increment using polynomial fitting coefficients, making the calculation process more stable and orderly, and helping to improve the efficiency and convergence of the iteration.

[0027] Step 108, calculate the magnitude of the orbit transfer velocity increment according to the polynomial fitting coefficients for the normalized time; establish the mapping relationship between the magnitude of the orbit transfer velocity increment and the initial value of the orbit transfer time iteration based on the high-precision force model through numerical integration; complete the solution of the parameters to be solved using the Newton iteration method based on the mapping relationship.

[0028] The azimuth angle of the orbit transfer velocity increment is defined as: the angle between the projection vector of the orbit transfer velocity increment vector on the lunar orbit plane and the axis direction of the L2 coordinate system (the counterclockwise direction is positive (the azimuth angle rate of change vector is in the same direction as the axis of the L2 coordinate system)). The elevation angle of the orbit transfer velocity increment is defined as: the angle between the orbit transfer velocity increment vector and the lunar orbit plane.

[0029] Calculate the magnitude of the orbit transfer velocity increment according to the following formula The initial value of the iteration is:

[0030] ;

[0031] Among them, the values of the coefficients , , , , , can be obtained by interpolating the polynomial fitting coefficients in Table 1 according to the flyby altitude of the ground point.

[0032] Table 1

[0033]

[0034] The parameters to be solved include the transfer orbit-changing time as , the azimuth angle of the transfer orbit-changing velocity increment , and the magnitude of the transfer orbit-changing velocity increment . The initial value of the iteration of the azimuth angle of the orbit-changing velocity increment is selected as 270°.

[0035] Based on the high-precision force model, the following mapping relationship can be established through numerical integration:

[0036] ;

[0037] According to the initial values of the parameters to be solved calculated, the Newton iteration method is used to complete the solution of the parameters to be solved.

[0038] For the above-mentioned transfer orbit design method of the HALO orbiter flying over a given ground point, firstly, in terms of obtaining high-precision calculation results, this application is based on a high-precision force model and uses numerical integration to establish a mapping relationship between the orbit-changing velocity increment and the initial values of the iteration of the orbit-changing time. Different from the traditional method that relies on a simplified force model, the high-precision force model can accurately reflect the actual force on the aircraft, avoid calculation errors caused by the distortion of the force model, and lay a foundation for accurate calculation. In terms of the rapidity and stability of convergence, by searching for the moment when the lunar declination matches the latitude of the ground point within the mission time and selecting the point closest to the initial moment as the initial value of the iteration of the orbit-changing time. The correlation between the lunar declination and the latitude of the ground point is fully utilized to set an initial value closer to the true solution for the iteration, greatly narrowing the search range, overcoming the drawback of blind search of the traditional intelligent search algorithm, and improving the convergence speed and stability. Secondly, the normalized time is introduced, and the flight duration at the orbit-changing point is divided by the HALO orbit period. This operation unifies the time scale, facilitates the calculation of the orbit-changing velocity increment in combination with the polynomial fitting coefficient, makes the calculation process more stable, and creates conditions for the efficient convergence of the iteration. Finally, the Newton iteration method is used to solve the parameters to be solved. Based on the established mapping relationship, the optimal solution can be quickly approximated, further ensuring the rapidity and stability of the iteration. In terms of response time, this application breaks through the limitations of the traditional design based on the invariant manifold of the libration point HALO orbit. Although the traditional design has low energy consumption, the transfer flight time is long and it is difficult to meet the requirements of rapid response. However, this application does not overly pursue the optimal energy consumption, focuses on rapid response, and significantly shortens the response time from the HALO orbit to above the given ground point by virtue of reasonable selection of the initial value of the iteration and an efficient iteration algorithm. Through the optimization of the force model, the initial value of the iteration, the calculation process, and the algorithm, this application effectively solves the problems existing in the traditional orbit design method, achieving the goals of short response time, high accuracy of calculation results, and rapid and reliable iteration convergence.

[0039] In one embodiment, calculating the starting time of the aircraft according to relevant information includes:

[0040] Integrating numerically backward from the initial position and initial velocity of the HALO orbiter to the starting point to obtain the starting time of the aircraft.

[0041] In one embodiment, the lunar declination value within a given mission time range is calculated according to the lunar ephemeris.

[0042] In one embodiment, calculating the flight duration of the orbit transfer point relative to the starting point using the starting time and the initial iteration value of the orbit transfer time includes:

[0043] The flight duration of the orbit transfer point relative to the starting point calculated using the starting time and the initial iteration value of the orbit transfer time is:

[0044] ;

[0045] Wherein, represents the initial iteration value of the orbit transfer time, represents the starting time.

[0046] In one embodiment, calculating the normalized time by dividing the flight duration by the HALO orbit period includes:

[0047] The normalized time calculated by dividing the flight duration by the HALO orbit period is:

[0048] ;

[0049] Wherein, represents the flight duration, represents the HALO orbit period.

[0050] In one embodiment, calculating the magnitude of the orbit transfer velocity increment based on the normalized time using polynomial fitting coefficients includes:

[0051] The magnitude of the orbit transfer velocity increment calculated based on the normalized time using polynomial fitting coefficients is:

[0052] ;

[0053] Wherein, the coefficients , , , , , are obtained by interpolating the polynomial fitting coefficients according to the flyby altitude of the ground point, represents the normalized time.

[0054] In one embodiment, a mapping relationship between the magnitude of the orbit transfer velocity increment and the initial iteration value of the orbit transfer time is established through numerical integration based on a high-precision force model, including:

[0055] The mapping relationship between the magnitude of the orbit transfer velocity increment and the initial iteration value of the orbit transfer time established through numerical integration based on a high-precision force model is:

[0056] ;

[0057] Among them, the perigee altitude, perigee latitude, and perigee longitude are given in advance.

[0058] It should be understood that although Figure 1 the steps in the flowchart of Figure 1 are shown in sequence according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise clearly stated in this article, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover,

[0059] In one embodiment, a computer device is provided. This computer device can be a terminal, and its internal structure diagram can be as Figure 2 shown. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, it realizes a method for designing a transfer orbit for a HALO orbiter to fly over a given ground point. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen. The input device of the computer device can be a touch layer covering the display screen, or a button, trackball, or touchpad set on the shell of the computer device, or an external keyboard, touchpad, or mouse, etc.

[0060] Those skilled in the art can understand that Figure 2The structure shown is only a block diagram of some structures related to the solution of this application, and does not constitute a limitation on the computer device to which the solution of this application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0061] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the various embodiments provided in this application can include non-volatile and / or volatile memories. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0062] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered to be within the scope described in this specification.

[0063] The above-described embodiments merely represent several implementation manners of this application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of this application, several modifications and improvements can still be made, and these all belong to the protection scope of this application. Therefore, the protection scope of this application should be subject to the appended claims.

Claims

1. A method for designing a transfer orbit of a HALO orbiter to fly over a given ground point, characterized in that, The method includes: Obtaining relevant information of the HALO orbiter; the relevant information includes the initial position, initial velocity, ground point longitude, latitude altitude, and flyby altitude; calculating the starting time of the aircraft based on the relevant information; Finding the moment when the lunar declination value is equal to the given ground point latitude value within the given mission time range, and selecting the time point closest to the initial moment as the initial value of the orbit transfer moment iteration; Calculating the flight duration of the orbit transfer point relative to the starting point using the starting time and the initial value of the orbit transfer moment iteration; calculating the normalized time by dividing the flight duration by the HALO orbit period; Calculating the magnitude of the orbit transfer velocity increment based on the normalized time according to the polynomial fitting coefficients; establishing a mapping relationship between the magnitude of the orbit transfer velocity increment and the initial value of the orbit transfer moment iteration through numerical integration based on a high-precision force model; solving the unknown parameters using the Newton iteration method based on the mapping relationship.

2. The method according to claim 1, wherein Calculating the starting time of the aircraft based on the relevant information includes: Integrating numerically backward from the initial position and initial velocity of the HALO orbiter to the starting point to obtain the starting time of the aircraft.

3. The method according to claim 1, characterized in that, The lunar declination value within the given mission time range is calculated according to the lunar ephemeris.

4. The method according to any one of claims 1 to 3, characterized in that, Calculating the flight duration of the orbit transfer point relative to the starting point using the starting time and the initial value of the orbit transfer moment iteration includes: The flight duration of the orbit transfer point relative to the starting point calculated using the starting time and the initial value of the orbit transfer moment iteration is: ； Among them, represents the initial value of the iteration at the orbit transfer moment, represents the starting time.

5. The method according to claim 1, wherein Calculating the normalized time by dividing the flight duration by the HALO orbit period includes: The normalized time calculated by dividing the flight duration by the HALO orbit period is: ； Among them, represents the flight duration, represents the HALO orbit period.

6. The method according to claim 1, characterized in that Calculating the magnitude of the orbit transfer velocity increment based on the normalized time according to the polynomial fitting coefficients includes: The magnitude of the orbit transfer velocity increment calculated based on the normalized time according to the polynomial fitting coefficients is: ； Among them, the coefficients , , , , , are obtained by interpolating the polynomial fitting coefficients according to the flyover height of the ground points, represents the normalized time.

7. The method according to claim 1, wherein Establishing a mapping relationship between the magnitude of the orbit transfer velocity increment and the initial value of the orbit transfer moment iteration through numerical integration based on a high-precision force model includes: The mapping relationship between the magnitude of the orbit transfer velocity increment and the initial value of the orbit transfer moment iteration established through numerical integration based on a high-precision force model is: ; Among them, the perigee altitude, perigee latitude, and perigee longitude are given in advance.

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