Satellite cluster orbit configuration control method and device under j2 perturbation and medium

Abstract

The present disclosure provides a method and device for controlling the orbit configuration of a satellite cluster under J2 perturbation and a medium; the method comprises: constructing a component form expression of relative motion dynamics equation; constructing a space perturbation model based on J2 perturbation interference and atmospheric resistance perturbation interference; describing the communication topology of the satellite cluster through an undirected graph; constructing the relative motion error of each satellite by setting a virtual reference star based on the component form expression of the relative motion dynamics equation and the space perturbation model; constructing a finite-time extended state observer corresponding to the relative motion error of each satellite; designing a self-organizing synchronization controller according to the relative motion error of each satellite, the finite-time extended state observer, the corresponding designed nonlinear fast terminal sliding mode surface, and the communication topology of the satellite cluster.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of spacecraft control technology, and in particular to a method, device and medium for orbit configuration control of a satellite constellation under J2 perturbation. Background Technology

[0002] Distributed spacecraft systems mainly include three structures: constellations, satellite clusters, and satellite formations. A satellite cluster refers to a distributed satellite system consisting of multiple spacecraft flying close together to accomplish a common mission. It consists of dozens or even hundreds of similar satellites, each with autonomous flight capabilities, and can cooperate to achieve tasks such as collision avoidance, orbit reconfiguration, and crew updates.

[0003] Compared to a single large satellite, one of the main advantages of satellite swarms is their ability to reconfigure into different formations to collaboratively perform a variety of missions. They offer rapid response, robustness, and scalability, enabling more complex space missions to be accomplished at a lower cost. Spacecraft swarm missions primarily involve three phases: initialization control, long-term loose orbit maintenance, and crew renewal and swarm reconfiguration control. Due to the complexity of the space environment, on-orbit satellite swarms are subject to various external disturbances, including J2 disturbances and atmospheric drag. Without active control, these satellites will gradually deviate from their desired orbits. Before the mission begins, the satellite swarm is in a loose state; then, the swarm needs to achieve the required specific orbital configuration. Therefore, how to handle external disturbances and uncertainties is a crucial issue that needs to be addressed. Summary of the Invention

[0004] In view of this, embodiments of the present invention aim to provide a method, apparatus and medium for orbit configuration control of a satellite constellation under J2 perturbation; enabling the satellite constellation to quickly and accurately synchronize to a specified configuration.

[0005] The technical solution of this invention is implemented as follows:

[0006] In a first aspect, embodiments of the present invention provide a method for orbit configuration control of a satellite constellation under J2 perturbation, the method comprising:

[0007] Construct component-form expressions for the equations of relative motion dynamics;

[0008] A space perturbation model is constructed based on J2 perturbation disturbance and atmospheric drag perturbation disturbance;

[0009] The communication topology of the satellite constellation is described using an undirected graph;

[0010] Based on the component form of the relative motion dynamics equation and the space perturbation model, the relative motion error of each satellite is constructed by setting a virtual reference star;

[0011] A finite-time extended state observer is constructed based on the relative motion error of each satellite.

[0012] Based on the relative motion error of each satellite, the finite-time dilation state observer, the corresponding nonlinear fast terminal sliding surface, and the communication topology of the satellite cluster, a self-organizing synchronization controller is designed to stabilize the orbital configuration of all satellites in the satellite cluster.

[0013] Secondly, embodiments of the present invention provide an orbit configuration control device for a satellite constellation under J2 perturbation, the device comprising: a first construction part, a second construction part, a topology description part, a third construction part, a fourth construction part, and a design part; wherein,

[0014] The first construction part is configured to construct the component form expression of the relative motion dynamics equation;

[0015] The second construction part is configured to construct a space perturbation model based on J2 perturbation interference and atmospheric drag perturbation interference;

[0016] The topology description section is configured to describe the communication topology of the satellite cluster using an undirected graph;

[0017] The third construction part is configured to construct the relative motion error of each satellite by setting up a virtual reference star based on the component form expression of the relative motion dynamics equation and the space perturbation model.

[0018] The fourth construction part is configured to construct a finite-time extended state observer based on the relative motion error of each satellite;

[0019] The design portion is configured to design a self-organizing synchronization controller based on the relative motion error of each satellite, the finite-time extended state observer, the corresponding nonlinear fast terminal sliding surface, and the communication topology of the satellite cluster, so as to stabilize the orbital configuration of all satellites in the satellite cluster.

[0020] Thirdly, embodiments of the present invention provide a computing device, the computing device comprising: a communication interface, a memory, and a processor; the various components are coupled together via a bus system; wherein...

[0021] The communication interface is used for receiving and sending signals during the process of sending and receiving information with other external network elements;

[0022] The memory is used to store computer programs that can run on the processor;

[0023] The processor is configured to execute the steps of the orbit configuration control method for the satellite constellation under J2 perturbation as described in the first aspect when running the computer program.

[0024] Fourthly, embodiments of the present invention provide a computer storage medium storing an orbit configuration control program for a satellite constellation under J2 perturbation. When the orbit configuration control program for a satellite constellation under J2 perturbation is executed by at least one processor, it implements the steps of the orbit configuration control method for a satellite constellation under J2 perturbation described in the first aspect.

[0025] This invention provides a method, apparatus, and medium for orbit configuration control of a satellite constellation under J2 perturbation. By considering the effects of J2 perturbation and atmospheric drag, perturbation estimation is performed based on a finite-time convergent extended state observer, and a continuous thrust orbit cooperative control scheme with non-singular fast terminal sliding mode is adopted. When this method is applied to the generation of large-scale satellite constellation configurations, it can enable the satellite constellation to be quickly and accurately synchronized to a specified configuration. Attached Figure Description

[0026] Figure 1 This is a schematic flowchart of a method for controlling the orbital configuration of a satellite constellation under J2 perturbation, provided in an embodiment of the present invention.

[0027] Figure 2 This is a schematic diagram illustrating the coordinate system of the master and slave stars provided in an embodiment of the present invention;

[0028] Figure 3 A schematic diagram of the desired topology in numerical simulation provided in an embodiment of the present invention;

[0029] Figure 4 This is a schematic diagram of the motion state of a satellite constellation in a numerical simulation provided in an embodiment of the present invention;

[0030] Figure 5 This is a schematic diagram of position tracking error in numerical simulation provided in an embodiment of the present invention;

[0031] Figure 6 This is a schematic diagram of velocity tracking error in numerical simulation provided in an embodiment of the present invention;

[0032] Figure 7 This is a schematic diagram of the composition of an orbit configuration control device for a satellite constellation under J2 perturbation, provided in an embodiment of the present invention.

[0033] Figure 8 This is a schematic diagram of the specific hardware structure of a computing device provided in an embodiment of the present invention. Detailed Implementation

[0034] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0035] Due to the complex space environment, satellites are subject to various constraints during orbital operation, such as J2 perturbations and atmospheric drag interference, collision avoidance constraints, and fuel constraints. Therefore, these constraints must be considered when studying the orbital configuration generation and control problem of satellite constellations. Large-scale satellite constellations have relatively small satellite masses and volumes, requiring precise control. Traditional pulse propulsion suffers from low fuel efficiency and inaccurate control. With continuous advancements in propulsion technology, continuous thrust is increasingly being applied to small satellite control. It possesses a high specific impulse, with some even providing up to 1N of thrust, making it an excellent choice for small satellite orbital control.

[0036] This invention aims to estimate disturbances by considering the effects of J2 perturbation and atmospheric drag, based on a finite-time convergent extended state observer, and employs a continuous thrust-orbit cooperative control scheme with non-singular fast terminal sliding mode. When applied to the generation of large-scale satellite constellation configurations, this method can enable satellite constellations to quickly and accurately synchronize to a specified configuration. Based on this, see [link to related documentation]. Figure 1 This illustrates an orbit configuration control method for a satellite constellation under J2 perturbation provided by an embodiment of the present invention. The method may include:

[0037] S101: Construct the component form expression of the equation of relative motion dynamics;

[0038] S102: Constructing a space perturbation model based on J2 perturbation disturbance and atmospheric drag perturbation disturbance;

[0039] S103: Describing the communication topology of a satellite constellation using an undirected graph;

[0040] S104: Based on the component form of the relative motion dynamics equation and the space perturbation model, the relative motion error of each satellite is constructed by setting a virtual reference star;

[0041] S105 constructs a finite-time extended state observer based on the relative motion error of each satellite;

[0042] S106: Based on the relative motion error of each satellite, the finite-time extended state observer, the corresponding nonlinear fast terminal sliding surface, and the communication topology of the satellite cluster, design a self-organizing synchronization controller to stabilize the orbital configuration of all satellites in the satellite cluster.

[0043] for Figure 1 In some possible implementations of the technical solution shown, the component form expression of the equations of relative motion includes:

[0044] The relative dynamic equations between the stars are established as follows:

[0045]

[0046] Where, r f It is the position vector of the star in the Earth's central inertial ECI coordinate system, f f It is the acceleration vector caused by disturbances and perturbations other than the Earth's central gravity, u f It is the thrust acceleration vector from the star;

[0047] Expanding the above equation by vectors, we obtain the component form of the dynamic equation of relative motion in the LVLH relative motion coordinate system as shown in Equation 1:

[0048]

[0049] Where, x i y i , z i Let r represent the three-axis position components of the i-th satellite relative to the primary star in the LVLH coordinate system; n represents the orbital angular velocity of the primary star; R = [r, 0, 0] T The position vector of the primary star in the Earth's inertial coordinate system; μ is the Earth's gravitational constant; m is the mass of the secondary star; u x u y u z To control the components of the force along the three axes, d x d y d z The acceleration components of the perturbation disturbance on the three axes; i =[x i ,y i ,z i ] T It is defined as the position vector of the star relative to the primary star.

[0050] Regarding the above implementation method, it should be noted that in the embodiments of the present invention, in order to describe the relative motion relationship of the satellite constellation, such as Figure 2 As shown, two coordinate systems need to be defined: the Earth-Centered Inertial Frame (ECI), used to locate the virtual reference point of the leader star, or main orbit; and the LVLH coordinate system, used to describe the relative position of the follower star with respect to the leader star.

[0051] for Figure 1 In some possible implementations of the technical solution shown, the construction of the space perturbation model based on J2 perturbation interference and atmospheric drag perturbation interference includes:

[0052] After differentiating the Earth's gravitational potential function, expanding the J2 perturbation term yields Equation 2:

[0053]

[0054] Where, μ e a is the gravitational constant; e Let r be the average radius of the Earth, and λ be the radius of the Earth. q = x, y, or z represents the spherical coordinates in the geocentric Earth-fixed coordinate system, i.e., geocentric distance, longitude, and geocentric latitude; J2 represents the harmonic coefficients in the Earth's gravitational potential function;

[0055] The formula for calculating the acceleration of a satellite due to atmospheric drag is shown in Equation 3:

[0056]

[0057] Among them, C D ρ is the drag coefficient, S is the reference area, m is the mass of the satellite, ρ is the atmospheric density, and ν is the velocity of the satellite relative to the atmosphere.

[0058] By constructing a spatial perturbation model using equations 2 and 3, the spatial perturbation term d is obtained. id .

[0059] Regarding the above implementation methods, it should be noted that all satellites in orbit are affected by space perturbations, among which J2 perturbations and atmospheric perturbations have the greatest impact on the relative motion of low-Earth orbit satellites. For the J2 perturbation, it is caused by the uneven density distribution of the Earth, and the Earth's gravitational potential function is shown below:

[0060]

[0061] Among them, P nm and P n For Legendre polynomials; J n It is the harmonic coefficient, J nm and λ nm Here are the field harmonic coefficients and fan harmonic coefficients. The band harmonic coefficient J2 is the main perturbation factor. After differentiating the Earth's gravitational potential function, the J2 perturbation term is expanded as shown in Equation 2. In addition to the perturbation of the J2 perturbation term, atmospheric drag perturbation is also a non-negligible perturbation force. For the atmospheric drag acceleration shown in Equation 3, the atmospheric density model is an exponential model, i.e. Where H is the density elevation, r and r0 are the distance between the Earth's centers, ρ0 is the atmospheric density at H0, and r0, ρ0, and H can be obtained from atmospheric tables.

[0062] for Figure 1The technical solution shown, in some possible implementations, due to the large number of satellite constellations and the potential changes in their positional relationships, can be described using a diagram in this embodiment of the invention for its communication topology. The communication topology diagram G is defined as containing (V, E), where V = {v1, v2, ..., v...}. p} is a finite non-empty set of points, where each node corresponds to a satellite in a satellite constellation, and the edge set is... It consists of a one-to-one correspondence between points of a finite nonempty set of points. Edges (v) i ,v j ) represents node v j Information can be transmitted to node v i Or, in other words, point v i It's point v j The neighbor, v i It is v j The parent node, v j It is v i The child node of point v. j Let N be the number of all neighbors. j :={v i |(v i ,v j An undirected graph can be considered a special case of a directed graph, or a "bidirectional graph", where edges (v) ∈ E}. i ,v j ) represents point v i and v j They can communicate with each other, corresponding to the edges (v) of the directed graph. i ,v j ) and edge (v j ,v i Based on this, the description of the communication topology of the satellite constellation using an undirected graph includes:

[0063] By treating the satellites in the satellite constellation as nodes in an undirected graph and the communication relationships between satellites as edges in the undirected graph, the adjacency matrix of the corresponding undirected graph is determined. Where, when node v i and v j If there is an edge between them, then a ij =1; otherwise a ij =0;

[0064] The corresponding asymmetric Laplacian matrix is ​​determined based on the adjacency matrix. The Laplacian matrix is ​​defined as follows:

[0065] for Figure 1In some possible implementations of the technical solution shown, the construction of the relative motion error of each satellite based on the component form expression of the relative motion dynamics equation and the space perturbation model by setting a virtual reference star includes:

[0066] In the LVLH coordinate system, the desired position vector of the i-th satellite is set relative to the position vector l of the virtual reference star. id =[x id ,y id ,z id ] T The desired velocity vector of the i-th satellite relative to the velocity vector of the virtual reference star. The position tracking error of the i-th satellite is e i1 =l i -l id The speed tracking error is The relative motion error of the i-th satellite is obtained by using the component form of the relative motion dynamics equation shown in Equation 1, as shown in Equation 4:

[0067]

[0068] in, It is a nonlinear equation, and is defined as follows: d id For space disturbances that include J2 perturbation and atmospheric drag, u i It is the control force applied to the i-th satellite;

[0069] The transformation matrix from the EACI coordinate system to the LVLH coordinate system is constructed as follows:

[0070] Γ LVLH =Γ z (ω+θ)Γ x (i)Γ z (Ω)Γ ECI

[0071] Where ω is the argument of perigee, θ is the true anomaly, i is the orbital inclination, and Ω is the right ascension of the ascending node;

[0072]

[0073]

[0074] Setting e i1 =x i1 e i2 =x i2 , the state variable x i Expand to x i =[x i1 ,xi2 ,x i3 ] T ;

[0075] definition The motion error of the i-th satellite in the satellite cluster relative to the virtual reference star is obtained based on Equation 4, as shown in Equation 5:

[0076]

[0077] Among them, l i , It is continuous and bounded; d id It is a continuous and slow change;

[0078] Based on the above implementation, in some examples, the construction of a finite-time extended state observer based on the relative motion error of each satellite includes:

[0079] Based on the assumption that the system is observable, a finite-time extended state observer is designed for the relative motion error of the i-th satellite as shown in Equation 5, as shown in Equation 6:

[0080]

[0081] in, and x i1 x i2 x i3 The estimated value; k∈(0,1); operator sig(·) k =sign(·)|·| k , sign(·) is the standard sign function, and λ1, λ2 and λ3 are the observer gains.

[0082] For the example above, it should be noted that the observer's observation error is set to... The dynamic of the observer estimation error is

[0083] Based on the above technical solutions, in some examples, the step of designing a self-organizing synchronization controller to stabilize the orbital configuration of all satellites in the satellite cluster, based on the relative motion error of each satellite, the finite-time dilation state observer, the correspondingly designed nonlinear fast terminal sliding surface, and the communication topology of the satellite cluster, includes:

[0084] The nonlinear fast terminal sliding surface is designed as shown in Equation 7:

[0085]

[0086] Where β1,β2>0,q<p<2q, and q,p are odd numbers;

[0087] Based on equations 4, 6, and 7, a self-organizing synchronization controller is designed as shown in equation 8:

[0088]

[0089] Among them, a ij These are the elements in the i-th row and j-th column of the adjacency matrix describing the satellite cluster communication topology; K i1 ,K i2 It is the control gain; u eq Used for observing and compensating nonlinear terms and spatial disturbances in the system; u es Used to bring the state of the satellite constellation to the terminal sliding surface; u sy This is a synchronization control term used to ensure that all satellites in the satellite constellation reach a stable state simultaneously.

[0090] Based on the description of the aforementioned technical solutions, their implementation methods, and examples, by considering the effects of J2 perturbation and atmospheric drag, perturbation estimation is performed based on a finite-time convergent extended state observer, and a continuous thrust orbit cooperative control scheme with non-singular fast terminal sliding mode is adopted. When this method is applied to the generation of large-scale satellite constellation configurations, it can enable satellite constellations to be synchronized to a specified configuration quickly and accurately.

[0091] Based on the aforementioned technical solution, this embodiment of the invention uses a satellite constellation of 19 satellites with autonomous flight capabilities as an example for numerical simulation analysis. Before the mission begins, all satellites are in a loose state but maintain bounded communication. The mission requires the constellation to form a double-layered regular hexagonal topology, with the inner hexagon having a side length of 5000m and the outer hexagon having a side length twice that of the inner hexagon. This topology must be maintained throughout the mission execution. The goal is to transform a large-scale constellation from a loose initial state into a topology with strict geometric relationships using minimal thrust. The desired topology that the satellites should ultimately achieve is as follows: Figure 3 As shown.

[0092] Based on the above description, the self-organized small thrust involved in the orbit configuration control method of the satellite constellation under J2 perturbation proposed in the aforementioned technical solution is simulated, and the motion state is as follows: Figure 4 As shown, it can be seen that the constellation can reach the desired configuration from its initial loose state and maintain that desired state. The relative position tracking errors of the first two satellites in the constellation are shown in Figure 5(a) and 5(a). Figure 5 As shown in (b), even when the satellite is affected by J2 perturbation and atmospheric drag, the position tracking error can still converge quickly to near zero. The convergence time is around 650s, and the tracking accuracy can reach 0.01m.

[0093] The relative velocity tracking errors of the first two satellites selected from the 19-satellite cluster are as follows: Figure 6 (a) and Figure 6 As shown in (b), the convergence time of the satellite is around 650s, and the velocity tracking accuracy can reach 0.01m / s. Based on the above simulation results, it is also proven that the self-organizing synchronization control law shown in Equation 8 has good control accuracy and fast convergence time.

[0094] Based on the same inventive concept as the aforementioned technical solution, see [link to inventive concept]. Figure 7 This illustration shows an orbit configuration control device 70 for a satellite constellation under J2 perturbation provided by an embodiment of the present invention. The device 70 includes: a first construction part 701, a second construction part 702, a topology description part 703, a third construction part 704, a fourth construction part 705, and a design part 706; wherein,

[0095] The first construction part 701 is configured to construct a component form expression of the relative motion dynamics equation;

[0096] The second construction part 702 is configured to construct a space perturbation model based on J2 perturbation interference and atmospheric drag perturbation interference;

[0097] The topology description section 703 is configured to describe the communication topology of the satellite cluster using an undirected graph;

[0098] The third construction part 704 is configured to construct the relative motion error of each satellite by setting a virtual reference star based on the component form expression of the relative motion dynamics equation and the space perturbation model.

[0099] The fourth construction part 705 is configured to construct a finite-time extended state observer based on the relative motion error of each satellite.

[0100] The design section 706 is configured to design a self-organizing synchronization controller based on the relative motion error of each satellite, the finite-time extended state observer, the corresponding nonlinear fast terminal sliding surface, and the communication topology of the satellite cluster, so as to stabilize the orbital configuration of all satellites in the satellite cluster.

[0101] It should be noted that for the specific implementation of the functions configured in each "part" of the above-mentioned device, please refer to the aforementioned... Figure 1 The implementation methods and examples of the corresponding steps in the orbit configuration control method of the satellite constellation under J2 perturbation shown are not repeated here.

[0102] Understandably, in this embodiment, "part" can be a part of a circuit, a part of a processor, a part of a program or software, etc., or it can be a unit, a module, or a non-modular one.

[0103] Furthermore, in this embodiment, the components 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 module.

[0104] If the integrated unit is implemented as a software functional module and not sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this embodiment, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the method described in this embodiment. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0105] Therefore, this embodiment provides a computer storage medium storing an orbit configuration control program for a satellite constellation under J2 perturbation. When the orbit configuration control program for a satellite constellation under J2 perturbation is executed by at least one processor, it implements the steps of the orbit configuration control method for a satellite constellation under J2 perturbation described in the above technical solution.

[0106] Based on the aforementioned orbit configuration control device 70 for the satellite constellation under J2 perturbation and the computer storage medium, see [link to relevant documentation]. Figure 8This illustration shows the specific hardware structure of a computing device 80 capable of implementing the orbit configuration control device 70 for a satellite constellation under the J2 perturbation described above, provided by an embodiment of the present invention. The computing device 80 can be a wireless device, mobile or cellular phone (including so-called smartphones), personal digital assistant (PDA), video game console (including video display, mobile video game device, mobile video conferencing unit), laptop computer, desktop computer, set-top box, tablet computing device, e-book reader, fixed or mobile media player, etc. The computing device 80 includes: a communication interface 801, a memory 802, and a processor 803; the various components are coupled together through a bus system 804. It is understood that the bus system 804 is used to realize the connection and communication between these components. In addition to a data bus, the bus system 804 also includes a power bus, a control bus, and a status signal bus. However, for clarity, in... Figure 8 The general designated all buses as Bus System 804.

[0107] The communication interface 801 is used for receiving and sending signals during the process of sending and receiving information with other external network elements;

[0108] The memory 802 is used to store computer programs that can run on the processor 803;

[0109] The processor 803 is used to execute the orbit configuration control method steps of the satellite cluster under J2 perturbation described in the above technical solution when running the computer program.

[0110] It is understood that the memory 802 in the embodiments of the present invention can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memory 802 of the systems and methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0111] The processor 803 may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the hardware of the processor 803 or by software instructions. The processor 803 can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this invention can be directly manifested as execution by a hardware decoding processor, or execution by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory 802, and the processor 803 reads the information in memory 802 and, in conjunction with its hardware, completes the steps of the above method.

[0112] It is understood that the embodiments described herein can be implemented in hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described herein, or combinations thereof.

[0113] For software implementation, the techniques described herein can be achieved through modules (e.g., procedures, functions, etc.) that perform the functions described herein. The software code can be stored in memory and executed by a processor. The memory can be implemented within the processor or externally.

[0114] It is understood that the exemplary technical solutions of the orbit configuration control device 70 and computing device 80 for the satellite constellation under J2 perturbation described above belong to the same concept as the technical solution of the orbit configuration control method for the satellite constellation under J2 perturbation described above. Therefore, all details not described in detail above regarding the technical solutions of the orbit configuration control device 70 and computing device 80 for the satellite constellation under J2 perturbation can be found in the description of the technical solution of the orbit configuration control method for the satellite constellation under J2 perturbation described above. This embodiment of the invention will not elaborate further on this.

[0115] It should be noted that the technical solutions described in the embodiments of the present invention can be combined arbitrarily without conflict.

[0116] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for orbit configuration control of a satellite constellation under J2 perturbation, characterized in that, The method includes: Construct component-form expressions for the equations of relative motion dynamics; A space perturbation model is constructed based on J2 perturbation disturbance and atmospheric drag perturbation disturbance; The communication topology of the satellite constellation is described using an undirected graph; Based on the component form of the relative motion dynamics equation and the space perturbation model, the relative motion error of each satellite is constructed by setting a virtual reference star; A finite-time extended state observer is constructed based on the relative motion error of each satellite. Based on the relative motion error of each satellite, the finite-time extended state observer, the corresponding nonlinear fast terminal sliding surface, and the communication topology of the satellite cluster, a self-organizing synchronization controller is designed to stabilize the orbital configuration of all satellites in the satellite cluster. The component-form expression for constructing the relative motion dynamics equations includes: The relative dynamic equations between the stars are established as follows: in, It is the position vector of the star in the Earth's central inertial ECI coordinate system. It is the acceleration vector caused by disturbances and perturbations other than the Earth's central gravity. It is the thrust acceleration vector from the star; Expanding the above equation by vectors, we obtain the component form of the dynamic equation of relative motion in the LVLH relative motion coordinate system as shown in Equation 1: （1） in, , , Represent the first digit in the LVLH coordinate system. The three-axis position components of each satellite relative to the host star; This indicates the orbital angular velocity of the primary star; The position vector of the primary star in the Earth's inertial coordinate system; The gravitational constant of Earth; The mass of the star; , , To control the components of the force along the three axes, , , The acceleration components of the perturbation disturbance on the three axes; Defined as the position vector of the star relative to the primary star; The relative motion error of each satellite, constructed by setting a virtual reference star, based on the component form expression of the relative motion dynamics equation and the space perturbation model, includes: In the LVLH coordinate system, set the first The desired position vector of a satellite relative to the position vector of a virtual reference star , No. The desired velocity vector of the satellite relative to the velocity vector of the virtual reference star ;No. The position tracking error of the satellite is The speed tracking error is The first equation is obtained by using the component form of the relative motion dynamics equation shown in Equation 1. The relative motion error of the satellites is shown in Equation 4: （4） in, It is a nonlinear equation, and is defined as follows: , , ; This refers to space disturbances that include J2 perturbation and atmospheric drag. It is the first The control force exerted by a satellite; The transformation matrix from the EACI coordinate system to the LVLH coordinate system is constructed as follows: in, It is the perigee argument. It's a true near-point angle. It is the track inclination angle. It is the right ascension of the ascending node; ， ， ； set up , , state variables Expand to ; definition Based on Equation 4, the first satellite in the constellation is obtained. The motion error of the satellite relative to the virtual reference star is shown in Equation 5: （5） in, , , It is continuous and bounded; It is a continuous and slow change; , Represents the upper bound of interference; The construction of a finite-time extended state observer based on the relative motion error of each satellite includes: Based on the system being observable, for the first equation shown in Equation 5 The finite-time extended state observer corresponding to the relative motion error design of the satellite is shown in Equation 6: （6） in, , and They are respectively , , The estimated value; ; operator , It is a standard symbolic function. , and For observer gain; The step of designing a self-organizing synchronization controller to stabilize the orbital configuration of all satellites in the constellation, based on the relative motion error of each satellite, the finite-time dilation state observer, the correspondingly designed nonlinear fast terminal sliding surface, and the communication topology of the satellite cluster, includes: The nonlinear fast terminal sliding surface is designed as shown in Equation 7: （7） in, , It is an odd number; Based on equations 4, 6, and 7, a self-organizing synchronization controller is designed as shown in equation 8: （8） in, It is the adjacency matrix describing the communication topology of a satellite constellation. row and number Column elements; It controls the gain; Used for observing and compensating nonlinear terms and spatial disturbances in the system; Used to bring the state of the satellite cluster to the terminal sliding surface; This is a synchronization control term used to ensure that all satellites in the satellite constellation reach a stable state simultaneously.

2. The method according to claim 1, characterized in that, The construction of the space perturbation model based on J2 perturbation interference and atmospheric drag perturbation interference includes: After differentiating the Earth's gravitational potential function, expanding the J2 perturbation term yields Equation 2: （2） in, It is the gravitational constant; The average radius of the Earth; , , These are spherical coordinates in the geocentric fixed coordinate system, namely geocentric distance, longitude, and geocentric latitude; q = x , y , or z Represents the components of the position vector; J 2 represents the coefficient of the harmonic term in the Earth's gravitational potential function; The formula for calculating the acceleration of a satellite due to atmospheric drag is shown in Equation 3: （3） in, The drag coefficient, For reference area, For the quality of the satellite, It is atmospheric density. The velocity of the satellite relative to the atmosphere; This indicates the magnitude of the satellite's velocity relative to the atmosphere; By constructing a spatial perturbation model using equations 2 and 3, the spatial perturbation term is obtained. .

3. The method according to claim 1, characterized in that, The description of the communication topology of the satellite constellation using an undirected graph includes: By treating the satellites in the satellite constellation as nodes in an undirected graph and the communication relationships between satellites as edges in the undirected graph, the adjacency matrix of the corresponding undirected graph is determined. Among them, when node and If there is an edge between them, then ;otherwise ; The corresponding asymmetric Laplacian matrix is ​​determined based on the adjacency matrix. The Laplacian matrix is ​​defined as follows: .

4. An orbit configuration control device for a satellite constellation under J2 perturbation, characterized in that, The device includes: a first construction part, a second construction part, a topology description part, a third construction part, a fourth construction part, and a design part; wherein, The first construction part is configured to construct the component form expression of the relative motion dynamics equation; The second construction part is configured to construct a space perturbation model based on J2 perturbation interference and atmospheric drag perturbation interference; The topology description section is configured to describe the communication topology of the satellite cluster using an undirected graph; The third construction part is configured to construct the relative motion error of each satellite by setting up a virtual reference star based on the component form expression of the relative motion dynamics equation and the space perturbation model. The fourth construction part is configured to construct a finite-time extended state observer based on the relative motion error of each satellite; The design portion is configured to design a self-organizing synchronization controller based on the relative motion error of each satellite, the finite-time extended state observer, the corresponding nonlinear fast terminal sliding surface, and the communication topology of the satellite cluster, so as to stabilize the orbital configuration of all satellites in the satellite cluster. The first construction part is also configured as follows: The relative dynamic equations between the stars are established as follows: in, It is the position vector of the star in the Earth's central inertial ECI coordinate system. It is the acceleration vector caused by disturbances and perturbations other than the Earth's central gravity. It is the thrust acceleration vector from the star; Expanding the above equation by vectors, we obtain the component form of the dynamic equation of relative motion in the LVLH relative motion coordinate system as shown in Equation 1: （1） in, , , Represent the first digit in the LVLH coordinate system. The three-axis position components of each satellite relative to the host star; This indicates the orbital angular velocity of the primary star; The position vector of the primary star in the Earth's inertial coordinate system; The gravitational constant of Earth; The mass of the star; , , To control the components of the force along the three axes, , , The acceleration components of the perturbation disturbance on the three axes; Defined as the position vector of the star relative to the primary star; The third construction part is further configured to: set the first in the LVLH coordinate system. The desired position vector of a satellite relative to the position vector of a virtual reference star , No. The desired velocity vector of the satellite relative to the velocity vector of the virtual reference star ;No. The position tracking error of the satellite is The speed tracking error is The first equation is obtained by using the component form of the relative motion dynamics equation shown in Equation 1. The relative motion error of the satellites is shown in Equation 4: （4） in, It is a nonlinear equation, and is defined as follows: , , ; This refers to space disturbances that include J2 perturbation and atmospheric drag. It is the first The control force exerted by each satellite; The transformation matrix from the EACI coordinate system to the LVLH coordinate system is constructed as follows: in, It is the perigee argument. It's a true near-point angle. It is the track inclination angle. It is the right ascension of the ascending node; ， ， ； set up , , state variables Expand to ; definition Based on Equation 4, the first satellite in the constellation is obtained. The motion error of the satellite relative to the virtual reference star is shown in Equation 5: （5） in, , , It is continuous and bounded; It is a continuous and slow change; , Represents the upper bound of interference; The fourth construction part is also configured to be based on the system being observable, for the first part shown in Equation 5. The finite-time extended state observer corresponding to the relative motion error design of the satellite is shown in Equation 6: （6） in, , and They are respectively , , The estimated value; ; operator , It is a standard symbolic function. , and For observer gain; The design portion is also configured to design a nonlinear fast terminal sliding surface as shown in Equation 7: （7） in, , It is an odd number; Based on equations 4, 6, and 7, a self-organizing synchronization controller is designed as shown in equation 8: （8） in, It is the adjacency matrix describing the communication topology of a satellite constellation. row and number Column elements; It controls the gain; Used for observing and compensating nonlinear terms and spatial disturbances in the system; Used to bring the state of the satellite cluster to the terminal sliding surface; This is a synchronization control term used to ensure that all satellites in the satellite constellation reach a stable state simultaneously.

5. A computing device, characterized in that, The computing device includes: a communication interface, a memory, and a processor; the various components are coupled together via a bus system; wherein... The communication interface is used for receiving and sending signals during the process of sending and receiving information with other external network elements; The memory is used to store computer programs that can run on the processor; The processor is configured to execute the steps of the orbit configuration control method for a satellite constellation under J2 perturbation as described in any one of claims 1 to 3 when running the computer program.

6. A computer storage medium, characterized in that, The computer storage medium stores an orbit configuration control program for a satellite constellation under J2 perturbation. When the orbit configuration control program for a satellite constellation under J2 perturbation is executed by at least one processor, it implements the steps of the orbit configuration control method for a satellite constellation under J2 perturbation as described in any one of claims 1 to 3.

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