Earth-moon L2 point Halo orbit satellite semi-analysis attitude adjustment unloading method and device

Abstract

The invention relates to the technical field of satellite orbit control, in particular to an earth-moon L2 point Halo orbit satellite semi-analysis attitude adjustment unloading method and device, and aims to improve the calculation efficiency and accuracy of the active unloading attitude of a satellite. Comprising the following steps: determining an initial speed increment required by orbit maintenance based on basic information of a satellite running in a current orbit, and determining an expected speed increment of orbit maintenance in a current orbit maintenance direction based on the initial speed increment; under the reference coordinate system, the attitude adjustment unloading residual speed increment is expressed through the azimuth angle and the pitch angle; under the reference coordinate system, taking the attitude adjustment unloading residual speed increment as an optimization target, optimizing the azimuth angle and the pitch angle, and determining a reference attitude adjustment unloading attitude according to the azimuth angle and the pitch angle obtained through optimization; and acquiring an actual orbit maintaining speed increment in a direction corresponding to the reference attitude adjustment unloading attitude, correcting the reference attitude adjustment unloading attitude according to the actual orbit maintaining speed increment, and determining a target unloading attitude of the satellite.

Description

Technical Field

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

[0002] Orbit maintenance is an important task in the operation of a spacecraft. Its purpose is to ensure that the spacecraft can continue to operate in the predetermined orbit and maintain the required orbital parameters. It is of great significance for ensuring mission success, extending the life of the spacecraft, and improving economic benefits.

[0003] Taking the Halo orbit of the Earth-Moon L2 Lagrange Point (L2) as an example, it has a unique spatial location and environment and is of great use in space missions. However, since the Halo orbit is an unstable orbit, it needs to be regularly maintained.

[0004] Generally, Halo orbit satellites generally adopt three-axis stable attitude and use momentum wheels for attitude control. The continuous action of interference torques such as solar pressure will cause the saturation of satellite momentum wheels. The saturated momentum wheel jet unloading will further destroy the orbital stability of Halo orbit satellites, increase the orbit maintenance propellant consumption while maintaining the interval unchanged, and thus shorten the satellite life. The passive unloading of satellite angular momentum wheels produces additional velocity increments, which can destroy the orbital stability of Halo orbit satellites. However, if used properly, active attitude adjustment unloading can effectively improve the orbital stability. This is the significance of active attitude adjustment unloading of Halo orbit satellites. Active attitude adjustment unloading can effectively utilize the unloading jet velocity increment. In particular, if the remaining velocity increment after attitude adjustment unloading is small, the Halo orbit satellite orbit can be maintained for a long time through continuous angular momentum unloading, thereby greatly reducing propellant consumption and extending the satellite life.

[0005] The active attitude adjustment unloading of Halo orbit satellites requires Halo orbit maintenance and angular momentum unloading. However, orbit maintenance generally requires numerical calculations, and active attitude adjustment unloading requires a large amount of numerical calculations, which has a relatively low calculation efficiency.

[0006] In summary, how to improve the calculation efficiency and accuracy of satellite active unloading attitude is an urgent problem to be solved. Summary of the invention

[0007] The embodiments of the present application provide a semi-analytical attitude adjustment and unloading method and device for a Halo orbit satellite at the Earth-Moon L2 point, so as to improve the calculation efficiency and accuracy of the satellite's active unloading attitude.

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

[0009] Determine an initial velocity increment required for orbit maintenance based on basic information of the satellite in the current orbit, and determine a desired velocity increment for orbit maintenance in the current orbit maintenance direction of the current orbit based on the initial velocity increment;

[0010] In a reference coordinate system established based on the expected speed increment, the attitude adjustment unloading remaining speed increment is represented by an azimuth angle and a pitch angle, wherein the attitude adjustment unloading remaining speed increment is the difference between the estimated orbit maintenance speed increment and the unloading speed increment in any direction; the azimuth angle and the pitch angle are the corresponding representation angles of any direction corresponding to the estimated orbit maintenance speed increment in the reference coordinate system;

[0011] In the reference coordinate system, taking the attitude adjustment and unloading residual speed increment as the optimization target, optimizing the azimuth and pitch angles, and determining a reference attitude adjustment and unloading posture according to the optimized azimuth and pitch angles;

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

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

[0014] a determination unit, configured to determine an initial velocity increment required for orbit maintenance based on basic information of the satellite in the current orbit, and determine a desired velocity increment for orbit maintenance in the orbit maintenance direction of the current orbit based on the initial velocity increment;

[0015] A representation unit, used for representing the attitude adjustment unloading remaining speed increment by an azimuth angle and a pitch angle in a reference coordinate system established based on the expected speed increment, wherein the attitude adjustment unloading remaining speed increment is the difference between the estimated orbit maintenance speed increment and the unloading speed increment in any direction; the azimuth angle and the pitch angle are the corresponding representation angles of any direction corresponding to the estimated orbit maintenance speed increment in the reference coordinate system;

[0016] An optimization unit, configured to optimize the azimuth and pitch angles in the reference coordinate system with the attitude adjustment and unloading residual speed increment as an optimization target, and determine a reference attitude adjustment and unloading posture according to the azimuth and pitch angles obtained by the optimization;

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

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

[0019] Determining the estimated track-maintaining speed increment in the arbitrary direction according to a first angle between the direction of the expected speed increment and the arbitrary direction, and the expected speed increment, wherein a modulus value of a speed component of the estimated track-maintaining speed increment in the direction of the expected speed increment is the same as a modulus value of the expected speed increment;

[0020] Based on the attitude information and unloading information of the satellite, combined with the azimuth and pitch angle, determine the unloading speed increment in the arbitrary direction;

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

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

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

[0024] The quotient of the expected velocity increment and the cosine value of the first angle is used as the estimated trajectory maintenance velocity increment in any direction.

[0025] Optionally, the unloading speed increment includes a speed increment upper limit value and a speed increment lower limit value, the attitude information includes a first angular momentum and a body attitude matrix of the satellite in this system, and a reference attitude matrix in the reference coordinate system, and the unloading information includes an unloading engine force arm of the satellite; 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 used as the second angular momentum in the arbitrary direction; wherein the first unit vector is: a unit vector in the arbitrary direction in the inertial system determined based on the product of the second unit vector and the transpose of the reference attitude matrix; the second unit vector is: a unit vector in the arbitrary direction determined according to the azimuth angle and the pitch angle in the reference coordinate system;

[0027] Based on the modulus value of the first angular momentum and the modulus value of the second angular momentum, determining an upper limit value and a lower limit value of the sum of the modulus values ​​of the angular momentum in two directions perpendicular to the second angular momentum by a vector decomposition method;

[0028] Determining the product of the unloading engine moment arm and the mass of the satellite;

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

[0030] Optionally, the estimated track maintenance speed increment, the unloading speed increment and the attitude adjustment unloading remaining speed increment have the same direction, the unloading speed increment includes a speed increment upper limit value and a speed increment lower limit value, and the representation unit is specifically used for:

[0031] If the modulus of the estimated track maintenance speed increment is less than the speed increment lower limit, the difference between the speed increment lower limit and the modulus of the estimated track maintenance speed increment is used as the modulus of the attitude adjustment unloading remaining speed increment;

[0032] If the modulus of the estimated track maintenance speed increment is greater than or equal to the speed increment lower limit, and the modulus of the estimated track maintenance speed increment is less than or equal to the speed increment upper limit, then the modulus of the attitude adjustment unloading remaining speed increment is set to 0;

[0033] If the modulus of the estimated track maintenance speed increment is greater than the speed increment upper limit, the difference between the modulus of the estimated track maintenance speed increment and the speed increment upper limit is used as the modulus of the attitude adjustment unloading remaining speed increment.

[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 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, and the determining unit is specifically used to:

[0035] Based on the basic information, a first initial velocity increment is determined using a Newton iteration method;

[0036] Based on the basic information and the direction of the first initial velocity increment, a second initial velocity increment is determined by using a Newton iteration method;

[0037] Based on the basic information and the preset direction, a 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 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, and the determining unit is specifically used to:

[0039] taking the difference between the first initial speed increment and the second initial speed increment as a first speed difference;

[0040] taking the difference between the second initial speed increment and the third initial speed increment as the second speed difference;

[0041] Determine a 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 expected speed increment, a modulus value of the expected speed increment is determined using Newton's iteration method.

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

[0044] In a new local 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, and a second angle between the angular momentum corresponding to the actual orbit maintenance velocity increment and the X-axis in the XOY plane is determined; the Z-axis of the new local system is consistent with the Z-axis direction of the reference attitude adjustment and unloading attitude;

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

[0046] An electronic device provided in an embodiment of the present 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 executes the steps of any one of the above-mentioned semi-analytical attitude adjustment and unloading methods for a Halo orbit satellite at the Earth-Moon L2 point.

[0047] An embodiment of the present application provides a computer-readable storage medium, which includes a computer program. When the computer program is run on an electronic device, the computer program is used to enable the electronic device to perform any step of the above-mentioned semi-analytical attitude adjustment unloading method for a Halo orbit satellite at the Earth-Moon L2 point.

[0048] An embodiment of the present application provides a computer program product, which includes a computer program, and the computer program is 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, so that the electronic device performs any step of the above-mentioned semi-analytical attitude adjustment unloading method for a Halo orbit satellite at the Earth-Moon L2 point.

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

[0050] The embodiment of the present application provides a semi-analytical attitude adjustment and unloading method, device, electronic device and storage medium for a Halo orbit satellite at the Earth-Moon L2 point. The embodiment of the present application first determines the expected speed increment for orbit maintenance in the current orbit maintenance direction of the current orbit based on the basic information of the satellite when it is operating in the current orbit through the initial speed increment required for orbit maintenance; the expected speed increment is solved by the geometric method; in a reference coordinate system established based on the expected speed increment, the remaining speed increment for attitude adjustment and unloading is represented by the azimuth and pitch angles, thereby avoiding the numerical calculation of the orbit maintenance amount in any direction, and directly representing the remaining speed increment for attitude adjustment and unloading analytically by the azimuth and pitch angles, which is more efficient; further, in the reference coordinate system, the remaining speed increment for attitude adjustment and unloading is taken as the optimization target, the azimuth and pitch angles are optimized, and the reference attitude adjustment and unloading posture is determined according to the azimuth and pitch angles obtained by the optimization, and the optimal solution under the safe unloading posture is determined by optimizing the azimuth and pitch angles; the actual orbit maintenance speed increment in the direction corresponding to the reference attitude adjustment and unloading posture is obtained, and the reference attitude adjustment and unloading posture is corrected according to the actual orbit maintenance speed increment to determine the target unloading posture of the satellite. By correcting the reference attitude adjustment and unloading posture, the target unloading posture with the minimum attitude adjustment and unloading residual velocity increment under the actual orbit maintenance velocity increment is determined, while taking into account the optimality of the understanding and the computational efficiency.

[0051] Other features and advantages of the present application will be described in the following description, and partly become apparent from the description, or be understood by practicing the present application. The purpose and other advantages of the present application can be realized and obtained by the structures specifically pointed out in the written description, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

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

[0054] Figure 2 A schematic diagram of the relationship between the speed increment required to maintain a track and the expected speed increment in any direction provided by an embodiment of the present application;

[0055] Figure 3 A schematic diagram of determining a desired speed increment direction provided by an embodiment of the present application;

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

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

[0058] Figure 6 A schematic diagram of a satellite attitude engine layout provided in an embodiment of the present application;

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

[0060] Figure 8 A schematic diagram of the structure of an electronic device for satellite attitude adjustment and unloading in an embodiment of the present application;

[0061] Fig. 9 A schematic diagram of a hardware structure of an electronic device to which an embodiment of the present application is applied;

[0062] Fig.10 A schematic diagram of the hardware composition structure of a computing device using an embodiment of the present application. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the technical solution of the present application, rather than all of the embodiments. Based on the embodiments recorded in the application documents, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the technical solution of the present application.

[0064] Due to its unique spatial location and environment, the Halo orbit at the Earth-Moon L2 point has important uses in space missions. However, the Halo orbit is an unstable orbit that requires regular orbit maintenance. Generally, Halo orbit satellites generally adopt a three-axis stable attitude and use momentum wheels for attitude control. The continuous action of interfering torques such as solar pressure will cause the angular momentum of the satellite's momentum wheel to saturate. Momentum wheel saturation triggers jet unloading, which will further destroy the orbital stability of the Halo orbit satellite, increase the consumption of orbit maintenance propellant while maintaining the interval unchanged, and thus shorten the satellite life.

[0065] Although the passive unloading of the satellite angular momentum wheel generates additional velocity increments, which can destroy the orbital stability of the Halo orbit satellite, if used properly, active attitude adjustment unloading can effectively improve the orbital stability. This is the significance of active attitude adjustment unloading of Halo orbit satellites. Active attitude adjustment unloading can effectively utilize the unloading jet velocity increment. In particular, if the remaining velocity increment after attitude adjustment unloading is small, the Halo orbit satellite can be continuously maintained for a long time through angular momentum unloading, thereby greatly reducing propellant consumption and extending the satellite life.

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

[0067] Establish a reference coordinate system with the expected speed increment. In the reference coordinate system, determine the track maintenance speed increment in any direction based on the empirical analytical method; calculate the unloading speed increment that can be generated by unloading in any direction based on the vector decomposition principle, and record the difference between the track maintenance speed increment and the unloading speed increment as the attitude adjustment unloading remaining speed increment. With the minimum attitude adjustment unloading remaining speed increment as the goal, use the optimization algorithm to optimize the unloading direction and determine the final attitude adjustment unloading target posture. This method omits the numerical calculations required to solve the track maintenance speed increment in any direction, significantly improving the solution efficiency. It specifically includes the following steps:

[0068] (1) Use geometric methods to solve the desired velocity increment vector required for track maintenance;

[0069] (2) A reference coordinate system is established with the expected velocity increment vector as the Z axis, and the azimuth and pitch angles are used to represent any direction in this coordinate system. The azimuth and pitch angles are then used to represent the attitude adjustment unloading residual velocity increment in the corresponding direction.

[0070] (3) In the half-space where the desired velocity increment vector is located, the azimuth angle and pitch angle are optimized so that the residual velocity increment of attitude adjustment unloading is minimized.

[0071] (4) A numerical method is used to solve the actual orbit maintenance velocity increment in the unloading direction, and the rotation angle of the unloading attitude around the Z axis of the satellite is corrected to finally determine the target unloading attitude.

[0072] The following is an introduction to some concepts involved in the embodiments of the present application.

[0073] The Earth-Moon L2 point is one of the five Lagrange points in the Earth-Moon system. It is located on the line connecting the Earth and the Moon, on the side of the Moon away from the Earth.

[0074] Halo orbit: a special type of orbit used for spacecraft when multiple gravitational sources are acting on it. This orbit uses the power source carried by the spacecraft itself to maintain the spacecraft's spatial position near the point of libration generated by the combined action of multiple gravitational sources in space, forming a quasi-circular trajectory.

[0075] The preferred embodiments of the present application are described below in conjunction with the drawings in the specification. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present application, and are not used to limit the present application. In addition, the embodiments and features in the embodiments of the present application may be combined with each other if there is no conflict.

[0076] In the embodiment of the present application, the attitude adjustment and unloading method is specifically divided into a geometric method to determine the desired speed increment, a semi-analytical method to determine the remaining speed increment for attitude adjustment and unloading, an optimal solution for the azimuth and pitch angles, and correction of the unloading attitude.

[0077] See also Figure 1 As shown, it is an implementation flow chart of a semi-analytical attitude adjustment and unloading method for a Halo orbit satellite at the Earth-Moon L2 point provided in an embodiment of the present application. The specific implementation process of the method is as follows:

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

[0079] Among them, the expected speed increment is the optimal speed increment, that is, in the direction of the optimal speed increment, the propellant consumed for orbit maintenance is the least.

[0080] It should be noted that the satellite attitude adjustment unloading method in the embodiment of the present application can be applied to the Halo orbits of different libration points, such as the Halo orbit of the Earth-Moon L1 point, the Halo orbit of the Earth-Moon L2 point, the Halo orbit of the Earth-Moon L3 point, etc., and the satellite attitude adjustment unloading method in the embodiment of the present application will be introduced by taking the Halo orbit of the Earth-Moon L2 point as an example.

[0081] Specifically, S11 is to determine the expected speed increment by a geometric method. The embodiment of the present application determines the expected speed increment based on the initial speed increment in any direction by taking into account the relationship between the speed increment required to maintain the track in any direction and the expected speed increment.

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

[0083] like Figure 2 As shown, it is a schematic diagram of the relationship between the velocity increment required to maintain the track in any direction and the expected velocity increment provided by an embodiment of the present application. best is the expected speed increment, V m1 To maintain the required velocity increment for the track in any direction, let the angle between the arbitrary direction and the desired velocity increment direction be α1. According to engineering experience, V best With V m1 The relationship between them is as shown in the following formula 1:

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

[0085] Still Figure 2 For example, it can be further known that the vector of the speed increment required for track maintenance in any direction has a vertex at O ​​and an end point on a plane passing through point E and perpendicular to OE. The speed increment corresponding to vector OE is the minimum speed increment, that is, the expected speed increment, and the direction of vector OE is the direction of the expected speed increment. Therefore, by determining the normal of the plane where the end point of the vector of the speed increment required for track maintenance is located, the direction of the expected speed increment is also determined.

[0086] Furthermore, before determining the expected velocity increment, the embodiment of the present application needs to first determine the velocity increment vectors required for track maintenance in several directions, and then determine the normal of the plane where the vector end point is located.

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

[0088] Taking the Halo orbit of 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 symmetric about the XOZ plane of the rotating coordinate system, that is, the speed in the X-axis and Z-axis directions when crossing the XOZ plane is 0. However, in the actual mechanical environment, due to the non-ideal circle and ellipse motion of the main celestial body and the presence of multiple perturbations, the trajectory of the spacecraft is no longer symmetric about the XOZ plane, and a periodic orbit cannot be formed, but only a quasi-periodic orbit can be formed. Since the actual speed in the Z-axis direction of the crossing point when crossing the XOZ plane is not zero, the method of correcting the speed of the spacecraft in the X, Y, and Z directions during operation under the actual force model so that the speed in the X-axis and Z-axis directions of the next crossing point is zero does not conform to the actual operation law. Therefore, the orbit obtained by such correction under the actual force model has poor repeatability. If the speed in the X-axis and Z-axis directions of the second or third crossing point is corrected, the orbit will be improved. On the basis of the above, the method of determining the speed increment required to maintain the orbit is introduced, which is mainly divided into the following two methods:

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

[0090] When the direction of the speed increment is not fixed, the control variable is the speed increment in three directions (Δv x , Δv z , Δv y ), taking the target quantity as the third time after the correction when the X-direction velocity is 0 when the rotation coordinate system XOZ plane of the Earth-Moon L2 point is crossed, the Newton iteration method is used to solve and the minimum norm solution can be obtained. Since three control variables are used to solve one target quantity, the minimum norm solution is not the only solution, nor is it the optimal solution.

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

[0092] If the direction of the velocity increment is fixed, the control variable is only the size of the velocity increment. Taking the target quantity as the third time the X-direction velocity is 0 when the Earth-Moon L2 point rotates through the XOZ plane of the coordinate system after correction as an example, the solution of a control variable to a target quantity can be solved by Newton iteration method or golden section method.

[0093] Therefore, the embodiment of the present application first uses the above method to determine three initial velocity increments, and then determines the plane where its vector terminal is located based on the three initial velocity increments.

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

[0095] Based on the basic information, the Newton iteration method is used to determine the first initial velocity increment; based on the basic information and the direction of the first initial velocity increment, the Newton iteration method is used to determine the second initial velocity increment; based on the basic information and the preset direction, the Newton iteration method is used to determine the third initial velocity increment in the preset direction.

[0096] 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 method for determining the velocity increment (1) is used to determine a first initial velocity increment whose direction is close to the expected velocity increment; then, when determining the second initial velocity increment, a fine adjustment is made in the direction of the first initial velocity increment as the direction of the second initial velocity increment, wherein the fine adjustment direction may be 10 degrees, 20 degrees, 30 degrees, etc., and the above method for determining the velocity increment (2) is used to determine the second initial velocity increment; finally, a direction different from the first initial velocity increment and the second initial velocity increment is arbitrarily selected, and the above method for determining the velocity increment (2) 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 is crossed in the XOZ plane of the rotating coordinate system after control, the Newton iteration method is used to solve the three-direction components of the velocity increment. The first initial velocity increment vector is denoted as V a ; (2) According to the calculation results of (1), at V a The second initial velocity increment vector is V. b (3) Select a new direction and use Newton's iteration method to calculate the velocity increment in this direction. The third initial velocity increment vector is V c .

[0100] After determining the above three initial velocity increments, the plane in which the vector is located can be determined according to its vector end point, and then the expected velocity increment can be determined by determining the direction of the plane normal.

[0101] In the embodiment of the present application, when determining the expected speed increment, an optional implementation 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 modulus of the desired velocity increment is determined using the Newton iteration method.

[0103] Specifically, considering that the cross product of two intersecting straight lines on a plane is a normal line, the embodiment of the present application subtracts the above three initial velocity increments from each other to determine two vectors on the plane where their vector end points are located, and then calculates the cross product of these two vectors. The direction pointed by the cross product result is the direction of the expected velocity increment, and then the expected velocity increment is determined according to the above method (2) for determining the velocity increment.

[0104] like Figure 3 As shown, it is a schematic diagram of determining the direction of the expected speed increment provided by an embodiment of the present application. Figure 3 The above assumptions are used in the above example, and the OA direction is the first initial velocity increment vector V a The OB direction is the second initial velocity increment vector V b The direction of OC is the third initial velocity increment vector V c The vector endpoint of each initial velocity increment is on plane 301. a and V b Calculate the difference between the two, that is, the first speed ΔV 302 ab , according to V a and V c Calculate the difference between the two, that is, the second speed ΔV 303 ac . Due to ΔV ab and ΔV ac In the same plane and not collinear, calculate V ab With V ac The direction of the cross product is the direction of the normal line of plane 301, that is, the direction of the expected velocity increment. The modulus of the expected velocity increment is calculated using the Newton iteration method in this direction, and the result is the expected velocity increment V best The modulus value of .

[0105] After the expected velocity increment is determined by the geometric method, the remaining velocity increment for attitude adjustment and unloading can be determined by the semi-analytical method as follows:

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

[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 angle and pitch angle are the corresponding representation angles of any direction in the reference coordinate system.

[0108] For the reference coordinate system, the direction of the expected velocity increment is the same as the positive direction of the Z axis of the reference coordinate system, and in the embodiment of the present application, the unloading velocity increment is determined only in the half space in the positive direction of the Z axis 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 the present application. Figure 4 The expected velocity increment V best The direction is the positive direction of the Z axis, and the estimated 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 speed increment for attitude adjustment and unloading is the difference between the estimated track maintenance speed increment and the unloading speed increment, if the remaining speed increment for attitude adjustment and unloading is calculated, the estimated track maintenance speed increment and the unloading speed increment must be calculated first.

[0111] In the embodiment of the present application, when determining the attitude adjustment unloading remaining speed increment, an optional implementation is:

[0112] The estimated orbit maintenance speed increment is determined according to the first angle between the expected speed increment and any direction, and the expected speed increment; the unloading speed increment in any direction is determined based on the attitude information and unloading information of the satellite, combined with the azimuth and pitch angles; the difference between the estimated orbit maintenance speed increment and the unloading speed increment is used as the remaining speed increment for attitude adjustment unloading.

[0113] Specifically, first, for the estimated track maintenance velocity increment, it can be seen from Formula 1 that the modulus of the velocity component of the estimated track maintenance velocity increment in the direction of the expected velocity increment is the same as the modulus of the expected velocity increment. Therefore, the quotient of the expected velocity increment and the cosine value of the first angle is used as the estimated track maintenance velocity increment. The first angle is the complementary angle of the pitch angle in the XOY plane in the reference coordinate system. Figure 4 Based on the assumptions shown, it is not difficult to obtain the following formula 2:

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

[0115] Then, the determination of the unloading speed increment is deduced in detail:

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

[0117] Taking the Halo orbit of 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 will not generate additional thrust, while 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, and its size is proportional to the sum of the angular momentum modulus values ​​in the two directions perpendicular to the active engine.

[0118] like Figure 5 As shown, it is a schematic diagram of a satellite momentum wheel distribution provided by an embodiment of the present application. Among them, momentum wheel 4 is a redundant backup, which can provide necessary bias torque when momentum wheels 1 to 3 are not working normally.

[0119] Continue to use Figure 5 The momentum wheel distribution assumption is as follows: Figure 6 The figure is a schematic diagram of a satellite attitude control engine layout provided in an embodiment of the present application. J5A / J5B and J6A / J6B are force-coupled attitude control engines used to orbit z b Axis yaw attitude adjustment, J3A / J3B, J4A / J4B are non-coupling attitude control engines, used to rotate around the y b Axis pitch attitude adjustment, J1A / J1B, J2A / J2B are non-coupling attitude control engines, used to orbit x b Axis roll attitude adjustment.

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

[0121] If the satellite mass is M, before unloading x b The angular momentum of the axis is H x , the corresponding thrust of the unloaded engine is F x , the lever arm is L x , the speed generated by unloading is v zx , the unloading jet duration is t x ;y b The angular momentum of the axis is H y , the corresponding thrust of the unloaded engine is F by , the lever arm is L y , the speed generated by unloading is v zy , the unloading jet duration is t y After unloading, the angular momentum of the entire star returns to zero, and the following formulas 3 and 4 are obtained:

[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 get v zx With H x The relationship is shown in the following formula 5:

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

[0126] It can be seen that the velocity increment generated by unloading is related to the angular momentum, the length of the unloading engine force arm and the mass of the entire satellite, but has nothing to do with the thrust of the unloading engine.

[0127] Similarly, for y b The speed v generated by the shaft unloading zy and angular momentum H x The relationship is shown in the following formula 6:

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

[0129] If the total velocity increment caused by unloading is v z , then v z v zx With v zy The sum of is shown in the following formula 7:

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

[0131] In general, L x =L y =L, the above formula can be further simplified as shown in the following formula 8:

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

[0133] (2) Determine the sum of the angular momentum moduli.

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

[0135] In the embodiment of the present application, when determining the unloading angular momentum, an optional implementation is:

[0136] The product of the first angular momentum, the transpose of the body attitude matrix and the first unit vector is used as the second angular momentum in any direction; wherein the first unit vector is: a unit vector in any direction in the inertial system determined based on 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 determined according to the azimuth and pitch angles in the reference coordinate system; based on the modulus of the first angular momentum and the modulus of the second angular momentum, the upper limit and lower limit of the sum of the moduli of the angular momentum in two directions perpendicular to the second angular momentum are determined by a vector decomposition method.

[0137] Specifically, first, in the reference coordinate system, the second unit vector of an arbitrary direction l is determined according to the azimuth angle and the elevation angle, as shown in the following formula 9:

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

[0139] Where [·] is the matrix representation of the vector.

[0140] Next, determine the first unit vector of an arbitrary direction l in the inertial system, as shown in the following formula 10:

[0141]

[0142] In the formula, [·] i is the matrix representation of the vector in inertial system i, the same below.

[0143] Therefore, the component of the first angular momentum in this direction, that is, the second angular momentum, is expressed as follows in Formula 11:

[0144]

[0145] From formula 11, we can see that L bi0 and H0 are known quantities, so H l is a function of A and E.

[0146] When the satellite is unloaded, the unloading velocity increment is mainly generated by the angular momentum components on the two axes perpendicular to the l direction. The sum of the unloading angular momentum on the two perpendicular axes is denoted as H a According to the vector decomposition principle, H a The size of is as shown in the following formula 12:

[0147]

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

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

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

[0151] Determine the product of the unloading engine force arm and the satellite mass; take the quotient of the product divided by the upper limit of the angular momentum as the upper limit of the velocity increment, and take the quotient of the product divided by the lower limit of the angular momentum as the lower limit of the velocity increment.

[0152] Specifically, the unloading speed increment v generated by unloading l As shown in the following formula 13:

[0153]

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

[0155] It should be noted that the directions of the estimated track maintenance speed increment, unloading speed increment and attitude adjustment unloading remaining speed increment are the same.

[0156] According to the relationship between the unloading speed increment and the estimated track maintenance speed increment, the attitude adjustment unloading remaining speed increment is determined by the following method:

[0157] If the modulus of the estimated track maintenance speed increment is less than the speed increment lower limit, the difference between the speed increment lower limit and the modulus of the estimated track maintenance speed increment is used as the modulus of the attitude adjustment unloading remaining speed increment;

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

[0159] If the modulus of the estimated track maintenance velocity increment is greater than the velocity increment upper limit, the difference between the modulus of the estimated track maintenance velocity increment and the velocity increment upper limit is used as the modulus of the remaining velocity increment for attitude adjustment unloading.

[0160] Specifically, the remaining speed increment after posture adjustment and unloading is as shown in the following formula 14:

[0161]

[0162] From the above content, it can be seen that satellite attitude unloading is a multi-solution problem. When the attitude and angular momentum before unloading are known, the residual velocity increment of attitude unloading is a function of A and E.

[0163] The purpose of calculating the target posture of attitude adjustment and unloading is to find the optimal posture so that the remaining speed increment of attitude adjustment and unloading is minimized. Therefore, after determining the remaining speed increment of attitude adjustment and unloading by analytical method, the embodiment of the present application can optimize the azimuth and pitch angles by the following method:

[0164] S13: In the reference coordinate system, the attitude adjustment unloading residual speed increment is taken as the optimization target, the azimuth angle and the pitch angle are optimized, and the reference attitude adjustment unloading posture is determined according to the azimuth angle and the pitch angle obtained by the optimization.

[0165] Specifically, the optimization algorithm is used to optimize the angles A and E, and the optimization goal is the remaining speed increment v of posture adjustment unloading e , where the optimization algorithm is the particle swarm optimization algorithm (PSO). That is, to determine v e A and E at their smallest.

[0166] Among them, the optimization variables are:

[0167] A: The angle between the projection of the direction vector l in the XOY plane and the X-axis, ranging from -180° to 180°;

[0168] E: The angle between the direction vector l and the XOY plane, ranging from 0° to 90°;

[0169] The optimization goal is to minimize the remaining speed increment after posture adjustment and unloading, that is:

[0170] J=v e (Formula 15)

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

[0172] Due to the randomness of the particle swarm algorithm solution, repeated calculations can obtain different results, so it can effectively solve the posture adjustment path safety problem. The so-called posture adjustment path safety problem refers to the need to ensure that the momentum wheels will not be saturated and unloaded due to angular momentum redistribution during the posture adjustment process when adjusting from the pre-unloading posture to the unloading posture. Therefore, when using the particle swarm algorithm for solving, after repeated calculations, the solution with a safe posture adjustment path is selected.

[0173] After adopting the particle swarm global optimization algorithm, if the remaining speed increment of the posture adjustment unloading does not meet the accuracy requirements (for example, the accuracy can be set to 1mm / s), it is necessary to further adopt a local optimization algorithm for optimization. The embodiment of the present application adopts the coordinate rotation method for local solution. When performing local optimization solution, the result of the particle swarm global optimization is used as its initial value. It should be noted that any method that can be used for local solution is applicable to the embodiment of the present application, which will not be described in detail here.

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

[0175] After optimizing the azimuth and pitch angles in the above way, the optimal unloading speed increment direction under semi-analytical conditions can be obtained. However, the actual speed increment in this direction is different from V best / sin(E) has certain differences, therefore, the embodiment of the present application corrects the unloading posture according to the actual track 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 unloading attitude, and correct the reference attitude adjustment unloading attitude according to the actual orbit maintenance velocity increment to determine the target unloading attitude of the satellite.

[0177] Specifically, the embodiment of the present application changes the unloading speed increment by adjusting the rotation angle around the Z axis, so that the posture adjustment unloading remaining speed increment is minimized.

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

[0179] In the new local 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, and 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 local system according to the second angle, the unloading attitude corresponding to the new local system is used as the target unloading attitude.

[0180] Among them, the Z-axis direction of the new system is consistent with the Z-axis direction of the reference attitude adjustment and unloading posture.

[0181] Specifically, firstly, the method (2) of determining the speed increment in S11 is used to calculate the actual track maintenance speed increment, and the modulus of the actual track maintenance speed increment is Δv m . Furthermore, according to Δv m The second angle γ between the unloaded angular momentum and the X-axis in the XOY plane is calculated back.

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

[0183]

[0184] The semi-analytical attitude adjustment and unloading method for the Halo orbit satellite at the Earth-Moon L2 point proposed in the embodiment of the present application utilizes the vector decomposition and synthesis principle of the orbit maintenance solution, and replaces 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 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 taking into account the optimality of the solution and the computational efficiency. The embodiment of the present application can be directly used for the orbit maintenance of the Halo orbit satellite at the Earth-Moon L2 point. Its principles and methods such as the use of the vector decomposition and synthesis principle to analytically calculate the velocity increment required for orbit maintenance in any direction and the correction of the solution after the semi-analytical calculation can also be used for the maintenance and control of other types of orbits.

[0185] In order to prove the feasibility of the solution proposed in the embodiment of the present application, a simulation verification process of a semi-analytical attitude adjustment and unloading method for a Halo orbit satellite at the Earth-Moon L2 point is given, as shown below:

[0186] Taking the Halo orbit of the Earth-Moon L2 point as an example, its J2000 series orbit epoch and position velocity are shown in the following table.

[0187] Table 1 Halo orbit position velocity of the Earth-Moon L2 point

[0188]

[0189]

[0190] Assume that the unloading time is 2024-07-27T09:00:00, and the satellite attitude quaternion Q at the unloading time is [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 between any direction and the expected direction.

[0192] First, the velocity increments in the three directions at the control moment are used as control variables, and the velocity in the X direction is 0 when the XOZ plane of the rotating coordinate system of the Earth-Moon L2 point is crossed for the third time as the control target. The initial velocity increment vector required for orbit maintenance is calculated, and the maintenance attitude is established. On the basis of maintaining the attitude, the X and Y angles are rotated by α3 respectively to obtain a new orbit maintenance direction. The initial maintenance velocity increment vector and modulus are calculated according to the fixed direction orbit maintenance method. Based on this orbit maintenance initial velocity increment vector, the method in S11 is used to calculate the direction of the desired velocity increment and the corresponding desired velocity increment modulus. The angle between the initial velocity increment and the desired velocity increment and the arc cosine angle of the ratio of the desired velocity increment modulus to the initial velocity increment modulus are calculated, and the sizes of the two are compared to verify the correctness of empirical formula 1.

[0193] The method of calculating the initial vector by Newton's iteration method is recorded as the iteration method. The direction of rotating around X by an angle of α3 is recorded as fixed direction 1, and the direction of rotating around Y by an angle of α3 is recorded 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 Calculation results when α3 angle is 30°

[0195]

[0196] Table 3 Calculation results when α3 angle is 20°

[0197]

[0198] Table 4 Calculation results when α3 angle is 10°

[0199]

[0200] From Tables 2 to 4, it can be seen that the velocity increment direction calculated by the method in S11 has the smallest velocity increment required for orbit maintenance, which can be used as the direction of the expected velocity increment. The strategy of solving the velocity increment in three directions using the Newton iteration method, the velocity increment modulus is close to the expected velocity increment, which can be used as an approximation of the expected velocity increment. The angle calculated by the two velocity increment moduli in formula 1 and the angle calculated according to the velocity increment vector, except for the case where the angle is small, the maximum deviation is less than 0.2°, which can fully prove the correctness of formula 1.

[0201] (2) Result verification.

[0202] According to the orbital parameters and simulation conditions, the semi-analytical method is used to calculate the unloading posture. The calculation results of the target unloading posture are shown in the following table.

[0203] Table 5 Calculation results of target unloading posture

[0204]

[0205]

[0206] Under the corresponding attitude in the above table, the estimated orbit maintenance velocity increment required for Halo orbit maintenance is 0.01469m / s, the unloading velocity increment is 0.01469m / s, the attitude adjustment unloading remaining velocity increment is 0.0m / s, and the target attitude is the optimal result. The unloading attitude is dynamically reviewed according to the orbit and input conditions. The projection of the satellite trajectory before and after unloading in the XOY plane of the rotating coordinate system is as follows Figure 7 It can be seen that the trajectory before unloading showed a divergent trend, and after attitude adjustment unloading, the satellite crossed the XOZ plane 4 times without showing a divergent trend, which fully demonstrated the correctness of the attitude parameters of the attitude adjustment unloading target and the effectiveness of the satellite attitude adjustment unloading method provided by this application.

[0207] Based on the same inventive concept, the present application also provides a semi-analytical attitude adjustment and unloading device for a Halo orbit satellite at the Earth-Moon L2 point. Figure 8 As shown, it is a schematic diagram of the structure of the satellite attitude adjustment 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 when it is running in the current orbit, and 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 attitude adjustment unloading remaining speed increment by the azimuth angle and the pitch angle in the reference coordinate system established based on the expected speed increment, where the attitude adjustment unloading remaining speed increment is the difference between the estimated orbit maintenance speed increment and the unloading speed increment in any direction; the azimuth angle and the pitch angle are the corresponding representation angles of any direction corresponding to the estimated orbit maintenance speed 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 attitude adjustment and unloading residual speed increment as the optimization target, and determine the reference attitude adjustment and unloading posture according to the azimuth and pitch angles obtained by the 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 unloading attitude, and correct the reference attitude adjustment unloading attitude according to the actual orbit maintenance velocity increment to determine the target unloading attitude of the satellite.

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

[0213] Determine an estimated track maintenance speed increment in the arbitrary direction according to a first angle between the direction of the expected speed increment and the arbitrary direction, and the expected speed increment, wherein a modulus value of a speed component of the estimated track maintenance speed increment in the direction of the expected speed increment is the same as a modulus value of the expected speed increment;

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

[0215] The difference between the estimated track maintenance speed increment and the unloading speed increment is taken as the attitude adjustment unloading remaining speed increment.

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

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

[0218] The quotient of the expected velocity increment and the cosine value of the first angle is taken as the estimated track maintenance velocity increment in any direction.

[0219] Optionally, the unloading speed increment includes a speed increment upper limit value and a speed increment lower limit value, the attitude information includes the first angular momentum and the body attitude matrix of the satellite in the system, and the reference attitude matrix in the reference coordinate system, and the unloading information includes the unloading engine force arm of the satellite; 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 used as the second angular momentum in any direction; wherein the first unit vector is: a unit vector in any direction in the inertial system determined based on 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 determined according to the azimuth and pitch angle in the reference coordinate system;

[0221] Based on the modulus value of the first angular momentum and the modulus value of the second angular momentum, determining the upper limit value and the lower limit value of the sum of the modulus values ​​of the angular momentum in two directions perpendicular to the second angular momentum by a vector decomposition method;

[0222] Determine the product of the unloaded engine moment arm and the satellite mass;

[0223] The speed increment upper limit is determined based on the quotient of the product and the upper limit of the sum of the angular momentum moduli, and the speed increment lower limit is determined based on the quotient of the product and the lower limit of the sum of the angular momentum moduli.

[0224] Optionally, the estimated track maintenance speed increment, the unloading speed increment and the attitude adjustment unloading remaining speed increment have the same direction, and the unloading speed increment includes a speed increment upper limit value and a speed increment lower limit value. The representation unit 802 is specifically used for:

[0225] If the modulus of the estimated track maintenance speed increment is less than the speed increment lower limit, the difference between the speed increment lower limit and the modulus of the estimated track maintenance speed increment is used as the modulus of the attitude adjustment unloading remaining speed increment;

[0226] If the modulus of the estimated track maintenance speed increment is greater than or equal to the speed increment lower limit, and the modulus of the estimated track maintenance speed increment is less than or equal to the speed increment upper limit, then the modulus of the remaining speed increments for attitude adjustment unloading are all set to 0;

[0227] If the modulus of the estimated track maintenance velocity increment is greater than the velocity increment upper limit, the difference between the modulus of the estimated track maintenance velocity increment and the velocity increment upper limit is used as the modulus of the remaining velocity increment for attitude adjustment 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 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, and the determining unit 801 is specifically used to:

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

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

[0231] Based on the basic information and the preset direction, a third initial velocity increment in the preset direction is determined using the Newton 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 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, and the determining unit 801 is specifically used to:

[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 used as the second velocity;

[0235] 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;

[0236] In the direction of the expected velocity increment, the Newton iteration method is used to determine the modulus of the expected velocity increment.

[0237] Optionally, the correction unit 804 is specifically configured to:

[0238] In 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, and 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; the Z-axis of the new system is consistent with the Z-axis direction of the reference attitude adjustment and unloading attitude;

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

[0240] Based on the same inventive concept, an electronic device is also provided in the embodiment of the present application. The structure of the electronic device can be as follows Fig. 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, wherein the program storage area may store an operating system and programs required for running the instant messaging function, etc.; the data storage area may store various instant messaging information and operation instruction sets, etc.

[0242] The memory 901 may be a volatile memory, such as a random-access memory (RAM); the memory 901 may also be a non-volatile memory, such as a read-only memory, a flash memory, a hard disk drive (HDD) or a solid-state drive (SSD); or the memory 901 may be any other medium that can be used to carry or store a desired computer program in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory 901 may be a combination of the above memories.

[0243] The processor 902 may include one or more central processing units (CPU) or a digital processing unit, etc. The processor 902 is used to implement the above-mentioned satellite attitude adjustment unloading method when calling the computer program stored in the memory 901.

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

[0245] The specific connection medium between the memory 901, the communication module 903 and the processor 902 is not limited in the embodiment of the present application. Fig. 9 In the embodiment, the memory 901 and the processor 902 are connected via a bus 904. The bus 904 is connected to the processor 902 via a bus 904. Fig. 9 The connections between the other components are only for illustration and are not intended to be limiting. The bus 904 can be divided into an address bus, a data bus, a control bus, etc. For ease of description, Fig. 9 The diagram shows that only one thick line is used, but this does not mean that there is only one bus or only one type of bus.

[0246] The memory 901 stores a computer storage medium, and the computer storage medium stores computer executable instructions, and the computer executable instructions are used to implement the satellite attitude adjustment unloading method of the embodiment of the present application. The processor 902 is used to execute the above satellite attitude adjustment unloading method.

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

[0248] The communication component 1010 is used to communicate with the server. In some embodiments, a wireless fidelity (WiFi) module may be included. The WiFi module belongs to a short-range wireless transmission technology. The electronic device can help the user to send and receive information through the WiFi module.

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

[0250] The display unit 1030 can also be used to display information input by the user or information provided to the user and a graphical user interface (GUI) of various menus of the terminal device. 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 in the form of a liquid crystal display, a light emitting diode, etc.

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

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

[0253] The camera 1040 can be used to capture static images, and the user can publish the images taken by the camera 1040 through the application. The camera 1040 can be one or more. The object generates an optical image through the lens and projects it onto the photosensitive element. The photosensitive element can be a charge coupled device (CCD) or a complementary metal-oxide-semiconductor (CMOS) phototransistor. The photosensitive element converts the optical signal into an electrical signal, and then passes the electrical signal to the processor 1080 to convert it into a digital image signal.

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

[0255] The audio circuit 1060, the speaker 1061, and the microphone 1062 can provide an audio interface between the user and the terminal device. The audio circuit 1060 can transmit the electrical signal converted from the received audio data to the speaker 1061, which is converted into a sound signal for output. The terminal device can also be equipped with a volume button for adjusting the volume of the sound signal. On the other hand, the microphone 1062 converts the collected sound signal into an electrical signal, which is received by the audio circuit 1060 and converted into audio data, and then the audio data is output to the communication component 1010 to be sent to, for example, another terminal device, or the audio data is output to the memory 1020 for further processing.

[0256] The Bluetooth module 1070 is used to exchange information with other Bluetooth devices having Bluetooth modules through the Bluetooth protocol. For example, the terminal device can establish a Bluetooth connection with a wearable electronic device (such as a smart watch) that also has a Bluetooth module through the Bluetooth module 1070 to exchange data.

[0257] The processor 1080 is the control center of the terminal device. It uses various interfaces and lines to connect various parts of the entire terminal. It executes various functions of the terminal device 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 processes the operating system, user interface, and application programs, and the baseband processor mainly processes wireless communications. It is understandable that the above-mentioned baseband processor may not be integrated into the processor 1080. In the present application, the processor 1080 can run the operating system, application programs, user interface display and touch response, as well as the satellite attitude adjustment unloading method of the embodiment of the present application. In addition, the processor 1080 is coupled to the display unit 1030.

[0258] In some possible implementations, various aspects of the satellite attitude adjustment offloading method provided in the present application may 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 is used to enable the electronic device to perform the steps of the satellite attitude adjustment offloading method according to various exemplary embodiments of the present application described above in this specification. For example, the electronic device may perform the following steps: Figure 1 Follow the steps shown in .

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

[0260] The program product of the embodiment of the present application may adopt a portable compact disk read-only memory (CD-ROM) and include a computer program, and can be run on an electronic device. However, the program product of the present application is not limited thereto, and in this document, a readable storage medium may be any tangible medium containing or storing a program, which can be used by or in combination 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, wherein a readable computer program is carried. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the foregoing. A readable signal medium may also be any readable medium other than a readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with a command execution system, apparatus, or device.

[0262] The computer program embodied on the readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0263] The computer program for performing the operation of the present application can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and also conventional procedural programming languages ​​such as "C" language or similar programming languages. The computer program can be executed entirely on the user electronic device, partially on the user electronic device, as a separate software package, partially on the user electronic device and partially on a remote electronic device, or entirely on a remote electronic device or server. In the case of a remote electronic device, the remote electronic device can be connected to the user electronic device through any type of network including a local area network (LAN) or a wide area network (WAN), or can be connected to an external electronic device (for example, using an Internet service provider to connect through the Internet).

[0264] It should be noted that, although several units or subunits of the device are mentioned in the above detailed description, this division is merely exemplary and not mandatory. In fact, according to the embodiments of the present 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 into multiple units to be embodied.

[0265] In addition, although the operations of the method of the present application are described in a specific order in the drawings, this does not require or imply that the operations must be performed in this specific order, or that all the operations shown must be performed to achieve the desired results. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step, and / or one step may be decomposed into multiple steps.

[0266] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0267] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0268] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0269] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0270] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0271] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A semi-analytical attitude adjustment and unloading method for a Halo orbit satellite at the Earth-Moon L2 point, characterized in that: The method comprises: Determine an initial velocity increment required for orbit maintenance based on basic information of the satellite in the current orbit, and determine a desired velocity increment for orbit maintenance in the orbit maintenance direction of the current orbit based on the initial velocity increment; In a reference coordinate system established based on the expected speed increment, the attitude adjustment unloading remaining speed increment is represented by an azimuth angle and a pitch angle, wherein the attitude adjustment unloading remaining speed increment is the difference between the estimated orbit maintenance speed increment and the unloading speed increment in any direction; the azimuth angle and the pitch angle are the corresponding representation angles of the estimated orbit maintenance speed increment in any direction in the reference coordinate system; In the reference coordinate system, taking the attitude adjustment and unloading residual speed increment as the optimization target, optimizing the azimuth and pitch angles, and determining a reference attitude adjustment and unloading posture according to the optimized azimuth and pitch angles; The actual orbit maintenance velocity increment in the direction corresponding to the reference attitude adjustment unloading attitude is obtained, and the reference attitude adjustment unloading attitude is corrected according to the actual orbit maintenance velocity increment to determine the target unloading attitude of the satellite.

2. The method according to claim 1, characterized in that The method of expressing the attitude adjustment unloading remaining velocity increment by azimuth and pitch angle in a reference coordinate system established based on the expected velocity increment comprises: Determining the estimated track-maintaining speed increment in the arbitrary direction according to a first angle between the direction of the expected speed increment and the arbitrary direction, and the expected speed increment, wherein a modulus value of a speed component of the estimated track-maintaining speed increment in the direction of the expected speed increment is the same as a modulus value of the expected speed increment; Based on the attitude information and unloading information of the satellite, combined with the azimuth and pitch angle, determine the unloading speed increment in the arbitrary direction; The difference between the estimated track maintenance speed increment and the unloading speed increment is used as the attitude adjustment unloading remaining speed increment.

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

4. The method according to claim 2, characterized in that Determining the estimated track maintenance speed increment in any direction according to a first angle between the direction of the expected speed increment and the arbitrary direction, and the expected speed increment, comprises: The quotient of the expected velocity increment and the cosine value of the first angle is used as the estimated trajectory maintenance velocity increment in any direction.

5. The method according to claim 2, characterized in that The unloading speed increment includes a speed increment upper limit value and a speed increment lower limit value, the attitude information includes a first angular momentum and a body attitude matrix of the satellite in the present system, and a reference attitude matrix in the reference coordinate system, and the unloading information includes an unloading engine force arm of the satellite; the unloading speed increment in the arbitrary direction is determined based on the attitude information and the unloading information of the satellite in the present system in combination with the azimuth and the pitch angle, including: The product of the first angular momentum, the transpose of the body attitude matrix and the first unit vector is used as the second angular momentum in the arbitrary direction; wherein the first unit vector is: a unit vector in the arbitrary direction in the inertial system determined based on the product of the second unit vector and the transpose of the reference attitude matrix; the second unit vector is: a unit vector in the arbitrary direction determined according to the azimuth angle and the pitch angle in the reference coordinate system; Based on the modulus value of the first angular momentum and the modulus value of the second angular momentum, determining an upper limit value and a lower limit value of the sum of the modulus values ​​of the angular momentum in two directions perpendicular to the second angular momentum by a vector decomposition method; Determining the product of the unloading engine moment arm and the mass of the satellite; The speed increment upper limit is determined according to the quotient of the product and the upper limit of the sum of the angular momentum moduli, and the speed increment lower limit is determined according to the quotient of the product and the lower limit of the sum of the angular momentum moduli.

6. The method according to any one of claims 1 to 5, characterized in that: The estimated track maintenance speed increment, the unloading speed increment and the attitude adjustment unloading remaining speed increment have the same direction, the unloading speed increment includes a speed increment upper limit value and a speed increment lower limit value, and the difference between the estimated track maintenance speed increment and the unloading speed increment is used as the attitude adjustment unloading remaining speed increment, including: If the modulus of the estimated track maintenance speed increment is less than the speed increment lower limit, the difference between the speed increment lower limit and the modulus of the estimated track maintenance speed increment is used as the modulus of the attitude adjustment unloading remaining speed increment; If the modulus of the estimated track maintenance speed increment is greater than or equal to the speed increment lower limit, and the modulus of the estimated track maintenance speed increment is less than or equal to the speed increment upper limit, then the modulus of the attitude adjustment unloading remaining speed increment is set to 0; If the modulus of the estimated track maintenance speed increment is greater than the speed increment upper limit, the difference between the modulus of the estimated track maintenance speed increment and the speed increment upper limit is used as the modulus of the attitude adjustment unloading remaining speed increment.

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 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, and determining the initial velocity increment required for orbit maintenance based on basic information of the satellite in the current orbit includes: Based on the basic information, a first initial velocity increment is determined using a Newton iteration method; Based on the basic information and the direction of the first initial velocity increment, a second initial velocity increment is determined by using a Newton iteration method; Based on the basic information and the preset direction, a 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 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, and determining the desired velocity increment for track maintenance in the track maintenance direction of the current track based on the initial velocity increment includes: taking the difference between the first initial speed increment and the second initial speed increment as a first speed difference; taking the difference between the second initial speed increment and the third initial speed increment as the second speed difference; Determine a cross product of the first speed difference and the second speed difference, and use the direction of the cross product result as the direction of the desired speed increment; In the direction of the expected speed increment, a modulus value of the expected speed increment is determined using Newton's 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 according to the actual orbit maintenance speed increment to determine the target unloading attitude of the satellite includes: In a new local 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, and a second angle between the angular momentum corresponding to the actual orbit maintenance velocity increment and the X-axis in the XOY plane is determined; the Z-axis of the new local system is consistent with the Z-axis direction of the reference attitude adjustment and unloading attitude; After determining the X-axis and the Y-axis of the new system according to the second angle, the unloading posture corresponding to the new system is used as the target unloading posture.

10. A semi-analytical attitude adjustment and unloading device for a Halo orbit satellite at the Earth-Moon L2 point, characterized in that: include: a determination unit, configured to determine an initial velocity increment required for orbit maintenance based on basic information of the satellite in the current orbit, and determine a desired velocity increment for orbit maintenance in the orbit maintenance direction of the current orbit based on the initial velocity increment; A representation unit, used for representing the attitude adjustment unloading remaining speed increment by an azimuth angle and a pitch angle in a reference coordinate system established based on the expected speed increment, wherein the attitude adjustment unloading remaining speed increment is the difference between the estimated orbit maintenance speed increment and the unloading speed increment in any direction; the azimuth angle and the pitch angle are the corresponding representation angles of any direction corresponding to the estimated orbit maintenance speed increment in the reference coordinate system; An optimization unit, configured to optimize the azimuth and pitch angles in the reference coordinate system with the attitude adjustment and unloading residual speed increment as an optimization target, and determine a reference attitude adjustment and unloading posture according to the azimuth and pitch angles obtained by the optimization; The correction unit is used to obtain the actual orbit maintenance speed increment in the direction corresponding to the reference attitude adjustment unloading attitude, and correct the reference attitude adjustment unloading attitude according to the actual orbit maintenance speed increment to determine the target unloading attitude of the satellite.

11. An electronic device, characterized in that: It comprises a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of any one of the methods of claims 1 to 9.

12. A computer-readable storage medium, characterized in that: It comprises a computer program. When the computer program is run on an electronic device, the computer program is used to enable the electronic device to execute the steps of any method described in claims 1 to 9.

13. A computer program product, characterized in that The method comprises 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, so that the electronic device executes the steps of any one of the methods described in claims 1 to 9.

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