Constellation network topology planning method based on robustness optimization

Abstract

The invention provides a constellation network topology planning method based on robustness optimization. According to the method, on the basis of multi-dimensional physical constraints, link feasibility and a network topology optimization target are considered, and periodic updating and rolling planning of a link state are realized by establishing a time slice discretization model. Furthermore, algebraic connectivity is used as a network robustness index, a continuous weight solution is solved by adopting positive semidefinite programming, and a discrete link scheme meeting node degree constraint is obtained through weight polarization and bipartite graph maximum weight matching, so that connectivity and structural stability of the constellation network are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of satellite internet / inter-satellite laser link / network topology optimization and graph optimization technology, and in particular to a constellation network topology planning method based on robustness optimization. Background Technology

[0002] In recent years, global demand for high-speed, low-latency broadband access has continued to rise, leading to the rapid advancement of large-scale low-Earth orbit (LEO) satellite constellations. Thanks to reusable launch vehicles, satellite miniaturization, and mass production, constellation deployment costs and network establishment cycles have significantly decreased, making large-scale, intensive launches and rapid on-orbit networking the norm. Under this trend, space-based internet, represented by commercial LEO constellations, is accelerating its development, becoming an important carrier form of space-based internet.

[0003] Laser inter-satellite links are a crucial means of supporting high-capacity interconnection of constellations. Compared to traditional radio frequency systems, laser links have significant advantages in terms of available bandwidth and transmission rate. The narrow beam provides anti-interception and anti-interference capabilities, as well as engineering characteristics such as miniaturized terminals and low power consumption. These have been verified in-orbit applications of various constellations, providing key support for achieving global low-Earth orbit satellite internet coverage.

[0004] However, introducing large-scale laser inter-satellite links into low-Earth orbit (LEO) constellations also brings systemic challenges to network topology management and planning. On the one hand, LEO satellites undergo rapid relative motion, and link visibility and connectivity status continuously change with orbital evolution, resulting in a network structure exhibiting significant time-varying characteristics. On the other hand, laser links are sensitive to attitude and pointing accuracy, and are easily constrained by multi-dimensional physical conditions such as elevation angle, azimuth angle, and relative angular velocity, leading to strong spatiotemporal correlations in link availability. Without effective planning and topology optimization, the network is prone to problems such as decreased connectivity, insufficient link utilization, and even periodic outages.

[0005] Existing research on topology optimization for satellite networks mainly focuses on two directions: one is dynamic topology control and handover optimization, which typically uses prediction or planning mechanisms to reduce unnecessary handovers and improve access and handover success rates, thereby enhancing local connectivity stability; the other is network performance analysis and optimization, which is usually based on geometric visibility modeling and orbit prediction to evaluate the efficiency of different constellation structures and formulate inter-satellite link allocation as a combinatorial optimization problem to seek a trade-off between latency and connectivity. Some works also introduce distributed priority strategies to support large-scale real-time maintenance, or consider routing optimization and benefit-cost balance under random failure scenarios.

[0006] In terms of structural robustness, spectral graph theory provides important analytical tools. Algebraic connectivity (the second eigenvalue of the Laplace matrix) is often used as an indicator of network resilience and connectivity margin, and related theoretical work has laid the foundation for topology design that improves algebraic connectivity under conditions such as degree constraints. Based on this, heuristic or intelligent optimization methods can construct highly robust network structures under certain rules and reveal the intrinsic balance between path efficiency and robustness.

[0007] Overall, existing technologies offer various approaches to network efficiency assessment, handover management, and routing optimization, but they still suffer from two common limitations: First, robustness metrics (such as algebraic connectivity) and efficiency metrics are often treated separately, lacking a comprehensive balance within the same framework; second, the unique multidimensional physical constraints of laser links are not adequately considered, making it difficult to achieve overall topology enhancement for large-scale, rapidly changing constellations under engineering feasibility. Therefore, how to balance connectivity, robustness, and transmission efficiency while satisfying physical constraints, and construct link planning and topology optimization methods suitable for large-scale dynamic constellations, remains a key technical problem that needs to be solved. Summary of the Invention

[0008] In order to solve the problems in the prior art, this invention proposes a constellation network topology planning method based on robustness optimization, which addresses the characteristics of time-varying link topology and multi-dimensional physical constraints in large-scale satellite networks.

[0009] This invention is achieved through the following technical solution: This invention proposes a constellation network topology planning method based on robustness optimization, the method comprising: Step 1: Constellation Modeling and Constraint Modeling: Based on the orbital elements, formation structure, and onboard terminal distribution of the target constellation, establish the inter-satellite geometric relationships and relative motion models; combine the terminal installation method and pointing capability to form a multi-dimensional set of physical constraints, including altitude angle threshold, azimuth angle boundary, relative angular velocity upper limit, and nodal degree / simultaneous connection number limit; Step 2: Feasible link screening and duration prediction: Based on the geometric and motion model in Step 1, candidate star pairs are enumerated at a given time or time slice to determine whether they simultaneously meet the multidimensional physical constraints; the usable duration of candidate links that meet the constraints is calculated, and short-term links below the minimum threshold are eliminated to obtain the "set of feasible links". Step 3: Time Slice Division and Backbone Topology Initialization: Based on the periodicity of the relative motion of the constellation, the continuous time is discretized into the shortest time slices; a stable "backbone topology" is constructed in the first time slice and retained in subsequent time slices as the base for subsequent dynamic enhancements; Step 4: Link Disconnection Prediction and Candidate Set Update: At the beginning of each time slice, links that are about to violate physical constraints or whose duration is about to expire in the next slice are predicted and marked as pending switching; after releasing the corresponding terminals, the "set of available links" is refreshed in the next time slice based on the real-time geometric status; Step 5: Convex relaxation optimization driven by algebraic connectivity: The link selection is expressed as a graph enhancement problem with network algebraic connectivity as the objective; under the constraints of node degree and edge number, the discrete decision variables are relaxed to interval variables, a linear matrix inequality is constructed and a positive semidefinite programming problem is solved to obtain the continuous weight solution for each candidate link. Step 6: Weighted polarization mapping and bipartite graph construction: The continuous weights obtained in Step 5 are subjected to nonlinear polarization mapping to enhance separability; based on the terminal orientation or installation location, the idle terminals are divided into two disjoint sets to construct a bipartite graph, and the mapped weights are used as edge weights. Step 7: Maximum weight matching solution and discrete link generation: Solve for the maximum weight matching on the bipartite graph and output a set of discrete links that satisfy the node degree and physical constraints; combine the new links with the backbone topology to form the final topology configuration of the segment and generate on-board execution instructions; Step 8: Full-cycle rolling execution and data recording: Repeat steps 4 to 8 in rolling order according to time slices until the planned time domain ends; record the topology and key indicators of each slice to provide data support for on-orbit operation and offline evaluation.

[0010] Furthermore, the constellation consists of P orbital planes, with S satellites on each plane. The orbital planes are staggered according to the phase factor F. Each satellite carries four two-degree-of-freedom laser communication terminals, which achieve complementary coverage in the east-west / front-back directions or equivalent installation positions.

[0011] Furthermore, the method employs graph theory to abstract the constellation and its internal connections: each satellite is viewed as a graph. A node forms a set of nodes. The possible inter-satellite laser links are considered as edges between nodes, forming a corresponding set of edges. Meanwhile, the constellation topology is represented by an undirected graph; the degree of a node is used to describe the number of connections between a node and other nodes in the network; and the adjacency matrix is ​​used as the matrix representation of the graph.

[0012] Furthermore, in the physical constraint definition in step one, the azimuth angle is used to limit the rotatable range of the laser link in the horizontal plane; the azimuth angle refers to the direction angle of the projection of the line of sight between the two satellites at both ends of the link onto the horizontal plane, which is used to describe the horizontal pointing of the link relative to the satellite body coordinate system; when the position of the target satellite exceeds the field of view boundary formed by the rotatable range of the laser terminal, the terminal cannot achieve pointing tracking, and the link does not meet the conditions for establishment.

[0013] Furthermore, in step three, inter-satellite links are divided into static links and dynamic links: the former remains unchanged throughout the constellation's operation and is used to form the backbone of the network; the latter is dynamically adjusted as time slices roll, and is used to provide enhanced connectivity when there is a local link break or changes in visibility. Based on this, the grid-like network topology is structured according to the satellite's orbit number and the parity of the satellite's serial number within the orbit, simplifying it into a static tri-regular topology with fixed connectivity.

[0014] Furthermore, directly optimizing using algebraic connectivity as an indicator is an NP-hard combinatorial optimization problem. By relaxing the integer constraints into interval constraints and equating the lower bound constraint of algebraic connectivity to a semidefinite matrix inequality, a semidefinite programming problem is obtained. The obtained decimal solutions are nonlinearly mapped as bipartite graph weights, and then the final set of buildable links is obtained through maximum weight matching.

[0015] Furthermore, the semidefinite programming problem includes four constraints: the first type of LMI constraint guarantees that the objective variable is the lower bound of the second smallest eigenvalue of the Laplace matrix; the second type of constraint restricts the number of selectable edges; and the third type of constraint optimizes the variable... The range of values ​​is broadened to an interval. The last type of constraint controls the node degree, ensuring that the number of edges each node participates in does not exceed a given upper limit; finally, the solution yields a lower bound that makes the algebraic connectivity less than or equal to the given upper limit. The largest optimization variable .

[0016] Furthermore, the maximum weight matching in a bipartite graph refers to selecting a set of non-adjacent edges from the candidate edge set between two subsets of nodes, such that the sum of the edge weights is maximized. Based on the bipartite graph model, let the decision variables... , indicating edge Whether a candidate edge is selected depends on the specific circumstances of that edge. The weights after mapping are expressed as Then the semidefinite programming problem is modeled as equation (30): (30) The above constraints guarantee that each node is matched with at most one edge, which conforms to the satellite degree constraint; the maximum weight matching solution corresponds to the edge set with the largest total weight under the connectable edge constraint, that is, the continuous link weight obtained based on convex relaxation, which is discretized into the actual edge set after nonlinear processing.

[0017] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the robustness-optimized constellation network topology planning method.

[0018] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the robustness-optimized constellation network topology planning method.

[0019] The beneficial effects of this invention are: This invention combines algebraic connectivity optimization theory with physically constrained dynamic link planning to achieve adaptive topology maintenance and performance enhancement for low-Earth orbit satellite constellation networks in complex, time-varying environments. Compared with traditional schemes based on static topology or local switching rules, this invention significantly improves structural robustness, communication continuity, and network utilization.

[0020] First, this invention comprehensively considers multi-dimensional physical constraints such as elevation angle, azimuth angle, and relative angular velocity during the modeling phase to ensure the physical feasibility of inter-satellite links. Through time-slice division and duration prediction, periodic updates of link states are achieved, effectively avoiding sudden link failures caused by changes in geometric relationships and significantly improving network connectivity stability.

[0021] Secondly, this invention introduces a topology optimization method with algebraic connectivity as the core indicator, quantifying network robustness into a computable eigenvalue index. Continuous optimal solutions are obtained through convex relaxation and positive semidefinite programming. Then, by combining weighted polarization and bipartite graph maximum weight matching algorithms, a discretized link scheme satisfying node degree constraints is obtained. This two-stage optimization structure balances solution accuracy and real-time performance, continuously improving the overall network performance during constellation operation.

[0022] Furthermore, through a "static backbone + dynamic enhancement" topology design, this invention maintains long-term constellation connectivity while possessing flexible link adaptive adjustment capabilities. Static links maintain a stable overall network framework, while dynamic links automatically switch when visibility changes or links fail, thereby achieving network self-recovery and seamless communication in complex orbital environments.

[0023] In summary, this invention not only improves the robustness and communication reliability of constellation networks during dynamic operation, but also has significant advantages in terms of algorithm complexity, real-time performance, and scalability. This method can be extended to various types of low-Earth orbit satellite constellations and inter-satellite laser communication systems, providing an efficient and stable technical solution for the on-orbit autonomy and intelligent networking of future space-based internet and large-scale distributed satellite networks. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0025] Figure 1 This is a schematic diagram of the laser terminal installation.

[0026] Figure 2 It is a constellation topology mapping diagram.

[0027] Figure 3 This is a schematic diagram of inter-satellite azimuth and elevation angles.

[0028] Figure 4 This is a schematic diagram of the distance constraint corresponding to the elevation angle.

[0029] Figure 5 This is a diagram illustrating the relative angular velocity of a satellite.

[0030] Figure 6 These are schematic diagrams of cross-shaped and X-shaped links.

[0031] Figure 7 This is a diagram showing the correspondence between the odd and even orbits and their serial numbers within a constellation and the satellites.

[0032] Figure 8 This is a schematic diagram of a constellation's fixed topology design.

[0033] Figure 9 This is a schematic diagram showing the orientation of the vacant terminal.

[0034] Figure 10 This is a schematic diagram of a bipartite graph model built based on the available links.

[0035] Figure 11 This is a diagram of a dynamic link.

[0036] Figure 12 This is a diagram illustrating the shortest time slice.

[0037] Figure 13 This is a diagram illustrating the time slice division. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] This invention employs a large-scale low-Earth orbit constellation with a Walker-Delta (T / P / F) architecture: the constellation consists of P orbital planes, each with S satellites, and the orbital planes are distributed at equal intervals with a phase factor F. Each satellite carries four two-degree-of-freedom (pitch and yaw) laser communication terminals, which achieve complementary coverage in the east-west / forward / backward directions or equivalent installation positions. During the orbital deployment phase and the on-orbit communication topology switching phase, constrained by factors such as elevation angle, azimuth angle, relative angular velocity, and the number of simultaneous terminal connections, the dynamic link planning method described in this invention, "based on convex relaxation and bipartite graph maximum weight matching," is used to generate physically feasible and highly robust link configurations under the time-varying geometric relationships of the Walker topology.

[0040] Specifically, in combination Figures 1-13 This invention proposes a constellation network topology planning method based on robustness optimization, the method comprising: Step 1: Constellation Modeling and Constraint Modeling: Based on the orbital elements, formation structure, and onboard terminal distribution of the target constellation, establish the inter-satellite geometric relationships and relative motion models; combine the terminal installation method and pointing capability to form a multi-dimensional set of physical constraints, including altitude angle threshold, azimuth angle boundary, relative angular velocity upper limit, and nodal degree / simultaneous connection number limit; Step 2: Feasible link screening and duration prediction: Based on the geometric and motion model in Step 1, candidate star pairs are enumerated at a given time or time slice to determine whether they simultaneously meet the multidimensional physical constraints; the usable duration of candidate links that meet the constraints is calculated, and short-term links below the minimum threshold are eliminated to obtain the "set of feasible links". Step 3: Time Slice Division and Backbone Topology Initialization: According to the periodicity of the relative motion of the constellation, the continuous time is discretized into the shortest time slice; a stable "backbone topology" (such as a three-regular or existing preserved topology) is constructed in the first time slice and retained in subsequent time slices as the basis for subsequent dynamic enhancements; Step 4: Link Disconnection Prediction and Candidate Set Update (Rolling Mechanism): At the beginning of each time slice, links that are about to violate physical constraints or whose duration is about to expire in the next slice are predicted and marked as pending switching; after the corresponding terminals are released, the "set of available links" is refreshed in the next time slice based on the real-time geometric status; Step 5: Convex relaxation optimization driven by algebraic connectivity: The link selection is expressed as a graph augmentation problem with network algebraic connectivity (second eigenvalue of the Laplacian matrix) as the objective; under the constraints of node degree and number of edges, the discrete decision variables are relaxed to interval variables, a linear matrix inequality (LMI) is constructed and a positive semidefinite programming problem (SDP) is solved to obtain the continuous weight solution for each candidate link; Step 6: Weighted polarization mapping and bipartite graph construction: The continuous weights obtained in Step 5 are subjected to nonlinear polarization mapping to enhance separability; based on the terminal orientation or installation location, the idle terminals are divided into two disjoint sets to construct a bipartite graph, and the mapped weights are used as edge weights. Step 7: Maximum weight matching solution and discrete link generation: Solve for the maximum weight matching on the bipartite graph and output a set of discrete links that satisfy the node degree and physical constraints; combine the new links with the backbone topology to form the final topology configuration of the segment and generate on-board execution instructions; Step 8: Full-cycle rolling execution and data recording: Repeat steps 4 to 8 in rolling order according to time slices until the planned time domain ends; record the topology and key indicators of each slice to provide data support for on-orbit operation and offline evaluation.

[0041] Furthermore, consider the laser terminal arrangement. In actual spaceborne platform configurations, four laser terminals are a common solution, meaning a single satellite can establish a maximum of four laser links simultaneously. Taking a satellite equipped with four laser terminals as the research object, in the graph theory model, this corresponds to a maximum degree of no more than 4 for each node. In the idealized case without introducing any additional link constraints, due to the topological symmetry of the satellites within the constellation, the entire constellation network can be abstracted as a four-regular graph, where each node has a degree of 4, reflecting the baseline topological structure of the satellite constellation under unconstrained conditions. Let the laser terminal model be... Figure 1 It is installed on the satellite.

[0042] The graph is a binary pair .in A non-empty set is called a point set. Each element in the array is called a node; the connections between nodes are called edges. for The set of edges between nodes is called the edge set, which is commonly used. Representation diagram. If If it is an undirected graph, meaning the edges have no direction, then Each element in the array is an unordered pair. , is called an undirected edge, or simply an edge, where .set up ,but and Called The endpoints.

[0043] To facilitate unified modeling and subsequent optimization, this invention uses graph theory to abstract the constellation and its internal connections: each satellite is treated as a graph. A node forms a set of nodes. The possible inter-satellite laser links are considered as edges between nodes, forming a corresponding set of edges. Considering that establishing an actual link in engineering means having a synchronous send and receive channel, to simplify the pointing association and fit the execution, this invention does not distinguish the direction of the edges at the topology level. Therefore, it represents the constellation topology as an undirected graph, such as... Figure 2 As shown.

[0044] In graph theory, node degree describes the number of connections a node has with other nodes in a network, and is an important parameter for measuring the adjacency of nodes. In the modeling framework of this invention, this concept is used to reflect the number of links established by a laser communication terminal on a single satellite. In other words, the higher the node degree, the stronger the connectivity of the satellite in the current network topology and the more links it participates in. Let the... The node degree of the satellite is Then, it can be calculated based on its connectivity with other satellites, which can be used for subsequent constraints and optimization solutions.

[0045] (1) Representative satellite and The system exhibits interconnected relationships. To characterize the connectivity between satellite nodes in a constellation network, this invention employs an adjacency matrix as a matrix representation of the graph. An adjacency matrix is ​​a method for describing network connectivity using a square matrix structure; its matrix elements indicate whether a link exists between any two nodes. In the modeling of a low-Earth orbit satellite constellation, the rows and columns of the matrix correspond to different satellite nodes, and the element values ​​reflect their connectivity status within the current time slice. If a feasible laser communication link exists between the i-th and j-th satellites, the corresponding element in the adjacency matrix is ​​set to 1; if they are not connected or are subject to physical constraints, the element is set to 0. Thus, the link relationship between any two satellite nodes within a large-scale constellation can be represented in matrix form as follows, thereby achieving a structured expression of the entire constellation network connectivity information.

[0046] (2) The link relationships between nodes can then be represented by an adjacency matrix. (3) Degree matrix It is a diagonal matrix used to represent the number of edges connecting each node in the graph. The elements on the diagonal are... Represents a node The degree of a graph is denoted by a matrix whose off-diagonal elements are all 0. The Laplacian matrix is ​​an important concept in graph theory and spectral graph theory, describing the connectivity between nodes in a graph. The Laplacian matrix of a graph is defined as: (4) The Laplacian matrix is ​​a positive semi-definite matrix, with all eigenvalues ​​greater than or equal to 0. The number of its zero eigenvalues ​​represents the number of connected components in the graph, and its second smallest eigenvalue is called the algebraic connectivity. It means that when This indicates that the graph is connected. (For illustration...) In relation to robustness, the concepts of cut sets and conductivity are introduced. For arbitrary graphs... If the vertex set is divided into Rather than the supplement Then the cut set is defined as: (5) That is, connection The set of edges that are adjacent to its complement. Size of the cut set. Depicting the time from The number of edges that need to be broken during a cut represents the bottleneck thickness of the network under that partition. A normalized evaluation system is further introduced based on conductivity. (6) in express The number of edges in the middle, express The sum of the degrees of all nodes in the array. If A very small value indicates the existence of sparse cut sets, meaning the network is easily cut by a small number of edges; if If the cut set is larger, all cut sets will be relatively thicker, and the overall network will be more robust.

[0047] According to Cheeger's inequality, algebraic connectivity With conductivity Satisfying Relationship: (7) From equation (7), we can see that An improvement in algebraic connectivity means an increase in minimum cut thickness, which directly enhances the robustness of the network. This demonstrates that algebraic connectivity not only characterizes connectivity but is also a core indicator for measuring network robustness.

[0048] In the physical constraint definition of step one, the azimuth angle is used to limit the rotatable range of the laser link in the horizontal plane. In this invention, the azimuth angle refers to the direction angle of the projection of the line of sight between the two satellites at both ends of the link onto the horizontal plane, used to describe the horizontal orientation of the link relative to the satellite's coordinate system. Since four laser communication terminals are usually symmetrically installed on the satellite platform, the main maneuvering direction of each terminal is concentrated in the horizontal direction of rotation. Therefore, the azimuth angle range is directly limited by the mechanical rotation capability of the terminal. To ensure that the link is physically reachable and avoids exceeding the terminal's limits, this invention sets a constraint range for the azimuth angle, so that link establishment only occurs within the allowed rotation range. The constraint diagram is shown below. Figure 3 As shown.

[0049] When the position of the target satellite exceeds the field of view boundary formed by the rotatable range of the laser terminal, the terminal cannot achieve pointing tracking, and the link cannot be established.

[0050] (1) Elevation angle constraint The elevation angle describes the angle of elevation of the laser link's line of sight relative to the local horizontal plane. When changes in the relative positions of satellites cause the target's elevation angle to exceed the terminal's allowed pitch range, the link will lose visibility. Given the limited mechanical rotation capability of the laser terminal in the pitch direction, this invention sets an allowable range for the elevation angle to ensure the link's direction remains physically accessible. The corresponding distance variation can be represented by a geometric model, such as... Figure 4 As shown, this is used to further define the spatial range of link establishment and attitude control boundaries.

[0051] Since the satellite platform is equipped with two pairs of laser communication terminals positioned opposite each other, the rotation range of these two symmetrical terminals should be considered simultaneously when calculating the elevation angle constraint to ensure the geometric consistency of the link establishment. Therefore, this invention sets the plane where the terminal is located to be perpendicular to the line connecting the Earth's center to the satellite's centroid, and establishes the elevation angle constraint model based on this plane. When the angle between the link direction and this plane exceeds the terminal's allowable pitch range... At that point, the line of sight between the two satellites becomes unreachable. Based on this geometric relationship, the geocentric angle corresponding to the line connecting the two satellites can be further derived. The calculation formula is used to determine the feasible range of a link under a given elevation angle constraint.

[0052] (8) The corresponding satellite connection distance is (9) When the interstellar distance exceeds the limit This indicates that the inter-satellite link connection exceeds the connection boundary relative to the current satellite's elevation angle, and the link cannot be established.

[0053] (2) Relative angular velocity constraint Relative angular velocity describes the rate of rotation of the laser link's line of sight relative to the local satellite coordinate system; that is, the magnitude of the angular velocity of the link direction vector over time. Since there is a physical upper limit to the rotation rate of the laser communication terminal on its attitude drive mechanism, to avoid exceeding its mechanical response capability, this invention sets constraints on the relative angular velocity of the link, limiting its rate of change to not exceeding the maximum allowable rotation speed range of the terminal. This constraint ensures that the link direction remains trackable and stably connected during dynamic constellation operation.

[0054] Consider two satellite nodes The corresponding position vector and velocity vector are respectively Calculate the relative angular velocity of satellite node 2 with respect to satellite node 1, such as... Figure 5 As shown.

[0055] Relative velocity and relative distance of node 2 relative to node 1 (10) The magnitude of the relative angular velocity is calculated as follows: (11) Among them when Exceeding a certain value indicates that the relative speed exceeds the tracking capability of the laser terminal, and the link cannot be maintained.

[0056] In summary, the establishment and maintenance of inter-satellite links are constrained by multiple physical conditions, including elevation angle, azimuth angle, and relative angular velocity. To maintain overall network connectivity and communication stability under these constraints, this invention, after modeling the physical constraints, further designs a fixed backbone topology. This topology, based on stable links that satisfy the constraints, constitutes the long-term maintenance framework of the constellation network, used to maintain basic network connectivity during dynamic switching and local link failures. By superimposing dynamically adjustable enhancement links on this basis, a hybrid topology of "static backbone + dynamic supplementation" is achieved, thus balancing network stability and performance and laying a structural foundation for subsequent link optimization and topology enhancement.

[0057] In the overall design of the constellation network, this invention comprehensively considers both network stability and performance. On the one hand, the network needs to maintain basic connectivity at all times to ensure continuous support for the constellation's core services; on the other hand, if the topology prioritizes stability above all else, the resulting static network will have a more balanced link length but an increased average communication distance, which is detrimental to transmission efficiency and latency control. Therefore, this invention proposes a hybrid topology structure of "backbone network + dynamic enhancement network," achieving a balance between network robustness and performance through the synergistic effect of the static and dynamic components.

[0058] For large-scale low-Earth orbit constellations, the satellites are densely distributed in space, relatively close together, and their relative motion changes slowly, making them suitable for constructing a geometrically regular basic network. For example... Figure 6As shown, a cross-shaped or "×"-shaped link layout can form a regular grid structure, with stable connections that are easy to maintain in orbit. However, if an optimization model is directly built based on this structure, the relative motion between satellites, due to its small scale, is difficult to accurately reflect the actual dynamic characteristics. Simply introducing multiple evaluation indicators can easily lead to deviations between the optimization results and engineering requirements. Therefore, this invention, based on the gridded topology, distinguishes between static and dynamic links: the former remains unchanged throughout the constellation's operation, forming the backbone of the network; the latter dynamically adjusts with time slices, providing enhanced connectivity during local link breaks or changes in visibility. This structure combines long-term stability with short-term flexibility, providing a reliable foundation for subsequent algebraic connectivity optimization and dynamic switching strategies.

[0059] This topology has the following advantages: (1) The static links that are retained maintain the original grid network properties, ensuring that the satellite network remains globally connected even if dynamic links are not established; (2) When satellites are used as optimization units, each satellite has only one corresponding link. For graph theory problems in the form of node-link, there are no singular conditions such as singular cycles. (3) The link optimization algorithm is optimized only in the dynamic link building space, which greatly reduces the algorithm complexity.

[0060] Based on this, this invention structures the grid network topology according to the satellite's orbital number and the parity of the satellite's serial number within the orbit, simplifying it into a static three-regular topology with fixed connectivity. In this design, each satellite maintains a long-term connection with its three stable links, while reserving one dynamic link for flexible adjustments during on-orbit operation, thus forming a link configuration scheme of "three static links + one dynamic link". This method ensures both the steady-state connectivity of the network and provides space and interfaces for subsequent dynamic switching.

[0061] During the topology partitioning process, to ensure structural balance and connectivity consistency across the entire constellation, this invention divides all satellites in the constellation into four subclasses. This allows for the formation of periodically repeating connection patterns within a gridded structure, resulting in an interwoven distribution of links between different satellite categories. Figure 7 As shown in the diagram. This structure maintains overall connectivity while making the directional distribution of inter-satellite links more uniform, facilitating unified configuration and control during engineering implementation.

[0062] From the above classification relationships, we can conclude that, taking the orbital plane of the satellite as the boundary, the pointing direction of the empty terminal of a satellite in an odd-numbered orbit is consistent with that of a satellite in an even-numbered orbit; however, it is opposite to the pointing direction of satellites in odd-numbered orbits and satellites in even-numbered orbits. Based on this pattern, a static tri-regular network topology can be further constructed to achieve the periodic correspondence and directional balancing of the connection relationships between various types of satellites. A schematic diagram of its overall structure is shown below. Figure 8 As shown.

[0063] Based on the aforementioned static three-regular network structure, this invention further divides satellite nodes of degree 3 according to the pointing differences of the spare laser communication terminals on the satellite. Specifically, when the spare terminal points to the west side of the satellite body, the satellite node is defined as a west-oriented node; when the spare terminal points to the east side, it is defined as an east-oriented node. To ensure the consistency of link establishment direction and the physical feasibility of pointing constraints, satellite nodes only allow nodes with opposite pointing directions to establish communication links, thus forming a network structure with clear directions and regular connections.

[0064] A bipartite graph is a special type of undirected graph whose vertex set can be divided into two disjoint subsets. and And each edge connects a vertex in each of these two subsets. Let the bipartite graph be represented as... ,in and edge set .

[0065] Establish the chain-building problem as Figure 10 The diagram shows a bipartite graph. One part contains satellite nodes with spare laser terminals pointing eastward into their vertical orbits, and the other part contains satellite nodes with spare laser terminals pointing westward into their vertical orbits. New links can only connect nodes located in these two parts. Considering physical constraints, the dynamic link is as follows: Figure 11 As shown.

[0066] After completing the construction and orientation division of the static topology, the constellation network possesses a basic connectivity framework at a global scale. However, due to the continuous relative motion of low-Earth orbit satellites during their orbital operation, the geometric relationships of the links change over time, and relying solely on a fixed topology cannot maintain an optimal connectivity state in the long term. To ensure that the network can maintain stable communication under different orbital positions and attitude conditions, this invention further introduces a time-slice partitioning mechanism based on the static topology. By discretizing the continuous operating cycle into several time slices, the link status within each time slice is independently determined and updated, enabling periodic management and optimization of dynamic links, and providing a temporal framework for subsequent dynamic enhancement and switching strategies.

[0067] Because low-Earth orbit satellites continuously change their relative positions and attitudes during their orbital operation, the geometric relationships between satellites adjust over time, and the connection status of inter-satellite links also changes dynamically. The establishment and maintenance of links depend on the relative state parameters of the satellites; when these parameters exceed physical constraints, the link loses visibility and is interrupted. Therefore, a single static connection method is insufficient to meet the continuous communication needs of the constellation throughout its entire orbital cycle. This invention addresses this characteristic by designing a dynamic link switching mechanism. By monitoring the geometric relationships between satellites and link feasibility in real time during the operational cycle, it promptly establishes, disconnects, and switches connections, thereby constructing a dynamic constellation network topology that can adaptively adjust with orbital motion. This effectively addresses issues such as link failures and terminal switching, ensuring stable communication performance of the network throughout all time periods.

[0068] To effectively address situations where inter-terminal connections in laser links exceed maintenance boundaries and enable timely link switching, a time-slot switching strategy is designed for constellation laser link networks. Taking Walker-type constellations as the research object, this study considers the periodicity of constellation operation, the uniform distribution of internal orbits and satellites within each orbit, and the existence of a shortest time slot where the initial and final states are identical.

[0069] like Figure 12 As shown, select several consecutive satellites in a single orbit within the constellation, and set the shortest time slice as... . time, ~ All are distributed in the corresponding areas, after back, exercise back to the original Location, in Moment ~ lie in Moment ~ In terms of location, if all satellites are considered isomorphic, the orbital states of corresponding satellites in the constellation are the same at two different times.

[0070] Therefore, a time-slice switching strategy is designed with the shortest time slice as the basic time unit. In each time slice, the link that is about to be disconnected is detected and the solution is found among the available links. Under the condition of satisfying all constraints, the solution that can make the constellation network communication performance better is found.

[0071] After completing time-slice partitioning and link state discretization, the temporal evolution law of the constellation network has been clearly expressed. The link connection states within different time slices are independent yet continuous, providing discretized input for subsequent optimization modeling. To quantitatively evaluate the network connectivity quality within each time slice and achieve smooth switching between consecutive segments, this invention further establishes a theoretical analysis and optimization model based on time-slice partitioning. By using the link set of each time slice as input variables and introducing indices such as algebraic connectivity, node degree constraints, and edge count limitations, a solvable objective function and constraint system are constructed, thus providing mathematical support for dynamic link scheduling and enhancement. Figure 13 As shown, this model uses time slices as the basic unit and achieves periodic updates to the constellation's dynamic topology and overall performance improvement by optimizing the solution of the link set within each slice.

[0072] During the network initialization phase, all satellites maintain only three static links, with no dynamic links established yet, and the node degree is fixed at 3. To reduce the control and computational overhead caused by frequent switching of subsequent dynamic links, this invention filters the sustainability duration of candidate links during the initial link establishment process: when the sustainability duration of a link is less than one shortest time slice, it is removed from the set of available links; only links with a sustainability duration of not less than one time slice are retained as valid candidates. Subsequently, all available links for each satellite node are checked, and the longest-lasting links are selected as priority links for establishment to form the initial set of dynamic links.

[0073] In the subsequent dynamic switching phase, this invention considers both link break detection and available link updates. First, links that will no longer meet the physical constraints in the next time slice are actively broken. This involves detecting connections in the currently established dynamic links whose duration is less than one time slice and actively releasing them before the time slice switch. Second, the network topology after the link break operation is completed is considered as the initial state of the new time slice. Based on the pointing state of the available laser terminals at this time, the set of available links is recalculated, providing the input basis for the next step of link reconstruction and topology update.

[0074] After processing, both the initial base topology and the topology after dynamically switching and deleting broken links can be considered as the initial graphs for the aforementioned graph augmentation problem. Let the graph corresponding to the initial base topology and the graph after deleting unsuitable edges during the subsequent dynamic switching be denoted as [the graphs described in the original text]. and alternative links are We all contribute to the problem input, This indicates that the links actually selected and established are used as optimization variables. This represents the maximum number of links that can be established. Therefore, when using the maximum algebraic connectivity corresponding to the Laplace matrix as the metric, the problem can be expressed in the following form: (12) in As input, it includes static links and dynamic links that are preserved during the dynamic renewal process of links.

[0075] All nodes with available links and the available links can form a bipartite graph structure, providing a candidate set for link selection. The next step is to make a decision based on network performance metrics. Considering that optimizing directly using algebraic connectivity as the metric is an NP-hard combinatorial optimization problem, we relax the integer constraints to interval constraints and equate the lower bound constraint of algebraic connectivity to a semidefinite matrix inequality, resulting in a semidefinite programming problem. The obtained fractional solutions are nonlinearly mapped as bipartite graph weights, and then the final link set is obtained through maximum weight matching.

[0076] SDP is a class of convex optimization problems, which take the form of optimizing a linear objective function in the variable space while satisfying linear and positive semidefinite constraints of a symmetric matrix. Because SDP can naturally characterize the spectral properties of matrices, especially eigenvalue-dependent optimization objectives, it has significant advantages in problems such as spectral theory and network design.

[0077] In the topology optimization problem of satellite networks, maximizing algebraic connectivity is equivalent to maximizing the second smallest eigenvalue of the Laplacian matrix of an undirected connected graph. Because the discrete link selection variables have integer constraints, it leads to... The spectral optimization problem with maximization as its objective is essentially a combinatorial nonconvex optimization problem. By introducing a convex relaxation method, the discrete constraints are relaxed to obtain a concave function maximization problem with a convex feasible region. Then, by converting the lower bound constraint of algebraic connectivity into a semidefinite matrix inequality, the nonconvex optimization problem is transformed into an SDP model. This convex form, under the relaxation sense, can provide a global optimum solution to measure the contribution of potential links to the overall robustness of the network and provide a weight reference for the subsequent discrete topology optimization stage.

[0078] Based on equation (12), Boolean vectors are used to replace the set of candidate links. ,set up The CCP includes Edge, let When the link for When using subsets, Otherwise, it is 0. Also, define the edge vectors. For a connected node and edge Define edge vectors As in equation (13): (13) The additional edges can be represented in the Laplace matrix as follows: Based on this, considering the constraint that each satellite can establish at most one link, let the set of nodes in the graph be... , which corresponds to satellite The set of candidate links is , representing a node The set of indexes that associate all alternative links, let As the variable, the Laplacian matrix corresponding to the input graph is... So for any node in the network, all correspond The sum of the indices should be less than or equal to 1, so equation (12) can be expressed as: (14) Define the target Laplacian matrix as , represented as (15) At the same time, for any vector, definition (16) Lemma 1. Courant-Fischer Minimax Theorem: For conjugate symmetric matrices... Arrange its eigenvalues ​​in ascending order as follows (17) Then for any There are two equivalent extreme value representations: (1) Min-Max Form (18) (2) Max-Min Form (19) Considering the properties of the Laplace matrix, we know For a positive semi-definite symmetric matrix, the smallest eigenvalue is 0, and the corresponding eigenvector is an all-1 vector. According to Lemma 1, its algebraic connectivity can be expressed as: (20) Lemma 2. For the function

[0079] (twenty one) in Then it is called For affine functions, It is affine.

[0080] Lemma 3. Let For a family of affine functions, define its pointwise infimum function. for (twenty two) but It is a concave function.

[0081] Substituting equation (16) into equation (15), we get (twenty three) According to Lemma 2, for any fixed , It is about The affine function. According to Lemma 1, substituting the above equation into equation (20), we can obtain the following form. (twenty four) The above formula represents It is all that meet the conditions. The pointwise infimum of the corresponding affine function. Therefore, equation (24) is a family of affine functions. (25) The infimum function. According to Lemma 3, we know For about The concave function. However, due to the feasible region... The problem is a non-convex Boolean set, and the overall problem remains a combinatorial optimization problem. To obtain a solvable convex optimization model, we need to... Perform a relaxation process.

[0082] Without changing the linear constraints, constrain the variables of the current problem. Relaxed to This leads to the relaxation problem. (26) Since the feasible solution set of this problem is larger than the feasible solution set corresponding to equation (14), the optimal solution corresponding to equation (26) is an upper bound of the optimal solution of equation (14). However, the objective of equation (26) is the spectral value, which is not convenient to solve, so a scalar is introduced. express The explicit lower bound, thus having (27) That's all The spectral value constraint is equivalently rewritten as a linear matrix inequality (LMI) constraint, further transforming equation (26) into an equivalent SDP form. This form, while maintaining the convex relaxation nature of the original problem, also belongs to the class of standard cone programming, and therefore can be solved efficiently using existing SDP solvers. As shown in equation (28): (28) The optimization problem (28) includes four constraints: the first type of LMI constraint guarantees that the objective variable is the lower bound of the second smallest eigenvalue of the Laplacian matrix; the second type of constraint restricts the number of edges that can be selected; the third type of constraint determines the optimization variable... The range of values ​​is broadened to an interval. The last type of constraint controls node degree, ensuring that the number of edges each node participates in does not exceed a given upper limit. The final solution yields a lower bound that satisfies the algebraic connectivity requirement. The largest optimization variable .

[0083] To solve the SDP problem (28), the optimal solution in its relaxed form is obtained using the CVX toolbox. The solution is a weight vector, where each element corresponds to the evaluation value of a candidate link, representing the importance measure of the candidate link in a global sense.

[0084] Because the SDP solution is in The distribution within the interval is relatively smooth, making it difficult to clearly distinguish the quality of links. Therefore, nonlinear mapping processing is required before using it as weight input. The tanh transformation of this solution is as follows: (29) in The weights corresponding to the original SDP solution. For the processed weights, Used to adjust the polarization intensity of the weights, when When the weights are large, the weight distribution is closer to binarization; when When the weights are smaller, the weight distribution is smoother. After processing, a weight distribution from... arrive The mapping, whose distribution is more inclined towards the weights at both ends, enhances the distinction between strong and weak links, makes the weight distribution more binarized, and avoids the problem of being too sensitive when solving based on the original weights. Based on this weight, the weights of the bipartite graph are designed, and a maximum weight matching model is further constructed to obtain the final discretized link configuration scheme.

[0085] Maximum weight matching in a bipartite graph aims to select a set of non-adjacent edges from the candidate edge set between two subsets of nodes, maximizing the sum of their edge weights. Based on the established bipartite graph model, let the decision variables... , indicating edge Whether a candidate edge is selected depends on the specific circumstances of that edge. The weights after mapping are expressed as Then the optimization problem can be modeled as Equation (30). (30) The above constraints guarantee that each node is matched with at most one edge, which conforms to the satellite degree constraint. The maximum weight matching solution corresponds to the set of edges with the largest total weight under the connectable edge constraint, which is the continuous link weight obtained based on convex relaxation, and then discretized into the actual edge set after nonlinear processing.

[0086] In summary, this invention addresses the challenges of high dynamics, complex physical constraints, and stringent network connectivity requirements in low-Earth orbit satellite constellations by proposing a robust dynamic link planning method that combines convex relaxation solutions with bipartite graph maximum weight matching. This method is based on multidimensional physical constraints, balancing link feasibility with network topology optimization objectives. By establishing a time-slice discretization model, it achieves periodic updates and rolling planning of link states. Furthermore, it utilizes algebraic connectivity as a network robustness index, employs positive semidefinite programming to solve for continuous weighted solutions, and obtains discrete link schemes that satisfy node degree constraints through weight polarization and bipartite graph maximum weight matching, thereby effectively improving the connectivity and structural stability of the constellation network.

[0087] The method of this invention enables adaptive maintenance and optimized configuration of links in dynamic operating environments, ensuring both long-term stable operation of satellite networks and balancing communication performance and topology robustness. This scheme boasts advantages such as strong versatility, good scalability, and high computational efficiency, making it suitable for various types of low-Earth orbit constellation structures and inter-satellite laser communication systems. It provides crucial technical support for the on-orbit autonomy and intelligent scheduling of future large-scale constellation networks.

[0088] Example To facilitate understanding of the technical solution of the present invention, the present invention will be further described in conjunction with the accompanying drawings and embodiments. It should be understood that the following embodiments are merely illustrative and not intended to limit the present invention.

[0089] 1. Overall Process The dynamic link planning method based on convex relaxation and bipartite graph maximum weight matching provided by this invention is applicable to low-Earth orbit satellite constellations using the Walker-Delta architecture. The overall process includes the following steps: (1) Constellation modeling and physical constraint definition; (2) Fixed backbone topology construction; (3) Time slice division and link status determination; (4) Dynamic link switching and duration prediction; (5) Topology optimization and two-stage solution; (6) Backbone topology maintenance and dynamic enhancement implementation.

[0090] Through the above process, the present invention can achieve dynamic network connectivity and highly robust topology maintenance during constellation operation.

[0091] 2. Constellation Network Modeling In this embodiment, the low-Earth orbit satellite constellation is abstracted as an undirected graph. .in: : Set of satellite nodes; Inter-satellite laser link set.

[0092] When satellite When the chain establishment condition is met, the adjacency matrix elements If not satisfied, then The node degree matrix is ​​defined as follows: Laplace matrix Its second smallest eigenvalue As an algebraic connectivity factor, it is used to evaluate the connectivity margin of a network.

[0093] The establishment and maintenance of a link are subject to the following constraints: (1) Azimuth constraint: The projection angle of the link line of sight on the horizontal plane shall not exceed the range of mechanical rotation of the terminal; (2) Elevation angle constraint: The line of sight elevation angle must be within the allowable pitch range; (3) Relative angular velocity constraint: The link rotation rate must not exceed the terminal tracking limit.

[0094] If any condition is triggered, the link is removed from the set of available links.

[0095] 3. Fixed backbone topology design Based on the constraints mentioned above, a static tri-regular topology is constructed. Each satellite maintains three long-term stable links, and one dynamic link is reserved for adjustment.

[0096] Satellites are classified into four categories based on their orbital number and the parity of their serial number: (1) Odd orbit and odd number satellite; (2) Odd-orbiting, even-numbered satellites; (3) Even-orbiting odd-numbered satellites; (4) Even orbit even number satellite.

[0097] Based on the direction of available terminals, nodes are further divided into two categories: east-facing and west-facing, and communication is only allowed with nodes facing the opposite direction.

[0098] 4. Time Slice Allocation and Dynamic Link Maintenance To address interstellar geometric variations, this invention discretizes the continuous time-series operation into multiple shortest time slices. And independently compute the set of feasible links within each time slice. .

[0099] (1) Initialization phase: All satellites maintain only static links (degrees of 3); Calculate the sustainability duration of each candidate link; Remove links with a duration of less than one time slice, and only retain links with a duration of ≥ The link; For each node, select the links with the longest duration as the initial dynamic link set.

[0100] (2) Dynamic switching phase: Detect links that do not meet the constraints in the next time slice and actively disconnect them; Use the topology after the link break as the initial state of the new time slice; The set of available links is recalculated based on the status of available terminals to achieve rolling updates.

[0101] 5. Topology Optimization and Solution In each time slice, the algebraic connectivity is used. For the objective function, establish a semidefinite programming (SDP) model: (31) Then, node degree, edge count, and concurrency constraints are applied. After obtaining the continuous weight solution, weight polarization mapping is performed: (32) Based on this, a maximum weight matching model for bipartite graphs is established: (33) The Hungarian algorithm is used to solve the problem, resulting in a set of discrete links that satisfy the constraints.

[0102] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the robustness-optimized constellation network topology planning method.

[0103] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the robustness-optimized constellation network topology planning method.

[0104] The memory in this application embodiment can be volatile memory or non-volatile memory, or it can 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 dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0105] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state disks (SSDs)).

[0106] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside 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, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0107] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor 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 application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as being executed by a hardware decoding processor, or executed 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, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0108] The above provides a detailed description of a robustness-optimized constellation network topology planning method proposed in this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A constellation network topology planning method based on robustness optimization, characterized in that, The method includes: Step 1: Constellation Modeling and Constraint Modeling: Based on the orbital elements, formation structure, and onboard terminal distribution of the target constellation, establish the inter-satellite geometric relationships and relative motion models; combine the terminal installation method and pointing capability to form a multi-dimensional set of physical constraints, including altitude angle threshold, azimuth angle boundary, relative angular velocity upper limit, and nodal degree / simultaneous connection number limit; Step 2: Feasible link screening and duration prediction: Based on the geometric and motion model in Step 1, candidate star pairs are enumerated at a given time or time slice to determine whether they simultaneously satisfy the multidimensional physical constraints; the usable duration of candidate links that satisfy the constraints is calculated, and short-term links below the minimum threshold are eliminated to obtain the "set of feasible links". Step 3: Time Slice Division and Backbone Topology Initialization: Based on the periodicity of the relative motion of the constellation, the continuous time is discretized into the shortest time slices; a stable "backbone topology" is constructed in the first time slice and retained in subsequent time slices as the base for subsequent dynamic enhancements; Step 4: Link Disconnection Prediction and Candidate Set Update: At the beginning of each time slice, links that are about to violate physical constraints or whose duration is about to expire in the next slice are predicted and marked as pending switching; after releasing the corresponding terminals, the "set of available links" is refreshed in the next time slice based on the real-time geometric status. Step 5: Convex relaxation optimization driven by algebraic connectivity: The link selection is expressed as a graph enhancement problem with network algebraic connectivity as the objective; under the constraints of node degree and edge number, the discrete decision variables are relaxed to interval variables, a linear matrix inequality is constructed and a positive semidefinite programming problem is solved to obtain the continuous weight solution for each candidate link. Step 6: Weighted polarization mapping and bipartite graph construction: The continuous weights obtained in Step 5 are subjected to nonlinear polarization mapping to enhance separability; based on the terminal orientation or installation location, the idle terminals are divided into two disjoint sets to construct a bipartite graph, and the mapped weights are used as edge weights. Step 7: Maximum weight matching solution and discrete link generation: Solve for the maximum weight matching on the bipartite graph and output a set of discrete links that satisfy the node degree and physical constraints; combine the new links with the backbone topology to form the final topology configuration of the segment and generate on-board execution instructions; Step 8: Full-cycle rolling execution and data recording: Repeat steps 4 to 8 in rolling order according to time slices until the planned time domain ends; record the topology and key indicators of each slice to provide data support for on-orbit operation and offline evaluation.

2. The method according to claim 1, characterized in that the constellation It consists of P orbital planes, with S satellites on each plane. The orbital planes are staggered according to the phase factor F. Each satellite carries 4 two-degree-of-freedom laser communication terminals, which achieve complementary coverage in the east-west / front-back directions or equivalent installation positions.

3. The method according to claim 2, characterized in that, The method uses graph theory to abstract constellations and their internal connections: each satellite is treated as a graph. A node forms a set of nodes. The possible inter-satellite laser links are considered as edges between nodes, forming a corresponding set of edges. Meanwhile, the constellation topology is represented by an undirected graph; the degree of a node is used to describe the number of connections between a node and other nodes in the network; and the adjacency matrix is ​​used as the matrix representation of the graph.

4. The method according to claim 3, characterized in that, In the physical constraint definition in step one, the azimuth angle is used to limit the rotatable range of the laser link in the horizontal plane; the azimuth angle refers to the direction angle of the projection of the line of sight between the two satellites at both ends of the link in the horizontal plane, which is used to describe the horizontal pointing of the link relative to the satellite body coordinate system; when the position of the target satellite exceeds the field of view boundary formed by the rotatable range of the laser terminal, the terminal cannot achieve pointing tracking, and the link does not meet the conditions for establishment.

5. The method according to claim 4, characterized in that, In step three, inter-satellite links are divided into static links and dynamic links: the former remains unchanged throughout the constellation's operation and is used to form the backbone of the network; the latter is dynamically adjusted as time slices roll, and is used to provide enhanced connectivity when there is a local link break or changes in visibility. Based on this, the grid-like network topology is structured according to the satellite's orbit number and the parity of the satellite's serial number within the orbit, simplifying it into a static tri-regular topology with fixed connectivity.

6. The method according to claim 5, characterized in that, Optimizing directly using algebraic connectivity as an indicator is an NP-hard combinatorial optimization problem. By relaxing the integer constraints into interval constraints and equating the lower bound constraint of algebraic connectivity to a semidefinite matrix inequality, a semidefinite programming problem is obtained. The obtained decimal solutions are nonlinearly mapped as bipartite graph weights, and then the final set of buildable links is obtained through maximum weight matching.

7. The method according to claim 6, characterized in that, The semidefinite programming problem includes four constraints: the first type of LMI constraint guarantees that the objective variable is a lower bound of the second smallest eigenvalue of the Laplace matrix; the second type of constraint restricts the number of edges that can be selected; the third type of constraint optimizes the variable... The range of values ​​is broadened to an interval. The last type of constraint controls the node degree, ensuring that the number of edges each node participates in does not exceed a given upper limit; finally, the solution yields a lower bound that makes the algebraic connectivity less than or equal to the given upper limit. The largest optimization variable .

8. The method according to claim 7, characterized in that, Maximum weight matching in a bipartite graph refers to selecting a set of non-adjacent edges from the candidate edge set between two subsets of nodes, such that the sum of the edge weights is maximized. Based on the bipartite graph model, let the decision variables... , indicating edge Whether a candidate edge is selected depends on the specific circumstances of that edge. The weights after mapping are expressed as Then the semidefinite programming problem is modeled as equation (30): （30） The above constraints guarantee that each node is matched with at most one edge, which conforms to the satellite degree constraint; the maximum weight matching solution corresponds to the edge set with the largest total weight under the connectable edge constraint, that is, the continuous link weight obtained based on convex relaxation, which is discretized into the actual edge set after nonlinear processing.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-8.

10. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-8.

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