A method for deploying large-scale low-orbit constellations based on multi-level space logistics supply

Abstract

The present invention relates to the field of constellation deployment technology, and specifically discloses a low-orbit large-scale constellation deployment method based on multi-level logistics supply in space. A comprehensive probability model of random events is constructed according to the influence of random events during satellite launch; a multi-level logistics supply model is constructed according to the characteristics of the multi-level supply chain of logistics and the characteristics of the multi-level network of satellite deployment to obtain the constellation deployment time; the constellation deployment time is discretized into multiple time segments by combining the time extension network method, and the comprehensive probability model of random events is connected to the time segments to construct a multi-level logistics constellation deployment model considering the time extension network under the triggering of random events, and the dynamic process of constellation deployment is converted into a static time extension network; a mixed integer programming model of large-scale constellation deployment is constructed according to the static time extension network, and a solution is performed to complete the low-orbit large-scale constellation deployment based on multi-level logistics supply in space.

Description

Technical Field

[0001] The present invention relates to the technical field of constellation deployment, and in particular to a low-orbit large-scale constellation deployment method based on multi-level space logistics supply. Background Art

[0002] Low-orbit satellites operate at a high speed, and a large number of satellites are required to form a constellation for continuous coverage. However, the space resources in the near-Earth orbit are very limited, and the number of large-scale low-orbit constellations is large, which involves huge costs. It is necessary to formulate a comprehensive strategy for the effective deployment, operation, maintenance and deorbit disposal of satellites in the constellation. Due to factors such as satellite production, manufacturing and testing, rocket launch capabilities and economic support, it is difficult for constellations to complete deployment and construction in a short period of time. Most constellations require several years or even more than ten years to complete the final deployment. Therefore, it is necessary to consider the trend of constellation scale and competitiveness in this field. Satellite deployment must be considered at the beginning of the design because satellite deployment has an important impact on life cycle costs. Satellite deployment affects both the number of launches and the complexity of the satellites to be launched. In the process of constellation deployment, the traditional deterministic deployment mechanism will be subject to certain limitations due to factors such as satellite launch sequence, satellite launch success rate, satellite launch delay and random failures. Therefore, it is urgent to provide a suitable deployment strategy for the deployment of large-scale constellations. Summary of the invention

[0003] In view of the above problems, the purpose of the present invention is to provide a method for deploying a large-scale constellation in low orbit based on multi-level space logistics supply, and to determine the deployment strategy of the optimal rocket launch sequence, satellite deployment sequence, and satellite orbit transfer scheme, so as to ensure technical feasibility and economic feasibility.

[0004] The technical solution adopted by the present invention is: a low-orbit large-scale constellation deployment method based on space multi-level logistics supply, comprising:

[0005] Step S01: constructing a comprehensive probability model of random events according to the impact of random events on the satellite launch process;

[0006] Step S02: construct a multi-level logistics supply model based on the characteristics of the multi-level logistics supply chain and the characteristics of the multi-level satellite deployment network, simulate the satellite deployment channel of a large-scale constellation, and use it to obtain the constellation deployment time;

[0007] Step S03: Discretize the constellation deployment time into multiple time segments in combination with the time extension network method, connect the comprehensive probability model of random events to the time segments, and construct a multi-level logistics constellation deployment model considering the time extension network under the triggering of random events, so as to transform the dynamic process of constellation deployment into a static time extension network;

[0008] Step S04: construct a mixed integer programming model for large-scale constellation deployment according to the static time extension network, take the minimum constellation deployment cost and the shortest constellation deployment time as the objective function, solve the mixed integer programming model for large-scale constellation deployment according to constraints and the NSGA-II algorithm, and complete the low-orbit large-scale constellation deployment based on space multi-level logistics supply.

[0009] Preferably, the comprehensive probability model of random events in step S01 includes three random event probability models, and the three random event probability models are: a probability model of supply delay caused by limited satellite production capacity, a probability model of rocket launch delay and a probability model of satellite failure.

[0010] Furthermore, the comprehensive probability model of random events P(J) is:

[0011] ;

[0012] ;

[0013] ;

[0014] ;

[0015] Among them, P(C) is the probability of supply delay due to limited satellite production capacity, P(EF) is the probability of equipment failure, P(MS) is the probability of delayed raw material supply, P(LU) is the probability of labor shortage, P(L) is the probability of rocket launch delay, P(W) is the probability of launch delay due to weather reasons, P(GP) is the probability of launch delay due to government policies, P(E) is the probability of launch delay due to environmental factors, P(F) is the probability of satellite failure, P(SE) is the probability of satellite failure caused by the space environment, and P(R) is the probability of failure caused by the satellite's own reliability problems.

[0016] Further, in step S02, the deployment channel includes direct launch into orbit and indirect launch into orbit;

[0017] The direct launch into orbit is to launch the satellite directly into the working orbit;

[0018] The indirect launch into orbit is to launch the satellite into a parking orbit and then into a working orbit.

[0019] Preferably, the constellation deployment time includes direct launch into orbit deployment time and indirect launch into orbit deployment time.

[0020] Preferably, in step S03, the constellation deployment time is discretized into multiple time segments :

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] in, is the set of discretized time segments, is a discrete time index, The final time for deployment, The constellation deployment start time, The final time for the constellation deployment process, The temporal set of deployment processes for time-expanding networks is considered.

[0026] Furthermore, in step S04, the objective function for minimizing the constellation deployment cost is expressed as:

[0027] ;

[0028] Where N is the total number of launches performed by the constellation deployment mission, For in time k Towards Track The cost of a single satellite launched at launch, is the number of satellites launched this time, For in time k The recurring and operating costs of the launch vehicle at launch.

[0029] Preferably, in step S04, the objective function of the shortest constellation deployment time is expressed as:

[0030] ;

[0031] ;

[0032] Where N is the total number of launches performed by the constellation deployment mission, The time series number of each launch is is the corresponding emission time sequence, For the The time required to complete the deployment of the satellite launched once, This is a simplified sequence of deployment completion times for each satellite launch.

[0033] Preferably, in step S04, the constraints include launch availability constraints, carrying capacity constraints of each rocket, number of remaining satellites in parking orbit constraints, deployment time constraints and node network flow balance constraints.

[0034] Preferably, the step S04 further comprises: making assumptions on the mixed integer programming model of the large-scale constellation deployment to improve universality and reduce complexity.

[0035] Beneficial effects of the above technical solution:

[0036] The present invention provides a low-orbit large-scale constellation deployment method based on space multi-level logistics supply, which can determine the optimal rocket launch sequence, satellite deployment sequence and deployment strategy of satellite orbit transfer plan, thereby ensuring technical feasibility and economic feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a flow chart of a method for deploying a large-scale low-orbit constellation based on multi-level space logistics supply according to the present invention;

[0038] Figure 2 A schematic diagram of a constellation deployment network flow provided for an embodiment of the present invention;

[0039] Figure 3 A schematic diagram of a satellite deployment multi-level network space provided for an embodiment of the present invention;

[0040] Figure 4 A schematic diagram of a multi-level logistics supply model provided for one embodiment of the present invention;

[0041] Figure 5 A schematic diagram of satellite phased deployment provided for an embodiment of the present invention;

[0042] Figure 6 A schematic diagram of time segments for adding random events provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0043] The following is a further detailed description of the implementation methods of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than an exhaustive list of all the embodiments. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other without conflict.

[0044] The terms "first", "second", etc. (if any) in the specification and claims are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the terms used in this way are interchangeable where appropriate so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products, or devices.

[0045] It should be understood that the term "and / or" used in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0046] Embodiment 1

[0047] like Figure 1 The figure shows a flow chart of a method for deploying a large-scale constellation in low orbit based on multi-level space logistics supply provided by the present invention, including:

[0048] Step S01: Construct a comprehensive probability model of random events. The comprehensive probability model comprehensively considers the influencing factors of the three random event probabilities. The probability models are constructed according to the three random events: (1) Probability model of supply delay caused by limited satellite production capacity: considering that during the mass production of satellites, various factors may limit the satellite production capacity and cause supply delays; (2) Probability model of rocket launch delay: considering that during the satellite launch, the rocket launch is delayed due to weather and other related factors, affecting the launch sequence, frequency, success rate, etc. of the rocket; (3) Probability model of satellite failure: considering that after the satellite is launched, the satellite may fail during the process of climbing from orbit to the nominal orbit and after the satellite is in orbit, due to factors such as the space environment and the satellite's own reliability, the satellite may fail, causing the satellite to fail.

[0049] Step S02: Establish a multi-level logistics supply model. This model introduces the concept of logistics supply chain architecture into the supply and demand model under random events, combines the advantages of direct launch into orbit and indirect launch into orbit, abstracts the constellation deployment model into a multi-level logistics supply model, regards ground launch as a supplier, parking orbit and working orbit as retailers and customer groups respectively, and the two deployment methods are regarded as two supply channels. A multi-level logistics supply model is established to simulate the movement of various elements and resources in the low-orbit space supply chain network.

[0050] Step S03: Construct a multi-level logistics constellation deployment model considering time-extended networks under random event triggering. Combined with the random event model, the dynamic multi-level characteristics of the nodes and edges of the ground, parking tracks and working tracks in the supply chain network are comprehensively analyzed. Based on the method of time-extended networks and combined with the dynamic network flow model of the supply chain, a multi-level logistics constellation deployment model considering time-extended networks under random event triggering is constructed.

[0051] Step S04: Based on the multi-level logistics constellation deployment model considering the time-extended network under random event triggering, a mixed integer programming model for large-scale constellation deployment is established with the goal of minimizing deployment cost and time, and the model is solved using an optimization algorithm.

[0052] In this embodiment, the specific models in step S01 are:

[0053] S11: Probability model of supply delay caused by satellite capacity constraints

[0054] Assume that P(C) represents the probability of delayed supply due to satellite capacity constraints. It may be affected by many factors such as equipment failure, delayed raw material supply, and labor shortage. Assume that these factors are independent of each other. Then:

[0055] (1)

[0056] Among them, P(EF) is the probability of equipment failure, P(MS) is the probability of delayed raw material supply, and P(LU) is the probability of labor shortage.

[0057] The subtraction between the probabilities is to avoid double counting, and the product term represents the probability of these events occurring at the same time.

[0058] S12: Rocket launch delay probability model

[0059] Assume that P(L) is the probability of rocket launch delay. Rocket launch may be affected by factors such as weather and environment. Assume that these factors are also independent of each other. Then:

[0060] (2)

[0061] Among them, P(W) is the probability of launch delay caused by weather reasons, P(GP) is the probability of launch delay caused by guiding policies, and P(E) is the probability of launch delay caused by environmental factors.

[0062] S13: Satellite failure probability model

[0063] Assume that P(F) represents the probability of satellite failure. Satellite failure may be affected by factors such as the space environment and the satellite's own reliability. Assume that these factors are independent of each other. Then:

[0064] (3)

[0065] Among them, P(SE) is the probability of satellite failure caused by the space environment, and P(R) is the probability of failure caused by the satellite's own reliability problems.

[0066] S14: Comprehensive probability model of random events

[0067] The joint probability distribution is used to represent the probability of capacity limitation, launch delay and satellite failure occurring simultaneously. Assume that P(J) represents the combined probability of random events occurring simultaneously, and each event is independent of each other. Then:

[0068] (4)

[0069] In this embodiment, the specific step S02 includes:

[0070] Figure 2 The network flow diagram of constellation deployment shows two deployment methods: one is to launch directly from the ground into the working orbit, and the other is to launch from the ground into the parking orbit, and finally climb to the working orbit after adjustment. Figure 2 Specifically shown is: using To define a network graph with a set of nodes and a set of directed arcs. is the set of all nodes, is the set of all directed arcs. A collection of orbitals for constellation work, is the total number of working tracks; is the set of parking orbits, is the total number of parking orbits. is an ordered set of index pairs of feasible arcs related to two deployment modes, where A collection of launch vehicles for satellite launches, the total number of launch vehicles required to deploy the constellation; is an ordered set of index pairs of feasible arcs (transfer arcs) associated with track transfer. , the corresponding allocated satellite launch capacity is Similarly, the track capacity value of each working track is , the orbital capacity of each parking orbit is , orbital capacity of the parking orbit Can be considered as a parking orbit The launch cost of a rocket is associated with each directed arc connecting a ground node and an orbital node, expressed as .

[0071] Satellite deployment multi-level network space diagram Figure 3 As shown. Combined with the characteristics of the multi-level supply chain of logistics, the ground launch is regarded as a supplier, and the satellite is launched into the orbit by a carrier rocket. This stage is repeated until all satellites are sent into space. The heterogeneous optimal launch vehicle, launch location, date, payload for each opportunity and orbital entry orbit are unknown; the second-level parking orbit is regarded as a retailer. Its orbital altitude is generally lower than the working orbit, and its inclination is the same as the constellation working orbit plane. During the parking orbit stage, the satellite will be debugged; the third level is the working orbit, which is regarded as the customer base in the logistics system, that is, the final delivery party of the goods. The parking orbit can be transferred to the working orbit plane through orbital maneuvers to realize the delivery of goods. During the satellite launch process, the satellite can be launched directly from the ground into the working orbit, or it can be launched into the parking orbit and wait until the right time to enter the working orbit. These two deployment methods are regarded as two supply channels.

[0072] Construct a multi-level logistics supply model, as shown in the schematic diagram Figure 4 As shown. The satellite to be deployed can be directly launched into orbit through channel 1, that is, the direct channel directly supplies it to customers. It can also be indirectly launched into orbit through channel 2, that is, the indirect channel, where the satellite is first launched into a parking orbit, supplied to customers through retailers, and then put into a working orbit after a period of operation. It is assumed that the logistics supply adopts a dedicated delivery service, that is, a dedicated launch is used for deployment, and other launch methods such as carpooling or piggyback are not considered. Launch deployment through two supply channels can make the launch mission more flexible in terms of time and cost.

[0073] Using the altitude difference between the parking orbit and the working orbit, it is determined that the satellite is only affected by Under the action of perturbation, the precession rate of the parking orbital plane relative to the working orbital plane is:

[0074] (5)

[0075] Where: is the relative change rate of right ascension of the ascending node of the orbital plane, is the Earth's gravitational constant, is the track height difference, is the orbital inclination, is the average radius of the Earth.

[0076] The supply capacity of direct and indirect channels depends on the payload capacity and launch interval of the launcher. The supply of the transfer arc depends on the supply capacity of the indirect channel, the inventory level of the parking orbit, the configuration of the parking orbit constellation, and the propulsion system of the satellite. According to the steps in the deployment process, it can be divided into multiple deployment event nodes, including launch nodes and transfer nodes. The optimal strategy for the mission objective is to provide launch or transfer decisions at each decision node at the deployment level. The launch node is allocated according to the launch interval between consecutive launches of the launch vehicle; the transfer node handles the inflow and outflow of moving satellites on the transfer arc.

[0077] The constellation deployment time includes direct launch into orbit deployment time and indirect launch into orbit deployment time. The direct launch into orbit method is relatively simple, and the time required from ground launch to entering the working orbit is shorter, so the direct launch into orbit deployment time can be considered .

[0078] Determine the time for indirect launch and orbital deployment. The indirect orbital deployment method is a batch deployment of multiple satellites and multiple orbits with one rocket. The deployment includes three different stages: In the first stage, the satellite climbs from the orbit of entry (where the rocket and satellite separate) to the parking orbit waiting for transfer. If the right ascension of the ascending node of the parking orbit meets the conditions, it can directly climb to the working orbit; the second stage is called the parking waiting stage, because the altitude of this orbit is lower than the working orbit, Under the action of the perturbation, the right ascension of the ascending node drifts and accumulates over time until the right ascension of the ascending node meets the separation condition; the third stage involves the second maneuver. After the right ascension of the ascending node of the satellite orbit meets the separation condition, the satellite climbs from the parking orbit to the working orbit. Among them, the duration of the second stage directly affects the deployment time. Satellites launched in the same batch can achieve satellite orbital plane separation through the accumulation of the right ascension of the ascending node during this stage. In addition, depending on the parking orbit, the deployment time may be longer or shorter. The required time is:

[0079] (6)

[0080] (7)

[0081] In the formula, is the right ascension of the ascending node at the end of this phase, is the right ascension of the ascending node when the satellite first enters the parking orbit, for The time rate of change of the right ascension of the node under the perturbation action, for The difference in the rate of change of the right ascension of the ascending node of different orbits under the action of perturbation is , Represent the orbital altitudes of the parking orbit and the working orbit respectively.

[0082] To better illustrate this deployment process, we will use examples as follows: Figure 5 The satellite deployment diagram is shown in the figure. , and They are the orbital heights of the rocket-satellite separation, parking orbit, and working orbit. Assuming that the satellites launched by the same batch of rockets need to be deployed to three orbital planes, the batch of satellites is divided into three groups. When the satellites climb to the parking orbit, the right ascension of the ascending node meets the orbital climbing conditions, then the first group of satellites will directly climb; the second and third groups of satellites will wait in the parking orbit. During this period, the satellites will use The ascending node right ascension drifts by perturbation; the second group of satellites climbs when they meet the orbit climbing conditions, and the third group continues to wait in the parking orbit until the ascending node right ascension meets the climbing conditions before starting to climb. The total deployment time is the sum of the three stages, which is:

[0083] (8)

[0084] in, and The satellite's climbing time and the corresponding relationship between the climbing time and the climbing height are calculated as follows:

[0085] (9)

[0086] in, is the orbital altitude of the satellite’s ascent start point, is the track height at the end of the climb, is the mass of a single satellite, is the mass flow rate of satellite thrusters, is a constant, generally F represents the continuous small thrust that the satellite propulsion system can provide.

[0087] Duration of the second phase is the drift time of the remaining two groups of satellites, including two parts and , the solution is shown in equations (6) and (7), which can be simplified as follows:

[0088] (10)

[0089] In the formula, and are the right ascension of the ascending node of the corresponding orbital plane.

[0090] In this embodiment, step S03 is specifically as follows:

[0091] S31: Constellation deployment is a continuous dynamic process with time-varying characteristics. The deployment process is divided into multiple stages using the time extension network method, i.e., time discretization. Specifically, the deployment process is discretized into multiple time segments. , ,in, is the set of discretized time segments, is a discrete time index, is the final time of deployment, i.e. constellation deployment starts at , the satellite supply launch begins and ends at At this moment, all satellites enter the nominal orbit and the constellation deployment is completed, so the total deployment time is .

[0092] The time set of the time-expanding network deployment process is:

[0093] (11);

[0094] In the formula, It is the final time of the constellation deployment process, indicating that the constellation deployment is completed.

[0095] S32: Add a probability model of random events in each time segment and introduce random events into the multi-level logistics supply model. The schematic diagram of adding random events in each time segment is as follows: Figure 6 shown.

[0096] S33: It is used to transform the dynamic process of constellation deployment into a static time-extended network by replicating the nodes at each time step within a given time range.

[0097] S34: Based on the multi-level logistics model of large-scale constellations, complete the construction of a constellation deployment model for multi-level logistics considering time-extended networks under random event triggering.

[0098] In this embodiment, step S04 is specifically as follows:

[0099] S41: Based on the constellation deployment model of multi-level logistics considering time-extended network under random event triggering, a mixed integer programming model for large-scale constellation deployment is established according to each time segment, including defining decision variables, determining objective functions, and establishing constraints. Specifically:

[0100] (1) Define decision variables:

[0101] Allocation variables: The selection of each launch channel, that is, whether to choose a working orbit or a parking orbit when launching a satellite to each orbital node, is defined as:

[0102] { x = [ x l d ] x l d ∈ { 0 , 1 } (12)

[0103] in, The time index for the launch vehicle; It is the track node type in the network diagram, 0 is the working track and 1 is the parking track.

[0104] Loading variable: The number of satellites supplied by each launcher through the selected channel, which is a non-negative integer variable. Time launch vehicle supply to The number of satellites in an orbit is defined as:

[0105] y = [ y l d ] (13)

[0106] Transfer variable: transfer arc within a specific time The corresponding number of satellites flowing out or in is an integer variable defined as:

[0107] z = [ z j , i d , q + , z j , i d , q − ] (14)

[0108] in, is the satellite outflow, i.e. Moment, time Launching a satellite into parking orbit The outflow at the node, ; is the satellite inflow, i.e. Moment, time Launch into parking orbit Satellites flow into working orbit The number of nodes.

[0109] (2) Determine the objective function

[0110] Objective 1: Constellation deployment cost. Assume that the launch cost of the launch vehicle is the main consideration, and the manufacturing and propellant-related costs of the satellite are not considered. The constellation deployment cost model is constructed according to the following relationship:

[0111] (15)

[0112] in, For time k Towards Track The cost of a single satellite launched at launch, is the number of satellites launched this time, For time k The recurring and operating costs of the launchers at launch. Recurring costs often drive the solution to a smaller number of launchers, regardless of the number of payloads delivered.

[0113] Objective 2: Constellation deployment time. In order to quickly build a constellation network, provide services to users as soon as possible, and provide economic benefits, the deployment time of the constellation should be as short as possible. According to the deployment method, the deployment time is divided into two types: channel 1 direct launch into orbit and channel 2 indirect launch into orbit. Generally, the time required for direct launch into orbit deployment is shorter. Ignoring the time required for rocket launch, the time for direct launch into orbit deployment mainly considers the launch interval time. Assuming that the minimum interval between two consecutive rocket launches is ideally The indirect orbital deployment takes a long time. Assuming that the rocket directly sends the satellite into the parking orbit and ignores the launch orbit time, the indirect orbital deployment time required for a single batch of launch deployment is the sum of the parking orbit drift time and the climb time. The time required for a single batch of indirect orbital deployment is: ; The total deployment time is the time from the start of deployment to the moment when the last satellite enters the working orbit Assume that the minimum time interval between two consecutive launches of the launch vehicle is ,when When the previous batch of satellites has not yet been deployed, the next batch can be launched. Considering factors such as satellite capacity constraints, launch failures and delays, the launch interval will increase, assuming ,but: (16)

[0114] In the formula, There is a time delay due to limited satellite capacity.

[0115] Assuming the constellation deployment has been cumulatively The total duration of the transmission is , each launch has two possibilities: parking orbit and working orbit, through the decision variables Sure.

[0116] In order to facilitate time statistics analysis and calculate the total duration of constellation deployment, the present invention numbers the launch sequence based on the time series method. Assuming that the constellation deployment task performs N launches in total, the time series numbers of each launch are , the corresponding emission time sequence is , the time interval is Assume that The time required to complete the deployment of the satellite launched is , then the deployment completion time sequence of each satellite launch is , when the direct-to-orbit launch method is adopted ( ),but , indicating that the deployment of this batch of satellites was completed at the moment of launch.

[0117] make The time is 0, using the time interval The deployment completion time sequence is further simplified as:

[0118] (17)

[0119] Therefore, according to the constellation satellite deployment completion time sequence, the total duration of constellation deployment can be obtained as:

[0120] (18)

[0121] (3) Establishing constraints

[0122] Launch availability constraint: A launch vehicle cannot be launched more than once at a time.

[0123] (19)

[0124] In the formula, Time index for rocket launch; It is an orbital node; each rocket can only launch a satellite to one orbit and can only launch it once at most.

[0125] Rocket carrying capacity constraint: The number of satellites launched each time cannot exceed the rocket’s carrying capacity. Figure 3 In the above figure, the flow rate of an arc cannot exceed the capacity of the arc.

[0126] (20)

[0127] In the formula, For launch time Launch vehicle to The number of satellites transported by the orbital node is the commodity flow on the arc in the logistics network diagram.

[0128] Constraints on the number of remaining satellites in parking orbits: The number of satellites launched into each parking orbit cannot be greater than the satellite capacity of the corresponding orbit; relative to logistics supply, the number of purchases by retailers cannot be greater than their own inventory capacity.

[0129] (twenty one)

[0130] In the formula, For the moment Parking track The number of satellites in operation, The orbital capacity for each parking orbit.

[0131] Deployment time constraint: The time for constellation deployment should be less than the deadline of the deployment plan.

[0132] (twenty two)

[0133] In the formula, Deployment time for constellation missions, The deadline planned for the deployment.

[0134] In addition to the above inequality constraints, the following constraints must also be met according to the logistics network diagram:

[0135] Node network flow balance constraint: also known as flow conservation constraint, which requires that at any time, the sum of all outflows of satellites in the intermediate node parking orbit must be equal to all inflows (in the generalized commodity flow model, the inflow is a non-negative value and the outflow is a non-positive value).

[0136] (twenty three)

[0137] In the formula, For satellites passing through the transfer arc From parking orbit To the working track The outflow, superscript The time information of the satellite and the Storage duration on Time ); express The number of satellites assigned to the parking orbit by the launch vehicle at any given moment.

[0138] exist At this moment, the cumulative sum of satellite outflows in each transfer arc (feasible outflow) must also satisfy:

[0139] (twenty four)

[0140] In the formula, For time Launched into parking orbit Satellites at time This value can be used to evaluate the parking orbit The remaining satellite volume is the retailer's inventory level of the product.

[0141] Similarly, in the transfer arc At the end of the transfer arc, the total cumulative inflow of the satellite within a certain period of time must satisfy:

[0142] (25)

[0143] In the formula, For in time The satellite transferred into orbit, at time Arrival working track The total number of satellites.

[0144] Working track The total number of satellites ultimately deployed should be equal to the demand for the corresponding orbits.

[0145] (26)

[0146] Finally, the number of satellites launched into all orbits should be equal to a predetermined value.

[0147] (27)

[0148] In addition, when the satellite meets the transfer conditions for the ascending node right ascension of the parking orbit, it enters the transfer phase and begins to climb.

[0149] S42: Deployment model related assumptions.

[0150] In order to improve the versatility of the proposed large-scale constellation deployment model and reduce its complexity, ideally, the following assumptions are made for the deployment model:

[0151] The payloads carried by all launch vehicles are deployment mission constellation satellites, and other launch situations such as carpooling are not considered.

[0152] Based on the current deployment of Starlink and OneWeb constellations, large-scale constellations can be deployed within the life cycle of satellites.

[0153] Ignore the energy loss problems of station-keeping maneuvers and anti-interference during orbit transfer.

[0154] It is assumed that the satellite orbit delay time is included in the parking orbit waiting for the ascending node right ascension drift time.

[0155] Other mechanical model assumptions involved in the deployment process, as well as random event probability model assumptions.

[0156] S43: Considering the two objectives of cost and time, it is more appropriate to use a multi-objective optimization algorithm to solve it. The NSGA-II algorithm is used as the solution algorithm for the mixed integer programming model of large-scale constellation deployment to solve it.

[0157] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not limitations on the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made on the basis of the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the protection scope of the present invention.

Claims

1. A method for deploying a large-scale low-orbit constellation based on multi-level space logistics supply, characterized in that: include: Step S01: constructing a comprehensive probability model of random events according to the impact of random events on the satellite launch process; Step S02: construct a multi-level logistics supply model based on the characteristics of the logistics multi-level supply chain and the characteristics of the satellite deployment multi-level network, simulate the satellite deployment channel of a large-scale constellation, and use it to obtain the constellation deployment time; Step S03: Discretize the constellation deployment time into multiple time segments in combination with the time extension network method, connect the comprehensive probability model of random events to the time segments, and construct a multi-level logistics constellation deployment model considering the time extension network under the triggering of random events, so as to transform the dynamic process of constellation deployment into a static time extension network; Step S04: construct a mixed integer programming model for large-scale constellation deployment according to the static time extension network, take the minimum constellation deployment cost and the shortest constellation deployment time as the objective function, solve the mixed integer programming model for large-scale constellation deployment according to constraints and the NSGA-II algorithm, and complete the low-orbit large-scale constellation deployment based on space multi-level logistics supply.

2. The method for deploying a large-scale low-orbit constellation based on multi-level space logistics supply according to claim 1, characterized in that: The comprehensive probability model of random events in step S01 includes three random event probability models, and the three random event probability models are: a probability model of supply delay caused by limited satellite production capacity, a probability model of rocket launch delay, and a probability model of satellite failure.

3. The method for deploying a large-scale low-orbit constellation based on multi-level space logistics supply according to claim 1, characterized in that: The comprehensive probability model of random events P(J) is: P(J)=P(C)·P(L)·P(F) P(C)=P(EF)+P(MS)+P(LU)-P(EF)·P(MS)-P(EF)·P(LU) -P(MS)·P(LU)+P(EF)P(MS)·P(LU) P(L)=P(W)+P(GP)+P(E)-P(W)·P(GP)-P(W)·P(E) -P(GP)·P(E)+P(W)·P(GP)·P(E) P(F)=P(SE)+P(R)-P(SE)·P(R); Among them, P(C) is the probability of supply delay due to limited satellite production capacity, P(EF) is the probability of equipment failure, P(MS) is the probability of delayed raw material supply, P(LU) is the probability of labor shortage, P(L) is the probability of rocket launch delay, P(W) is the probability of launch delay due to weather reasons, P(GP) is the probability of launch delay due to government policies, P(E) is the probability of launch delay due to environmental factors, P(F) is the probability of satellite failure, P(SE) is the probability of satellite failure caused by the space environment, and P(R) is the probability of failure caused by the satellite's own reliability problems.

4. The method for deploying a large-scale low-orbit constellation based on multi-level space logistics supply according to claim 1, characterized in that: In step S02, the deployment channel includes direct launch into orbit and indirect launch into orbit; The direct launch into orbit is to launch the satellite directly into the working orbit; The indirect launch into orbit is to launch the satellite into a parking orbit and then into a working orbit.

5. The method for deploying a large-scale low-orbit constellation based on multi-level space logistics supply according to claim 1, characterized in that: The constellation deployment time includes direct launch into orbit deployment time and indirect launch into orbit deployment time.

6. The method for deploying a large-scale low-orbit constellation based on multi-level space logistics supply according to claim 1, characterized in that: In step S03, the constellation deployment time is discretized into multiple time segments t k : t k ∈T T={t1=0,…,t M =t f } k∈K={1,…,M} D={kk∈K,t k ≤t f }; Where T is the set of discretized time segments, k∈K={1,…,M} is the discrete time index, and t f is the final time of deployment, t1 is the start time of constellation deployment, D = {kk∈K,t k ≤t f } is the time set of the deployment process considering the time expansion network.

7. The method for deploying a large-scale low-orbit constellation based on multi-level space logistics supply according to claim 6, characterized in that: In step S04, the objective function for minimizing the constellation deployment cost is expressed as: Where N is the total number of launches performed by the constellation deployment mission, is the cost of launching a single satellite into orbit l at time k, is the number of satellites launched this time, is the recurring and operating cost of the launch device when launching at time k.

8. The method for deploying a large-scale low-orbit constellation based on multi-level space logistics supply according to claim 1, characterized in that: In step S04, the objective function of the shortest constellation deployment time is expressed as: △T=t i -t i-1 ; Where N is the total number of launches performed in the constellation deployment mission, {1,2,…,N} is the time series number of each launch, {t1,t2,…,t N } is the corresponding launch time sequence, △ti is the time required for the satellite deployment to be completed for the ith launch, This is a simplified version of the deployment completion time sequence for each satellite launch.

9. The method for deploying a large-scale low-orbit constellation based on multi-level space logistics supply according to claim 1, characterized in that: In step S04, the constraints include launch availability constraints, carrying capacity constraints of each rocket, number of remaining satellites in parking orbit constraints, deployment time constraints and node network flow balance constraints.

10. The method for deploying a large-scale low-orbit constellation based on multi-level space logistics supply according to claim 1, characterized in that: The step S04 also includes: making assumptions on the mixed integer programming model of the large-scale constellation deployment to improve universality and reduce complexity.

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