A method for restoring formation control of a quad-rotor unmanned aerial vehicle under network attack

Abstract

A method for restoring formation control of quadcopter drones under network attacks, belonging to the field of drone formation control. The method involves analyzing the tag signals from the leader drone to the following drones and the directed paths of neighboring drones. Using OR logic operations, it determines whether the following drone can receive information from the leader drone, classifying the quadcopter drones as healthy or harmful. For healthy quadcopter drones, cooperative flight based on a distributed control strategy is employed. For harmful quadcopter drones, the trajectory data of each harmful quadcopter drone at n time steps is input into a trained LSTM neural network model, outputting the trajectory data of each harmful quadcopter drone at the next m time steps. This data is then combined with a proportional-derivative (PD) control strategy for flight control. This invention improves the stability and autonomous recovery capability of drone formation communication under network attack scenarios.

Description

Technical Field

[0001] This invention relates to a method for restoring formation control of quadcopter drones under cyberattacks, belonging to the field of drone formation control technology. Background Technology

[0002] With the rapid development of drone technology, quadcopter drones, due to their excellent flexibility, maneuverability and adaptability, are widely used in many fields such as military reconnaissance, environmental monitoring, logistics transportation, and agricultural spraying. They can quickly deploy to perform tasks such as high-altitude photography, intelligence gathering and target surveillance, and carry out tasks such as air quality monitoring, water body detection and ecological environment assessment by carrying a variety of sensors.

[0003] The rise of drone swarm technology has enabled multiple drones to coordinate operations and complete complex missions. However, with the increasing prevalence of drone swarms across various fields, the cybersecurity threats faced by drone swarm communication during mission execution are also growing, especially in critical application scenarios such as military and public safety. The potential risks of cyberattacks targeting drone swarm communication are particularly prominent, potentially leading to drones losing control, chaotic formations, and even affecting the entire mission execution. This poses a severe challenge to the security and reliability of drone swarms. Therefore, how to maintain the stability and coordination of drone swarms under cyberattacks has become an important topic in current drone research. Traditional drone swarm control methods often rely on preset flight paths and simple control algorithms, which have weak adaptability to environmental changes and are difficult to cope with complex external interference and emergencies. These methods often fail to achieve effective self-recovery and adaptation when facing cyberattacks, leading to a loss of coordination and ultimately affecting mission completion. Furthermore, most existing swarm control algorithms are based on distributed control strategies. In distributed control, each drone can make independent decisions, theoretically enhancing the flexibility of the swarm. However, when drone swarm communications are subjected to sophisticated cyberattacks, the lack of effective coordination mechanisms disrupts information transmission between drones, leading to information asymmetry and decision-making errors, which in turn exacerbates the instability of the drone swarm. Individual drones may react inappropriately to emergencies, causing the drone swarm to become chaotic or even completely out of control. Summary of the Invention

[0004] To address the problem of drone formation chaos caused by cyberattacks on drone swarm communication, this invention aims to provide a method for restoring quadcopter formation control under cyberattacks. By analyzing the tag signals from the leader drone to the follower drones and the directed paths of neighboring drones, the method uses OR logic operations to determine whether the follower drone can receive information from the leader drone, classifying quadcopter drones as healthy or harmful, and constructing corresponding quadcopter formation control methods accordingly. This improves the stability and autonomous recovery capability of quadcopter formation communication under cyberattack scenarios, enabling drones to perform formation control more efficiently and accurately under cyberattacks, and enhancing the formation's execution and response capabilities in complex environments.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] This invention discloses a method for restoring formation control of quadcopter drones under network attacks. By analyzing the tag signals between the leader drone and follower drones, as well as the directed paths of neighboring drones, the method determines the status of follower drones. If a follower drone can receive information from the leader drone, it is determined to be a healthy quadcopter drone; conversely, if a follower drone cannot receive information from the leader drone, it is determined to be a harmful quadcopter drone.

[0007] For healthy quadcopter drones, a cooperative flight strategy based on a distributed control approach is adopted. This strategy relies solely on local information exchange among neighboring drones, rather than global information from the communication graph. Furthermore, compared to traditional control strategies that require full access to reference acceleration or neighboring drone control acceleration, this strategy only introduces an upper limit to the control of the leading drone and satisfies the Lyapunov stability condition through the design of the control strategy, ensuring that the position errors of each drone converge to zero when formation is complete.

[0008] For harmful quadrotor drones, an LSTM neural network model for quadrotor drone trajectory prediction is constructed. The historical trajectory information of the quadrotor drone is used as training data. A sliding window approach is used, with the trajectory data of n historical time steps as the input feature sequence and the trajectory data of m future time steps as the output feature sequence. The LSTM neural network model is trained using this training data. The trajectory data of each harmful quadrotor drone at n time steps is input into the trained LSTM neural network model, and the trajectory data of each harmful quadrotor drone at the next m time steps is output. This is then combined with a proportional-derivative (PD) control strategy for flight control. This invention can address the uncertainty caused by network attacks on quadrotor drone communication, enabling quadrotor drone formation communication to quickly restore its formation state even under network attacks, ensuring mission continuity and security.

[0009] Therefore, this invention significantly improves the stability and autonomous recovery capability of quadcopter drone formations in network attack scenarios, enabling drones to complete formation tasks more efficiently and accurately, and enhancing the formation's execution and response capabilities in complex environments.

[0010] This invention discloses a method for restoring formation control of a quadcopter drone under a cyberattack, comprising the following steps:

[0011] Step 1: A quadcopter drone swarm consists of one leader drone and N follower drones. The leader drone's position and speed information are known, and it is responsible for transmitting status information to one of the follower drones. The remaining follower drones can only communicate locally with their neighboring drones, forming an interconnected network. For quadcopter drone swarm communication, a directed graph is defined, where nodes represent each quadcopter drone in the swarm, and edges represent the communication relationships between quadcopters. A tag signal is introduced as the status information transmitted by the leader drone to the follower drones. When the quadcopter drone swarm communication is under network attack, the status of the follower drones is determined by analyzing the tag signal between the leader drone and the follower drones, as well as the directed paths of neighboring drones. If a follower drone can receive information from the leader drone, it is considered a healthy quadcopter drone, and the process proceeds to Step 2; otherwise, if a follower drone cannot receive information from the leader drone, it is considered a harmful quadcopter drone, and the process proceeds to Step 4.

[0012] To distinguish whether a quadcopter drone under a DoS attack is healthy or harmful to its neighboring drones, a logical detection algorithm is constructed to determine whether a follower drone can obtain the status information of the leader drone. This algorithm introduces a tag signal between the leader and follower drones and combines it with the directed paths between the follower drones and neighboring drones to determine the status of the follower drones. In the case of a quadcopter drone swarm communication being attacked, there exists a path from the leader drone to the nth drone... o A directed path following the drone. Define the nodes and edges of the directed graph of the quadrotor drone formation as follows: and in definition Let be the set of neighbors of node i. Introduce As a tag signal transmitted from the leader drone to the follower drones. For Detection information passed Provided. The logic detection algorithm based on equation (1) can identify and isolate harmful quadcopter drones in a timely manner, and can effectively adjust the control strategy to prevent them from posing a potential threat to formation missions or other quadcopter drones, thus maintaining the stability and security of quadcopter drone formations:

[0013]

[0014] Where ∨ is the OR logical operation, resulting in Obviously, This indicates the existence of a directed path from the leader drone i to the follower drone i, where... This means that drone i is healthy in relation to its neighboring drones. Otherwise, when It indicates that there is no directed path from the leader drone to the follower drone i, where This indicates that following drone i is harmful to its neighboring drones.

[0015] Step Two: For healthy quadcopter drones, a cooperative flight mode based on a distributed control strategy is adopted. Each quadcopter drone coordinates and adjusts its control strategy by sharing the status information of the leader drone and data from its neighbors in real time, thereby achieving efficient collective movement. During the cooperative formation flight, each quadcopter drone calculates its tracking error with its neighbors, including position error and velocity error. The former represents the difference between the current position and the target position, and the latter represents the difference between the current flight speed and the desired speed. Based on the tracking error and incorporating real-time feedback, each quadcopter drone can generate appropriate control forces. This allows the quadcopter drones to not only maintain coordination with the leader and neighbors but also dynamically adjust based on real-time status information. Furthermore, a dynamic error adjustment mechanism is introduced into the control strategy to ensure that the quadcopter drones can quickly respond to environmental changes and the status changes of other quadcopter drones. A positive constant is introduced to adjust the error response speed, ensuring the stability and flexibility of the quadcopter formation. Compared to traditional quadcopter drone formation control strategies, the control strategy of this invention only requires local information exchange between neighboring drones, rather than relying on global information from the communication graph. Furthermore, compared to traditional control strategies that require complete access to the reference acceleration or the control acceleration of neighboring drones, the control strategy of this invention only introduces an upper limit to the control of the leading drone and, through the design of the control strategy, satisfies the Lyapunov stability condition, ensuring that the tracking errors of each drone converge to zero when the formation is completed. This effectively reduces the communication burden between quadcopter drones, improves control efficiency, and ensures the stability and reliability of the quadcopter drone formation.

[0016] The kinematic model of the quadcopter UAV is shown in equations (2) and (3).

[0017]

[0018] Where p is the drone's center of gravity, v is the drone's velocity, T is the applied control force, and g is the acceleration due to gravity. Assume that the leader's control u0 is bounded, i.e. in It is a normal number.

[0019] For healthy quadrotor drones, a cooperative flight mode based on a distributed control strategy is adopted. In this mode, each drone coordinates and adjusts its flight path by sharing the status information of the leader drone and the data of its neighboring drones in real time, achieving efficient quadrotor drone formation flight. This not only enhances the overall flexibility of the quadrotor drone formation but also improves its ability to cope with emergencies in complex environments. A normalization function is defined. This function is used to handle the directionality problem of the state vector of a quadcopter UAV. It can normalize any non-zero vector, thereby maintaining directional consistency in the control algorithm. if but Define the position error and velocity error of a quadcopter UAV as follows: and The control force is designed as shown in equation (4) to reduce the communication burden between quadcopter drones, improve control efficiency, and ensure the stability and reliability of quadcopter drone formations.

[0020]

[0021] in:

[0022]

[0023] Among them κ β and It is a positive constant. and

[0024] Step 3: For harmful quadrotor drones, construct an LSTM neural network model for quadrotor drone trajectory prediction. Use the historical position and velocity information of the quadrotor drone as training data. A sliding window approach is used to input the position or velocity data of n historical time steps as the input feature sequence, and the position or velocity data of the next m time steps as the output feature sequence. Train the LSTM neural network model using the training data. Input the position and velocity data of each harmful quadrotor drone at n time steps into the trained LSTM neural network model, and output the position and velocity data of each harmful quadrotor drone at the next m time steps. Combine this with a proportional-derivative (PD) control strategy for flight control. This approach can address the uncertainties caused by network attacks on quadrotor drone communication, enabling the quadrotor drone formation communication to quickly restore its formation state in the event of a network attack, ensuring mission continuity and security.

[0025] Step 3.1: In the trajectory prediction task of harmful quadcopter drones, since the motion characteristics of each dimension may differ, in order to improve the prediction accuracy and model flexibility, an independent LSTM neural network model for quadcopter drone trajectory prediction is constructed for each dimension. This allows for targeted optimization and tuning of each neural network, thereby better capturing the dynamic changes and trends of each dimension. Specifically, for each dimension, a sliding window technique is used to extract the position or velocity data of the first n time steps of each training sample in the training dataset as the input feature sequence, and the position or velocity data of the next m time steps as the output feature sequence. The selection of the sliding window size n and the prediction step size m is crucial, as the settings of these two parameters directly affect the model's performance and prediction accuracy.

[0026] For harmful quadcopter drones, the sliding window technique is used to extract the position data of the first n time steps of each training sample in the training dataset along the x, y, and z axes. i (t-n+1),p i (t-n+2),…,p i (t)} and velocity data {v i (t-n+1),v i (t-n+2),…,v i (t)}, i = x, y, z are extracted as input feature sequences, and the position data {p} of the next m time steps are used as input feature sequences. i (t+1),…,p i (t+m)} and velocity data {v i (t+1),…,v i (t+m)}, i = x, y, z are extracted as output feature sequences respectively.

[0027] Step 3.2: Construct an LSTM neural network model for predicting the trajectory of harmful quadcopter drones. The LSTM network model includes an input layer, an LSTM layer, a dropout layer, a fully connected layer, a ReLU activation layer, and a regression layer. The input layer feeds the feature sequences from the training dataset into the LSTM layer. The LSTM sub-model is a Long Short-Term Memory network that fully exploits the motion patterns of the quadcopter drone at different time steps by performing time-series modeling on the input feature sequences. When processing trajectory data at the current moment, the LSTM layer can utilize past trajectory information to perform serialized feature fusion, thereby better representing the dynamic relationship between the current trajectory and historical trajectories and improving the LSTM network model's ability to predict drone trajectories. The dropout layer randomly discards a certain proportion of neurons to prevent overfitting of the LSTM neural network model and ensure the model's generalization ability during training. Its output is passed to the fully connected layer. The fully connected layer is responsible for linearly combining the output features of the LSTM layer to generate the final predicted features. The ReLU activation layer is added to the fully connected layer to introduce non-linear features, enabling the LSTM neural network model to better learn complex trajectory patterns. The regression layer outputs the prediction results, mapping the output of the fully connected layer to the target value space to generate a prediction of the drone's future trajectory. This study utilizes an LSTM neural network model for trajectory prediction of harmful quadcopter drones, improving the accuracy and reliability of the LSTM neural network model's predictions.

[0028] An LSTM neural network model for predicting the trajectory of a harmful quadcopter drone is constructed. The LSTM network model includes an input layer, an LSTM layer, a dropout layer, a fully connected layer, a ReLU activation layer, and a regression layer.

[0029] The input layer will take the feature sequence {p} from the training dataset. i (t-n+1),p i (t-n+2),…,p i (t),p i (t+1),…,p i (t+m)},{v i (t-n+1),v i (t-n+2),…,v i (t),v i (t+1),…,v i (t+m)}, i = x, y, z are respectively input to the LSTM layer of different LSTM neural network models.

[0030] The LSTM layer addresses the issue of needing to base trajectory prediction on long-term historical data by introducing a gating mechanism. Its internal structure includes input gates, forget gates, and output gates. The gating unit dynamically adjusts the transmission and storage of motion-related information of the quadcopter, thereby capturing complex patterns and temporal relationships between different time steps. For time t, the LSTM module's processing procedure is as follows:

[0031] f t =σ(W f ·[h t-1 ,x t ]+b f (7)

[0032] i t =σ(W i ·[h t-1 ,x t ]+b i (8)

[0033]

[0034] o t =σ(W o ·[h t-1 ,x t ]+b o (11)

[0035] h t =o t ⊙tan h(C t (12)

[0036] Among them, W f W i W C W o Given the current input and the hidden layer state from the previous time step [h] t-1 ,x t The weight parameter matrix, b f b i b C b o Let be the bias parameter matrix, σ(·) be the Sigmoid function, and ⊙ denote the Hadamard product.

[0037] The output of the LSTM layer is h i ={h i (t-n+1),h i (t-n+2),…,h i (t),h i (t+1),…,h i(t+m)},i=x,y,z completes the information fusion of the nonlinear interference relationship between the current new high position or velocity of the quadrotor UAV and the historical position or velocity signals of the quadrotor UAV.

[0038] The dropout layer is used to prevent overfitting. It randomly sets the output of the LSTM layer to zero with probability p, making the LSTM neural network model more robust during training. The output feature sequence of the dropout layer is input into the fully connected layer to generate the feature vector of the quadcopter drone's future trajectory.

[0039] h ic =W fc ·h i +b fc (13)

[0040] Among them, W fc Let b represent the weight matrix of the fully connected layer. fc This represents the bias term. Subsequently, the ReLU activation layer performs a non-linear transformation on the output of the fully connected layer to enhance the LSTM neural network model's ability to learn complex trajectory patterns.

[0041] y ReLU =max(0,h) ic (14)

[0042] The regression layer is based on the output y of the ReLU activation layer. ReLU The feature vectors are mapped to the prediction value space to generate trajectory prediction results for the quadcopter drone at future time steps:

[0043] y = W reg ·r ReLU +b reg (15)

[0044] Among them, W reg and b reg The weights and biases of the regression layer are not represented by these.

[0045] Step 3.3: For the LSTM neural network constructed in Step 3.2 for predicting the trajectory of harmful quadcopter drones, configure the parameters required for model training, setting the learning rate, number of hidden layers, dropout rate, and number of iterations. Using the constructed training dataset, train the LSTM neural network model for drone trajectory prediction. The trained LSTM neural network model constructs a nonlinear relationship between the current historical trajectory data of the drone and its corresponding future trajectory. This nonlinear relationship can fully characterize the influence of various dynamic factors on the drone during flight, thereby improving the accuracy and reliability of trajectory prediction. Use the trained LSTM neural network model in Step 4 to predict the trajectory of harmful quadcopter drones.

[0046] For the LSTM neural network model for predicting the trajectory of harmful quadcopter drones constructed in step 3.2, configure the parameters required for model training, and set the learning rate, number of hidden layers, dropout rate, and number of iterations.

[0047] For the three dimensions of the harmful quadcopter drone—x, y, and z—the training dataset {p} constructed in step 3.1 was used. i (t-n+1),p i (t-n+2),…,p i (t),p i (t+1),…,p i (t+m)},{v i (t-n+1),v i (t-n+2),…,v i (t),v i (t+1),…,v i (t+m)}, i=x,y,z, train the LSTM neural network model constructed in step 3.2 respectively, and use the Adam parameter optimization algorithm to determine the optimal model parameters to obtain the trained LSTM neural network model. The trained LSTM network model is used to construct a nonlinear relationship between the current UAV's historical trajectory data and its corresponding future trajectory. This nonlinear relationship can fully characterize the influence of various dynamic factors on the UAV during flight, thereby improving the accuracy and reliability of trajectory prediction.

[0048] Step 4: For harmful quadcopter drones, the trajectory data of the first n time steps are input into the trained LSTM neural network model, and the predicted trajectory of each drone is output, including the predicted position and velocity information. The output prediction results are used as the expected position and expected velocity of the drone. Combined with the proportional-derivative (PD) control strategy, the expected trajectory is tracked and controlled to obtain the control force of the harmful quadcopter drone. Based on the control force, the problem that the harmful quadcopter drone cannot indirectly obtain the state of the leader drone is solved, thereby improving the stability and reliability of the quadcopter drone formation.

[0049] For the three dimensions of the harmful quadcopter drone—x, y, and z—the trajectory data of the first n time steps {p i (t-n+1),p i (t-n+2),…,p i (t)},{v i (t-n+1),v i (t-n+2),…,v i The values ​​of (t)}, i = x, y, z are input into the trained LSTM neural network model, and the output is the predicted trajectory of the harmful quadcopter drone.

[0050] The output prediction results are used as the expected future trajectory of a harmful quadcopter drone, including 3D position information. The control force u is designed as shown in equation (16) by combining the proportional-derivative (PD) control strategy. i This addresses the problem that harmful quadcopter drones cannot indirectly obtain the status of the leader drone, thereby improving the stability and reliability of quadcopter drone formations.

[0051]

[0052] Among them, K p It is the proportional gain, which determines the degree to which the error affects the control signal; K d It is the differential gain, which determines the degree to which the rate of change of error affects the control signal. p is the expected value of the predicted position at time T = t + j. i It is the current position value at time T = t + j. It is the expected value of the predicted position at time T = t + j, v i It is the current position value at time T = t + j, where j = 1, 2, ..., m. This allows harmful quadcopter drones to form an effective formation even without information from the leader drone, thus improving the stability and accuracy of quadcopter drone formation flight.

[0053] Beneficial effects:

[0054] 1. This invention discloses a method for restoring formation control of quadcopter drones under network attacks. It constructs a logical detection algorithm to determine whether a follower drone can obtain the status information of the leader drone. It introduces tag signals between the leader and follower drones and combines this with the directed paths between the follower drones and neighboring drones to determine the status of the follower drones. If the follower drone can receive information from the leader drone, it is determined to be a healthy quadcopter drone; conversely, if the follower drone cannot receive information from the leader drone, it is determined to be a harmful quadcopter drone. Furthermore, by timely identifying and isolating harmful quadcopter drones, control strategies can be effectively adjusted to prevent them from posing a potential threat to formation missions or other quadcopter drones, maintaining the stability and security of the quadcopter formation, thus enabling quadcopter formation flight even under network attacks.

[0055] 2. This invention discloses a method for restoring formation control of quadrotor drones under network attacks. For healthy quadrotor drones, a distributed control strategy is constructed. This strategy only requires local information exchange between neighboring drones, rather than relying on global information from the communication graph. Furthermore, compared to traditional control strategies that require complete access to reference acceleration or neighboring drone control acceleration, this strategy only introduces an upper limit to the control of the leading drone. By designing the control strategy to satisfy the Lyapunov stability condition, it ensures that the position errors of each drone converge to zero when formation is complete. This effectively reduces the communication burden between quadrotor drones, improves control efficiency, and ensures the stability and reliability of the quadrotor drone formation.

[0056] 3. This invention discloses a method for restoring formation control of quadcopter drones under network attacks. Targeting harmful quadcopter drones, this invention discloses an LSTM neural network model for quadcopter drone trajectory prediction. The historical trajectory information of the harmful quadcopter drones is used as training data. A sliding window approach is used to input the trajectory data of n historical time steps as the input feature sequence, and the trajectory data of m future time steps as the output feature sequence. The LSTM neural network model is trained using the training data. The trajectory data of each harmful quadcopter drone at n time steps is input into the trained LSTM neural network model, and the trajectory data of each harmful quadcopter drone at the next m time steps is output. This is combined with a proportional-derivative (PD) control strategy for flight control, thereby achieving effective monitoring and control of harmful quadcopter drones to prevent them from posing a potential threat to formation missions or other quadcopter drones. Furthermore, combined with the PD control strategy, dynamic tracking and control of harmful drones can be achieved, ensuring the safety and stability of formation in complex environments, thus ensuring the continuity and safety of quadcopter drone formation missions. Attached Figure Description

[0057] Figure 1 Schematic diagram of coordinate system setting for a quadcopter drone.

[0058] Figure 2 A schematic diagram illustrating the principle of a long short-term memory neural network.

[0059] Figure 3 A flowchart of a method for restoring formation control of a quadcopter drone under a network attack according to the present invention. Detailed Implementation

[0060] To overcome the shortcomings of existing technologies, this invention aims to propose a recoverable formation control method for quadcopter UAVs under cyberattacks, thereby optimizing and improving UAV formation control methods under cyberattacks. The technical solution adopted in this invention mainly addresses two aspects: first, employing a fully distributed control strategy that requires only the upper limit of leader control; and second, using LSTM to predict UAV trajectories and employing a proportional-derivative (PD) control strategy to independently generate force control information.

[0061] like Figure 1 As shown in the figure, this embodiment discloses a method for restoring formation control of a quadcopter drone under a network attack. The specific steps are as follows:

[0062] Step 1: A quadcopter drone swarm consists of one leader drone and four follower drones. The leader drone's position and speed information are known, and it is responsible for transmitting status information to one of the follower drones. The remaining follower drones can only communicate locally with their neighboring drones, forming an interconnected network. For quadcopter drone swarm communication, a directed graph is defined, where nodes represent each quadcopter drone in the swarm, and edges represent the communication relationships between the quadcopters.

[0063] We designed scenarios under different network attack states. First, without a network attack, the drone flew for 40 seconds. Then, it experienced a first network attack, lasting 5 seconds, after which the network recovered for 20 seconds. Next, the drone encountered a second network attack, also lasting 5 seconds, with a recovery time of 60 seconds. Finally, the drone faced a third network attack for 5 seconds. The changes in the communication graph are shown in equations (19)-(22):

[0064] cal_A1=[0,0,0,0;1,0,1,0;1,1,0,0;0,0,1,0] (19)

[0065] cal_A2=[0,0,0,0;1,0,0,0;1,0,0,0;0,0,1,0] (20)

[0066] cal_A3=[0,0,0,0;0,0,0,0;1,0,0,0;0,0,1,0] (21)

[0067] cal_A4=[0,0,0,0;1,0,1,0;1,1,0,0;0,0,0,0] (22)

[0068] In this diagram, cal_A1 represents the communication graph before the attack; cal_A2 represents the communication graph after the first attack, where communication between nodes 2 and 3 is affected; cal_A3 represents the communication graph after the second attack, where communication between nodes 2 and 3 is affected, as is communication between node 2 and the leader; and cal_A4 represents the communication graph after the third attack, where communication between node 4 and the leader is affected.

[0069] To distinguish whether a quadcopter drone under a DoS attack is healthy or harmful to its neighboring drones, a logical detection algorithm is constructed to determine whether follower drones can obtain the status information of the leader drone. This algorithm introduces a tag signal between the leader drone and follower drones and combines it with the directed paths between follower drones and neighboring drones to determine the status of the follower drones. Under a network attack on quadcopter drone swarm communication, there exists a directed path from the leader drone to the four follower drones. The nodes and edges of the directed graph of the quadcopter drone swarm are defined as follows: and in definition Let be the set of neighbors of node i. Introduce As a tag signal transmitted from the leader drone to the follower drones. For Detection information passed Provided. The logic detection algorithm based on equation (23) can identify and isolate harmful quadcopter drones in a timely manner, and can effectively adjust the control strategy to prevent them from posing a potential threat to formation missions or other quadcopter drones, thus maintaining the stability and security of quadcopter drone formations:

[0070]

[0071] Where ∨ is the OR logical operation, resulting in Obviously, This indicates the existence of a directed path from the leader drone i to the follower drone i, where... This means that drone i is healthy in relation to its neighboring drones. Otherwise, when It indicates that there is no directed path from the leader drone to the follower drone i, where This indicates that following drone i is harmful to its neighboring drones.

[0072] like Figure 3 As shown, if the follower drone can receive information from the leader drone, it is determined to be a healthy quadcopter drone, and the process proceeds to step two; otherwise, if the follower drone cannot receive information from the leader drone, it is determined to be a harmful quadcopter drone, and the process proceeds to step four.

[0073] Step 2: For healthy quadcopter drones, a cooperative flight mode based on a distributed control strategy is adopted. Each quadcopter drone coordinates and adjusts its control strategy by sharing the status information of the leader drone and the data of its neighboring drones in real time, thereby achieving efficient collective movement.

[0074] The kinematic model of the quadcopter UAV is shown in equations (24) and (25).

[0075]

[0076] Where p is the drone's center of gravity, v is the drone's velocity, T is the applied control force, and g is the acceleration due to gravity. Assume that the leader's control u0 is bounded, i.e. in It is a normal number.

[0077] The mass of the UAV is determined to be m = 0.85 * [0.5, 1.2, 0.8, 1.3] kg, and the above physical quantity is substituted into the dynamic model of the quadcopter UAV.

[0078] For healthy quadrotor drones, a cooperative flight mode based on a distributed control strategy is adopted. In this mode, each drone coordinates and adjusts its flight path by sharing the status information of the leader drone and the data of its neighboring drones in real time, achieving efficient quadrotor drone formation flight. This not only enhances the overall flexibility of the quadrotor drone formation but also improves its ability to cope with emergencies in complex environments. A normalization function is defined. This function is used to handle the directionality problem of the state vector of a quadcopter UAV. It can normalize any non-zero vector, thereby maintaining directional consistency in the control algorithm. if but Let its reference trajectory be set as px0 = 6 * cos(0.1 * t), py0 = 6 * sin(0.2 * t), pz0 = 1 * (1 - exp(-0.05 * t)), and define the position error and velocity error of the quadcopter UAV as follows: and The control force is designed as shown in equation (22) to reduce the communication burden between quadcopter drones, improve control efficiency, and ensure the stability and reliability of quadcopter drone formations.

[0079]

[0080] in:

[0081]

[0082] Where k β and It is a positive constant. and

[0083] Determine the control parameters as follows κ β =5, The above parameters are then incorporated into the design of a healthy quadcopter drone control force.

[0084] Step 3: For harmful quadrotor drones, construct an LSTM neural network model for quadrotor drone trajectory prediction. Use the historical position and velocity information of the quadrotor drone as training data. Use a sliding window method to input the position or velocity data of the past 6 time steps as the input feature sequence and the position or velocity data of the future 1 time step as the output feature sequence. Train the LSTM neural network model using the training data. Input the position and velocity data of each harmful quadrotor drone for 6 time steps into the trained LSTM neural network model. Output the position and velocity data of each harmful quadrotor drone for the future 1 time step. Combine this with a proportional-derivative (PD) control strategy for flight control. This can cope with the uncertainty caused by network attacks on quadrotor drone communication, enabling quadrotor drone formation communication to quickly restore its formation state in the event of a network attack, ensuring mission continuity and security.

[0085] Step 3.1: In the trajectory prediction task of harmful quadcopter drones, since the motion characteristics of each dimension may differ, in order to improve the prediction accuracy and model flexibility, an independent LSTM neural network model for quadcopter drone trajectory prediction is constructed for each dimension. This allows for targeted optimization and tuning of each neural network, thereby better capturing the dynamic changes and trends of each dimension. Specifically, for each dimension, a sliding window technique is used to extract the position or velocity data of the first 6 time steps of each training sample in the training dataset as the input feature sequence, and the position or velocity data of the next time step as the output feature sequence.

[0086] For harmful quadcopter drones, the sliding window technique is used to extract the position data of the first 6 time steps of each training sample in the training dataset along the x, y, and z axes. i (t-5),p i (t-4),…,p i (t)} and velocity data {v i (t-5),v i (t-4),…,v i(t)}, i = x, y, z are extracted as input feature sequences, and the position data {p} of the next time step are used. i (t+1)} and velocity data {v i (t+1)}, i = x, y, z are extracted as output feature sequences respectively.

[0087] Step 3.2: Construct an LSTM neural network model for predicting the trajectory of harmful quadcopter drones. The LSTM network model includes an input layer, an LSTM layer, a dropout layer, a fully connected layer, a ReLU activation layer, and a regression layer. The input layer takes the feature sequences from the training dataset and feeds them into the LSTM layer. The LSTM network sub-model is a Long Short-Term Memory network that performs time-series modeling on the input feature sequences to fully exploit the motion patterns of the quadcopter drone at different time steps. When processing the trajectory data at the current moment, such as... Figure 2 As shown, the LSTM layer can utilize past trajectory information to perform sequential feature fusion, thereby better representing the dynamic relationship between the current trajectory and historical trajectories, and improving the LSTM network model's ability to predict drone trajectories. The dropout layer randomly discards a certain proportion of neurons to prevent overfitting and ensure the model's generalization ability during training; its output is then passed to the fully connected layer. The fully connected layer is responsible for linearly combining the output features of the LSTM layer to generate the final prediction features. A ReLU activation layer is added to the fully connected layer to introduce non-linear features, enabling the LSTM network model to better learn complex trajectory patterns. The regression layer outputs the prediction results, mapping the output of the fully connected layer to the target value space to generate the predicted future trajectory of the drone. This demonstrates how to use the LSTM neural network model for trajectory prediction of harmful quadcopter drones, improving the accuracy and reliability of the LSTM neural network model's predictions.

[0088] Step 3.3: For the LSTM neural network constructed in Step 3.2 for predicting the trajectory of harmful quadcopter drones, configure the parameters required for model training, setting the learning rate, number of hidden layers, dropout rate, and number of iterations. Using the constructed training dataset, train the LSTM neural network model for drone trajectory prediction. The trained LSTM neural network model constructs a nonlinear relationship between the current historical trajectory data of the drone and its corresponding future trajectory. This nonlinear relationship can fully characterize the influence of various dynamic factors on the drone during flight, thereby improving the accuracy and reliability of trajectory prediction. Use the trained LSTM neural network model in Step 4 to predict the trajectory of harmful quadcopter drones.

[0089] For the LSTM neural network model for predicting the trajectory of harmful quadcopter drones constructed in step 3.2, configure the parameters required for model training, setting the learning rate, number of hidden layers, dropout rate, and number of iterations. The specific parameters of the neural network are drop_rate = 0.2, learnRate = 0.01, numHiddenUnits = 64, and Train_number = 300.

[0090] For the three dimensions of the harmful quadcopter drone—x, y, and z—the training dataset {p} constructed in step 3.1 was used. i (t-5),p i (t-4),…,p i (t),p i (t+1)},{v i (t-5),v i (t-4),…,v i (t),v i (t+1)}, i = x, y, z, train the LSTM neural network model constructed in step 3.2 respectively, and use the Adam parameter optimization algorithm to determine the optimal model parameters to obtain the trained LSTM neural network model. The trained LSTM network model is used to construct a nonlinear relationship between the current UAV's historical trajectory data and its corresponding future trajectory. This nonlinear relationship can fully characterize the influence of various dynamic factors on the UAV during flight, thereby improving the accuracy and reliability of trajectory prediction.

[0091] Step 4: For harmful quadcopter drones, the trajectory data from the first 6 time steps are input into the trained LSTM neural network model, and the output is the prediction result of the trajectory of each drone at the next moment, including the predicted position and velocity information. The output prediction results are used as the expected position and expected velocity of the drones. Combined with the proportional-derivative (PD) control strategy, the expected trajectory is tracked and controlled to obtain the control force of the harmful quadcopter drones. Based on the control force, the problem of harmful quadcopter drones being unable to indirectly obtain the state of the leader drone is solved, thereby improving the stability and reliability of the quadcopter drone formation.

[0092] For the three dimensions of the harmful quadcopter drone—x, y, and z—the trajectory data of the first n time steps {p i (t-5),p i (t-4),…,p i (t)},{v i (t-5),v i (t-4),…,v iThe values ​​of (t)}, i = x, y, z are input into the trained LSTM neural network model, and the output is the predicted trajectory of the harmful quadcopter drone.

[0093] The output prediction results are used as the expected future trajectory of a harmful quadcopter drone, including 3D position information. The control force u is designed as shown in equation (25) by combining the proportional-derivative (PD) control strategy. i This addresses the problem that harmful quadcopter drones cannot indirectly obtain the status of the leader drone, thereby improving the stability and reliability of quadcopter drone formations.

[0094]

[0095] Among them, K p It is the proportional gain, which determines the degree to which the error affects the control signal; K d It is the differential gain, which determines the degree to which the rate of change of error affects the control signal. p is the expected value of the predicted position at time T = t + 1. i It is the current position value at time T = t + 1. It is the expected value of the predicted position at time T = t + 1, v i It is the current position value at time T = t+1, which allows harmful quadcopter drones to still form an effective formation even without information from the leader drone, thus improving the stability and accuracy of quadcopter drone formation flight.

[0096] The control strategy parameter is selected as K. p =1,K d =0.4, and substitute the above parameters into equation (25) for flight verification.

[0097] As seen in this specific implementation, the quadcopter UAV can perform formation control under cyberattacks, track the reference trajectory well, and fly with small position errors. The applied force can also be adjusted well within the control range, with short convergence time and good formation tracking performance.

[0098] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for restoring formation control of a quadcopter drone under a cyberattack, characterized in that: Includes the following steps, Step 1: A quadcopter drone swarm consists of one leader drone and N follower drones. The leader drone's position and speed information are known, and it is responsible for transmitting status information to one of the follower drones. The remaining follower drones can only communicate locally with their neighboring drones, forming an interconnected network. For quadcopter drone swarm communication, a directed graph is defined, where nodes represent each quadcopter drone in the swarm, and edges represent the communication relationships between quadcopters. A tag signal is introduced as the status information transmitted by the leader drone to the follower drones. When the quadcopter drone swarm communication is under network attack, the status of the follower drones is determined by analyzing the tag signal between the leader drone and the follower drones, as well as the directed paths of neighboring drones. If the follower drone can receive the information from the leader drone, it is considered a healthy quadcopter drone, and the process proceeds to Step 2. Conversely, if the follower drone cannot receive the information from the leader drone, it is considered a harmful quadcopter drone, and the process proceeds to Step 4. Step 2: For healthy quadcopter drones, a cooperative flight mode based on a distributed control strategy is adopted. Each quadcopter drone coordinates and adjusts its control strategy by sharing the status information of the leader drone and the data of its neighboring drones in real time, thereby achieving efficient collective movement. During the cooperative formation flight of quadcopter drones, each quadcopter drone calculates the tracking error with its neighboring drones, including position error and velocity error. The former represents the difference between the current position of the quadcopter drone and the target position, and the latter represents the difference between the current flight speed of the quadcopter drone and the desired speed. Based on tracking errors and by introducing real-time feedback on these errors, each quadcopter drone can generate appropriate control forces. This allows the quadcopter drones to not only maintain coordination with the leader drone and neighboring drones, but also to make dynamic adjustments based on real-time status information. Furthermore, the control strategy incorporates a dynamic error adjustment mechanism to ensure that the quadcopter drones can quickly respond to environmental changes and the status changes of other quadcopter drones. By introducing a positive constant to adjust the error response speed, the stability and flexibility of the quadcopter drone formation are guaranteed. Step 3: For harmful quadrotor drones, construct an LSTM neural network model for quadrotor drone trajectory prediction. Use the historical position and velocity information of the quadrotor drone as training data. A sliding window approach is used to input the position or velocity data of n historical time steps as the input feature sequence, and the position or velocity data of the next m time steps as the output feature sequence. Train the LSTM neural network model using the training data. Input the position and velocity data of each harmful quadrotor drone at n time steps into the trained LSTM neural network model, and output the position and velocity data of each harmful quadrotor drone at the next m time steps. Combine this with a proportional-derivative (PD) control strategy for flight control. This approach can address the uncertainties caused by network attacks on quadrotor drone communication, enabling the quadrotor drone formation communication to quickly restore its formation state in the event of a network attack, ensuring mission continuity and security. Step 4: For harmful quadcopter drones, the trajectory data of the first n time steps are input into the trained LSTM neural network model, and the predicted trajectory of each drone is output, including the predicted position and velocity information. The output prediction results are used as the expected position and expected velocity of the drone. Combined with the proportional-derivative (PD) control strategy, the expected trajectory is tracked and controlled to obtain the control force of the harmful quadcopter drone. Based on the control force, the problem that the harmful quadcopter drone cannot indirectly obtain the state of the leader drone is solved, thereby improving the stability and reliability of the quadcopter drone formation.

2. The method for restoring formation control of a quadcopter drone under a network attack as described in claim 1, characterized in that: In step one, To distinguish whether a quadcopter drone under a DoS attack is healthy or harmful to its neighboring drones, a logical detection algorithm is constructed to determine whether a follower drone can obtain the status information of the leader drone. This algorithm introduces a tag signal between the leader and follower drones and combines it with the directed paths between the follower drones and neighboring drones to determine the status of the follower drones. When quadcopter drone swarm communication is under a network attack, there exists a path from the leader drone to the nth drone... o A directed path following the drone; define the nodes and edges of the directed graph of the quadrotor drone formation as follows: and in definition Let i be the set of neighbors of node i; introduce As a tag signal transmitted from the leader drone to the follower drones; for Detection information passed Provided; the logic detection algorithm based on equation (1) can promptly identify and isolate harmful quadcopter drones, adjust control strategies to prevent them from posing a potential threat to formation missions or other quadcopter drones, and maintain the stability and security of quadcopter drone formations: Where ∨ is the OR logical operation, resulting in Obviously, This indicates the existence of a directed path from the leader drone i to the follower drone i, where... This means that the drone i following its neighboring drones is healthy; otherwise, when It indicates that there is no directed path from the leader drone to the follower drone i, where This indicates that following drone i is harmful to its neighboring drones.

3. The method for restoring formation control of a quadcopter drone under a network attack as described in claim 2, characterized in that: In step two, The kinematic model of the quadcopter UAV is shown in equations (2) and (3). Where p is the position of the UAV's center of gravity, v is the velocity of the UAV, T is the applied control force, and g is the acceleration due to gravity. Assume that the leader's control u0 is bounded, i.e. in It is a positive constant; For healthy quadrotor drones, a cooperative flight mode based on a distributed control strategy is adopted. In this mode, each drone coordinates and adjusts its flight path by sharing the status information of the leader drone and the data of its neighboring drones in real time, achieving efficient quadrotor drone formation flight. This not only enhances the overall flexibility of the quadrotor drone formation but also improves its ability to cope with emergencies in complex environments. A normalization function is defined. This function is used to handle the directionality problem of the state vector of a quadcopter UAV. It can normalize any non-zero vector, thereby maintaining directional consistency in the control algorithm. if but Define the position error and velocity error of a quadcopter UAV as follows: and The control force is designed as shown in equation (4) to reduce the communication burden between quadcopter drones, improve control efficiency, and ensure the stability and reliability of quadcopter drone formations. in: Among them κ β and It is a positive constant. and 4. The method for restoring formation control of a quadcopter drone under a network attack as described in claim 3, characterized in that: The method for implementing step three is as follows: Step 3.1: In the trajectory prediction task of harmful quadcopter drones, since the motion characteristics of each dimension may differ, in order to improve the prediction accuracy and model flexibility, an independent LSTM neural network model for quadcopter drone trajectory prediction is constructed for each dimension. At the same time, targeted optimization and tuning of each neural network are allowed to better capture the dynamic changes and trends of each dimension. Specifically, for each dimension, the sliding window technique is used to extract the position data or velocity data of the first n time steps of each training sample in the training dataset as the input feature sequence, and the position data or velocity data of the next m time steps as the output feature sequence. The selection of the sliding window size n and the prediction step size m is crucial, and the setting of these two parameters will directly affect the performance of the model and the accuracy of the prediction. For harmful quadcopter drones, the sliding window technique is used to extract the position data of the first n time steps of each training sample in the training dataset along the x, y, and z axes. i (t-n+1),p i (t-n+2),…,p i (t)} and velocity data {v i (t-n+1),v i (t-n+2),…,v i (t)}, i = x, y, z are extracted as input feature sequences, and the position data {p} of the next m time steps are used as input feature sequences. i (t+1),…,p i (t+m)} and velocity data {v i (t+1),…,v i (t+m)}, i = x, y, z are extracted as output feature sequences respectively; Step 3.2: Construct an LSTM neural network model for predicting the trajectory of harmful quadcopter drones. The LSTM neural network model includes an input layer, an LSTM layer, a dropout layer, a fully connected layer, a ReLU activation layer, and a regression layer. The input layer inputs the feature sequences from the training dataset into the LSTM layer. The LSTM network sub-model is a long short-term memory network that fully explores the motion patterns of the quadcopter drone at different time steps by performing time series modeling on the input feature sequences. When processing the trajectory data at the current moment, the LSTM layer can utilize past trajectory information to perform serialized feature fusion, thereby better representing the dynamic relationship between the current trajectory and historical trajectories and improving the LSTM neural network model's ability to predict drone trajectories. The dropout layer randomly drops a certain proportion of neurons to prevent overfitting of the LSTM neural network model and ensure the model's generalization ability during training. Its output is passed to the fully connected layer. The fully connected layer is responsible for linearly combining the output features of the LSTM layer to generate the final predicted features. After ReLU activation layers are added to fully connected layers, non-linear features are introduced, enabling LSTM neural network models to better learn complex trajectory patterns. The regression layer is used to output the prediction results, mapping the output of the fully connected layer to the target value space to generate the prediction results of the future trajectory of the drone; the trajectory prediction of harmful quadcopter drones is performed by the LSTM neural network model, improving the accuracy and reliability of the LSTM neural network model prediction. An LSTM neural network model for predicting the trajectory of a harmful quadcopter drone is constructed, the LSTM neural network model including an input layer, an LSTM layer, a dropout layer, a fully connected layer, a ReLU activation layer, and a regression layer; The input layer will take the feature sequence {p} from the training dataset. i (t-n+1),p i (t-n+2),…,p i (t),p i (t+1),…,p i (t+m)},{v i (t-n+1),v i (t-n+2),…,v i (t),v i (t+1),…,v i (t+m)}, i = x, y, z are respectively input to the LSTM layer of different LSTM neural network models; The LSTM layer addresses the issue of needing to predict quadcopter drone trajectories based on long-term historical data by introducing a gating mechanism. Its internal structure includes an input gate, a forget gate, and an output gate. The gating unit dynamically adjusts the transmission and storage of information related to the quadcopter drone's motion, thereby capturing complex patterns and temporal relationships between different time steps. For time t, the LSTM module's processing procedure is as follows: f t =σ(W f ·[h t-1 ,x t ]+b f ) (7) i t =σ(W i ·[h t-1 ,x t ]+b i ) (8) the t =σ(W o ·[h t-1 ,x t ]+b o ) (11) h t =o t ⊙tanh(C t ) (12) Among them, W f W i W C W o Given the current input and the hidden layer state from the previous time step [h] t-1 ,x t The weight parameter matrix, b f b i b C b o Here is the bias parameter matrix, σ(·) is the Sigmoid function, and ⊙ represents the Hadamard product; The output of the LSTM layer is h i ={h i (t-n+1),h i (t-n+2),…,h i (t),h i (t+1),…,h i (t+m)},i=x,y,z completes the information fusion of the nonlinear interference relationship between the current new high position or velocity of the quadrotor UAV and the historical position or velocity signals of the quadrotor UAV; The dropout layer is used to prevent overfitting. It randomly sets the output of the LSTM layer to zero with probability p, making the LSTM neural network model more robust during training. The output feature sequence of the dropout layer is input into the fully connected layer to generate the feature vector of the quadcopter drone's future trajectory. h ic =W fc ·h i +b fc (13) Among them, W fc Let b represent the weight matrix of the fully connected layer. fc This represents the bias term; subsequently, the ReLU activation layer performs a nonlinear transformation on the output of the fully connected layer to enhance the LSTM neural network model's ability to learn complex trajectory patterns. y ReLU =max(0,h ic ) (14) The regression layer is based on the output y of the ReLU activation layer. ReLU The feature vectors are mapped to the prediction value space to generate trajectory prediction results for the quadcopter drone at future time steps: y=W reg ·y ReLU +b reg (15) Among them, W reg and b reg Do not represent the weights and biases of the regression layer; Step 3.3: For the LSTM neural network constructed in Step 3.2 for predicting the trajectory of harmful quadcopter drones, configure the parameters required for model training, setting the learning rate, number of hidden layers, dropout rate, and number of iterations; use the constructed training dataset to train the LSTM neural network model for drone trajectory prediction, and construct a nonlinear relationship between the current historical trajectory data of the drone and its corresponding future trajectory through the trained LSTM neural network model. This nonlinear relationship can fully characterize the influence of various dynamic factors on the drone during flight, thereby improving the accuracy and reliability of trajectory prediction; use the trained LSTM neural network model in Step 4 to predict the trajectory of harmful quadcopter drones. For the LSTM neural network model for predicting the trajectory of harmful quadcopter drones constructed in step 3.2, configure the parameters required for model training, and set the learning rate, number of hidden layers, dropout rate and number of iterations; For the three dimensions of the harmful quadcopter drone—x, y, and z—the training dataset {p} constructed in step 3.1 was used. i (t-n+1),p i (t-n+2),…,p i (t),p i (t+1),…,p i (t+m)},{v i (t-n+1),v i (t-n+2),…,v i (t),v i (t+1),…,v i (t+m)}, i=x,y,z, respectively train the LSTM neural network model constructed in step 3.2, and use the Adam parameter optimization algorithm to determine the optimal model parameters to obtain the trained LSTM neural network model; construct the nonlinear relationship between the current UAV historical trajectory data and its corresponding future trajectory through the trained LSTM neural network model. The nonlinear relationship can fully characterize the influence of various dynamic factors on the UAV during flight, thereby improving the accuracy and reliability of trajectory prediction.

5. The method for restoring formation control of a quadcopter drone under a network attack as described in claim 4, characterized in that: In step four, For harmful quadcopter drones, the trajectory data of the first n time steps are analyzed along the x, y, and z axes. The inputs are fed into a trained LSTM neural network model, and the output is a prediction of the trajectory of a harmful quadcopter drone. The output prediction results are used as the expected future trajectory of a harmful quadcopter drone, including 3D position information. The control force u is designed as shown in equation (16) by combining the proportional-derivative (PD) control strategy. i This addresses the problem that harmful quadcopter drones cannot indirectly obtain the status of the leader drone, thereby improving the stability and reliability of quadcopter drone formations. Among them, K p It is the proportional gain, which determines the degree to which the error affects the control signal; K d It is the differential gain, which determines the degree of influence of the error rate of change on the control signal; p is the expected value of the predicted position at time T = t + j. i It is the current position value at time T = t + j. It is the expected value of the predicted position at time T = t + j, v i It is the current position value at time T = t + j, where j = 1, 2, ..., m. This allows harmful quadcopter drones to form an effective formation even without information from the leader drone, thus improving the stability and accuracy of quadcopter drone formation flight.

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