Distributed satellite dynamic grid load distribution method based on potential energy game

Abstract

The invention relates to a multi-satellite dynamic grid load distribution method based on a potential energy game, and the method comprises the steps: obtaining satellite data at a ground station and grid data divided by a management end based on a satellite position, carrying out the DAG problem modeling, carrying out the sDAG problem modeling at the ground station, building a potential energy game model of distributed satellite dynamic grid load distribution, and carrying out the sDAG problem modeling. Compared with the prior art, the distributed satellite grid load distribution method has the advantages that the distributed satellite grid load distribution method is more efficient and has superiority in the DGA problem solving process.

Description

Technical Field

[0001] The present invention belongs to the field of mission planning and scheduling, and particularly relates to a multi-satellite dynamic grid load distribution method based on potential game. Background Art

[0002] A distributed satellite system refers to multiple satellite platforms operating in different space orbits, which are equipped with sensors to perform observation tasks. The so-called observation task refers to the imaging activity of the sensors carried by the satellites within a specific time period. With the rapid increase in the demand for observation tasks and the continuous progress of space technology, satellite technology has evolved from a single large spacecraft to a large-scale distributed satellite system. For example, Planet Company has successfully launched more than 150 Dove satellites, building a large-scale distributed satellite network. Although the distributed satellite system has obvious advantages, it also brings new challenges in terms of control and collaborative operations. In a dynamic environment, it is a complex task to allocate a large number of observation tasks to satellites in real time, which requires huge computing resources. Therefore, as Figure 1 shown, the current trend is to divide the observation tasks into different grids according to geographical information for target allocation.

[0003] The advantages of introducing a grid model to represent online imaging tasks are as follows: (1) In the grid model, the number of tasks within a grid is quantified by the observation load value of each grid. The arrival and disappearance of online tasks (whether they are completed or invalidated due to exceeding the deadline) can achieve dynamic balance in the grid observation load value, thereby alleviating the dynamicity in the cluster coordination problem to a certain extent and reducing the energy consumption caused by inter-satellite communication. (2) Due to the fixity and regularity of the grid boundaries, combined with the prediction information of satellite orbits, the visibility calculation of geographical grids can be pre-completed. This method can not only shorten the preprocessing time for processing a large number of online tasks compared with the real-time task-based visibility calculation, but also unify the time points for visibility calculation of each satellite in the absence of a cluster head satellite, effectively avoiding chaos in the coordination process. (3) In addition, using the geographical grid model to represent satellite imaging tasks can achieve unified identity coding of remote sensing targets, facilitating the effective transfer of remote sensing targets, coordination schemes, and execution results among different autonomous satellites in the coordination process, reducing the complexity of the inter-satellite communication protocol, and saving inter-satellite communication link resources as much as possible; (4) At the same time, by monitoring the change of the grid load value, each satellite can macroscopically control the completion of remote sensing tasks at the lowest storage cost to cope with the lack of a global macroscopic perspective caused by the absence of a cluster head satellite. (5) Considering the possible imbalance problem in task allocation, the grid model takes minimizing the maximum grid observation load value as the objective function, striving to achieve the most balanced task allocation and improve the utilization efficiency of resources.

[0004] However, at the present stage, in the process of actual control, the distributed satellite dynamic grid load allocation faces the following problems: 1) There is a lack of a standardized and intuitive mathematical model for the distributed satellite dynamic grid load, which presents the time-dependent characteristics of constraints and benefits, and thus guides the design of algorithms. Due to the limited observation time window, time-dependent observation quality, and unpredictable changes in grid observation load, how to scientifically and intuitively describe this dynamic network and its time-dependent characteristics, and normatively give the mathematical expressions of decision variables, constraints, and benefits, to help understand the combinatorial optimization essence of the dynamic grid load allocation problem, and thus better guide the design of algorithms and operators, is an important topic. 2) Due to considering robustness, scalability, and management overhead, the centralized method designed for a single large satellite is not suitable for solving problems involving distributed satellites in an uncertain environment. The concept of distributed self-organization provides a comprehensive solution to solve the resource allocation problem between tasks within a satellite group in a distributed environment. Different from the centralized allocation mechanism, the distributed allocation mechanism does not rely on a single master controller; on the contrary, each agent jointly achieves the global goal through mutual interaction and communication. 3) However, without a centralized controller, it is difficult to obtain theoretical guarantees for high-quality solutions. Therefore, designing an individual decision-making algorithm that theoretically contributes to the global goal has become the core challenge of the distributed satellite dynamic grid load allocation method. Summary of the Invention

[0005] Aiming at the problems of the above-mentioned prior art, the present invention proposes a distributed satellite dynamic grid load allocation method based on potential game for the dynamic grid composed of online tasks: ① Use a grid model to uniformly describe the satellite tasks arriving online, and establish a mathematical model for distributed satellite dynamic grid load allocation (Dynamic Grid Allocation, DGA); ② In order to achieve reasonable decision-making for each satellite without a central decision-making node, introduce the potential game theory to decompose the objective function of the DGA problem into the local efficacy functions of each satellite, and design equivalent global efficacy functions and potential functions; ③ To improve the online decision-making and coordination efficiency of satellites, propose an algorithm of Selective Time Variant-parameter Better Reply Process (SeTVBRP); ④ Conduct algorithm analysis experiments and algorithm comparison experiments in different task scale and satellite group scale simulation scenarios, conduct comparison experiments with five advanced potential game learning algorithms, clarify its high efficiency and superiority in solving the DGA problem, and objectively verify the algorithm performance through experiments.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A multi-satellite dynamic grid load distribution method based on potential game, which performs the following steps:

[0008] S1. The ground station obtains satellite data and grid data divided by the management end based on satellite positions, and conducts DAG problem modeling;

[0009] N = {1, 2,..., n} represents the satellite index set, where the index of satellite s i is i, and i ∈ N;

[0010] M = {1, 2,..., m} represents the grid index set, where the index of grid r j is j, and j ∈ M;

[0011] S2. The ground station divides the DAG problem into single-stage DAG problems according to the time slicing method and conducts sDAG problem modeling; among them, the single-stage DAG problem is the sDAG problem;

[0012] Each grid r j requires a satellite to complete the observation task within the grid to reduce its observation load β i ;

[0013] In the sDAG problem modeling, the observation ability of satellite s i for grid r j is represented by α ij The time amount allocated by satellite s i to grid r j is represented by x ij ;

[0014] Define the remaining observation load y j of grid r j as follows:

[0015]

[0016] S3. Establish a potential game model for distributed satellite dynamic grid load distribution;

[0017] Let G P = {N, {A i}, {U i}} represent a game, where N = {1, 2,..., n} is the satellite set; A = A 1 × A 2 … × A n is the joint action set, and U i : A i → R is the local utility function of participant i;

[0018] For the action set a = (a 1 , a 2,…,a n ) ∈ A, where; a i ∈ A i is an action of participant i,;

[0019] S4. Obtain a distributed satellite grid load allocation scheme based on the improved best response process at the time of selection;

[0020] Generate an initial allocation scheme for all satellites according to the greedy strategy;

[0021] Randomly select a satellite update action at each iteration time to generate a new allocation scheme.

[0022] Furthermore, in step S1,

[0023] At any time, each satellite can only perform imaging tasks within a specific grid;

[0024] The observation load of the grid changes dynamically over time;

[0025] The change in the observation load is directly affected by the increase or decrease in the number of imaging tasks within its grid.

[0026] Furthermore, in the DAG problem modeling, for each satellite s i , the corresponding grid r j has a time window w ij = [c ij , d ij ,

[0027] where c ij represents the start time of the time window, and d ij represents the end time of the time window.

[0028] Furthermore, in step S1, in the DAG problem modeling, the state change point t k is a specific moment when the time window changes, and the time interval [t k , t k +Δt] is called stage k.

[0029] Furthermore, in the DAG problem modeling, is the observation ability of satellite s i for grid r j ; the observation ability and the observation load both take non - negative constant values;

[0030] represents the set of visible grids of satellite s i in decision - making stage k, that is:

[0031]

[0032] Furthermore, in the DAG problem modeling, For the allocation grid set of satellite s in decision stage k i and

[0033] If there is no intersection between the allocation grid sets of two adjacent decision stages, that is then satellite s i needs to adjust the imaging payload angle to turn from the grid in set to the grid in set .

[0034] Furthermore, in the DAG problem modeling, for satellite s in decision stage k i the conversion time η ik is:

[0035]

[0036] where H represents a non - negative constant used to represent the simplified imaging payload conversion time;

[0037] When the intersection of the allocation grid sets of satellite s under decision stage k - 1 and decision stage k i is an empty set, the conversion time between the two stages is H, otherwise it is 0.

[0038] Furthermore, in step S2, if a satellite is assigned to two or more grids, the time for the satellite to perform imaging payload attitude conversion between different grids is considered.

[0039] Furthermore, in the sDAG problem modeling, represents the allocation grid set of satellite s i satisfying For satellite s i , its conversion time ρ i The calculation formula is as follows:

[0040]

[0041] Furthermore, in the sDAG problem modeling, in decision stage k, the problem model P0 is constructed as follows

[0042]

[0043] where x ij is a decision variable representing the time amount of assigning satellite s i to grid r j ;

[0044] Since the sDAG problem is a single-stage DAG problem divided from the DAG problem by the time slicing method, satellite s i and grid r j have the same physical meaning as that expressed by the model DGA;

[0045] Δt is the total allocable time for this stage; the objective function U(x) is an exponential function that minimizes the maximum value of the remaining observation load, where represents the observation load on grid r j in all satellite total allocation schemes x;

[0046] represents the conversion time ρ i and the total satellite allocation time s i shall not exceed the allocable time Δt when added together. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for use in the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0048] Figure 1 Schematic diagram of the grid model.

[0049] Figure 2 is the distribution diagram of satellites and grids.

[0050] Figure 3 is the schematic diagram of the observation capabilities of different satellites for different grids.

[0051] Figure 4 is the schematic diagram of the conversion time.

[0052] Figure 5 is the schematic diagram of the objective function of the single-stage DGA problem.

[0053] Figure 6 is the schematic diagram of multi-stage dynamic allocation.

[0054] Figure 7 is the analysis of the ablation experiment results of the improvement strategy in a small-scale scenario.

[0055] Figure 8 is the convergence performance of 6 algorithms with 500 iterations in a small-scale scenario.

[0056] Figure 9 is the convergence performance of 2000 iterations in a large-scale scenario. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0057] The exemplary embodiments of the present application will be described below in conjunction with the accompanying drawings. Various details of the embodiments of the present application are included to facilitate understanding, and they should be considered merely exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present application. Similarly, for the sake of clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0058] In order to enable those skilled in the art of this technology to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts should fall within the scope of protection of the present invention.

[0059] For the dynamic grid composed of online tasks, a distributed satellite dynamic grid load allocation method based on potential game is proposed: ① A grid model is used to uniformly describe the online arriving satellite tasks, and a mathematical model of distributed satellite dynamic grid allocation (DGA) is established; ② In order to achieve reasonable decision-making for each satellite without a central decision-making node, the potential game theory is introduced to decompose the objective function of the DGA problem into the local efficiency functions of each satellite, and an equivalent global efficiency function and potential function are designed; ③ To improve the online decision-making and cooperation efficiency of satellites, an algorithm of Selective Time Variant-parameter Better Reply Process (SeTVBRP) is proposed; ④ Algorithm analysis experiments and algorithm comparison experiments are carried out under different task scales and satellite constellation scale simulation scenarios, and comparison experiments are carried out with five advanced potential game learning algorithms, clarifying its high efficiency and superiority in solving the DGA problem, and objectively verifying the algorithm performance through experiments.

[0060] The present invention relates to the problem of Dynamic Grid with a time-window Allocation (DGA). First, according to the characteristics of satellites and grids, the invention defines the research subjects of the DGA problem and clarifies the attributes of grids and satellites. Further, to eliminate the dynamicity in the DGA problem, it is decomposed into a single-stage Dynamic Grid with a time-window Allocation (sDGA) problem. After analyzing the relationship between each stage in the DGA problem, the invention constructs a mathematical model for the sDGA problem.

[0061] S1. The ground station obtains satellite data and grid data divided by the management end based on satellite positions, and models the DAG problem

[0062] The DGA problem involves a set of satellites S = {s i | i ∈ N} and a set of grids R = {r j | j ∈ M}, where N = {1, 2,..., n} and M = {1, 2,..., m} represent the index sets of satellites and grids respectively. At any moment, each satellite can only perform imaging tasks within a specific grid. The observation load of the grid changes dynamically over time. The change in the observation load is directly affected by the increase or decrease in the number of imaging tasks within its grid. As Figure 2 shown, the dots in the figure represent specific imaging tasks, and the depth of the grid color intuitively maps the observation load of the grid.

[0063] For each satellite s i , define the time window of its corresponding grid r j as w ij = [c ij , d ij , where c ij represents the start time of the time window, and d ij represents the end time of the time window. Given the certainty and regularity of the grid boundaries, combined with the forecast information of the satellite orbit, the calculation of the visibility of geographical grids can be completed in advance. Define the specific moment when the time window changes as the state change point t k , and define the time interval [t k , t k + ΔT k as stage k. According to the visible time windows of satellites and grids, the entire time axis of DGA can be divided into several decision-making stages, as Figure 3 shown.

[0064] Therefore, to reflect the dynamic characteristics of DGA in each stage, the DGA problem is divided into a series of consecutive single-stage DGAs (sDGAs) according to different decision-making stages. In each stage, different model parameters reflect the specific attributes of DGA in that stage. For each stage k, the observed load of grid r j is denoted as As Figure 4 shown, a time window can be divided into multiple decision-making stages, and the observation capabilities of satellites vary under each stage. For example, the decision-making stage close to the center of the time window has higher observation capabilities. Meanwhile, define as the observation capability of satellite s i for grid r j According to the definition of the DGA problem stage division in the previous section, the values of both the observation capability and the observed load are non-negative constants. Let represent the set of visible grids of satellite s i in decision-making stage k, that is:

[0065]

[0066] Let be the set of allocated grids of satellite s i in decision-making stage k, and If there is no intersection between the sets of allocated grids in two adjacent decision-making stages, that is then satellite s i needs to spend a certain amount of time adjusting the angle of its imaging payload to switch from the grids in set to the grids in set Therefore, define the switching time η i of satellite s ik in decision-making stage k as:

[0067]

[0068] where H represents a non-negative constant used to represent the simplified imaging payload switching time. As shown in the figure, when the intersection of the sets of allocated grids of satellite s i in decision-making stage k - 1 and k is an empty set, the switching time between the two stages is H, otherwise it is 0.

[0069] Based on the above analysis, in this section, the time line of the DGA problem is divided into several sub-problems sDGA to cope with the dynamic changes of the grid observation load and satellite observation capabilities within the time window. The mutual relationship between adjacent decision-making stages is mainly reflected in the imaging payload conversion time between allocation results, which transforms the DGA problem into a sequential decision-making problem, that is, the sDGA allocation result of the next stage depends on the allocation result of sDGA in the previous stage. Therefore, by solving the single-stage DGA problem (sDGA problem) one by one in sequence, the entire DGA problem can be effectively solved.

[0070] S2. The ground station models the sDAG problem

[0071] The present invention will analyze and model the sDGA problem (also known as the single-stage DGA problem). In sDGA, R i represents the set of visible grids of satellite s i , S j represents the set of visible satellites of grid r j . Each grid r j requires a satellite to complete the observation task within the grid to reduce its observation load β i . The observation capability of satellite s i for grid r j is represented by α ij , while the time amount allocated by satellite s i to grid r j is represented by x ij . The remaining observation load y j of grid r j is defined as follows:

[0072]

[0073] To achieve the effective and balanced allocation of the grid load, the optimization objective of the sDGA problem is set to minimize the maximum remaining load.

[0074] To further intuitively understand the meaning of the objective function, Figure 5 shows an example of the sDGA problem with 10 grids, where Figure 5 (a) the height of the rectangle represents the observation load of each grid, while Figure 5 (b) the height of the rectangle represents the remaining observation load of each grid after the satellite performs the imaging task, and the ordinate value corresponding to the dotted line is the maximum remaining load maxy j of the remaining observations.

[0075] If a satellite is allocated to two or more grids, the time for the satellite to perform the imaging payload attitude conversion between different grids needs to be considered. Define Denote the satellite as s i The set of allocated grids, satisfying For the satellite s i its conversion time ρ i The calculation formula is as follows:

[0076]

[0077] Based on the above analysis, in the decision-making stage k, construct the problem model P0 as follows

[0078]

[0079] s.t.

[0080]

[0081] where x ij is the decision variable, representing the amount of time to allocate the satellite s i to the grid r j Since the sDAG problem is a single-stage DAG problem divided from the DAG problem by the time slicing method, the physical meanings of the satellite s i and the grid r j are the same as those expressed by the model DGA. Δt is the total allocable time of this stage. The objective function U(x) is an exponential function that minimizes the maximum value of the remaining observation load, where represents the observation load on the grid r j in all satellite total allocation schemes x. Formula (6) means that the sum of the conversion time ρ i and the total satellite allocation time s i shall not exceed the allocable time Δt.

[0082] S3. Establish a potential game model for distributed satellite dynamic grid load allocation

[0083] Let G P ={N,{A i},{U i}} represent a game, where N = {1, 2,..., n} is the set of participants, which is the set of satellites in this chapter; A = A 1 ×A 2 …×A n is the joint action set, and U i : A i →R is the local utility function of participant i. For the action set a = (a 1 , a 2 ,..., a n ) ∈ A, where a i ∈A i is an action of participant i.

[0084] U(x) is the objective function of the problem mathematical model P0 and can also serve as the global utility function of the game G P = {N, {A i}, {U i}}. To ensure that the action sets of the participants satisfy the constraints of the problem model P0, a preliminary screening of the initial action sets of the participants will be carried out. Specifically, when constructing the action space in the potential game model, the actions of the participants that do not conform to the P0 constraints will be deleted. On the above premise, the action set a i of participant i is expressed as:

[0085] a i = (x i1 , x i2 ,..., x ij ,..., x im ) (7)

[0086] where x ij is the amount of time allocated by satellite s i to grid r j . Let a -i = (a 1 , a 2 ..., a i-1 , a i+1 ,..., a n ) be the action set of satellites other than satellite s i , represents the specific null action of participant i. Therefore, each x ij in it is zero.

[0087] According to the global utility function U(x), based on the Wonderful Life Utility rule, the local utility function of the individual is designed as

[0088]

[0089] where, is the set of grids assigned to satellite s i in action a i , is the set of satellites assigned to grid r j in the action space a.

[0090] Then, the local utility function proposed above is normalized:

[0091]

[0092] In formula (9), α max is the maximum observation ability of the satellite, βmax is the maximum observed load value of the grid, N max represents the maximum number of grids that a satellite can be assigned to, that is

[0093]

[0094] Let the local utility function U of satellite s can be obtained i be i (a i , a -i ) is as follows

[0095]

[0096] In a potential game, Nash equilibrium is a key concept that describes a state of game participants: given that the strategies of other participants remain unchanged, if all participants have no incentive to unilaterally change their own strategies, then the state at this time is called Nash equilibrium. The formal definition of Nash equilibrium is as follows.

[0097] Definition 6.1 Nash Equilibrium: For game G P ={N, {A i}}, {U i∈N}} i}}, action a i∈N is called Nash equilibrium, then for each participant i, there is N

[0098]

[0099] Definition 6.2 Exact Potential Game: Game G P ={N, {A i}}, {U i∈N}}, φ} can be defined as an exact potential game if and only if its potential function φ: A i → R satisfies i∈N i

[0100] Lemma 6.1 If the potential function φ is defined as Equation 14, then the task allocation game G A ={N, {A i}}, {U i}} is a potential game.

[0101]

[0102] Proof: According to the definition of the local utility function, we have:

[0103] ​​​

[0104] Thus, it can be obtained that:

[0105]

[0106] According to Definition 6.2, φ = 1 / P·U is the potential function of the game G P and the game G with the function φ as the potential function P is a strict potential game. Q.E.D.

[0107] Theorem 6.2 For the potential game G P = {N, {A i} i∈N , {U i} i∈N , φ} defined in Lemma 6.1, the Nash equilibrium a N of the game is the optimal solution a * of Problem P0.

[0108] Proof: Assume that the optimal solution is not the Nash equilibrium of the potential game G P , that is, there exists

[0109]

[0110] According to Definition 6.2, it can be obtained that

[0111]

[0112] Therefore, it can be obtained that

[0113]

[0114] The above formula contradicts the condition that a * is the optimal solution of Problem P0. Then the proof is completed.

[0115] S4. Obtain a distributed satellite grid load distribution scheme based on the improved best response process at the time of selection

[0116] For the above potential game model of distributed satellite dynamic grid load distribution, a distributed satellite grid load distribution method based on the Selective Time Variant-parameter Better Reply Process (SeTVBRP) is provided below. This algorithm adopts a decentralized online collaboration method, which can dynamically adjust parameters to adapt to the changing actions and states of each game participant, and then extends it to the dynamic multi-stage DGA problem. In addition, different from the recursive average action update mode commonly used in potential games, SeTVBRP adopts a single-step update method, which only selects one participant to update the action in one negotiation step, and has higher adaptability for satellite systems with limited communication conditions and delay tolerance. The specific process of the SeTVBRP algorithm is as follows:

[0117] First, generate the initial allocation scheme of all satellites according to the greedy strategy, and then randomly select a satellite at each iteration moment to update the action to generate a new allocation scheme. The satellite update action rules include: after updating the time-varying parameters ε(t) and ω(t) at the current moment, satellite s i Applies the selective action strategy to obtain the selective action set at time t Exchanges the allocation scheme information with other satellites in the information exchange satellite set Γ i After that, calculate the local efficacy function value according to formula (11) where a i (t) is the action of satellite si at time t, a -i (t) is the set of actions of satellites other than satellite si at time t, and then select actions from the selective action set to form the better reply set

[0118]

[0119] If the better reply set i of satellite s at the current moment t is not an empty set, then select a pending update action with equal probability from it (i.e., the pending update allocation scheme), and update the next action a i (t + 1) to the selected pending update action with probability θ In the above process, based on the traditional BRP algorithm, the present invention introduces two improvement mechanisms: the selective action strategy and the time-varying parameter strategy in the SeTVBRP algorithm.

[0120] (1) Selective action strategy

[0121] In the BRP algorithm, the calculation of the effectiveness function needs to be carried out for all potential actions in each iteration, but ultimately only one action is selected for the next round of update, resulting in a relatively low computational efficiency of the algorithm. To solve this problem, the SeTVBRP algorithm designs a selective action strategy. This strategy guides the participants to calculate the effectiveness function only for a partial set of actions in each iteration and obtain a better set of actions B from them. i (a). Specifically, in each iteration t of the selective action strategy, the participant randomly selects ω(t)·|A| actions from its action set A i to form a selective action set i where ω(t) ∈ [0, 1] represents the selection ratio and is a monotonically non-decreasing value related to the iteration time t.

[0122] (2) Time-varying parameter strategy

[0123] The design idea of the time-varying parameter strategy comes from the simulated annealing algorithm, where the temperature ζ determines the amplitude of the noise, indicating the possibility for the participant to take the best response action. When ζ approaches 0, the participant is more likely to select the best response action. In the potential game model constructed in this chapter, a similar influence of the utility function U on the parameter ε is observed. A larger ε provides an overall perspective of the utility function, and at this time, the participant (i.e., the satellite in the DGA problem) tends to take actions that reduce the sum of all grid observation loads. However, when ε approaches zero, the utility function U will guide the participant to be more inclined to select actions that directly minimize the global objective (i.e., the largest grid observation load). The time-varying parameter method designs the time-varying parameter ε to monotonically decrease as the iteration time t increases. This method ensures that the SeTVBRP algorithm focuses on exploring the possibility of better actions in the early iterations and utilizes and improves the current actions in the later stage. i i

[0124] The specific pseudocode of the SeTVBRP algorithm is as follows:

[0125]

[0126]

[0127] However, the original SeTVBRP algorithm can only solve the single-stage DAG problem. Now, the SeTVBRP algorithm is extended to the multi-stage case. Specifically, when the system state (including the grid load value β or the satellite observation ability α) changes, a single-stage decentralized cooperation process will be triggered. Within a single stage, the SeTVBRP algorithm proposed in the previous section is used to generate the action a k ​​​。Different from the SeTVBRP algorithm in the single-stage case, in the multi-stage case, satellite s i must consider the impact of the actions in the previous stage on the current stage. This impact is mainly reflected in the transition time η ik between the two stages, which is closely related to the actions in the previous stage. Therefore, after receiving the new dynamic parameters, all satellites combine the actions a k-1 in the previous stage to obtain the initial actions of their own satellites. Subsequently, within the satellite cluster, a "relay" communication mechanism is adopted. Under the pre-set communication order, the satellites execute lines 4 to 16 of the SeTVBRP algorithm, update their allocation schemes in turn, and pass them on to the next satellite in a relay manner until the termination condition is reached.

[0128] The collaborative termination conditions are as follows: ① The number of communications reaches the pre-set maximum number of iterations T Max ; ② The satellites reach a consensus: the current action a k reaches the Nash equilibrium state, that is, in this state, all satellites cannot improve their local efficiency values by updating their actions. Once the collaborative termination condition is reached, the satellite that receives the final action will broadcast this scheme to all satellites, thus ending the collaboration in this decision-making stage. After that, the satellite that receives the final action will execute this scheme until another change in the system state triggers the collaboration in the next decision-making stage.

[0129] The present invention also sets up an experimental process to verify the effect of the solution of the present invention through experiments.

[0130] The present invention designs two simulation experiment scenarios, named "small-scale scenario" and "large-scale scenario" respectively. In the small-scale scenario, the simulation involves 25 heterogeneous remote sensing satellites, aiming to simulate the decentralized collaborative effect of the satellite constellation when the number of satellites is small; the large-scale scenario involves 100 heterogeneous remote sensing satellites to explore the complexity and efficiency of the decentralized collaboration of the satellite constellation when the number of satellites is large.

[0131] The basic parameters of the remaining experimental scenarios are shown in Table 1. The grid is divided into rectangular units with a longitude and latitude length of 10° to ensure the extensiveness of the coverage range. The observation load values of each grid are randomly generated between 30 and 80, and this value is intended to reflect the observation requirements and load differences in different grid areas. The observation capabilities of the satellites are initially set as integers between 2 and 3, reflecting the differences in the observation capabilities of different satellites in different decision-making stages.

[0132] Table 1 Basic parameters of the experimental scenarios

[0133]

[0134] The present invention introduces a series of ablation experiments to explore the specific impacts of time-varying parameter strategies and selective action strategies on the performance of the SeTVBRP algorithm. By comparing the performance of the complete algorithm (i.e., the SeTVBRP algorithm) with the original BRP algorithm, the BRP algorithm with the time-varying parameter strategy introduced (i.e., the TVBRP algorithm), and the BRP algorithm with the selective action strategy introduced (i.e., the SeBRP algorithm), the contributions of different strategies to the algorithm effect are quantitatively discussed. Table 2 provides the statistical results of each algorithm running independently 50 times in a small-scale scenario, including the best value, worst value, average value R, average running time T, variance σ, and the number of times N to obtain the optimal solution after 50 algorithm runs best . And the convergence curves of different algorithms in the regional scenario are as Figure 7 shown

[0135] It can be observed from the statistical data in Table 2 that all performance indicators of the proposed SeTVBRP algorithm perform the best, demonstrating the significant impacts of the time-varying parameter strategy and the selective action strategy on improving the solution quality and efficiency of the algorithm:

[0136] The time-varying parameter strategy significantly improves the optimization ability of the algorithm by dynamically adjusting the balance between exploration and exploitation. Specifically, the average objective value of the BRP algorithm is about 30% higher than that of the TVBRP algorithm after introducing the time-varying parameter, and the average objective value of the SeBRP algorithm is about 48% higher than that of the SeTVBRP algorithm. This result indicates that the time-varying parameter strategy plays a key role in improving the optimization of the objective value

[0137] The selective action strategy effectively reduces the computational cost by reducing the size of the solution space considered in each iteration. The computational time of the BRP algorithm is about 35% less than that of the SeBRP algorithm, and the computational time of the TVBRP algorithm is about 38% less than that of the SeTVBRP algorithm, verifying that the selective action strategy can effectively reduce the computational time of the algorithm

[0138] Table 2 Allocation results of different algorithms in a small-scale scenario

[0139]

[0140] In the stage of iteration times from 100 to 300, the SeBRP and SeTVBRP algorithms adopting the selective action method show a faster convergence speed. This is because the selective action strategy allows the algorithm to search more concentratedly in the promising regions of the solution space, thus accelerating the early convergence process. While in the stage of iteration times from 300 to 500, the TVBRP and SeTVBRP algorithms adopting the time-varying method show better performance, indicating that the time-varying parameter strategy provides a more refined adjustment in the later stage, which helps the algorithm to approximate the optimal solution more accurately

[0141] In summary, the time-varying parameter strategy and the selective action strategy can effectively improve the original BRP algorithm, achieving significant improvements in both the quality and efficiency of the solutions. Among them, the time-varying parameter strategy enhances the algorithm's ability to search for the optimal solution, while the selective action strategy improves the algorithm's computational efficiency. The synergistic effect of these two strategies enables the SeTVBRP algorithm to quickly and accurately find high-quality solutions when solving the potential game problem in this chapter.

[0142] The following are the comparison results between the solution of the present invention and other algorithms.

[0143] The effectiveness of the proposed SeTVBRP algorithm of the present invention is illustrated by a set of comparative experiments. The comparative algorithms include: BRA

[150] , DT2A

[146] , SeSAP

[149] , TVLLA

[161] and TVCBLLA

[160] . The solution efficiency is reflected by two indicators: the global objective value and the CPU solution time.

[0144] The SeTVBRP algorithm successfully obtained 32 optimal solutions in 50 runs, and the average calculation time was approximately 0.7 seconds. In contrast, the number of optimal solutions obtained by the BRA, DT2A, SeSAP, and TVLLA algorithms was less than 15. Secondly, the SeTVBRP algorithm had the smallest variance among the 50 experimental results of the six algorithms, and the value of its worst-case solution was also the smallest, indicating that the SeTVBRP algorithm has high robustness and can have good convergence in various experimental scenarios. In contrast, although BRA takes little time to calculate the solution by introducing a pure greedy strategy, due to the lack of randomness, BRA performs poorly in the indicators related to the solution quality. The DT2A algorithm has a slightly better average solution quality than BRA due to its high randomness of action selection, but the calculation time is long and the robustness is insufficient. Since the TVCBLLA algorithm could not converge after 500 iterations, the results after 20,000 iterations are shown in Table 3, denoted as TVCBLLA(20000). Compared with the SeTVBRP algorithm, TVCBLLA(20000) not only has more iterations but also longer calculation time, about 10 times that of the SeTVBRP algorithm, and its efficiency and robustness are both inferior to the SeTVBRP algorithm.

[0145] Table 3 Allocation results of different algorithms in small-scale scenarios

[0146]

[0147] Next, focus on the convergence curves of each potential game algorithm. After 200 iterations, the average objective value of the SeTVBRP algorithm starts to be significantly better than other baseline algorithms. Before 200 iterations, the performance of the SeTVBRP algorithm is slightly inferior to the BRA, SeSAP, and TVLLA algorithms. This phenomenon can be attributed to the strong greedy characteristics shared by these comparison algorithms. They tend to quickly capture better solutions in the early iterations but may sacrifice the ability to converge to the optimal solution in the long term. In contrast, the DT2A algorithm introduces a large degree of randomness in the rule for updating the actions of participants. Although this design may lead to poor performance in the early evolutionary process, in the long run, it helps the algorithm avoid getting trapped in local optima and ultimately achieve better convergence. It is worth noting that the initial solution values obtained by the DT2A algorithm are significantly different from those of other algorithms because the DT2A algorithm initializes the solution in a random manner rather than using the greedy method of other algorithms. The SeTVBRP algorithm proposed in the present invention lies between the above two, maintaining a balance between greediness and randomness. This balanced strategy enables the SeTVBRP algorithm to perform well in the early iterations and gradually demonstrate its best performance in subsequent iterations. Therefore, after 200 iterations, the average objective value of the SeTVBRP algorithm is better than other algorithms, indicating that it can effectively narrow the solution space during the solution process and quickly converge to high-quality solutions.

[0148] In the algorithm comparison experiments in large-scale scenarios, the conclusions drawn are generally consistent with the experimental results in small-scale scenarios, and at the same time reveal the advantages of the SeTVBRP algorithm in dealing with larger-scale problems. Due to the increase in the number of grids and satellites in large-scale scenarios, the number of iterations in the experiment is increased from 500 to 2000 to ensure that the algorithm has enough iterations to explore the solution space. At the same time, the time-varying parameter τ value is set to 0.85 to adapt to large-scale scenarios.

[0149] In this case, the SeTVBRP algorithm proposed in this chapter still has an average objective value better than other algorithms. It is worth noting that the SeTVBRP algorithm obtained 17 optimal solutions in 50 runs, while other algorithms did not find optimal solutions. This result highlights the significant advantage of the SeTVBRP algorithm in large-scale search ability compared to other algorithms.

[0150] Table 4 Allocation results of different algorithms in large-scale scenarios

[0151]

[0152] From Figure 9It can be seen that there is a rapid decline stage in the average objective value of the SeTVBRP algorithm when the number of iterations reaches around 1700. In the convergence curve graph of the small-scale scenario, there is a similar trend when the number of iterations is between 300 and 350, indicating that the time-varying parameter strategy of the SeTVBRP algorithm effectively enters the solution development and optimization stage in the later iteration. Therefore, since the τ value is set to 0.85 at this time, the convergence curve of SeTVBRP starts to accelerate when the iteration reaches τT max = 1700 times. However, this does not mean that SeTVBRP can only achieve better results than other algorithms when τ = 0.85. In fact, as Figure 6 shown, the SeTVBRP algorithm is generally superior to similar algorithms in the range of τ from 0.2 to 0.95, showing the wide applicability of the algorithm. In addition, although the performance of the SeTVBRP algorithm may not be prominent during the early iteration, its computing time is the shortest among all algorithms, only 4.628 seconds.

[0153] Based on the above comparative experiment analysis, the summary of the algorithm comparative experiment results is as follows:

[0154] (1) Performance of the SeTVBRP algorithm: In two different experimental scenarios of small-scale and large-scale scenarios, the SeTVBRP algorithm demonstrates remarkable performance: the average objective values of this algorithm reach 0.66 and 1.16 respectively, and as time extends infinitely, the algorithm can gradually approach the optimal solution. In addition, in terms of the solution efficiency and solution stability for the problems in this chapter, compared with the other comparative algorithms, the SeTVBRP algorithm also achieves good results.

[0155] (2) Applicability and limitations of the algorithm: From the experimental results, it can be concluded that the SeTVBRP algorithm has certain advantages in dealing with large-scale and complex task allocation problems. However, the algorithm may encounter performance bottlenecks when facing allocation problems with extremely small time granularity. Specifically, to further verify the robustness of the SeTVBRP algorithm, the number of satellites is increased to 200 and 300 respectively in the experiment. The results show that even when the number of satellites increases significantly, the SeTVBRP algorithm can still maintain good performance. However, when the measurement granularity of the allocation time decreases, such as from minutes to seconds, the performance of the algorithm deteriorates. This is because as the time granularity decreases, the space of the optional allocation action set will increase exponentially, greatly increasing the difficulty for satellites to find the optimal solution in the huge action space.

[0156] Those skilled in the art should understand that the above-mentioned modules or steps of the present invention can be implemented by a general-purpose computer device. Optionally, they can be implemented by program codes executable by the computing device, so that they can be stored in the storage device and executed by the computing device, or they can be separately fabricated into individual integrated circuit modules, or multiple modules or steps among them can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0157] Although the specific implementation manners of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation to the protection scope of the present invention. Those skilled in the art should understand that, based on the technical solutions of the present invention, various modifications or deformations that can be made without creative efforts by those skilled in the art are still within the protection scope of the present invention.

[0158] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A multi-satellite dynamic grid load distribution method based on potential energy game, characterized in that: Follow these steps: S1. The ground station obtains satellite data and grid data divided by the management end based on satellite positions, and performs DAG problem modeling; N = {1, 2, ..., n} represents a set of satellite indices, where satellite s i The index of is i, i∈N; M = {1, 2, ..., m} represents a grid index set, where grid r j The index of is j, j∈M; S2. The ground station divides the DAG problem into a single-stage DAG problem according to the time slicing method, and performs sDAG problem modeling; wherein the single-stage DAG problem is an sDAG problem; Each grid r j Satellites are needed to complete the observation tasks within the grid to reduce the observation load β i ; In sDAG problem modeling, satellite s i For the grid j The observation ability is α ij Said satellite s i Assign to grid r j The amount of time is x ij express; Define the grid r j The remaining observed load y j as follows: S3. Establish a potential game model for distributed satellite dynamic grid load distribution; Let G P ={N,{A i },{U i }} represents a game, where N = {1,2,...,n} is the satellite set; A = A1×A2…×A n is the joint action set, U i :A i →R is the local utility function of participant i; For an action set a=(a1,a2,...,a n )∈A, where; a i ∈A i is an action of participant i; S4. Obtaining a distributed satellite grid load allocation scheme based on a selection time-varying optimal response process; Generate the initial allocation plan for all satellites according to the greedy strategy; A satellite update action is randomly selected at each iteration to generate a new allocation solution.

2. A multi-satellite dynamic grid load distribution method based on potential energy game as claimed in claim 1, characterized in that: In step S1, At any given moment, each satellite can only perform imaging tasks within a specific grid; The observed load of the grid changes dynamically over time; The change in observation load is directly affected by the increase or decrease in the number of imaging tasks within the grid.

3. A multi-satellite dynamic grid load distribution method based on potential energy game as claimed in claim 2, characterized in that: In DAG problem modeling, for each satellite s i , the corresponding grid r j The time window is w ij =[c ij ,d ij ], where c ij Represents the start time of the time window, d ij Indicates the end time of the time window.

4. A multi-satellite dynamic grid load distribution method based on potential energy game as claimed in claim 1, characterized in that: In step S1, in DAG problem modeling, the state change point t k is the specific moment when the time window changes, and the time interval [t k ,t k +Δt] is called stage k.

5. A multi-satellite dynamic grid load distribution method based on potential energy game as claimed in claim 4, characterized in that: In DAG problem modeling, For satellites i For the grid j observation ability and observed load The values ​​of are all non-negative constants; represents the satellite s in the decision stage k i The visible grid set is:

6. A multi-satellite dynamic grid load distribution method based on potential energy game as claimed in claim 5, characterized in that: In DAG problem modeling, is the satellite s in the decision stage k i The set of allocation grids, and If there is no intersection between the allocation grid sets of two adjacent decision stages, that is, Satellite s i The imaging payload angle needs to be adjusted to obtain The grid turn collection in The grid in .

7. A multi-satellite dynamic grid load distribution method based on potential energy game as claimed in claim 6, characterized in that: In DAG problem modeling, satellite s in decision stage k i The conversion time η ik for: Where H represents a non-negative constant, which is used to represent the simplified imaging load conversion time; When the k-1 decision stage and the k decision stage have satellite s i When the intersection of the allocation grid sets is an empty set, the transition time between the two stages is H, otherwise it is 0.

8. A multi-satellite dynamic grid load distribution method based on potential energy game as claimed in claim 7, characterized in that: In step S2, if the satellite is assigned to two or more grids, the time for the satellite to perform imaging payload attitude conversion between different grids is considered.

9. A multi-satellite dynamic grid load distribution method based on potential energy game as claimed in claim 8, characterized in that: In sDAG problem modeling, Indicates satellites i The set of allocation grids that satisfies For satellites i , its conversion time ρ i The calculation formula is as follows:

10. A multi-satellite dynamic grid load distribution method based on potential energy game as claimed in claim 9, characterized in that: In sDAG problem modeling, in the decision stage k, the problem model P0 is constructed as follows Among them, x ij is the decision variable, indicating that the satellite s i Assign to grid r j the amount of time; Since the sDAG problem is a single-stage DAG problem divided by the DAG problem according to the time slicing method, the satellite s i and grid r j The physical meaning is the same as that expressed by the model DGA; Δt is the total allocatable time for this phase; the objective function U(x) is an exponential function that minimizes the maximum value of the remaining observed load, where represents the total allocation of all satellites to grid r j The observed load; represents the conversion time ρ i Total allocation time with satellite s i The sum shall not exceed the allocatable time Δt.

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