Deployment method of low-orbit large-scale satellite constellation

Abstract

The invention relates to the technical field of satellites, in particular to a deployment method of a low-orbit large-scale satellite constellation, which comprises the following steps: S1, establishing a static network for launching deployment by taking each orbit and a launching site as nodes and taking a satellite transportation path between the nodes as an edge; the network side comprises non-time dimension information of each node; s2, on the basis of the static network, traversing all possible paths according to launch interval time of the vehicle and orbit dynamics to obtain a time expansion network; s3, a parking track and a target track are obtained, and a two-channel logistics network model is constructed according to the parking track and the target track; s4, based on the two-channel logistics network model, establishing a multivariable mixed integer optimal mathematical equation according to information contained in nodes and edges in the time expansion network; and S5, solving the two-channel logistics network model according to the mathematical equation to obtain an optimal launching deployment scheme of the satellite constellation.

Description

Technical Field

[0001] The present invention relates to the field of satellite technology, and in particular to a method for deploying a large-scale low-orbit satellite constellation. Background Art

[0002] Limited by satellite production testing, launch capacity and economic factors, the deployment of large-scale low-orbit constellations is a long-term, high-cost and highly coupled problem with the time dimension. Therefore, it is urgent to build a mathematical model for the optimal launch deployment of constellations under the constraints of the launch cycle of the carrier, the satellite orbit transfer cycle, and the parking orbit capacity, and to develop a large-scale variable efficient optimization algorithm to solve the optimal launch deployment method and achieve the goal of minimizing the cost of constellation construction and maximizing the cumulative efficiency.

[0003] The traditional static space logistics network model fails to fully consider the time effect. It can only obtain the number of satellites at each location node, but it is difficult to obtain when the satellites are transformed between the locations. In other words, it cannot guide the formulation of the optimal satellite launch deployment plan. The limitation of the static model is that it cannot describe the state and position changes of satellites at different time points, resulting in the global distortion of the optimal solution of the static network under long-term missions. Summary of the invention

[0004] In view of the above problems, the purpose of the present invention is to provide a deployment method for a large-scale low-orbit satellite constellation, which expands the traditional static space logistics network model in the time dimension and constructs a dynamic network that can describe the satellite launch, transfer and deployment process. It can not only fully describe the transfer strategy of each satellite at different locations and times, but also effectively avoid the problem of geometric growth of optimization variables as time expands.

[0005] The present invention provides a method for deploying a large-scale low-orbit satellite constellation, comprising:

[0006] S1, using each orbit and launch site as a node and the satellite transportation paths between the nodes as edges, establish a static network of launch deployment; the network edges include non-time dimension information of each node;

[0007] S2, based on the static network, traverse all possible paths according to the launch interval time of the carrier and the orbital dynamics to obtain a time extension network;

[0008] S3, obtaining a parking track and a target track, and constructing a dual-channel logistics network model according to the parking track and the target track;

[0009] S4, based on the dual-channel logistics network model, establishing a multivariable mixed integer optimal mathematical equation according to the information contained in the nodes and edges in the time-expanded network;

[0010] S5, solving the dual-channel logistics network model according to the mathematical equation to obtain the optimal launch deployment plan for the satellite constellation.

[0011] In a possible implementation, the equality constraints of the mathematical equation include: conservation of network node satellite transfer amount;

[0012] The inequality constraints of the mathematical equation include: satellite capacity and vehicle availability at each node.

[0013] In a possible implementation, the time extension network includes a time layer and a network arc segment;

[0014] The time layer includes: a route layer and a waiting layer;

[0015] The network arc segments include: access arc segments, exit arc segments, state transition arc segments, path arc segments and waiting arc segments.

[0016] In a possible implementation, the route layer includes: time arcs and time nodes extended from the static network;

[0017] Wherein, each of the time nodes is uniquely identified as a tuple by time, space, and path information;

[0018] All time nodes in the same route are arranged in chronological order, and adjacent nodes are connected by time arcs.

[0019] In a possible implementation, the entry arc segment includes: a source node and a path entry node;

[0020] The source node represents the moment when the satellite is manufactured and put into storage. It is connected by accessing the arc segment and the launch time node to store the time cost information and deployment cost information from storage in the warehouse to the integration of the satellite and the rocket for launch after the satellite is developed.

[0021] In a possible implementation, the exit arc includes: a sink node and a time-state node of the satellite entering the target orbit;

[0022] The sink node indicates the satellite phase adjustment completion state, and the arc segment stores the time cost and deployment cost information required for satellite phase adjustment.

[0023] In a possible implementation, the satellite constellation optimal launch deployment scheme includes basic decision nodes and corresponding event nodes;

[0024] The basic decision nodes include: a vehicle launch node and a satellite orbit transfer maneuver node;

[0025] The event nodes include: a satellite storage node, a satellite phase adjustment node and a satellite end-of-life node.

[0026] In a possible implementation, the method further includes:

[0027] Determine the launch node of the vehicle based on the influence of the Earth's rotation and J2 orbital perturbation on the orbital ascending node;

[0028] The launch time window Δt of the vehicle is calculated according to the following formula:

[0029]

[0030] Among them, n is the average number of times the satellite orbits the earth in a unit time, p is the semi-path of the orbit, R e is the radius of the earth, θ is the inclination of the orbit, and J2 is the secondary gravitational field coefficient of the earth.

[0031] In a possible implementation, the method further includes:

[0032] Under the J2 perturbation force, the parking orbit and the target orbit are transferred coplanarly to determine the satellite orbit transfer node;

[0033] The precession angular velocity ω of each orbit is calculated according to the following formula p :

[0034]

[0035] Among them, ω p is the orbital precession angular velocity, a is the semi-major axis of the orbit, n is the average number of circles the satellite orbits the earth per unit time, R e is the radius of the earth, θ is the inclination of the orbit, and J2 is the secondary gravitational field coefficient of the earth.

[0036] In a possible implementation, the method further includes:

[0037] Determine the event node of the satellite orbit transfer node according to the Hohmann rotation;

[0038] The orbital period T is calculated according to the following formula:

[0039]

[0040] Where T is the orbital period, r i is the radius of the parking orbit, r j is the radius of the target orbit, i is the parking orbit code, j is the target orbit code, and μ is the standard gravitational parameter.

[0041] The deployment method of a large-scale low-orbit satellite constellation provided by the present invention expands the time dimension of the traditional static space logistics network model to construct a dynamic network that can describe the satellite launch, transfer and deployment process. The nodes in the model represent locations such as launch sites, parking orbits and target orbits, and the edges represent the connections between these locations, including information such as the number and time of satellite transfers. By locally extending the path to cover the time state nodes, not only can the transfer strategy of each satellite at different locations and times be fully described, but also the problem of geometric growth in the number of optimization variables as time expands can be effectively avoided. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A schematic diagram of a flow chart of a method for deploying a large-scale low-orbit satellite constellation provided by an embodiment of the present invention;

[0043] Figure 2 A schematic diagram of a dual-channel logistics network model provided by an embodiment of the present invention;

[0044] Figure 3 A schematic diagram of a mathematical equation fitting curve provided in an embodiment of the present invention;

[0045] Figure 4 A schematic diagram of time-state node expansion for a path provided by an embodiment of the present invention;

[0046] Figure 5 A schematic diagram of a time extension network provided by an embodiment of the present invention;

[0047] Figure 6 A schematic diagram of each satellite mission window provided in an embodiment of the present invention;

[0048] Figure 7 A schematic diagram of the XML file structure of a time extension network provided by an embodiment of the present invention;

[0049] Figure 8 A schematic diagram of the relationship between the longitude of the ascending node of the orbital plane at the time of launch and the ground launch site provided by an embodiment of the present invention;

[0050] FIG9( a ) is a schematic diagram of forward phase modulation under the Hohmann shift strategy provided by an embodiment of the present invention;

[0051] FIG9( b ) is a schematic diagram of backward phase modulation under the Hohmann shift strategy provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The following detailed description of the embodiments of the present invention is further described in detail in conjunction with the accompanying drawings and examples. The detailed description of the following embodiments and the accompanying drawings are used to exemplarily illustrate the principles of the present invention, but cannot be used to limit the scope of the present invention, that is, the present invention is not limited to the preferred embodiments described, and the scope of the present invention is defined by the claims.

[0053] In the description of the present invention, it should be noted that, unless otherwise specified, “plurality” means two or more than two; the terms “first”, “second”, etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance; for ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances.

[0054] Figure 1 A schematic diagram of a process for deploying a large-scale low-orbit satellite constellation provided by an embodiment of the present invention is shown in FIG. Figure 1 As shown, the present invention provides a method for deploying a large-scale low-orbit satellite constellation, comprising:

[0055] S1, establishes a static network of launch deployment with each orbit and launch site as nodes and satellite transportation paths between nodes as edges;

[0056] The network edges include the non-time dimension information of each node. Nodes represent locations such as launch sites, parking orbits, and target orbits. Edges represent the connections between these locations, specifically including information such as the number and time of satellite transfers. The time state nodes are covered by local extension paths. The static network can not only fully describe the transfer strategies of each satellite at different locations and times, but also effectively avoid the problem of geometric growth in the number of optimization variables as time expands.

[0057] The batch launch and deployment of large-scale low-orbit constellations is an optimization problem that is highly correlated with the time dimension. The optimization goal of this problem is to minimize the deployment cycle while optimizing the cumulative efficiency of intermediate deployments. Traditional static networks do not contain deployment information in the time dimension, which means that it is impossible to solve the long-term deployment problem of large-scale constellations that is highly correlated with time information.

[0058] S2, based on the static network, traverses all possible paths according to the launch interval time and orbital dynamics of the carrier to obtain the time extension network;

[0059] The possible paths refer to the geographical nodes that the satellite will pass through and the time information of passing through the nodes.

[0060] In one possible implementation, the time extension network includes a time layer and a network arc;

[0061] The time layer includes: route layer and waiting layer;

[0062] Network arcs include: access arcs, exit arcs, state transition arcs, path arcs and waiting arcs.

[0063] The route layer includes: time arcs and time nodes extended from the static network;

[0064] Each time node is uniquely identified as a tuple by time, space, and path information; all time nodes in the same route are arranged in chronological order, and adjacent nodes are connected by time arcs.

[0065] The entry arc includes: source node and path entry node; the source node represents the moment when the satellite is completed and put into storage, and is connected through the access arc and the launch time node to store the time cost information and deployment cost information from storage to satellite-rocket integration and launch after the satellite is developed.

[0066] The exit arc includes: a sink node and a time-state node when the satellite enters the target orbit; the sink node indicates the state of satellite phase adjustment completion, and the arc stores the time cost and deployment cost information required for satellite phase adjustment.

[0067] In the problem of optimal batch launch deployment of constellations, there are not only location nodes such as launch sites, parking orbits, and target orbits, but also edges connecting the location nodes. These edges also contain information such as the number of satellite transfers and the time of satellite transfer. Therefore, it can be effectively equivalent to the minimum value problem of the space logistics network.

[0068] Among them, the location node is the network node, the location node connection is the network edge, and each network edge contains information such as time / transmission cost.

[0069] The traditional static space logistics network model fails to consider the time effect and can only obtain the number of satellites at each location node. It is difficult to obtain when the satellite is transformed between the various location nodes, that is, it cannot guide the formulation of the satellite optimal launch deployment plan. The time expansion network constructed by the present invention expands the traditional static network in the time dimension, and only partially expands the path to cover the time state node. It can not only fully describe the launch transfer position and time strategy of each satellite, but also effectively avoid the problem of geometric growth of optimization variables with time expansion.

[0070] On the basis of the static network constructed based on each spatial node and edge, the launch node, transfer maneuver node and satellite phasing node that meet the dynamic conditions are constructed in the form of a layered graph based on the relevant theory of orbital dynamics, and the parameters required for the expansion of the time dimension of the static network are initialized.

[0071] On the basis of the static network, according to the generated "time-state" nodes and initialization parameters, the corresponding nodes are placed in the corresponding hierarchical graphs respectively, and the node links and time dimension information are implied by the corresponding arc types according to the events constructed by each node. In this way, the time dimension of the static network is expanded according to the time expansion network structure. Figure 5 Schematic diagram of a time extension network provided by an embodiment of the present invention. i represents the satellite state at the ith node on a path, t irepresents the time at the i-th node on a path, r dir represents the direct launch path from the launch site to one of the target orbits, and similarly r indir Refers to an indirect launch path from a launch site to the same target orbit.

[0072] like Figure 5 As shown, the time extension network includes: a transport layer and a waiting layer, an access arc segment, an exit arc segment and a state transfer arc segment.

[0073] (1) Transport layer and waiting layer: The transport layer contains all time arcs and time nodes extended from the static network. Each time node is uniquely identified as a tuple (s, t, r) to identify it from the time and space dimensions.

[0074] For example, node i = (P1, tk, 001_to_T1_aux_indirect) indicates that the carrier is at t k At that time, the vehicle arrives at parking track No. 1 along the route with id 001_to_T1_aux_indirect. All time nodes in the same route are arranged in chronological order. Adjacent nodes are connected by time arcs. Different types of arcs in the same path map different deployment stages in real deployment activities, so as to generate their own time cost and deployment cost, which is convenient for later projection on the same underlying network to solve the problem by solving the minimum path method.

[0075] (2) Access arc and exit arc: In order to describe the problem as a multi-commodity logistics network problem, a source node (o0, t0) and a sink node (d0, t8) are added to each traveling satellite in the network. The source node represents the time when the satellite is completed and put into storage. The time cost information from the storage to the launch of the satellite after the satellite is developed is stored through the access arc and the launch time node. and deployment cost information The sink node describes the process of satellite phase adjustment to the final working space position d0. The arc connecting it with the satellite orbit entry node is the exit arc, which stores the time cost and deployment cost required for satellite phase adjustment.

[0076] (3) State transition arc: In order to realize the transition from the maneuvering state to the orbit maintenance state of the satellite, the state transition arc is used to connect the nodes with the same time and space information in different path layers and waiting layers. r ,r∈R points to the waiting layer G s ,s∈S, and vice versa. From the transport node i=(s,t,r)∈V r To the waiting node i=(s,t)∈V s The state transition a=(i,j)∈A costs C ij Set to 0, capacity κij Set to Infinity.

[0077] So far, through the transport layer and the waiting layer V = V r ∪V s Realize the characterization of satellite and carrier maneuvering behavior and state maintenance phase between different geographical nodes, through A=A r ∪A w ∪A t ∪A a ∪A e The deployment model is characterized by equal arc segments, including satellite storage, orbit climbing, orbit raising and berthing, maneuvering and changing orbits, phase adjustment, and orbit entry. The exclusive time and deployment cost of different arc segments are established through one-to-one mapping of arc segments and actual deployment stages, and the network implicitness of time information is realized, which makes it easier to regard the complex planning problem as the shortest path problem and solve it using the column generation method in the later stage.

[0078] Figure 4 A schematic diagram of time-state node expansion for a path provided in an embodiment of the present invention shows the meaning correspondence between each node and arc type in the time expansion network model and each decision node in a specific launch task.

[0079] S3, obtaining the parking track and the target track, and building a dual-channel logistics network model according to the parking track and the target track;

[0080] The space logistics network model is used to model the launch and deployment of large-scale constellations in low orbit. The concepts of parking orbit and target orbit are abstracted as a dual-channel logistics network model. Each orbit and launch site is abstracted as a node, and each node is linked by a network edge, in which the network edge contains non-time dimension information such as the geographical location relationship between nodes, thereby establishing a static network for launch deployment.

[0081] Figure 2 A schematic diagram of a dual-channel logistics network model provided by an embodiment of the present invention, Figure 2 The square in the middle is the satellite, the triangle is the launch site, the rectangle is the carrier carrying the satellite, the circle at the bottom is the earth, the solid black line represents the target orbit, the dotted gray line represents the parking orbit, the strategy one path represents the path of direct launch to the target orbit, and the strategy two path represents the path of maneuvering transfer from the parking orbit to the target orbit. The transfer of the satellite in the upper left corner of the figure along the dotted line to another orbit parallel to the orbit is a coplanar transfer, and the transfer of the satellite in the lower left corner of the figure on the same orbit is a feedforward phase transfer.

[0082] Setting up a dual-channel logistics network model, that is, using two launch modes, means the following: The model established in the present invention takes into account that various types of satellites (commodities) need to be sent to the predetermined orbit (destination) through different launch stations (source points) with different types of carriers. Due to the number of rockets, transportation capacity, and launch intervals, the deployment process may not meet the launch deployment restrictions imposed by the satellite life. The present invention adds a parking orbit so that the model can seek the optimal solution in a higher dimension. Each link of satellite deployment is accompanied by specific costs and time, as well as technical and safety constraints.

[0083] S4, based on the dual-channel logistics network model, establishes a multivariable mixed integer optimal mathematical equation according to the information contained in the nodes and edges in the time-expanded network;

[0084] Based on the multi-commodity logistics network model, according to the information contained in the nodes and edges in the partial time expansion dynamic network model, the hierarchical graph structure is transformed into a multivariable mixed integer optimization mathematical equation. According to the specific mission scenario of constellation deployment, equations, inequality constraints and optimization objectives are set, and the variables to be optimized are the number of satellites and carriers at each spatial position and time.

[0085] In a possible implementation, the equality constraints of the mathematical equation include: conservation of satellite transfer volume of network nodes; and the inequality constraints of the mathematical equation include: satellite capacity of each node and carrier availability. Figure 3 A schematic diagram of a mathematical equation fitting curve provided in an embodiment of the present invention. Figure 3 It is expressed as constructing an efficiency function to evaluate the efficiency values ​​of all intermediate deployments of the constellation, namely U(k). Multiple intermediate deployment configurations are randomly generated for the target constellation, and the intermediate deployment efficiency evaluation function is fitted with the deployment percentage of each intermediate deployment configuration as the independent variable and the global coverage as the dependent variable.

[0086] The utility function is a measure of the performance level of a constellation. In the construction of the utility function, considering that the goal of this model is global broadband service, the global coverage percentage is used as the performance indicator. In the study, a simulation platform based on STK11+Python is developed to evaluate the impact of different satellite configurations on ground coverage. For satellite objects, a two-body orbit prediction model is used for orbit propagation.

[0087] To simulate the Walker constellation, the number of satellite planes (num_planes) and the number of satellites per plane (sats_per_plane) are defined, and the constellation parameters are configured through the Connect command of STK. In addition, corresponding sensor objects are generated for each satellite to simulate its observation capabilities.

[0088] Before conducting coverage analysis, a portion of satellites are randomly selected as intermediate deployment configurations to explore the impact of different deployment strategies on coverage. A new coverage definition object is created, and the boundary type and grid resolution of the custom area are set to precisely control the granularity of the coverage analysis. By adding the selected satellite sensors to the asset list for coverage analysis, the ground coverage under a specific configuration can be calculated and analyzed. The coverage results of some configurations are shown in Table 1.

[0089] Table 1

[0090]

[0091]

[0092] For the regression-based utility function construction, the percentage coverage of the partially deployed constellation is evaluated. The minimum elevation angle for calculating the instantaneous coverage is assumed to be 55 degrees. 145 partial configurations of the target constellation are randomly generated and their global percentage coverage is evaluated using numerical simulations. The assumed regression model (logarithmic) is convex and monotonically increasing. The following table gives the regression formula for simulating the proportion of deployed satellites (n≡N / NT), while the figure shows the regression results. Table 2 below shows the effectiveness of the regression model through the goodness of fit (R2).

[0093] Table 2

[0094]

[0095] S5, solve the dual-channel logistics network model according to the mathematical equations to obtain the optimal launch deployment plan for the satellite constellation.

[0096] The dual-channel logistics network model is connected to the corresponding algorithm framework for solution, and the launch deployment schedule information of each satellite is output, thereby establishing the optimal launch deployment plan for the satellite constellation to achieve the goals of minimizing the constellation construction cost and maximizing the cumulative efficiency. Figure 6 Schematic diagram of each satellite mission window provided by an embodiment of the present invention. The horizontal axis is time, the vertical axis is the satellite launch mission number, the dark color represents the satellite waiting time on the ground, and the light color represents the satellite in-orbit operation time.

[0097] In one example, Figure 6One of the drawn data is: 3863.7113066666666,,[source_1,623,source node,(34.7,-120.6),001,738.4,waiting layer,(34.7,-120.6),001,740.03333333333333,route layer,(7771.0,10.0),T2,740.63333333333333,waitinglayer,(7771.0,10.0),sink_1,713,sink node,(7771,0.0)],416.

[0098] 3863.7113066666666 is the total weighted satellite launch cost and satellite time cost. The information of each node is in brackets. Four nodes form a group, which are node code, time from mission zero, node type or network layer, and geographical location (latitude and longitude for launch site, and orbital altitude and right ascension of orbital node). The number after the brackets is the number of nodes traversed to find the path. Finally, the satellite deployment decision process is obtained, for example, satellites 1, 3, 4, and 7 are used for direct launch, and satellites 2, 5, and 6 are used for indirect launch. The visualization results of multiple plotted data are as follows. Figure 6 Since some processes are too short to be reflected, they are simplified into the launch waiting phase and the on-orbit maneuvering phase.

[0099]

[0100] Where l and L are orbital indices, s and S are satellite indices, v and V are vehicle indices, a and A are the underlying network arc sets, and U k (n) is the performance evaluation of the constellation at time k, is the flow situation of node i, k ij is the arc flow capacity between nodes i and j, u s Produce source nodes for satellite s, is the satellite s transmitting node, Δt i,j is the time difference between time node i and time node j, is the decision variable for launching vehicle v to orbit l at time k, The launch cost for launching vehicle v into orbit l, To reach orbit l satellite development costs, Storage fees for satellites, is the number of satellites carried by carrier v launched into orbit l at time k.

[0101] The present invention defines two optimization objectives, namely, minimizing the cost and maximizing the mid-term deployment efficiency of the satellite constellation, wherein is the decision variable for launching a vehicle v to the target orbit l at time k, x represents the number of satellites carried by each vehicle, Represents the manufacturing cost of each satellite.

[0102] Assuming it is proportional to the weight of the satellite, It represents the storage cost of the satellite per unit time. The time here is defined as the time from the source node to the launch site node, that is, the time from the completion of satellite development to the preparation for launch.

[0103] In summary, the satellite deployment cost can be summarized as three parts: vehicle launch cost, development cost, and satellite manufacturing cost. The second optimization goal is the utility function, which requires the maximum cumulative benefit of the constellation in the intermediate deployment. Therefore, a function is established to evaluate the constellation efficiency at each time and integrate it in the time dimension.

[0104] In one possible implementation, the optimal launch deployment plan for a satellite constellation includes basic decision nodes and corresponding event nodes. Taking into account that there is a phase adjustment stage before the satellite enters the final orbit, in order to better characterize the entire process of satellite constellation deployment, the basic decision nodes include: carrier launch nodes and satellite orbit transfer maneuvering nodes; the corresponding event nodes include: satellite storage nodes, satellite phase adjustment nodes and satellite end-of-life nodes.

[0105] (1) Decision Node Formulation

[0106] Regarding the decision-making node formulation problem, according to Cornara's division of the entire satellite constellation deployment cycle, the event launch node, orbit transfer node and satellite scrapping node are divided.

[0107] The decision node event information can be obtained by solving the model. The corresponding event node time information is determined by the decision node and the satellite and carrier-related performance indicators. For the dual-channel model, during the constellation deployment, the satellite can be injected through two launch methods: direct launch and indirect launch, and the corresponding node series are also different. As the satellite orbit zero time node, the launch node is allocated according to the launch interval of the carrier and the right ascension of the orbital ascending node and the launch site.

[0108] (1) Satellite storage node

[0109] Under the pulsating satellite production method, the cost incurred during the storage and launch of the satellite after it is manufactured is an important part of the satellite constellation deployment project. Once the satellite is manufactured, it enters the storage phase, during which there will be continuous storage costs, including but not limited to safety, environmental control and regular maintenance costs. These cost factors have a direct impact on the economic benefits of the entire project.

[0110] (2) Launch vehicle node

[0111] The launch waiting time refers to the length of time from when the launch is ready to when the launch window opens. In order to save fuel and reduce costs, coplanar launch is used for all launch orbits. For the launch timing of a fixed point, on the one hand, the launch point is required to pass through the specified orbital plane, that is, to meet the plane window condition. On the other hand, after the satellite is launched into orbit, it needs to fly over the target area at a specified time, that is, to meet the phase window condition. Based on the knowledge of spacecraft orbital dynamics and spherical geometry, the angular velocity of the earth's rotation relative to the satellite orbital plane can be expressed as:

[0112] Among them, is the angular velocity of the Earth's rotation, is the drift rate of the ascending node's longitude caused by orbital perturbations, is the J2-term harmonic coefficient of the Earth's gravitational potential function, is the Earth's equatorial radius, is the orbit's semi-major axis, is the Earth's gravitational constant, and n is the average angular velocity of the orbit: The plane window condition requires that the satellite's orbital plane passes through the ground launch site at the launch time. Figure 8 As shown in the figure, according to the plane window condition, in the Earth Centered Fixed Coordinate System (ECEF), the launch waiting time is equivalent to the time required for the launch site L to move to the point at an angular velocity. Assuming that the satellite orbital plane passes through the launch site at the current moment, the relationship between the longitude of the ascending node of the orbital plane at the launch moment and the ground launch site is shown in the figure.

[0113] (3) Satellite orbit maneuver transfer node

[0114] There are two ways to change the satellite orbit: direct maneuvering and indirect orbit change using J2 perturbation. Direct maneuvering has a short response time but consumes more fuel. Indirect orbit change using J2 perturbation reduces costs as much as possible. The right ascension drift of the orbital ascending node caused by J2 orbit perturbation makes two orbits with the same orbital inclination in the same plane, thereby achieving in-plane Hohmann transfer and saving fuel consumed by satellite lateral maneuvers. The transfer node is calculated according to the J2 perturbation transfer strategy, and the precession rate of each orbital ascending node is calculated as follows:

[0115]

[0116] In addition, to calculate the transit window, we also need to solve the transit time. Assuming that the satellite uses Hohmann transfer as its in-plane transfer strategy, the interval between the first and second ignitions is used as its transit time:

[0117]

[0118] Among them, R g is the equatorial radius of the Earth, J2 is its second-order directional harmonic coefficient. a, e, i, n are the semi-major axis, eccentricity, inclination and average rotation speed of the Earth. i and r jRepresent the radii of the parking orbit and the target orbit respectively, and u is the earth's gravitational constant. In the model, the time of the ascending nodes of the two orbits is calculated by the formula, and the transfer window from the parking orbit to the target orbit is determined in combination with the Hohmann transfer formula, thereby determining the transfer node from orbit j∈J to orbit i∈I. The above two formulas are combined to obtain the satellite orbit transfer maneuver time.

[0119] (4) Satellite phase adjustment node

[0120] In addition, in the mode of launching multiple satellites with one rocket, the first satellite in the same orbital plane enters orbit directly after separation from the carrier, and the other satellites need to implement corresponding phase adjustments to enter the operating orbit. This requires additional resources to control the final position of the satellite. In this model, the Hohmann transfer strategy is used to adjust the phase of the satellite. After the satellite separates from the carrier and reaches the phase adjustment maneuver point, an orbit change maneuver is implemented to enter the transfer orbit. The period of the transfer orbit is greater than or less than the period of the satellite's operating orbit. After the satellite has run several circles in the transfer orbit and reached the phase adjustment position condition, it maneuvers again to re-enter the operating orbit to achieve phase adjustment. When the transfer orbit period is less than the operating orbit, it is called forward adjustment, and when the transfer orbit period is greater than the operating orbit period, it is called backward adjustment. The phase adjustment diagram under the Hohmann transfer strategy is shown in Figure 9.

[0121] In the same orbital plane of the Walker constellation, the satellites are evenly distributed along the latitude depression angle. Let the latitude depression angle of satellite No. 1 and the number of satellites deployed in the orbital plane in the same orbital plane be taken as design variables. Then the phase adjustment required for satellite No. k is:

[0122]

[0123] The time cost and deployment cost required for phase adjustment under the Hohmann transfer strategy are:

[0124]

[0125] Among them, T sat is the orbit period, and is the number of phase modulation orbit flight circles. Obviously, the longer the satellite runs on the phase modulation orbit, the higher the phase modulation loss time and deployment cost. In order to reduce the deployment cost and achieve fast and low-cost deployment, the flight time of the satellite phase modulation process should be minimized. Therefore, N0 is set to 1 here.

[0126] In a possible implementation, the method further includes:

[0127] Determine the launch node of the vehicle based on the influence of the Earth's rotation and J2 orbital perturbation on the orbital ascending node;

[0128] The launch time window Δt of the vehicle is calculated according to the following formula:

[0129]

[0130] Among them, n is the average number of times the satellite orbits the earth in a unit time, p is the semi-path of the orbit, R e is the radius of the earth, θ is the inclination of the orbit, and J2 is the secondary gravitational field coefficient of the earth.

[0131] In a possible implementation, the method further includes:

[0132] Under the J2 perturbation force, the parking orbit and the target orbit are transferred coplanarly to determine the satellite orbit transfer node;

[0133] The precession angular velocity ω of each orbit is calculated according to the following formula p :

[0134]

[0135] Among them, ω p is the orbital precession angular velocity, a is the semi-major axis of the orbit, n is the average number of circles the satellite orbits the earth per unit time, R e is the radius of the earth, θ is the inclination of the orbit, and J2 is the secondary gravitational field coefficient of the earth.

[0136] In a possible implementation, the method further includes:

[0137] Determine the event node of the satellite orbit transfer node according to the Hohmann rotation;

[0138] The orbital period T is calculated according to the following formula:

[0139]

[0140] Where T is the orbital period, r i is the radius of the parking orbit, r j is the radius of the target orbit, i is the parking orbit code, j is the target orbit code, and μ is the standard gravitational parameter.

[0141] The following is a simulation experiment for the optimal launch deployment plan of a low-orbit communication satellite constellation. The process is as follows:

[0142] Step 1: Given a large-scale low-orbit constellation, satellites and launch vehicle related parameters.

[0143] This example sets a parking orbit constellation and a target orbit constellation, two types of vehicles, the main vehicle and the auxiliary vehicle, and a type of communication satellite, and its related parameters are shown in Tables 3 and 4. In order to normalize the time, mass, and cost data to the same order of magnitude, MU (mass unit) = 150 kg, CU (cost unit) = 1,000,000 US dollars, and TU (time cost) = 30 solar days.

[0144] Table 3

[0145]

[0146] Table 4

[0147]

[0148] Step 2: Take each orbit and virtual launch site as a node, and establish corresponding edges between nodes to simulate the satellite transportation path to establish a static network with topological structure. Traverse all possible paths according to the launch interval of the carrier and orbital mechanics and strategy to establish a time expansion network. Formulate the XML file structure according to the problem requirements and actual launch deployment. Figure 7 A schematic diagram of the XML file structure of a time extension network provided in an embodiment of the present invention.

[0149] Among them, the static network defines the underlying traffic topology network:

[0150] Nodes: defines nodes in the network, which can be ground stations or satellites. Ground stations use the launch site latitude and longitude originX and originY attributes to define their location, while satellite nodes use a series of orbital parameters (such as semi_major_axis, eccentricity, incllination, etc.) to describe their orbital characteristics.

[0151] Links: Defines the connections between nodes, including connection properties such as length, freespeed (to simulate path congestion when deploying at high spatial density), capacity, one-way or two-way, and modes.

[0152] The time-extended network structure represents a vehicle schedule (transitSchedule), which contains multiple launch routes (transitRoute). Each launch route defines the vehicle type and launch mode (transportMode), route traversal node information (routeProfile), specific route (route) and launch time (departures).

[0153] transitRoute: represents a specific route and has a unique ID.

[0154] transportMode: Indicates the carrier used for this route, for example "primary".

[0155] routeProfile: describes the detailed stop information of the route, including the reference ID (refId), arrival offset (arrivalOffset), and departure offset (departureOffset) of each stop.

[0156] route: defines the specific links of the route, each link is identified by a reference ID (refId).

[0157] departures: Lists all vehicle launch times for the route. Each vehicle launch mission time includes a unique ID, the specific vehicle launch time (departureTime), and the vehicle reference ID used (vehicleRefId).

[0158] Step 3: Actually input constellation parameters, vehicle, satellite related configuration and launch site to create relevant orbit objects and vehicle, satellite objects and establish corresponding databases; Generate each space node and inter-node links based on orbit information and launch site information to establish the underlying static network;

[0159] The launch window calculation under the J2 perturbation is performed: for the indirect launch mode orbit, the satellite maneuvering window calculation under the J2 perturbation coplanar strategy and the maneuvering time calculation under the Hohmann transfer strategy are performed, where the coplanar strategy under the J2 perturbation is calculated by ω p The maneuvering time of the Hohmann transfer strategy is obtained by T, and finally the phase transfer time under the feedforward phase transfer strategy is obtained. The phase transfer time is obtained, and the calculation completes the preparation work for the time expansion network generation.

[0160] Step 4: Considering the different cost generation methods of different processes in the deployment task and the silent state description requirements when the carrier and satellite are maintaining their status, the route layer and waiting layer are generated. The route layer generates corresponding arcs and arc time costs, deployment costs, and arc types according to the preliminary preparation data and node types. The XML file is traversed to capture the silent state of each object, and all related nodes (s, t, r) are copied to the waiting layer to link the related time nodes for the waiting layer nodes (s, t) to generate the waiting layer. Finally, the silent state related time nodes and the corresponding time nodes of the route layer are linked with state transition arcs, and the time expansion network is generated.

[0161] Step 5: According to the combination of STK11 and Python3, 200 satellite constellation intermediate deployment configurations are randomly generated to calculate the efficiency function. The efficiency function optimization goal is to improve the global coverage. The simulation condition is a grid with a resolution of 6°×6°. The simulation configuration parameters are summarized in Table 3: Table 3 According to the global coverage rate under each configuration, the performance function is fitted by polynomial fitting method as follows: Figure 3 .

[0165] Step 6: Connect to the low-orbit large-scale constellation launch deployment solution algorithm framework to generate each satellite mission window, thereby realizing the formulation of the launch deployment strategy for the entire satellite constellation.

[0166] The deployment method of a large-scale low-orbit satellite constellation provided by the present invention can effectively guide the formulation of a satellite optimal launch deployment plan and improve the efficiency and effectiveness of constellation deployment. This method not only optimizes the deployment cycle and reduces costs, but also improves the adaptability of the launch mission, so that it can better cope with uncertain launch windows and changing mission requirements. By extending the traditional static network model to a dynamic model including a time dimension, the present invention can more accurately simulate and predict various dynamic behaviors in the satellite launch and deployment process, thereby improving the controllability and predictability of the entire deployment process. In addition, the time dimension expansion method of realizing each time-state node according to the satellite path is adopted, which can not only fully describe the transfer strategy of each satellite at different positions and times, but also effectively avoid the problem of geometric growth of the number of optimization variables over time. In addition, the present invention uses a dual-channel logistics network model to provide an accurate mathematical description for satellite deployment, so that resource allocation and traffic management in the deployment process are more efficient and accurate. The application of the present invention is not limited to satellite launch, but can also be extended to other types of space missions, such as space station construction and space exploration missions, providing new tools and methods for the planning and execution of these missions.

[0167] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for deploying a large-scale low-orbit satellite constellation, characterized in that: include: S1, establish a static network of launch deployment with each orbit and launch site as nodes and satellite transportation paths between the nodes as edges; The network edge includes non-time dimension information of each node; S2, based on the static network, traverse all possible paths according to the launch interval time of the carrier and the orbital dynamics to obtain a time extension network; S3, obtaining a parking track and a target track, and constructing a dual-channel logistics network model according to the parking track and the target track; S4, based on the dual-channel logistics network model, establishing a multivariable mixed integer optimal mathematical equation according to the information contained in the nodes and edges in the time-expanded network; S5, solving the dual-channel logistics network model according to the mathematical equation to obtain the optimal launch deployment plan for the satellite constellation.

2. The deployment method according to claim 1, characterized in that: The equality constraints of the mathematical equation include: conservation of network node satellite transfer volume; The inequality constraints of the mathematical equation include: satellite capacity and vehicle availability at each node.

3. The deployment method according to claim 1, characterized in that: The time extension network includes a time layer and a network arc segment; The time layer includes: a route layer and a waiting layer; The network arc segments include: access arc segments, exit arc segments, state transition arc segments, path arc segments and waiting arc segments.

4. The deployment method according to claim 3, characterized in that: The route layer includes: time arcs and time nodes extended from the static network; Wherein, each of the time nodes is uniquely identified as a tuple by time, space, and path information; All time nodes in the same route are arranged in chronological order, and adjacent nodes are connected by time arcs.

5. The deployment method according to claim 3, characterized in that: The entry arc segment includes: a source node and a path entry node; The source node represents the moment when the satellite is manufactured and put into storage. It is connected by accessing the arc segment and the launch time node to store the time cost information and deployment cost information from storage into storage to satellite-rocket integration and launch after the satellite is developed and completed.

6. The deployment method according to claim 3, characterized in that: The exit arc segment includes: a sink node and a time-state node of the satellite entering the target orbit; The sink node indicates the satellite phase adjustment completion state, and the arc segment stores the time cost and deployment cost information required for satellite phase adjustment.

7. The deployment method according to claim 1, characterized in that: The optimal launch deployment scheme for the satellite constellation includes basic decision nodes and corresponding event nodes; The basic decision nodes include: a vehicle launch node and a satellite orbit transfer maneuver node; The event nodes include: a satellite storage node, a satellite phase adjustment node and a satellite end-of-life node.

8. The deployment method according to claim 7, characterized in that: Also includes: Determine the launch node of the vehicle based on the influence of the Earth's rotation and J2 orbital perturbation on the orbital ascending node; The launch time window Δt of the vehicle is calculated according to the following formula: Among them, n is the average number of times the satellite orbits the earth in a unit time, p is the semi-path of the orbit, and R e is the radius of the earth, θ is the inclination of the orbit, and J2 is the secondary gravitational field coefficient of the earth.

9. The deployment method according to claim 7, characterized in that: Also includes: Under the J2 perturbation force, the parking orbit and the target orbit are transferred coplanarly to determine the satellite orbit transfer node; The precession angular velocity ω of each orbit is calculated according to the following formula p : Among them, ω p is the orbital precession angular velocity, a is the semi-major axis of the orbit, n is the average number of circles the satellite orbits the earth per unit time, R e is the radius of the earth, θ is the inclination of the orbit, and J2 is the secondary gravitational field coefficient of the earth.

10. The deployment method according to claim 7, characterized in that: Also includes: Determine the event node of the satellite orbit transfer node according to the Hohmann rotation; The orbital period T is calculated according to the following formula: Where T is the orbital period, r i is the radius of the parking orbit, r j is the radius of the target orbit, i is the parking orbit code, j is the target orbit code, and μ is the standard gravitational parameter.

Images