Unmanned aerial vehicle formation optimization method and system

Abstract

The invention relates to an unmanned aerial vehicle formation optimization method, belongs to the technical field of unmanned aerial vehicle formation cooperative control, and solves the technical problem that the real-time performance of unmanned aerial vehicle formation topological structure change in a dynamic environment and multi-constraint coupling and cyclic dependence of unmanned aerial vehicle fault node failure are not considered in an existing optimization method. Comprising the following steps: taking unmanned aerial vehicles in a formation as nodes, and constructing an unmanned aerial vehicle formation weighted graph based on an interaction relationship among the unmanned aerial vehicles; searching an optimal communication topology based on the weighted graph to obtain an optimal communication network structure; identifying key nodes in the unmanned aerial vehicle formation based on the optimal communication network structure; matching at most one candidate node for the key node; and when the unmanned aerial vehicle breaks down, real-time reconstruction and communication recovery are carried out on the unmanned aerial vehicle formation based on the matching relationship between the candidate nodes and the key nodes. And real-time reconstruction and communication recovery of the unmanned aerial vehicle formation are realized.

Description

Technical Field

[0001] The present invention relates to the technical field of UAV formation collaborative control, and in particular to a UAV formation optimization method and system. Background Art

[0002] As an efficient and flexible multi-agent system, drone formations hold great promise in a variety of key application areas, including disaster relief and logistics. By enabling the coordinated operation of multiple drones, they achieve wide-area coverage, rapid response, and efficient execution of complex tasks, significantly improving mission efficiency and effectiveness. However, in complex and dynamic mission environments, drone formations face numerous interference factors, including dynamic topological changes, node failures, and communication interference, which severely impact the overall formation's collaborative performance and mission completion quality.

[0003] In recent years, research in the field of cooperative control of UAV formations has made significant progress. However, existing research still has limitations in assessing node importance in dynamic environments. On the one hand, existing methods do not fully consider the real-time nature of topological changes and the multi-constraint coupling effects in dynamic environments, making it difficult to adapt to the dynamic evolution of formation networks. On the other hand, the lack of joint modeling and analysis of UAV heterogeneous capabilities and differences in task priorities limits the optimization potential in complex scenarios. In addition, existing research often evaluates node importance based on static network indicators such as degree centrality and betweenness centrality. Although these methods can reveal dependencies between systems, they have difficulty characterizing dynamic conflicts and circular dependencies in directed relationships during dynamic interactions, ultimately causing task allocation schemes to easily fall into local optimality or resource conflicts. Summary of the Invention

[0004] In view of the above analysis, the embodiments of the present invention aim to provide a drone formation optimization method and system to solve the technical problems that the existing methods and existing optimization methods do not consider the real-time changes in the drone formation topology structure in a dynamic environment and the multi-constraint coupling and cyclic dependency of the failure of drone fault nodes.

[0005] The purpose of the present invention is mainly achieved through the following technical solutions:

[0006] The present invention provides a method for optimizing a UAV formation, comprising the following steps:

[0007] A weighted graph of UAV formation is constructed based on the interaction relationship between UAVs and each UAV in the formation is used as a node.

[0008] Searching for an optimal communication topology based on the weighted graph to obtain an optimal communication network structure; identifying key nodes in the UAV formation based on the optimal communication network structure;

[0009] Match at most one candidate node for the key node;

[0010] When a UAV fails, the UAV formation is reconstructed and communication is restored in real time based on the matching relationship between candidate nodes and key nodes.

[0011] Furthermore, the interaction relationship of the UAV formation is abstracted into a weighted graph G = (V, E, W); where the node set V = {v1,…,v N} represents N drones; the edge set E = {e ij |(v i ,v j )} indicates that there is a communication link between UAVs i and j; W represents the edge weight set between any two UAVs.

[0012] Furthermore, a genetic algorithm is used to search for an optimal communication topology based on the weighted graph to obtain an optimal communication network structure, including:

[0013] Based on the edge weights of the weighted graph, the population is initialized and all two-node pairs randomly generate chromosome individuals Z = [z 11 、z 12 ,…,z ij ,…,z NN ]∈{0,1} N×N ; Where Z is the communication network structure, 1 means that the nodes have established communication with each other and there is a communication link; 0 means that the nodes have not established communication with each other and there is no communication link;

[0014] Calculating the fitness of the chromosome individual;

[0015] In each generation, the roulette wheel strategy is used to select individuals according to their fitness to obtain the selected individuals;

[0016] A parent individual is selected from the selected individuals to generate two offspring individuals, which are then added to the population; the population mutates;

[0017] The operation is repeated until the fitness tends to be stable, and the chromosome individual with the largest fitness is obtained. The optimal communication network structure is obtained based on the communication link relationship of the chromosome individual.

[0018] Furthermore, the fitness of individual chromosomes is calculated using the following formula:

[0019]

[0020] Among them, d ij is the Euclidean distance between two nodes i and j; F(Z) is the fitness of the chromosome individual; ρ is the penalty coefficient, 1 {·} is an indicative function used to penalize connections that exceed the maximum communication radius R; (i,j)∈E zij d ij +ε represents all the communication links z in the communication network structure ij =1; ε is the anti-zero constant.

[0021] Furthermore, the key nodes in the UAV formation are identified based on the optimal communication network structure, including:

[0022] Using the Hodge decomposition method to perform structural analysis on each edge in the optimal communication network structure, each edge is decomposed into an orthogonal sum of three parts: gradient flow, curl flow, and harmonic flow; wherein the gradient flow is the product of the gradient matrix and the node potential function;

[0023] The gradient component of the node potential function is defined as the Hodge score of all nodes in the UAV formation;

[0024] Sort the Hodge score of each drone node and select the top K' nodes with the highest scores to form the key node set T in the drone formation.

[0025] Furthermore, matching the key node with at most one candidate node includes:

[0026] The remaining nodes in the UAV formation except the key nodes are regarded as candidate nodes;

[0027] For each candidate node p∈N and each key node t∈T, extract the edge weight ω pt As the matching weight, the maximum matching weight between the candidate node and the key node is obtained as follows:

[0028]

[0029] Count the number of matches between each key node and candidate nodes;

[0030] If the number of matches between a key node and a candidate node is c t >1, then the key node is redistributed according to the second largest matching weight to obtain the corresponding matching number c t =1;

[0031] If the number of matches of a key node c t =0, then the number of candidate nodes is less than the number of key nodes;

[0032] Iterate until all key nodes c t ≤1, and get the mapping π between key nodes and candidate nodes.

[0033] Furthermore, if a UAV fails, the UAV formation is reconstructed and communication is restored in real time based on the matching relationship between the candidate nodes and the key nodes, including:

[0034] If the faulty node is a non-critical node and is not a candidate node for a critical node, delete the faulty node and its associated edges from G and reconstruct the weighted graph of the UAV formation;

[0035] If the faulty node is a non-critical node and is a candidate node for a critical node, the faulty node and its associated edges are deleted, and the weighted graph of the UAV formation is reconstructed;

[0036] If the faulty node is a key node t∈T, delete the node and its associated edges from G, replace the key node with a paired candidate node, and reconstruct the weighted graph of the UAV formation;

[0037] Based on the reconstructed weighted graph of the drone formation, the communication network structure of the drone formation is updated. Furthermore, the Hodge scores of all nodes in the drone formation are as follows:

[0038]

[0039] Among them, B g ∈R N×|E| is the gradient matrix, φ∈R N is the node potential function, φ1, φ2, ..., φ2 are the node potential functions of the UAV nodes; R is a real number set;

[0040] To B g φ1,…,B g φ N Arrange them in descending order from large to small, and select the top K' nodes with the highest scores and similar gradients to form the key node set.

[0041] Furthermore, the edge weight between any two drones is calculated, including:

[0042] Calculate the Euclidean distance d between any two drone nodes ij ,as follows:

[0043] d ij =||X i -X j ||2

[0044] Among them, X i 、X j are the positions of drones i and j respectively;

[0045] Calculate the edge weight ω of each corresponding communicative link edge based on the Euclidean distance ij ,as follows:

[0046]

[0047] Where R is the communication radius and ε is the anti-zero constant.

[0048] The present invention also provides a UAV formation optimization system, comprising the following modules:

[0049] The formation weighted graph construction module is used to construct a UAV formation weighted graph based on the interaction relationship between UAVs and each UAV in the formation as a node;

[0050] A communication optimization and key node identification module is used to search for an optimal communication topology based on the weighted graph to obtain an optimal communication network structure; and identify key nodes in the UAV formation based on the optimal communication network structure;

[0051] A key node matching module, configured to match at most one candidate node to the key node;

[0052] The fault reconstruction and communication recovery module is used to perform real-time reconstruction and communication recovery of the UAV formation based on the matching relationship between candidate nodes and key nodes when a UAV fails.

[0053] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0054] 1. This invention constructs a weighted graph of UAV formations and uses a genetic algorithm to search for the optimal communication topology. This allows real-time adaptation to the dynamic evolution of the formation network (such as node failures and communication interference), addressing the problem of delayed response to topology changes in dynamic environments in existing methods. This approach fully considers the real-time nature of topology changes and the multi-constraint coupling effect, effectively addressing the problem of affected collaborative performance in complex dynamic mission environments in existing methods.

[0055] 2. Introducing the Hodge decomposition method to perform structural analysis on each edge in the communication network structure, quantifying the dynamic interaction relationship between nodes, and dynamically and accurately identifying key nodes in the formation. This method breaks through the limitations of traditional static indicators (such as degree centrality) and avoids the drawbacks of existing technologies that cause task allocation schemes to fall into local optimality or resource conflicts due to static network indicators. This provides a more efficient and reasonable solution for formation optimization in complex scenarios.

[0056] 3. Match the remaining nodes in the formation except the key nodes to the key nodes according to the edge weight to ensure load balancing. Each key node is matched with at most one candidate drone. This can not only ensure the smooth execution of the mission, but also maintain the robustness of the system, effectively avoid communication overload or redundant resource waste, and improve the overall mission execution efficiency of the formation;

[0057] 4. In the calculation of communication link edge weights, the heterogeneous capabilities of drones and communication radius limitations are comprehensively considered, and multi-constraint collaborative optimization is achieved through a dynamic weighting strategy to improve the adaptability and flexibility of formation mission execution in complex scenarios;

[0058] 5. For failures of key nodes and non-key nodes, a hierarchical fault handling strategy (direct deletion, candidate replacement, and topology reconstruction) is designed. Combined with the optimal communication network rapid recovery mechanism, when a key node or non-key node fails, a real-time reconstruction mechanism can be triggered to quickly re-identify the node score and allocation plan based on the updated communication structure to ensure the stable and reliable operation of the formation, minimize mission interruption time, ensure the continuity and reliability of the formation mission, and enhance the adaptability and recovery capabilities of the UAV formation when facing node failure problems.

[0059] In the present invention, the above-mentioned technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of the present invention will be described in the following description, and some advantages will become apparent from the description or be learned through practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0061] Figure 1 This is a flow chart of a method for optimizing a UAV formation according to an embodiment of the present invention;

[0062] Figure 2 Schematic diagram of multi-stage UAV network optimization and location allocation in an embodiment of the present invention;

[0063] Figure 3 This is a schematic diagram of the range and coordinate definition of the UAV cluster flight area in an embodiment of the present invention;

[0064] Figure 4 A schematic diagram of a UAV formation optimization system module. DETAILED DESCRIPTION

[0065] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, and are not used to limit the scope of the present invention.

[0066] Example 1:

[0067] This paper proposes a UAV formation optimization method. By combining an improved genetic algorithm and using Hodge decomposition theory, a dynamic task allocation strategy is designed to effectively deal with problems such as changes in the UAV formation topology and node failures, and optimize the UAV formation position and communication links.

[0068] like Figure 2 As shown in the figure, starting from the initial UAV position, the complete process goes through communication graph construction, key node identification, optimal matching allocation, and finally fault response processing. First, this method calculates the edge weights between nodes based on Euclidean distance and communication radius and generates a directed weighted graph. Then, a genetic algorithm is used to search for the optimal communication topology in the feasible structure space to ensure global optimal connectivity and efficiency. Next, Hodge decomposition is applied to the graph to extract gradient flow components as node scores, and a set of key nodes with the greatest structural influence are selected based on this ranking. On this basis, the remaining nodes are matched to key nodes based on edge weights to form binding relationships while ensuring load balancing. Finally, when a key node or non-key node fails, a real-time reconstruction mechanism for fault processing is implemented to re-identify the node scores and allocation schemes based on the updated communication structure to ensure the stability and reliability of the UAV formation communication network structure.

[0069] A specific embodiment of the present invention, as Figure 1 As shown, a UAV formation optimization method is disclosed, comprising the following steps:

[0070] Step S1: constructing a weighted graph of the UAV formation based on the interaction relationship between the UAVs and taking each UAV in the formation as a node;

[0071] Step S2: searching for an optimal communication topology based on the weighted graph to obtain an optimal communication network structure; identifying key nodes in the UAV formation based on the optimal communication network structure;

[0072] Step S3: matching at most one candidate node for the key node;

[0073] Step S4: When a UAV fails, the UAV formation is reconstructed and communication is restored in real time based on the matching relationship between the candidate nodes and the key nodes.

[0074] Step S1: construct a weighted graph of the UAV formation based on the interaction relationship between the UAVs and taking each UAV in the formation as a node.

[0075] The interaction relationship of the UAV formation is abstracted into a weighted graph G = (V, E, W); where the node set V = {v1,…,v N} represents N drones; the edge set E = {e ij |(v i ,v j)} indicates that there is a communication link between UAVs i and j; W represents the edge weight set between any two UAVs.

[0076] Drone's position X i =(x i ,y i )∈[0,LEN] 2 In the region [0,LEN] 2 uniform random distribution within the i ,y i is the position coordinate of the i-th UAV; LEN is the range of the UAV cluster flight area. The position of the UAV is restricted to a square area with a side length of LEN.

[0077] like Figure 3 As shown, the coordinates of the four corners of the LEN×LEN rectangle are (0,0), (0,L), (LEN,0), and (LEN,LEN).

[0078] LEN sets the initial value based on the number of drones N and the communication radius R in the drone swarm, and then dynamically sets the homogeneous and heterogeneous models of drones in the drone swarm and the flight missions; it can be adjusted according to specific needs.

[0079] The side length LEN of the flight area is expressed as follows:

[0080]

[0081] Where η∈(0,1) is the coverage coefficient, usually set to 0.6 to 0.8.

[0082] For example, in the application scenario of disaster area search, N=30, and the task requirement is to cover 5km 2 In the area, real-time transmission of disaster scene images is performed, R=800m, the coverage coefficient is η=0.7, and based on formula (1), LEN≥9280m. For example, LEN can be set to 9.29KM.

[0083] Calculate the edge weight between any two drones, including:

[0084] Calculate the Euclidean distance d between any two drone nodes ij ,as follows:

[0085] d ij =||X i -X j ||2 Formula (2)

[0086] Among them, X i 、X j are the positions of drones i and j respectively;

[0087] Calculate the edge weight ω of each corresponding communicative link edge based on the Euclidean distance ij ,as follows:

[0088]

[0089] Where R is the communication radius and ε is the anti-zero constant.

[0090] The anti-zero constant ε>0; illustratively, the anti-zero constant ε is set to 0.1; it can be adjusted according to specific needs.

[0091] When the Euclidean distance d between two UAV nodes ij When the communication radius is less than or equal to R, the corresponding edge weight is A communication link is established between them, and the communication strength is inversely proportional to the distance. At the same time, in order to avoid the situation where the distance is infinite when it is zero, an anti-zero constant ε is added to correct the distance; otherwise, it is considered that they cannot communicate directly, and the corresponding edge weight is 0, indicating that there is no communication link.

[0092] The weight relationship between nodes represents the strength or quality of the communication link between drones.

[0093] Regarding the setting of the communication radius R, it should be reasonably selected based on the actual hardware performance of the drone (such as signal transmission power and environmental interference). Too large a value may cause network congestion, while too small a value may reduce connectivity.

[0094] For example, in a disaster rescue scenario, obtaining images of the disaster area requires high resolution, and R is set to 800m, which can be adjusted according to specific needs.

[0095] Weight Matrix The communication strength and reachability between drones in a drone cluster are characterized, providing basic data for subsequent optimization.

[0096] The function of step S1 is to abstract the UAV formation into a weighted graph, characterize the communication relationship between each UAV in the UAV formation, and lay the foundation for subsequent optimization.

[0097] Step S2 includes steps S21-S22.

[0098] Step S21: Search for an optimal communication topology based on the weighted graph to obtain an optimal communication network structure.

[0099] To optimize the connection relationship between drone nodes, a genetic algorithm is introduced to solve the problem of optimizing the structure of drone communication network. Genetic algorithm is a global search algorithm based on biological evolution mechanism, which includes selection, crossover and mutation operations.

[0100] Searching for an optimal communication topology based on the weighted graph using a genetic algorithm to obtain an optimal communication network structure includes:

[0101] Based on the edge weights of the weighted graph, the population is initialized and all two-node pairs randomly generate chromosome individuals Z = [z 11 、z 12 ,…,z ij ,…,z NN ]∈{0,1} N×N ; Where Z is the communication network structure, 1 means that the nodes have established communication with each other and there is a communication link; 0 means that the nodes have not established communication with each other and there is no communication link;

[0102] Calculating the fitness of the chromosome individual;

[0103] In each generation, the roulette wheel strategy is used to select individuals according to their fitness to obtain the selected individuals;

[0104] A parent individual is selected from the selected individuals to generate two offspring individuals, which are then added to the population; the population mutates;

[0105] The operation is repeated until the fitness tends to be stable, and the chromosome individual with the largest fitness is obtained. The optimal communication network structure is obtained based on the communication link relationship of the chromosome individual.

[0106] Z is a binary matrix.

[0107] (1) Initial population generation: The initial communication state is 0 or 1.

[0108] (2) Selection: Roulette strategy is used in each generation to select individuals according to their fitness, and individual Z is selected. k The probability P k for:

[0109]

[0110] Where M is the population size; F(Z k ) is Z k Fitness; F(Z l ) is Z l Fitness.

[0111] The probability of each individual is accumulated in sequence to form a cumulative probability sequence with an interval of [0,1]:

[0112]

[0113] Generate a random number r uniformly distributed in the interval [0,1]. Find a random number that satisfies Q n-1 <r≤Q nThe individual n is the selected individual.

[0114] (3) Crossover: Two parent individuals are selected from the population through a selection strategy. Offspring are generated through a single-point crossover strategy: a position is randomly selected in the coding sequence of the parent individual as the crossover point, and the gene segments of the two parent individuals after the crossover point are exchanged to generate two offspring individuals, which are directly added to the new population.

[0115] (4) Mutation: Using random mutation strategy, set a mutation probability p m , which is set to 2% for example, represents the probability of each gene position mutating. For each gene position of each individual in the population, a random number d∈[0,1] is generated. If d <p m , then the gene bit is mutated. The gene bit is modified according to the encoding method, that is, the value of the bit is flipped. The mutated individual joins the new generation population and participates in subsequent evolution together with the unmutated individuals.

[0116] (5) Repeat the operation until the fitness becomes stable and finally obtain the optimal communication network structure.

[0117] The fitness of chromosome individuals is calculated using the following formula:

[0118]

[0119] Among them, d ij is the Euclidean distance between two nodes i and j; F(Z) is the fitness of the chromosome individual; ρ is the penalty coefficient, 1 {·} is an indicative function used to penalize connections that exceed the maximum communication radius R; (i,j)∈E z ij d ij +ε represents all the communication links z in the communication network structure ij =1; ε is the anti-zero constant.

[0120] Individual fitness is determined by both communication efficiency and reachability.

[0121] Indicates communication efficiency. The shorter the total length of the communication link, the higher the communication efficiency and the higher the adaptability.

[0122] The characteristic function shows that d ij >R, the value is 1, otherwise the value is 0, which is used to determine whether the distance between nodes i and j exceeds the communication radius.

[0123] Represents the communication reachability penalty term, which aims to penalize connections that exceed the communication radius to prevent the communication link from being too long and unreliable. The penalty coefficient ρ is used to control the penalty intensity.

[0124] The anti-zero constant ε is used to measure the total length of the communication link and avoid the denominator being zero.

[0125] The penalty coefficient ρ>0; the larger ρ is, the heavier the penalty for over-distance connections;

[0126] Exemplarily, the penalty coefficient ρ is defined as follows:

[0127]

[0128] The coefficient k∈[10,1000] is adjusted according to the task requirements. The exemplary settings are shown in Table 1.

[0129] Table 1 Example of setting penalty coefficient ρ

[0130]

[0131]

[0132] Step S22: Identify key nodes in the UAV formation based on the optimal communication network structure.

[0133] In order to identify the key nodes in the UAV network, the Hodge decomposition method is introduced to perform structural analysis on the edge functions on the optimal communication network structure graph.

[0134] Based on the optimal communication network structure, key nodes in the UAV formation are identified, including:

[0135] Using the Hodge decomposition method to perform structural analysis on each edge in the optimal communication network structure, each edge is decomposed into an orthogonal sum of three parts: gradient flow, curl flow, and harmonic flow; wherein the gradient flow is the product of the gradient matrix and the node potential function;

[0136] The gradient component of the node potential function is defined as the Hodge score of all nodes in the UAV formation;

[0137] Sort the Hodge score of each drone node and select the top K' nodes with the highest scores to form the key node set T in the drone formation.

[0138] Each edge function f in the optimal communication network structure edge Decomposed into the orthogonal sum of gradient flow, curl flow and harmonic flow:

[0139] f edge =B g φ+B cψ+h Formula (8)

[0140] in, is the gradient matrix, is the node potential function, is the curl matrix, φ represents the circulatory component, h is the harmonic flow, and h satisfies Im(B g ) and Im(B c ) are orthogonal, as follows:

[0141] h⊥Im(B g ),h⊥Im(B c ) Formula (9)

[0142] Among them, Im(B g ) represents the matrix B g Image space (Image), that is, there is a vector x such that B g The set of all vectors y where x=y. Im(B g ) describes the matrix B g The output space that can be "covered".

[0143] In the Hodge decomposition, the gradient flow and the curl flow come from Im(B g ) and Im(B c ), and the harmonic flow h is the orthogonal complement of these two spaces, so it cannot be linearly generated by the node potential function or the cycle function.

[0144] In addition, the Hodge decomposition satisfies an important property:

[0145]

[0146] That is, the product of the gradient matrix and the curl matrix is always a zero matrix, reflecting their orthogonality in the edge function space.

[0147] According to Hodge theory, the node potential function φ i The gradient component B g φ i Defined as drone node v i Hodge score.

[0148] The Hodge scores of all nodes in the drone formation are as follows:

[0149]

[0150] Among them, B g ∈R N×|E| is the gradient matrix, φ∈R N is the node potential function, φ1, φ2, …, φ2 are the node potential functions of the UAV nodes; R is a real number set;

[0151] To B g φ1,…,B g φ N Arrange them in descending order from large to small, and select the top K' nodes with the highest scores and similar gradients to form the key node set.

[0152] s is the result of all gradient flows. There are N elements in s. s is a vector and is related to the number of drones in the drone formation. The Hodge score s of each drone node in the drone formation is i The higher the drone node v i The more critical.

[0153] For example, the node gradients vary greatly; for example, among 10 drones, 1-4 have relatively high, stable, and similar gradients, while 6-10 have relatively low and similar gradients, which are quite different from the gradients of the first 4 drones.

[0154] Sort the importance of nodes and select the top K' nodes with the highest scores to form the key node set T = {t1,…,t K'}, effectively identifying high-impact critical UAVs in the center of the structure.

[0155] According to Hodge solution theory, the gradient component is the component of the edge function generated by the node potential function. To decompose the edge function into gradient components, we need to find the node potential function φ so that its gradient B g φ is as close as possible to the actual edge function f edge This is a least squares optimization problem, which is to minimize: ||B g φ-f edge || 2 .

[0156] By taking the derivative and setting it to zero, we can derive the equation as follows:

[0157] Lφ=B g * f edge Formula (12)

[0158] Where L = B g * B g Is the graph Laplace matrix. In the UAV formation communication network structure diagram, L = DA, where D is the degree matrix and A is the adjacency matrix. B g * is the adjoint matrix of the gradient matrix.

[0159] When the graph is connected, the null space of the Laplace matrix L consists of constant vectors, so L is not invertible. In this case, the pseudo-inverse L is needed. + Solve the equation and get the unique minimum norm solution, which is:

[0160] φ=L + ·B g * f edge Formula (13)

[0161] Finally, the gradient component B is obtained g φ, based on the gradient component B g φ obtains the s vector of formula (11), and then obtains the key node.

[0162] The role of step S2 is to search for the optimal communication topology based on the weighted graph and identify key nodes to improve the efficiency and stability of formation coordination.

[0163] Step S3: Match at most one candidate node for the key node.

[0164] Match at most one candidate node for the key node, including:

[0165] The remaining nodes in the UAV formation except the key nodes are regarded as candidate nodes;

[0166] For each candidate node p∈N and each key node t∈T, extract the edge weight ω pt As the matching weight, the maximum matching weight between the candidate node and the key node is obtained as follows:

[0167]

[0168] Count the number of matches between each key node and candidate nodes;

[0169] If the number of matches between a key node and a candidate node is c t >1, then the key node is redistributed according to the second largest matching weight to obtain the corresponding matching number c t =1;

[0170] If the number of matches of a key node c t =0, then the number of candidate nodes is less than the number of key nodes;

[0171] Iterate until all key nodes c t ≤1, and get the mapping π between key nodes and candidate nodes.

[0172] After obtaining the key node set T, the remaining node set N = V\T (that is, all drone nodes V in the drone formation minus the key node set T).

[0173] Then count the number of matches for each key node as follows:

[0174]

[0175] If the number of matches between a key node and a candidate node is c t >1, then multiple candidate nodes are matched to the key node, there is a conflict, redistribute according to the next largest weight, and iterate until all c t ≤1.

[0176] Finally, the mapping of key nodes and candidate nodes is obtained as follows:

[0177] π:N→T formula (16)

[0178] A key node matches at most one candidate node.

[0179] To ensure smooth mission execution while maintaining system robustness, each key node is matched with at most one candidate drone, thus achieving a balance between communication quality and redundant backup. This matching strategy effectively avoids communication overload or waste of redundant resources, ensuring the efficient operation of key nodes in the formation. At the same time, backup nodes can quickly fill in the gaps in the event of a failure, ensuring the stability and flexibility of the drone formation.

[0180] The purpose of step S3 is to match at most one candidate node for each key node to ensure that it can be quickly replaced when a failure occurs, maintaining the communication quality of the UAV formation and the robustness of the system.

[0181] Step S4: When a UAV fails, the UAV formation is reconstructed and communication is restored in real time based on the matching relationship between the candidate nodes and the key nodes.

[0182] If a UAV fails, the UAV formation is reconstructed and communication is restored in real time based on the matching relationship between candidate nodes and key nodes, including:

[0183] If the faulty node is a non-critical node and is not a candidate node for a critical node, delete the faulty node and its associated edges from G and reconstruct the weighted graph of the UAV formation;

[0184] If the faulty node is a non-critical node and is a candidate node for a critical node, the faulty node and its associated edges are deleted, and the weighted graph of the UAV formation is reconstructed;

[0185] If the faulty node is a key node t∈T, delete the node and its associated edges from G, replace the key node with a paired candidate node, and reconstruct the weighted graph of the UAV formation;

[0186] Based on the reconstructed UAV formation weighted graph, the communication network structure of the UAV formation is updated.

[0187] In order to improve the robustness of the system, the present invention designs a hierarchical fault handling strategy.

[0188] If the faulty node is a non-critical node And if it is not a candidate node of a key node, it is only necessary to delete the node and all its associated edges from the weighted graph G, and then reconstruct the weighted graph of the UAV formation;

[0189] Otherwise, if the faulty node is a non-critical node If the node is a candidate node for a key node, the faulty node and its associated edges are deleted; the weighted graph of the UAV formation is reconstructed; a new candidate node is found for pairing with the key node of the deleted candidate node; a check is performed to see if there are any candidate nodes in the UAV formation that are not paired with the key node; if so, a candidate node is matched for the key node from the remaining candidate nodes that are not mapped to the key node based on the method in step S21; if not, no further matching is performed;

[0190] If the faulty node is a critical node t∈T, delete the node and its associated edges from G, and replace the deleted critical node with the candidate node corresponding to the deleted critical node; reconstruct the weighted graph of the UAV formation; and pair the candidate node for the replaced critical node.

[0191] Based on the reconstructed UAV formation weighted graph, the communication network structure of the UAV formation is updated to achieve real-time reconstruction and communication recovery of the UAV formation.

[0192] The function of step S4 is to reconstruct the communication network structure of the UAV formation in real time based on the matching relationship between key nodes and candidate nodes when a UAV fails, so as to restore communication and maintain the stability of the UAV formation.

[0193] Example 2:

[0194] Another embodiment of the present invention discloses a drone formation optimization system, thereby implementing the drone formation optimization method of embodiment 1. The specific implementation of each module refers to the corresponding description in embodiment 1.

[0195] like Figure 4 As shown, a UAV formation optimization system in this embodiment includes the following modules:

[0196] The formation weighted graph construction module M1 is used to construct a UAV formation weighted graph based on the interaction relationship between UAVs and each UAV in the formation as a node;

[0197] The communication optimization and key node identification module M2 is used to search for the optimal communication topology based on the weighted graph to obtain the optimal communication network structure; and identify the key nodes in the UAV formation based on the optimal communication network structure;

[0198] A key node matching module M3 is used to match at most one candidate node for the key node;

[0199] The fault reconstruction and communication recovery module M4 is used to perform real-time reconstruction and communication recovery of the UAV formation based on the matching relationship between candidate nodes and key nodes when a UAV fails.

[0200] In summary, the UAV formation optimization method according to an embodiment of the present invention has the following beneficial effects:

[0201] 1. This invention constructs a weighted graph of UAV formations and uses a genetic algorithm to search for the optimal communication topology. This allows real-time adaptation to the dynamic evolution of the formation network (such as node failures and communication interference), addressing the problem of delayed response to topology changes in dynamic environments in existing methods. This approach fully considers the real-time nature of topology changes and the multi-constraint coupling effect, effectively addressing the problem of affected collaborative performance in complex dynamic mission environments in existing methods.

[0202] 2. Introducing the Hodge decomposition method to perform structural analysis on each edge in the communication network structure, quantifying the dynamic interaction relationship between nodes, and dynamically and accurately identifying key nodes in the formation. This method breaks through the limitations of traditional static indicators (such as degree centrality) and avoids the drawbacks of existing technologies that cause task allocation schemes to fall into local optimality or resource conflicts due to static network indicators. This provides a more efficient and reasonable solution for formation optimization in complex scenarios.

[0203] 3. Match the remaining nodes in the formation except the key nodes to the key nodes according to the edge weight to ensure load balancing. Each key node is matched with at most one candidate drone. This can not only ensure the smooth execution of the mission, but also maintain the robustness of the system, effectively avoid communication overload or redundant resource waste, and improve the overall mission execution efficiency of the formation;

[0204] 4. In the calculation of communication link edge weights, the heterogeneous capabilities of drones and communication radius limitations are comprehensively considered, and multi-constraint collaborative optimization is achieved through a dynamic weighting strategy to improve the adaptability and flexibility of formation mission execution in complex scenarios;

[0205] 5. For failures of key nodes and non-key nodes, a hierarchical fault handling strategy (direct deletion, candidate replacement, and topology reconstruction) is designed. Combined with the optimal communication network rapid recovery mechanism, when a key node or non-key node fails, a real-time reconstruction mechanism can be triggered to quickly re-identify the node score and allocation plan based on the updated communication structure to ensure the stable and reliable operation of the formation, minimize mission interruption time, ensure the continuity and reliability of the formation mission, and enhance the adaptability and recovery capabilities of the UAV formation when facing node failure problems.

[0206] Those skilled in the art will appreciate that all or part of the process steps of the above-described embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, such as a magnetic disk, an optical disk, a read-only memory, or a random access memory.

[0207] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A UAV formation optimization method, characterized in that: The steps include: A weighted graph of UAV formation is constructed based on the interaction relationship between UAVs and each UAV in the formation is used as a node. Searching for an optimal communication topology based on the weighted graph to obtain an optimal communication network structure; Identifying key nodes in the UAV formation based on the optimal communication network structure; Match at most one candidate node for the key node; When a UAV fails, the UAV formation is reconstructed and communication is restored in real time based on the matching relationship between candidate nodes and key nodes.

2. The method according to claim 1, characterized in that The interaction relationship of the UAV formation is abstracted into a weighted graph G = (V, E, W); where the node set V = {v1,…,v N } represents N drones; the edge set E = {e ij |(v i ,v j )} indicates that there is a communication link between UAVs i and j; W represents the edge weight set between any two UAVs.

3. The method according to claim 2, characterized in that Searching for an optimal communication topology based on the weighted graph using a genetic algorithm to obtain an optimal communication network structure includes: Based on the edge weights of the weighted graph, the population is initialized and all two-node pairs randomly generate chromosome individuals z=[z 11 、z 12 ,…,z ij ,…,z NN ]∈{0,1} N×N ; Where Z is the communication network structure, 1 means that the nodes have established communication with each other and there is a communication link; 0 means that the nodes have not established communication with each other and there is no communication link; Calculating the fitness of the chromosome individual; In each generation, the roulette wheel strategy is used to select individuals according to their fitness to obtain the selected individuals; A parent individual is selected from the selected individuals to generate two offspring individuals, which are then added to the population; the population mutates; The operation is repeated until the fitness tends to be stable, and the chromosome individual with the largest fitness is obtained. The optimal communication network structure is obtained based on the communication link relationship of the chromosome individual.

4. The method according to claim 3, characterized in that The fitness of individual chromosomes is calculated using the following formula: Among them, d ij is the Euclidean distance between two nodes i and j; F(Z) is the fitness of the chromosome individual; ρ is the penalty coefficient, 1 {·} is an indicative function used to penalize connections that exceed the maximum communication radius R; (i,j)∈E z ij d ij +ε represents all the communication links z in the communication network structure ij =1; ε is the anti-zero constant.

5. The method according to claim 1, characterized in that: Based on the optimal communication network structure, key nodes in the UAV formation are identified, including: Using the Hodge decomposition method to perform structural analysis on each edge in the optimal communication network structure, each edge is decomposed into an orthogonal sum of three parts: gradient flow, curl flow, and harmonic flow; wherein the gradient flow is the product of the gradient matrix and the node potential function; The gradient component of the node potential function is defined as the Hodge score of all nodes in the UAV formation; Sort the Hodge score of each drone node and select the top K' nodes with the highest scores to form the key node set T in the drone formation.

6. The method according to claim 5, characterized in that Match at most one candidate node for the key node, including: The remaining nodes in the UAV formation except the key nodes are regarded as candidate nodes; For each candidate node p∈N and each key node t∈T, extract the edge weight ω pt As the matching weight, the maximum matching weight between the candidate node and the key node is obtained as follows: Count the number of matches between each key node and candidate nodes; If the number of matches between a key node and a candidate node is c t >1, then the key node is redistributed according to the second largest matching weight to obtain the corresponding matching number c t =1; If the number of matches of a key node c t =0, then the number of candidate nodes is less than the number of key nodes; Iterate until all key nodes c t ≤1, and get the mapping π between key nodes and candidate nodes.

7. The method according to claim 6, characterized in that If a UAV fails, the UAV formation is reconstructed and communication is restored in real time based on the matching relationship between candidate nodes and key nodes, including: If the faulty node is a non-critical node and is not a candidate node for a critical node, delete the faulty node and the associated edges from G and reconstruct the weighted graph of the UAV formation; If the faulty node is a non-critical node and is a candidate node for a critical node, the faulty node and its associated edges are deleted, and the weighted graph of the UAV formation is reconstructed; If the faulty node is a key node t∈T, delete the node and its associated edges from G, replace the key node with a paired candidate node, and reconstruct the weighted graph of the UAV formation; Based on the reconstructed UAV formation weighted graph, the communication network structure of the UAV formation is updated.

8. The method according to any one of claims 5 to 7, characterized in that: The Hodge scores of all nodes in the drone formation are as follows: s=(B g φ1,…,B g f N ) T Among them, B g ∈R N×|E| is the gradient matrix, φ∈R N is the node potential function, φ1, φ2, …, φ2 are the node potential functions of the UAV nodes; R is a real number set; To B g φ1,…,B g φ N Arrange them in descending order from large to small, and select the top K' nodes with the highest scores and similar gradients to form the key node set.

9. The method according to claim 2, characterized in that: Calculate the edge weight between any two drones, including: Calculate the Euclidean distance d between any two drone nodes ij ,as follows: d ij =||X i -X j ||2 Among them, X i 、X j are the positions of drones i and j respectively; Calculate the edge weight ω of each corresponding communicative link edge based on the Euclidean distance ij ,as follows: Where R is the communication radius and ε is the anti-zero constant.

10. A UAV formation optimization system, characterized in that: include: The formation weighted graph construction module is used to construct a UAV formation weighted graph based on the interaction relationship between UAVs and each UAV in the formation as a node; A communication optimization and key node identification module is used to search for an optimal communication topology based on the weighted graph to obtain an optimal communication network structure; and identify key nodes in the UAV formation based on the optimal communication network structure; A key node matching module, configured to match at most one candidate node to the key node; The fault reconstruction and communication recovery module is used to perform real-time reconstruction and communication recovery of the UAV formation based on the matching relationship between candidate nodes and key nodes when a UAV fails.

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