Quadrotor unmanned aerial vehicle formation control method suitable for asynchronous packet loss and random UDP attack

Abstract

The invention discloses a quad-rotor unmanned aerial vehicle formation control method suitable for asynchronous packet loss and random UDP attack, and the method comprises the steps: defining a state error of an unmanned aerial vehicle formation system according to an unmanned aerial vehicle formation model, constructing a formation system distributed controller according to the state error, obtaining an error state equation according to the formation system distributed controller, and carrying out the formation control according to the error state equation. Constructing a formation error state vector considering the influence of asynchronous packet loss and random UDP (User Datagram Protocol) attack; constructing a dual-threshold dynamic event triggering mechanism based on historical memory fusion to design an unmanned aerial vehicle formation control law; and aiming at the established unmanned aerial vehicle formation control law, the error state equation and the formation error state vector, constructing a closed-loop equation of a quad-rotor unmanned aerial vehicle formation system, and realizing quad-rotor unmanned aerial vehicle formation control under asynchronous packet loss and random UDP attack in combination with a formation system distributed controller. The problem that distributed formation control of the quad-rotor unmanned aerial vehicles is difficult to realize under asynchronous packet loss and random UDP attacks by the existing method is solved.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) formation control technology, and in particular to a method for controlling quadcopter UAV formations under asynchronous packet loss and random UDP attacks. Background Technology

[0002] In recent years, formation control of multiple quadcopter UAVs capable of performing various complex tasks has become a future development trend. Unlike centralized control with a central control unit [1] and distributed control with one-to-one correspondence between controller and UAV [2], distributed control has no control core. Each UAV in the formation needs to interact with neighboring nodes to achieve control of the entire formation, as in reference [3]. A new distributed reinforcement learning behavior control method was proposed, as in reference [4], which can reduce the cumulative and instantaneous costs in the distributed formation and obstacle avoidance process. Reference [5] designed a new distributed formation control method, which selects the additional state in Model Predictive Contour Control (MPCC) as the cooperative parameter and requires QUAV to communicate the cooperative parameter and position to its neighbors. However, existing formation control schemes lack a comprehensive response mechanism to hybrid communication anomalies (such as network attacks and non-attack failures). Most existing studies deal with malicious attacks or random packet loss problems in isolation, failing to fully reflect the complexity of asynchronous occurrence of anomalies in the actual communication environment, thus making it difficult to ensure the stable operation of the system under real and unreliable communication conditions.

[0003] Whether it's information exchange between adjacent drones or communication between drones and ground stations, network information security for drone swarms is paramount. User Datagram Protocol (UDP) Protocol (UDP) is a protocol that operates at the transport layer in the Open Systems Interconnection model. Its main characteristics are connectionless, no guarantee of reliable transmission, and message-oriented [6]. This has drawn attention to QUAV networks, especially network security issues, and led to the design of a new intrusion detection and response scheme that can detect anomalies in threat networks [7]; a scheme based on region volume or parallel polyhedron ( A novel detection method for UAVs[8] was proposed; considering the flight process of UAVs, a system model of UAVs was established using quaternions to effectively detect attacks on UAV systems[9]; Reference

[10] analyzed the impact of random packet loss on the stability of similar problems; Reference

[11] took a single fixed-wing aircraft as an example and considered the control of asynchronous UDP attacks and packet loss; Reference

[12] proposed a predictive compensation method and used the predicted value of lost data to design the controller. Reference

[13] considered its control model when considering packet loss or UDP attacks, applied Markov chains, and its goal was to find a strategy that maximizes long-term rewards. Most of the above studies attribute packet loss to network attacks. However, in actual UAV formations, packet loss may also be caused by non-aggressive factors such as network congestion and link delay. More importantly, current research generally fails to distinguish and model special scenarios where attacks and various types of packet loss occur asynchronously.

[0004] Distributed formation control of UAVs requires frequent state information communication between neighboring UAVs. Event triggering mechanisms are usually introduced to reduce the communication pressure of the system. Reference

[14] designed an event-triggered discrete-time neural control for quadrotor UAVs using a discrete-time disturbance observer, which can effectively control the external disturbances and input saturation of UAVs. Reference

[15] considered the characteristics of model dynamic uncertainty of quadrotor UAV systems and studied the existence of disturbances, and proposed an adaptive event triggering control method to reduce the update frequency of the designed controller. Reference

[16] proposed an event triggering mechanism based on deep learning control strategy to realize real-time trajectory tracking of quadrotor aircraft, and used event-triggered model predictive control (ETMPC) to generate training data. However, existing literature mostly adopts event triggering mechanisms with single dynamic thresholds or static thresholds. In the face of the complex working conditions of communication congestion, packet loss and resource constraints in actual UAV formation, such mechanisms are not good in terms of flexibility, coordination and adaptability, and it is difficult to ensure system performance and communication efficiency at the same time. Summary of the Invention

[0005] This invention provides a method for controlling the formation of quadcopter drones under asynchronous packet loss and random UDP attacks, in order to overcome the above-mentioned technical problems.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A method for controlling the formation of quadcopter drones under asynchronous packet loss and random UDP attacks, specifically including the following steps: S1: Construct follower drone models and leader drone models to establish drone swarm models; S2: Define the state error of the UAV formation system according to the UAV formation model, construct a distributed controller for the formation system according to the state error, and obtain the error state equation according to the distributed controller for the formation system; S3: Based on the state error of the UAV formation system, construct a formation error state vector considering the impact of asynchronous packet loss and random UDP attacks; S4: Construct a dual-threshold dynamic event triggering mechanism based on historical memory fusion, and design a UAV formation control law based on the dual-threshold dynamic event triggering mechanism; S5: Based on the established UAV formation control law, error state equation, and formation error state vector, construct the closed-loop equation of the quadrotor UAV formation system. Based on the closed-loop equation of the quadrotor UAV formation system and combined with the distributed controller of the formation system, quadrotor UAV formation control suitable for asynchronous packet loss and random UDP attacks is realized.

[0007] Furthermore, the drone formation model established in S1 is as follows: (1) In the formula: Describes the coefficient matrix and Indicates that drones are in Damping coefficients in the three axes; Indicates the first The position vectors of the aforementioned follower drones, and ; They represent the first The horizontal, vertical, and axial coordinates of the position of each follower drone; Indicates the first The velocity vector of the follower drone, and ; They represent the first A follower drone along Velocity components in the three axes; Indicates the first A follower drone External environmental disturbances in the three axes and ; Indicates the first A follower drone Control input signals in three axes and ; Indicates transpose; express The first derivative; Indicating that the leader's drone is in Position vectors along the three axes and ; Describes the velocity vector of the leader drone and , The damping coefficient of the leader drone is... ; This indicates the number of follower drones.

[0008] Furthermore, step S2 specifically includes the following steps: S21: Based on the UAV formation model, the state error of the UAV formation system is defined as follows: (2) In the formula: , These represent position error and velocity error, respectively. Indicates the first The expected distance between a follower drone and a leader drone; S22: Based on the state error, the distributed controller of the formation system is constructed as follows: (3) In the formula: This refers to follower drones capable of exchanging state information with each other. Neighbor drones Indicates a collection of neighboring drones; , They represent the first The weight of the communication links between a follower drone and its neighboring drones and the leader drone; Indicates the controller gain; This represents the control signals of the distributed controller in the formation system; S23: The derivative of the state error of the UAV formation system is obtained by taking the derivative of the state error: (4) By defining the error vector The error state equation obtained from the distributed controller of the formation system is as follows: (5) (6) In the formula: Represents the error vector The first derivative; Represents the parameter matrix; Represents the identity matrix.

[0009] Furthermore, step S3 specifically includes the following steps: S31: Define the sampling period sequence used to sample the state information of UAV formations. And define the event trigger time sequence as ,and ; S32: When the The follower drone and the first Normal communication is maintained between the follower drones, and the state error of the drone formation system is obtained. Input signals in the design of a drone controller and for: (7) In the formula: Indicates the current sampling time; Indicates the first The expected distance vector between the follower drone and the leader drone; Indicates the current sampling time Corresponding to the The position and velocity vectors of the follower drone; Indicates the current sampling time The corresponding position and velocity vectors of the leader drone; S33: Based on step S32, obtain the input signals considering the effects of asynchronous packet loss and random UDP attacks, including: If subjected to a UDP attack, then... The first follower drone communication The following is obtained by adding a perturbation to the state information of each follower drone, i.e., the neighboring drone: (8) In the formula: , These represent the inputs from the current sampling time to the [number]th [time]. The first follower drone after interference The position and velocity vectors of the follower drones; Represents the attack strength matrix and , Indicates the sampling time triggered by the most recent event; Indicates the sampling time triggered by the event. The corresponding position vector and velocity vector; If packet loss occurs during network communication, in the context of the first... The first follower drone communication The status information of each follower drone, i.e., the neighboring drone, is as follows: (9) In the formula: , Indicates the previous sampling time The The state values ​​of a follower drone are its position vector and velocity vector; S34: Define two independent sets of parameter variables that follow a Bernoulli distribution. and for: (10) In the formula: Let these represent the probability of communication failure and the probability of being attacked by UDP, respectively. ; And based on parameter variables and To confirm whether communication was successful, whether there was packet loss, or whether a UDP attack occurred, the following steps are taken: when This indicates a communication error. This indicates that communication is normal; If communication is abnormal and This indicates that the drone formation communication is under UDP attack; If communication is abnormal and This indicates that packet loss has occurred in the drone formation communication; Furthermore, the expressions for whether communication was successful, whether there was packet loss, or whether a UDP attack occurred are as follows: (11) S35: Obtaining the system state vector of the UAV formation based on S34 for: (12) In the formula: Indicates the relationship with the first The first follower drone communication The state of a follower drone after being attacked by a UDP attack; This refers to the neighboring drone that communicated at the previous moment, i.e., the [number]th drone. Status of a follower drone; This indicates the state of the neighboring drone at the time of the most recent event-triggered sampling. S36: Based on equations (8), (9), and (12), construct a system that considers the impact of asynchronous packet loss and random UDP attacks, and... The first follower drone communication Formation error state vector of a follower drone for: (13) In the formula: Indicates the first The parameter variables of each follower drone follow a Bernoulli distribution. , ; Indicates the previous moment. The follower drone was input to the first Input signals for the drone controller; Indicates the sampling time triggered by the most recent event, the th The follower drone was input to the first Input signals for the drone controller; express The manifestations of a UDP attack.

[0010] Furthermore, step S4 specifically includes the following steps: S41: The dual-threshold dynamic event triggering mechanism based on historical memory fusion is constructed as follows: (14) (15) (16) In the formula: Indicates the current trigger time of the dual-threshold dynamic event; Indicates the sampling time triggered by the most recent event; Indicates the number of sampling steps between adjacent trigger times and , Indicates the maximum number of sampling steps; Indicates the system's sampling period; Represents the error weight matrix; Indicates design constants; , Represents a dynamic threshold function and , This represents the basic parameter values ​​of the dynamic threshold function. Indicates the upper bound of the dynamic threshold; This indicates the data difference between the error status information to be transmitted now and the error status information transmitted most recently. This represents the data difference between the error status information to be transmitted now and the average of multiple historical error status information. , , These represent the current status information that the sending drone is about to transmit, the most recently transmitted status information, and the historical transmitted information data, respectively. Indicate design parameters; S42: The time-varying delay is defined according to the dual-threshold dynamic event triggering mechanism as follows: (17) (18) In the formula: Indicates the most recent trigger time; Indicates the current sampling step size; Indicates the start time within the current triggering cycle. up to the current time The offset; These represent the lower bound of network latency, the maximum network latency, and the maximum communication latency, respectively. S43: According to equations (14) to (16), we can obtain: (19) In the formula: Represents a global intermediate variable and ; ;

[0011] And according to equation (17), equation (19) can be rewritten as: (20) In the formula: ; S44: Based on equation (20) combined with a dual-threshold dynamic event triggering mechanism, obtain the first... Drone Swarm Control Law for Follower Drones for: (twenty one) In the formula: Indicates intermediate parameters and , Indicate Enter time up to the number The first follower drone after interference The position and velocity vectors of the follower drones; This indicates the control gain.

[0012] Furthermore, S5 specifically includes the following steps: S51: Based on the established UAV formation control law and error state equation, the UAV formation system's first... The state error system of an unmanned aerial vehicle (UAV) based on a dual-threshold dynamic event triggering mechanism is represented as follows: (twenty two) S52: Define the global intermediate variable as: , ,(twenty three)

[0013]

[0014] And by combining equations (5), (13), (22), and (23), the closed-loop equation of the quadcopter UAV formation system based on the dual-threshold dynamic event triggering mechanism is obtained as follows: (twenty four) In the formula: Indicates intermediate parameters and , Represents the communication link weight parameter matrix and Represents the Laplace matrix ; Represents the parameter matrix and Represents intermediate variables and Describes the adjacency matrix and Represent real numbers; Represents the identity matrix; express The manifestations after interference; S53: Based on the closed-loop equation of the quadrotor UAV formation system and the distributed controller of the formation system, realize quadrotor UAV formation control suitable for asynchronous packet loss and random UDP attacks.

[0015] Beneficial effects: This invention provides a quadcopter UAV formation control method applicable to asynchronous packet loss and random UDP attacks. Based on the state error of the UAV formation system, a formation error state vector considering the impact of asynchronous packet loss and random UDP attacks is constructed. A dual-threshold dynamic event triggering mechanism based on historical memory fusion is constructed. This mechanism dynamically constructs triggering conditions by introducing historical information. Compared with traditional methods that rely solely on single-step information, it can more accurately determine the necessity of communication, effectively reduce redundant data transmission, alleviate communication burden, and balance triggering conditions with system performance. Based on the established UAV formation control law, error state equation, and formation error state vector, a closed-loop equation for a quadrotor UAV formation system is constructed. Since communication delay is a common factor leading to data packet loss, and the system may also be susceptible to asynchronous UDP attacks, this invention establishes two independent Bernoulli models for each UAV to accurately describe this combined effect. These models describe the communication state and packet loss / attack respectively. By combining the constructed closed-loop equation of the quadrotor UAV formation system with the distributed controller of the formation system, the distributed formation control problem of quadrotor UAVs under asynchronous packet loss and random UDP attacks is solved, improving the accuracy and efficiency of quadrotor UAV formation control. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0017] Figure 1 This is a flowchart of the quadcopter UAV formation control method applicable to asynchronous packet loss and random UDP attacks according to the present invention; Figure 2 This is a diagram of the formation communication topology in this embodiment; Figure 3 This is a simulation diagram of UDP attack and packet loss moments in this embodiment; Figure 4 This is a simulation diagram of the formation spiral ascent trajectory under asynchronous packet loss and random UDP attacks in this embodiment; Figure 5 This is a graph showing the formation tracking error of the follower UAVs in the x-direction in this embodiment; Figure 6 This is a graph showing the tracking error curve of the follower UAVs in the y-direction in this embodiment. Figure 7 This is a graph showing the formation tracking error curve of the follower UAVs in the z-direction in this embodiment; Figure 8 This is a schematic diagram showing the event triggering times of each follower drone in this embodiment; Figure 9 This example illustrates the circular motion trajectory curve of the formation ascending diagonally in a straight line. Figure 10 This is a graph showing the x-direction formation tracking error of the follower UAV during the segmented motion process in this embodiment. Figure 11 This is a graph showing the y-direction formation tracking error of the follower UAV during the segmented motion process in this embodiment. Figure 12 This is a graph showing the z-direction formation tracking error curve of the follower UAV during the segmented motion process in this embodiment; Figure 13 This is a schematic diagram showing the event triggering times of each follower drone during the segmented motion process in this embodiment; Figure 14 This is a simulation diagram of the HMF-DETS triggering time and triggering interval in this embodiment; Figure 15 This is a simulation diagram of the triggering time and triggering interval of the single dynamic threshold METM in this embodiment; Figure 16This is a graph showing the formation flight trajectory under a single dynamic threshold METM in this embodiment; Figure 17 This is a graph showing the x-direction formation tracking error under a single dynamic threshold METM in this embodiment; Figure 18 This is a graph showing the y-direction formation tracking error under a single dynamic threshold METM in this embodiment; Figure 19 This is a graph showing the z-direction formation tracking error under a single dynamic threshold METM in this embodiment. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] This embodiment provides a method for controlling the formation of quadrotor UAVs under asynchronous packet loss and random UDP attacks. Specifically, this embodiment considers a quadrotor UAV formation control method... A directed communication network composed of individual drones, using graphs Describe the information interaction relationships between individual drones in the formation system, where This represents the individual drones in the formation; each individual drone is a node. Representation diagram The set of edges in the diagram represents the communication links between individual drones. If the nodes Able to start from nodes Receive message and Then individual drones Becoming an individual drone Neighbors, nodes The neighbor node can be defined as ,picture adjacency matrix Defined as ,if and If there is a path between them, then ,on the contrary Define the Laplace matrix. ,in and Furthermore, the definition , When a communication link exists with the leader, ,otherwise .

[0020] The communication topology of the quadcopter UAV formation control system considered in this embodiment is described as follows: 1) Leader Drone It only sends messages to the follower drones and does not receive their status information.

[0021] 2) With the leader drone as the root node, the communication topology of the drone formation system forms a directed spanning tree, and the follower drones and neighboring drones can obtain each other's state information. After that, we will consider having [the following] This embodiment describes a formation system consisting of four quadcopter drones. Each drone transmits its position and speed information to neighboring drones via a wireless network. The method described in this embodiment will sequentially and in detail explain the formation system model, formation errors under asynchronous packet loss and random UDP attacks, and a dual dynamic threshold event triggering mechanism based on historical memory fusion. Figure 1 As shown, the specific steps include: S1: Construct follower drone models and leader drone models to establish drone swarm models; Specifically, the established UAV formation model, namely the QUAV formation model, is as follows: (1) In the formula: Describes the coefficient matrix and Indicates that drones are in Damping coefficients in the three axial directions and , This indicates the design parameters and the mass of the drone; Indicates the first The position vectors of the aforementioned follower drones, and ; They represent the first The horizontal, vertical, and axial coordinates of the position of each follower drone; Indicates the first The velocity vector of the follower drone, and ; They represent the first A follower drone along Velocity components in the three axes; Indicates the first A follower drone External environmental disturbances in the three axes and , Indicate design parameters; Indicates the first A follower drone Control input signals in three axes and ; Indicates transpose; express The first derivative; Indicating that the leader's drone is in Position vectors along the three axes and ; Describes the velocity vector of the leader drone and , The damping coefficient of the leader drone is... ; This indicates the number of follower drones.

[0022] S2: Define the state error of the UAV formation system based on the UAV formation model, construct a distributed controller for the formation system based on the state error, and obtain the error state equation based on the distributed controller. This includes the following steps: S21: Based on the UAV formation model, the state error of the UAV formation system is defined as follows: (2) In the formula: , These represent position error and velocity error, respectively. Indicates the first The expected distance between a follower drone and a leader drone; S22: Based on the state error, the distributed controller of the formation system is constructed as follows: (3) In the formula: This refers to follower drones capable of exchanging state information with each other. Neighbor drones Indicates a collection of neighboring drones; , They represent the first The weight of the communication links between a follower drone and its neighboring drones and the leader drone; , Indicates the controller gain; This represents the control signals of the distributed controller in the formation system; S23: The derivative of the state error of the UAV formation system is obtained by taking the derivative of the state error: (4) By defining the error vector The error state equation obtained from the distributed controller of the formation system is as follows: (5) (6) In the formula: Represents the error vector The first derivative; Represents the parameter matrix; Represents the identity matrix.

[0023] S3: Based on the state error of the UAV formation system, construct the formation error state vector considering the impact of asynchronous packet loss and random UDP attacks. Specific steps include: S31: This embodiment selects a fixed sampling period. To sample the state information of the QUAV formation, a sampling period sequence is defined for sampling the state information of the UAV formation. And define the event trigger time sequence as ,and ; S32: When individuals in a QUAV formation communicate with each other, the controller's response to the state inputs of neighboring UAVs may be affected differently. The follower drone and the first Normal communication is maintained between the follower drones, and the state error of the drone formation system is obtained. Input signals in the design of a drone controller and for: (7) In the formula: Indicates the current sampling time; Indicates the first The expected distance vector between the follower drone and the leader drone; Indicates the current sampling time Corresponding to the The position and velocity vectors of the follower drone; Indicates the current sampling time The corresponding position and velocity vectors of the leader drone; S33: Based on step S32, obtain the input signals considering the effects of asynchronous packet loss and random UDP attacks, including: If subjected to a UDP attack, then... The first follower drone communication The following is obtained by adding a perturbation to the state information of each follower drone, i.e., the neighboring drone: (8) In the formula: , These represent the inputs from the current sampling time to the [number]th [time]. The first follower drone after interference The position and velocity vectors of the follower drones; Represents the attack strength matrix and , Indicates the sampling time triggered by the most recent event; Indicates the sampling time triggered by the event. The corresponding position vector and velocity vector; In network communication, besides network attacks causing packet loss, network congestion and latency can also lead to packet loss. If packet loss occurs in network communication, it will affect the next step. The first follower drone communication The status information of each follower drone, i.e., the neighboring drone, is as follows: (9) In the formula: , Indicates the previous sampling time The The follower drone's state values ​​are its position vector and velocity vector; in this embodiment, the state value from the previous sampling time is used. and To describe the error at the current moment, during the formation flight of quadcopter drones, frequent state exchanges may cause network congestion and network latency. This embodiment considers the special case of asynchronous UDP attacks and packet loss. In order to establish an accurate mathematical model to represent the phenomena of packet loss and UDP attacks, the binary nature and independence of the Bernoulli distribution are used to describe this special case.

[0024] S34: Define two independent sets of parameter variables that follow a Bernoulli distribution. and These indicate whether communication was successful and whether a UDP attack occurred, respectively. This indicates a communication error, and the corresponding time is... This indicates that communication is normal; if communication fails, if If the ping is positive, it indicates that the platoon communication is under a UDP attack; otherwise... This indicates that packet loss has occurred during communication, and the distribution of the two can be represented as follows: (10) In the formula: Let these represent the probability of communication failure and the probability of being attacked by UDP, respectively. ; And based on parameter variables and To confirm whether communication was successful, i.e. whether there was packet loss and whether a UDP attack occurred, the following steps are taken: when This indicates a communication error. This indicates that communication is normal; If communication is abnormal and This indicates that the drone formation communication is under UDP attack; If communication is abnormal and This indicates that packet loss has occurred in the drone formation communication; Furthermore, the expressions for whether communication was successful (i.e., whether there was packet loss) and whether a UDP attack occurred are as follows: (11) This embodiment uses parameter variables that follow a Bernoulli distribution. and The design enables the drone formation controller to adapt to the impact of communication failures, thereby improving the robustness of the entire formation system.

[0025] S35: Obtaining the system state vector of the UAV formation based on S34 for: (12) In the formula: Indicates the relationship with the first The first follower drone communication The state of a follower drone after being attacked by a UDP attack; This refers to the neighboring drone that communicated at the previous moment, i.e., the [number]th drone. Status of a follower drone; Indicates the state of the neighboring drone at the time of the most recent event-triggered sampling and Since the strength of UDP attacks is limited, this embodiment can restrict the signal after a UDP attack:

[0026] S36: Based on equations (8), (9), and (12), construct a system that considers the impact of asynchronous packet loss and random UDP attacks, and... The first follower drone communication Formation error state vector of a follower drone for: (13) In the formula: Indicates the first The parameter variables of each follower drone follow a Bernoulli distribution. , ; Indicates the previous moment. The follower drone was input to the first Input signals for the drone controller; Indicates the sampling time triggered by the most recent event, the th The follower drone was input to the first Input signals for the drone controller; express The manifestations of a UDP attack.

[0027] S4: During the flight of a quadcopter drone formation, neighboring drones frequently exchange information such as position and velocity. This data leads to a significant waste of network resources and increases the communication burden of the entire system. Therefore, this embodiment proposes a novel history memory fusion with dual-threshold dynamic event triggering scheme (HMF-DETS) to reduce the number of communications. In this dual-threshold dynamic event triggering mechanism, neighboring drones only exchange state information when the set trigger conditions are met, thus saving communication resources during formation flight. Furthermore, since the battery capacity of drones is limited during flight, inter-drone communication is one of the most energy-consuming functions. Therefore, setting an event triggering mechanism can further extend the formation mission time. The specific steps include: S41: The dual-threshold dynamic event triggering mechanism based on historical memory fusion is constructed as follows: (14) (15) (16) In the formula: Indicates the current trigger time of the dual-threshold dynamic event; Indicates the sampling time triggered by the most recent event; Indicates the number of sampling steps between adjacent trigger times and , Indicates the maximum number of sampling steps; Indicates the system's sampling period; Represents the error weight matrix; This represents a design constant used to prevent the drone from not triggering indefinitely when its flight state has zero error; , Represents a dynamic threshold function and , This represents the basic parameter values ​​of the dynamic threshold function. Indicates the upper bound of the dynamic threshold; This indicates the data difference between the error status information to be transmitted now and the error status information transmitted most recently. This represents the data difference between the error status information to be transmitted now and the average of multiple historical error status information. , , These represent the current status information that the sending drone is about to transmit, the most recently transmitted status information, and the historical transmitted information data, respectively. Indicate design parameters; The purpose of designing the dynamic threshold function in this embodiment is to enable the threshold to be dynamically adjusted according to the current error norm. When the system is subjected to a UDP attack or in the initial stage where the error is large, it is desirable to relax the triggering conditions, i.e., increase the threshold. and decrease This allows for more data transmission to quickly adjust the drone's status, especially when the error is small, such as during stable drone formation flight, thus reducing... and increase Tighten the triggering conditions to reduce unnecessary communication.

[0028] S42: Define a sub-time set based on the dual-threshold dynamic event triggering mechanism: , in Indicates the number of sampling steps between adjacent trigger times and Therefore, there is ;for In this embodiment, in order to associate the discrete state under the dual-threshold dynamic event triggering mechanism with the continuous-time system, the time-varying delay is defined as: (17) The time-varying delay is bounded: (18) In the formula: Indicates the most recent trigger time; Indicates the current sampling step size; Indicates the start time within the current triggering cycle. up to the current time The offset; These represent the lower bound of network latency, the maximum network latency, and the maximum communication latency, respectively; where It is the minimum data transmission time from the sensor to the controller, which is the inherent delay time of the system; S43: According to equations (14) to (16), we can obtain: (19) In the formula: Represents a global intermediate variable and ; ;

[0029] And according to equation (17), equation (19) can be rewritten as: (20) In the formula: ; S44: Based on equation (20) combined with a dual-threshold dynamic event triggering mechanism, obtain the first... Drone Swarm Control Law for Follower Drones for: (twenty one) In the formula: Indicates intermediate parameters and , Indicate Enter time up to the number The first follower drone after interference The position and velocity vectors of the follower drones; This indicates the control gain.

[0030] S5: Based on the established UAV formation control law, error state equation, and formation error state vector, construct the closed-loop equation of the quadrotor UAV formation system; based on the closed-loop equation of the quadrotor UAV formation system and combined with the distributed controller of the formation system, implement quadrotor UAV formation control suitable for asynchronous packet loss and random UDP attacks, specifically including the following steps: S51: Based on the established UAV formation control law and error state equation, the UAV formation system's first... The state error system of an unmanned aerial vehicle (UAV) based on a dual-threshold dynamic event triggering mechanism is represented as follows: (twenty two) S52: To simplify the analysis, this embodiment defines the global intermediate variable as: , ,(twenty three)

[0031]

[0032] And by combining equations (5), (13), (22), and (23), the closed-loop equation of the quadcopter UAV formation system based on the dual-threshold dynamic event triggering mechanism is obtained as follows: (twenty four) In the formula: Indicates intermediate parameters and , Represents the communication link weight parameter matrix and Represents the Laplace matrix ; Represents the parameter matrix and Represents intermediate variables and Describes the adjacency matrix and Represent real numbers; Represents the identity matrix; express The manifestations after interference; S53: Based on the closed-loop equation of the quadrotor UAV formation system and the distributed controller of the formation system, realize quadrotor UAV formation control suitable for asynchronous packet loss and random UDP attacks.

[0033] This embodiment also includes the following simulation verification: In this embodiment, a QUAV formation system consisting of four follower UAVs and one leader UAV is used to verify the effectiveness of the proposed method. The relevant parameter settings are shown in Table 1. Simulation verification is performed using MATLAB software. The formation communication topology is set as follows: Figure 2 As shown: Table 1. Simulation Correlation Coefficient Settings

[0034] according to Figure 1 In the QUAV formation system, the adjacency matrix between the leader QUAV and the follower QUAVs, and the corresponding Laplacian matrix between the follower QUAVs, are as follows: , Distributed control gain of QUAV formation system , Error matrix of the proposed HMF-DETS The solution is as follows: The controller gain is: , . The error weight matrix is: , , , . like Figure 3 The image shows a drone within the formation. The distribution of moments affected by UDP attacks and packet loss shows that the two types of events occur asynchronously, consistent with the assumption in this embodiment that two independent sets of Bernoulli equations are used in the controller design. When the drone formation moves in a spiral ascent, the leader... The set position expectation value is The expected speed is The desired formation is: . The formation is centered on the leader drone, with the other four follower drones arranged in a square around it. The initial positions are relatively large and dispersed around the leader drone. After takeoff, they spiral upwards around the leader drone.

[0035] Figure 4 This demonstrates the effect of finite-strength UDP attacks and asynchronous packet loss. At that time, although the flight path of the quadcopter drones fluctuated due to these two factors, in general, there was no collision between the drones, and the adjacent drones maintained the expected safe distance. The four follower drones always maintained a square formation with the leader drone as the center during the movement, and the controller designed in this embodiment can quickly make the drone formation state tend to be stable.

[0036] Figures 5 to 7 The position tracking error curves of the four follower QUAVs in the x, y, and z directions are given. It can be seen that the tracking error of the QUAVs can converge to near 0 relatively quickly. Even after the state information fluctuations caused by asynchronous packet loss and UDP attacks, the tracking error can always be kept stable within a small range, which also verifies the stability of the UUB proposed in this embodiment. Figure 8 The image shows the trigger times of four follower drones under HMF-DETS, with trigger rates of 31.6%, 31.5%, 30.1%, and 27.6%, respectively. It can be seen that the drone formation system based on HMF-DETS can achieve good control even with a low trigger rate.

[0037] In this embodiment, when the drone formation moves in a straight line, diagonally upwards in a circular motion, the leader drone... The set trajectory is divided into two stages: Phase 1 At that time, the leader ascends diagonally in a straight line from the starting point: , when At that time, the leader reached the cruising altitude. The leader drone begins its second phase: tracing a circle at its cruising altitude, with the trajectory function as follows: , Define the rising phase time cruising altitude Center coordinates ,radius and angular velocity The desired drone formation is as follows: . Figure 9 This demonstrates the effect of finite-strength UDP attacks and asynchronous packet loss. At that time, the formation flight trajectory of the quadcopter drones is as follows: the formation flies diagonally upward from the starting point to the predetermined height and begins to move in a circle. The four follower drones maintain a square formation around the leader drone throughout the process, and there is no collision between the formations. The controller designed in this embodiment can effectively enable the follower drones to track the leader.

[0038] Figures 10 to 12 The position tracking error curves of four follower QUAVs in the x, y, and z directions are presented. It can be seen that the QUAV formation can control the follower UAVs to maintain a small tracking error during the ascent and circle phases, even when packet loss and UDP attacks occur asynchronously. Figure 13 The diagram shows the trigger times of four follower drones under HMF-DETS, with trigger rates of 38.4%, 41.2%, 42.4%, and 38.6%, respectively. Compared to Scenario 1, the trigger rates are relatively high due to changes in movement trajectories, but the drone formation system based on HMF-DETS can still achieve good control results with a relatively low trigger rate.

[0039] Figures 14 to 15 Comparing the trigger intervals of the HMF-DETS (a) and the single dynamic threshold METM (b) designed in this embodiment, taking a single QUAV as an example, it is evident that both mechanisms result in a small portion of the state signal being transmitted. However, the trigger frequency of the HMF-DETS proposed in this embodiment is significantly lower than that of the single dynamic threshold METM. Even with a longer trigger interval, the UAV formation can still maintain the desired flight formation, demonstrating that the integration of the new triggering mechanism and the designed controller can effectively reduce the communication frequency between UAVs and conserve system resources for the UAV formation. This embodiment sets the same communication failure probability. UDP attack rate and packet loss rate ,like Figures 16 to 19As shown, comparing the HMF-DETS designed in this embodiment with the single dynamic threshold METM, it can be clearly seen that although the information exchange frequency of the system is low under HMF-DETS, it has a better control effect than the traditional adaptive memory event triggering mechanism (METM).

[0040] As shown in Table 2, with the increase of the UDP attack rate, the trigger rate of HMF-DETS and the trigger rate of single dynamic threshold METM both increase significantly. However, it is also clear that under the same conditions, i.e., when the probability of communication failure and the probability of being attacked by UDP are the same, the HMF-DETS designed in this embodiment greatly reduces the number of triggers compared to the traditional ETS, further demonstrating the superiority of the method described in this embodiment. In addition, when the quadcopter UAV formation is attacked by UDP, the impact on the system is significantly greater than the impact of the increased packet loss probability. When the UDP attack probability is 0.9, the formation flight cannot maintain its formation, and the system cannot control it.

[0041] Table 2. Event trigger rate under different attack and packet loss probabilities

[0042] Compared to existing quadcopter UAV formation control technologies, the method described in this embodiment maintains good control performance during UAV formation flight under conditions of asynchronous packet loss and random UDP attacks. Furthermore, by introducing a dual dynamic threshold event triggering mechanism, it simultaneously ensures system performance and communication efficiency. This method effectively solves the problem of quadcopter UAV formation flight control under asynchronous packet loss and UDP attacks. First, it uses two independent Bernoulli equations to describe whether communication is successful and whether a UDP attack has occurred, respectively, integrating them into the controller design to improve the UAV formation's resistance to these two adverse communication factors. Second, to reduce the frequency of state information exchange in quadcopter UAV formations and to mitigate the impact of sudden state error changes caused by UDP attacks and packet loss, this paper proposes a novel event triggering mechanism, HMF-DETS. This mechanism introduces a historical memory fusion mechanism and combines two dynamic threshold settings to dynamically adjust the triggering conditions based on system errors, reducing the triggering frequency, significantly saving formation system resources, and enhancing control of the formation system under the aforementioned conditions.

[0043] The relevant literature for this embodiment is as follows: [1].Li X, Zhou H. UAV formation centralized control method undercooperative flight missions[C] / / 2023 5th International Conference onRobotics, Intelligent Control and Artificial Intelligence (RICAI). IEEE,2023: 366-369. [2].Ali Z A, Shafiq M, Farhi L. Formation control of multiple UAV’svia decentralized control approach[C] / / 2018 5th International Conference onSystems and Informatics (ICSAI). IEEE, 2018: 61-64. [3].Nguyen H T T, Do H T, Tran H T, et al. Collision-Free DistributedFormation Control of Multi-Agent Systems Based on Formation Graph[C] / / 2023International Conference on Control, Robotics and Informatics (ICCRI). IEEE,2023: 34-38. [4].Zhang Z, Xie S, Dong J. Optimal Policy Learning for DistributedFormation Control of Behavior-based UAVs[C] / / 2024 7th InternationalConference on Robotics, Control and Automation Engineering (RCAE). IEEE,2024: 230-234. [5].Zhao M, Li H. Distributed Formation Control of Quadrotors UsingModel Predictive Contouring Control[C] / / IECON 2023-49th Annual Conference ofthe IEEE Industrial Electronics Society. IEEE, 2023: 1-6. [6].Sahraoui Y, Ghanam A, Zaidi S, et al. Performance evaluation ofTCP and UDP based video streaming in vehicular ad-hoc networks[C] / / 2018International Conference on Smart Communications in Network Technologies(SaCoNeT). IEEE, 2018: 67-72. [7].Sedjelmaci H, Senouci S M, Ansari N. A hierarchical detection andresponse system to enhance security against lethal cyber-attacks in UAVnetworks[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems,2017, 48(9): 1594-1606. [8].Meriaux E, Weitzen J. Robustness of Couzin Swarming to PacketLoss and Methods to Improve Robotic Swarm Communication[C] / / 2024 IEEEInternational Conference on Microwaves, Communications, Antennas, BiomedicalEngineering and Electronic Systems (COMCAS). IEEE, 2024: 1-6. [9].Shi S, Zhou Y. Stable control of the virtually coupled train setwith considering packet loss[C] / / 2022 IEEE 25th International Conference onIntelligent Transportation Systems (ITSC). IEEE, 2022: 1870-1875.

[10] .Lu Q, Zhang L, Basin M, et al. Analysis and synthesis fornetworked control systems with uncertain rate of packet losses[J]. Journal ofthe Franklin Institute, 2012, 349(7): 2500-2514.

[11] .Yang F, Wang W, Niu Y, et al. Observer-based H∞ control fornetworked systems with consecutive packet delays and losses[J]. InternationalJournal of Control, Automation and Systems, 2010, 8(4): 769-775.

[12] .Liu Y, Ling Q. Stabilizing bit rate conditions for a scalarlinear event-triggered system with Markov dropouts[J]. Automatica, 2022, 146:110635.

[13] .Mamduhi M H, Toli D, Molin A, et al. Event-triggered scheduling for stochastic multi-loop networked control systems with packet dropouts[C] / / 53rd IEEE Conference on Decision and Control. IEEE, 2014: 2776-2782.

[14] .Shao S, Chen M, Hou J, et al. Event-triggered-based discrete-time neural control for a quadrotor UAV using disturbance observer[J]. IEEE / ASME Transactions on Mechatronics, 2021, 26(2): 689-699.

[15] . Cao Chengjie, Zhao Zhongyuan, Deng Zhiliang. Adaptive event-triggered control algorithm for flight attitude of quadrotor UAV [J]. Control Engineering, 2023: 1-9.

[16] .Zhu C, Chen J, Iwasaki M, et al. Event-triggered deep learningcontrol of quadrotors for trajectory tracking[J]. IEEE Transactions onIndustrial Electronics, 2023, 71(3): 2726-2736. Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for formation control of quadcopter UAVs under asynchronous packet loss and random UDP attacks, characterized in that, The specific steps include: S1: Construct follower drone models and leader drone models to establish drone swarm models; S2: Define the state error of the UAV formation system according to the UAV formation model, construct a distributed controller for the formation system according to the state error, and obtain the error state equation according to the distributed controller for the formation system; S3: Based on the state error of the UAV formation system, construct a formation error state vector considering the impact of asynchronous packet loss and random UDP attacks; S4: Construct a dual-threshold dynamic event triggering mechanism based on historical memory fusion, and design a UAV formation control law based on the dual-threshold dynamic event triggering mechanism; S5: Based on the established UAV formation control law, error state equation, and formation error state vector, construct the closed-loop equation of the quadrotor UAV formation system. Based on the closed-loop equation of the quadrotor UAV formation system and combined with the distributed controller of the formation system, quadrotor UAV formation control suitable for asynchronous packet loss and random UDP attacks is realized.

2. The method for quadcopter UAV formation control under asynchronous packet loss and random UDP attacks as described in claim 1, characterized in that, The drone formation model established in S1 is as follows: （1） In the formula: Describes the coefficient matrix and Indicates that drones are in Damping coefficients in the three axes; Indicates the first The position vectors of the aforementioned follower drones, and ; They represent the first The horizontal, vertical, and axial coordinates of the position of each follower drone; Indicates the first The velocity vector of the follower drone, and ; They represent the first A follower drone along Velocity components in the three axes; Indicates the first A follower drone External environmental disturbances in the three axes and ; Indicates the first A follower drone Control input signals in three axes and ; Indicates transpose; express The first derivative; Indicating that the leader's drone is in Position vectors along the three axes and ; Describes the velocity vector of the leader drone and , The damping coefficient of the leader drone is... ; This indicates the number of follower drones.

3. The quadcopter UAV formation control method according to claim 2, characterized in that, S2 specifically includes the following steps: S21: Based on the UAV formation model, the state error of the UAV formation system is defined as follows: （2） In the formula: These represent position error and velocity error, respectively. Indicates the first The expected distance between a follower drone and a leader drone; S22: Based on the state error, the distributed controller of the formation system is constructed as follows: （3） In the formula: This refers to follower drones capable of exchanging state information with each other. Neighbor drones Indicates a collection of neighboring drones; They represent the first The weight of the communication links between a follower drone and its neighboring drones and the leader drone; Indicates the controller gain; This represents the control signals of the distributed controller in the formation system; S23: The derivative of the state error of the UAV formation system is obtained by taking the derivative of the state error: （4） By defining the error vector The error state equation obtained from the distributed controller of the formation system is as follows: （5） （6） In the formula: Represents the error vector The first derivative; Represents the parameter matrix; Represents the identity matrix.

4. The quadcopter UAV formation control method according to claim 3, characterized in that, S3 specifically includes the following steps: S31: Define the sampling period sequence used to sample the state information of UAV formations. And define the event trigger time sequence as ,and ; S32: When the The follower drone and the first Normal communication is maintained between the follower drones, and the state error of the drone formation system is obtained. Input signals in the design of a drone controller and for: （7） In the formula: Indicates the current sampling time; Indicates the first The expected distance vector between the follower drone and the leader drone; Indicates the current sampling time Corresponding to the The position and velocity vectors of the follower drone; Indicates the current sampling time The corresponding position and velocity vectors of the leader drone; S33: Based on step S32, obtain the input signals considering the effects of asynchronous packet loss and random UDP attacks, including: If subjected to a UDP attack, in relation to the first The first follower drone communication The following is obtained by adding a perturbation to the state information of each follower drone, i.e., the neighboring drone: （8） In the formula: , These represent the inputs from the current sampling time to the [number]th [time]. The first follower drone after interference The position and velocity vectors of the follower drones; Represents the attack strength matrix and , Indicates the sampling time triggered by the most recent event; Indicates the sampling time triggered by the event. The corresponding position vector and velocity vector; If packet loss occurs during network communication, then... The first follower drone communication The status information of each follower drone, i.e., the neighboring drone, is as follows: （9） In the formula: , Indicates the previous sampling time The The state values ​​of a follower drone are its position vector and velocity vector; S34: Define two independent sets of parameter variables that follow a Bernoulli distribution. and for: （10） In the formula: Let these represent the probability of communication failure and the probability of being attacked by UDP, respectively. ; And based on parameter variables and To confirm whether communication was successful and whether there was packet loss or a UDP attack, the following steps are taken: when This indicates a communication error. This indicates that communication is normal; If communication is abnormal and This indicates that the drone formation communication is under UDP attack; If communication is abnormal and This indicates that packet loss has occurred in the drone formation communication; Furthermore, the expressions for whether communication was successful, whether packets were lost, and whether a UDP attack occurred are as follows: （11） S35: Obtaining the system state vector of the UAV formation based on S34 for: （12） In the formula: Indicates the relationship with the first The first follower drone communication The state of a follower drone after being attacked by a UDP attack; This refers to the neighboring drone that communicated at the previous moment, i.e., the [number]th drone. Status of a follower drone; This indicates the state of the neighboring drone at the time of the most recent event-triggered sampling. S36: Based on equations (8), (9), and (12), construct a system that considers the impact of asynchronous packet loss and random UDP attacks, and... The first follower drone communication Formation error state vector of a follower drone for: （13） In the formula: Indicates the first The parameter variables of each follower drone follow a Bernoulli distribution. , ; Indicates the previous moment. The follower drone was input to the first Input signals for the drone controller; Indicates the sampling time triggered by the most recent event, the th The follower drone was input to the first Input signals for the drone controller; express The manifestations of a UDP attack.

5. The quadcopter UAV formation control method according to claim 4, characterized in that, S4 specifically includes the following steps: S41: The dual-threshold dynamic event triggering mechanism based on historical memory fusion is constructed as follows: （14） （15） （16） In the formula: Indicates the current trigger time of the dual-threshold dynamic event; Indicates the sampling time triggered by the most recent event; Indicates the number of sampling steps between adjacent trigger times and , Indicates the maximum number of sampling steps; Indicates the system's sampling period; Represents the error weight matrix; Indicates design constants; , Represents a dynamic threshold function and , This represents the basic parameter values ​​of the dynamic threshold function. Indicates the upper bound of the dynamic threshold; This indicates the data difference between the error status information to be transmitted now and the error status information transmitted most recently. This represents the data difference between the error status information to be transmitted now and the average of multiple historical error status information. , , These represent the current status information that the sending drone is about to transmit, the most recently transmitted status information, and the historical transmitted information data, respectively. Indicate design parameters; S42: The time-varying delay is defined according to the dual-threshold dynamic event triggering mechanism as follows: （17） （18） In the formula: Indicates the most recent trigger time; Indicates the current sampling step size; Indicates the start time within the current triggering cycle. up to the current time The offset; These represent the lower bound of network latency, the maximum network latency, and the maximum communication latency, respectively. S43: According to equations (14) to (16), we can obtain: （19） In the formula: Represents a global intermediate variable and ; ; And according to equation (17), equation (19) can be rewritten as: （20） In the formula: ; S44: Based on equation (20) combined with a dual-threshold dynamic event triggering mechanism, obtain the first... Drone Swarm Control Law for Follower Drones for: （21） In the formula: Indicates intermediate parameters and , Indicate Enter time up to the number The first follower drone after interference The position and velocity vectors of the follower drones; This indicates the control gain.

6. The quadcopter UAV formation control method according to claim 5, characterized in that, S5 specifically includes the following steps: S51: Based on the established UAV formation control law and error state equation, the UAV formation system's first... The state error system of an unmanned aerial vehicle (UAV) based on a dual-threshold dynamic event triggering mechanism is represented as follows: （22） S52: Define the global intermediate variable as: , ,（23） And by combining equations (5), (13), (22), and (23), the closed-loop equation of the quadcopter UAV formation system based on the dual-threshold dynamic event triggering mechanism is obtained as follows: （24） In the formula: Indicates intermediate parameters and , Represents the communication link weight parameter matrix and Represents the Laplace matrix ; Represents the parameter matrix and Represents intermediate variables and Describes the adjacency matrix and Represent real numbers; Represents the identity matrix; express The manifestations after interference; S53: Based on the closed-loop equation of the quadrotor UAV formation system and the distributed controller of the formation system, realize quadrotor UAV formation control suitable for asynchronous packet loss and random UDP attacks.

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