Method and device for calculating unloading attitude of momentum wheel of Halo orbit satellite

Abstract

The invention discloses a Halo orbit satellite momentum wheel unloading attitude calculation method and device, and the method comprises the steps: estimating the speed increment generated in the historical unloading process through precise orbit determination, and fitting the relation between the speed increment and the angular momentum at the historical unloading moment to obtain a fitting coefficient; and determining nominal control parameters required by the satellite for maintaining the Halo orbit configuration and a nominal position speed of the satellite passing through the XZ plane of the earth-moon rotating coordinate system for the first time after nominal control. And determining a speed increment generated by unloading based on the angular momentum at the unloading moment and the fitting coefficient, and determining a post-unloading track and a post-unloading position speed of passing through the XZ plane for the first time after unloading in combination with an unloading attitude. Obtaining the deviation between the nominal controlled orbit and the post-unloading orbit according to the nominal position speed and the post-unloading position speed, optimizing the unloading attitude to enable the deviation to be minimum based on a coordinate rotation method, obtaining the optimal unloading attitude quaternion, achieving the purpose that the speed increment generated by unloading is used for maintaining the satellite Halo orbit configuration, counteracting the divergence trend of the Halo orbit, and achieving the optimal unloading attitude quaternion. And maintenance frequency is reduced.

Description

Technical Field

[0001] The present invention relates to the field of aerospace dynamics and control, and particularly to a method and device for calculating the attitude of a momentum wheel unloading of a satellite in a Halo orbit. Background Art

[0002] In the field of aerospace dynamics, the Halo orbit in the Earth-Moon space has extensive applications. When a satellite located in a Halo orbit operates for a long time, due to the instability of the Halo orbit itself and long-term disturbances such as solar radiation pressure and the gravitational force of large celestial bodies, it is necessary to frequently implement orbit control to maintain the Halo orbit configuration, which will greatly consume the remaining propellant of the satellite.

[0003] Modern satellites usually use momentum wheels as the actuators of the attitude control system. When the rotational speed of the momentum wheel reaches the critical value, it is necessary to unload and restore to the initial rotational speed. A satellite located in a Halo orbit is subject to a disturbing torque generated by solar radiation pressure for a long time. The satellite absorbs the disturbing torque through the momentum wheel to maintain the target attitude. After the momentum wheel is saturated, it is necessary to consume propellant for unloading, and the velocity increment generated by unloading will further perturb the orbit.

[0004] Therefore, how to utilize the inevitable momentum wheel unloading of the satellite to reduce the orbit maintenance frequency and reduce the propellant consumption is an urgent problem to be solved at present. Summary of the Invention

[0005] An embodiment of the present invention provides a method for calculating the attitude of a momentum wheel unloading of a satellite in a Halo orbit, which is used to actively unload the momentum wheel in a suitable attitude, and use the velocity increment generated by unloading for maintaining the satellite orbit configuration, so as to realize using the momentum wheel unloading to offset the divergence trend of the Halo orbit, reduce the orbit maintenance frequency, and reduce the propellant consumption of the satellite.

[0006] In a first aspect, an embodiment of the present invention provides a method for calculating the attitude of a momentum wheel unloading of a satellite in a Halo orbit, including:

[0007] Planning the satellite unloading time, determining the nominal control direction and the nominal post-control orbit required for the satellite to maintain the Halo orbit configuration at the unloading time, and based on the nominal post-control orbit, determining the nominal position velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit;

[0008] Establishing an angular momentum coordinate system of the satellite based on the angular momentum vector in the inertial system at the unloading time and the nominal control direction, and determining the angular optimization variables of the satellite, where the angular optimization variables are the Euler angles for the satellite to rotate around the coordinate axes of the angular momentum coordinate system in a specific order;

[0009] Determine the velocity increment generated by the satellite during the unloading process based on the angular momentum vector and the fitting coefficient, determine the post-unloading orbit, and determine the post-unloading position and velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system after unloading; the fitting coefficient represents the fitting relationship between the angular momentum of the satellite at the unloading moment and the velocity increment generated during the unloading process;

[0010] Obtain the deviation between the nominal post-control orbit and the post-unloading orbit based on the nominal position and velocity and the post-unloading position and velocity, and optimize the deviation based on the coordinate rotation method according to the angle optimization variable to obtain the optimal attitude quaternion for the satellite momentum wheel unloading, so that the satellite can perform momentum wheel unloading according to the optimal attitude quaternion, achieving the goal of maintaining the halo orbit configuration through active unloading.

[0011] In the above technical solution, it is first necessary to plan the satellite unloading moment according to the rotation speed of the satellite momentum wheel. Among them, the halo orbit can also be called the Halo orbit. Then, according to the Halo orbit maintenance control method of the satellite, determine the nominal control direction and the nominal post-control orbit of the satellite. Then, according to the position of the satellite when it runs on the nominal post-control orbit, determine the nominal position and velocity of the satellite when it first crosses the XZ plane of the Earth-Moon rotating coordinate system. The nominal position and velocity include the nominal position and the nominal velocity of the satellite when it crosses the XZ plane. When the satellite momentum wheel unloads, it will generate an angular momentum vector. Therefore, the velocity increment generated by the satellite during the unloading process can be determined based on the angular momentum vector and the fitting coefficient, and the post-unloading orbit of the satellite can be determined based on the velocity increment of the satellite. The fitting coefficient represents the fitting relationship between the angular momentum of the satellite at the unloading moment and the velocity increment generated during the unloading process, and the product of the angular momentum and the fitting coefficient is the velocity increment. Then, according to the position of the satellite when it runs on the post-unloading orbit, determine the post-unloading position and velocity of the satellite when it first crosses the XZ plane of the Earth-Moon rotating coordinate system. The post-unloading position and velocity include the post-unloading position and the post-unloading velocity of the satellite when it crosses the XZ plane. Finally, according to the deviation between the post-unloading position and velocity and the nominal position and velocity, obtain the deviation between the nominal post-control orbit and the post-unloading orbit. Finally, by adjusting the attitude of the satellite at the unloading moment, optimize the deviation between the nominal post-control orbit and the post-unloading orbit to obtain the optimal attitude quaternion for the satellite momentum wheel unloading, realizing the use of the velocity increment generated by unloading for satellite orbit configuration maintenance, reducing the orbit maintenance frequency, and reducing the propellant consumption of the satellite.

[0012] Optionally, before planning the satellite unloading moment, the method further includes:

[0013] Obtain the attitude quaternion at the historical unloading moment, the angular momentum at the historical unloading moment, and the corresponding historical unloading velocity increment; the historical unloading velocity increment is the velocity increment generated during the historical unloading process of the satellite in the inertial system, and the historical unloading velocity increment is obtained based on the precise orbit determination results before and after the satellite unloading. The angular momentum at the historical unloading moment is the three-axis angular momentum of the satellite in its own system at the unloading moment;

[0014] Based on the attitude quaternion at the historical unloading moment, determine the first transformation matrix for converting from the inertial system to the system of the satellite at the unloading moment;

[0015] Based on the first transformation matrix, convert the historical unloading velocity increment from the inertial system to the system of the satellite at the unloading moment, and obtain the fitting coefficient according to the fitting relationship between the historical unloading velocity increment in the system of the satellite at the unloading moment and the angular momentum at the historical unloading moment.

[0016] In the above technical solution, it can be understood that at different historical unloading moments, the positions of the satellite are also different. Therefore, the systems of the satellite at the unloading moments are also different.

[0017] Optionally, when determining the nominal position and velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal controlled orbit, it includes:

[0018] According to a specified step size, perform dynamic integration on the position and velocity of the satellite in the inertial system based on the nominal controlled orbit to obtain the position and velocity of the satellite at the k-th moment, and calculate the rotation matrix for converting from the inertial system to the Earth-Moon rotating coordinate system at the k-th moment; k is an integer greater than or equal to 1, and the first moment is after the unloading moment and is separated from the unloading moment by a preset time period;

[0019] Based on the rotation matrix, convert the position and velocity at the k-th moment from the inertial system to the Earth-Moon rotating coordinate system at the k-th moment to obtain the position coordinates at the k-th moment in the Earth-Moon rotating coordinate system at the k-th moment;

[0020] Calculate the product result of the Y-axis component of the position coordinates at the k-th moment and the Y-axis component of the position coordinates at the (k + 1)-th moment;

[0021] When the product result is less than 0 for the first time, the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal controlled orbit. Perform precise iteration on the k-th moment and the (k + 1)-th moment to obtain the nominal position and velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal controlled orbit.

[0022] Optionally, establish an angular momentum coordinate system of the satellite based on the angular momentum vector in the inertial system at the unloading moment and the nominal control direction, and determine the angle optimization variables of the satellite, including:

[0023] Take the direction of the angular momentum vector as the Y-axis of the angular momentum coordinate system, take the direction of the cross product result of the Y-axis and the nominal control direction as the X-axis, determine the Z-axis based on the right-hand rule, establish the angular momentum coordinate system, and determine the second transformation matrix for converting from the inertial system to the angular momentum coordinate system;

[0024] Determine the angle optimization variables based on the angles of the satellite rotating around the coordinate axes of the angular momentum coordinate system, and determine the third transformation matrix from the angular momentum coordinate system to the body system at the unloading moment;

[0025] Based on the second transformation matrix and the third transformation matrix, obtain the fourth transformation matrix for converting from the inertial system to the body system at the unloading moment.

[0026] Optionally, determine the velocity increment generated by the satellite during unloading based on the angular momentum vector and the fitting coefficient, and determine the post-unloading orbit, as well as the post-unloading position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit, including:

[0027] Based on the fourth transformation matrix, convert the angular momentum vector from the inertial system to the body system at the unloading moment, and based on the angular momentum vector in the body system at the unloading moment and the fitting coefficient, obtain the velocity increment generated by the satellite during unloading in the body system at the unloading moment;

[0028] Based on the inverse matrix of the fourth transformation matrix, convert the velocity increment generated during unloading from the body system at the unloading moment to the inertial system, and based on the velocity increment generated during unloading, determine the post-unloading orbit;

[0029] Integrate the position and velocity of the satellite in the inertial system dynamically based on the post-unloading orbit at a specified step size to obtain the position and velocity of the satellite at the m-th moment, and calculate the rotation matrix for converting from the inertial system to the Earth-Moon rotating coordinate system at the m-th moment; m is an integer greater than or equal to 1, and the first moment is after the unloading moment and is separated from the unloading moment by a preset time period;

[0030] Based on the rotation matrix, convert the position and velocity at the m-th moment from the inertial system to the Earth-Moon rotating coordinate system at the m-th moment to obtain the position coordinates at the m-th moment in the Earth-Moon rotating coordinate system at the m-th moment;

[0031] Calculate the product result of the Y-axis component of the position coordinates at the m-th moment and the Y-axis component of the position coordinates at the (m + 1)-th moment;

[0032] When the product result is less than 0 for the first time, the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit, and precisely iterates the m-th moment and the (m + 1)-th moment when the product result is less than 0 for the first time, to obtain the post-unloading position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit.

[0033] Optionally, obtaining the deviation between the nominal post-control orbit and the post-unloading orbit according to the nominal position and velocity and the post-unloading position and velocity includes:

[0034] Calculating the product result of the modulus of the vector difference between the satellite position in the post-unloading position and velocity and the satellite position in the nominal position and velocity and the position weight as the position deviation;

[0035] Calculating the product result of the modulus of the vector difference between the satellite velocity in the post-unloading position and velocity and the satellite velocity in the nominal position and velocity and the velocity weight as the velocity deviation; the position weight is less than the velocity weight, and the sum of the position weight and the velocity weight is 1;

[0036] Calculating the summation result of the position deviation and the velocity deviation as the deviation between the nominal post-control orbit and the post-unloading orbit.

[0037] Optionally, based on the coordinate rotation method, optimizing the deviation according to the angle optimization variable to obtain the optimal attitude quaternion for satellite momentum wheel unloading, includes:

[0038] Dividing according to the positive direction and the negative direction of the X-axis of the angular momentum coordinate system to obtain two half-spaces, and determining the value range of the angle optimization variable in each half-space;

[0039] For any one of the two half-spaces, based on the coordinate rotation method, according to the value range of the angle optimization variable in the half-space, optimizing the deviation according to the angle optimization variable until the deviation is minimized, to obtain the optimal value of the angle optimization variable corresponding to the half-space and the minimum deviation;

[0040] Taking the optimal value of the angle optimization variable corresponding to the smaller minimum deviation among the minimum deviations corresponding to the two half-spaces as the optimal value of the angle optimization variable of the satellite;

[0041] Based on the fourth transformation matrix corresponding to the optimal value of the angle optimization variable of the satellite, obtaining the optimal attitude quaternion for satellite momentum wheel unloading.

[0042] In a second aspect, an embodiment of the present invention provides a calculation device for the attitude of a Halo orbit satellite momentum wheel unloading, including:

[0043] An acquisition module, configured to plan the satellite unloading moment, determine the nominal control direction and the nominal post-control orbit required for the satellite to maintain the halo orbit configuration at the unloading moment, and based on the nominal post-control orbit, determine the nominal position and velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit;

[0044] A processing module, configured to establish an angular momentum coordinate system of the satellite based on the angular momentum vector in the inertial system at the unloading moment and the nominal control direction, and determine the angular optimization variables of the satellite, where the angular optimization variables are the Euler angles for the satellite to rotate around the respective coordinate axes of the angular momentum coordinate system in a sequential order;

[0045] Based on the angular momentum vector and the fitting coefficient, determine the velocity increment generated by the satellite during the unloading process, determine the post-unloading orbit, and the post-unloading position and velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit; the fitting coefficient represents the fitting relationship between the angular momentum of the satellite at the unloading moment and the velocity increment generated during the unloading process;

[0046] Obtain the deviation between the nominal post-control orbit and the post-unloading orbit according to the nominal position and velocity and the post-unloading position and velocity, and based on the coordinate rotation method, optimize the deviation according to the angular optimization variables to obtain the optimal attitude quaternion for the satellite to perform momentum wheel unloading, so that the satellite performs momentum wheel unloading according to the optimal attitude quaternion, achieving the goal of maintaining the halo orbit configuration through active unloading.

[0047] Optionally, the processing module is further configured to:

[0048] Obtain the historical unloading moment attitude quaternion, the historical unloading moment angular momentum, and the corresponding historical unloading velocity increment; the historical unloading velocity increment is the velocity increment generated by the satellite during the historical unloading process in the inertial system, the historical unloading velocity increment is obtained according to the precise orbit determination results before and after the satellite unloading, and the historical unloading moment angular momentum is the three-axis angular momentum of the satellite in its own system at the unloading moment;

[0049] Based on the historical unloading moment attitude quaternion, determine the first transformation matrix for converting from the inertial system to the system at the unloading moment;

[0050] Based on the first transformation matrix, convert the historical unloading velocity increment from the inertial system to the system at the unloading moment, and according to the fitting relationship between the historical unloading velocity increment in the system at the unloading moment and the historical unloading moment angular momentum, obtain the fitting coefficient.

[0051] Optionally, the processing module is specifically configured to:

[0052] Integrate the position and velocity of the satellite in the inertial system dynamically based on the nominal post-control orbit at a specified step size to obtain the position and velocity of the satellite at the k-th moment, and calculate the rotation matrix for converting from the inertial system to the Earth-Moon rotating coordinate system at the k-th moment; k is an integer greater than or equal to 1, and the first moment is after the unloading moment and at a preset time interval from the unloading moment.

[0053] Based on the rotation matrix, convert the position and velocity at the k-th moment from the inertial system to the Earth-Moon rotating coordinate system at the k-th moment to obtain the position coordinates at the k-th moment in the Earth-Moon rotating coordinate system at the k-th moment.

[0054] Calculate the product result of the Y-axis component of the position coordinates at the k-th moment and the Y-axis component of the position coordinates at the (k + 1)-th moment.

[0055] When the product result is less than 0 for the first time, the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit. Perform precise iteration on the k-th moment and the (k + 1)-th moment to obtain the nominal position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit.

[0056] Optionally, the processing module is specifically configured to:

[0057] Take the direction of the angular momentum vector as the Y-axis of the angular momentum coordinate system, take the direction of the cross product result of the Y-axis and the nominal control direction as the X-axis, determine the Z-axis based on the right-hand rule, establish the angular momentum coordinate system, and determine the second conversion matrix for converting from the inertial system to the angular momentum coordinate system.

[0058] Determine the angle optimization variable based on the angles of the satellite rotating around the coordinate axes of the angular momentum coordinate system, and determine the third conversion matrix from the angular momentum coordinate system to the body system at the unloading moment.

[0059] Based on the second conversion matrix and the third conversion matrix, obtain the fourth conversion matrix for converting from the inertial system to the body system at the unloading moment.

[0060] Optionally, the processing module is specifically configured to:

[0061] Based on the fourth conversion matrix, convert the angular momentum vector from the inertial system to the body system at the unloading moment, and based on the angular momentum vector in the body system at the unloading moment and the fitting coefficient, obtain the velocity increment generated during the unloading process of the satellite in the body system at the unloading moment.

[0062] Based on the inverse matrix of the fourth conversion matrix, convert the velocity increment generated during the unloading process from the body system at the unloading moment to the inertial system, and based on the velocity increment generated during the unloading process, determine the post-unloading orbit.

[0063] Integrate the position and velocity of the satellite in the inertial system based on the post-unloading orbit at a specified step size to obtain the position and velocity of the satellite at the m-th moment, and calculate the rotation matrix from the inertial system to the Earth-Moon rotating coordinate system at the m-th moment; m is an integer greater than or equal to 1, and the first moment is after the unloading moment and at a preset time interval from the unloading moment.

[0064] Based on the rotation matrix, transform the position and velocity at the m-th moment from the inertial system to the Earth-Moon rotating coordinate system at the m-th moment to obtain the position coordinates at the m-th moment in the Earth-Moon rotating coordinate system at the m-th moment.

[0065] Calculate the product result of the Y-axis component of the position coordinates at the m-th moment and the Y-axis component of the position coordinates at the (m + 1)-th moment.

[0066] When the product result is less than 0 for the first time, the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit, and perform precise iteration on the m-th moment and the (m + 1)-th moment when the product result is less than 0 for the first time to obtain the post-unloading position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit.

[0067] Optionally, the processing module is specifically configured to:

[0068] Calculate the product result of the modulus of the vector difference between the satellite position in the post-unloading position and velocity and the satellite position in the nominal position and velocity and the position weight as the position deviation.

[0069] Calculate the product result of the modulus of the vector difference between the satellite velocity in the post-unloading position and velocity and the satellite velocity in the nominal position and velocity and the velocity weight as the velocity deviation; the position weight is less than the velocity weight, and the sum of the position weight and the velocity weight is 1.

[0070] Calculate the sum result of the position deviation and the velocity deviation as the deviation between the nominal post-control orbit and the post-unloading orbit.

[0071] Optionally, the processing module is specifically configured to:

[0072] Divide according to the positive and negative directions of the X-axis of the angular momentum coordinate system to obtain two half-spaces, and determine the value range of the angle optimization variable in each half-space.

[0073] For any one of the two half-spaces, based on the coordinate rotation method, optimize the value range of the angle optimization variable in the half-space, and optimize the deviation according to the angle optimization variable until the deviation is minimized, so as to obtain the optimal value of the angle optimization variable corresponding to the half-space and the minimum deviation;

[0074] Among the minimum deviations corresponding to the two half-spaces, take the optimal value of the angle optimization variable corresponding to the smaller minimum deviation as the optimal value of the angle optimization variable of the satellite;

[0075] Based on the fourth transformation matrix corresponding to the optimal value of the angle optimization variable of the satellite, obtain the optimal attitude quaternion for satellite momentum wheel unloading.

[0076] In a third aspect, an embodiment of the present invention further provides a computer device, including:

[0077] A memory for storing program instructions;

[0078] A processor for calling the program instructions stored in the memory and executing the above-mentioned calculation method for the attitude of the Halo orbit satellite momentum wheel unloading according to the obtained program.

[0079] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium, where the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to make a computer execute the above-mentioned calculation method for the attitude of the Halo orbit satellite momentum wheel unloading.

[0080] In a fifth aspect, an embodiment of the present invention further provides a computer program product, where the computer program product includes an executable program, and the executable program is executed by a processor to perform the above-mentioned calculation method for the attitude of the Halo orbit satellite momentum wheel unloading. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for description in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0082] Figure 1 It is a schematic diagram of a system architecture provided by an embodiment of the present invention;

[0083] Figure 2 It is a schematic flowchart of a calculation method for the attitude of the Halo orbit satellite momentum wheel unloading provided by an embodiment of the present invention;

[0084] Figure 3A structural schematic diagram of a method for calculating the attitude of a momentum wheel unloading of a Halo orbit satellite provided by an embodiment of the present invention. Detailed implementation manners

[0085] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0086] The application scenarios described in the embodiments of the present application are for more clearly illustrating the technical solutions protected by the embodiments of the present application, and do not constitute a limitation on the technical solutions provided by the embodiments of the present application. Those of ordinary skill in the art can know that with the emergence of new application scenarios, the technical solutions provided by the embodiments of the present application are equally applicable to similar technical problems. The terms "first" and "second" in the specification and claims of the present application and the above-mentioned drawings are used to distinguish different objects, rather than to describe a specific order. In the description of the present application, unless otherwise stated, the meaning of "a plurality" is two or more.

[0087] Before introducing a method for calculating the attitude of a momentum wheel unloading of a Halo orbit satellite provided by the embodiments of the present application, for the convenience of understanding, the nouns related to the embodiments of the present application will be introduced first.

[0088] Halo Orbit: Also known as the halo orbit or the halo orbit, it is an important concept in the three-body problem of orbital mechanics. It is a periodic three-dimensional orbit that orbits around one of the Lagrangian points L1, L2, or L3. The Lagrangian point is a hypothetical point in space, but its unique feature is that it can be orbited by a spacecraft. Halo orbits exist in any three-body system, such as the sun-earth orbit satellite system and the earth-moon orbit satellite system. Near each Lagrangian point, there are continuous clusters of southward or northward Halo orbit curves.

[0089] Six orbital elements: They are the basic parameters required to describe the motion of a spacecraft in an orbit. These parameters together determine the motion trajectory and position of the spacecraft. The six orbital elements include the following specific parameters:

[0090] 1. Semi-major axis (a): Half of the major axis of an elliptical orbit, used to describe the size of the orbit. The larger the semi-major axis, the higher the orbital energy.

[0091] 2. Eccentricity (e): It represents the shape of the orbit and is a quantitative index of the ellipticity of the orbit. When the eccentricity e = 0, it is a circular orbit; when 0 < e < 1, it is an elliptical orbit; when e ≥ 1, it is a parabolic or hyperbolic orbit.

[0092] 3. Orbital inclination (i): The angle between the orbital plane and the reference plane (usually the Earth's equatorial plane), which determines the degree of inclination of the orbit.

[0093] 4. Right ascension of the ascending node (Ω): The angle of the ascending node (the intersection where the orbit crosses the equator from south to north) relative to the reference direction (usually the vernal equinox).

[0094] 5. Argument of perigee (ω): The angle from the ascending node to the perigee of the orbit, which describes the orientation of the orbital ellipse.

[0095] 6. True anomaly The instantaneous angle measured counterclockwise from the perigee to the position of the satellite, which is used to determine the specific position of the spacecraft in the orbit.

[0096] Normal: Literally understood, the normal direction is the direction of the normal line, which is perpendicular to the tangential direction, that is, the direction of the tangent line. Both the tangential and normal directions are relative to the interface, trajectory, etc.

[0097] Lunar orbit: An astronomical term referring to the projection of the lunar orbit on the celestial sphere. The angle between the lunar orbit and the ecliptic varies between 4°57′ and 5°19′, with an average value of about 5°09′, and the variation period is about 173 days. Due to the gravitational force of the sun on the moon, the line connecting the two intersection points moves westward along the ecliptic in the opposite direction of the lunar motion. This phenomenon is called the regression of the nodes.

[0098] Satellite attitude quaternion: A parameter that describes the direction of the satellite's body frame relative to the reference frame and is used to determine the attitude of the satellite.

[0099] Figure 1 Exemplarily, a system architecture applicable to the embodiments of the present invention is shown. The system architecture includes a server 100, and the server 100 may include a processor 110, a communication interface 120, and a memory 130.

[0100] Among them, the communication interface 120 is used for data transmission.

[0101] The processor 110 is the control center of the server 100, connecting various parts of the entire server 100 through various interfaces and circuits. By running or executing software programs / modules stored in the memory 130 and calling data stored in the memory 130, it executes various functions of the server 100 and processes data. Optionally, the processor 110 may include one or more processing units.

[0102] The memory 130 can be used to store software programs and modules. The processor 110 executes various functional applications and data processing by running the software programs and modules stored in the memory 130. The memory 130 mainly includes a program storage area and a data storage area. Among them, the program storage area can store an operating system, application programs required for at least one function, etc.; the data storage area can store data created according to service processing, etc. In addition, the memory 130 can include high-speed random access memory, and can also include non-volatile memory, such as at least one magnetic disk storage device, flash memory device, or other volatile solid-state storage devices.

[0103] It should be noted that Figure 1 the structure shown above is only an example, and the embodiments of the present invention are not limited thereto.

[0104] Based on the above description, Figure 2 The flowchart of a method for calculating the momentum wheel unloading attitude of a Halo orbit satellite provided by an embodiment of the present invention is exemplarily shown. This process can be executed by a calculation device for the momentum wheel unloading attitude of a Halo orbit satellite.

[0105] As Figure 2 shown, this process specifically includes:

[0106] Step 210, plan the satellite unloading time, determine the nominal control direction and the nominal post-control orbit required for the satellite to maintain the Halo orbit configuration at the unloading time, and based on the nominal post-control orbit, determine the nominal position and velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit.

[0107] In the embodiments of the present invention, the momentum wheel of the satellite continuously accumulates energy. Before the rotational speed of the momentum wheel reaches the limit, it is necessary to perform momentum wheel unloading to restore the initial rotational speed of the momentum wheel. Therefore, it is necessary to plan the time of momentum wheel unloading to avoid the rotational speed of the momentum wheel exceeding the limit due to too long an interval between satellite unloading times, or wasting propellant due to too short an interval between satellite unloading times resulting in too high an unloading frequency. After the satellite unloading time is planned, it is necessary to determine the nominal control direction and the nominal post-control orbit required for the satellite to maintain the Halo orbit configuration at the unloading time. Among them, the Halo orbit can also be called the Halo orbit. Exemplarily, at the satellite unloading time, according to the precise orbit determination result of the satellite, the nominal control information for the satellite to maintain the Halo orbit configuration is calculated through the Halo orbit maintenance control method. Among them, the Halo orbit maintenance control method in this embodiment can be any method, and the Halo orbit maintenance control method is not specifically limited here. The nominal control information can include the nominal control direction, the nominal velocity increment, and the nominal post-control orbit, where the nominal post-control orbit includes the epoch of the orbit and the six orbital elements.

[0108] Then, based on the nominal post-control orbit, determine the nominal position velocity of the satellite in the inertial system when it first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit. Specifically, first, according to the specified step size, the position velocity of the satellite in the inertial system is dynamically integrated based on the nominal post-control orbit to obtain the position velocity of the satellite at the kth moment, where k is an integer greater than or equal to 1, and the first moment is after the unloading moment and is separated from the unloading moment by a preset time period. The specified step size is a value set based on experience, such as 2 hours, 1 hour, etc., and is not specifically limited here. It can be understood that in order to prevent the nominal control point of the satellite on the orbit from being too close to the crossing point of the XZ plane of the Earth-Moon rotating coordinate system, resulting in a decrease in calculation accuracy, therefore, the first moment needs to be after the unloading moment and separated from the unloading moment by a preset time period, where the preset time period is a value preset based on experience, such as 2 days, and the value of the preset time period is not specifically limited here. For example, taking the nominal post-control orbit as the reference, the orbit prediction is continuously performed according to the specified step length dT. The forces on the satellite include the gravity of the earth and the moon, the gravity of other large celestial bodies and the solar pressure. The dynamic model is as follows:

[0109]

[0110] Based on the six orbital numbers of the nominal post-control orbit at the time of unloading, the position and velocity of the satellite at the time of unloading are obtained, and then the position and velocity of the satellite at the time of unloading are dynamically integrated to obtain the position and velocity of the satellite at the kth time. It can be understood that because the dynamic integration is performed according to the specified step size, the specified step size is separated between the kth time and the k+1th time.

[0111] Then, calculate the rotation matrix of the inertial system to the Earth-Moon rotating coordinate system at the kth moment. Exemplarily, this article takes the halo orbit around the Lagrange point L2 as an example, so the Earth-Moon rotating coordinate system is the Earth-Moon L2 point rotating coordinate system. Later, the Earth-Moon L2 point rotating coordinate system at the kth moment is taken as an example. The coordinate system is defined as follows: the origin O is the Earth-Moon L2 point, the X-axis is the direction of the Earth pointing to the Moon at the kth moment, the Y-axis is parallel to the tangent direction of the Moon's revolution at the kth moment, and the Z-axis is parallel to the normal direction of the ecliptic at the kth moment. Calculate the rotation matrix L from the J2000 inertial system to the Earth-Moon rotating coordinate system ri and the angular velocity ω r , the formula is as follows:

[0112]

[0113] in, is the relative position between the moon and the earth, is the relative speed between the moon and the earth, m represents the moon, e represents the earth, and is the position and velocity of the moon at the kth moment in the inertial system, and are the position and velocity of the Earth at the k-th moment in the inertial system, and X, Y, and Z are the unit vectors in the directions of the X-axis, Y-axis, and Z-axis of the rotating coordinate system of the Earth-Moon L2 point.

[0114] Based on the rotation matrix, the position and velocity at the k-th moment are transformed from the inertial system to the rotating coordinate system of the Earth-Moon at the k-th moment, obtaining the position coordinates at the k-th moment in the rotating coordinate system of the Earth-Moon at the k-th moment. It can be understood that in addition to obtaining the position coordinates, the velocity at the k-th moment also needs to be transformed from the inertial system to the rotating coordinate system of the Earth-Moon at the k-th moment, obtaining the velocity at the k-th moment in the rotating coordinate system of the Earth-Moon at the k-th moment. Exemplarily, determine the change rate V of the Earth-Moon distance em :

[0115]

[0116] Then determine the position and velocity of the center of mass of the Earth-Moon system:

[0117]

[0118] where M m is the weight of the Moon, M e is the weight of the Earth, is the position of the center of mass of the Earth-Moon system, is the velocity of the center of mass of the Earth-Moon system.

[0119] Rotate the position and velocity of the satellite from the inertial system to the rotating coordinate system:

[0120]

[0121] where is the position of the satellite in the rotating coordinate system, is the velocity of the satellite in the rotating coordinate system, is the position of the satellite in the inertial system, is the velocity of the satellite in the inertial system.

[0122] Finally, rotate the position and velocity of the satellite from the inertial system to the rotating coordinate system of the Earth-Moon L2 point:

[0123]

[0124] where is the position of the satellite in the rotating coordinate system of the Earth-Moon L2 point, is the velocity of the satellite in the rotating coordinate system of the Earth-Moon L2 point, L 2 is the normalized distance of the L2 point relative to the center of mass of the Earth-Moon system.

[0125] Then, calculate the product result of the Y-axis component of the position coordinate at the k-th moment and the Y-axis component of the position coordinate at the (k + 1)-th moment. Exemplarily, the calculation formula is as follows:

[0126] flag = r eml，k (y)·r eml，k+1 (y)

[0127] where, eml is the earth-moon rotating coordinate system, r eml , k (y) is the Y-axis component of the position coordinate at the k-th moment in the earth-moon rotating coordinate system at the k-th moment, r eml , k+1 (y) is the Y-axis component of the position coordinate at the (k + 1)-th moment in the earth-moon rotating coordinate system at the (k + 1)-th moment, and flag is the product result.

[0128] When the product result is less than 0 for the first time, the satellite first crosses the XZ plane of the earth-moon rotating coordinate system on the nominal post-control orbit. Perform precise iteration on the k-th moment and the (k + 1)-th moment to obtain the nominal position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the earth-moon rotating coordinate system on the nominal post-control orbit. Among them, the method of performing precise iteration on the k-th moment and the (k + 1)-th moment can be selected according to experience, such as the 618 method. Here, the method of precise iteration is not specifically limited. Exemplarily, determine whether the product result of the Y-axis component of the position coordinate at the 1st moment and the Y-axis component of the position coordinate at the 2nd moment is less than 0 for the first time. If not, then determine whether the product result of the Y-axis component of the position coordinate at the 2nd moment and the Y-axis component of the position coordinate at the 3rd moment is less than 0 for the first time. If not, then continue to make judgments in sequence until the product result is less than 0 for the first time. If the product result of the Y-axis component of the position coordinate at the 6th moment and the Y-axis component of the position coordinate at the 7th moment is less than 0 for the first time, it indicates that the satellite first crosses the XZ plane of the earth-moon rotating coordinate system on the nominal post-control orbit between the 6th moment and the 7th moment. Then, perform precise iteration on the 6th moment and the 7th moment through the 618 method, set the time convergence threshold to 1.0e-2 seconds, and finally obtain the nominal position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the earth-moon rotating coordinate system on the nominal post-control orbit

[0129] In a possible implementation manner, before planning the satellite unloading moment, it is also necessary to determine the fitting coefficient of the satellite. It can be understood that usually, for a Halo orbit satellite, both directions of the body system are torque engines, and unloading hardly generates a velocity increment and has no impact on the orbit. The other direction is a non-torque engine, which generates a velocity increment to offset the angular momentum. Assume that the Z-axis direction is the non-torque engine, and the X and Y axes are torque engines. The angular momentum of the satellite body system at the unloading moment is H b = [H bx Hby H bz , where b represents the system at the unloading moment, and the fitting relationship between the velocity increment and the angular momentum under this system is:

[0130]

[0131] The process of determining the fitting coefficient is as follows: First, obtain the attitude quaternion at the historical unloading moment, the angular momentum at the historical unloading moment, and the corresponding historical unloading velocity increment. Among them, the angular momentum at the historical unloading moment is the three-axis angular momentum of the satellite in the system at the unloading moment. The historical unloading velocity increment is the velocity increment generated by the satellite during the historical unloading process in the inertial system, and the historical unloading velocity increment is obtained based on the precise orbit determination results before and after the satellite unloading.

[0132] Then, based on the attitude quaternion at the historical unloading moment, determine the first transformation matrix from the inertial system to the system at the unloading moment. Exemplarily, according to the satellite attitude quaternion Q = [Q c , Q 1 , Q 2 , Q 3 at the unloading moment, calculate the transformation matrix M bi from the inertial system to the system of the satellite, where i represents the inertial system, and the formula is as follows:

[0133]

[0134] Finally, based on the first transformation matrix, transform the historical unloading velocity increment from the inertial system to the system at the unloading moment, and obtain the fitting coefficient according to the fitting relationship between the historical unloading velocity increment and the angular momentum at the unloading moment under the system at the unloading moment. Exemplarily, the historical unloading velocity increment in the inertial system is Transform it to the system at the unloading moment as Then let V b,orb = V b , that is Finally, the fitting coefficient K can be obtained.

[0135] It can be understood that in order to ensure the accuracy of the calculated fitting coefficient, a large amount of data at the historical unloading moment needs to be used for calculation, that is, for any historical unloading moment, the fitting coefficient corresponding to the historical unloading moment is calculated according to the attitude quaternion at the historical unloading moment, the angular momentum at the historical unloading moment, and the corresponding historical unloading velocity increment. Finally, the least squares method is used to fit the fitting coefficients corresponding to all historical unloading moments to determine the final fitting coefficient K. And through the above calculation process, it can be seen that the fitting coefficient represents the fitting relationship between the angular momentum of the satellite at the unloading moment and the velocity increment generated during the unloading process under the system at the unloading moment.

[0136] Step 220: Based on the angular momentum vector in the inertial system at the unloading moment and the nominal control direction, establish the angular momentum coordinate system of the satellite, and determine the angle optimization variables of the satellite. The angle optimization variables are the Euler angles by which the satellite rotates around each coordinate axis of the angular momentum coordinate system in a specific order.

[0137] In the embodiment of the present invention, the angular momentum vector in the inertial system at the unloading moment can be obtained according to the rotation speed of the momentum wheel at the unloading moment. The angle optimization variables of the satellite are the Euler angles by which the satellite rotates around each coordinate axis of the angular momentum coordinate system in a specific order. The order of the Euler angles is set according to experience, for example, the order is 123 or 213, and no specific limitation is made here. Specifically, take the direction of the angular momentum vector in the inertial system at the unloading moment as the Y-axis of the angular momentum coordinate system, which is expressed as a formula Take the direction of the cross product result of the Y-axis and the nominal control direction as the X-axis, which is expressed as a formula Determine the Z-axis based on the right-hand rule, which is expressed as z = x × y; establish the angular momentum coordinate system of the satellite, and determine the second transformation matrix from the inertial system to the angular momentum coordinate system, which is expressed as a formula M jdl,i =[x y z] T , where jdl represents the angular momentum coordinate system.

[0138] Determine the angle optimization variables of the satellite based on the angles by which the satellite rotates around each coordinate axis of the angular momentum coordinate system, and determine the third transformation matrix from the angular momentum coordinate system to the body system at the unloading moment. Exemplarily, first rotate around the X-axis of the angular momentum coordinate system The transformation matrix is Then rotate around the Y-axis The transformation matrix is Finally, rotate around the Z-axis To obtain the unloading attitude, the transformation matrix is Where M x , M y , M z Are elementary transformation matrices. Determine the angle optimization variables Taking the angular momentum coordinate system as the reference, rotate in sequence according to the Euler angle order 123 Then the third transformation matrix M b,jdl From the angular momentum coordinate system to the body system at the unloading moment is:

[0139]

[0140] Finally, based on the second transformation matrix and the third transformation matrix, obtain the fourth transformation matrix from the inertial system to the body system at the unloading moment. Exemplarily, calculate the cross product result between the second transformation matrix M jdl,i And the third transformation matrix M b,jdl As the fourth transformation matrix M b,i =Mb,jdl ×M jdl,i 。

[0141] Step 230: Determine the velocity increment generated by the satellite during the unloading process based on the angular momentum vector and the fitting coefficient, determine the post-unloading orbit, and determine the post-unloading position and velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit; the fitting coefficient represents the fitting relationship between the angular momentum of the satellite at the unloading moment and the velocity increment generated during the unloading process.

[0142] In the embodiments of the present invention, through the above calculation process of the fitting coefficient, it can be known that the fitting coefficient represents the fitting relationship between the angular momentum of the satellite in the current system at the unloading moment and the velocity increment generated during the unloading process. Therefore, when determining the velocity increment generated during the unloading process based on the angular momentum vector at the unloading moment and the fitting coefficient, coordinate system conversion is required. Specifically, based on the fourth transformation matrix, the angular momentum vector is converted from the inertial system to the current system at the unloading moment, and based on the angular momentum vector and the fitting coefficient in the current system at the unloading moment, the velocity increment generated by the satellite during the unloading process in the current system at the unloading moment is obtained. Exemplarily, calculate the angular momentum vector H in the inertial system i The components of the three axes in the current system at the unloading moment are H b = M b,i ×H i =(H b,x H b,y H b,z ). Then, based on the fitting coefficient K and the angular momentum vector H in the current system at the unloading moment b , calculate the velocity increment in the current system at the unloading moment

[0143] Then, based on the inverse matrix of the fourth transformation matrix, the velocity increment generated during the unloading process is converted from the current system at the unloading moment to the inertial system, as expressed by the formula And based on the velocity increment generated during the unloading process, the post-unloading orbit is determined. Among them, the post-unloading orbit includes the epoch of the orbit and the six orbital elements.

[0144] Finally, based on the post-unloading orbit, determine the post-unloading position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit. Specifically, at a specified step size, perform dynamic integration on the position and velocity of the satellite in the inertial system based on the post-unloading orbit to obtain the position and velocity of the satellite at the m-th moment, and calculate the rotation matrix from the inertial system to the Earth-Moon rotating coordinate system at the m-th moment. Here, m is an integer greater than or equal to 1, and the first moment is after the unloading moment and separated from the unloading moment by a preset time period. Based on the rotation matrix, transform the position and velocity at the m-th moment from the inertial system to the Earth-Moon rotating coordinate system at the m-th moment to obtain the position coordinates at the m-th moment in the Earth-Moon rotating coordinate system at the m-th moment. Calculate the product result of the Y-axis component of the position coordinates at the m-th moment and the Y-axis component of the position coordinates at the (m + 1)-th moment. When the product result is less than 0 for the first time, the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit, and perform precise iteration on the m-th moment and the (m + 1)-th moment when the product result is less than 0 for the first time to obtain the post-unloading position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit. It can be understood that the calculation process of determining the post-unloading position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the Earth-Moon rotating coordinate system based on the post-unloading orbit is the same as the calculation process of determining the nominal position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the Earth-Moon rotating coordinate system based on the nominal post-control orbit in step 210 above, so it will not be elaborated here. Finally, it is obtained that the post-unloading position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit

[0145] Step 240, obtain the deviation between the nominal post-control orbit and the post-unloading orbit according to the nominal position and velocity and the post-unloading position and velocity, and optimize the deviation according to the angle optimization variable based on the coordinate rotation method to obtain the optimal attitude quaternion for the satellite momentum wheel unloading, so that the satellite performs momentum wheel unloading according to the optimal attitude quaternion to achieve the goal of maintaining the halo orbit configuration through active unloading.

[0146] In the embodiments of the present invention, the deviation between the nominal controlled orbit and the orbit after unloading can be obtained through the deviation between the nominal position velocity and the position velocity after unloading, that is, the deviation between the nominal control and the unloading control of the satellite. Specifically, calculate the product result of the modulus of the vector difference between the satellite position in the position velocity after unloading and the satellite position in the nominal position velocity and the position weight as the position deviation. Calculate the product result of the modulus of the vector difference between the satellite velocity in the position velocity after unloading and the satellite velocity in the nominal position velocity and the velocity weight as the velocity deviation. Among them, the position weight is less than the velocity weight, and the sum of the position weight and the velocity weight is 1. It can be understood that since both the nominal position velocity and the position velocity after unloading are the position velocities when the satellite first crosses the XZ plane of the earth-moon rotating coordinate system, and the XZ plane of the earth-moon rotating coordinate system is the same, the weight of the position deviation is smaller. Finally, calculate the sum result of the position deviation and the velocity deviation as the deviation between the nominal controlled orbit and the orbit after unloading. Exemplarily, the deviation between the nominal controlled orbit and the orbit after unloading is calculated by the following formula:

[0147]

[0148] Where S err is the deviation between the nominal controlled orbit and the orbit after unloading when the satellite is at the rotation angle ; n is the velocity weight; (1 - n) is the position weight; is the satellite position in the position velocity after unloading; is the satellite position in the nominal position velocity; is the satellite velocity in the position velocity after unloading; is the satellite velocity in the nominal position velocity.

[0149] Then, based on the coordinate rotation method, optimize the deviation between the nominal controlled orbit and the orbit after unloading according to the angle optimization variable to obtain the optimal attitude quaternion for satellite momentum wheel unloading. Specifically, divide according to the positive and negative directions of the X-axis of the angular momentum coordinate system to obtain two half-spaces, and determine the value range of the angle optimization variable in each half-space. Exemplarily, the value range of the angle optimization variable in half-space 1 is The value range of the angle optimization variable in half-space 2 is For any one of the two half-spaces, based on the coordinate rotation method, according to the value range of the angle optimization variable in this half-space, optimize the deviation between the nominal controlled orbit and the orbit after unloading according to the angle optimization variable until the deviation is the smallest, and obtain the optimal value of the angle optimization variable corresponding to this half-space and the minimum deviation. Finally, take the optimal value of the angle optimization variable corresponding to the smaller minimum deviation among the minimum deviations corresponding to the two half-spaces as the optimal value of the angle optimization variable of the satellite, such as

[0150]

[0151] Based on the fourth transformation matrix corresponding to the optimal value of the satellite-based angle optimization variable, the optimal attitude quaternion for satellite momentum wheel unloading is obtained. Exemplarily, the optimal value of the satellite-based angle optimization variable The corresponding fourth transformation matrix is Transform the fourth transformation matrix corresponding to the optimal value of the angle optimization variable to obtain the optimal attitude quaternion for satellite momentum wheel unloading. The satellite performs momentum wheel unloading according to the optimal attitude quaternion, and the goal of maintaining the Halo orbit configuration through active unloading can be achieved.

[0152] Next, an example of the implementation of Figure 2 will be given:[[]]END]]

[0153] Taking a certain on-orbit Halo orbit satellite at the Earth-Moon L2 point as an example, first, the relationship between the three-axis angular momentum of the satellite at the unloading moment and the velocity increment generated during the unloading process is fitted. Taking the unloading data of the satellite on January 3, 2024 as an example, the unloading moment is 11:30, and the angular momentum of the satellite in its own body coordinate system at this time is:[[]]END]]

[0154] X-axis Y-axis Z-axis Angular momentum of this system 0.848391 -2.809106 -0.28722

[0155] Then the velocity increment V generated by the unloading in the satellite's own body coordinate system is b,z = K(H b,x + H b,y ) = K × 3.657497.

[0156] The attitude quaternion of the satellite at the unloading moment at this time is:[[]]END]]

[0157] Attitude quaternion Value QC 0.28699928 Q1 -0.66184163 Q2 -0.61272231 Q3 -0.32275136

[0158] The transformation matrix for the satellite to rotate from the inertial coordinate system to its own body coordinate system calculated through the attitude quaternion is

[0159]

[0160] According to the precise orbit determination results of the satellite before and after unloading, estimate the velocity increment V generated by the satellite unloading in the inertial coordinate system i,orb = (0.0012 0.0125 -0.01) T , and transform it to the satellite's own body coordinate system according to the above transformation matrix as

[0161]

[0162] Let V b,orb = V b , and the fitting coefficient K = 0.00438893 can be obtained.

[0163] By calculating the long-term on-orbit angular momentum unloading data of the satellite and the precise orbit determination results before and after unloading, the relationship between the satellite's three-axis angular momentum at the unloading moment and the velocity increment generated by unloading is fitted, and the fitted coefficient is K = 0.0044.

[0164] Taking the satellite unloading on December 5, 2024 as an example for calculation. The satellite's orbital elements and initial attitude quaternion are as follows, epoch 2024-12-05T10:00:00.

[0165] Orbital elements Value Semi-major axis (m) 841364788.8626 Eccentricity 0.4781437406329836 Orbital inclination (°) 30.4744 Right ascension of the ascending node (°) 356.1490 Argument of perigee (°) 314.4349 Mean anomaly (°) 354.5827

[0166]

[0167]

[0168] The planned unloading moment is 2024-12-05T12:30:00, and the three-axis telemetry angular momentum at this time is (1.224229 -2.362641 -1.686074). If the satellite's orbit is maintained at this moment, the nominal control attitude quaternion is as follows, and the nominal velocity increment is 0.0154m / s.

[0169] Nominal control attitude quaternion Value QC 0.30159259 Q1 0.72125952 Q2 0.22798981 Q3 0.58038544

[0170] The nominal controlled orbit after is as follows:

[0171] Orbital elements Value Semi-major axis (m) 859972472.1059 Eccentricity 0.4903719701563828 Orbital inclination (°) 30.4881 Right ascension of the ascending node (°) 356.0979 Argument of perigee (°) 315.4140 Mean anomaly (°) 354.9126

[0172] Taking the nominal controlled orbit after as the reference, with a step size of 1 hour, calculate the time when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system and the position and velocity in the rotating coordinate system centered on the L2 point as follows:

[0173]

[0174] Through the 618 method, precisely iterate the time when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system and the position and velocity in the rotating coordinate system centered on the L2 point. The results are as follows:

[0175] Item (unit) Value Epoch 2024-12-09T10:21:02.56 X (m) -15560976.552 Y (m) -0.258 Z (m) 10710243.526 VX (m / s) 0.311948 VY (m / s) 203.354995 VZ (m / s) -0.660270

[0176] Establish the angular momentum coordinate system of the satellite according to the content in step 220 above, and calculate the transformation matrix from the inertial coordinate system to the angular momentum coordinate system.

[0177] Obtain the deviation between the nominal controlled orbit after and the orbit after unloading through the methods in step 230 and step 240 above. And based on the coordinate rotation method, optimize the calculation of the deviation, and sequentially rotate different angles of the optimization variable according to the Euler angle 123 rotation sequence on the basis of the angular momentum coordinate system Obtain the optimal value of the angular optimization variable of the satellite is as follows:

[0178]

[0179] At this time, the optimal attitude quaternion of the satellite is as follows:

[0180] Attitude quaternion Value QC 0.72379567 Q1 -0.64775000 Q2 -0.16537506 Q3 0.17085330

[0181] In the unloading attitude coordinate system, the satellite angular momentum vector is (-1.236071, -1.235012, -1.753562), the velocity increment generated after unloading is 0.024073 m / s. If the satellite performs orbit maintenance according to the optimal attitude quaternion, the required velocity increment is 0.024082 m / s. Therefore, the remaining velocity increment of the satellite after unloading is only 9e-6 m / s.

[0182] In the embodiments of the present invention, based on the long-term on-orbit unloading angular momentum data of the satellite and the precise orbit determination results before and after unloading, the relationship between the angular momentum of the satellite at the unloading moment and the velocity increment generated during the unloading process is fitted. When the satellite unloads, the nominal control parameters for maintaining the Halo orbit configuration are calculated, and the nominal position and velocity when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system after control are calculated. According to the angular momentum vector and the nominal control direction at the unloading moment, an angular momentum coordinate system is defined. In this coordinate system, the angular optimization variable is rotated by the Euler angle sequence 123 to obtain the unloading attitude. The three-axis distribution of the angular momentum in the unloading attitude is calculated, and the velocity increment generated by unloading is calculated according to the fitting relationship to obtain the orbit after unloading in this unloading attitude. The position and velocity after unloading when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system after unloading control are calculated, and the deviation between the orbit after unloading and the nominal orbit after control is evaluated based on the position and velocity after unloading and the nominal position and velocity. The coordinate rotation method is used to calculate the optimal attitude quaternion to minimize the deviation between the orbit after unloading and the nominal orbit after control. By continuously performing momentum wheel unloading through the optimal attitude quaternion in the long term, the satellite can maintain the Halo orbit configuration to the greatest extent, realize using the velocity increment generated by unloading for satellite orbit configuration maintenance, use momentum wheel unloading to offset the divergence trend of the Halo orbit, reduce the orbit maintenance frequency, and reduce the propellant consumption of the satellite.

[0183] Based on the same technical concept, Figure 3 An exemplary structural schematic diagram of a calculation device for the momentum wheel unloading attitude of a Halo orbit satellite provided by an embodiment of the present invention is shown. This device can execute the process of the calculation method for the momentum wheel unloading attitude of a Halo orbit satellite.

[0184] As Figure 3 shown, this device specifically includes:

[0185] An acquisition module 310 is configured to plan the satellite unloading moment, determine the nominal control direction and the nominal post-control orbit required for the satellite to maintain the halo orbit configuration at the unloading moment, and based on the nominal post-control orbit, determine the nominal position and velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit;

[0186] A processing module 320 is configured to establish an angular momentum coordinate system of the satellite based on the angular momentum vector in the inertial system at the unloading moment and the nominal control direction, and determine the angular optimization variables of the satellite, where the angular optimization variables are the Euler angles by which the satellite rotates around the respective coordinate axes of the angular momentum coordinate system in a sequential order;

[0187] Based on the angular momentum vector and the fitting coefficient, determine the velocity increment generated by the satellite during the unloading process, and determine the post-unloading orbit, as well as the post-unloading position and velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit; the fitting coefficient represents the fitting relationship between the angular momentum of the satellite at the unloading moment and the velocity increment generated during the unloading process;

[0188] Obtain the deviation between the nominal post-control orbit and the post-unloading orbit based on the nominal position and velocity and the post-unloading position and velocity, and based on the coordinate rotation method, optimize the deviation according to the angular optimization variables to obtain the optimal attitude quaternion for the satellite momentum wheel unloading, so that the satellite performs momentum wheel unloading according to the optimal attitude quaternion, achieving the goal of maintaining the halo orbit configuration through active unloading.

[0189] Optionally, the processing module 320 is further configured to:

[0190] Obtain the attitude quaternion at the historical unloading moment, the historical angular momentum at the historical unloading moment, and the corresponding historical unloading velocity increment; the historical unloading velocity increment is the velocity increment generated by the satellite during the historical unloading process in the inertial system, and the historical unloading velocity increment is obtained based on the precise orbit determination results before and after the satellite unloading, and the historical angular momentum at the historical unloading moment is the three-axis angular momentum of the satellite in its own system at the unloading moment;

[0191] Based on the attitude quaternion at the historical unloading moment, determine the first transformation matrix for converting from the inertial system to the system at the unloading moment;

[0192] Based on the first transformation matrix, convert the historical unloading velocity increment from the inertial system to the system at the unloading moment, and according to the fitting relationship between the historical unloading velocity increment in the system at the unloading moment and the historical angular momentum at the historical unloading moment, obtain the fitting coefficient.

[0193] Optionally, the processing module 320 is specifically configured to:

[0194] Integrate the position and velocity of the satellite in the inertial system based on the nominal post-control orbit at a specified step size to obtain the position and velocity of the satellite at the k-th moment, and calculate the rotation matrix for converting from the inertial system to the Earth-Moon rotating coordinate system at the k-th moment; k is an integer greater than or equal to 1, and the first moment is after the unloading moment and separated from the unloading moment by a preset time period;

[0195] Based on the rotation matrix, convert the position and velocity at the k-th moment from the inertial system to the Earth-Moon rotating coordinate system at the k-th moment to obtain the position coordinates at the k-th moment in the Earth-Moon rotating coordinate system at the k-th moment;

[0196] Calculate the product result of the Y-axis component of the position coordinates at the k-th moment and the Y-axis component of the position coordinates at the (k + 1)-th moment;

[0197] When the product result is less than 0 for the first time, the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit. Perform precise iteration on the k-th moment and the (k + 1)-th moment to obtain the nominal position and velocity of the satellite in the inertial system when it first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit.

[0198] Optionally, the processing module 320 is specifically configured to:

[0199] Take the direction of the angular momentum vector as the Y-axis of the angular momentum coordinate system, take the direction of the cross product result of the Y-axis and the nominal control direction as the X-axis, determine the Z-axis based on the right-hand rule, establish the angular momentum coordinate system, and determine the second conversion matrix for converting from the inertial system to the angular momentum coordinate system;

[0200] Determine the angle optimization variable based on the angles of the satellite rotating around the coordinate axes of the angular momentum coordinate system, and determine the third conversion matrix from the angular momentum coordinate system to the body system at the unloading moment;

[0201] Based on the second conversion matrix and the third conversion matrix, obtain the fourth conversion matrix for converting from the inertial system to the body system at the unloading moment.

[0202] Optionally, the processing module 320 is specifically configured to:

[0203] Based on the fourth conversion matrix, convert the angular momentum vector from the inertial system to the body system at the unloading moment, and based on the angular momentum vector in the body system at the unloading moment and the fitting coefficient, obtain the velocity increment generated during the unloading process of the satellite in the body system at the unloading moment;

[0204] Based on the inverse matrix of the fourth transformation matrix, convert the velocity increment generated during the unloading process from the current system at the unloading moment to the inertial system, and determine the orbit after unloading based on the velocity increment generated during the unloading process;

[0205] According to a specified step size, perform dynamic integration on the position and velocity of the satellite in the inertial system based on the orbit after unloading to obtain the position and velocity of the satellite at the m-th moment, and calculate the rotation matrix for converting from the inertial system to the Earth-Moon rotating coordinate system at the m-th moment; m is an integer greater than or equal to 1, and the first moment is after the unloading moment and is separated from the unloading moment by a preset time period;

[0206] Based on the rotation matrix, convert the position and velocity at the m-th moment from the inertial system to the Earth-Moon rotating coordinate system at the m-th moment to obtain the position coordinates at the m-th moment in the Earth-Moon rotating coordinate system at the m-th moment;

[0207] Calculate the product result of the Y-axis component of the position coordinates at the m-th moment and the Y-axis component of the position coordinates at the (m + 1)-th moment;

[0208] When the product result is less than 0 for the first time, the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the orbit after unloading, and perform precise iteration on the m-th moment and the (m + 1)-th moment when the product result is less than 0 for the first time to obtain the position and velocity after unloading in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the orbit after unloading.

[0209] Optionally, the processing module 320 is specifically configured to:

[0210] Calculate the product result of the modulus of the vector difference between the satellite position in the position and velocity after unloading and the satellite position in the nominal position and velocity and the position weight as the position deviation;

[0211] Calculate the product result of the modulus of the vector difference between the satellite velocity in the position and velocity after unloading and the satellite velocity in the nominal position and velocity and the velocity weight as the velocity deviation; the position weight is less than the velocity weight, and the sum of the position weight and the velocity weight is 1;

[0212] Calculate the sum result of the position deviation and the velocity deviation as the deviation between the nominal orbit after control and the orbit after unloading.

[0213] Optionally, the processing module 320 is specifically configured to:

[0214] Divide according to the positive and negative directions of the X-axis of the angular momentum coordinate system to obtain two half-spaces, and determine the value range of the angle optimization variable in each half-space;

[0215] For any one of the two half-spaces, based on the coordinate rotation method, the value range of the angle optimization variable in the half-space is optimized according to the angle optimization variable, and the deviation is optimized according to the angle optimization variable until the deviation is minimized, so as to obtain the optimal value of the angle optimization variable corresponding to the half-space and the minimum deviation.

[0216] Take the optimal value of the angle optimization variable corresponding to the smaller minimum deviation among the minimum deviations corresponding to the two half-spaces as the optimal value of the angle optimization variable of the satellite.

[0217] Based on the fourth transformation matrix corresponding to the optimal value of the angle optimization variable of the satellite, the optimal attitude quaternion for satellite momentum wheel unloading is obtained.

[0218] Based on the same technical concept, an embodiment of the present invention further provides a computer device, including:

[0219] A memory for storing program instructions;

[0220] A processor for calling the program instructions stored in the memory and executing the method for calculating the attitude of the Halo orbit satellite momentum wheel unloading according to the obtained program.

[0221] Based on the same technical concept, an embodiment of the present invention further provides a computer-readable storage medium, which stores computer-executable instructions, and the computer-executable instructions are used to make a computer execute the method for calculating the attitude of the Halo orbit satellite momentum wheel unloading.

[0222] Based on the same technical concept, an embodiment of the present invention further provides a computer program product, characterized in that the computer program product includes an executable program, and the executable program is executed by a processor to perform the method for calculating the attitude of the Halo orbit satellite momentum wheel unloading.

[0223] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes.

[0224] This application is described with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to the application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processors of general-purpose computers, special-purpose computers, embedded processors, or other programmable data processing devices to generate a machine, such that the instructions executed by the processors of the computer or other programmable data processing devices generate means for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or means for implementing the functions specified in multiple blocks.

[0225] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or means for implementing the functions specified in multiple blocks.

[0226] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or means for implementing the functions specified in multiple blocks.

[0227] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalent technologies, this application is also intended to include these modifications and variations.

Claims

1. A method for calculating the momentum wheel unloading attitude of a Halo orbit satellite, characterized in that: include: Planning the satellite unloading time, determining the nominal control direction and the nominal post-control orbit required for the satellite to maintain the halo orbit configuration at the unloading time, and determining the nominal position velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit based on the nominal post-control orbit; An angular momentum coordinate system of the satellite is established based on the angular momentum vector in the inertial system at the time of unloading and the nominal control direction, and an angle optimization variable of the satellite is determined, where the angle optimization variable is the Euler angle of the satellite rotating around each coordinate axis of the angular momentum coordinate system in a rotation order; Determine the velocity increment generated by the satellite during the unloading process based on the angular momentum vector and the fitting coefficient, and determine the post-unloading orbit, and the post-unloading position velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit; the fitting coefficient represents the fitting relationship between the angular momentum of the satellite at the time of unloading and the velocity increment generated during the unloading process; The deviation between the nominal post-control orbit and the post-unloading orbit is obtained according to the nominal position velocity and the post-unloading position velocity, and based on the coordinate rotation method, the deviation is optimized according to the angle optimization variable to obtain the optimal attitude quaternion of the satellite momentum wheel unloading, so that the satellite can perform momentum wheel unloading according to the optimal attitude quaternion, thereby achieving the goal of maintaining the halo orbit configuration through active unloading.

2. The method according to claim 1, characterized in that Before planning the satellite unloading time, the method further includes: Acquire the attitude quaternion at the historical unloading time, the angular momentum at the historical unloading time, and the corresponding historical unloading speed increment; the historical unloading speed increment is the speed increment generated by the satellite during the historical unloading process in the inertial system, the historical unloading speed increment is obtained according to the precise orbit determination results before and after the satellite unloading, and the historical unloading time angular momentum is the three-axis angular momentum of the satellite in the system at the unloading time; Based on the historical unloading moment attitude quaternion, determining a first transformation matrix from the inertial system to the system at the unloading moment; The historical unloading velocity increment is converted from the inertial system to the local system at the unloading moment based on the first conversion matrix, and a fitting coefficient is obtained according to a fitting relationship between the historical unloading velocity increment in the local system at the unloading moment and the angular momentum at the historical unloading moment.

3. The method according to claim 1, characterized in that Determining the nominal position velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit based on the nominal post-control orbit includes: According to the specified step size, the position velocity of the satellite in the inertial system is dynamically integrated based on the nominal post-control orbit to obtain the position velocity of the satellite at the kth moment, and the rotation matrix of the Earth-Moon rotation coordinate system converted from the inertial system to the kth moment is calculated; k is an integer greater than or equal to 1, and the first moment is located after the unloading moment and is separated from the unloading moment by a preset time period; Based on the rotation matrix, convert the position velocity at the k-th moment from the inertial system to the Earth-Moon rotating coordinate system at the k-th moment, and obtain the position coordinates at the k-th moment in the Earth-Moon rotating coordinate system at the k-th moment; Calculate the product of the Y-axis component of the position coordinate at the k-th moment and the Y-axis component of the position coordinate at the k+1-th moment; When the product result is less than 0 for the first time, the satellite crosses the XZ plane of the Earth-Moon rotating coordinate system for the first time on the nominal post-control orbit, and the kth moment and the k+1th moment are accurately iterated to obtain the nominal position velocity of the satellite in the inertial system when it crosses the XZ plane of the Earth-Moon rotating coordinate system for the first time on the nominal post-control orbit.

4. The method according to claim 1, characterized in that The angular momentum coordinate system of the satellite is established based on the angular momentum vector of the inertial system at the time of unloading and the nominal control direction, and the angle optimization variable of the satellite is determined, including: The direction of the angular momentum vector is used as the Y axis of the angular momentum coordinate system, the direction of the cross product of the Y axis and the nominal control direction is used as the X axis, the Z axis is determined based on the right-hand rule, the angular momentum coordinate system is established, and a second conversion matrix for converting from an inertial system to the angular momentum coordinate system is determined; Determine the angle optimization variable based on the rotation angle of the satellite around each coordinate axis of the angular momentum coordinate system, and determine the third transformation matrix from the angular momentum coordinate system to the system at the unloading time; Based on the second conversion matrix and the third conversion matrix, a fourth conversion matrix of the system from the inertial system to the system at the unloading moment is obtained.

5. The method according to any one of claims 1 to 4, characterized in that: The velocity increment generated by the satellite during the unloading process is determined based on the angular momentum vector and the fitting coefficient, and the post-unloading orbit and the post-unloading position velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit are determined, including: Based on the fourth conversion matrix, the angular momentum vector is converted from the inertial system to the local system at the unloading time, and based on the angular momentum vector in the local system at the unloading time and the fitting coefficient, the velocity increment generated by the satellite during the unloading process in the local system at the unloading time is obtained; Based on the inverse matrix of the fourth conversion matrix, the velocity increment generated during the unloading process is converted from the local system at the time of unloading to the inertial system, and based on the velocity increment generated during the unloading process, the post-unloading trajectory is determined; According to the specified step length, the position velocity of the satellite in the inertial system is dynamically integrated based on the post-unloading orbit to obtain the position velocity of the satellite at the mth moment, and the rotation matrix of the Earth-Moon rotation coordinate system converted from the inertial system to the mth moment is calculated; m is an integer greater than or equal to 1, and the first moment is located after the unloading moment and is separated from the unloading moment by a preset time period; Based on the rotation matrix, convert the position velocity at the mth moment from the inertial system to the Earth-Moon rotating coordinate system at the mth moment, and obtain the position coordinates at the mth moment in the Earth-Moon rotating coordinate system at the mth moment; Calculate the product of the Y-axis component of the position coordinate at the m-th moment and the Y-axis component of the position coordinate at the m+1-th moment; When the product result is less than 0 for the first time, the satellite crosses the XZ plane of the Earth-Moon rotating coordinate system for the first time on the post-unloading orbit, and the mth moment and the m+1th moment when the product result is less than 0 for the first time are accurately iterated to obtain the post-unloading position velocity of the satellite in the inertial system when it crosses the XZ plane of the Earth-Moon rotating coordinate system for the first time on the post-unloading orbit.

6. The method according to any one of claims 1 to 4, characterized in that: Obtaining a deviation between the nominal post-control track and the post-unloading track according to the nominal position speed and the post-unloading position speed, including: Calculate the product of the modulus of the vector difference between the satellite position in the post-unloading position velocity and the satellite position in the nominal position velocity and the position weight as the position deviation; Calculate the product of the modulus of the vector difference between the satellite velocity in the unloading position velocity and the satellite velocity in the nominal position velocity and the velocity weight as the velocity deviation; the position weight is less than the velocity weight, and the sum of the position weight and the velocity weight is 1; The sum of the position deviation and the speed deviation is calculated as the deviation between the nominal post-control track and the post-unloading track.

7. The method according to any one of claims 1 to 4, characterized in that Based on the coordinate rotation method, the deviation is optimized according to the angle optimization variable to obtain the optimal attitude quaternion of the satellite momentum wheel unloading, including: Dividing the angular momentum coordinate system according to the positive direction and the negative direction of the X-axis to obtain two half-spaces, and determining the value range of the angle optimization variable in each half-space; For any half space of the two half spaces, based on the coordinate rotation method, according to the value range of the angle optimization variable in the half space, the deviation is optimized according to the angle optimization variable until the deviation is minimized, so as to obtain the optimal value and minimum deviation of the angle optimization variable corresponding to the half space; The optimal value of the angle optimization variable corresponding to the smaller minimum deviation of the minimum deviations corresponding to the two half spaces is taken as the optimal value of the angle optimization variable of the satellite; Based on the fourth conversion matrix corresponding to the optimal value of the satellite's angle optimization variable, an optimal attitude quaternion for satellite momentum wheel unloading is obtained.

8. A device for calculating the momentum wheel unloading attitude of a Halo orbit satellite, characterized in that: include: An acquisition module is used to plan the satellite unloading time, determine the nominal control direction and nominal post-control orbit required for the satellite to maintain the halo orbit configuration at the unloading time, and determine the nominal position velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the nominal post-control orbit based on the nominal post-control orbit; A processing module, used to establish an angular momentum coordinate system of the satellite based on the angular momentum vector in the inertial system at the time of unloading and the nominal control direction, and determine an angle optimization variable of the satellite, wherein the angle optimization variable is the Euler angle of the satellite rotating around each coordinate axis of the angular momentum coordinate system according to the rotation order; Determine the velocity increment generated by the satellite during the unloading process based on the angular momentum vector and the fitting coefficient, and determine the post-unloading orbit, and the post-unloading position velocity of the satellite in the inertial system when the satellite first crosses the XZ plane of the Earth-Moon rotating coordinate system on the post-unloading orbit; the fitting coefficient represents the fitting relationship between the angular momentum of the satellite at the time of unloading and the velocity increment generated during the unloading process; The deviation between the nominal post-control orbit and the post-unloading orbit is obtained according to the nominal position velocity and the post-unloading position velocity, and based on the coordinate rotation method, the deviation is optimized according to the angle optimization variable to obtain the optimal attitude quaternion of the satellite momentum wheel unloading, so that the satellite can perform momentum wheel unloading according to the optimal attitude quaternion, thereby achieving the goal of maintaining the halo orbit configuration through active unloading.

9. A computer device, characterized in that: include: A memory for storing program instructions; A processor, configured to call the program instructions stored in the memory, and execute the method according to any one of claims 1 to 7 according to the obtained program.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the method according to any one of claims 1 to 7.

11. A computer program product, characterized in that The computer program product comprises an executable program, which is executed by a processor to implement the method according to any one of claims 1 to 7.

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