A self-healing control method for drone swarms under individual failure

Abstract

This paper discloses a self-healing control method for drone swarms under individual failure conditions. From the perspective of bionic clusters, this paper focuses on the self-organizing dynamic configuration, consistency, trajectory tracking, and self-healing control of large-scale drone swarms. From both the network and physical configuration levels, this paper explores practical challenges faced by large-scale drone swarm systems in denial environments, including multiple concurrent individual failures, normalized member node failures, and model uncertainty. It systematically analyzes the impact and damage of varying degrees of failure on the swarm network and configuration, and explores optimal control schemes for maintaining and restoring system health. This approach demonstrates considerable originality.

Description

Technical Field

[0001] The present invention belongs to the field of multi-agent technology, and specifically relates to a self-healing control method for a drone cluster under individual failure. Background Art

[0002] As a product of high-tech development, drones, with their superior maneuverability, adaptability to harsh environments, low operating costs, and high cost-effectiveness, have seen unprecedented development and application in various sectors critical to the national economy. With breakthroughs in communications, sensors, and artificial intelligence technologies, drones are becoming increasingly intelligent. With comprehensive onboard control systems, they are now able to autonomously perform tasks such as target search, identification, tracking, and strike without the need for external commands.

[0003] In a denial environment characterized by adversarial forces, communication jamming, and other uncertainties, drone swarms face real challenges such as member failures, combat damage, and strong electrical interference. These challenges can lead to cascading system failures, configuration dispersion, and instability, severely restricting their practical application. Therefore, researching intelligent fault-tolerant and self-healing control methods for drone swarm systems to improve their fault tolerance and self-healing capabilities in denial environments is crucial for achieving practical application. On the one hand, complex constraints significantly increase the probability of concurrent actuator failures in multiple individuals in a swarm system. Furthermore, given the diversity and heterogeneity of existing drone platforms, the types of failures under different dynamic models vary widely, posing significant challenges to the fault-tolerant control of drone swarm systems. Therefore, addressing practical challenges such as concurrent failures in multiple individuals in swarm systems, model uncertainty, or the absence of precise models, developing effective fault diagnosis and intelligent fault-tolerant control methods for systems with model uncertainty is a critical and challenging issue that needs to be addressed. On the other hand, while fault-tolerant control can effectively mitigate the disruptions to the swarm configuration and consistency caused by member failures and inefficiencies, it cannot repair physical damage to the swarm configuration. Furthermore, given the vulnerability of swarm systems to attacks and strong electrical interference in a denial environment, member node failure (primarily referring to drones being unable to communicate with their neighbors, such as being destroyed) is a common occurrence. This can lead to localized instability and fragmentation of the entire system, and even to the failure of the entire system's mission functionality, significantly reducing the swarm's battlefield survivability. Currently, research in this area is relatively limited, and there is no effective method for restoring a damaged system to its original healthy state. Therefore, addressing the type of damage to the system's physical and network structures caused by member node failures and communication interference, which is difficult to address with fault-tolerant control, further analyzing the interference or damage caused by normalized node failures on the system's network and physical configuration, and developing effective self-healing control methods to quickly restore the system's inherent network structure and cluster configuration, thereby enabling the swarm system to possess continuous self-healing capabilities and improving its resilience, is another key and difficult issue that needs to be addressed. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a self-healing control method for a drone cluster under individual failure.

[0005] A self-healing control method for a drone swarm under individual failure conditions, comprising:

[0006] Step 1: Hypergraph modeling

[0007] For a group of n drones, the topology of interactions between them is modeled using a hypergraph. Let X denote the set of vertices and E the set of hyperedges e. A hyperedge is any set of nodes containing any number of vertices. Each hyperedge e is assigned a weight, denoted by W, representing the weight of the hyperedge e. Let W denote the diagonal matrix of hyperedge weights. Let H = (X, E, W) denote a weighted hypergraph.

[0008] Step 2: Multi-layer recursive grouping of drone clusters

[0009] The drone swarm is divided into multiple layers, each layer includes some subgroups; these subgroups are composed of cluster master nodes and slave nodes. The cluster master nodes of the subgroups will form a higher-level network, and then a hierarchical network structure is constructed. A hypergraph is used to describe the hierarchical network structure:

[0010] For a group of n drones in three-dimensional space, a k-uniform hypergraph and a multi-layer recursive grouping method are used to divide the large-scale drone swarm into n / k different non-uniform subgroups and independent subgroups, each of which has k vertices; the first layer is a k-uniform hypergraph defined as: H 1 =(X 1 ,E 1 ),in The second-level k-uniform hypergraph is defined as H 2 =(X 2 ,E 2 ),in By recursive grouping, the ρ-th level hypergraph is defined as:

[0011] H ρ =(X ρ ,E ρ )

[0012] in:

[0013]

[0014]

[0015] Step 3: Perform multi-layer self-organizing aggregation control on the drone swarm;

[0016] Step 4: Multiple Agent Self-Healing Control

[0017] Calculate the fault recoverability index μ and determine whether it satisfies If the conditions are met, multi-layer self-organizing aggregation control or dynamic cluster maintenance mechanism is used to repair the network of the drone group; the threshold Represents the expected level of fault recoverability.

[0018] Preferably, in step 4, the calculation formula of the fault recoverable index μ is as follows:

[0019]

[0020] Among them, I(V j ) represents node V j Importance; H LRC represents the maximum connected component of the maximally recoverable system network after the faulty node in a given network H is removed; n represents the number of nodes in the network; ρ = 1, 2, …, τ represents the number of network layers, and τ is the total number of layers; w1 and w2 are the node size and node importance weights, respectively, and w1 + w2 = 1; n(H) represents the number of valid nodes in the network.

[0021] The present invention has the following beneficial effects:

[0022] This paper focuses on the self-organizing dynamic configuration, consistency, trajectory tracking, and self-healing control of large-scale drone swarms from the perspective of bionic clusters. From the network and physical configuration levels of large-scale drone swarm systems, it explores practical issues such as multiple concurrent failures, normalized member node failures, and model uncertainty faced by them in a denial environment. It systematically analyzes the impact and damage of different levels of failure on the swarm network and configuration, and explores the optimal control scheme for maintaining and restoring the system's health, demonstrating its high originality. The main innovations of this paper are as follows:

[0023] (1) A recursive grouping multi-layer network structure that meets the scalability and robustness requirements of bee colonies is proposed. Different from the traditional cluster structure based on the leader-follower model, its innovation lies in proposing a scalable, decentralized hierarchical network architecture. Based on the idea of ​​recursive grouping, the large-scale complex bee colony system is simplified into several independent and non-overlapping subsystems; a matching relationship between individuals and complex cluster configurations is established, and a configuration phase change adjustment mechanism based on neighborhood local information is designed to ensure that any number of bee colony systems can adaptively and dynamically adjust the cluster morphology under complex constraint environments, thereby improving the scalability and robustness of the system; it provides new methods and ideas for the study of the problem of bee colony configuration damage caused by random node failure, which has certain application and theoretical innovations.

[0024] (2) A near-optimal continuous self-healing control strategy for swarm configurations under normalized node failures is proposed. The main innovation lies in further studying the problem of system configuration instability and decentralized damage caused by node failures that cannot be solved by fault-tolerant control. A recoverability assessment method for UAV swarm networks after failures is proposed for the local instability and decentralized problems caused by different degrees of physical damage to the two types of configurations. Furthermore, a self-repair and continuous self-healing control method for swarm configurations is proposed, which enables the damaged system to quickly recover to a healthy state and have the ability to continue to perform its assigned tasks. Currently, there is relatively little research in this area, and it has good theoretical and application innovations. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a hypergraph of a hierarchical network;

[0026] Figure 2 This is a schematic diagram of the failure of the first-layer network member nodes;

[0027] Figure 3 Schematic diagram of failure of member nodes in the ρth layer network;

[0028] Figure 4 Schematic diagram of cluster extinction, merger and splitting;

[0029] Figure 5 Form a flow chart for routing;

[0030] Figure 6 Maintaining flow charts for routing;

[0031] Figure 7 Reconstruct the flow chart for routing;

[0032] Figure 8 The simulation results of self-healing control under the simultaneous failure of two individuals are shown;

[0033] Figure 9 The impact of the failure of two UAVs on the cluster configuration;

[0034] Figure 10 The impact on consistency when two drones fail;

[0035] Figure 11 The simulation results of self-healing control under the simultaneous failure of three individuals are shown;

[0036] Figure 12 The influence of three individual failures on the configuration;

[0037] Figure 13 The impact on consistency under 3 individual failures;

[0038] Figure 14 The simulation results of self-healing control under three consecutive failures are shown;

[0039] Figure 15 The effect of three consecutive individual failures on the configuration;

[0040] Figure 16 This is the impact of three consecutive individual failures on consistency. DETAILED DESCRIPTION

[0041] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0042] Step 1: Hypergraph modeling

[0043] A hypergraph is a generalization of a graph where an edge can connect any number of vertices. For a set of n drones, the topology of interactions between them can be modeled by a hypergraph. A hypergraph H is a pair H = (X, E), where X = {v1, v2, ..., v n} is a set of vertices, and E={e1,e2,...,e k} is a set of non-empty subsets of X, called hyperedges. Unlike graph edges, which are pairs of vertices, hyperedges are arbitrary sets of nodes and can contain any number of vertices. Unlike graph edges, which are pairs of vertices, hyperedges are arbitrary sets of nodes and can contain any number of vertices. It is often useful to study hypergraphs where all hyperedges have the same cardinality: a k-uniform hypergraph is a hypergraph such that all its hyperedges are of size k, e.g., a 2-uniform hypergraph is actually a graph, and a 3-uniform hypergraph is a set of triples. A weighted hypergraph is also a hypergraph where each hyperedge e is assigned a weight w(e), which represents the weight of the hyperedge e. Let W be the diagonal matrix of hyperedge weights, we have diag(W) = [w(e1), w(e2), ..., w(e k )]. Let H = (X, E, W) represent a weighted hypergraph. The structure of the hypergraph is usually represented by the incidence matrix h∈{0,1} |X|×|E| It can be expressed as:

[0044]

[0045] Define the degree of hyperedge e and vertex v as:

[0046]

[0047]

[0048] Let D e ∈R |E|*|E| and D v ∈R |X|*|X| Denote as a diagonal matrix containing vertex degrees and hyperedge degrees respectively, let W denote a diagonal matrix containing hyperedge weights. Then define the adjacency matrix A of the hypergraph H as:

[0049] A=HWH T -D v

[0050] Among them H T is the transpose of H, and the adjacency matrix represents the adjacency relationship between each node. i The neighbors are defined as:

[0051] N i ={j∈X:h ij =0}={j∈X:(i,j)∈e}

[0052] For hypergraphs, the Laplacian matrix is ​​more complicated and is defined as:

[0053] L=D v -A

[0054] For a hypergraph, the Laplacian matrix L is positive semidefinite. For a connected hypergraph, L has a single eigenvalue and the corresponding eigenvector has dimension [1,1,...,1] T .

[0055] Step 2: Multi-layer recursive grouping of drone clusters

[0056] In order to improve the scalability and robustness of networked drone systems, a multi-layer recursive grouping method is proposed based on graph theory and dynamic cluster maintenance mechanism to describe the scalable communication topology. The large drone swarm is divided into several different layers, each layer including some subgroups. These subgroups are composed of cluster nodes and slave nodes. The cluster nodes of the subgroups will form a higher-level network. Then, a hierarchical network structure is constructed and a hypergraph is used to describe the complex hierarchical network, such as Figure 1 shown.

[0057] For a group of n drones in three-dimensional space, we use k-uniform hypergraph and multi-layer recursive grouping method to divide the large-scale drone group into n / k different non-uniform subgroups and independent subgroups, each with k vertices. The first layer is a k-uniform hypergraph defined as: H 1 =(X 1 ,E 1 ),in The second-level k-uniform hypergraph is defined as H 2 =(X 2 ,E 2 ),in By recursive grouping, the ρ-th level hypergraph is defined as:

[0058] H ρ =(X ρ ,E ρ)

[0059] in:

[0060]

[0061]

[0062] For simplicity, we consider n = (k) λ ,λ∈N+, which means that each drone (group) has k - 1 neighbor. In practical applications, we can adjust the number of neighbors per layer to suit the size of the swarm. Considering that the failure of a master node will result in the failure of the entire cluster, this invention employs a dynamic cluster maintenance mechanism to enable a drone cluster to select a new cluster node based on cluster election rules to replace the missing cluster node, maintaining communication with its neighboring clusters and ensuring full connectivity across the entire network. Here, we assume that a new cluster node can be selected shortly after a cluster node fails. It can also be assumed that the missing nodes are all slave nodes in the subgroup.

[0063] Step 3: Multi-layer self-organizing aggregation control

[0064] Due to the limitations of communication and the complexity of the internal topology, it is difficult to coordinate a large number of drones to achieve aggregate control. Therefore, the present invention adopts a multi-layer self-organizing aggregate control algorithm, and the detailed steps described in Chinese patent CN114594689B can be seen in detail. Through the multi-layer graph model, the entire system can be divided into λ layers, and each layer contains multiple subgroups. In order to achieve multi-layer self-organizing aggregate control, we divide the problem into two parts: intra-layer aggregation and inter-layer aggregation, where the intra-layer aggregation enables the members of each subgroup to form a specified shape, and inter-layer aggregation, where the subgroups form a desired shape. In the present invention, the inter-layer aggregation of each layer can be regarded as the intra-layer aggregation of the upper layer (for example, the inter-layer aggregation of the first layer is the intra-layer aggregation of the second layer). Therefore, in order to coordinate a large number of drones to achieve aggregate control, we design an aggregate control law for each layer.

[0065] (1) First-layer self-organizing aggregation control

[0066] Given a swarm of N drones, randomly distributed over a specific work area, our main task is to assign neighbors to each drone based on the neighbor priority principle, dividing the entire swarm into many inconsistent subgroups and establishing interactions and aggregation control relationships between individuals within these subgroups. First, we define three types of neighborhoods for each drone, with N1, N2, and N3 representing the neighbors in the exclusion zone, desired zone, and attraction zone, respectively. The formula is as follows:

[0067] N1={j∈N i |dr >||d ij ||}

[0068] N2={j∈N i |d r ≤||d ij ||≤d s}

[0069] N3={j∈N i |d s <||d ij || <d m}

[0070] where d ij =q i -q j Indicates A i and A j The relative position vector of .

[0071] At the same time, suppose UAV A i Know the location and number of neighbors i , the expected distance between adjacent drones, and the total number of drones. i The following control law is designed to achieve the first level of aggregation through distributed controllers. It consists of three items:

[0072]

[0073] where k c is a positive constant that realizes the damping action. The first term, F ij , used to adjust UAV A i and A j The relative positions between them are responsible for collision avoidance and cohesion in the group and are represented by a collective potential function P ij (q) is derived from the field generated by the potential function, and the value of the potential function depends on the UAV A i and A j The relative distance between them. ij and F io The expressions are as follows:

[0074]

[0075]

[0076] Among them, P ij (d ij ) and P io (d io ) are as follows:

[0077]

[0078]

[0079] According to the above control law, collision avoidance and aggregation in the UAV cluster can be achieved, while the distance between each UAV reaches the desired position.

[0080] (2) Self-organizing aggregation control at the ρth layer

[0081] When the first layer of drones forms some inconsistent subgroups and establishes positioning and communication relationships between individuals in these subgroups, through the multi-layer graph model, the specific subgroups of the upper layer will be organized to form many larger subgroups. In this way, large-scale drones are organically organized through a hierarchical framework, which can effectively improve the efficiency of inter-layer interaction, improve scalability and aggregation, and avoid system fragmentation. In the ρth layer, there are k ρ We will group these into i ρ ,i=(1,2,....,k ρ ) is considered as a new individual, and the class of the neighbor is defined as:

[0082]

[0083]

[0084]

[0085] in Indicates V i ρ and The relative position vector of It is V i ρ The neighbor set of and Represents V i ρ The maximum radius in the repulsive, desirable, and attractive regions. V i ρ The coordinates can be expressed as:

[0086]

[0087] in, and Indicates V i ρ-1 The adjacent coordinates of .

[0088] Furthermore, a ρ layer of autonomous aggregation rules is proposed, which allows adjacent groups to aggregate with each other, and the entire system will automatically assemble into kρ subgroups. ijSimilarly, the potential function between subgroups of the ρth layer can be defined as follows:

[0089]

[0090] in, is a positive coefficient. Then we get V i ρ and The corresponding force between them is:

[0091]

[0092] In summary, the design of the multi-UAV self-organizing aggregation controller is as follows:

[0093]

[0094] Step 4: Multiple Agent Self-Healing Control

[0095] Step 41: Network analysis after multiple agents fail

[0096] In a network, the failure of one or a few nodes or links can trigger the failure of other nodes through the coupling relationships between nodes, creating a cascading effect that can ultimately lead to the collapse of a significant number of nodes or even the entire network. This phenomenon is called cascading failure, sometimes figuratively referred to as an "avalanche." In a denial environment characterized by adversarial forces, communication interference, and other uncertainties, drone swarms face real challenges such as member failures, combat damage, and strong electrical interference. These can lead to cascading system failures, configuration dispersion, and instability, severely restricting their practical application.

[0097] This invention mainly studies the cascading failure model of the hierarchical recursive grouping network structure proposed in Chapter 2. Under this network framework, failed nodes can be mainly divided into two situations: the first situation is the failure of the slave node in the first layer. Thanks to the advantages of the hierarchical network structure proposed in this invention, the failure of this type of node will not affect the connectivity of the swarm network; the second situation is the failure of the cluster node. The failure of this type of node will inevitably cause the cascading failure of the member nodes in the cluster, and even cause the connectivity of the system network to be destroyed, thereby causing local or global instability of the system, configuration dispersion and other phenomena. Therefore, for the drone swarm system of the present invention, the degree of damage to the system caused by the failure of different types of nodes is different. We first need to analyze the importance of the system nodes and the cascading effect of the failed nodes. First, we give the following definitions.

[0098] Definition 4.1: (Failed Node) For a networked system, if a node loses the ability to move and communicate and never regains its original capabilities, we call it a failed node. In addition, when multiple nodes fail in the same control cycle, we call it a multi-node failure.

[0099] Definition 4.2: (Isolated Node) For a networked system, if a node fails to establish a network connection with other member nodes in the system within a time period T due to the failure of a neighboring node or a new node joining the system, we call the node an isolated node within time T. Once the isolated node establishes a network connection with other neighboring nodes, it becomes a normal node.

[0100] Definition 4.3: (Network stage) For a given network G, the network stage refers to the part of G that remains after removing some nodes and edges.

[0101] Based on the hierarchical recursive grouping network framework proposed in this paper, the cascading failure model of the network structure is analyzed:

[0102] First layer network: Deactivate drone node V i 1 ∈X 1 ∩d(V i 1 )=1,(i=1,2,…,n) moves out of the network without causing its neighbor nodes to become isolated nodes and without affecting the connectivity of the swarm network. We record such nodes as the first-layer member nodes like Figure 2 As shown, a 2-layer network structure, nodes and Failure, removing the failed node LRC is still fully connected.

[0103] The ρth layer network: the failed drone node V i ρ ∈X ρ ∩d(V i ρ )=2,(i=1,2,…,n / ρ) moves out of the network, which will cause its neighbor nodes to become isolated nodes or affect the connectivity of the swarm network and produce many disconnected subgraphs. We record such nodes as the ρ-th layer member nodes like Figure 3 As shown, in the same two-layer network, the second-layer network member nodes Failure, due to the cascade effect, will cause two unconnected subgraphs to appear in the entire network, causing the system to be decentralized and thus affecting the normal operation of the system.

[0104] Considering that in a drone swarm system operating in a denial environment, node failures primarily occur due to communication interference, combat damage to members, or destruction. Therefore, node failures are highly random, and system node failures are a regular, continuous occurrence. Next, we will analyze the impact of continuous random node failures on the entire system and examine the system's resilience to failures.

[0105] Step 42: Fault recoverability analysis

[0106] The present invention mainly focuses on the analysis of network recoverability after node failure, and the time period can be set freely according to the time. First, we give two methods to estimate whether an undirected graph is connected.

[0107] Lemma 4.1: For a hypergraph network H with n nodes, suppose the characteristic roots of its Laplacian matrix L are λ1(L),λ2(L),…,λ n (L) satisfies λ1(L)≤λ2(L≤…≤λ n (L). If the network H is connected, then 0 = λ1(L) ≤ λ2(L) ≤ ... ≤ λ n (L) Established.

[0108] Lemma 4.2: For a hypergraph network H with n nodes, if H has m ≥ 1 disconnected subgraphs, then its Laplacian matrix L has m zero-fold roots, and L can be written as a block diagonal matrix as follows:

[0109]

[0110] Among them, each block matrix L i ,i=1,2,…,m is also the Laplacian matrix of the corresponding subgraph.

[0111] When a node fails in a drone swarm system, it inevitably causes changes in the system's network structure, which in turn affects the stability of the system's cluster configuration. This section focuses on the impact of failed nodes on network connectivity. For a swarm network H described by a hierarchical hypergraph, we define node connectivity κ(H) as the minimum number of nodes that can be removed to increase the number of connected branches, and the second smallest Laplace eigenvalue λ2 of H satisfies κ(H) ≥ λ2(L(H)). Therefore, the following gravitational force can be used to evaluate the connectivity of H.

[0112] Lemma 4.3: For any k ≤ κ(H), if λ2(L(H)) > k-1, then the hypergraph network H is k-connected. For example, when k = 1, we have λ2(L(H)) > 0, and the network H is connected. This lemma is an extension of Lemma 4.1.

[0113] Lemma 4.4: The second largest eigenvalue λ2(A(H)) of the adjacency matrix A of network H is often used to evaluate the stability and robustness of the entire network. Smaller changes in λ2(A(H)) indicate better stability and robustness.

[0114] For the two types of nodes in the swarm, we give the definitions of node importance at different network levels.

[0115] Definition 4.5: For a given hypergraph network H, the higher the level of the hyperedge, the higher the importance of the hyperedge member nodes. The node importance is defined as I(·)

[0116]

[0117] Among them, n′ ρ represents the number of isolated nodes / components generated after the failure of the ρth layer node. c1 and c2 are the number of isolated nodes and the importance weight of the node in the layer, respectively.

[0118] Definition 4.6: For a given network H, define H LRC It is the largest connected component of the network that can be restored after the network failure node is removed. It not only includes the largest number of valid nodes, but also the largest sum of the importance of all valid nodes. Define H′ i ,i∈{1,2,…,z} is the z connected components or isolated points generated after the network node fails, n(H′ i ) represents H′ i ,i∈{1,2,…,z} the number of valid nodes, such as H′ i is an isolated point, then n(H′ i )=1. Among them, w1 and w2 are the node scale and node importance weight respectively, and w1+w2=1.

[0119] Definition 4.7: For a given drone swarm system with cascading node failures, the fault recoverability index μ is defined as:

[0120]

[0121] It is not difficult to see from the above formula that the indicator μ is H LRC The ratio of the number of active drones and node importance in the network to the initial number of active drones and node importance can be used to effectively evaluate the swarm's resilience after individual failures. A smaller μ value indicates fewer and less important nodes remain in the network, making recovery more challenging. Due to the random nature of node failures, we will next discuss how to calculate μ under random node failures.

[0122] For a drone swarm system, when a random node fails, the failure node ratio in each layer is 1-R ρ , the remaining nodes in the first layer that are directly connected to the nodes in the second layer are recorded as The remaining nodes in the ρth layer that are directly connected to the ρth + 1th layer nodes are recorded as Among them, n ρis the number of nodes in each layer before the system is destroyed, ρ=1,2,…,τ is the number of network layers. Therefore, after removing the failed drone, the network H LRC The number of nodes n(H LRC ) can be calculated as:

[0123]

[0124] Assume that the degree distribution between each layer of the hierarchical network is Poisson distribution, and the average degree of the node is d ave , we can get

[0125]

[0126] Here, <·> represents the degree distribution at the initial moment.

[0127] Before the network failure, the probability that there is no connection between each layer is The probability of each layer being connected is

[0128]

[0129] According to the above formula, we can get:

[0130]

[0131] Finally, we can set the conditions for fault recovery based on whether the drone swarm can still complete the established work tasks.

[0132] Theorem 4.8: For a given hierarchical network H, when the number of failed nodes in each layer of the network is (1-R ρ )n ρ . Given a threshold The recoverability of the system depends on the following conditions:

[0133]

[0134] Among them, the threshold Represents the expected level of fault recoverability, which is usually set based on system performance, security, mission and other requirements.

[0135] Step 43: Drone swarm self-healing control

[0136] This step mainly studies the phenomenon that after the drone cluster forms the desired configuration, the random drone node failure caused by physical failure (irrecoverable), member combat loss, etc., leads to local (partial loss of configuration) or global instability (cluster dispersion) of the drone cluster configuration and network. The present invention mainly considers two typical cases: the first case is that a small number of slave node failures that the swarm system can tolerate will lead to local loss or instability of the swarm configuration. In this case, the network failure recoverability index meets The second situation is that due to confrontation and strong electrical interference, a large number of nodes or key nodes in the cluster fail, resulting in cascading failures in the drone swarm network structure, configuration dispersion or global instability. It is believed that the system has been destroyed and there is no need for self-healing. Therefore, for the second case, the main research For these two situations, the present invention will further analyze the interference or damage caused by the disappearance of nodes to the network structure and physical configuration of the system, and how to quickly and effectively restore the system's inherent network structure and cluster configuration, thereby improving the continuous self-healing ability of the swarm system and improving the system's anti-destruction capabilities.

[0137] First, we give the definition of self-healing control for cluster configurations.

[0138] Definition 4.9: For a cluster system capable of achieving global networking and stable configuration, when random individual failures lead to local or global instability in the network structure and cluster physical configuration, the remaining individuals in the system can effectively cope with this situation and restore the network structure and cluster physical stable configuration to their previous state. This invention refers to the process from system destruction to restoration of original function as self-healing control.

[0139] 1) Self-healing control in the first case

[0140] In large-scale swarm systems, the number of slave nodes is far greater than the number of cluster nodes, resulting in a high probability of random slave node failure. Given the characteristics of the hierarchical recursive marshaling network architecture, slave node failures do not lead to cascading failures in the system network; the network remains connected after a slave node failure. This only results in partial loss or instability of the physical configuration within the swarm, without causing the system configuration to fragment. In this case, the failed individual causes changes in the degree, edges, and loads of adjacent nodes, altering the total potential force of adjacent nodes in the configuration and driving adjacent nodes to adjust their positions until the potential force approaches zero. Therefore, the self-healing process eliminates the local loss and instability of the configuration caused by the failed individual, ensuring that the subgroup configuration of the failed individual and the overall system configuration return to stability. Next, we analyze the impact of random slave node failure from both the network and physical configuration levels.

[0141] Theorem 4.10: For a hierarchical UAV network H = (X, E), A is the adjacency matrix of H. The order of failed nodes is described as The cofactor of the adjacency matrix corresponding to the failed node is Define the second smallest characteristic root of the corresponding cofactor as After the node sequence fails, the necessary and sufficient conditions for the drone swarm system network to remain connected are

[0142]

[0143] Where s represents the number of failed nodes.

[0144] Proof: We use the inverse method to prove that, assuming Among them, if i>0 slave nodes fail, then after the disappearance of i>0 nodes, the system will have at least two disconnected subnets. According to the characteristics of hierarchical network cascading failure described above, the failure of a slave node will not affect the connectivity of the entire network. Then r i f It must be a cluster node, which is consistent with the theorem r i f It is a contradiction from the node, so the assumption does not hold. The theorem is proved.

[0145] In cluster configurations, based on the recursive grouping configuration control method proposed in this invention, when a slave node fails, resulting in a partial loss of configuration and a change in the stable configuration within the group, the potential field forces exerted on the failed node's neighbors within the configuration cause them to adjust their positions, restoring a stable configuration within the group. For example, if a node fails in a stable spatial tetrahedron configuration composed of four drones, three drones will remain within the group. According to the configuration control rules, these three drones will form a spatial triangle to achieve self-healing control of the configuration.

[0146] 2) Self-healing control in the second case

[0147] In order to repair the system network, the present invention adopts a dynamic cluster maintenance mechanism, which mainly includes: cluster extinction, cluster merging, and cluster splitting, such as Figure 4 shown.

[0148] 1) Cluster extinction means that when all or most of the nodes in a cluster have disappeared, the cluster can be considered to be extinct, and its members can be set as free nodes and join other clusters.

[0149] 2) Cluster merging allows two smaller clusters to be combined into a larger cluster, as long as the number of nodes in the merged cluster does not exceed the set value. Cluster merging can be divided into two steps. First, a specific cluster disappears, and its member nodes are set to a free state. Then, the free nodes autonomously form a new cluster and establish a new network topology.

[0150] 3) Cluster splitting refers to the demise of a cluster where most of its member nodes disappear, and the distribution of its member nodes to other clusters where members are damaged.

[0151] It should be noted that if a cluster node disappears, the original cluster will re-search for nodes in the nearby area, and the Raft algorithm will be used to select a new cluster gateway and establish a new subnet.

[0152] In the design of the routing method, the overhearing mechanism of data transmission is fully utilized and the special needs of node positioning are taken into consideration. The routing method adopts the improved on-demand AODV routing algorithm.

[0153] First, the timing of sending RREQ messages in the route request mechanism is controlled to reduce the channel occupancy and node energy loss caused by RREQ messages. When a node broadcasts a route request message RREQ in a flooding manner, the listening nodes record the routing relationship between the sending node and the node. If a regular node already has routing relationships with four or more cluster nodes through the listening nodes, the regular node will no longer broadcast the route request message RREQ in a flooding manner. If the regular node still does not have routing relationships with more than four cluster nodes after sending the maximum number of RREQs, it will directly establish an indirect connection relationship with the cluster nodes through the located nodes that have established routing relationships with more than four cluster nodes and are directly connected to the regular node.

[0154] Secondly, the Hello mechanism was modified. Instead of all nodes broadcasting Hello messages periodically, when nodes communicate, the communicating nodes perform route maintenance, while other nodes perform route maintenance through a listening mechanism. Only when ordinary nodes have not performed route maintenance for a certain period of time will they send Hello multicast messages to maintain the routes of cluster nodes. A Hello multicast message means that only cluster nodes respond to the Hello message. If a cluster node fails to respond to Hello messages multiple times within a certain period of time, the route connected to that cluster node will be removed.

[0155] Step 431: Route formation

[0156] After the monitoring station and the intelligent body are powered on, they access the network through the wireless communication module, process the various messages formed by the routing, and form a basic routing table. Figure 5 The specific steps of route formation are as follows:

[0157] 1) The node sends a broadcast routing request message RREQ;

[0158] 2) After receiving the route request message, the cluster node responds to the RREQ message, sends a RREP message and discards the RREQ message and does not forward it;

[0159] 3) After receiving the routing request message, the ordinary node does not respond to the RREQ message, but forms a routing relationship between the node and the sending node;

[0160] 4) After the node that sent the route request message receives the RREP message, it forms a routing relationship between itself and the cluster node; other listening nodes form corresponding routing relationships based on the content of the RREP message;

[0161] 5) If a node exceeds the maximum number of times it has sent route request messages and does not have a routing relationship with more than four cluster nodes, it sends an inter-connection route request message RREQJ;

[0162] 6) After receiving the inter-connection route request message, if the node has been located, it will send a RREP message and discard the RREQJ message without forwarding it until the node and the routing table have four cluster nodes or the route of the located node;

[0163] 7) If a node exceeds the maximum number of times it sends indirect routing request messages and does not have a routing relationship with more than four cluster nodes, directly or indirectly connected, the node is considered an isolated point.

[0164] 8) Route formation is completed.

[0165] Step 432: Route maintenance

[0166] After the multi-agent network is built, it is necessary to passively or actively manage and maintain the network regularly, perform monitoring maintenance on the routing and periodic maintenance of various message processing, and maintain the routing table. Figure 6 The specific steps of route maintenance are as follows:

[0167] 1) The node extracts routing information from all messages received on the channel and performs routing maintenance;

[0168] 2) If the node does not perform route maintenance within a certain period of time, it sends a Hello message for route maintenance. The Hello message contains the node's positioning method, which is divided into direct positioning and indirect positioning.

[0169] 3) After receiving the Hello message, the cluster node responds to the Hello message;

[0170] 4) After receiving the Hello message, the ordinary node responds to the Hello message if the positioning method is indirect positioning, otherwise it does not respond;

[0171] 5) If a node fails to receive a Hello message from a cluster node for multiple times within a certain period of time, the route to this cluster node will be removed;

[0172] 6) Route maintenance is completed.

[0173] Step 433: Route Reconstruction

[0174] When some cluster nodes or slave nodes disappear in the system, causing the system network to be damaged, it is necessary to restore the system network through routing reconstruction. When the route in the network does not exist, when routing reconstruction is performed, various reconstruction messages are processed to form a new routing relationship. The routing reconstruction flow chart is as follows Figure 7 The specific steps for route reconstruction are as follows:

[0175] 1) The node sends a routing query message RREQM to find the destination node in a broadcast manner;

[0176] 2) If the node receiving the RREQM message is the destination node, it responds to the RREQM message and sends an RREPM message;

[0177] 3) When the node receives the RREPM message, the route reconstruction ends; if the maximum number of times the RREQM message is sent has not been exceeded and there is no route to the destination node, the node continues to send the route query message;

[0178] 4) If the maximum number of RREQM messages sent has been exceeded and there is no route to the destination node, a destination node inter-route query message RREQMJ is sent; all nodes that receive the RREQMJ message, if the node is the destination node or has a route to the destination node, respond to the RREQMJ message by sending a RREPMJ message;

[0179] 5) The node receives the RREPMJ message and the routing reconstruction is completed.

[0180] Step 5: Simulation experiment

[0181] This section conducts a series of simulation experiments to verify the effectiveness of the proposed self-healing control method. After the drone swarm completes its self-organizing configuration and consistency control, it randomly disables one or more individuals in the system to analyze the impact on the overall system configuration and consistency.

[0182] The swarm system consists of 27 drones. The network is divided into three layers. Each individual has two neighbors. The initial position of the drone cluster conforms to the random Gaussian distribution in the area [0,60]×[0,60]. In the simulation, the expected distance between drones in each layer is The parameter settings are: r =d s =4, d m =200,ε=0.1,k ij =1,k io =20,k c =1.

[0183] Figure 8 、 Figure 9 and Figure 10 It shows that 27 randomly distributed drones autonomously form the desired configuration and achieve consistency control. At 620s, the system converges to a stable configuration and consistency. When at 1500s, two individuals are randomly disabled, as shown in Figure 4-8 , 4-9, will not affect the system configuration and consistency. The system continues to maintain its original configuration and consistency.

[0184] Figure 11 、 Figure 12 and Figure 13 It shows that 27 randomly distributed drones autonomously form the desired configuration and achieve consistency control. At 700s, the system converges to a stable configuration and consistency. When 1500s, 3 individuals are randomly disabled, as shown in the following figure. Figure 4-11 , as shown in 4-12, will not affect the system configuration and consistency. The system continues to maintain its original configuration and consistency.

[0185] Figure 14 、 15 Figures 16 and 17 show that 27 randomly distributed drones autonomously form the desired configuration and achieve consistency control. At 650s, the system converges to a stable configuration and consistency. At 1000s, 1200s, and 1500s, one individual is randomly disabled. Figure 4-14 , as shown in 4-15, it will not affect the system configuration and consistency, and the system will continue to maintain its original configuration and consistency.

[0186] This step studies the self-healing control of a drone swarm under random node failures in a denial environment, proposes a network invulnerability measurement method, further analyzes the invulnerability of a hierarchical recursive grouping network, and separately studies the cascading effects of two different degrees of node failure on the system network. The network's recoverability after failure is analyzed, and a method for calculating the maximum recoverability index is presented. Furthermore, self-healing control methods under two types of failures are studied, and the self-healing capabilities of the two types of failures are analyzed separately. A self-healing control method based on dynamic cluster maintenance intelligence is proposed, which realizes the self-healing control of a drone swarm configuration under normalized node failures. Finally, the proposed method is verified through simulation experiments, and good self-healing control results are achieved.

[0187] This paper provides a theoretical framework for the design and analysis of self-organizing aggregation control for large drone swarms. A multi-layered graph model can flexibly describe the internal communication topology of any drone swarm system. Leveraging this multi-layered graph model, an effective potential-based self-organizing aggregation control law is proposed. Theoretical analysis demonstrates that all drones converge to a stable state and automatically aggregate to the desired swarm configuration.

[0188] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A self-healing control method for a drone swarm under individual failure, characterized by: include: Step 1: Hypergraph modeling For a group of n drones, the interaction topology between drones is modeled by a hypergraph; Let X denote the set of vertices and E the set of hyperedges e. A hyperedge is any set of nodes containing any number of vertices. Each hyperedge e is assigned a weight, which represents the weight of the hyperedge e. Let W be the diagonal matrix of hyperedge weights. Let H = (X, E, W) represent a weighted hypergraph. Step 2: Multi-layer recursive grouping of drone clusters The drone swarm is divided into multiple layers, each layer includes some subgroups; these subgroups are composed of cluster master nodes and slave nodes. The cluster master nodes of the subgroups will form a higher-level network, and then a hierarchical network structure is constructed. A hypergraph is used to describe the hierarchical network structure: For a group of n drones in three-dimensional space, a k-uniform hypergraph and a multi-layer recursive grouping method are used to divide the large-scale drone swarm into n / k different non-uniform subgroups and independent subgroups, each of which has k vertices; the first layer is a k-uniform hypergraph defined as: H 1 =(X 1 ,E 1 ),in The second-level k-uniform hypergraph is defined as H 2 =(X 2 ,E 2 ),in By recursive grouping, the ρ-th level hypergraph is defined as: H ρ =(X ρ ,E ρ ) in: Step 3: Perform multi-layer self-organizing aggregation control on the drone swarm; Step 4: Multiple Agent Self-Healing Control Calculate the fault recoverability index μ and determine whether it satisfies If the conditions are met, multi-layer self-organizing aggregation control or dynamic cluster maintenance mechanism is used to repair the network of the drone group; the threshold Represents the expected level of fault recoverability.

2. The method for controlling a drone swarm self-healing under individual failure according to claim 1, characterized in that: In step 4, the fault recoverability index μ is calculated as follows: Among them, I(V j ) represents node V j Importance; H LRC represents the maximum connected component of the maximally recoverable system network after the faulty node in a given network H is removed; n represents the number of nodes in the network; ρ = 1, 2, …, τ represents the number of network layers, and τ is the total number of layers; w1 and w2 are the node size and node importance weights, respectively, and w1 + w2 = 1; n(H) represents the number of valid nodes in the network.

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