Method, device, electronic equipment, medium and product for controlling deorbiting of constellation satellites

Abstract

The application discloses a method and device for controlling orbit departure of constellation satellites, electronic equipment, medium and product. The method comprises: obtaining current orbit parameters and target orbit parameters of the constellation satellites, the current orbit parameters comprising a current semi-major axis and a current eccentricity of the current orbit, and the target orbit parameters comprising a target semi-major axis and a target eccentricity of the target orbit; constructing a target function about the orbit departure direction of the constellation satellites based on the current orbit parameters and the target orbit parameters, and a semi-major axis weight and an eccentricity weight; adjusting the semi-major axis weight and / or the eccentricity weight in the target function at multiple discrete nodes of the orbit departure of the constellation satellites to obtain a target orbit departure direction of the constellation satellites at each discrete node, the target orbit departure direction being a trajectory that makes the orbit departure time of the constellation satellites shortest; and controlling the orbit departure of the constellation satellites along the target orbit departure direction. The scheme provided by the application can reduce the complexity of calculating the orbit departure trajectory of the satellites, thereby improving the orbit departure efficiency of the satellites.

Description

Technical Field

[0001] This application belongs to the field of aerospace technology, and in particular relates to a method, apparatus, electronic equipment, medium and product for controlling the deorbiting of constellation satellites. Background Technology

[0002] Currently, mega-constellations are deployed in low Earth orbit to provide high-speed telecommunications services globally. These mega-constellations consist of hundreds or even thousands of satellites. To maintain the safety and sustainable development of low Earth orbit, it is necessary to control the rapid deorbiting of constellation satellites when they reach the end of their lifespan.

[0003] In related technologies, electric propulsion systems can be used to control the deorbiting of constellation satellites. Orbit design for electric propulsion systems typically employs either indirect or direct methods. However, both indirect and direct methods yield open-loop guidance laws. During actual flight, constellation satellites may deviate from their nominal trajectories due to various unpredictable perturbations, requiring ground control to recalculate the guidance law, thus reducing the efficiency of satellite deorbiting. Summary of the Invention

[0004] This application provides a method, apparatus, electronic device, medium, and product for controlling the deorbiting of constellation satellites, which can reduce the complexity of calculating the deorbiting trajectory of constellation satellites, improve the calculation efficiency of the deorbiting trajectory of constellation satellites, and thus improve the deorbiting efficiency of constellation satellites.

[0005] In a first aspect, embodiments of this application provide a method for controlling the deorbiting of a constellation satellite. The method includes: acquiring the current orbital parameters and target orbital parameters of the constellation satellite, wherein the current orbital parameters include the current semi-major axis and current eccentricity of the current orbit, and the target orbital parameters include the target semi-major axis and target eccentricity of the target orbit; constructing an objective function regarding the deorbiting direction of the constellation satellite based on the current orbital parameters, the target orbital parameters, and the semi-major axis weight and eccentricity weight; adjusting the semi-major axis weight and / or eccentricity weight in the objective function at multiple discrete nodes where the constellation satellite is deorbiting, to obtain the target deorbiting direction of the constellation satellite at each discrete node, wherein the target deorbiting direction is the trajectory that minimizes the deorbiting time of the constellation satellite; and controlling the deorbiting of the constellation satellite along the target deorbiting direction.

[0006] Secondly, embodiments of this application provide an apparatus for controlling the deorbiting of constellation satellites. The apparatus includes: a parameter acquisition module for acquiring current orbital parameters and target orbital parameters of the constellation satellites, wherein the current orbital parameters include the current semi-major axis and current eccentricity of the current orbit, and the target orbital parameters include the target semi-major axis and target eccentricity of the target orbit; a function construction module for constructing an objective function regarding the deorbiting direction of the constellation satellites based on the current orbital parameters, the target orbital parameters, and the semi-major axis weight and eccentricity weight; a weight adjustment module for adjusting the semi-major axis weight and / or eccentricity weight in the objective function at multiple discrete nodes during the deorbiting of the constellation satellites, to obtain the target deorbiting direction of the constellation satellites at each discrete node, wherein the target deorbiting direction is the trajectory that minimizes the deorbiting time of the constellation satellites; and a satellite deorbiting module for controlling the deorbiting of the constellation satellites along the target deorbiting direction.

[0007] Thirdly, embodiments of this application provide an electronic device, which includes: a processor and a memory storing computer program instructions; the processor executes the computer program instructions to implement the method for controlling the deorbiting of constellation satellites as described in the first aspect.

[0008] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer program instructions that, when executed by a processor, implement the method for controlling the deorbiting of constellation satellites as described in the first aspect.

[0009] Fifthly, embodiments of this application provide a computer program product in which instructions, when executed by a processor of an electronic device, cause the electronic device to perform the method for controlling the deorbiting of constellation satellites as described in the first aspect.

[0010] As can be seen from the above, in this embodiment, the objective function is constructed based on orbital parameters and control weights (i.e., semi-major axis weights and eccentricity weights). During the flight of the constellation satellites, the semi-major axis weights and eccentricity weights are adjusted, transforming the optimal control problem into a parameter optimization problem. Compared with the method of recalculating the guidance law in related technologies, this embodiment only needs to adjust the weight parameters, which reduces the complexity of calculating the deorbit trajectory of the constellation satellites, improves the calculation efficiency of the deorbit trajectory of the constellation satellites, and thus improves the deorbit efficiency of the constellation satellites. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart illustrating a method for controlling the deorbiting of constellation satellites according to an embodiment of this application;

[0013] Figure 2 This is a schematic diagram of the semi-major axis and eccentricity provided in one embodiment of this application;

[0014] Figure 3 This is a schematic diagram of an RTN coordinate system provided in one embodiment of this application;

[0015] Figure 4 This is a schematic diagram of the electric thrust direction provided in one embodiment of this application;

[0016] Figure 5 This is a schematic diagram illustrating the deorbiting process of a constellation satellite according to one embodiment of this application;

[0017] Figure 6 This is a schematic diagram of the time history of the semi-major axis during the satellite deorbiting process provided in one embodiment of this application;

[0018] Figure 7 This is a schematic diagram of the time history of eccentricity during satellite deorbiting provided in one embodiment of this application;

[0019] Figure 8 This is a schematic diagram of the time history of the perigee altitude during the satellite deorbiting process provided in one embodiment of this application;

[0020] Figure 9 This is a schematic diagram of a device for controlling the deorbiting of constellation satellites according to another embodiment of this application;

[0021] Figure 10 This is a schematic diagram of the structure of an electronic device provided in another embodiment of this application. Detailed Implementation

[0022] The features and exemplary embodiments of various aspects of this application will be described in detail below. To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain this application and not to limit it. For those skilled in the art, this application can be implemented without some of these specific details. The following description of the embodiments is merely to provide a better understanding of this application by illustrating examples.

[0023] It should be noted that, in this document, relational terms such as "first" and "second" are used merely 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..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes said element.

[0024] To facilitate understanding, before explaining the solution provided in this application, the background of the solution provided in this application will be explained first.

[0025] Currently, an increasing number of mega-constellations are being deployed in low Earth orbit to provide high-speed telecommunications services globally. These mega-constellations, composed of hundreds or even thousands of satellites, have opened up new prospects for international space exploration but have also brought new risks to low Earth orbit safety. To maintain the safety and sustainable development of low Earth orbit, satellites should be deorbited rapidly when they reach the end of their lifespan.

[0026] As a new type of propulsion system, electric propulsion systems have advantages over traditional chemical propulsion systems, such as high specific impulse, low thrust, light weight, continuous operation and repeated restart. They have been widely used in various space missions, such as orbit transfer, space station maintenance, rendezvous and approach tracking-avoidance.

[0027] The design of orbits for electric propulsion systems is mainly divided into two methods: indirect and direct methods. The indirect method transforms the orbit design problem into a two-point boundary value problem, solved using a target-shooting method, which has high solution accuracy. However, because the costate variables lack physical meaning, the convergence radius is small, and it is sensitive to initial estimation, making it difficult to obtain the optimal solution. The direct method transforms the orbit design problem into a nonlinear programming problem, possessing a larger convergence radius and computational efficiency. However, in missions using electric propulsion systems, orbit transfer times typically last tens or even hundreds of days, making the nonlinear programming problem difficult to solve. Considering that both the direct and indirect methods yield open-loop guidance laws, during actual flight, constellation satellites may deviate from their nominal trajectories due to many perturbations that cannot be accurately estimated. Ground control centers need to recalculate the guidance rate. Therefore, open-loop guidance laws are not suitable for low-thrust, long-duration orbit transfer processes.

[0028] To address the aforementioned issues, this application provides a method, apparatus, electronic device, medium, and product for controlling the deorbiting of constellation satellites, thereby solving the problem of rapid deorbiting of constellation satellites with low thrust.

[0029] The method for controlling the deorbiting of constellation satellites provided in the embodiments of this application will be described below.

[0030] Figure 1 A flowchart illustrating a method for controlling the deorbiting of a constellation satellite according to an embodiment of this application is shown. Figure 1 As shown, the method includes the following steps:

[0031] Step S101: Obtain the current orbital parameters and target orbital parameters of the constellation satellites.

[0032] In step S101, the current orbit parameters include the current semi-major axis and the current eccentricity of the current orbit, and the target orbit parameters include the target semi-major axis and the target eccentricity of the target orbit. Here, the current orbit is the orbit in which the constellation satellite was located before deorbiting, and the target orbit is the orbit in which the constellation satellite will reach after deorbiting.

[0033] It should be noted that in practical applications, the current orbital parameters of the constellation satellites are known values, while the target orbital parameters can be determined based on the actual deorbit requirements. For example, the perigee altitude corresponding to the target orbit can be determined based on the actual deorbit requirements, and then the target orbital parameters can be determined based on the correspondence between perigee altitude and orbital parameters.

[0034] Step S102: Based on the current orbit parameters and target orbit parameters, as well as the semi-major axis weight and eccentricity weight, construct an objective function for the deorbit direction of the constellation satellites.

[0035] In step S102, the objective function can be a quadratic Lyapunov function, which can be expressed by formula (1):

[0036]

[0037] In formula (1), V is the Lyapunov function; X is a parameter matrix composed of the current orbital parameters and the target orbital parameters, where, a and e represent the real-time semi-major axis and real-time eccentricity of the constellation satellites, respectively; a t and e t Let a0 and e0 represent the target semi-major axis and target eccentricity of the target orbit, respectively; and let a0 and e0 represent the current semi-major axis and current eccentricity of the current orbit, respectively. Q is a weight matrix composed of semi-major axis weights and eccentricity weights. ka is the semi-major axis weight, and ke is the eccentricity weight.

[0038] Step S103: At multiple discrete nodes where the constellation satellites de-orbit, adjust the semi-major axis weight and / or eccentricity weight in the objective function to obtain the target de-orbit direction of the constellation satellites at each discrete node.

[0039] In step S103, the discrete nodes are multiple nodes equidistantly set according to the perigee altitude variation range based on the deorbit requirements. By setting multiple discrete nodes, the NSGA-II optimization method is used at each discrete node to adjust the semi-major axis weight and / or eccentricity weight, thereby transforming the optimal control problem into a parameter optimization problem. Compared with related technologies, this reduces the computational complexity of the deorbit trajectory of constellation satellites and improves the deorbit efficiency of constellation satellites.

[0040] Step S104: Control the constellation satellites to deorbit along the target deorbit direction.

[0041] It should be noted that in step S104, the target deorbit direction is the trajectory that minimizes the deorbit time of the constellation satellites. That is, deorbiting according to this target deorbit direction minimizes the deorbit time of the constellation satellites, thereby improving the deorbit efficiency of the constellation satellites.

[0042] Based on the scheme defined in steps S101 to S104 above, it can be understood that in this embodiment, the objective function is constructed based on orbital parameters and control weights (i.e., semi-major axis weights and eccentricity weights). During the flight of the constellation satellites, the semi-major axis weights and eccentricity weights are adjusted, transforming the optimal control problem into a parameter optimization problem. Compared with the method of recalculating the guidance law in related technologies, this embodiment only needs to adjust the weight parameters, which reduces the complexity of calculating the deorbit trajectory of the constellation satellites, improves the calculation efficiency of the deorbit trajectory of the constellation satellites, and thus improves the deorbit efficiency of the constellation satellites.

[0043] The methods provided in the embodiments of this application will be explained in detail below.

[0044] Before controlling the deorbiting of constellation satellites, the target orbit parameters must be determined. Specifically, firstly, based on the deorbiting requirements of the constellation satellites, the target perigee altitude corresponding to the target orbit is determined; then, a target data set matching the target perigee altitude is selected from multiple data sets, and the semi-major axis and eccentricity contained in the target data set are used to determine the target semi-major axis and target eccentricity, respectively.

[0045] In the above embodiments, each data set includes a semi-major axis and an eccentricity.

[0046] As an example, when the perigee altitude is fixed, the relationship between the semi-major axis and the eccentricity is also fixed, for example, in Figure 2In the diagram illustrating the relationship between semi-major axis and eccentricity, the green curve represents the combination of semi-major axis and eccentricity at perigee altitude. The red asterisks correspond to the current semi-major axis and eccentricity of the constellation satellites, respectively, while the blue squares represent the target semi-major axis and target eccentricity. Deorbiting requires moving the constellation satellites from the red asterisks to the blue squares.

[0047] Furthermore, after determining the current orbital parameters and the target orbital parameters, a Lyapunov function can be constructed based on formula (1). Then, the semi-major axis weight and / or eccentricity weight in the Lyapunov function are adjusted to determine the deorbit direction of the constellation satellites.

[0048] Specifically, firstly, the first-order partial derivative of the objective function with respect to the true anomaly angle is calculated. Then, the electric thrust direction of the constellation satellites in the satellite orbit coordinate system is determined based on the first-order partial derivative. Next, the perigee altitude range between the current orbit's perigee altitude and the target orbit's perigee altitude is sampled to obtain multiple discrete nodes. Then, based on the electric thrust direction corresponding to each discrete node, the semi-major axis weight and / or eccentricity weight corresponding to each discrete node are adjusted to obtain the target deorbit direction corresponding to each discrete node.

[0049] As an example, solving for the first-order partial derivative of formula (1) yields formula (2), that is, the first-order partial derivative can be expressed by formula (2):

[0050]

[0051] In formula (2), E is the true anomaly angle; f(X) is the atmospheric drag experienced by the constellation satellite; and u is the electric thrust experienced by the constellation satellite in the satellite orbit coordinate system.

[0052]

[0053] Where a is the semi-major axis; e is the eccentricity; and μ is the Earth's gravitational constant.

[0054] f(X) can be expressed by formula (3):

[0055]

[0056] In formula (3), C d This is the atmospheric drag coefficient, typically 2.0; Let A be the surface area to mass ratio of the satellite, where A is the area of ​​the constellation satellite, m is the mass of the constellation satellite, ρ is the atmospheric density, and v is the atmospheric density. r The speed of the constellation satellites.

[0057] The electric thrust u experienced by a constellation satellite in the satellite orbit coordinate system can be expressed by formula (4):

[0058]

[0059] In formula (4), u is the electric thrust experienced by the constellation satellite in the satellite orbital coordinate system RTN; η is the efficiency of the electric thruster that propels the constellation satellite; P is the power of the electric thruster; I sp α is the specific impulse of the electric thruster; m is the mass of the constellation satellite; g0 is the Earth's gravitational constant; α is the angle between the thrust vector in the orbital plane and the R direction; β is the angle between the thrust vector and the orbital plane.

[0060] It should be noted that the RTN coordinate system can be used to analyze specific perturbation forces, for example, in Figure 3 In the schematic diagram of the RTN coordinate system shown, O is the origin, R is the radial direction, T is the tangential direction, and N is the normal direction; I, J, and K are the three axes of the three-dimensional coordinate system. Figure 4 A schematic diagram showing the direction of electric thrust is provided. Figure 4 In this context, F represents electric thrust, and the direction of electric thrust is the deorbiting direction of the constellation satellites. The direction of electric thrust can be expressed by formula (5):

[0061]

[0062] In formula (5), u * In the direction of electric thrust; This represents the maximum thrust of the electric thrusters of the constellation satellites.

[0063] It should be noted that the electric thrust direction is u * The optimal control vector that stably converges to 0 using the Lyapunov function is obtained by considering the perturbations of Earth's shadow and atmospheric drag. As can be seen from formula (2), in the process of designing the Lyapunov function and deriving the first-order partial derivative of the Lyapunov function with respect to the true anomaly angle in this embodiment, the influence of Earth's shadow and atmospheric drag perturbations on satellite deorbiting is taken into account. The deorbiting direction of the constellation satellites determined by the method provided in this embodiment is more realistic, and the calculation results are more accurate.

[0064] Furthermore, it should be noted that, as shown in formula (2), when (f(X)+u) and (X) T QB) T When the included angle between them is greater than 90°, The electric propulsion system gradually stabilizes; when The larger the value, the faster the constellation satellites change and the shorter the deorbit time, i.e., formula (5).

[0065] Furthermore, after constructing the objective function, N discrete nodes can be set at equal intervals according to the perigee altitude variation range based on the deorbit requirements, transforming the optimal control problem into a parameter optimization problem. The NSGA-II optimization method is used to correct the parameters, thereby obtaining the shortest deorbit control strategy for constellation satellites with low thrust.

[0066] Specifically, firstly, the shortest deorbit time corresponding to each discrete node is determined as the performance index corresponding to each discrete node; under preset constraints, the semi-major axis weight and eccentricity weight corresponding to each discrete node are adjusted to minimize the performance index, thereby obtaining the target semi-major axis weight and / or target eccentricity weight corresponding to each discrete node; based on the target semi-major axis and / or target eccentricity weight, the electric thrust direction is calculated to obtain the target deorbit direction corresponding to each discrete node.

[0067] As an example, the thrust direction calculated according to formula (5) can make the Lyapunov function value decrease the fastest and eventually stabilize at 0. However, it can be seen that the magnitudes of ka and ke in the Q matrix affect the performance of the semi-major axis and eccentricity changes. Therefore, using the perigee height variation range, six discrete nodes are set at equal intervals to parameterize ka and ke, and then the parameters are corrected using the NSGA-II optimization method. Among them, the optimization variable K for the shortest time deorbit problem can be represented by formula (6):

[0068]

[0069] In formula (6), r pi i = 0, 1, 2, representing different perigee altitudes.

[0070] The optimization problem of electric propulsion deorbit control strategy for constellation satellites can be described as follows: Under given constraints, calculate the optimal control direction to satisfy the optimal performance index, as shown in the following form:

[0071] (1) For the performance index: J = {t} f (u)}, where t f denoted as de-orbiting time, and u as de-orbiting direction.

[0072] (2) Regarding the constraints:

[0073] ① Equations of motion:

[0074] ② Initial value constraint: X0 = [a0 e0 m0] T

[0075] ③Terminal constraints:

[0076] Where, Δa err and Δe errThese represent the maximum allowable deviations of the semi-major axis and eccentricity in the final state, respectively. When the terminal constraint is less than 1, it indicates that the final goal has been achieved.

[0077] Under the above constraints, the NSGA-II optimization method is used to optimize the set of control weight parameters K for the semi-major axis and eccentricity to minimize the performance index. The optimal weight set is obtained through the optimization method and substituted into formula (5) to obtain the optimal control strategy for the constellation satellites. The deorbit trajectory is calculated by integrating the optimized parameters and the optimal control direction until the perigee meets the deorbit requirements.

[0078] The following examples illustrate the method provided in this application. This process can be carried out by... Figure 5 To indicate, by Figure 5 It can be seen that the process of controlling the deorbiting of constellation satellites mainly includes the following four steps:

[0079] Step S501: Based on the off-track requirements, design a data set for the semi-major axis and eccentricity that conforms to the perigee height.

[0080] Step S502: Design the Lyapunov function, derive the first-order partial derivative of the Lyapunov function with respect to the true anomaly angle, and obtain the optimal control vector that allows the Lyapunov function to stably converge to 0 under the consideration of Earth's shadow and atmospheric drag perturbation.

[0081] Step S503: Based on the deorbiting requirements, N discrete nodes are set at equal intervals according to the perigee altitude variation range. The optimal control problem is transformed into a parameter optimization problem. The NSGA-II optimization method is used to correct the parameters to obtain the deorbiting control strategy with the shortest small thrust time for constellation satellites.

[0082] Step S504: Calculate the derailment trajectory by integrating the optimized parameters and the optimal control direction until the perigee meets the derailment requirements.

[0083] The method provided in the embodiments of this application is simulated and calculated. The constellation satellites are set as OneWeb constellation satellites. The orbital parameters and small thrust system parameters corresponding to the OneWeb constellation are shown in Table 1.

[0084] Table 1

[0085] semi-long shaft <![CDATA[a0]]> 7578.137 km Eccentricity <![CDATA[e0]]> 0.001 track inclination <![CDATA[i0]]> 87.9 deg True near point angle <![CDATA[E0]]> 10 deg Target semi-major axis <![CDATA[a f ]]> 6910.432 km Target eccentricity <![CDATA[e f ]]> 0.0408 satellite quality <![CDATA[m0]]> 150 kg Small thruster power P 200 W Small thruster efficiency η 50 ％ Small thruster specific impulse <![CDATA[I sp ]]> 1500 s

[0086] For step S501, based on the derailment requirements and Table 1, calculate the data set of semi-major axis and eccentricity that conform to the perigee altitude, thereby obtaining... Figure 2 The graph shown. According to... Figure 2 The curve shown indicates that the semi-major axis of the target is 6910.432 km and the eccentricity of the target is 0.0408.

[0087] For step S502, design the Lyapunov function, derive the first-order partial derivative of the Lyapunov function with respect to the true anterior angle, and obtain the optimal control vector for the Lyapunov function to stably converge to 0, thus obtaining formula (5).

[0088] For step S503, based on the deorbiting requirements, six discrete nodes are set at equal intervals according to the perigee altitude variation range. The optimal control problem is transformed into a parameter optimization problem. The NSGA-II optimization method is used to correct the parameters, obtaining the shortest deorbiting control strategy for constellation satellites with low thrust. The optimized parameter values ​​are: [719,347,761,391,761,391], and the flight time is 56.41 days.

[0089] For step S504, the deorbit trajectories of the constellation satellites are calculated based on the optimized parameters and the optimal control direction integration, such as... Figures 6 to 8 As shown, where, Figure 6 This is a time history diagram of the semi-major axis during the satellite's deorbiting process. Figure 7 This is a time history diagram of the eccentricity during the satellite's deorbiting process. Figure 8 This is a time history diagram of the perigee altitude during the satellite's deorbiting process.

[0090] As described above, this application provides a method for controlling the deorbiting of constellation satellites. This method is based on Lyapunov to achieve rapid deorbiting of a giant constellation under a low-thrust system. The method calculates the orbital parameters of the target orbit based on the orbital parameters of the satellite's current orbit; after setting the orbital parameters of the target orbit, a Lyapunov function is established; the optimal control strategy is determined based on Lyapunov stability; and the semi-major axis weight and eccentricity weight are adjusted by linear parameterization of the perigee altitude, transforming the optimal control strategy problem into a parameter optimization problem. Finally, the NSGA-II optimization method is used to optimize the parameters, solving the problem of the shortest time deorbiting of constellation satellites under low thrust.

[0091] In the above process, the perigee altitude can be rapidly reduced by using a closed-loop feedback control strategy based on the Lyapunov function; the optimal control direction based on the perigee angle can introduce perturbation terms and Earth shadow, which is beneficial for simulating actual tasks, establishing time-optimal performance indicators, transforming the optimal control problem into a parameter optimization problem, and using the NSGA-II optimization method to meet the task requirements.

[0092] This application also provides a device for controlling the deorbiting of constellation satellites, such as... Figure 9 As shown, the device 900 includes: a parameter acquisition module 901, a function construction module 902, a weight adjustment module 903, and a satellite deorbiting module 904.

[0093] The parameter acquisition module 901 is used to acquire the current orbit parameters and target orbit parameters of the constellation satellites. The current orbit parameters include the current semi-major axis and current eccentricity of the current orbit, and the target orbit parameters include the target semi-major axis and target eccentricity of the target orbit.

[0094] Function construction module 902 is used to construct an objective function about the deorbit direction of constellation satellites based on the current orbit parameters, the target orbit parameters, the semi-major axis weight, and the eccentricity weight.

[0095] The weight adjustment module 903 is used to adjust the semi-major axis weight and / or eccentricity weight in the objective function at multiple discrete nodes of the constellation satellite's deorbiting, so as to obtain the target deorbiting direction of the constellation satellite at each discrete node, wherein the target deorbiting direction is the trajectory that minimizes the deorbiting time of the constellation satellite.

[0096] Satellite deorbit module 904 is used to control the deorbiting of constellation satellites along the target deorbiting direction.

[0097] In one example, the parameter acquisition module is specifically used to determine the target perigee altitude corresponding to the target orbit based on the deorbit requirement information of the constellation satellites; to determine the target data group that matches the target perigee altitude from multiple data groups, wherein each data group includes a semi-major axis and an eccentricity; and to determine the target semi-major axis and target eccentricity respectively from the semi-major axis and eccentricity contained in the target data group.

[0098] In one example, the objective function is expressed as follows:

[0099]

[0100] Where V is the Lyapunov function; X is the parameter matrix consisting of the current orbital parameters and the target orbital parameters; and Q is the weight matrix consisting of the semi-major axis weight and the eccentricity weight.

[0101] In one example, the weight adjustment module includes a calculation module, a sampling module, and a direction determination module. The calculation module calculates the first-order partial derivative of the objective function with respect to the true anomaly angle; it then determines the electric thrust direction of the constellation satellites in the satellite orbit coordinate system based on the first-order partial derivative, where the electric thrust direction is the deorbit direction of the constellation satellites. The sampling module samples the perigee altitude range between the current orbit's perigee altitude and the target orbit's perigee altitude, obtaining multiple discrete nodes. The direction determination module adjusts the semi-major axis weight and / or eccentricity weight corresponding to each discrete node based on the electric thrust direction corresponding to each discrete node, obtaining the target deorbit direction corresponding to each discrete node.

[0102] In one example, the first partial derivative of the Lyapunov function with respect to the true anomaly angle is expressed by the following equation:

[0103]

[0104] Where E is the true anomaly angle; f(X) is the atmospheric drag experienced by the constellation satellite; and u is the electric thrust experienced by the constellation satellite in the satellite orbital coordinate system.

[0105]

[0106] Where a is the semi-major axis; e is the eccentricity; and μ is the Earth's gravitational constant.

[0107] In one example, the direction of electric thrust is represented by the following formula:

[0108]

[0109] Among them, u * In the direction of electric thrust; This represents the maximum thrust of the electric thrusters of the constellation satellites.

[0110] In one example, the direction determination module is specifically used to determine the shortest de-orbit time corresponding to each discrete node as the performance index corresponding to each discrete node; under preset constraints, the semi-major axis weight and eccentricity weight corresponding to each discrete node are adjusted to minimize the performance index, thereby obtaining the target semi-major axis weight and / or target eccentricity weight corresponding to each discrete node; based on the target semi-major axis and / or target eccentricity weight, the electric thrust direction is calculated to obtain the target de-orbit direction corresponding to each discrete node.

[0111] The device for controlling the deorbiting of constellation satellites provided in this application embodiment can realize the various processes implemented in the aforementioned method embodiments, and will not be described again here to avoid repetition.

[0112] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0113] Figure 10 A schematic diagram of the hardware structure of the electronic device provided in an embodiment of this application is shown.

[0114] The electronic device may include a processor 1001 and a memory 1002 storing computer program instructions.

[0115] Specifically, the processor 1001 may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0116] Memory 1002 may include mass storage for data or instructions. For example, and not limitingly, memory 1002 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 1002 may include removable or non-removable (or fixed) media. Where appropriate, memory 1002 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 1002 is non-volatile solid-state memory.

[0117] Memory may include read-only memory (ROM), random access memory (RAM), disk storage media devices, optical storage media devices, flash memory devices, and electrical, optical, or other physical / tangible memory storage devices. Therefore, typically, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the methods according to one aspect of this disclosure.

[0118] The processor 1001 reads and executes computer program instructions stored in the memory 1002 to implement any of the methods for controlling the deorbiting of constellation satellites in the above embodiments.

[0119] In one example, the electronic device may also include a communication interface 1003 and a bus 1010. For example, Figure 10 As shown, the processor 1001, memory 1002, and communication interface 1003 are connected through bus 1010 and complete communication with each other.

[0120] The communication interface 1003 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0121] Bus 1010 includes hardware, software, or both, that couples components of an electronic device together. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 1010 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, any suitable bus or interconnect is contemplated herein.

[0122] Furthermore, in conjunction with the methods for controlling the deorbiting of constellation satellites in the above embodiments, this application embodiment can provide a computer-readable storage medium for implementation. This computer-readable storage medium stores computer program instructions; when executed by a processor, these computer program instructions implement any of the methods for controlling the deorbiting of constellation satellites in the above embodiments.

[0123] Furthermore, in conjunction with the methods for controlling the deorbiting of constellation satellites in the above embodiments, this application embodiment can provide a computer program product to implement this method. When the instructions in this computer program product are executed by the processor of an electronic device, the electronic device performs any of the methods for controlling the deorbiting of constellation satellites as described in the above embodiments.

[0124] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0125] The functional modules shown in the above-described block diagram can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, they can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. Programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. Code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0126] It should also be noted that the exemplary embodiments mentioned in this application describe methods or systems based on a series of steps or apparatus. However, this application is not limited to the order of the above steps; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0127] The foregoing flowcharts and / or block diagrams describing methods, apparatuses, electronic devices, media, and products for controlling the deorbiting of constellation satellites according to embodiments of this disclosure have described various aspects of the present disclosure. It should be understood that each block in the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to create a machine such that these instructions, executable via the processor of the computer or other programmable data processing apparatus, enable the implementation of the functions / actions specified in one or more blocks of the flowcharts and / or block diagrams. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field-programmable logic circuit. It is also understood that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by dedicated hardware performing the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0128] The above description is merely a specific implementation of this application. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the protection scope of this application.

Claims

1. A method for controlling the deorbiting of a constellation of satellites, characterized in that, include: Obtain the current orbital parameters and target orbital parameters of the constellation satellites, wherein the current orbital parameters include the current semi-major axis and current eccentricity of the current orbit, and the target orbital parameters include the target semi-major axis and target eccentricity of the target orbit; Based on the current orbit parameters and the target orbit parameters, as well as the semi-major axis weight and eccentricity weight, an objective function is constructed regarding the deorbit direction of the constellation satellites; At multiple discrete nodes where the constellation satellites de-orbit, the semi-major axis weight and / or the eccentricity weight in the objective function are adjusted to obtain the target de-orbit direction of the constellation satellites at each discrete node, wherein the target de-orbit direction is the trajectory that minimizes the de-orbit duration of the constellation satellites. Control the deorbiting of the constellation satellites along the target deorbiting direction; The objective function is expressed by the following equation: in, For Lyapunov functions; It is a parameter matrix composed of the current orbit parameters and the target orbit parameters; The weight matrix is ​​composed of the semi-major axis weight and the eccentricity weight; At multiple discrete nodes where the constellation satellites deorbit, the semi-major axis weights and / or eccentricity weights in the objective function are adjusted to obtain the target deorbit direction of the constellation satellites at each discrete node. This includes: calculating the first-order partial derivative of the objective function with respect to the true anomaly angle; determining the electric thrust direction of the constellation satellites in the satellite orbit coordinate system based on the first-order partial derivative, wherein the electric thrust direction is the deorbit direction of the constellation satellites; sampling the perigee altitude range between the current orbit's perigee altitude and the perigee altitude corresponding to the target orbit to obtain the multiple discrete nodes; and adjusting the semi-major axis weights and / or eccentricity weights corresponding to each discrete node based on the electric thrust direction corresponding to each discrete node to obtain the target deorbit direction corresponding to each discrete node.

2. The method according to claim 1, characterized in that, Obtain the target orbital parameters of the constellation satellites, including: Based on the deorbit requirement information of the constellation satellites, determine the target perigee altitude corresponding to the target orbit; From multiple data sets, a target data set that matches the perigee height of the target is determined, wherein each data set includes a semi-major axis and an eccentricity; The target semi-major axis and the target eccentricity are determined by the semi-major axis contained in the target data set and the eccentricity, respectively.

3. The method according to claim 1, characterized in that, The first-order partial derivative of the Lyapunov function with respect to the true anomaly angle is expressed by the following equation: in, The true near angle; The atmospheric drag experienced by the satellites in the constellation; The electric thrust experienced by the satellites in the constellation, in the satellite orbital coordinate system. in, It is the semi-major axis; Eccentricity; is the Earth's gravitational constant.

4. The method according to claim 3, characterized in that, The direction of the electric thrust is represented by the following formula: in, The direction of the electric thrust; This represents the maximum thrust of the electric thrusters of the satellites in the constellation.

5. The method according to claim 4, characterized in that, Based on the electric thrust direction corresponding to each discrete node, the semi-major axis weight and / or eccentricity weight corresponding to each discrete node are adjusted to obtain the target deorbit direction corresponding to each discrete node, including: The shortest off-track time corresponding to each discrete node is determined as the performance index corresponding to each discrete node; Under preset constraints, the semi-major axis weight and eccentricity weight corresponding to each discrete node are adjusted to minimize the performance index, thereby obtaining the target semi-major axis weight and / or target eccentricity weight corresponding to each discrete node. Based on the target semi-major axis and / or the target eccentricity weight, the electric thrust direction is calculated to obtain the target derailment direction corresponding to each discrete node.

6. A device for controlling the deorbiting of constellation satellites, characterized in that, include: The parameter acquisition module is used to acquire the current orbit parameters and target orbit parameters of the constellation satellites. The current orbit parameters include the current semi-major axis and current eccentricity of the current orbit, and the target orbit parameters include the target semi-major axis and target eccentricity of the target orbit. The function construction module is used to construct an objective function about the deorbit direction of the constellation satellites based on the current orbit parameters, the target orbit parameters, the semi-major axis weight, and the eccentricity weight. The weight adjustment module is used to adjust the semi-major axis weight and / or the eccentricity weight in the objective function at multiple discrete nodes where the constellation satellites de-orbit, so as to obtain the target de-orbit direction of the constellation satellites at each discrete node, wherein the target de-orbit direction is the trajectory that minimizes the de-orbit time of the constellation satellites. A satellite deorbiting module is used to control the deorbiting of the constellation satellites along the target deorbiting direction; The objective function is expressed by the following equation: in, For Lyapunov functions; It is a parameter matrix composed of the current orbit parameters and the target orbit parameters; The weight matrix is ​​composed of the semi-major axis weight and the eccentricity weight; The weight adjustment module includes: a calculation module for calculating the first-order partial derivative of the objective function with respect to the true anomaly angle; determining the electric thrust direction of the constellation satellite in the satellite orbit coordinate system based on the first-order partial derivative, wherein the electric thrust direction is the deorbit direction of the constellation satellite; a sampling module for sampling the perigee altitude range between the current orbit's perigee altitude and the target orbit's perigee altitude to obtain the plurality of discrete nodes; and a direction determination module for adjusting the semi-major axis weight and / or eccentricity weight corresponding to each discrete node based on the electric thrust direction corresponding to each discrete node to obtain the target deorbit direction corresponding to each discrete node.

7. An electronic device, characterized in that, Electronic devices include: processors and memory storing computer program instructions; When the processor executes the computer program instructions, it implements the method for controlling the deorbiting of constellation satellites as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, A computer-readable storage medium stores computer program instructions that, when executed by a processor, implement the method for controlling the deorbiting of constellation satellites as described in any one of claims 1-5.

9. A computer program product, characterized in that, When the instructions in the computer program product are executed by the processor of an electronic device, the electronic device causes the electronic device to perform the method for controlling the deorbiting of constellation satellites as described in any one of claims 1-5.

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