An unmanned aerial vehicle cluster connectivity maintenance control algorithm and system

Abstract

Currently, the cooperative formation control problem of UAV swarm mostly assumes that the communication range of all UAVs is the same, mainly faces the situation that the communication topology network is undirected graph, cannot realize the connectivity maintenance control under the directed topology network, and often is difficult to effectively maintain the stability and connectivity of the formation. The application provides a UAV swarm connectivity maintenance control algorithm, constructs a directed graph describing the communication among members in the UAV formation, analyzes the communication link and relationship among members based on the directed graph; a directed network topology structure is constructed according to the communication link and relationship, a correlation matrix of the UAV is derived according to the directed network topology structure, and each member is represented as an edge state according to the correlation matrix; through the edge consistent algorithm combined with the potential function method, the position and speed state of each UAV in the correlation matrix are dynamically adjusted; a finite time attitude control strategy is adopted to ensure that the attitude angle of the UAV converges in a finite time, thereby realizing the effective maintenance of the connectivity of the UAV swarm.

Description

Technical Field

[0001] This application relates to the field of collaborative control technology for unmanned aerial vehicle (UAV) swarms, and in particular to an algorithm and system for maintaining connectivity control in UAV swarms. Background Technology

[0002] In recent years, the rapid development of research on UAV swarm formation and coordination has significantly improved the capability and efficiency of multi-UAV collaborative operations. Through refined formation and coordination strategies, not only has the safety of mission execution been enhanced, but its outstanding efficiency has also led to its widespread application in various fields, such as joint surveillance, precision target tracking and strike, logistical resource allocation, environmental monitoring, and search and rescue. However, UAV swarm control is a complex and sophisticated technology, integrating efficient information exchange, intelligent decision-making, and precise coordination among multiple UAVs. In this process, the system inevitably faces diverse dynamic challenges, including differences in the dynamic performance of the UAVs themselves, complex interactions, and uncertainties in communication links.

[0003] Autonomous drone swarms face strict communication distance constraints during flight. To ensure effective communication and coordination among the drones in the swarm, they must strictly remain within a set maximum communication range. This range ensures real-time and accurate information transmission and is the foundation for coordinated swarm operations. Simultaneously, to avoid accidental collisions, the distance between drones must not be less than a set minimum collision avoidance range. This range is designed taking into full account the drones' flight speed, maneuverability, and potential environmental interference factors, and is crucial for ensuring swarm flight safety. Under these constraints, the drone swarm can maintain stable connectivity, enabling it to perform tasks collaboratively, continuously, and stably. To achieve this goal, a position controller is designed during swarm flight. This controller adjusts in real time based on the drones' current position and velocity status, ensuring that each drone remains within the communication range. In this way, swarm connectivity can be effectively maintained, ensuring the overall coordination and stability of the drone swarm during mission execution.

[0004] However, most current drone swarm collaborative formation control problems assume that all drones have the same communication range and are mainly aimed at the case where the communication topology is an undirected graph. They cannot achieve connectivity maintenance control under directed topology networks, and often fail to effectively maintain the stability and connectivity of the formation.

[0005] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] This application provides a drone swarm connectivity maintenance control algorithm. First, a directed graph describing the communication between members of the drone swarm is constructed. Based on the directed graph, the communication links and relationships between the members are analyzed. A directed network topology is constructed based on the communication links and relationships. The drone correlation matrix is ​​derived from the directed network topology. Each member is represented as an edge state based on the correlation matrix. The position and velocity state of each drone in the correlation matrix are dynamically adjusted using an edge-consistency algorithm combined with a potential function method. A finite-time attitude control strategy is employed to ensure that the drone attitude angles converge within a finite time, thereby effectively maintaining the connectivity of the drone swarm.

[0007] Specifically, step 1: In the research of UAV formation technology, the first step is to establish a UAV formation model. This model considers the flight dynamics of the UAVs and various communication constraints during the formation process. To explore the impact of these communication constraints on formation performance, graph theory is used to model the communication graph. By constructing a directed communication graph, the communication links and relationships between the members of the UAV formation can be seen.

[0008] Step 2: Each drone is abstracted as a point in the network structure. However, for the convenience and effectiveness of dynamic modeling, an innovative transformation method is designed to convert the vertex states representing drones into edge states. This transformation can construct the network topology and derive the drone correlation matrix based on this structure. A dynamic model is then established based on velocity and edge states as state variables.

[0009] Step 3: Design a connectivity maintenance control algorithm based on edge consensus and potential function. Maintaining the connectivity of the UAV formation by designing a position controller hinges on constructing a potential function. By dynamically adjusting the position and velocity of each UAV, the distance between UAVs in the formation is controlled within two key thresholds during flight: maximum connectivity range and minimum collision avoidance range. First, the maximum connectivity range refers to the maximum distance at which UAVs can maintain effective communication and data transmission. Second, the minimum collision avoidance range is a safe distance set to prevent physical collisions between UAVs. When the distance between UAVs falls below this safe threshold, the potential function forces the UAVs to separate, avoiding a collision.

[0010] Step 4: Since connectivity maintenance control requires communication distance constraints and fast attitude control, a finite-time attitude controller is designed to make the UAV attitude angle converge within a finite time to track the desired attitude angle generated by the position controller.

[0011] Step 5: Simulate and verify the formation control algorithm. For the position controller, the simulation verifies that the distance between each UAV converges to the desired distance, the distance error eventually approaches zero, and the position and velocity of each UAV also converge to the desired value. For the attitude controller, the attitude angle converges to the desired angle, and the angular acceleration also eventually converges over time.

[0012] Another implementation method provided in this application is as follows: the construction of the directed communication graph includes abstracting each drone in the drone swarm as a vertex in the graph, and determining the connection relationship of the directed edges formed between the vertices according to the actual communication capabilities and directional relationships of each drone; and establishing a directed graph describing the information flow direction within the drone formation according to the connection relationship of the directed edges.

[0013] Another implementation method provided in this application is as follows: the directed graph of communication explicitly represents the one-way transmission relationship of information between UAVs through directed edges, and is used to analyze the communication links of each member in the formation; based on the directed graph, key communication nodes are identified, the strength of link connectivity is evaluated, and it is determined whether there are information islands or transmission bottlenecks, thereby analyzing the communication links and relationships between each member in the UAV formation.

[0014] Another implementation method provided by this application is: representing each member as an edge state, that is, transforming the UAV from the "vertex" state to the "edge" state, including obtaining the correlation matrix based on the directed graph, and mapping the absolute position vector of the UAV to the edge state vector representing the relative position relationship between the UAVs according to the correlation matrix, thereby shifting the focus of description and analysis from the individual state to the connection relationship state between the formation members, that is, characterizing the system characteristics through the edge state.

[0015] In this study of UAV swarms, each UAV is cleverly abstracted as a point in the network structure, greatly simplifying the complex relationships between UAVs in the swarm. However, to improve the convenience of modeling and ensure the effectiveness of the model when modeling the dynamics, an innovative transformation method is designed. This method abandons the traditional approach of representing UAVs with vertex states and instead focuses on the states of edges, achieving a transformation from vertex states to edge states. Through this transformation, a network topology can be constructed in an unprecedented way, clearly showing the communication links and interrelationships between the members of the UAV swarm. Based on this network topology, the association matrix of the UAVs can be derived.

[0016] Another implementation method provided in this application is: The connection relationship between the vertices and directed edges of the UAV is transformed into a mathematical representation based on the directed graph: if the edge... From node Pointing to node Then the correlation matrix middle , Otherwise, it is 0; the correlation matrix fully describes the relationship between nodes and edges in the directed network topology.

[0017] Another implementation provided in this application is as follows: the edge consistency algorithm includes each UAV calculating its own error with the desired edge state based on neighbor communication using the correlation matrix, and generating control commands; driving the state variables of all edges to converge through a distributed control law, thereby achieving accurate formation and maintenance without the need for global information; that is, the algorithm designs a distributed control law through the correlation matrix, utilizes the information interaction of adjacent edges to coordinately adjust the UAV pose, and finally achieves the coordinated convergence of the edge states of the entire formation and the maintenance of topological connectivity.

[0018] Another implementation provided in this application is as follows: the potential function method includes regulating the interaction between UAVs by constructing a non-negative function based on relative distance; when the distance between UAVs approaches the minimum collision avoidance distance, the potential function value increases sharply, generating a repulsive force to prevent collision; when the distance approaches the maximum communication distance, the potential function generates an attractive force to maintain link connectivity; the potential function reaches its minimum value at the desired distance, thereby achieving formation stability within a safe distance range.

[0019] This application designs a connectivity-preserving control algorithm based on edge consensus and potential functions. In the research of UAV formation technology, an innovative connectivity-preserving control algorithm is designed, which integrates the ideas of edge consensus and potential functions. The edge consensus algorithm, as the core, ensures the stability of communication links within the UAV formation, allowing information to flow smoothly. The introduction of the potential function adds greater intelligence and adaptability to the algorithm, enabling it to dynamically adjust the control strategy based on the relative positions and distances between UAVs to maintain the connectivity and stability of the formation. Through this unique design, the control algorithm can not only effectively cope with complex flight environments and changing mission requirements, but also significantly improve the overall performance and collaborative combat capabilities of the UAV formation.

[0020] Another implementation method provided in this application is as follows: the finite-time attitude control method enables the UAV attitude angle to converge within a finite time by designing a nonlinear feedback control law, which ensures that the UAV attitude angle tracking error system converges to zero within a finite time. The control method includes fractional power terms and a sign function. To achieve fast, accurate, and disturbance-resistant attitude angle tracking during UAV formation flight, a hierarchical control architecture is required. The top-level formation algorithm generates the desired trajectory, the middle level calculates the desired attitude commands for each UAV, and the bottom level is the core, employing a model-based feedforward-feedback composite control. Feedforward provides a fast response, while feedback ensures accuracy and eliminates steady-state errors. Crucially, a nonlinear disturbance observer must be introduced to estimate and compensate for model uncertainties, initial deviations, and lumped disturbances such as external gusts in real time, greatly enhancing robustness. A high-bandwidth controller design ensures that the system response is much faster than the command update, ultimately meeting the stringent real-time requirements of formation connection.

[0021] Another implementation provided in this application includes: verifying the stability of the algorithm to obtain a stable UAV swarm connectivity maintenance control algorithm, and using the stable UAV swarm connectivity maintenance control algorithm to control the UAV formation.

[0022] This application also provides a system based on the UAV swarm connectivity maintenance control algorithm, the system including a UAV formation model, the UAV formation model having a dynamic model, the dynamic model including a position controller and an attitude controller connected to each other.

[0023] In the field of UAV formation technology research, the primary task of this application is to construct a comprehensive and accurate UAV formation model, including a dynamic model of the UAV formation process. This model goes beyond simply describing the flight dynamics of UAVs; it also considers various communication constraints that may be encountered during formation. Therefore, to explore the specific impact of these constraints on formation performance, graph theory tools are used to model the communication graph. By constructing a graph theory model of the UAV communication topology—that is, a directed graph—the communication links and relationships between the members of the UAV formation can be clearly revealed. This directed graph not only intuitively shows the communication flow between UAVs but also helps to understand how communication constraints affect the overall performance and stability of the formation. With this model, the communication strategies of UAV formations can be analyzed and optimized more accurately. This application establishes a dynamic model of the formation process through dynamic analysis of the UAV formation process. This application uses graph theory and algebraic graph theory methods to describe the communication between UAVs.

[0024] This application considers the importance of connectivity maintenance control in UAV formation flying, and this control process requires communication distance constraints to ensure that each UAV in the formation can continuously and stably exchange information and adjust its attitude to maintain a suitable distance from other UAVs in the formation. Therefore, a finite-time attitude controller needs to be designed. This finite-time attitude controller ensures that the UAV's attitude angle can track the desired attitude angle generated by the position controller while achieving rapid convergence of the attitude angle within a finite time. This means that regardless of the UAV's current attitude, as long as it receives a new desired attitude angle command, it can complete the attitude adjustment within a preset finite time, thereby meeting the connectivity and response speed requirements of formation flying.

[0025] This application utilizes the MATLAB simulation platform to comprehensively and thoroughly verify the formation control algorithm. During the simulation, six UAVs were selected, and relevant images were generated to verify the stability of the control algorithm. This series of simulation verifications not only validated the effectiveness and feasibility of the formation control algorithm but also laid a solid foundation for its subsequent optimization and practical application.

[0026] This application provides a drone swarm connectivity maintenance control algorithm, which has at least the following beneficial effects:

[0027] (1) This application uses a directed graph structure to explore the cooperative problem of UAV swarms. Compared with undirected graphs, directed graphs, by assigning a clear direction to each edge, characterize the unidirectionality and dependency of information transmission between UAVs. It abstracts each UAV as a node and uses directed edges to indicate the start and end points of communication, thereby describing the asymmetric communication links, information flow paths, and network topology, providing a structured model foundation for analyzing connectivity, identifying key nodes, and designing cooperative control algorithms. This structure not only helps to understand the communication mechanism of UAV swarms more deeply, but also provides new ideas and methods for designing and controlling the flow of information between UAVs. Therefore, using a directed graph structure to study the UAV swarm control problem is a more advanced and effective approach.

[0028] (2) This application designs a distributed collaborative controller based on the edge consensus algorithm, aiming to solve the problem of maintaining the connectivity of UAV clusters in directed topology networks.

[0029] (3) This application proposes a method based on edge consensus algorithm combined with potential function to solve the connectivity maintenance control problem in directed topological networks. The position cooperative controller based on edge consensus algorithm enables UAVs to ensure that they are always within the maximum connectivity range and minimum obstacle avoidance range. During formation flight, UAVs will intelligently plan their flight trajectories and speed information transmission based on real-time status and position, realizing the stability and connectivity of formation flight. Based on the desired attitude information obtained from the position controller, an attitude tracking controller is designed to track and control the desired attitude, ultimately realizing the connectivity maintenance control of the UAV swarm. This method not only maintains the stable flight mode of the UAV swarm, but also ensures that there is no interruption between the connected swarm members, thereby ensuring effective coordination and the operation of the entire swarm.

[0030] (4) The UAV swarm connectivity maintenance control algorithm based on the edge consensus algorithm in this application; the UAV formation connectivity maintenance is achieved based on the edge consensus algorithm and the potential function method, mainly through the following process: First, the absolute state of the UAV is converted into the edge state representing the relative relationship; the edge consensus algorithm drives the collaborative convergence of all edge states through distributed control; the potential function dynamically generates adjustment force according to the real-time distance, repelling collisions when too close and attracting to maintain connectivity when too far; finally, the command is quickly tracked through finite-time control to ensure that the formation dynamically adjusts under the directed topology and always maintains connectivity. And the final desired formation configuration is achieved. Attached Figure Description

[0031] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0032] Figure 1 This is a schematic diagram of the drone swarm model in this application;

[0033] Figure 2 This is the directed graph between drone formations in this application;

[0034] Figure 3 This application simulates the distances between all drones;

[0035] Figure 4 This refers to the distance error of the simulated drone in this application;

[0036] Figure 5 This is the current speed of the simulated drone in this application;

[0037] Figure 6 This is the current location of the simulated drone in this application;

[0038] Figure 7 This refers to the speed error of the simulated drone in this application;

[0039] Figure 8 This is the simulated attitude angle of this application;

[0040] Figure 9 This is the error of the simulated attitude angle in this application;

[0041] Figure 10 This is the simulated attitude angular acceleration of this application;

[0042] Figure 11 This is the unmanned aerial vehicle control system of this application. Detailed Implementation

[0043] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided to make this application more comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0044] Furthermore, the accompanying drawings are merely illustrative of this application and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0045] The following will provide a more detailed description of the UAV swarm connectivity maintenance control algorithm proposed in this example embodiment.

[0046] See Figures 1-11 This application provides a drone swarm connectivity maintenance control algorithm. First, a directed graph describing the communication between members of the drone swarm is constructed. Based on the directed graph, the communication links and relationships between the members are analyzed. A directed network topology is constructed based on the communication links and relationships. The drone association matrix is ​​derived from the directed network topology. Each member is represented as an edge state based on the association matrix. The position and velocity state of each drone in the association matrix are dynamically adjusted using an edge-consistency algorithm combined with a potential function method. A finite-time attitude control strategy is employed to ensure that the drone attitude angles converge within a finite time, thereby effectively maintaining the connectivity of the drone swarm.

[0047] Traditional connectivity preservation control for undirected graphs is mostly based on vertex consensus algorithms to design cooperative controllers, which cannot solve the connectivity preservation control problem in directed topology cases.

[0048] If every edge in a graph has a direction, it is called a directed graph.

[0049] Maintaining connectivity in directed graphs is more challenging than in undirected graphs. When the communication distances between UAVs are equal, the topology is undirected; when the distances are unequal, the communication network is directed. The difficulty of directed graphs compared to undirected graphs lies in the asymmetry of communication links. Traditional connectivity maintenance controllers based on the potential function method cannot maintain connectivity in directed topologies. This application solves the connectivity maintenance problem in directed topologies by introducing an edge consistency algorithm and combining it with the potential function method. First, it utilizes the directed graph incidence matrix... absolute position of the drone Mapped to edge states ,in It is the distance between the edges of the drones. Indicates 3 A 3-unit identity matrix is ​​used to describe the relative motion relationships between unmanned aerial vehicles (UAVs). This represents the Kronecker product. The edge consensus algorithm is derived through the design of a virtual controller: Adjust the edge state, where It is the desired drone. , It is a positive constant. It is an internal correlation matrix. It is the gradient of the potential function based on the edge error. Based on the first derivative of the potential function of the expected edge, It is the error between the edges of the drones. The distance of the desired edge is the velocity, which drives the relative distance and velocity between all drones to tend to be consistent. Potential function. Control force is dynamically generated based on real-time distance: when the distance between the drones... Approaching the minimum collision avoidance distance At that time, among them Indicates the first An edge, the potential function generates a repulsive force to prevent collisions; when approaching the maximum communication distance... At that time, an attractive force is generated to maintain link connectivity. Under the condition of initial connectivity, this system guarantees asymptotic convergence of edge state errors and strictly satisfies... ,in Indicates the first The L2 norm of the edges ensures that the directed topology remains connected during dynamic changes in the network.

[0050] This application presents a method for maintaining connectivity in UAV formation based on an edge consensus algorithm. Previous research primarily focused on undirected graph network structures for UAV cooperative formation design. This application employs a directed graph structure to explore the cooperative problem of UAV formation, enabling connectivity maintenance control under varying UAV communication distances. Final stability analysis and formation simulations demonstrate that all UAVs can converge to their desired formation positions.

[0051] Furthermore, the construction of the directed communication graph includes abstracting each drone in the drone swarm as a vertex in the graph, and determining the connection relationship of the directed edges formed between the vertices based on the actual communication capabilities and directional relationships of each drone; and establishing a directed graph describing the information flow within the drone formation based on the connection relationship of the directed edges.

[0052] Furthermore, the directed graph of communication explicitly represents the unidirectional transmission relationship of information between UAVs through directed edges, which is used to analyze the communication links of each member in the formation; based on the directed graph, key communication nodes are identified, the strength of link connectivity is evaluated, and it is determined whether there are information islands or transmission bottlenecks, thereby analyzing the communication links and relationships between each member in the UAV formation.

[0053] Furthermore, representing each member as an edge state, that is, transforming the UAV from a "vertex" state to an "edge" state, includes obtaining an association matrix based on the directed graph, and mapping the absolute position vector of the UAV to an edge state vector representing the relative positional relationship between the UAVs according to the association matrix. This shifts the focus of description and analysis from individual states to the connection relationship states between formation members, that is, characterizing system characteristics through edge states.

[0054] Furthermore, based on the directed graph, the connection relationship between the vertices and directed edges of the UAV is transformed into a mathematical representation: if the edge From node Pointing to node Then the correlation matrix middle This indicates that the direction of the torque generated by the motor is opposite to the positive direction we define. This indicates that the direction of the torque generated by the motor is the same as the positive direction we defined; otherwise, it is 0. The association matrix fully describes the relationship between nodes and edges in the directed network topology.

[0055] Furthermore, the edge consistency algorithm includes each UAV calculating its own error with the desired edge state based on neighbor communication using the correlation matrix, and generating control commands; driving the state variables of all edges to converge through a distributed control law, thereby achieving precise formation and maintenance without the need for global information; that is, the algorithm designs a distributed control law through the correlation matrix, utilizes the information interaction of adjacent edges to collaboratively adjust the UAV pose, and finally achieves collaborative convergence of the edge states of the entire formation and maintenance of topological connectivity.

[0056] Furthermore, the potential function method includes regulating the interaction between UAVs by constructing a non-negative function based on relative distance; when the distance between UAVs approaches the minimum collision avoidance distance, the potential function value increases sharply, generating a repulsive force to prevent collision; when the distance approaches the maximum communication distance, the potential function generates an attractive force to maintain link connectivity; the potential function reaches its minimum value at the desired distance, thereby achieving formation stability within a safe distance range.

[0057] Furthermore, the finite-time attitude control method, which enables the UAV attitude angle to converge within a finite time, involves designing a nonlinear feedback control law to ensure the UAV attitude angle tracking error system converges to zero within a finite time. The control method includes fractional power terms and a sign function. To achieve fast, accurate, and disturbance-resistant attitude angle tracking during UAV formation flight, a hierarchical control architecture is required. The top-level formation algorithm generates the desired trajectory, the middle level calculates the desired attitude commands for each UAV, and the bottom level is the core, employing a model-based feedforward-feedback composite control. Feedforward provides a fast response, while feedback ensures accuracy and eliminates steady-state errors. Crucially, a nonlinear disturbance observer must be introduced to estimate and compensate for model uncertainties, initial deviations, and lumped disturbances such as external gusts in real time, greatly enhancing robustness. A high-bandwidth controller design ensures that the system response is much faster than the command update, ultimately meeting the stringent real-time requirements of formation connectivity.

[0058] Furthermore, it also includes verifying the stability of the algorithm to obtain a stable UAV swarm connectivity maintenance control algorithm, and using the stable UAV swarm connectivity maintenance control algorithm to control the UAV formation.

[0059] This application also provides a system based on the UAV swarm connectivity maintenance control algorithm, the system including a UAV formation model, the UAV formation model having a dynamic model, the dynamic model including a position controller and an attitude controller connected to each other.

[0060] This application provides a method for maintaining UAV formation connectivity based on an edge consensus algorithm, designing position and attitude controllers. The position controller algorithm, based on a potential function, works as follows: when the distance between UAVs is less than the desired formation distance, the potential function adjusts the control input, i.e., the position and velocity of the UAVs, to increase the distance between them, thus avoiding collisions. Conversely, when the distance between UAVs approaches or exceeds the maximum connectivity distance, the potential function similarly adjusts the control input to decrease the distance between them, ensuring they remain within the connectable range. The attitude controller is designed as a finite-time attitude subsystem for tracking the required attitude angles generated by the position. This method decouples the attitude equations through the potential function of the position controller and then tracks the attitude based on the attitude controller. Since attitude control needs to strictly adhere to communication distance limitations, a certain stability is required. Compared with other control methods, finite-time attitude control stands out for its excellent convergence speed. To verify the effectiveness of the algorithm, this application provides stability proofs and simulation experiments.

[0061] To achieve the above objectives, the technical solution adopted in this application is:

[0062] Step 1: In the research of UAV formation technology, the first step is to establish a UAV formation model. This model considers the flight dynamics of the UAVs and various communication constraints during the formation process. To explore the impact of these communication constraints on formation performance, graph theory is used to model the communication graph. By constructing a directed communication graph, the communication links and relationships between the members of the UAV formation can be observed.

[0063] Define a set of unmanned aerial vehicle (UAV) system position quantities as ,in Indicates the first A drone Distance on the axis Indicates the first A drone Distance on the axis Indicates the first A drone The distance on the axis, its speed is ,in Indicates the first A drone Speed ​​on the axis Indicates the first A drone Speed ​​on the axis Indicates the first A drone Speed ​​on the axis This represents the transpose of a matrix, and its rotation matrix is... This represents the attitude of the UAV's body coordinate system relative to a fixed world coordinate system. The three-dimensional special orthogonal group represents the position dynamics model of the UAV in the inertial coordinate system, which can be expressed as:

[0064] (1)

[0065] (2)

[0066] in Indicates the speed of the drone. This indicates the acceleration of the drone's motion. It's about the quality of the drone. It's the speed of the drone. Gravitational acceleration , The lift provided by the four rotors Represents normal coefficients. Rotation matrix. Defined as:

[0067] (3)

[0068] in Indicates pitch angle, Indicates the roll angle. To represent the heading angle, for ease of position controller design, let the control input be: The model is rewritten as follows:

[0069] (4)

[0070] in . Represents a set, It represents the set of real numbers. The superscript 3n indicates "an n-fold set composed of 3-dimensional real vectors".

[0071] Dynamic communication networks are modeled using graph theory. Define a graph. ,in Let be the set of points in the graph, and Let be the edge set of the graph. Consider each drone as a vertex in the graph, and the communication between drones as an edge. Define the incidence matrix of the graph. It is a matrix where rows represent points consisting of individual drones, and columns represent edges between drones. If... It is the edge The terminal node, then the element The definition is as follows: ;if It is the edge The initial node, then ;otherwise, . Represents the incidence matrix, which includes the inner incidence matrix. External correlation matrix .

[0072] (5)

[0073] Step 2: To simplify the problem, the UAV node state equations are transformed into edge state equations. In UAV swarm research, each UAV is cleverly abstracted as a point in the network structure, which greatly simplifies the complex relationships between UAVs in the swarm. However, when modeling the dynamics, an innovative transformation method is designed to improve the convenience of modeling and ensure the effectiveness of the model. This method abandons the traditional way of representing UAVs with vertex states and instead focuses on the edge states, realizing a transformation from vertex states to edge states. Through this transformation, the network topology can be constructed in an unprecedented way, clearly showing the communication links and interrelationships between the members of the UAV swarm. Based on this network topology, the UAV correlation matrix can be derived.

[0074] The primary goal of this formation control is to manipulate drones in a three-dimensional space centered at specific coordinate points, ultimately forming the desired formation through precise control. From a control perspective, achieving connectivity within the formation requires managing the relative positions of the drones. To achieve this, position variables must be transformed into state variables describing the edges between drones. Therefore, the transition to cooperative formation involves a transformation from individual points to edges, generating state variables and error state variables for these edges:

[0075] (6)

[0076] (7)

[0077] in , , It is the expected value of the distance between drones. It's the location of the drone. It is the error between the expected distance and the actual distance between drones. Represents a third-order identity matrix. Indicates that there is One drone, The number of edges in the directed graph formed by the drones is [number]. strip.

[0078] Since the derivative of formula (5) can be obtained as follows:

[0079] (8)

[0080] According to formula (3), we can conclude that:

[0081] (9)

[0082] in The derivative of velocity is used to represent the dynamics model and communication network model for the multiple UAVs. The control requirements of this application are as follows:

[0083] 1) The distance between drones should be less than the maximum communication distance of the drones. To maintain the connectivity of the drone communication network, the distance between drones should be greater than their collision avoidance distance. This is to prevent drones from colliding with each other. This represents the maximum connectivity range between drones. It is the minimum collision avoidance range between drones.

[0084] 2) The expected distance error between UAVs should be: , , Indicates the first [number] between drones Edge.

[0085] 3) The expected speed of the drone should be , .

[0086] Step 3: A connectivity-preserving control algorithm based on edge consensus algorithm and potential function was designed. In the research of UAV formation technology, an innovative connectivity-preserving control algorithm was designed, which integrates the ideas of edge consensus algorithm and potential function. The edge consensus algorithm, as the core, ensures the stability of communication links within the UAV formation, allowing information to flow smoothly. The introduction of the potential function adds greater intelligence and adaptability to the algorithm, dynamically adjusting the control strategy based on the relative positions and distances between UAVs to maintain the connectivity and stability of the formation. This unique design enables the control algorithm to effectively cope with complex flight environments and changing mission requirements, and significantly improves the overall performance and collaborative combat capabilities of the UAV formation.

[0087] Based on system feedback, and with the help of drone state variables, when At this time, the initial expected velocity is 0, and the relationship between the drone's velocity and state variables can be derived by designing a virtual controller.

[0088] (10)

[0089] And because , Indicates the error in speed. Expressing the desired speed, we can conclude that:

[0090] (11)

[0091] (12)

[0092] in This application proposes a method for designing a controller by constructing a potential function, wherein the virtual control input is:

[0093] (13)

[0094] in , and These are the coefficients of the control parameters, and all of them are positive definite. and It is the gradient of the potential function. and It is the derivative of the gradient.

[0095] Based on the requirements of connectivity maintenance and formation, the potential function should satisfy the following conditions: 1) When the distance between UAVs approaches the maximum communication distance, the potential function will provide a force that reduces the distance between UAVs. 2) When the distance between UAVs approaches zero, the potential function will provide a force that increases the distance between UAVs. 3) When the distance between UAVs is the desired formation distance, the potential function will not provide a force. Therefore, the potential function is:

[0096] (14)

[0097] in It is positive definite. Indicates the first [unclear] between drones Distance error of the strip edge, Indicates the first [unclear] between drones The expected distance of an edge is defined as follows: ,in Indicates the first [unclear] between drones The maximum distance of the strip edges, Indicates the first [unclear] between drones The minimum distance between the edges. , It is a positive constant coefficient. Indicates the first [unclear] between drones Given the distance to the edge, the gradient of the potential function and the derivative of the gradient are as follows:

[0098] (15)

[0099] in , .

[0100] (16)

[0101] in , , Indicates the first The expected distance of the edge. , , Let each denote the derivative with respect to the other.

[0102] Step 4: Since connectivity maintenance control requires communication distance constraints and fast attitude control, a finite-time attitude controller is designed to make the UAV attitude angle converge within a finite time to track the desired attitude angle generated by the position controller.

[0103] The expected attitude and virtual lift of the drone are determined by three virtual control inputs. Confirmed, among which Indicates the first A drone Virtual control input in the axial direction, Indicates the first A drone Virtual control input in the axial direction, Indicates the first A drone Virtual control inputs along the axis, with each input corresponding to a different control dimension, enable precise and rapid adjustment of the UAV's attitude.

[0104] (17)

[0105] in Indicates the first The lift expected by the drone Indicates pitch angle, Indicates the roll angle. Indicates the heading angle.

[0106] To simplify the analysis, we set up a... This means that the required yaw angle is zero, i.e., the system or object remains in a specific direction or heading without yawing. For the attitude dynamics model, the attitude tracking controller is designed as follows:

[0107] (18)

[0108] in , , , It is a positive constant coefficient. Indicates pitch angle, Indicates the desired pitch angle. Indicates the roll angle. Indicates the desired roll angle. Indicates the heading angle. This represents the desired heading angle. This represents the moment of inertia in the direction of the pitch angle. This represents the moment of inertia in the roll direction. It represents the moment of inertia in the heading angle direction.

[0109] Step 5: The formation control algorithm was comprehensively and thoroughly verified using the MATLAB simulation platform. During the simulation, six UAVs were selected, and relevant images were generated to verify the stability of the control algorithm. This series of simulations not only verified the effectiveness and feasibility of the formation control algorithm but also laid a solid foundation for its further optimization and practical application.

[0110] To demonstrate the effectiveness of the controller proposed in this application, step 6 presents a simulation of six drones. The parameters are as follows: the mass of the drone is 0.5 kg; the initial positions of the six drones are... , , , , , Initial velocity of the six drones , , , , , Maximum communication distance Minimum collision avoidance distance ; expected distance between all drones , , , , The control coefficients are as follows: The added disturbance is

[0111] .

[0112] in The disturbance was caused by the first drone. The disturbance was caused by the second drone. The disturbance was caused by the third drone. The disturbance was caused by the fourth drone. The disturbance was caused by the fifth drone. The disturbance was introduced by the sixth UAV. The connectivity maintenance control problem aims to ensure the connectivity of the topology network while achieving the final formation configuration under communication distance constraints. Traditional formation control methods typically assume that the topology network is always connected, while the connectivity maintenance control method in this application only requires initial network connectivity and dynamically maintains this property through an algorithm. Its core lies in the synergistic effect of the potential function and the edge consensus algorithm: the potential function dynamically adjusts the interaction between UAVs according to the real-time distance—generating repulsive forces to prevent collisions when the distance is too close, and applying attractive forces to prevent chain breakage when the communication limit is approached; the edge consensus algorithm, through distributed coordination, drives the consistent convergence of the states of all edges, thereby ensuring that the formation autonomously maintains communication connectivity during movement, without relying on the strong assumption that the topology is always connected.

[0113] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0114] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0115] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in this application, and these modifications or substitutions should all be covered within the scope of protection of this application.

[0116] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein.

Claims

1. A drone swarm connectivity maintenance control algorithm, characterized in that, A directed graph describing the communication between members in a UAV formation is constructed, and the communication links and relationships between the members are analyzed based on the directed graph. A directed network topology is constructed based on the communication links and relationships, and the UAV correlation matrix is ​​derived based on the directed network topology. Each member is represented as an edge state based on the correlation matrix. The position and velocity state of each UAV in the correlation matrix are dynamically adjusted by combining an edge consistency algorithm with a potential function method. The finite-time attitude control method is used to ensure that the attitude angle of the UAV converges within a finite time, thereby effectively maintaining the connectivity of the UAV swarm. The construction of the directed graph describing the communication between members in the drone swarm includes abstracting each drone in the drone swarm as a vertex in the graph, and determining the connection relationship of the directed edges formed between the vertices based on the actual communication capabilities and directional relationships of each drone; and establishing a directed graph describing the information flow within the drone swarm based on the connection relationship of the directed edges. Representing each member as an edge state, that is, transforming the UAV from a "vertex" state to an "edge" state, includes obtaining an association matrix based on the directed graph, and mapping the absolute position vector of the UAV to an edge state vector representing the relative positional relationship between UAVs according to the association matrix, thereby shifting the focus of description and analysis from individual states to the connection relationship states between formation members, that is, characterizing system characteristics through edge states. Based on the directed graph, the connection relationship between the vertices and directed edges of the UAV is transformed into a mathematical representation: if the edge By node Pointing to node In the correlation matrix middle, , In other cases, the value is... The correlation matrix provides a complete description of the relationships between nodes and edges in the directed network topology. The edge consistency algorithm includes each UAV calculating its own error relative to the desired edge state based on neighbor communication using the correlation matrix, and generating control commands; driving the state variables of all edges to converge through a distributed control law, thereby achieving precise formation and maintenance without the need for global information; that is, the edge consistency algorithm designs a distributed control law through the correlation matrix, utilizes the information interaction of adjacent edges to collaboratively adjust the UAV pose, and ultimately achieves collaborative convergence of the edge states of the entire formation and maintenance of topological connectivity. The potential function method includes constructing a non-negative function based on relative distance to regulate the interaction between UAVs; when the distance between UAVs approaches the minimum collision avoidance distance, the potential function value increases sharply, generating a repulsive force to prevent collision; when the distance approaches the maximum communication distance, the potential function generates an attractive force to maintain link connectivity; the potential function reaches its minimum value at the desired distance, thereby achieving formation stability within a safe distance range.

2. The UAV swarm connectivity maintenance control algorithm according to claim 1, characterized in that, The directed graph of communication explicitly represents the unidirectional transmission relationship of information between UAVs through directed edges, and is used to analyze the communication links of each member in the formation; based on the directed graph, key communication nodes are identified, the strength of link connectivity is evaluated, and it is determined whether there are information islands or transmission bottlenecks, thereby analyzing the communication links and relationships between each member in the UAV formation.

3. The UAV swarm connectivity maintenance control algorithm according to claim 1, characterized in that, The method of using finite-time attitude control to make the UAV attitude angle converge within a finite time includes designing a nonlinear feedback control law to make the UAV attitude angle tracking error system converge to zero within a finite time. The control method includes fractional power terms and sign functions. The control method adopts a hierarchical control architecture, which includes a top-level array algorithm, a middle-level solution instruction, and a bottom-level feedforward-feedback composite control.

4. The UAV swarm connectivity maintenance control algorithm according to claim 3, characterized in that, It also includes verifying the stability of the algorithm to obtain a stable UAV swarm connectivity maintenance control algorithm, and using the stable UAV swarm connectivity maintenance control algorithm to control the UAV formation.

5. A system for a UAV swarm connectivity maintenance control algorithm according to any one of claims 1 to 4, characterized in that, The system includes a drone formation model, which contains a dynamic model, including a position controller and an attitude controller that are interconnected.

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