Large-scale satellite formation design method and system based on parallel satellite array

Abstract

The application provides a large-size satellite formation design method and system based on a parallel satellite array, and relates to the technical field of satellite display. The parallel satellite array comprises a plurality of relatively annular orbiting tracks arranged in parallel. The annular orbiting track is projected in the xy plane of the LVLH coordinate system. The projection track is composed of a projection ellipse and a projection circle. The projection circle appears and becomes larger as the size of the annular orbiting track increases. According to the diameter of the projection circle, the orbit parameter of the virtual main star, the configuration parameter of the slave star and the constructed orbit root number difference model between the slave star and the virtual main star, the orbit parameter of the slave star is determined to realize the slave star formation. In the case that the formation size is significantly increased, the position deviation of each satellite can be effectively reduced, and the accuracy of the formation array is ensured.

Description

Technical Field

[0001] This invention relates to the field of satellite display technology, and more specifically, to a method and system for designing large-size satellite formations based on parallel satellite arrays. Background Technology

[0002] As an emerging aerial display technology, drone swarm display has achieved a leapfrog development from early swarms of hundreds to swarms of tens of thousands, with China currently holding a leading position globally in this field. Its core working principle is as follows: a central control system precisely schedules multiple drones equipped with LED light sources, utilizing RTK differential positioning technology to achieve centimeter-level positioning of the drones. Pre-set images, text, and other display content are broken down into corresponding flight trajectories and lighting control commands for each drone. Through the coordinated flight of multiple drones and synchronized lighting switching, a clear, dynamic, and visual image is formed in the air.

[0003] However, drone swarm displays have obvious application limitations. Their flight altitude is usually maintained between 100 and 300 meters. Due to various factors such as the brightness of the drones themselves, the overall size of the swarm, the obstruction of the observation angle, and the characteristics of human vision, the ground visibility range is only about 1 to 5 kilometers. It cannot achieve wide-area display across cities and countries, and it is difficult to meet the needs of scenarios such as large-scale information transmission and public display.

[0004] To overcome these limitations, the industry has proposed extending this type of aerial display to space to construct space displays, enabling visualization over wide areas or even globally. However, in the actual design process, it was discovered that existing satellite formation design methods have significant flaws when the size of the satellite formation used for space displays increases: as the formation size expands, the calculated positional deviations of the satellites in the formation gradually increase, reducing formation accuracy and resulting in significant deviations in the actual formation constructed collaboratively by multiple satellites. Summary of the Invention

[0005] The problem this invention aims to solve is that, as the size of the formation increases, the positional deviation of each satellite in the formation array calculated by existing satellite formation design methods gradually increases, resulting in a decrease in formation accuracy.

[0006] To address the aforementioned problems, in a first aspect, the present invention provides a method for designing large-size satellite formations based on parallel satellite arrays, wherein the parallel satellite array includes multiple parallel and relatively circular orbits, and multiple slave satellites are arranged on each circular orbit. The virtual primary star is located in an elliptical orbit centered on Earth. Multiple secondary stars orbit the virtual primary star in relative circular motion, forming a circular orbit. The circular orbit is projected onto the xy plane of the LVLH coordinate system to obtain the projected trajectory. The projected trajectory is a combination of a projected ellipse and a projected circle. The projected circle appears and increases in size as the size of the circular orbit increases. The square root of the result is obtained by subtracting the square of the maximum amplitude of the orbital semi-major axis of the virtual primary star from the square of the orbital semi-major axis of the star ring on the z-axis of the LVLH coordinate system. Analyze the difference between the semi-major axis of the virtual primary star's orbit and the square root result, and take half of the difference as the diameter of the projected circle; Based on the diameter of the projection circle, the orbital parameters of the virtual primary star, the configuration parameters of the secondary stars, and the constructed orbital element difference model between the secondary stars and the virtual primary star, the orbital parameters of the secondary stars are determined to achieve secondary star formation. The secondary stars are positioned within... Initial phase offset of directional motion and from the stars Initial phase bias in the plane Equal to ensure that the projection of the same circular flight path onto the yz plane of the LVLH coordinate system is a straight line or an approximation of a straight line; Based on the orbital element difference model, the orbital parameters of the virtual primary star, and the configuration parameters of the secondary stars, the orbital parameters of the secondary stars are determined to achieve secondary star formation.

[0007] Secondly, the present invention also provides a large-size satellite formation design system based on a parallel satellite array, wherein the parallel satellite array includes multiple parallel and relatively circular orbits, and multiple slave satellites are arranged on each circular orbit. The virtual primary star is located in an elliptical orbit centered on Earth. Multiple secondary stars orbit the virtual primary star in relative circular motion, forming a circular orbit. The circular orbit is projected onto the xy plane of the LVLH coordinate system to obtain the projected trajectory. The projected trajectory is a combination of a projected ellipse and a projected circle. The projected circle appears and increases in size as the size of the circular orbit increases. The projection circle analysis module is used to take the square root of the difference between the square of the semi-major axis of the virtual master star's orbit and the square of the maximum amplitude of the orbit around the star ring on the z-axis of the LVLH coordinate system; it is also used to take half of the difference between the semi-major axis of the virtual master star's orbit and the square root result as the diameter of the projection circle. The model building module is used to determine the orbital parameters of the slave stars based on the diameter of the projection circle, the orbital parameters of the virtual primary star, the configuration parameters of the slave stars, and the constructed orbital element difference model between the slave stars and the virtual primary star, in order to achieve slave star formation. The slave stars are located in... Initial phase offset of directional motion and from the stars Initial phase bias in the plane Equal to ensure that the projection of the same circular flight path onto the yz plane of the LVLH coordinate system is a straight line or an approximation of a straight line; The orbital parameter confirmation module is used to determine the orbital parameters of the slave stars based on the orbital element difference model, the orbital parameters of the virtual primary star, and the configuration parameters of the slave stars, so as to realize the slave star formation.

[0008] This invention provides a method and system for designing large-size satellite formations based on parallel satellite arrays. Compared with existing technologies, it has the following advantages: By analyzing the projection of the circular orbits onto the xy-plane of the LVLH coordinate system, the complex three-dimensional spatial motion is transformed into a two-dimensional projection trajectory, and the projection circle that appears in the projection trajectory as the size increases is identified. The diameter of the projection circle is determined based on the semi-major axis of the virtual master star's orbit and the maximum amplitude of the follower star's circular orbit on the z-axis of the LVLH coordinate system, providing a precise calculation method for its diameter. This allows for more accurate description and control of the relative motion of follower stars when designing large-sized satellite formations. Compared to existing technologies where satellite position deviations gradually increase with formation size, this method constructs an orbital element difference model and specifically sets the initial phase offset of the follower star's directional motion and its initial phase offset in the plane to be equal, ensuring that the projections of follower stars on the same circular orbit are aligned in a specific plane, thus significantly improving the configuration accuracy and stability of the formation. Based on the diameter of the projection circle, the orbital parameters of the virtual master star, the configuration parameters of the follower stars, and the orbital element difference model between the follower stars and the virtual master star, the precise calculation of the follower star's orbital parameters is achieved. This formation design method can effectively reduce the positional deviation of each satellite, even when the formation size is significantly increased, thus ensuring the accuracy of the formation array. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a schematic diagram of the projection trajectory of the circular flight track in the xy plane provided in an embodiment of the present invention; Figure 2 A schematic diagram of the LVLH coordinate system provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the projection of the annular flight track in the yz plane provided in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the variation of the projection of the circular orbit in the yz plane with inter-satellite distance, as provided in an embodiment of the present invention. Figure 5 A schematic diagram of a large-size satellite formation design system based on a parallel satellite array is provided for an embodiment of the present invention; Figure 6 This is a schematic diagram of the spatial configuration distribution of a small-sized parallel satellite array provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of the projection of a large-size parallel satellite array in the yz plane provided in an embodiment of the present invention; Figure 8 This is a schematic diagram of the spatial configuration distribution of a large-size parallel satellite array provided in an embodiment of the present invention. Detailed Implementation

[0011] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application are described clearly and completely. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0012] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0013] This application provides a method for designing large-scale satellite formations based on parallel satellite arrays. The large-scale satellite formation includes a parallel satellite array designed using this method. The parallel satellite array includes multiple parallel, relatively circular orbits, each orbit containing multiple slave satellites. For example, three or more relatively circular orbits can be set up, which are parallel to each other in space, forming a planar or curved array.

[0014] The virtual primary star is located in an elliptical orbit centered on Earth. Multiple secondary stars orbit the virtual primary star in relative circular motions, forming a circular orbit. The circular orbit is projected onto the xy-plane of the LVLH coordinate system (Local Vertical Local Horizontal coordinate system, a commonly used orbital coordinate system) to obtain the projected trajectory, as shown below. Figure 1 As shown, the projection trajectory is a combination of a projection ellipse and a projection circle, wherein the projection circle appears and increases in size as the size of the circular orbital increases. Figure 2 As shown, the LVLH coordinate system is defined as follows: Origin Located at the center of mass of the primary star, The position vector of the axis pointing to the primary star direction, The axis points in the direction of the primary star's velocity. The axis points in the direction of the normal vector of the main star's orbit, forming a right-handed coordinate system.

[0015] like Figure 1 As shown, assuming the number of satellites in the circular orbit remains constant, when the inter-satellite distance is large (the satellite formation size is large), the relative circular orbit... The projected trajectory in the plane is a combination of a projected ellipse and a projected circle. However, when the interstellar distance is small (the size of the star formation is small), the projected circle component disappears, and the relative circular orbit is... The projected trajectory in the plane degenerates into a standard ellipse with a major-to-minor axis ratio of 2:1. That is, the projected circle appears and increases in size as the size of the circular orbit increases. Therefore, the projected circle can be considered a correction term for the circular orbit. When the size of the circular orbit increases, and the inter-satellite distance increases, a projected circle component needs to be added to the projected ellipse. By fitting the projected ellipse and the projected circle, the circular orbit can be constructed, making the analysis of the circular orbit more accurate and suitable for large-sized satellite formations.

[0016] The square root of the result is obtained by subtracting the square of the maximum amplitude of the orbital semi-major axis of the virtual primary star from the square of the orbital semi-major axis of the star ring on the z-axis of the LVLH coordinate system.

[0017] The difference between the semi-major axis of the virtual primary star's orbit and the square root result is used, and half of the difference is taken as the diameter of the projected circle.

[0018] Specifically, the circular flight trajectory in the LVLH coordinate system The diameter of the projected circle in the plane for: in, For example, the semi-major axis of the virtual primary star's orbit; Figure 3 As shown, This represents the maximum amplitude of the circular orbit on the z-axis of the LVLH coordinate system. Since the diameter of the projected circle is a key input parameter for constructing the orbital element difference model between the slave star and the virtual master star, its accurate determination directly improves the accuracy of the orbital element difference model, thereby ensuring the accuracy of the slave star orbital parameter calculations, and thus making the constructed slave star formation more stable and accurate.

[0019] Based on the diameter of the projection circle, the orbital parameters of the virtual primary star, the configuration parameters of the secondary stars, and the constructed orbital element difference model between the secondary stars and the virtual primary star, the orbital parameters of the secondary stars are determined to achieve secondary star formation. The secondary stars are positioned within... Initial phase offset of directional motion and from the stars Initial phase bias in the plane Equal to ensure that the projection of the same circular flight path onto the yz plane of the LVLH coordinate system is a straight line or an approximation of a straight line (e.g., Figure 4 The projection shown is either a straight line or a figure-eight shape, so that an observer on Earth can see multiple stars arranged in a straight line in the circular orbit.

[0020] Specifically, after establishing the orbital element difference model, by substituting the orbital parameters of the virtual master star and the configuration parameters of the slave stars, the orbital element difference between each slave star and the virtual master star can be directly calculated using this model. Adding these differences to the corresponding orbital parameters of the virtual master star yields the precise orbital parameters of each slave star. In this way, each slave star can be given precise flight instructions in space, ensuring that the entire parallel satellite array can work collaboratively to form a stable slave star formation. All slave stars together constitute a configurationally self-stabilizing parallel satellite array, with multiple slave stars orbiting the virtual master star in relative circular motion. The virtual master star serves only as the central reference point for displaying the array and does not objectively exist. Projecting the circular orbits of the slave stars onto the virtual master star's LVLH coordinate system yields the relative circular orbits of the slave stars with respect to the virtual master star.

[0021] like Figure 4 As shown, in 10 4 At the m-scale, a parallel satellite array contains multiple parallel relative orbits, with several slave satellites evenly distributed along each orbit. The center points of these orbits are in the LVLH coordinate system. In-plane edge The axes are arranged at equal intervals, and multiple relative orbital paths are in The projections in the plane are parallel and have the same shape. This parallel satellite array contains 5 relative orbits, with 6 satellites evenly distributed on each orbit. Each orbit is in the LVLH coordinate system. The projections in the plane are parallel to each other. As time changes, satellites on the same orbit will rotate cyclically, which is represented in the LVLH coordinate system. Within a plane, satellites will move up and down along their orbital trajectory, but the orbit itself remains largely unchanged over time, thus forming a self-stabilizing parallel satellite array in space.

[0022] In this embodiment, by introducing the relative circular orbital motion of a virtual primary star and its slave stars, and performing projection analysis based on the LVLH coordinate system, the approach to orbit design and control is fundamentally changed. Specifically, by analyzing the projection of the circular orbital motion onto the xy plane of the LVLH coordinate system, the complex three-dimensional spatial motion is transformed into a projection trajectory on a two-dimensional plane, and the projection circle that appears in the projection trajectory as the size increases is identified. By introducing the concept of the projection circle and determining its diameter based on the semi-major axis of the virtual primary star's orbit and the maximum amplitude of the slave star's circular orbital motion on the z-axis of the LVLH coordinate system, a precise method for calculating its diameter is provided. This allows for a more accurate description and control of the relative motion of the slave stars when designing large-sized satellite formations. Compared to the problem of gradually increasing satellite position deviation as the formation size increases in existing technologies, this method constructs an orbital element difference model and specifically sets the initial phase offset of the slave star's directional motion and its initial phase offset in the plane to be equal, ensuring that the projections of slave stars on the same circular orbital motion are aligned in a specific plane, thereby significantly improving the configuration accuracy and stability of the formation. By using the diameter of the projection circle, the orbital parameters of the virtual primary star, the configuration parameters of the secondary stars, and the orbital element difference model between the secondary stars and the virtual primary star, the orbital parameters of the secondary stars were accurately calculated. This formation design method can effectively reduce the positional deviation of each satellite, ensuring the accuracy of the formation array, even when the formation size is significantly increased.

[0023] In an optional embodiment of this application, a method for designing the orbital parameters of virtual primary and secondary satellites in a large-scale satellite formation is provided. The orbital parameters of the virtual primary satellite in the geocentric inertial frame are expressed using the semi-major axis. eccentricity Track inclination Right ascension of ascending node Near the arch point angle , and the near point angle To describe. In large-scale satellite formations, the orbital eccentricity of the virtual primary star should be taken as... This means the virtual primary satellite is located in a circular orbit. To improve the satellite's luminous display effect, minimize light pollution in space, and extend the satellite's lifespan, the virtual primary satellite is located in a near-Earth circular orbit at an altitude of [missing information]. A range of 300km to 500km is preferred, and the semi-major axis of the virtual primary star's orbit should be taken as... ,in The radius is the Earth's radius. The orbital inclination of the virtual primary star. This will affect the visibility of large satellite formations across the Earth's latitude range and their orbital inclination. and coverage of the highest latitude Approximately satisfy Right ascension of the ascending node Near the arch point angle , and the near point angle The value only needs to be in Within the specified range.

[0024] like Figure 1 and Figure 3 As shown, the configuration parameters of the star are as follows: For the circular flight trajectory in the LVLH coordinate system The semi-minor axis of the projected ellipse in the plane. This represents the maximum amplitude of the circular flight trajectory on the z-axis of the LVLH coordinate system. The center point of the circular flight orbit axis coordinate values, For the stars Initial phase offset in the plane For the stars Initial phase offset for directional motion. The circular flight path was determined along shaft and Dimensions along the axis The relative circular flight path was determined along Dimensions along the axial direction The relative circular orbit center point is determined along The sparsity of the axial distribution, and This determines the direction of the relative circular orbit. Let and Equal, relative to the circular flight orbit in The projection in the plane is approximately a straight line.

[0025] By setting configuration parameters The values ​​of these parameters are used to obtain a satellite constellation with specific geometric characteristics for a parallel satellite array. The configuration parameters of the aforementioned satellites are set to form a regularly shaped satellite constellation.

[0026] (1) Circular flight trajectory in LVLH coordinate system Semi-minor axis of the projected ellipse in the plane The maximum amplitude of the circular flight trajectory on the z-axis of the LVLH coordinate system Take a positive real number, and and The maximum value is less than If a circular flight path is required... If the projected trajectory in the plane approximates a straight line, then set... and The maximum values ​​are all less than If set The smaller the value, the more likely the circular flight path will be. The more perpendicular the projection trajectory in the plane is to axis.

[0027] In the design methodology for large-scale satellite formations based on parallel satellite arrays, the projected trajectory of the circular orbit in the xy-plane of the LVLH coordinate system can be precisely controlled, approximating a straight line. This enables the space display interface to generate clear and accurate linear patterns, greatly enriching the expressiveness of the displayed content. Furthermore, by further adjusting the semi-minor axis of the projection ellipse, the tilt angle of these straight-line trajectories can be finely controlled, making them perpendicular to the y-axis of the LVLH coordinate system, thereby achieving precise control over the orientation of the parallel satellite array.

[0028] (2) The center point of the circular orbit axis coordinates Take a real number, and The absolute maximum value is less than If different circular flight paths are required in... If the projection trajectories in the plane are basically the same, then set The absolute maximum value is less than If different circular flight paths With the same interval Then different circular flight paths in The projection trajectory within the plane is uniformly distributed.

[0029] By limiting the maximum absolute value of the axial coordinates of the center points of the circular orbits, the projected trajectory shapes of the different circular orbits in the plane are ensured to remain essentially consistent. Simultaneously, by setting the same intervals between the different circular orbits, these consistent projected trajectories are evenly distributed within the display area, significantly improving the overall continuity, uniformity, and visual quality of the display image. This allows the designed large-size space display to present clearer, more stable, and visually appealing images, meeting the application requirements of high-precision space displays.

[0030] (3) Assume that the number of slave stars uniformly distributed in the circular orbit is The phase difference between adjacent slave stars should satisfy .

[0031] (4) As the interstellar distance increases, the size of the circular orbit increases, and the circular orbit in The projected trajectory in the plane changes from a straight line to a figure-eight shape. For example... Figure 4 As shown, in 10 6 At the m-scale, the relative circular flight path is The projection trajectory in the plane is a narrow figure-eight shape, but multiple figure-eight projection trajectories remain parallel to each other.

[0032] Setting the initial phase offsets of the two satellite configuration parameters to zero allows for the convenient generation of linear projection trajectories, which is crucial for constructing regular and clear satellite formations. Simultaneously, by adjusting the inter-satellite distances to increase the size of the circular orbit, the projection trajectory can be transformed from a straight line to a figure-eight shape, resulting in richer formation shapes and providing a wider range of pattern choices and enhanced expressiveness for space displays. This flexible control over the projection trajectory shape enables large-scale satellite formations to generate more diverse formation effects, greatly enhancing the application potential of satellite formations.

[0033] (5) Different circular flight paths have the same and This ensures that the circular flight path is in The projected trajectories in the plane are parallel to each other. If different circular flight paths have the same... Parallel projected trajectories are easier to identify. Uniform distribution is crucial for forming continuous, smooth, and visually consistent satellite formations, effectively improving the regularity and aesthetics of the formation. Simultaneously, precise phase difference settings simplify the orbit maintenance and control strategies for the satellite formations, enhancing the operational stability and reliability of the entire parallel satellite array.

[0034] (6) and The value of is related to the apparent diameter observed from the ground. The relevant relationship is as follows: in, H This represents the orbital altitude of the virtual primary star, and the semi-major axis of its orbit. , The radius is the Earth's radius.

[0035] Solve for the orbital parameters of the secondary star. Based on the orbital parameters of the virtual primary star. and from star configuration parameters Based on the orbital element difference model, the orbital element difference between the secondary star and the virtual primary star is calculated. The orbital element difference model is as follows: in, This represents the difference in the number of elements of the semi-major axis. This represents the difference in the orbital eccentricity roots. This represents the difference in the inclination elements of the orbit. This represents the difference in the right ascension roots of the ascending nodes. Indicates the difference in latitude angle. This represents the difference in the roots of the angles at the nearest point. This represents the difference in the angle elements near the apex. Represents the arctangent function with quadrants; additionally, the first intermediate variable in the orbital element difference model. Second intermediate variable Third intermediate variable and the fourth intermediate variable The calculation formula is: in, , e The orbital eccentricity of the virtual primary star. For the semi-major axis of the virtual primary star's orbit, i The orbital inclination of the virtual primary star. Near the arch point angle, For the circular flight trajectory in the LVLH coordinate system The semi-minor axis of the projection ellipse of a projection onto a plane. This represents the maximum amplitude of the circular flight trajectory on the z-axis of the LVLH coordinate system. The center point of the circular flight orbit axis coordinate values, For the stars Initial phase offset in the plane For the stars Initial phase offset for directional motion.

[0036] The orbital parameters of each satellite are as follows: Completed the design of orbital parameters for parallel satellite arrays used in large-size satellite formations.

[0037] When the primary star is directly overhead, if the observer's observation direction is set to be consistent with the x-axis of the virtual primary star's LVLH coordinate system, the observer will see a projection of the circular orbit onto the yz plane of the LVLH coordinate system.

[0038] In addition, considering gravity and After 10 hours of simulation, orbital perturbations, including those affecting low Earth orbit (the primary source of perturbations) and atmospheric drag, resulted in a slight deviation in the satellite formation configuration. To eliminate this deviation, the configuration of the circular display array can be periodically corrected. This can be achieved through simple orbital controls such as orbital lifting to maintain the formation configuration, or by retransmitting the configuration parameters of the slave satellites to correct their positions within the circular array. The control frequency can be set to daily, allowing for a relatively low control frequency.

[0039] This application provides a clear and computable orbital element difference model, enabling precise quantification of the orbital relationship between slave satellites and a virtual master satellite. This model establishes a direct mathematical link between geometric configuration parameters in the LVLH coordinate system and orbital element differences, greatly simplifying the calculation and design process of slave satellite orbits. This ensures that parallel satellite arrays can stably and accurately form predetermined slave satellite formations, thereby improving the efficiency and accuracy of large-scale satellite formation design. For example, when the formation size expands from the hundreds of kilometers to the thousands of kilometers, this design method dynamically adjusts the diameter of the projection circle and intermediate parameters in the orbital element difference model to ensure that the projection image of the circular orbit on the yz plane of the LVLH coordinate system highly matches the desired preset formation shape. Through this technical solution, the system effectively solves the problem that as the formation size increases, the positional deviation of each satellite in the formation array gradually increases, leading to a decrease in formation accuracy.

[0040] In an optional embodiment of this application, the aforementioned large-size parallel satellite array of satellites is used as a display interface. Light-emitting devices are mounted on the satellites, and the brightness and color of the light-emitting devices on each satellite are controlled to form the desired display pattern, thus enabling the construction of a display interface in space.

[0041] Specifically, multiple satellites are located in low Earth orbit, each with active light-emitting capability. These satellites carry light-emitting devices, which can be LED light payloads, enabling low-power, high-brightness illumination. The brightness and color of the light payloads are controllable. To meet the requirements for ground-based naked-eye observation, the brightness of the light payloads must be less than magnitude 6; the lower the magnitude, the brighter the satellite. The satellite carries an LED light array, which can be observed from the ground when illuminated. This technology has been implemented and verified on the Ladybeetle-I satellite. The Ladybeetle-I satellite operates at an altitude of 547 km. Its light-emitting payload, composed of an LED array and lenses, was launched into orbit in December 2018 and completed flashing tests in orbit, flashing according to Morse code rules. Ground-based experiments have shown that the Ladybeetle-I beacon light has a brightness of at least [missing value] within a divergence angle range of ±3°. Brightness higher than that of sporadic stars ( The brightness of the beacon light, even in its scattered areas, is easily observed with the naked eye. Therefore, laboratory measurements show that when the Ladybeetle-I satellite is in orbit, the beacon light can be directly observed with the naked eye, and its flight path is visible on clear nights in most cities (such as Xi'an, Beijing, and Shenzhen). Furthermore, the Ladybeetle-I satellite's on-orbit test report also measured the actual illumination range and brightness of the beacon light. Below the satellite, within a 25km diameter radius centered on the satellite's vertical projection onto the Earth, the light is visible to the human eye; directly below the satellite, the beacon light's brightness is estimated at -0.6829 magnitude. In conclusion, the Ladybeetle-I satellite demonstrates the technical feasibility of ground-based visible light payloads through this example.

[0042] Each orbit of a parallel satellite array can have, for example, 10, 20, or more satellites evenly distributed. These satellites emit light collaboratively through their onboard light-emitting devices, collectively forming the displayed image. This multi-orbit, multi-satellite configuration provides the foundation for realizing large-size, high-resolution space displays.

[0043] When using formation arrays as display interfaces, clear and accurate large-scale space displays can be achieved, overcoming the limitations of display pattern distortion in existing technologies. For example, by accurately determining the diameter of the projection circle and constructing an orbital element difference model, even when the display size reaches tens of kilometers, the orbital parameters of each satellite can be accurately calculated, thus controlling the positional deviation of the satellites within an acceptable range and ensuring the clarity and accuracy of the final display pattern. This avoids the error accumulation problem caused by directly extending absolute orbital parameters in traditional methods, providing a more stable and accurate design approach for large-scale space displays. By correlating the relative motion configuration with absolute orbital parameters through an orbital element difference model, high-precision display effects can be maintained even in large-scale display scenarios, effectively improving the practicality and reliability of space displays. This provides reliable technical support for achieving high-precision space visualization displays across cities and even globally.

[0044] In summary, by constructing a self-stabilizing satellite array using multiple orbiting satellites, a dynamic pixel array that remains stable over a long period can be formed, achieving a display effect visible to the naked eye on the ground. The maximum physical size of the display interface (display system) can reach [missing information]. The scale is enormous. Because the satellite's altitude is far higher than any existing display system, this space-based display system can simultaneously cover multiple regions to deliver information. Furthermore, unlike internet communication, even observers in areas with no signal or sparse population can still see the information, enabling its dissemination. The large-scale satellite formation design method presented in this application provides an important technological foundation for constructing a globally covered broadcast media platform, and can be used in various mission scenarios such as cross-regional advertising, large-scale ceremonial performances, disaster relief, and emergency navigation.

[0045] like Figure 5 As shown in the embodiment of this application, a large-size satellite formation design system based on a parallel satellite array is provided. The parallel satellite array includes multiple parallel and relatively circular orbits, and multiple slave satellites are arranged on each circular orbit. The virtual primary star is located in an elliptical orbit centered on Earth. Multiple secondary stars orbit the virtual primary star in relative circular motion, forming a circular orbit. The circular orbit is projected onto the xy plane of the LVLH coordinate system to obtain the projected trajectory. The projected trajectory is a combination of a projected ellipse and a projected circle. The projected circle appears and increases in size as the size of the circular orbit increases. The projection circle analysis module is used to take the square root of the difference between the square of the semi-major axis of the virtual master star's orbit and the square of the maximum amplitude of the orbit around the star ring on the z-axis of the LVLH coordinate system; it is also used to take half of the difference between the semi-major axis of the virtual master star's orbit and the square root result as the diameter of the projection circle. The orbital parameter confirmation module is used to determine the orbital parameters of the slave stars based on the diameter of the projection circle, the orbital parameters of the virtual primary star, the configuration parameters of the slave stars, and the constructed orbital element difference model between the slave stars and the virtual primary star, in order to achieve slave star formation. The slave stars are located in... Initial phase offset of directional motion and from the stars Initial phase bias in the plane The projections of the same circular flight path onto the yz plane of the LVLH coordinate system are equal to ensure that the projections are straight lines or approximate straight lines.

[0046] By combining the projection circle analysis module with the orbital element difference model in a specific manner, the positional deviation of the satellites can be precisely controlled as the formation size increases. The projection circle analysis module provides accurate input parameters for model construction by precisely calculating the projection circle diameter; simultaneously, the orbital parameter verification module sets equal initial phase offsets to ensure the projection alignment of the satellites in the critical plane. This design effectively overcomes the deficiency in existing technologies where positional deviation increases with formation size, significantly improving the accuracy of large-size satellite formations. This allows satellite formations to stably form the desired display pattern, meeting the needs of wide-area display.

[0047] The following two examples correspond to small-sized satellite formations and large-sized satellite formations, respectively, both of which are constructed using parallel satellite arrays.

[0048] 1. Small-sized satellite formations The virtual primary star's orbital parameters are directly set to the values ​​shown in Table 1, with the Earth's radius at 6378.137 km and the orbital altitude H at 500 km.

[0049] Table 1. Orbital parameters of the virtual primary star like Figure 4 As shown, a total of 5 relative orbits were set up, with 6 satellites evenly arranged on each orbit. The overall display array size is on the order of 10km. The satellite configuration parameters were directly set to the values ​​shown in Table 2.

[0050] Table 2 Configuration parameters of satellites in small-sized satellite formations The orbital parameters of the slave star were obtained by solving the virtual primary star orbital parameters, slave star configuration parameters, and orbital element difference model, as shown in Table 3. In Table 3, This indicates the orbital eccentricity of the star. Indicates the semi-major axis of the star's orbit. Indicates the inclination of a star's orbit. Indicates the right ascension from the ascending node of the star. Indicates the angle from the near-circumference point of the star. This indicates the angle from the star's level anterior point.

[0051] Table 3. Orbital parameters of some satellites in a small-sized satellite formation. In the LVLH coordinate system of the virtual primary star, the parallel satellite array is... Projection in a plane, such as Figure 4 As shown, the ground observation results appear in the form of a parallel linear array.

[0052] The orbital parameters of the generated parallel satellite display array are input into the satellite simulation software, and the resulting spatial configuration changes over time as follows: Figure 6 As shown, the designed parallel satellite array consistently orbits the virtual master star in a stable, synchronous orbit, presenting a regular and orderly arrangement of parallel straight lines. By rationally planning the on / off state, brightness, and color adjustment of the lights on the satellites, precise display of matrix-style information such as text, icons, and simple patterns can be achieved.

[0053] 2. Large-size satellite formations The virtual primary star's orbital parameters are still set directly to the values ​​shown in Table 1, with the Earth's radius at 6378.137 km and the orbital altitude H at 500 km.

[0054] like Figure 4 As shown, a total of 5 relative orbits are set up, with 6 slave satellites evenly arranged on each orbit. The overall display array size is on the order of 1000km. The configuration parameters of the slave satellites are directly set to the values ​​shown in Table 4.

[0055] Table 4 Configuration parameters of satellites in large-size satellite formations The orbital parameters of the slave star were obtained by solving the virtual primary star orbital parameters, slave star configuration parameters, and orbital element difference model, as shown in Table 5. In Table 5, This indicates the orbital eccentricity of the star. Indicates the semi-major axis of the star's orbit. Indicates the inclination of a star's orbit. Indicates the right ascension from the ascending node of the star. Indicates the angle from the near-circumference point of the star. This indicates the angle from the star's level anterior point.

[0056] Table 5 shows the orbital parameters of some satellites in a large-size satellite formation. In the LVLH coordinate system of the virtual primary star, the parallel satellite array is... Projection in a plane, such as Figure 7 As shown, the ground observation results appear in the form of a parallel array, with the projection of each relative flight trajectory approximating a narrow figure-eight shape (approaching a straight line).

[0057] The orbital parameters of the generated parallel satellite display array are input into the satellite simulation software, and the resulting spatial configuration changes over time as follows: Figure 8 As shown, the designed parallel satellite array always orbits the virtual master star in a synchronous orbit, presenting a parallel array arrangement. Although the satellite distribution is not very uniform, the display effect can be improved by increasing the number of satellites in each orbit.

[0058] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0059] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for designing large-size satellite formations based on parallel satellite arrays, characterized in that, The parallel satellite array consists of multiple parallel, relatively circular orbits, with multiple satellites deployed on each circular orbit; The virtual master star is located in an elliptical orbit centered on Earth, and multiple secondary stars orbit the virtual master star in relative circular motions, forming a circular orbit. The circular flight path is projected onto the xy plane of the LVLH coordinate system to obtain the projected trajectory. The projected trajectory is a combination of a projected ellipse and a projected circle. The projected circle appears and increases in size as the size of the circular flight path increases. The square root of the result is obtained by subtracting the square of the maximum amplitude of the orbital semi-major axis of the virtual primary star from the square of the orbital semi-major axis of the star ring on the z-axis of the LVLH coordinate system. Analyze the difference between the semi-major axis of the virtual primary star's orbit and the square root result, and take half of the difference as the diameter of the projected circle; Based on the diameter of the projection circle, the orbital parameters of the virtual primary star, the configuration parameters of the secondary stars, and the constructed orbital element difference model between the secondary stars and the virtual primary star, the orbital parameters of the secondary stars are determined to achieve secondary star formation; among them, the secondary stars in Initial phase offset of directional motion and from the stars Initial phase bias in the plane The projections of the same circular flight path onto the yz plane of the LVLH coordinate system are equal to ensure that the projections are straight lines or approximate straight lines.

2. The method for designing large-size satellite formations based on parallel satellite arrays as described in claim 1, characterized in that, The configuration parameters of the satellite also include the semi-minor axis of the projected ellipse. The maximum amplitude of the circular flight trajectory on the z-axis of the LVLH coordinate system The center point of the projected trajectory of the circular flight path in the xy plane of the LVLH coordinate system axis coordinates ; Wherein, the semi-minor axis of the projected ellipse and maximum amplitude Take positive real numbers whose maximum value is less than ; axis coordinates Take real numbers and The absolute maximum value is less than ; Followers in different circular orbits have the same and So that multiple circular flight paths are in the LVLH coordinate system The projected trajectories in the plane are parallel to each other; Maximum amplitude and axis coordinates The value of is related to the apparent diameter observed from the ground. The relevant relationship is as follows: in, H This represents the orbital altitude of the virtual primary star. semi-major axis of the virtual primary star's orbit , The radius is the Earth's radius.

3. The large-size satellite formation design method based on parallel satellite arrays as described in claim 2, characterized in that, If a circular orbit is required... If the projected trajectory in the plane approximates a straight line, then set the semi-minor axis of the projected ellipse. and maximum amplitude The maximum values ​​are all less than ; If set The smaller the value, the more likely the circular flight path will be. The more perpendicular the projection trajectory in the plane is to axis.

4. The method for designing large-size satellite formations based on parallel satellite arrays as described in claim 2, characterized in that, If different circular flight paths are required, If the projected trajectories in the plane are basically the same, then the center point of the circular orbital flight path is set. axis coordinates The absolute maximum value is less than ; If different circular flight paths With the same interval Then different circular flight paths in The projection trajectory within the plane is uniformly distributed.

5. The method for designing large-size satellite formations based on parallel satellite arrays as described in claim 2, characterized in that, As the distance from the stars increases, the size of the circular orbit increases, and the circular orbit in... The projection trajectory in the plane is transformed into a figure-eight shape.

6. The method for designing large-size satellite formations based on parallel satellite arrays as described in claim 2, characterized in that, Assuming the number of slave stars is uniformly distributed in the circular orbit is Then the phase difference between adjacent slave stars should satisfy .

7. The method for designing large-size satellite formations based on parallel satellite arrays as described in claim 1, characterized in that, The orbital element difference between the slave star and the virtual master star is: The orbital element difference model is as follows: in, This represents the difference in the number of elements of the semi-major axis. This represents the difference in the orbital eccentricity roots. This represents the difference in the inclination elements of the orbit. This represents the difference in the right ascension roots of the ascending nodes. Indicates the difference in latitude angle. This represents the difference in the roots of the angles at the nearest point. This represents the difference in the angle elements near the apex. Represents the arctangent function with quadrants; additionally, the first intermediate variable in the orbital element difference model. Second intermediate variable Third intermediate variable and the fourth intermediate variable The calculation formula is: in, , e The orbital eccentricity of the virtual primary star. For the semi-major axis of the virtual primary star's orbit, i The orbital inclination of the virtual primary star. Near the arch point angle, For the circular flight trajectory in the LVLH coordinate system The semi-minor axis of the projection ellipse of a projection onto a plane. Indicates the circular orbit in the LVLH coordinate system The diameter of the projected circle in the plane. This represents the maximum amplitude of the circular flight trajectory on the z-axis of the LVLH coordinate system. The center point of the circular flight orbit axis coordinate values, For the stars Initial phase offset in the plane For the stars Initial phase offset for directional motion.

8. The method for designing large-size satellite formations based on parallel satellite arrays as described in claim 1, characterized in that, If the observation direction of the ground observer is set to be consistent with the x-axis direction of the virtual primary star's LVLH coordinate system, then the observation image seen by the ground observer is the projection image of the circular orbit on the yz plane of the LVLH coordinate system.

9. The method for designing large-size satellite formations based on parallel satellite arrays as described in claim 1, characterized in that, The parallel satellite array of the satellite constellation will serve as the display interface. Each satellite will carry a light-emitting device, and the brightness and color of the light-emitting device on each satellite will be controlled to form the desired display pattern.

10. A large-size satellite formation design system based on parallel satellite arrays, characterized in that, The parallel satellite array consists of multiple parallel, relatively circular orbits, with multiple satellites deployed on each circular orbit; The virtual master star is located in an elliptical orbit centered on Earth, and multiple secondary stars orbit the virtual master star in relative circular motions, forming a circular orbit. The circular flight path is projected onto the xy plane of the LVLH coordinate system to obtain the projected trajectory. The projected trajectory is a combination of a projected ellipse and a projected circle. The projected circle appears and increases in size as the size of the circular flight path increases. The projection circle analysis module is used to take the square root of the difference between the square of the semi-major axis of the virtual master star's orbit and the square of the maximum amplitude of the orbit around the star ring on the z-axis of the LVLH coordinate system; it is also used to take half of the difference between the semi-major axis of the virtual master star's orbit and the square root result as the diameter of the projection circle. The orbital parameter confirmation module is used to determine the orbital parameters of the slave stars based on the diameter of the projection circle, the orbital parameters of the virtual primary star, the configuration parameters of the slave stars, and the constructed orbital element difference model between the slave stars and the virtual primary star, in order to achieve slave star formation. The slave stars are located in... Initial phase offset of directional motion and from the stars Initial phase bias in the plane The projections of the same circular flight path onto the yz plane of the LVLH coordinate system are equal to ensure that the projections are straight lines or approximate straight lines.

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