A Finite State Machine-Based Cooperative Service Allocation Method for Low-Earth Orbit Satellite Clusters

Abstract

This invention proposes a collaborative service allocation method for low-Earth orbit (LEO) satellite constellations based on finite state machines, belonging to the field of LEO satellite constellation technology. First, this invention constructs an extended finite state machine spatiotemporal graph model to accurately represent on-board resources and state transitions while shielding the dynamics of LEO satellites. Then, a directed acyclic graph (DAG) model is used to represent services, establishing a graph mapping relationship between the DAG and the extended finite state machine spatiotemporal graph, and establishing a latency optimization problem. Finally, a constrained selection adaptive binary particle swarm optimization algorithm is used to solve the latency optimization problem of the graph mapping relationship, finding the mapping strategy with the lowest latency to complete the collaborative service allocation of the satellite constellation. This invention is designed for LEO satellite constellation scenarios. The service collaborative computation based on finite state machines meets the computational requirements of latency-sensitive services in these scenarios, effectively overcomes the heterogeneity of LEO satellite networks, and achieves latency optimization for LEO satellites during simultaneous transmission and computation.

Description

Technical Field

[0001] This invention relates to the field of low-Earth orbit (LEO) satellite constellation technology, and in particular to a method for collaborative service allocation of LEO satellite constellations based on finite state machines. Background Technology

[0002] Low Earth Orbit (LEO) satellites, characterized by wide coverage and high resilience, are widely used in various scenarios. In disaster relief operations, due to damage to ground infrastructure, satellites can be rapidly deployed as efficient communication nodes to provide necessary communication support to ground rescue personnel. However, a single satellite has limited resources and cannot independently process complex mission information. Offloading missions to remote ground cloud centers may result in high latency, impacting disaster relief efficiency. With the continuous development of wireless communication technology, multi-satellite on-orbit edge collaborative computing technology has received widespread attention. By directly offloading missions to multiple nodes within a constellation, LEO satellites can collaborate effectively to transmit and compute data, thereby reducing loss of life and property caused by disasters.

[0003] Regarding edge collaborative computing research for LEO clusters, Wang et al. proposed a game-theoretic approach to optimize satellite edge computing offloading strategies in their paper "A Game-Theoretic Approach to Computation Offloading in Satellite Edge Computing" (Wang, J. Yang, X. Guo and Z. Qu, IEEE Access, vol. 8, pp. 12510-12520, 2020). This method considers the intermittency of satellite communication caused by orbit, establishes a system model for computation offloading, and constructs an offloading framework. It uses the response time and energy consumption of computational tasks based on queuing theory as performance indicators. Cheng et al., in their paper "Dynamic Computation Offloading in Satellite Edge Computing" (Cheng, G. Feng, Y. Sun, M. Liu and S. Qin, ICC 2022-IEEE International Conference on Communications, Seoul, Korea, Republic of, 2022, pp. 4721-4726), formulated a dynamic offloading strategy to minimize the overall latency of ground user tasks in satellite networks. This paper, considering the limited energy and computational power of LEO (Low Energy Optimization), transforms the long-term stochastic problem with time-varying energy constraints into multiple deterministic single-slot problems parameterized by the system state, based on Lyapunov optimization theory. To explore collaborative computing capabilities, Zhang et al., in their paper "Energy-Efficient Computation Peer Offloading in SatelliteEdge Computing Networks" (X. Zhang et al., IEEE Transactions on MobileComputing, vol. 23, no. 4, pp. 3077-3091, April 2024.), designed a satellite peer-to-peer offloading scheme, i.e., offloading along multi-hop paths, aiming to minimize latency and energy consumption under system resource and backlog constraints. To adapt to network dynamics, a latency-based online learning method was used to optimize the workload decision-making process, and a practical online distributed algorithm was developed.

[0004] However, the above works all assume that LEO has the ability to handle all tasks. In actual low-Earth orbit satellite networks (E-LEOSN), on-board computing resources are heterogeneous, such as optical imaging sensors, environmental monitoring equipment, and image grayscale processing units. This heterogeneity leads to different types of tasks that LEO can handle. In existing work on task offloading in heterogeneous resource networks, research on E-LEOSN is relatively limited. Considering the heterogeneity of UAVs, Wang et al., in their paper "Service function chain scheduling in heterogeneous multi-UAV edge computing" (Y.Wang, H.Wang, X.Wei, K.Zhao, J.Fan, J.Chen, Y.Hu, and R.Jia, Drones, vol.7, no.2, pp.132, 2023.), divided artificial intelligence applications into service function chains and scheduled them to multiple UAVs that can create instances, with the UAVs creating instances to provide the required services. In their paper "Minimizing the latency of embedding dependence-aware SFCs into mec network via graph theory" (S. Zheng, Z. Ren, W. Cheng, and H. Zhang, 2021 IEEE Global Communications Conference (GLOBECOM), 2021, pp. 1-6), Zheng et al. considered the dependency and concurrency of virtual network functions in heterogeneous edge computing networks and proposed using element graphs to abstract virtual network functions as independent nodes connected to servers. The aforementioned work focuses on network services, studying the construction and mapping of service function chains, and all scenarios are static networks. However, tasks in low-Earth orbit satellite networks are complex and diverse. In dynamic scenarios, classifying different service traffic and constructing different service function chains to meet service requests will lead to low rescue efficiency. Furthermore, nodes in the network have multiple states, which may be triggered by the same or different physical functions, and there are transitions between states, resulting in dependencies between on-board resources. Therefore, existing collaborative computing strategies for low-Earth orbit satellite clusters cannot be applied to practical E-LEOSN, which poses challenges to the scheduling and efficient rescue of latency-sensitive services. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a collaborative service allocation method for low-Earth orbit satellite clusters based on finite state machines. This method enables latency optimization for low-Earth orbit satellites that perform simultaneous transmission and computation.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] The method for collaborative service allocation of low-Earth orbit satellite constellations based on finite state machines includes the following steps:

[0008] Step 1: Construct an extended finite state machine spatiotemporal diagram model to accurately represent on-board resources and state transitions while shielding the dynamics of the low-Earth orbit satellite network.

[0009] Step 2: Represent the business using a directed acyclic graph model, establish a graph mapping relationship between the directed acyclic graph and the extended finite state machine spatiotemporal graph, and establish a latency optimization problem based on the graph mapping relationship;

[0010] Step 3: The constrained selection adaptive binary particle swarm optimization algorithm is used to solve the latency optimization problem of graph mapping relationship, find the mapping strategy with the lowest latency, establish the correspondence between satellites and sub-services, and complete the collaborative service allocation of the satellite cluster.

[0011] Furthermore, assuming there are p satellite nodes in the low-Earth orbit satellite network; in the spatiotemporal extended graph model, the topological period T of the satellites is divided into n time slots, and the topology remains unchanged within each time slot Δt = T / n; the delay-weighted adjacency matrix of the satellite network in the nth time slot is expressed as:

[0012]

[0013] in, Indicates satellite u in the nth time slot i With satellite u j Transmission delay for transmitting a unit of data between different data units;

[0014] The network delay weighted adjacency matrix between adjacent time slots is expressed as:

[0015]

[0016] Among them, the weight of the inter-slot edge Defined as the unit data buffering delay for the same satellite between adjacent time slots n-1 and n; the weights between different satellite nodes in adjacent time slots are set to infinity;

[0017] The low-Earth orbit satellite model based on a finite state machine is represented as a quintuple:

[0018] S LEO ={Q,E,δ,q0,O} (3)

[0019] Where Q is the set of all finite states of the low-Earth orbit satellite, E is the set of triggering conditions that cause state transitions, δ represents state transition, that is, the process of transitioning from one state to another under different triggering conditions, and q0∈Q is the initial state. For the set of terminating states;

[0020] Assume that a low-Earth orbit satellite exists in N states, where the l-th state is represented as... 1≤l≤N, (representing satellite u) j There exists a state of type l, 1≤j≤p; combining the low-Earth orbit satellite model based on finite state machine with the spatiotemporal extended graph model, the service delay weighted adjacency matrix of the extended finite state machine spatiotemporal graph model is obtained as follows:

[0021]

[0022] In this matrix, the rows and columns represent the number of time slots, and the diagonal elements Gp n This is the delay-weighted adjacency matrix for the satellite cluster within the nth time slot, specifically including the delays of low-Earth orbit satellites' service transmission, processing, state calls, and transitions within that time slot; the diagonally adjacent element Gp (n-1),n This is a delay-weighted adjacency matrix for satellite clusters between adjacent time slots, specifically representing the data buffering delay of satellite nodes between adjacent time slots, Gp. n,1 This is the adjacency matrix from the nth time slot of the previous topological cycle to the 1st time slot of the next topological cycle; excluding diagonal elements, elements directly above the diagonal, and Gp. n,1 Apart from that, all other elements are infinite.

[0023] Furthermore, the specific method for step 2 is as follows:

[0024] Establish a directed acyclic graph model of the business Φ = (Ψ, Γ), where Let Γ represent the set of subtasks in a directed acyclic graph, where q is the total number of subtasks and Γ represents the logical relationship between subtasks.

[0025] definition for Let i,j = 1,2,...,q be the set of forward sub-businesses. Task D j for:

[0026]

[0027] Where, η i ∈(0,1] is the data scaling factor, which represents the change in the amount of data after processing;

[0028] Definition B: Ψ→U represents the mapping relationship between the set of subtasks and the low-Earth orbit satellite constellation, where U is the set of low-Earth orbit satellites; the mapping relationship B specifies the first subtask. Mapped to the low-Earth orbit satellite accessed by the user initiating the task, the last subtask The mapping is assigned to receive low-Earth orbit satellites, while other subtasks are mapped to arbitrary nodes; the specific mapping method is as follows:

[0029]

[0030] Where, ρ i For computing sub-services The number of time slots spanned;

[0031] Define Z:Γ→E as the edge mapping relationship, where E is the set of edges in the extended finite state machine's spacetime graph, i.e., the set of triggering conditions that cause state transitions; mapping the edges of the directed acyclic graph to... Last node arrive First node Shortest route between:

[0032]

[0033] For the same business, there are multiple mapping results that simultaneously satisfy the above mapping rules. The decision matrix X is defined as follows:

[0034]

[0035] when When, it means Mapped to node

[0036]

[0037] Based on the mapping relationships B and Z and the decision matrix X, the latency of service Φ is expressed as:

[0038]

[0039] in, express The computational delay, Indicates progress to a subtask Cumulative delay over time; For nodes computing power Indicates following the shortest path from Transmit unit data volume to The transmission delay, α i Represented as subtask The computational complexity is expressed in cycles / bit. express The last node in the mapping;

[0040] A latency optimization problem is established based on graph mapping relationships, namely, finding the mapping decision matrix X that minimizes the business computation latency; this latency optimization problem is expressed as:

[0041] X = argmin(T(X)) (12).

[0042] st(9),(10)

[0043] Furthermore, the specific method for step 3 is as follows:

[0044] Step 301: Set up a particle swarm consisting of M particles, and set the maximum number of iterations for the swarm to I. max The initial value and the final value of the inertial weight are defined. The position and velocity of the m-th (≤M-th) particle during the I-th iteration are defined as follows:

[0045]

[0046] Using the task delay formula T(X) as the fitness function, the fitness value of each particle at a certain position is evaluated:

[0047]

[0048] Step 302: Randomly initialize the position of each particle. and speed m = 1, 2, ..., M; and set the current position as the optimal position P of the corresponding particle. mbest The optimal position of the particle with the lowest fitness among all particles is taken as the global optimal position g. best ;

[0049] Step 303: Perform the iterative process until the maximum number of iterations I is reached. max The specific method for each iteration is as follows:

[0050] C1, for each particle, the inertia weight μ is updated in each iteration using the following formula: I :

[0051] μ I =μ start -(μ start -μ end (I / I) max ) 2 (16)

[0052] C2 updates the position and velocity of each particle using the following formula:

[0053]

[0054] in:

[0055]

[0056] In the formula, γ1 and γ2 are learning factors, and β1 and β2 are random values ​​uniformly distributed in the interval [0,1].

[0057] C3, for each particle, calculate the fitness value of the new position and compare it with the current particle's best position P. mbest The fitness values ​​of the particles are compared, and the position with the smaller fitness value is selected as the optimal position P for that particle. mbest ;

[0058] C4, all particles have completed this iteration and updated the optimal particle position P. mbest Then, the optimal position of the particle with the lowest fitness value among all particles is set as the global optimal position g. best ;

[0059] Step 304: After the iteration is complete, the optimal position P of each particle is determined. mbest The position with the minimum fitness value for this particle in all iterations; for the entire particle swarm, the global optimal position g is... best The optimal position of the particle with the smallest fitness value among all particles is the service mapping decision matrix with the smallest latency among all decision matrices X. This matrix represents the correspondence between satellites and sub-services.

[0060] The beneficial effects of this invention are as follows:

[0061] 1. To shield the dynamic nature of E-LEOSN while simultaneously managing network resources for service purposes, this invention proposes an Extended Finite State Machine Space-time Graph (EFSMSG) model to represent on-board resources and state transitions, effectively overcoming the heterogeneity of low-Earth orbit satellite networks. The mathematical model of the finite state machine, starting from state definitions, possesses the advantages of forced modularity and ease of response to environmental changes, making it highly suitable for highly dynamic low-Earth orbit satellite networks.

[0062] 2. In order to meet the requirements of latency-sensitive services in the scenario, this invention is based on the EFSMSG model, which can minimize the service processing latency and realize simultaneous transmission and computation.

[0063] 3. In order to introduce cross-time slot mechanism and node functional constraints, the traditional BPSO algorithm is improved. This invention proposes CSABPSO algorithm to solve the delay optimization problem. Attached Figure Description

[0064] Figure 1 This is a schematic diagram of a low-Earth orbit satellite network architecture.

[0065] Figure 2 This is a schematic diagram of the LEO trajectory model.

[0066] Figure 3 This is a schematic diagram of the LEO finite state machine model.

[0067] Figure 4 This is a schematic diagram of the E-LEOSN finite state machine model.

[0068] Figure 5 This is a schematic diagram of the EFSMSG model. Detailed Implementation

[0069] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0070] The method for collaborative service allocation of low-Earth orbit satellite constellations based on finite state machines includes the following steps:

[0071] Step 1: Construct an extended finite state machine spatiotemporal diagram model to accurately represent on-board resources and state transitions while shielding the dynamics of the low-Earth orbit satellite network.

[0072] Step 2: Represent the business using a directed acyclic graph model, establish a graph mapping relationship between the directed acyclic graph and the extended finite state machine spatiotemporal graph, and establish a latency optimization problem based on the graph mapping relationship;

[0073] Step 3: The constrained selection adaptive binary particle swarm optimization algorithm is used to solve the latency optimization problem of graph mapping relationship, find the mapping strategy with the lowest latency, establish the correspondence between satellites and sub-services, and complete the collaborative service allocation of the satellite cluster.

[0074] This method assumes that there are p satellite nodes in a certain low-Earth orbit satellite network. In the spatiotemporal spread graph model, the topological period T of the satellites is divided into n time slots, and the topology remains unchanged within Δt = T / n. The delay-weighted adjacency matrix of the satellite network in the nth time slot is expressed as:

[0075]

[0076] in, Indicates satellite u in the nth time slot i With satellite u j Transmission delay per unit of data transmitted between time slots. The network delay weighted adjacency matrix between adjacent time slots is represented as:

[0077]

[0078] Among them, the weight of the inter-slot edge Defined as the unit data buffering delay for the same satellite between adjacent time slots n-1 and n. Since there is no data buffering relationship between different satellite nodes between adjacent time slots, its weight is set to infinity.

[0079] Based on this, in order to construct an extended finite state machine spatiotemporal diagram model, the low-Earth orbit satellite model based on the finite state machine is represented as a quintuple:

[0080] S LEO ={Q,E,δ,q0,O} (3)

[0081] Where Q is the set of all finite states of the low-Earth orbit satellite, E is the set of triggering conditions that cause state transitions, δ represents state transition, that is, the process of transitioning from one state to another under different triggering conditions, and q0∈Q is the initial state. For the set of terminating states;

[0082] Assuming a low-Earth orbit satellite exists in N states, the l-th (1≤l≤N) state is represented as... Representative satellite u j There exists a state of type l; combining the low-Earth orbit satellite model based on a finite state machine with the spatiotemporal extended graph model, the delay-weighted adjacency matrix in the nth time slot is extended as follows:

[0083]

[0084] Where, UF = [Uf] 1 ,Uf 2 ,…,Uf l ,…,Uf N ], Uf N This indicates that the low-orbit satellite is in state f. N The time delay matrix for processing a unit of data volume, where the rows of the matrix represent satellite u. i , column represents 1≤i,j≤p; A matrix element is meaningful if and only if i=j, and is defined as ct. iN , indicating satellite u i In state The time delay for processing a unit of data is specified, and all other off-diagonal elements are infinite; if satellite u i Does not exist In the state, then ct iN =∞. FU = [f 1 U,f 2 U,…,f l U,…,f N U] T f N U indicates the low-orbit satellite call status.N The delay is represented by FU; FF represents the state transition delay of the low-Earth orbit satellite. Since the state change function is deployed inside the satellite, the diagonal elements of the delay matrices FU and FF are all 0, and the remaining off-diagonal elements are all infinite.

[0085] The delay-weighted adjacency matrix between adjacent time slots is expanded as shown in the following equation, where the matrix contains [U] n-1 ,f 1 ,...,f N ], listed as [U n ,f 1 ,...,f N ].

[0086]

[0087] In summary, the service delay weighted adjacency matrix of the extended finite state machine spatiotemporal graph model is:

[0088]

[0089] In this matrix, the rows and columns represent the number of time slots, and the diagonal elements Gp n The delay for processing services within the nth time slot is represented by the element Gp above the diagonal. (n-1),n Gp is ​​used to buffer the latency of services between adjacent time slots. n,1 This is the adjacency matrix from the nth time slot of the previous topological cycle to the 1st time slot of the next topological cycle; excluding diagonal elements, elements directly above the diagonal, and Gp. n,1 Apart from that, all other elements are infinite;

[0090] The specific method for step 2 is as follows:

[0091] Establish a directed acyclic graph model of the business Φ = (Ψ, Γ), where Let Γ represent the set of subtasks in a directed acyclic graph, where q is the total number of subtasks and Γ represents the logical relationship between subtasks.

[0092] definition for Let i,j = 1,2,...,q be the set of forward sub-businesses. Task D j for:

[0093]

[0094] η i ∈(0,1] is the data scaling factor, which represents the change in the amount of data after processing;

[0095] Definition B: Ψ→U represents the mapping relationship between the set of subtasks and the low-Earth orbit satellite constellation, where U is the set of low-Earth orbit satellites. The mapping relationship B specifies the first subtask... Mapped to the low-Earth orbit satellite accessed by the user initiating the task, the last subtask The mapping is assigned to receive low-Earth orbit satellites, while other subtasks are mapped to arbitrary nodes; the specific mapping method is as follows:

[0096]

[0097] Where, ρ i For computing sub-services The number of time slots spanned;

[0098] Define Z:Γ→E as the edge mapping relationship, where E is the set of edges in the extended finite state machine's spacetime graph, i.e., the set of triggering conditions that cause state transitions; mapping the edges of the directed acyclic graph to... Last node arrive First node Shortest route between:

[0099]

[0100] Based on the mapping relationships B and Z, the latency of service Φ is calculated as follows.

[0101]

[0102] in, express The computational delay, Indicates progress to a subtask Cumulative delay over time. For nodes computing power Represented as following the shortest path from Transmit unit data volume to The transmission delay, α i Represented as subtask The computational complexity is expressed in cycles / bit.

[0103] For the same business, there are multiple mapping results that simultaneously satisfy the above mapping rules. Therefore, the decision matrix X is defined as follows:

[0104]

[0105] when When, it means Mapped to node

[0106]

[0107] Therefore, the latency of service Φ can be further expressed as:

[0108]

[0109] in express The last node in the mapping.

[0110] As mentioned earlier, the same business operation may have multiple mapping results, i.e., multiple decision matrices X. Different mapping results will have different business computation latencies T(X). Therefore, a latency optimization problem needs to be established based on graph mapping relationships, i.e., finding the mapping decision matrix X with the lowest business computation latency. This latency optimization problem is expressed as:

[0111] X = argmin(T(X)) (15)

[0112] st(12),(13)

[0113] The specific method for step 3 is as follows:

[0114] Step 301: Set up a particle swarm consisting of M particles, and set the maximum number of iterations for the swarm to I. max The initial value and the final value of the inertial weight. The position and velocity of the m-th ≤ M-th particle during the I-th iteration are defined as follows:

[0115]

[0116] Using the task delay formula T(X) as the fitness function, the fitness value of each particle at a certain position is evaluated:

[0117]

[0118] Step 302: Randomly initialize the position of each particle. and speed m = 1, 2, ..., M; and set the current position as the optimal position P of the corresponding particle. mbest The optimal position of the particle with the lowest fitness among all particles is taken as the global optimal position g. best .

[0119] Step 303: Perform the iterative process until the maximum number of iterations I is reached. max The specific method for each iteration is as follows:

[0120] C1, for each particle, the inertia weight μ is updated in each iteration using the following formula: I :

[0121] μ I=μ start -(μ start -μ end (I / I) max ) 2 (19)

[0122] C2 updates the position and velocity of each particle using the following formula:

[0123]

[0124] in:

[0125]

[0126] In the formula, γ1 and γ2 are learning factors, and β1 and β2 are random values ​​uniformly distributed in the interval [0,1].

[0127] C3, for each particle, calculate the fitness value of the new position and compare it with the current particle's best position P. mbest The fitness values ​​of the particles are compared, and the position with the smaller fitness value is selected as the optimal position P for that particle. mbest .

[0128] C4, all particles have completed this iteration and updated the optimal particle position P. mbest Then, the optimal position of the particle with the lowest fitness value among all particles is set as the global optimal position g. best .

[0129] Step 304: After the iteration is complete, the optimal position P of each particle is determined. mbest The position with the minimum fitness value for this particle in all iterations; for the entire particle swarm, the global optimal position g is... best The optimal position of the particle with the smallest fitness value among all particles is the business mapping decision matrix with the smallest latency among all decision matrices X.

[0130] In summary, after the final iteration, the globally optimal position is the service mapping decision matrix with the minimum latency, and this decision matrix is ​​the low-Earth orbit satellite cluster collaborative service strategy.

[0131] The specific principle behind this method is as follows:

[0132] 1) System Model and Problem Construction

[0133] Figure 1The typical architecture of E-LEOSN is shown (see Leng T, Duan P, Hu D, et al. Cooperative user association and resource allocation for task offloading in hybrid GEO-LEO satellite networks[J]. International Journal of Satellite Communications and Networking, vol.40, no.3, pp.230-243, 2022.). This network architecture typically consists of three layers, responsible for handling various latency-sensitive tasks and improving computing and communication efficiency through satellite cooperation. The first layer consists of ground users. Within the disaster area, ground users initiate task requests to and receive results from LEO satellites within their coverage area via terminal devices. The second layer consists of multiple satellites operating in low Earth orbit. These satellites build a dynamic network through inter-satellite links, and each satellite works collaboratively according to its mission attributes to provide services to users. The central satellite in the third layer (usually a medium Earth orbit or high Earth orbit satellite) is responsible for task scheduling and network planning. Furthermore, it monitors the status of inter-satellite communication links and computing resources to ensure efficient task execution.

[0134] 1.1) E-LEOSN model

[0135] This method employs a spatiotemporal graph model to analyze low-Earth orbit (LEO) satellite networks, which has been widely applied in dynamic networks (see P. Wang, X. Zhang, S. Zhang, H. Li, and T. Zhang, “Time-expanded graph-based resource allocation over the satellite networks”, IEEE Wireless Communications Letters, vol. 8, no. 2, pp. 360-363, 2019). Considering a general scenario, we assume that the LEO cluster revolves around the Earth in a periodic circular motion centered at the Earth's center. To facilitate trajectory modeling, we establish a spatial rectangular coordinate system with the Earth's center as the origin, the equatorial plane as the plane containing the x and y axes, and the z-axis passing through the Earth's center and perpendicular to the equatorial plane pointing towards the North Pole. We define U = {u1, ..., u...} d ,…,u p Let} be the set of LEOs, where p is the total number of LEOs. For any low-Earth orbit satellite u d ∈U, generally {r d ,θ d ,α d ,β dIt is described by four parameters. Among them, r d For satellite u d orbital radius, θ d As the initial phase, α d β represents the orbital inclination of a satellite. d For u d The angle between the line of intersection of the orbit and the equatorial plane and the positive half-axis of the y-axis.

[0136] like Figure 2 As shown, at time t, u d The coordinates are represented as:

[0137] x d (t)=r d cos(ωt+θ d sin(β) d )+r d sin(ωt+θ d cos(α) d cos(β) d (1)

[0138] y d (t)=r d cos(ωt+θ d cos(β) d )-r d sin(ωt+θ d cos(α) d sin(β) d (2)

[0139] z d (t)=r d sin(ωt+θ d sin(α) d (3)

[0140] Where ω represents the angular velocity of the satellite.

[0141] Therefore, at time t, any two low-orbit satellites u i u j The distance between them is obtained by the following formula:

[0142]

[0143] According to the literature "Adaptive Coded Modulation based on Continuous Phase Modulation for Inter-satellite Links of Global Navigation Satellite Systems[J]" (RXue, H Yu and Q.Cheng, IEEE Access, pp.1-1, 2018.), the transmission loss in free space is expressed by the following formula:

[0144] L ij (t)=(4πd ij (t) / λ) 2 =(4πd) ij (t)f / c) 2 (5)

[0145] Where f represents the carrier frequency, λ = c / f represents the carrier wavelength, and c is the speed of light. The losses in inter-satellite link communication mainly consist of free space loss, antenna pointing loss, and polarization loss, with free space path loss dominating the signal transmission loss. Based on equation (5), satellite u j The received signal power is:

[0146]

[0147] In the formula, For u i The transmission power, For u j The receiving antenna gain coefficient. Therefore, the signal-to-noise ratio is given by the following formula:

[0148]

[0149] Where, σ 2 This represents the power of additive white Gaussian noise. According to Shannon's formula, the inter-satellite link capacity is:

[0150] C ij (t)=Blog2(1+SNR ij (t)) (8)

[0151] Where B is the inter-satellite link channel bandwidth. Assume the minimum capacity of the inter-satellite link is C. o The conditions for the existence of links between satellites are defined as follows:

[0152]

[0153] Among them, link ij(t) = 1 indicates the link is connected, otherwise it is disconnected. If the link is connected, the capacity of the inter-satellite link is C. o .

[0154] At time t, the transmission rates between satellites are as follows:

[0155] R ij (t) = link ij (t)×C o (10)

[0156] Divide the topology period T into n time slots, and the topology remains unchanged within Δt = T / n. The transmission delay per unit data volume is... The delay-weighted adjacency matrix of E-LEOSN in the nth time slot is expressed as:

[0157]

[0158] In addition, virtual links are introduced. This represents the data buffer latency within the same node between two adjacent time slots. This represents the time consumed by the preceding data processing of the i-th node in the (n-1)-th time slot. The delay weighting matrix between two time slots is expressed as:

[0159]

[0160] Because the satellite's orbital trajectory is periodic, the adjacency matrix G from time slot n to time slot 1... n,1 This also satisfies the above equation, therefore the time spread graph model of E-LEOSN is as follows:

[0161]

[0162] 1.2) EFSMSG model

[0163] Based on the Space-time Graph (SG), the steady-state operation of E-LEOSN can be achieved. However, when formulating LEO cluster coordination strategies in the E-LEOSN system, the heterogeneous nature of satellite functions must be fully considered. Therefore, based on the SG, a finite state machine is used to represent the resources and state transitions on the LEOs, and combined with the communication topology, the SG is further upgraded to an EFSMSG model.

[0164] Finite state machines (FSMs) are tools used for modeling the behavior of objects, effectively describing the LEO (Leadership in State) and the sequence of states experienced by the system. The LEO model based on a finite state machine is defined as a quintuple, as shown in the following equation:

[0165] S LEO ={Q,E,δ,q0,O} (14)

[0166] Where Q is the set of all finite states of LEO, E is the set of triggering conditions that cause state transitions, δ represents the state transition, that is, the process of transitioning from one state to another under different triggering conditions, and q0∈Q is the initial state. This is the set of terminating states. For example, a LEO finite state machine model performing simple image processing tasks would look like this: Figure 3 As shown in the diagram, the arrows represent state transitions, and the text on the arrows indicates the triggering conditions for the state transitions. For information on simple image processing operations, please refer to "Credibility computation offloading based task-driven routing strategy for emergency UAVs network" (B.Ma, Z.Ren, and W.Cheng, 2021 IEEE Global Communications Conference (GLOBECOM), 2021, pp.1-6).

[0167] Complex tasks often cannot be completed on a single, limited-functionality LEO and require the collaboration of multiple LEOs. This process involves not only the state transitions of each LEO but also communication between them. Therefore, this method models E-LEOSN as EFSMSG. For example, an EFSM (Extended Finite State Machine) model for performing complex image processing tasks would look like this: Figure 4 As shown. State transitions occur within each LEO, and communication between LEOs is also considered a state transition process. For details on complex image processing operations, see "UAV-based forest fire detection and tracking using image processing techniques" (C. Yuan, Z. Liu, and Y. Zhang, 2015 International Conference on Unmanned Aircraft Systems (ICUAS), 2015, pp. 639-643).

[0168] Based on the EFSM and SG models, construct the EFSMSG model, such as... Figure 5 As shown in the figure, this model includes the LEO group connectivity and states.

[0169] like Figure 5As shown, for intuitive purposes, the state is abstracted as a node connected to the LEO node. Multiple states of the same LEO node may transition between each other. Suppose that E-LEOSN has N states, and the l-th (1≤l≤N) state is represented as... in Representative satellite u j There exists a state of type l. Then all states in E-LEOSN are represented by F = {f}. 1 ,f 2 ,...,f N The delay adjacency matrix of E-LEOSN in the nth time slot is represented as follows:

[0170]

[0171] UF = [Uf] 1 ,Uf 2 ,…,Uf l ,…,Uf N ], Uf N This indicates that LEO is in state f. N The time delay matrix for processing a unit amount of data, Uf N The i-th row (1≤i≤p) in the matrix represents node u i The j-th (1≤j≤p) column represents From the above As defined, a matrix element is meaningful if and only if i = j, and is defined as ct. iN , represented as satellite u i In state The time delay for processing a unit of data is defined, and all other off-diagonal elements are infinite. If satellite u... i Does not exist In the state, then ct iN =∞. FU = [f 1 U,f 2 U,…,f N U] T f N U indicates the LEO call status f N The call latency is represented by FF, which represents the transition latency of the LEO state. Since the functions that trigger state changes, such as state calls and transitions, are all deployed inside LEO, the diagonal elements of the FU and FF latency matrices are both 0, and the other off-diagonal elements are infinite.

[0172] The EFSM delay adjacency matrix of adjacent time slots is represented as follows, with the behavior [U n-1 ,f 1 ,...,f N ], listed as [U n ,f 1 ,...,f N]:

[0173]

[0174] The delay-weighted adjacency matrix of EFSMSG is then:

[0175]

[0176] 2) Calculation of unloading based on the EFSMSG model

[0177] The following section describes a collaborative computing strategy for a low-Earth orbit satellite constellation based on EFSMG. Without loss of generality, the service is represented as a Directed Acyclic Graph (DAG) model, and a graph mapping problem from the DAG to EFSMG is established. Let Φ = (Ψ, Γ) be the DAG model of the service, where... Γ represents the set of subtasks in a Directed Acyclic Graph (DAG), and Γ represents the logical relationships between the subtasks. for If the set of forward sub-businesses is j, then j j The workload is D j Represented as:

[0178]

[0179] η i ∈(0,1] is the data scaling factor, representing the change in data volume after processing. Define B:Ψ→U to represent the mapping relationship between the subtask set and the low-Earth orbit satellite constellation. Mapped to the LEO accessed by the user who initiated the task. Mapping to the result receiving LEO, and mapping other subtasks to arbitrary nodes. Considering the possibility of link interruption during transmission, the data needs to be buffered on the LEO until the next time slot. ρ i For computing sub-services The number of time slots spanned. The specific mapping method is as follows:

[0180]

[0181] Define Z:Γ→E as the edge mapping (E is the edge set of the EFSSG). Mapping the edges of a DAG to... Last node arrive First node The shortest route between them, i.e.:

[0182]

[0183] Based on the above mapping rules, the task latency is as follows:

[0184]

[0185] in, express The computational delay, Indicates progress to sub-business Cumulative delay over time. For nodes computing power To follow the shortest path, from Transmission unit bit to The time delay. α i This represents the computational complexity of the subtask, expressed in cycles / bit.

[0186] For the same business logic, multiple mapping results may simultaneously satisfy the mapping rules, leading to varying processing latencies. Therefore, minimizing business processing latency means finding the mapping strategy that minimizes latency. The decision matrix X is defined as follows:

[0187]

[0188] The elements in the decision matrix X satisfy:

[0189]

[0190] when When, it means Mapped to node

[0191] In summary, the processing latency of service Φ can be expressed as:

[0192]

[0193] in, express The last node in the mapping. Therefore, the latency optimization problem is expressed as:

[0194]

[0195] 3) CSABPSO algorithm

[0196] Equation (26) is a multidimensional NP-hard problem, and the computational complexity of using an exact algorithm is high. Therefore, in order to solve the time delay optimization problem, this invention proposes the Constraint Selection Adaptive Binary Particle Swarm Optimization (CSABPSO) algorithm. The feasible region of this algorithm will adaptively change with the increase of time slots, and node function constraints are introduced to restrict the selection of particle positions.

[0197] Assume the particle swarm size is M, and at the same time, I max Let represent the maximum number of iterations for the group, i.e., the termination condition of the algorithm. Then, the position and velocity of the m-th ≤ M-th particle during the I-th iteration are expressed as:

[0198]

[0199] Furthermore, the velocity of the m-th ≤ M-th particle is updated by the following formula. To improve convergence speed and solution accuracy, the inertia weight μ... I Employing a nonlinear variation strategy:

[0200] μ I =μ start -(μ start -μ end (I / I) max ) 2 (29)

[0201]

[0202] Where γ1 and γ2 are learning factors, β1 and β2 are random values ​​uniformly distributed in the interval [0,1], and μ start and μ end These represent the initial and final values ​​of the inertial weight, respectively. The sigmoid function is used to map the particle velocity to the [0,1] interval:

[0203]

[0204] The position of each particle This represents a mapping strategy where subtasks can only be mapped to LEO nodes that have a processing state for that subtask. Assume... exist Processing status Represented as The particle position update formula for the CSABPSO algorithm is as follows:

[0205]

[0206] express With a probability of 1, rand() generates a random number in the interval [0,1].

[0207] Fitness values ​​are calculated using a time-delay method:

[0208]

[0209] In summary, this invention is designed for low-Earth orbit (LEO) satellite constellation scenarios. It implements collaborative service computing for LEO satellite constellations based on finite state machines, enabling latency optimization for LEO satellites to perform simultaneous transmission and computation.

Claims

1. A method for collaborative service allocation of low-Earth orbit satellite constellations based on finite state machines, characterized in that, Includes the following steps: Step 1: Construct an extended finite state machine spatiotemporal diagram model to accurately represent on-board resources and state transitions while shielding the dynamics of the low-Earth orbit satellite network. Step 2: Represent the business using a directed acyclic graph model, establish a graph mapping relationship between the directed acyclic graph and the extended finite state machine spatiotemporal graph, and establish a latency optimization problem based on the graph mapping relationship; Step 3: The constrained selection adaptive binary particle swarm optimization algorithm is used to solve the latency optimization problem of graph mapping relationship, find the mapping strategy with the lowest latency, establish the correspondence between satellites and sub-services, and complete the collaborative service allocation of the satellite cluster.

2. The method for collaborative service allocation of low-Earth orbit satellite constellations based on finite state machines according to claim 1, characterized in that, Assume there are p satellite nodes in the low-Earth orbit satellite network; in the spatiotemporal spread graph model, the topological period T of the satellites is divided into n time slots, and the topology remains unchanged within each time slot Δt = T / n; the delay-weighted adjacency matrix of the satellite network in the nth time slot is represented as: in, Indicates satellite u in the nth time slot i With satellite u j Transmission delay for transmitting a unit of data between different data units; The network delay weighted adjacency matrix between adjacent time slots is expressed as: Among them, the weight of the inter-slot edge Defined as the unit data buffering delay for the same satellite between adjacent time slots n-1 and n; the weights between different satellite nodes in adjacent time slots are set to infinity; The low-Earth orbit satellite model based on a finite state machine is represented as a quintuple: WITH LEO ={Q,E,δ,q0,O} (3) Where Q is the set of all finite states of the low-Earth orbit satellite, E is the set of triggering conditions that cause state transitions, δ represents state transition, that is, the process of transitioning from one state to another under different triggering conditions, and q0∈Q is the initial state. For the set of terminating states; Assume that a low-Earth orbit satellite exists in N states, where the l-th state is represented as... 1≤l≤N, (representing satellite u) j There exists a state of type l, 1≤j≤p; combining the low-Earth orbit satellite model based on finite state machine with the spatiotemporal extended graph model, the service delay weighted adjacency matrix of the extended finite state machine spatiotemporal graph model is obtained as follows: In this matrix, the rows and columns represent the number of time slots, and the diagonal elements Gp n This is the delay-weighted adjacency matrix for the satellite cluster within the nth time slot, containing the service transmission, processing, state call, and transition delays of low-Earth orbit satellites within the time slot; the diagonally adjacent element Gp (n-1),n This is a delay-weighted adjacency matrix for satellite clusters between adjacent time slots, specifically representing the data buffering delay of satellite nodes between adjacent time slots, Gp. n,1 This is the adjacency matrix from the nth time slot of the previous topological cycle to the 1st time slot of the next topological cycle; excluding diagonal elements, elements directly above the diagonal, and Gp. n,1 Apart from that, all other elements are infinite.

3. The method for collaborative service allocation of low-Earth orbit satellite constellations based on finite state machines according to claim 2, characterized in that, The specific method for step 2 is as follows: Establish a directed acyclic graph model of the business Φ = (Ψ, Γ), where Let Γ represent the set of subtasks in a directed acyclic graph, where q is the total number of subtasks and Γ represents the logical relationship between subtasks. definition for Let i,j = 1,2,...,q be the set of forward sub-businesses. Task D j for: Where, η i ∈(0,1] is the data scaling factor, which represents the change in the amount of data after processing; Definition B: Ψ→U represents the mapping relationship between the set of subtasks and the low-Earth orbit satellite constellation, where U is the set of low-Earth orbit satellites; the mapping relationship B specifies the first subtask. Mapped to the low-Earth orbit satellite accessed by the user initiating the task, the last subtask The mapping is assigned to receive low-Earth orbit satellites, while other subtasks are mapped to arbitrary nodes; the specific mapping method is as follows: Where, ρ i For computing sub-services The number of time slots spanned; Define Z:Γ→E as the edge mapping relationship, where E is the set of edges in the extended finite state machine's spacetime graph, i.e., the set of triggering conditions that cause state transitions; mapping the edges of the directed acyclic graph to... Last node arrive First node Shortest route between: For the same business, there are multiple mapping results that simultaneously satisfy the above mapping rules. The decision matrix X is defined as follows: when When, it means Mapped to node Based on the mapping relationships B and Z and the decision matrix X, the latency of service Φ is expressed as: in, express The computational delay, Indicates progress to a subtask Cumulative delay over time; For nodes computing power Indicates following the shortest path from Transmit unit data volume to The transmission delay, α i Represented as subtask The computational complexity is expressed in cycles / bit. express The last node in the mapping; A latency optimization problem is established based on graph mapping relationships, namely, finding the mapping decision matrix X that minimizes the business computation latency; this latency optimization problem is expressed as: X = argmin(T(X)) (12). st(9),(10) 4. The method for collaborative service allocation of low-Earth orbit satellite constellations based on finite state machines according to claim 3, characterized in that, The specific method for step 3 is as follows: Step 301: Set up a particle swarm consisting of M particles, and set the maximum number of iterations for the swarm to I. max The initial value and the final value of the inertial weight are defined. The position and velocity of the m-th (≤M-th) particle during the I-th iteration are defined as follows: Using the task delay formula T(X) as the fitness function, the fitness value of each particle at a certain position is evaluated: Step 302: Randomly initialize the position of each particle. and speed Set the current position as the optimal position P for the corresponding particle. mbest The optimal position of the particle with the lowest fitness among all particles is taken as the global optimal position g. best ; Step 303: Perform the iterative process until the maximum number of iterations I is reached. max The specific method for each iteration is as follows: C1, for each particle, the inertia weight μ is updated in each iteration using the following formula: I : m I =μ start -(m start -m end )(I / I max ) 2 (16) C2 updates the position and velocity of each particle using the following formula: in: In the formula, γ1 and γ2 are learning factors, and β1 and β2 are random values ​​uniformly distributed in the interval [0,1]. C3, for each particle, calculate the fitness value of the new position and compare it with the current particle's best position P. mbest The fitness values ​​of the particles are compared, and the position with the smaller fitness value is selected as the optimal position P for that particle. mbest ; C4, all particles have completed this iteration and updated the optimal particle position P. mbest Then, the optimal position of the particle with the lowest fitness value among all particles is set as the global optimal position g. best ; Step 304: After the iteration is complete, the optimal position P of each particle is determined. mbest The position with the minimum fitness value for this particle in all iterations; for the entire particle swarm, the global optimal position g is... best The optimal position of the particle with the smallest fitness value among all particles is the service mapping decision matrix with the smallest latency among all decision matrices X. This matrix represents the correspondence between satellites and sub-services.

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