Semi-analytical attitude adjustment and unloading method and device for Halo orbit satellites at Earth-Moon L2 point

Abstract

This application relates to the field of satellite orbit control technology, and particularly to a semi-analytical attitude adjustment and unloading method and apparatus for a Halo orbit satellite at the Earth-Moon L2 point, to improve the computational efficiency and accuracy of the satellite's active attitude unloading. It includes: determining the initial velocity increment required for orbit maintenance based on basic information about the satellite's current orbital operation; determining the desired velocity increment for orbit maintenance in the current orbit maintenance direction based on the initial velocity increment; representing the remaining velocity increment for attitude adjustment and unloading in a reference coordinate system using azimuth and elevation angles; optimizing the azimuth and elevation angles in the reference coordinate system with the remaining velocity increment for attitude adjustment and unloading as the optimization objective; determining a reference attitude adjustment and unloading attitude based on the optimized azimuth and elevation angles; obtaining the actual orbit maintenance velocity increment in the direction corresponding to the reference attitude adjustment and unloading attitude; correcting the reference attitude adjustment and unloading attitude based on the actual orbit maintenance velocity increment; and determining the satellite's target unloading attitude.

Description

Technical Field

[0001] This application relates to the field of satellite orbit control technology, and in particular to a semi-analytical attitude adjustment and unloading method and apparatus for a Halo orbit satellite at the Earth-Moon L2 point. Background Technology

[0002] Orbit maintenance is a crucial task in spacecraft operation. Its purpose is to ensure that the spacecraft can continue to operate in its predetermined orbit and maintain the required orbital parameters. This is of great significance for ensuring mission success, extending spacecraft lifespan, and improving economic efficiency.

[0003] Taking the halo orbit around the Earth-Moon L2 Lagrange Point (L2) as an example, it has a unique spatial location and environment, making it important for space missions. However, because the halo orbit is unstable, it requires regular orbit maintenance.

[0004] Generally, Halo-orbiting satellites employ a three-axis stable attitude control system using momentum wheels. The continuous action of disturbance torques such as solar radiation pressure can cause momentum wheel saturation. Saturated momentum wheel jet unloading further degrades the orbital stability of Halo-orbiting satellites, increasing propellant consumption for orbit maintenance while maintaining a constant interval, thus shortening the satellite's lifespan. Passive unloading of the satellite's angular momentum wheel generates additional velocity increments, which can disrupt the orbital stability of Halo-orbiting satellites. However, if utilized properly through active attitude adjustment unloading, orbital stability can be effectively improved. This is the significance of active attitude adjustment unloading for Halo-orbiting satellites. Active attitude adjustment unloading effectively utilizes the velocity increments from unloading jets. In particular, if the remaining velocity increment after attitude adjustment unloading is small, continuous angular momentum unloading can maintain the Halo-orbiting satellite's orbit for a long period, significantly reducing propellant consumption and extending the satellite's lifespan.

[0005] Active attitude control unloading for Halo-orbiting satellites requires Halo orbit maintenance and angular momentum unloading. However, orbit maintenance generally requires numerical calculations, and active attitude control unloading requires even more numerical calculations, resulting in relatively low computational efficiency.

[0006] In summary, improving the computational efficiency and accuracy of satellite active unloading attitude is an urgent problem to be solved. Summary of the Invention

[0007] This application provides a semi-analytical attitude adjustment and unloading method and apparatus for a Halo orbit satellite at Earth-Moon L2 point, which improves the calculation efficiency and accuracy of the satellite's active attitude unloading.

[0008] This application provides a semi-analytical attitude adjustment and unloading method for a Halo orbit satellite at the Earth-Moon L2 point, comprising:

[0009] Based on the basic information of the satellite operating in its current orbit, the initial velocity increment required for orbit maintenance is determined, and based on the initial velocity increment, the desired velocity increment for orbit maintenance is determined in the current orbit maintenance direction of the current orbit.

[0010] In the reference coordinate system established based on the expected velocity increment, the remaining velocity increment of attitude adjustment unloading is represented by the azimuth and pitch angles. The remaining velocity increment of attitude adjustment unloading is the difference between the estimated orbit maintenance velocity increment and the unloading velocity increment in any direction. The azimuth and pitch angles are the characterization angles corresponding to any direction of the estimated orbit maintenance velocity increment in the reference coordinate system.

[0011] In the reference coordinate system, with the remaining velocity increment of the attitude adjustment unloading as the optimization target, the azimuth and pitch angles are optimized, and the reference attitude adjustment unloading attitude is determined based on the optimized azimuth and pitch angles.

[0012] The actual orbital maintenance velocity increment in the direction corresponding to the reference attitude adjustment and unloading attitude is obtained, and the reference attitude adjustment and unloading attitude is corrected according to the actual orbital maintenance velocity increment to determine the target unloading attitude of the satellite.

[0013] This application provides a semi-analytical attitude adjustment and unloading device for a Halo orbit satellite at the Earth-Moon L2 point, comprising:

[0014] The determining unit is used to determine the initial velocity increment required for orbit maintenance based on basic information about the satellite operating in its current orbit, and to determine the desired velocity increment for orbit maintenance in the orbit maintenance direction of the current orbit based on the initial velocity increment.

[0015] The representation unit is used to represent the remaining velocity increment of attitude adjustment unloading in the reference coordinate system established based on the expected velocity increment, by means of azimuth and pitch angles. The remaining velocity increment of attitude adjustment unloading is the difference between the estimated orbit maintenance velocity increment and the unloading velocity increment in any direction. The azimuth and pitch angles are the characterization angles corresponding to any direction of the estimated orbit maintenance velocity increment in the reference coordinate system.

[0016] The optimization unit is used to optimize the azimuth and pitch angles in the reference coordinate system with the remaining velocity increment of the attitude adjustment unloading as the optimization target, and to determine the reference attitude adjustment unloading attitude based on the optimized azimuth and pitch angles.

[0017] The correction unit is used to obtain the actual orbit maintenance velocity increment in the direction corresponding to the reference attitude adjustment and unloading attitude, and correct the reference attitude adjustment and unloading attitude according to the actual orbit maintenance velocity increment to determine the target unloading attitude of the satellite.

[0018] Optionally, the representation unit is specifically used for:

[0019] Based on the first angle between the direction of the desired velocity increment and the arbitrary direction, and the desired velocity increment, the estimated orbital maintenance velocity increment in the arbitrary direction is determined, wherein the magnitude of the velocity component of the estimated orbital maintenance velocity increment in the direction of the desired velocity increment is the same as the magnitude of the desired velocity increment.

[0020] Based on the satellite's attitude and unloading information, and in conjunction with the azimuth and pitch angles, the unloading speed increment in any direction is determined.

[0021] The difference between the estimated orbital maintenance speed increment and the unloading speed increment is used as the attitude adjustment unloading remaining speed increment.

[0022] Optionally, the direction of the desired velocity increment is the same as the positive Z-axis direction of the reference coordinate system, and the first included angle is the complementary angle of the pitch angle in the ZOY plane under the reference coordinate system.

[0023] Optionally, the representation unit is specifically used for:

[0024] The quotient of the desired velocity increment and the cosine of the first included angle is taken as the estimated orbital sustaining velocity increment in any direction.

[0025] Optionally, the unloading velocity increment includes an upper limit and a lower limit; the attitude information includes the satellite's first angular momentum and body attitude matrix in its own system, as well as the reference attitude matrix in the reference coordinate system; the unloading information includes the satellite's unloading engine lever arm; the representation unit is specifically used for:

[0026] The product of the first angular momentum, the transpose of the body attitude matrix, and the first unit vector is taken as the second angular momentum in the arbitrary direction; wherein, the first unit vector is: the unit vector in the arbitrary direction in the inertial frame determined by the product of the second unit vector and the transpose of the reference attitude matrix; the second unit vector is: the unit vector in the arbitrary direction in the reference coordinate system, determined by the azimuth angle and the pitch angle.

[0027] Based on the magnitude of the first angular momentum and the magnitude of the second angular momentum, the upper and lower limits of the sum of the magnitudes of the angular momentum in two directions perpendicular to the second angular momentum are determined by the vector decomposition method.

[0028] Determine the product of the unloading engine lever arm and the satellite mass;

[0029] The upper limit of the velocity increment is determined by the quotient of the product and the upper limit of the sum of the angular momentum moduli, and the lower limit of the velocity increment is determined by the quotient of the product and the lower limit of the sum of the angular momentum moduli.

[0030] Optionally, the estimated orbit maintenance speed increment, the unloading speed increment, and the attitude adjustment unloading remaining speed increment are in the same direction, and the unloading speed increment includes an upper limit value and a lower limit value. The representation unit is specifically used for:

[0031] If the magnitude of the estimated orbital sustaining speed increment is less than the lower limit of the speed increment, then the difference between the lower limit of the speed increment and the magnitude of the estimated orbital sustaining speed increment is taken as the magnitude of the remaining speed increment of the attitude unloading.

[0032] If the magnitude of the estimated orbital maintenance velocity increment is greater than or equal to the lower limit of the velocity increment, and the magnitude of the estimated orbital maintenance velocity increment is less than or equal to the upper limit of the velocity increment, then the magnitude of the remaining velocity increment of the attitude unloading is set to 0.

[0033] If the magnitude of the estimated orbital maintenance velocity increment is greater than the upper limit of the velocity increment, then the difference between the magnitude of the estimated orbital maintenance velocity increment and the upper limit of the velocity increment is used as the magnitude of the remaining velocity increment for attitude unloading.

[0034] Optionally, the initial velocity increment includes a first initial velocity increment, a second initial velocity increment, and a third initial velocity increment; the directions of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are different, and the vector terminals of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are all in the same plane. The determining unit is specifically used for:

[0035] Based on the aforementioned basic information, the first initial velocity increment is determined using Newton's iteration method.

[0036] Based on the aforementioned basic information and the direction of the first initial velocity increment, the second initial velocity increment is determined using the Newton-Raphson iteration method.

[0037] Based on the aforementioned basic information and the preset direction, the third initial velocity increment in the preset direction is determined using Newton's iteration method.

[0038] Optionally, the initial velocity increment includes a first initial velocity increment, a second initial velocity increment, and a third initial velocity increment; the directions of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are different, and the vector terminals of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are all in the same plane. The determining unit is specifically used for:

[0039] The difference between the first initial velocity increment and the second initial velocity increment is taken as the first velocity difference;

[0040] The difference between the second initial velocity increment and the third initial velocity increment is taken as the second velocity difference;

[0041] Determine the cross product of the first speed and the second speed, and use the direction of the cross product result as the direction of the desired speed increment;

[0042] In the direction of the desired velocity increment, the modulus of the desired velocity increment is determined using the Newton-Raphson iteration method.

[0043] Optionally, the correction unit is specifically used for:

[0044] Under the new system of attitude control and unloading of the satellite, the reference attitude control and unloading attitude is corrected according to the actual orbital maintenance velocity increment, and the second angle between the angular momentum corresponding to the actual orbital maintenance velocity increment and the X-axis in the XOY plane is determined; the Z-axis of the new system is consistent with the Z-axis direction of the reference attitude control and unloading attitude.

[0045] After determining the new X-axis and Y-axis of the system based on the second included angle, the unloading posture corresponding to the new system is taken as the target unloading posture.

[0046] An electronic device provided in this application includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of any of the above-described semi-analytical attitude adjustment and unloading methods for Halo orbit satellites at the Earth-Moon L2 point.

[0047] This application provides a computer-readable storage medium including a computer program. When the computer program is run on an electronic device, the computer program is used to cause the electronic device to perform the steps of any of the above-described semi-analytical attitude adjustment and unloading methods for Halo orbit satellites at the Earth-Moon L2 point.

[0048] This application provides a computer program product, which includes a computer program stored in a computer-readable storage medium. When the processor of an electronic device reads the computer program from the computer-readable storage medium, the processor executes the computer program, causing the electronic device to perform the steps of any of the above-described semi-analytical attitude adjustment and unloading methods for Halo orbit satellites at the Earth-Moon L2 point.

[0049] The beneficial effects of this application are as follows:

[0050] This application provides a semi-analytical attitude adjustment and unloading method, apparatus, electronic device, and storage medium for a Halo orbit satellite at Earth-Moon L2. First, based on the satellite's basic information during its current orbital operation, the desired velocity increment for orbit maintenance is determined in the current orbital maintenance direction using the initial velocity increment required for orbital maintenance. The desired velocity increment is solved geometrically. In a reference coordinate system established based on the desired velocity increment, the remaining velocity increment for attitude adjustment and unloading is represented by azimuth and elevation angles, avoiding numerical calculations of orbital maintenance quantities in arbitrary directions. This direct analytical representation of the remaining velocity increment for attitude adjustment and unloading using azimuth and elevation angles is more efficient. Furthermore, in the reference coordinate system, the remaining velocity increment for attitude adjustment and unloading is optimized using the azimuth and elevation angles as the optimization objective. A reference attitude adjustment and unloading attitude is determined based on the optimized azimuth and elevation angles, and the optimal solution for a safe unloading attitude is determined by optimizing the azimuth and elevation angles. The actual orbital maintenance velocity increment in the direction corresponding to the reference attitude adjustment and unloading attitude is obtained, and the reference attitude adjustment and unloading attitude is corrected based on the actual orbital maintenance velocity increment to determine the satellite's target unloading attitude. By correcting the reference attitude adjustment and unloading attitude, the target unloading attitude with the smallest remaining velocity increment under the actual orbital maintenance velocity increment was determined, while taking into account both the optimality of the solution and computational efficiency.

[0051] Other features and advantages of this application will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the application. The objectives and other advantages of this application may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0052] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0053] Figure 1 A flowchart illustrating the implementation of a semi-analytical attitude adjustment and unloading method for a Halo orbit satellite at the Earth-Moon L2 point, provided as an embodiment of this application;

[0054] Figure 2 This is a schematic diagram illustrating the relationship between the required velocity increment and the desired velocity increment for maintaining a track in any direction, as provided in an embodiment of this application.

[0055] Figure 3 A schematic diagram illustrating the determination of the desired velocity increment direction, provided as an embodiment of this application;

[0056] Figure 4 A schematic diagram of a reference coordinate system provided in an embodiment of this application;

[0057] Figure 5 A schematic diagram of satellite momentum wheel distribution provided in an embodiment of this application;

[0058] Figure 6 A schematic diagram of a satellite attitude engine layout provided for an embodiment of this application;

[0059] Figure 7 A satellite flight trajectory diagram before and after unloading is provided in an embodiment of this application;

[0060] Figure 8 This is a schematic diagram of the structure of an electronic device for satellite attitude adjustment unloading in an embodiment of this application;

[0061] Figure 9 This is a schematic diagram of the hardware structure of an electronic device using an embodiment of this application;

[0062] Figure 10 This is a schematic diagram of the hardware structure of a computing device according to an embodiment of this application. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this application. Obviously, the described embodiments are only some embodiments of the technical solutions of this application, and not all embodiments. Based on the embodiments recorded in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the technical solutions of this application.

[0064] Due to its unique spatial location and environment at the Earth-Moon L2 point, the Halo orbit has important applications in space missions. However, the Halo orbit is unstable and requires periodic orbit maintenance. Generally, Halo orbit satellites employ a three-axis stabilized attitude, using momentum wheels for attitude control. The continuous action of disturbance torques such as solar radiation pressure can cause angular momentum saturation of the satellite's momentum wheels. Momentum wheel saturation triggers jet unloading, which further degrades the orbital stability of Halo orbit satellites. With the maintenance interval remaining constant, this increases the consumption of orbit maintenance propellant, thereby shortening the satellite's lifespan.

[0065] While passive unloading of the satellite's angular momentum wheel generates additional velocity increments that can disrupt the orbital stability of Halo-orbiting satellites, active attitude control unloading, if used properly, can effectively improve orbital stability. This is the significance of active attitude control unloading for Halo-orbiting satellites. Active attitude control unloading effectively utilizes the velocity increment from the unloading jets. In particular, if the remaining velocity increment after attitude control unloading is small, angular momentum unloading can be used to maintain the Halo-orbiting satellite's orbit for a long period, thereby significantly reducing propellant consumption and extending the satellite's lifespan.

[0066] In view of this, this application proposes a semi-analytical attitude adjustment and unloading method and apparatus for a Halo orbit satellite at the Earth-Moon L2 point. It establishes the relationship between the velocity increment required for orbit maintenance in any direction and the velocity increment for orbit maintenance in the optimal direction, thereby omitting the numerical calculation when solving for the velocity increment required for orbit maintenance in any direction and improving the efficiency of finding the optimal unloading attitude.

[0067] A reference coordinate system is established based on the desired velocity increment. Within this system, the track maintenance velocity increment in any direction is determined using empirical analytical methods. Based on the principle of vector decomposition, the unloading velocity increment that can be generated by unloading in any direction is calculated. The difference between the track maintenance velocity increment and the unloading velocity increment is denoted as the remaining velocity increment for attitude adjustment unloading. With the goal of minimizing the remaining velocity increment for attitude adjustment unloading, an optimization algorithm is used to optimize the unloading direction, determining the final attitude adjustment unloading target posture. This method omits the numerical calculations necessary for solving the track maintenance velocity increment in any direction, significantly improving the solution efficiency. The specific steps include:

[0068] (1) Use the geometric method to solve for the desired velocity increment vector required to maintain the trajectory;

[0069] (2) Establish a reference coordinate system with the desired velocity increment vector as the Z-axis, and use the azimuth and pitch angles to represent any direction in this coordinate system. Then, use the azimuth and pitch angles to represent the attitude adjustment unloading remaining velocity increment in the corresponding direction.

[0070] (3) In the half space where the desired velocity increment vector is located, optimize the azimuth and pitch angles to minimize the remaining velocity increment after attitude adjustment and unloading.

[0071] (4) The actual orbital maintenance velocity increment in the unloading direction is solved by numerical method, and the rotation angle of the unloading attitude around the Z-axis of the star is corrected to finally determine the target unloading attitude.

[0072] The following describes some of the concepts involved in the embodiments of this application.

[0073] Earth-Moon L2: One of the five Lagrange points in the Earth-Moon system, located on the line connecting the Earth and the Moon, on the side of the Moon furthest from the Earth.

[0074] Halo orbit: A special type of orbit used by spacecraft when multiple gravitational sources are at play. This orbit uses the spacecraft's own onboard power source to maintain the spacecraft's position near the translational point caused by the combined gravitational influence of multiple sources in space, forming a near-circular trajectory.

[0075] The preferred embodiments of this application are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit this application. Furthermore, the embodiments and features in the embodiments of this application can be combined with each other without conflict.

[0076] In the embodiments of this application, the attitude adjustment and unloading method is specifically divided into geometric method to determine the desired velocity increment, semi-analytical method to determine the remaining velocity increment of attitude adjustment and unloading, optimization solution of azimuth and pitch angles, and correction of unloading attitude.

[0077] See Figure 1 The diagram shown is an implementation flowchart of a semi-analytical attitude adjustment and unloading method for a Halo orbit satellite at the Earth-Moon L2 point provided in this application. The specific implementation process of this method is as follows:

[0078] S11: Based on the basic information of the satellite operating in its current orbit, determine the initial velocity increment required for orbit maintenance, and based on the initial velocity increment, determine the expected velocity increment for orbit maintenance in the orbit maintenance direction of the current orbit.

[0079] Among them, the desired velocity increment is the optimal velocity increment, which means that the minimum amount of propellant is consumed for orbit maintenance in the direction of the optimal velocity increment.

[0080] It should be noted that the satellite attitude adjustment and unloading method in this application embodiment can be applied to Halo orbits with different translation points. For example, Halo orbits with Earth-Moon L1 point, Earth-Moon L2 point, Earth-Moon L3 point, etc. The following description of the satellite attitude adjustment and unloading method in this application embodiment will take the Halo orbit with Earth-Moon L2 point as an example.

[0081] Specifically, S11 is to determine the desired velocity increment through a geometric method. In this embodiment, the desired velocity increment is determined based on the relationship between the velocity increment required to maintain the track in any direction and the desired velocity increment.

[0082] First, the relationship between the velocity increment required to maintain the orbit in any direction and the desired velocity increment is introduced:

[0083] like Figure 2 As shown, this is a schematic diagram illustrating the relationship between the required velocity increment and the desired velocity increment for maintaining a track in any direction, according to an embodiment of this application. Wherein, V best For the desired speed increment, V m1 To maintain the required velocity increment in an arbitrary trajectory, let the angle between this arbitrary direction and the desired velocity increment direction be α1. Then, based on engineering experience, V can be obtained. best With V m1 The relationship between them is as shown in Formula 1 below:

[0084] V m1 =V best / cos(α1) (Formula 1)

[0085] Still with Figure 2 For example, it can be further seen that the vector of the velocity increment required to maintain the track in any direction is a plane with its vertex at O ​​and its endpoint at point E, perpendicular to OE. The velocity increment corresponding to vector OE is the minimum velocity increment, which is also the desired velocity increment, and the direction of vector OE is the direction of the desired velocity increment. Therefore, determining the normal to the plane containing the endpoint of the velocity increment vector required to maintain the track also determines the direction of the desired velocity increment.

[0086] Therefore, in this embodiment of the application, before determining the desired velocity increment, it is necessary to first determine the velocity increment vector required for the track to maintain in several directions, and then determine the normal of the plane where the vector endpoint is located.

[0087] Therefore, the method for determining the velocity increment vector will be introduced below:

[0088] Taking the Halo orbit at the Earth-Moon L2 point as an example, it is designed based on the relevant theories of the Circular Restricted Three-Body Problem (CR3BP). The Halo orbit is symmetrical about the XOZ plane of the rotating coordinate system, meaning that the velocity in the X and Z axes when crossing the XOZ plane is 0. However, in actual mechanical environments, due to the non-ideal circular and elliptical motion of the main celestial body and the existence of various perturbations, the spacecraft's trajectory is no longer symmetrical about the XOZ plane, and it cannot form a periodic orbit, but only a quasi-periodic orbit. Since the actual velocity in the Z-axis direction at the crossing point is not zero, the method of correcting the spacecraft's velocity in the X, Y, and Z directions during actual force model operation to make the velocity in the X and Z axes of the next crossing point zero does not conform to the actual operational laws. Therefore, the orbit obtained by such correction under the actual force model has poor repeatability. If the velocity in the X and Z axes of the second or third crossing point is considered, the orbit will be improved. Based on the above, the method for determining the velocity increment required to maintain the orbit is introduced, mainly divided into the following two methods:

[0089] (1) The direction of velocity increment is not fixed.

[0090] When the direction of the velocity increment is not fixed, that is, the control variable is the velocity (Δv) in the three directions of the velocity increment. x Δv z Δv y Taking the objective quantity as an example where the X-direction velocity is 0 during the third crossing of the Earth-Moon L2 point rotating coordinate system XOZ plane after correction, the Newton-Raphson iteration method is used to solve for the minimum norm solution. Since the solution involves three control variables for a single objective quantity, this minimum norm solution is neither unique nor optimal.

[0091] (2) The direction of velocity increment is fixed.

[0092] If the direction of the velocity increment is fixed, the only control variable is the magnitude of the velocity increment. Taking the target quantity as the X-direction velocity being 0 when the third crossing of the Earth-Moon L2 point rotating coordinate system XOZ plane after correction as an example, it is a solution for a target quantity with one control variable, which can be solved using methods such as Newton's iteration method or the golden section method.

[0093] Therefore, in this embodiment, the above method is first used to determine three initial velocity increments, and then the plane where the vector terminal is located is determined based on these three initial velocity increments.

[0094] In this application embodiment, when determining the initial velocity increment, an optional implementation method is as follows:

[0095] Based on the basic information, the first initial velocity increment is determined using Newton's iteration method; based on the basic information and the direction of the first initial velocity increment, the second initial velocity increment is determined using Newton's iteration method; based on the basic information and the preset direction, the third initial velocity increment in the preset direction is determined using Newton's iteration method.

[0096] Among them, the directions of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are different, and the vector terminals are in the same plane.

[0097] Specifically, when determining the first initial velocity increment, the control target is that the velocity of the third crossing point in the X-axis direction is 0.

[0098] When determining the first initial velocity increment, since the direction of the velocity increment is unknown, the above-mentioned method (1) for determining the velocity increment is used to determine a first initial velocity increment with a direction close to the desired velocity increment. Then, when determining the second initial velocity increment, the direction of the first initial velocity increment is finely adjusted to serve as the direction of the second initial velocity increment. The fine-tuning direction can be 10 degrees, 20 degrees, 30 degrees, etc. The above-mentioned method (2) for determining the velocity increment is used to determine the second initial velocity increment. Finally, an arbitrary direction different from the first and second initial velocity increments is selected, and the above-mentioned method (2) for determining the velocity increment is used to determine the third initial velocity increment.

[0099] For example, (1) with the goal of the X-direction velocity being 0 when the third time the Earth-Moon L2 point rotates through the XOZ plane, the Newton-Raphson iteration method is used to solve for the three-directional components of the velocity increment. The first initial velocity increment vector is denoted as V. a (2) Based on the calculation results of (1), in V a Increase the direction by 20 degrees, and calculate the second initial velocity increment using Newton's iteration method in that direction. Let the vector of the second initial velocity increment be V. b (3) Select a new direction and use Newton's iteration method to calculate the maintaining velocity increment in that direction. Let the third initial velocity increment vector be V. c .

[0100] After determining the three initial velocity increments, the plane in which they lie can be determined based on their vector endpoints. Then, by determining the direction of the plane normal, the desired velocity increment can be determined.

[0101] In this application embodiment, when determining the desired speed increment, an optional implementation method is as follows:

[0102] The difference between the first initial velocity increment and the second initial velocity increment is taken as the first velocity difference; the difference between the second initial velocity increment and the third initial velocity increment is taken as the second velocity difference; the cross product of the first velocity and the second velocity is calculated, and the direction of the cross product result is taken as the direction of the desired velocity increment; in the direction of the desired velocity increment, the Newton-Raphson iteration method is used to determine the magnitude of the desired velocity increment.

[0103] Specifically, considering that the cross product of two intersecting lines on a plane is the normal, the embodiments of this application subtract the three initial velocity increments in pairs to determine two vectors on the plane where their vector endpoints are located, and then calculate the cross product of these two vectors. The direction of the cross product result is the direction of the desired velocity increment. Then, the desired velocity increment is determined according to the method (2) for determining the velocity increment described above.

[0104] like Figure 3 As shown, it is a schematic diagram of determining the direction of the desired velocity increment provided in an embodiment of this application. Figure 3 Following the above assumptions, the direction of OA is the first initial velocity increment vector V. a The direction of OB is the second initial velocity increment vector V. b The direction of OC is the third initial velocity increment vector V. c The direction. The vector endpoint of each initial velocity increment lies on plane 301, according to V. a and V b Calculate the difference between the two, i.e., the first velocity ΔV of 302. ab According to V a and V c Calculate the difference between the two, i.e., the second velocity ΔV of 303. ac Due to ΔV ab and ΔV ac Calculate V, where the elements are in the same plane and not collinear. ab With V ac The cross product of these two terms is in the direction of the plane's 301 normal, which is also the direction of the desired velocity increment. The magnitude of the desired velocity increment is calculated using Newton's iteration method in this direction, and the result is the desired velocity increment V. best The modulus.

[0105] After determining the desired velocity increment using the geometric method, the remaining velocity increment for attitude adjustment and unloading can be determined using a semi-analytical method as follows:

[0106] S12: In the reference coordinate system established based on the desired velocity increment, the remaining velocity increment of attitude adjustment unloading is represented by the azimuth and pitch angles.

[0107] Among them, the attitude adjustment unloading residual velocity increment is the difference between the estimated orbit maintenance velocity increment and the unloading velocity increment in any direction; the azimuth and pitch angles are the corresponding characterizing angles in any direction in the reference coordinate system.

[0108] For the reference coordinate system, the direction of the desired velocity increment is the same as the positive Z-axis direction of the reference coordinate system, and in this embodiment, the unloading velocity increment is determined only in the half-space of the positive Z-axis direction of the reference coordinate system.

[0109] like Figure 4 As shown, it is a schematic diagram of a reference coordinate system provided in an embodiment of this application. Figure 4 In the middle, the expected velocity increment V best The direction is the positive Z-axis direction, and the predicted orbital maintenance velocity increment V in any direction l. m2 The azimuth angle is A, and the elevation angle is E. α2 is the complementary angle of E.

[0110] Since the remaining velocity increment after attitude adjustment and unloading is the difference between the estimated orbital maintenance velocity increment and the unloading velocity increment, the estimated orbital maintenance velocity increment and the unloading velocity increment must be calculated first before calculating the remaining velocity increment after attitude adjustment and unloading.

[0111] In this application embodiment, when determining the remaining velocity increment for attitude adjustment unloading, one optional implementation method is:

[0112] Based on the first angle between the expected velocity increment and any direction, and the expected velocity increment, determine the estimated orbit maintenance velocity increment; based on the satellite's attitude and unloading information, combined with the azimuth and elevation angles, determine the unloading velocity increment in any direction; the difference between the estimated orbit maintenance velocity increment and the unloading velocity increment is taken as the attitude adjustment unloading remaining velocity increment.

[0113] Specifically, firstly, for the estimated orbital maintenance velocity increment, as shown in Formula 1, the magnitude of the velocity component of the estimated orbital maintenance velocity increment in the direction of the desired velocity increment is the same as the magnitude of the desired velocity increment. Therefore, the quotient of the desired velocity increment and the cosine of the first included angle is taken as the estimated orbital maintenance velocity increment. Here, the first included angle is the complementary angle of the pitch angle in the XOY plane in the reference coordinate system. Following the... Figure 4 Based on the given assumptions, it is not difficult to obtain the following formula 2:

[0114] V m2 =V best / cos(α2)=V best / sin(E) (Formula 2)

[0115] Furthermore, a detailed derivation is performed to determine the unloading speed increment:

[0116] (1) Relationship between unloading velocity increment and angular momentum.

[0117] Taking the Halo orbit at the Earth-Moon L2 point as an example, for a three-axis stabilized satellite, the angular momentum unloading in the direction of the main engine generally adopts a couple mode, which does not generate additional thrust. However, the angular momentum unloading in the two directions perpendicular to the active engine adopts a non-couple mode, which will generate a velocity increment along the thrust direction of the main engine. The magnitude of this increment is proportional to the sum of the angular momentum moduli in the two directions perpendicular to the active engine.

[0118] like Figure 5 The diagram shown is a schematic representation of the distribution of satellite momentum wheels according to an embodiment of this application. Momentum wheel 4 is a redundant backup, providing necessary bias torque when momentum wheels 1-3 are not operating normally.

[0119] Continue Figure 5 The momentum wheel distribution assumption, such as Figure 6 The diagram shown is a schematic representation of a satellite attitude control engine layout according to an embodiment of this application. J5A / J5B and J6A / J6B are force-coupled attitude control engines used for orbiting the z-axis. b Axis yaw attitude adjustment; the J3A / J3B and J4A / J4B are non-force-coupled attitude control engines used for yaw control. b Pitch attitude adjustment; J1A / J1B and J2A / J2B are non-force-coupled attitude control engines used for x-axis rotation. b Axis rolling posture adjustment.

[0120] It can be seen that satellite z b When the axial angular momentum is unloaded, the attitude control engine (force coupling) jet will not generate +z. b Directional thrust, x b and y b When the shaft angular momentum is unloaded, the attitude control engine (non-force-coupled) jet will generate +z b Directional thrust.

[0121] If the satellite's mass is M, then before unloading, x b The axial angular momentum is H x The corresponding thrust of the unloaded engine is F. x The lever arm is L x The unloading speed is v zx The unloading jet duration is t x ;y b The axial angular momentum is H y The corresponding thrust of the unloaded engine is F. by The lever arm is L y The unloading speed is v zy The unloading jet duration is t y After unloading, the angular momentum of the entire star returns to zero, which gives us the following formulas 3 and 4:

[0122] Hx =L x F x t x (Formula 3)

[0123] v zx =F x t x / M (Formula 4)

[0124] In summary, we can obtain v zx With H x The relationship is shown in Formula 5 below:

[0125] v zx =H x / L x M (Formula 5)

[0126] It is evident that the velocity increment generated by unloading is related to angular momentum, the length of the unloading engine lever arm, and the mass of the entire satellite, but is independent of the magnitude of the unloading engine thrust.

[0127] Similarly, for y b The speed v generated by shaft unloading zy With angular momentum H x The relationship is shown in Formula 6 below:

[0128] v zy =H y / L y M (Formula 6)

[0129] If the total speed increment caused by unloading is v z Then v z For v zx With v zy The sum is shown in Formula 7 below:

[0130] v z =v zx +v zy =(H x / L x +H y / L y ) / M (Formula 7)

[0131] Under normal circumstances, L x =L y =L, then the above formula can be further simplified to the following formula 8:

[0132] v z =(H x +H y ) / LM (Formula 8)

[0133] (2) Determine the angular momentum modulus and .

[0134] If the satellite's current system is OX b Y b Z b If the corresponding attitude quaternion is Q0, then the ontology attitude matrix in the attitude information is denoted as L. bi0 The first angular momentum is denoted as H0 = [H x H y H z ] T Its magnitude is H. The attitude quaternion corresponding to the reference coordinate system O-XYZ is Q, then the reference attitude matrix in the attitude information is L. bi The unloading information includes the satellite's unloading engine lever arm L.

[0135] In this embodiment of the application, when determining the unloading angular momentum, one possible implementation method is as follows:

[0136] The product of the first angular momentum, the transpose of the body attitude matrix, and the first unit vector is taken as the second angular momentum in any direction. The first unit vector is a unit vector in any direction in the inertial frame, determined by the product of the second unit vector and the transpose of the reference attitude matrix. The second unit vector is a unit vector in any direction in the reference coordinate system, determined by the azimuth and pitch angles. Based on the magnitudes of the first and second angular momentum, the upper and lower limits of the sum of the magnitudes of the angular momentum in two directions perpendicular to the second angular momentum are determined by vector decomposition.

[0137] Specifically, firstly, in the reference coordinate system, the second unit vector in any direction l is determined based on the azimuth and elevation angles, as shown in the following formula 9:

[0138] [l]=[cos(E)cos(A)cos(E)sin(A)sin(A)] T (Formula 9)

[0139] In the formula, [·] represents the matrix representation of a vector.

[0140] Secondly, determine the first unit vector in any direction l in the inertial frame, as shown in Equation 10 below:

[0141]

[0142] In the formula, [·] i Let i be the matrix representation of a vector in inertial frame i, and so on.

[0143] Therefore, the component of the first angular momentum in this direction, i.e., the second angular momentum, is as shown in Equation 11 below:

[0144]

[0145] As can be seen from Formula 11, L bi0 Both H and H0 are known quantities, therefore H l It is a function of A and E.

[0146] During satellite unloading, the increase in unloading velocity is mainly generated by the angular momentum components on two axes perpendicular to the l direction. Let H be the sum of the unloading angular momentum on the two perpendicular axes. a According to the principle of vector decomposition, H a The size is shown in Formula 12 below:

[0147]

[0148] (3) Determine the unloading speed increment.

[0149] The unloading speed increment includes an upper limit and a lower limit.

[0150] Since the unloading speed increment and the unloading angular velocity satisfy the relationship shown in Formula 8 above, an optional implementation method for determining the unloading speed increment in this application embodiment is as follows:

[0151] Determine the product of the unloading engine lever arm and the satellite mass; divide the product by the upper limit of angular momentum to obtain the upper limit of velocity increment, and divide the product by the lower limit of angular momentum to obtain the lower limit of velocity increment.

[0152] Specifically, the uninstallation speed increment v generated by uninstallation l As shown in Formula 13 below:

[0153]

[0154] Equation 13 shows that, with the same angular momentum vector and unloading direction, the unloading velocity increments are different when rotating around the Z-axis at different angles. This is very beneficial for making full use of angular momentum for attitude adjustment and unloading.

[0155] It should be noted that the predicted orbital maintenance speed increment, unloading speed increment, and attitude adjustment unloading remaining speed increment are in the same direction.

[0156] Based on the relationship between the unloading speed increment and the estimated orbit maintenance speed increment, the remaining speed increment for attitude adjustment unloading is determined as follows:

[0157] If the magnitude of the estimated orbital sustaining velocity increment is less than the lower limit of the velocity increment, then the difference between the lower limit of the velocity increment and the magnitude of the estimated orbital sustaining velocity increment will be used as the magnitude of the remaining velocity increment for attitude control unloading.

[0158] If the magnitude of the estimated orbital sustaining velocity increment is greater than or equal to the lower limit of the velocity increment, and the magnitude of the estimated orbital sustaining velocity increment is less than or equal to the upper limit of the velocity increment, then the magnitude of the remaining velocity increment after attitude adjustment and unloading is 0.

[0159] If the magnitude of the estimated orbital sustaining velocity increment is greater than the upper limit of the velocity increment, then the difference between the magnitude of the estimated orbital sustaining velocity increment and the upper limit of the velocity increment will be used as the magnitude of the remaining velocity increment for attitude control unloading.

[0160] Specifically, the remaining velocity increment after attitude adjustment and unloading is shown in the following formula 14:

[0161]

[0162] As can be seen from the above, satellite attitude adjustment and unloading is a problem with multiple solutions. Given the attitude and angular momentum before unloading, the remaining velocity increment after attitude adjustment and unloading is a function of A and E.

[0163] The purpose of attitude adjustment and unloading target attitude calculation is to find the optimal attitude that minimizes the remaining velocity increment after attitude adjustment and unloading. Therefore, in this embodiment of the application, after determining the remaining velocity increment after attitude adjustment and unloading through analytical methods, the azimuth and pitch angles can be optimally solved using the following method:

[0164] S13: In the reference coordinate system, with the remaining velocity increment of attitude adjustment unloading as the optimization target, the azimuth and pitch angles are optimized, and the reference attitude adjustment unloading attitude is determined based on the azimuth and pitch angles obtained from the optimization.

[0165] Specifically, an optimization algorithm is used to optimize angles A and E, with the optimization objective being the remaining velocity increment v after attitude adjustment and unloading. e The optimization algorithm used is Particle Swarm Optimization (PSO). That is, determining v... e The smallest values ​​of A and E.

[0166] Among them, the optimization variables are:

[0167] A: The angle between the projection of the direction vector l onto the XOY plane and the X-axis, with a value range of -180° to 180°;

[0168] E: The angle between the direction vector l and the XOY plane, with a value range of 0° to 90°;

[0169] The optimization objective is to minimize the remaining velocity increment after attitude adjustment and unloading, i.e.:

[0170] J = v e (Formula 15)

[0171] When using the PSO algorithm for optimization, the population size is set to 10.

[0172] Due to the randomness of the particle swarm optimization (PSO) algorithm, repeated calculations can yield different results, thus effectively solving the attitude adjustment path safety problem. The attitude adjustment path safety problem refers to ensuring that, during the attitude adjustment from the pre-unloading attitude to the unloading attitude, the momentum wheels do not become saturated due to angular momentum redistribution. Therefore, when using the PSO algorithm, multiple repeated calculations are performed, and the solution with the safest attitude adjustment path is selected.

[0173] If the remaining velocity increment after attitude adjustment and unloading does not meet the accuracy requirements after employing the global particle swarm optimization algorithm (for example, the accuracy can be set to 1 mm / s), then a local optimization algorithm is needed for further optimization. This embodiment uses the coordinate rotation method for local solution, and the result of the global particle swarm optimization is used as its initial value during local optimization. It should be noted that any method applicable to local solution is suitable for this embodiment, and will not be elaborated upon here.

[0174] After determining the optimal azimuth and pitch angles, the reference attitude adjustment and unloading attitude can be preliminarily determined.

[0175] After optimizing the azimuth and pitch angles using the above method, the optimal unloading velocity increment direction under semi-analytical conditions can be obtained. However, the actual velocity increment in this direction differs from V. best Since there is a certain difference between / sin(E), the embodiments of this application correct the unloading attitude according to the actual orbital maintenance speed increment in the following manner:

[0176] S14: Obtain the actual orbit maintenance velocity increment in the direction corresponding to the reference attitude adjustment and unloading attitude, and correct the reference attitude adjustment and unloading attitude based on the actual orbit maintenance velocity increment to determine the target unloading attitude of the satellite.

[0177] Specifically, in this embodiment, the unloading speed increment is changed by adjusting the rotation angle around the Z-axis, so as to minimize the remaining speed increment of the attitude adjustment unloading.

[0178] In this application embodiment, when determining the target unloading attitude of the satellite, an optional implementation method is as follows:

[0179] Under the new system for attitude adjustment and unloading of the satellite, the reference attitude adjustment and unloading attitude is corrected according to the actual orbit maintenance velocity increment. The second angle between the angular momentum corresponding to the actual orbit maintenance velocity increment and the X-axis in the XOY plane is determined. After determining the X-axis and Y-axis of the new system based on the second angle, the unloading attitude corresponding to the new system is taken as the target unloading attitude.

[0180] In this system, the Z-axis direction is consistent with that of the reference attitude adjustment and unloading attitude.

[0181] Specifically, the actual track maintenance velocity increment is first calculated using the method (2) used in S11 to determine the velocity increment, and the magnitude of the actual track maintenance velocity increment is denoted as Δv. m Furthermore, according to Δv m The second angle γ between the unloading angular momentum and the X-axis in the XOY plane is calculated.

[0182] like Then γ has 4 solutions: 0, π / 2, π, and 3π / 2; when When , γ has 4 solutions: π / 4, 3π / 4, 5π / 4, and 7π / 4; otherwise, γ has 8 solutions, as shown in Formula 16 below:

[0183]

[0184] The semi-analytical attitude adjustment and unloading method for Halo orbit satellites at the Earth-Moon L2 point proposed in this application utilizes the vector decomposition and synthesis principle of orbit maintenance solutions, replacing the numerical calculation of the velocity increment required for orbit maintenance in any direction during optimization with analytical calculation. After obtaining the reference unloading attitude of the semi-analytical solution, a numerical calculation method is used to solve for the actual velocity increment required for orbit maintenance in the Z direction of the reference attitude, and this is used to correct the reference attitude adjustment and unloading attitude, while balancing the optimality of the solution and computational efficiency. This application embodiment can be directly used for attitude adjustment and unloading orbit maintenance of Halo orbit satellites at the Earth-Moon L2 point. Its principles and methods, such as the analytical calculation of the velocity increment required for orbit maintenance in any direction using the vector decomposition and synthesis principle and the correction of the solution after semi-analytical calculation, can also be used for the maintenance and control of other types of orbits.

[0185] To demonstrate the feasibility of the proposed solution in this application, a simulation verification process for a semi-analytical attitude adjustment and unloading method for a Halo orbit satellite at the Earth-Moon L2 point is presented, as follows:

[0186] Taking the Halo orbit at the Earth-Moon L2 point as an example, its J2000 series orbital epochs and position velocities are shown in the table below.

[0187] Table 1. Position and velocity of the Halo orbital point L2 between the Earth and the Moon.

[0188]

[0189]

[0190] Let the unloading time be 2024-07-27T09:00:00, and the satellite attitude quaternion Q at the unloading time be [0.3720555 -0.0967062 0.5464672 0.7440404], where the scalar comes first. The satellite angular momentum H at the unloading time is [0.875 -1.32-1.4] Nms.

[0191] (1) Verification of the angle relationship between any direction and the desired direction.

[0192] First, using the velocity increments in the three directions at the control moment as control variables, and taking the zero velocity in the X-direction during the third crossing of the Earth-Moon L2 point rotating coordinate system XOZ plane as the control target, the initial velocity increment vector required for orbit maintenance is calculated, and the maintenance attitude is established. Based on the maintenance attitude, the orbit is rotated by an angle α3 around the X and Y directions respectively to obtain the new orbit maintenance direction. The initial maintenance velocity increment vector and its magnitude are calculated according to the fixed-direction orbit maintenance method. Based on this initial velocity increment vector, the direction of the desired velocity increment and the corresponding desired velocity increment magnitude are calculated using the method in S11. The angle between the initial velocity increment and the desired velocity increment, as well as the inverse cosine angle of the ratio of the desired velocity increment magnitude to the initial velocity increment magnitude, are calculated, and their magnitudes are compared to verify the correctness of empirical formula 1.

[0193] The method of calculating the initial vector using Newton's iteration method is denoted as the iteration method. The direction of rotation around X by an angle α3 is denoted as fixed direction 1, and the direction of rotation around Y by an angle α3 is denoted as fixed direction 2. When the angle α3 is 30°, 20°, and 10° respectively, the calculation results are shown in Tables 2 to 4.

[0194] Table 2 shows the calculation results for α3 angle being 30°.

[0195]

[0196] Table 3 shows the calculation results for α3 angle being 20°.

[0197]

[0198] Table 4 shows the calculation results when α3 is 10°.

[0199]

[0200] As shown in Tables 2-4, the velocity increment direction calculated using the method in S11 has the smallest velocity increment required for track maintenance and can be used as the direction of the desired velocity increment. The strategy of using Newton's iteration method to solve for the three-directional velocity increments yields velocity increment magnitudes close to the desired velocity increments and can be used as an approximation. The angle calculated using the two velocity increment magnitudes in Formula 1 and the angle calculated using the velocity increment vector, except in cases where the angle is small, have a maximum deviation of less than 0.2°, which fully proves the correctness of Formula 1.

[0201] (2) Result verification.

[0202] Based on the orbital parameters and simulation conditions, the unloading attitude was calculated using a semi-analytical method. The calculation results of the target unloading attitude are shown in the table below.

[0203] Table 5 Calculation results of target unloading attitude

[0204]

[0205]

[0206] Under the attitudes corresponding to the table above, the estimated orbit maintenance velocity increment required for Halo orbit maintenance is 0.01469 m / s, the unloading velocity increment is 0.01469 m / s, the remaining velocity increment for attitude adjustment unloading is 0.0 m / s, and the target attitude is the optimal result. Based on the orbit and input conditions, a dynamic verification of the unloading attitude is performed. The projections of the satellite trajectory before and after unloading onto the rotating coordinate system XOY plane are as follows. Figure 7 As shown, the trajectory before unloading exhibited a diverging trend, but after attitude adjustment and unloading, the satellite crossed the XOZ plane four times without showing any diverging trend. This fully demonstrates the correctness of the target attitude parameters during attitude adjustment and unloading and the effectiveness of the satellite attitude adjustment and unloading method provided in this application.

[0207] Based on the same inventive concept, this application also provides a semi-analytical attitude adjustment and unloading device for a Halo orbit satellite at the Earth-Moon L2 point. For example... Figure 8 As shown, this is a schematic diagram of the satellite attitude adjustment and unloading device, which may include:

[0208] The determining unit 801 is used to determine the initial velocity increment required for orbit maintenance based on the basic information of the satellite operating in the current orbit, and to determine the expected velocity increment for orbit maintenance in the orbit maintenance direction of the current orbit based on the initial velocity increment.

[0209] The representation unit 802 is used to represent the remaining velocity increment of attitude adjustment unloading in the reference coordinate system based on the expected velocity increment, by means of azimuth and pitch angles. The remaining velocity increment of attitude adjustment unloading is the difference between the estimated orbit maintenance velocity increment and the unloading velocity increment in any direction. The azimuth and pitch angles are the representation angles of any direction corresponding to the estimated orbit maintenance velocity increment in the reference coordinate system.

[0210] The optimization unit 803 is used to optimize the azimuth and pitch angles in the reference coordinate system with the remaining velocity increment of attitude adjustment unloading as the optimization target, and to determine the reference attitude adjustment unloading attitude based on the azimuth and pitch angles obtained by optimization.

[0211] The correction unit 804 is used to obtain the actual orbit maintenance velocity increment in the direction corresponding to the reference attitude adjustment and unloading attitude, and correct the reference attitude adjustment and unloading attitude according to the actual orbit maintenance velocity increment to determine the target unloading attitude of the satellite.

[0212] Optionally, unit 802 is specifically used for:

[0213] Based on the first angle between the direction of the desired velocity increment and any direction, and the desired velocity increment, the estimated orbital maintenance velocity increment in any direction is determined, wherein the magnitude of the velocity component of the estimated orbital maintenance velocity increment in the direction of the desired velocity increment is the same as the magnitude of the desired velocity increment.

[0214] Based on the satellite's attitude and unloading information, combined with azimuth and elevation angles, the unloading speed increment in any direction is determined.

[0215] The difference between the estimated orbital maintenance speed increment and the unloading speed increment is used as the remaining speed increment for attitude adjustment and unloading.

[0216] Optionally, the direction of the desired velocity increment is the same as the positive Z-axis of the reference coordinate system, and the first included angle is the complementary angle of the pitch angle in the ZOY plane in the reference coordinate system.

[0217] Optionally, unit 802 is specifically used for:

[0218] The quotient of the desired velocity increment and the cosine of the first included angle is used as the estimated orbital sustaining velocity increment in any direction.

[0219] Optionally, the unloading velocity increment includes an upper limit and a lower limit, the attitude information includes the satellite's first angular momentum and body attitude matrix in this system, and the reference attitude matrix in the reference coordinate system, and the unloading information includes the satellite's unloading engine lever arm; the representation unit 802 is specifically used for:

[0220] The product of the first angular momentum, the transpose of the body attitude matrix, and the first unit vector is taken as the second angular momentum in any direction; wherein, the first unit vector is: a unit vector in any direction in the inertial frame determined by the product of the second unit vector and the transpose of the reference attitude matrix; the second unit vector is: a unit vector in any direction in the reference coordinate system determined by the azimuth and pitch angles.

[0221] Based on the magnitudes of the first and second angular momentum, the upper and lower limits of the sum of the magnitudes of the angular momentum in two directions perpendicular to the second angular momentum are determined by vector decomposition.

[0222] Determine the product of the unloading engine lever arm and the satellite mass;

[0223] The upper limit of the velocity increment is determined by the quotient of the product and the upper limit of the sum of the angular momentum magnitudes, and the lower limit of the velocity increment is determined by the quotient of the product and the lower limit of the sum of the angular momentum magnitudes.

[0224] Optionally, the directions of the estimated orbit maintenance speed increment, the unloading speed increment, and the attitude adjustment unloading remaining speed increment are the same. The unloading speed increment includes an upper limit value and a lower limit value. Unit 802 is specifically used for:

[0225] If the magnitude of the estimated orbital sustaining velocity increment is less than the lower limit of the velocity increment, then the difference between the lower limit of the velocity increment and the magnitude of the estimated orbital sustaining velocity increment is used as the magnitude of the remaining velocity increment for attitude control unloading.

[0226] If the magnitude of the estimated orbital sustaining velocity increment is greater than or equal to the lower limit of the velocity increment, and the magnitude of the estimated orbital sustaining velocity increment is less than or equal to the upper limit of the velocity increment, then the magnitude of the remaining velocity increment after attitude adjustment unloading is set to 0.

[0227] If the magnitude of the estimated orbital sustaining velocity increment is greater than the upper limit of the velocity increment, then the difference between the magnitude of the estimated orbital sustaining velocity increment and the upper limit of the velocity increment will be used as the magnitude of the remaining velocity increment for attitude control unloading.

[0228] Optionally, the initial velocity increment includes a first initial velocity increment, a second initial velocity increment, and a third initial velocity increment; the directions of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are different, and the vector terminals of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are all in the same plane. The determining unit 801 is specifically used for:

[0229] Based on the basic information, the first initial velocity increment is determined using Newton's iteration method;

[0230] Based on the basic information and the direction of the first initial velocity increment, the second initial velocity increment is determined using the Newton-Raphson iteration method.

[0231] Based on basic information and a preset direction, the third initial velocity increment in the preset direction is determined using Newton's iteration method.

[0232] Optionally, the initial velocity increment includes a first initial velocity increment, a second initial velocity increment, and a third initial velocity increment; the directions of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are different, and the vector terminals of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are all in the same plane. The determining unit 801 is specifically used for:

[0233] The difference between the first initial velocity increment and the second initial velocity increment is taken as the first velocity;

[0234] The difference between the second initial velocity increment and the third initial velocity increment is taken as the second velocity;

[0235] Determine the cross product of the first and second velocities, and use the direction of the cross product result as the direction of the desired velocity increment;

[0236] In the direction of the desired velocity increment, the modulus of the desired velocity increment is determined using the Newton-Raphson iteration method.

[0237] Optionally, the correction unit 804 is specifically used for:

[0238] Under the new system for attitude control and unloading of the satellite, the reference attitude control and unloading attitude is corrected based on the actual orbital maintenance velocity increment, and the second angle between the angular momentum corresponding to the actual orbital maintenance velocity increment and the X-axis in the XOY plane is determined; the Z-axis of the new system is consistent with the Z-axis direction of the reference attitude control and unloading attitude.

[0239] After determining the new X-axis and Y-axis of the system based on the second included angle, the unloading posture corresponding to the new system is taken as the target unloading posture.

[0240] Based on the same inventive concept, this application also provides an electronic device. The structure of the electronic device can be as follows: Figure 9 As shown, it includes a memory 901, a communication module 903, and one or more processors 902.

[0241] The memory 901 is used to store computer programs executed by the processor 902. The memory 901 may mainly include a program storage area and a data storage area. The program storage area may store the operating system and programs required to run instant messaging functions, etc.; the data storage area may store various instant messaging information and operation instruction sets, etc.

[0242] Memory 901 may be volatile memory, such as random-access memory (RAM); memory 901 may also be non-volatile memory, such as read-only memory, flash memory, hard disk drive (HDD), or solid-state drive (SSD); or memory 901 may be any other medium capable of carrying or storing a desired computer program having the form of instructions or data structures and accessible by a computer, but is not limited thereto. Memory 901 may be a combination of the above-described memories.

[0243] The processor 902 may include one or more central processing units (CPUs) or digital processing units, etc. The processor 902 is used to implement the aforementioned satellite attitude adjustment and unloading method when it calls the computer program stored in the memory 901.

[0244] The communication module 903 is used to communicate with terminal devices and other servers.

[0245] This application embodiment does not limit the specific connection medium between the memory 901, communication module 903, and processor 902 described above. This application embodiment... Figure 9 The memory 901 and the processor 902 are connected via a bus 904, which is in... Figure 9 The diagram uses thick lines to describe the connections between other components; these are for illustrative purposes only and should not be considered limiting. The 904 bus can be divided into address bus, data bus, control bus, etc. For ease of description, Figure 9 It is described using only a thick line, but does not indicate that there is only one bus or one type of bus.

[0246] The memory 901 stores a computer storage medium containing computer-executable instructions for implementing the satellite attitude adjustment and unloading method of this application embodiment. The processor 902 is used to execute the above-described satellite attitude adjustment and unloading method.

[0247] In another embodiment, the electronic device can also be other electronic devices. In this embodiment, the structure of the electronic device can be as follows: Figure 10 As shown, it includes components such as: communication component 1010, memory 1020, display unit 1030, camera 1040, sensor 1050, audio circuit 1060, Bluetooth module 1070, processor 1080, etc.

[0248] The communication component 1010 is used to communicate with the server. In some embodiments, it may include a Circuit-Based Wireless Fidelity (WiFi) module. WiFi is a short-range wireless transmission technology, and electronic devices can use WiFi modules to help users send and receive information.

[0249] The memory 1020 can be used to store software programs and data. The processor 1080 executes various functions of the terminal device and data processing by running the software programs or data stored in the memory 1020. The memory 1020 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state storage device. The memory 1020 stores an operating system that enables the terminal device to run. In this application, the memory 1020 may store the operating system and various application programs, and may also store a computer program that executes the satellite attitude adjustment and unloading method of the embodiments of this application.

[0250] The display unit 1030 can also be used to display information input by the user or information provided to the user, as well as various menus of the terminal device, in a graphical user interface (GUI). Specifically, the display unit 1030 may include a display screen 1032 disposed on the front of the terminal device. The display screen 1032 may be configured as a liquid crystal display, a light-emitting diode, or the like.

[0251] The display unit 1030 can also be used to receive input digital or character information and generate signal inputs related to user settings and function control of the terminal device. Specifically, the display unit 1030 may include a touch screen 1031 disposed on the front of the terminal device, which can collect touch operations of the user on or near it, such as clicking buttons, dragging scroll boxes, etc.

[0252] The touchscreen 1031 can be placed on top of the display screen 1032, or the touchscreen 1031 and the display screen 1032 can be integrated to realize the input and output functions of the terminal device. After integration, it can be referred to as a touch display screen. In this application, the display unit 1030 can display the application and the corresponding operation steps.

[0253] Camera 1040 can be used to capture still images, which users can then share via an application. There can be one or multiple cameras 1040. An object is projected onto a photosensitive element through a lens, generating an optical image. This photosensitive element can be a charge-coupled device (CCD) or a complementary metal-oxide-semiconductor (CMOS) phototransistor. The photosensitive element converts the light signal into an electrical signal, which is then transmitted to the processor 1080 for conversion into a digital image signal.

[0254] The terminal device may also include at least one sensor 1050, such as an accelerometer 1051, a proximity sensor 1052, a fingerprint sensor 1053, and a temperature sensor 1054. The terminal device may also be equipped with other sensors such as a gyroscope, barometer, hygrometer, thermometer, infrared sensor, light sensor, and motion sensor.

[0255] Audio circuitry 1060, speaker 1061, and microphone 1062 provide an audio interface between the user and the terminal device. Audio circuitry 1060 converts received audio data into electrical signals, which are then transmitted to speaker 1061, where they are converted into sound signals for output. The terminal device can also be equipped with volume buttons for adjusting the volume of the sound signal. Conversely, microphone 1062 converts collected sound signals into electrical signals, which are then received by audio circuitry 1060, converted back into audio data, and output to communication component 1010 for transmission to, for example, another terminal device, or to memory 1020 for further processing.

[0256] The Bluetooth module 1070 is used to interact with other Bluetooth devices that also have a Bluetooth module via the Bluetooth protocol. For example, a terminal device can establish a Bluetooth connection with a wearable electronic device (such as a smartwatch) that also has a Bluetooth module through the Bluetooth module 1070, thereby exchanging data.

[0257] The processor 1080 is the control center of the terminal device, connecting various parts of the terminal through various interfaces and lines. It executes various functions and processes data by running or executing software programs stored in the memory 1020 and calling data stored in the memory 1020. In some embodiments, the processor 1080 may include one or more processing units; the processor 1080 may also integrate an application processor and a baseband processor, wherein the application processor mainly handles the operating system, user interface, and applications, and the baseband processor mainly handles wireless communication. It is understood that the baseband processor may not be integrated into the processor 1080. In this application, the processor 1080 can run the operating system, applications, user interface display and touch response, as well as the satellite attitude adjustment offloading method of this embodiment. Furthermore, the processor 1080 is coupled to the display unit 1030.

[0258] In some possible implementations, various aspects of the satellite attitude adjustment unloading method provided in this application can also be implemented in the form of a program product, which includes a computer program. When the program product is run on an electronic device, the computer program causes the electronic device to perform the steps in the satellite attitude adjustment unloading method according to the various exemplary embodiments of this application described above. For example, the electronic device can perform actions such as... Figure 1 The steps are shown in the figure.

[0259] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of readable storage media include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0260] The program product of the embodiments of this application may employ a portable compact disc read-only memory (CD-ROM) and include a computer program, and may run on an electronic device. However, the program product of this application is not limited thereto. In this document, the readable storage medium may be any tangible medium that contains or stores a program that may be used by or in conjunction with a command execution system, apparatus, or device.

[0261] A readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying a readable computer program. This propagated data signal may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting a program for use by or in conjunction with a command execution system, apparatus, or device.

[0262] Computer programs contained on readable media may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0263] Computer programs for performing the operations of this application can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The computer program can execute entirely on the user's electronic device, partially on the user's electronic device, as a standalone software package, partially on the user's electronic device and partially on a remote electronic device, or entirely on a remote electronic device or server. In cases involving remote electronic devices, the remote electronic device can be connected to the user's electronic device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external electronic device (e.g., via the Internet using an Internet service provider).

[0264] It should be noted that although several units or sub-units of the device have been mentioned in the detailed description above, this division is merely exemplary and not mandatory. In fact, according to embodiments of this application, the features and functions of two or more units described above can be embodied in one unit. Conversely, the features and functions of one unit described above can be further divided and embodied by multiple units.

[0265] Furthermore, although the operations of the method of this application are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0266] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0267] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0268] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0269] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0270] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0271] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A semi-analytical attitude adjustment and unloading method for a Halo orbit satellite at Earth-Moon L2 point, characterized in that, The method includes: Based on the basic information of the satellite operating in its current orbit, the initial velocity increment required for orbit maintenance is determined, and based on the initial velocity increment, the desired velocity increment for orbit maintenance is determined in the orbit maintenance direction of the current orbit. In the reference coordinate system established based on the expected velocity increment, the remaining velocity increment of attitude adjustment unloading is represented by the azimuth and pitch angles. The remaining velocity increment of attitude adjustment unloading is the difference between the estimated orbit maintenance velocity increment and the unloading velocity increment in any direction. The azimuth and pitch angles are the characterization angles of the arbitrary direction corresponding to the estimated orbit maintenance velocity increment in the reference coordinate system. In the reference coordinate system, with the remaining velocity increment of the attitude adjustment unloading as the optimization target, the azimuth and pitch angles are optimized, and the reference attitude adjustment unloading attitude is determined based on the optimized azimuth and pitch angles. The actual orbital maintenance velocity increment in the direction corresponding to the reference attitude adjustment and unloading attitude is obtained, and the reference attitude adjustment and unloading attitude is corrected according to the actual orbital maintenance velocity increment to determine the target unloading attitude of the satellite.

2. The method as described in claim 1, characterized in that, The step of representing the remaining velocity increment of attitude control unloading in the reference coordinate system established based on the desired velocity increment, using azimuth and pitch angles, includes: Based on the first angle between the direction of the desired velocity increment and the arbitrary direction, and the desired velocity increment, the estimated orbital maintenance velocity increment in the arbitrary direction is determined, wherein the magnitude of the velocity component of the estimated orbital maintenance velocity increment in the direction of the desired velocity increment is the same as the magnitude of the desired velocity increment. Based on the satellite's attitude and unloading information, and in conjunction with the azimuth and pitch angles, the unloading speed increment in any direction is determined. The difference between the estimated orbital maintenance speed increment and the unloading speed increment is used as the attitude adjustment unloading remaining speed increment.

3. The method as described in claim 2, characterized in that, The direction of the desired velocity increment is the same as the positive Z-axis direction of the reference coordinate system, and the first included angle is the complementary angle of the pitch angle in the reference coordinate system.

4. The method as described in claim 2, characterized in that, Determining the estimated orbital maintenance velocity increment in any direction based on the first angle between the direction of the desired velocity increment and the arbitrary direction, and the desired velocity increment, includes: The quotient of the desired velocity increment and the cosine of the first included angle is taken as the estimated orbital sustaining velocity increment in any direction.

5. The method as described in claim 2, characterized in that, The unloading speed increment includes an upper limit value and a lower limit value of the speed increment; the attitude information includes the satellite's first angular momentum and body attitude matrix in the system, as well as the reference attitude matrix in the reference coordinate system; and the unloading information includes the unloading engine lever arm of the satellite. The determination of the unloading velocity increment in any direction based on the satellite's attitude and unloading information, combined with the azimuth and pitch angles, includes: The product of the first angular momentum, the transpose of the body attitude matrix, and the first unit vector is taken as the second angular momentum in the arbitrary direction; wherein, the first unit vector is: the unit vector in the arbitrary direction in the inertial frame determined by the product of the second unit vector and the transpose of the reference attitude matrix; the second unit vector is: the unit vector in the arbitrary direction in the reference coordinate system, determined by the azimuth angle and the pitch angle. Based on the magnitude of the first angular momentum and the magnitude of the second angular momentum, the upper and lower limits of the sum of the magnitudes of the angular momentum in two directions perpendicular to the second angular momentum are determined by the vector decomposition method. Determine the product of the unloading engine lever arm and the satellite mass; The upper limit of the velocity increment is determined by the quotient of the product and the upper limit of the sum of the angular momentum moduli, and the lower limit of the velocity increment is determined by the quotient of the product and the lower limit of the sum of the angular momentum moduli.

6. The method as described in claim 2, characterized in that, The estimated orbit maintenance velocity increment, the unloading velocity increment, and the attitude adjustment unloading remaining velocity increment are in the same direction. The unloading velocity increment includes an upper limit value and a lower limit value. The step of using the difference between the estimated orbit maintenance velocity increment and the unloading velocity increment as the attitude adjustment unloading remaining velocity increment includes: If the magnitude of the estimated orbital sustaining speed increment is less than the lower limit of the speed increment, then the difference between the lower limit of the speed increment and the magnitude of the estimated orbital sustaining speed increment is taken as the magnitude of the remaining speed increment of the attitude unloading. If the magnitude of the estimated orbital sustaining speed increment is greater than or equal to the lower limit of the speed increment, and the magnitude of the estimated orbital sustaining speed increment is less than or equal to the upper limit of the speed increment, then the magnitude of the remaining speed increment of the attitude unloading is set to 0. If the magnitude of the estimated orbital maintenance velocity increment is greater than the upper limit of the velocity increment, then the difference between the magnitude of the estimated orbital maintenance velocity increment and the upper limit of the velocity increment is used as the magnitude of the remaining velocity increment for attitude unloading.

7. The method according to any one of claims 1 to 5, characterized in that, The initial velocity increment includes a first initial velocity increment, a second initial velocity increment, and a third initial velocity increment; the directions of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are different, and the vector terminals of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are all in the same plane. Determining the initial velocity increment required for orbit maintenance based on the basic information of the satellite operating in its current orbit includes: Based on the aforementioned basic information, the first initial velocity increment is determined using Newton's iteration method. Based on the aforementioned basic information and the direction of the first initial velocity increment, the second initial velocity increment is determined using the Newton-Raphson iteration method. Based on the aforementioned basic information and the preset direction, the third initial velocity increment in the preset direction is determined using Newton's iteration method.

8. The method according to any one of claims 1 to 5, characterized in that, The initial velocity increment includes a first initial velocity increment, a second initial velocity increment, and a third initial velocity increment; the directions of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are different, and the vector terminals of the first initial velocity increment, the second initial velocity increment, and the third initial velocity increment are all in the same plane. Determining the desired velocity increment for track maintenance in the track maintenance direction of the current track based on the initial velocity increment includes: The difference between the first initial velocity increment and the second initial velocity increment is taken as the first velocity difference; The difference between the second initial velocity increment and the third initial velocity increment is taken as the second velocity difference; Determine the cross product of the first speed difference and the second speed difference, and take the direction of the cross product result as the direction of the desired speed increment; In the direction of the desired velocity increment, the modulus of the desired velocity increment is determined using the Newton-Raphson iteration method.

9. The method according to any one of claims 1 to 5, characterized in that, The step of correcting the reference attitude adjustment and unloading attitude based on the actual orbit maintenance velocity increment to determine the target unloading attitude of the satellite includes: Under the new system of attitude control and unloading of the satellite, the reference attitude control and unloading attitude is corrected according to the actual orbital maintenance velocity increment, and the second angle between the angular momentum corresponding to the actual orbital maintenance velocity increment and the X-axis in the XOY plane is determined; the Z-axis of the new system is consistent with the Z-axis direction of the reference attitude control and unloading attitude. After determining the new X-axis and Y-axis of the system based on the second included angle, the unloading posture corresponding to the new system is taken as the target unloading posture.

10. A semi-analytical attitude adjustment and unloading device for a Halo orbit satellite at Earth-Moon L2 point, characterized in that, include: The determining unit is used to determine the initial velocity increment required for orbit maintenance based on basic information about the satellite operating in its current orbit, and to determine the desired velocity increment for orbit maintenance in the orbit maintenance direction of the current orbit based on the initial velocity increment. The representation unit is used to represent the remaining velocity increment of attitude adjustment unloading in the reference coordinate system established based on the expected velocity increment, by means of azimuth and pitch angles. The remaining velocity increment of attitude adjustment unloading is the difference between the estimated orbit maintenance velocity increment and the unloading velocity increment in any direction. The azimuth and pitch angles are the characterization angles corresponding to any direction of the estimated orbit maintenance velocity increment in the reference coordinate system. The optimization unit is used to optimize the azimuth and pitch angles in the reference coordinate system with the remaining velocity increment of the attitude adjustment unloading as the optimization target, and to determine the reference attitude adjustment unloading attitude based on the optimized azimuth and pitch angles. The correction unit is used to obtain the actual orbit maintenance velocity increment in the direction corresponding to the reference attitude adjustment and unloading attitude, and correct the reference attitude adjustment and unloading attitude according to the actual orbit maintenance velocity increment to determine the target unloading attitude of the satellite.

11. An electronic device, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of any of the methods described in claims 1 to 9.

12. A computer-readable storage medium, characterized in that, It includes a computer program that, when run on an electronic device, causes the electronic device to perform the steps of any of the methods described in claims 1 to 9.

13. A computer program product, characterized in that, The method includes a computer program stored in a computer-readable storage medium; when a processor of an electronic device reads the computer program from the computer-readable storage medium, the processor executes the computer program, causing the electronic device to perform the steps of any one of claims 1 to 9.

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