Quad-rotor unmanned aerial vehicle formation recovery control method under network attack

Abstract

The invention discloses a quad-rotor unmanned aerial vehicle formation recovery control method under network attack, and belongs to the field of unmanned aerial vehicle formation control. The implementation method comprises the following steps: analyzing label signals from a leader unmanned aerial vehicle to a following unmanned aerial vehicle and directed paths of neighbor unmanned aerial vehicles, judging whether the following unmanned aerial vehicle can receive information of the leader unmanned aerial vehicle by utilizing or logical operation, classifying the four-rotor unmanned aerial vehicle as healthy or harmful, and for the healthy four-rotor unmanned aerial vehicle, judging whether the following unmanned aerial vehicle can receive the information of the leader unmanned aerial vehicle or not. Cooperative flight based on a distributed control strategy is adopted. And for the harmful four-rotor unmanned aerial vehicles, inputting the trajectory data of the n time steps of each harmful four-rotor unmanned aerial vehicle into the trained LSTM neural network model, outputting and obtaining the trajectory data of the future m time steps of each harmful four-rotor unmanned aerial vehicle, and performing flight control in combination with a proportional differential PD control strategy. According to the method, the stability and the autonomous recovery capability of unmanned aerial vehicle formation communication in a network attack situation can be improved.

Description

Technical Field

[0001] The invention relates to a method for restoring formation control of a quad-rotor unmanned aerial vehicle under a network attack, and belongs to the technical field of unmanned aerial vehicle formation control. Background Art

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

[0003] The rise of drone formation technology enables multiple drones to work together to complete complex tasks. However, with the popularity of drone formations in various fields, the cybersecurity threats faced by drone formation communications during the execution of tasks are also increasing. Especially in key application scenarios such as military and public safety, the potential risks of cyber attacks on drone formation communications are particularly prominent, which may cause drones to lose control, the formation to be chaotic, and even affect the execution of the entire mission, which poses a severe challenge to the safety and reliability of drone formations. Therefore, how to maintain the stability and coordination of drone formations when drone formation communications are attacked by cyber attacks has become an important topic in current drone research. Traditional drone formation control methods often rely on preset flight paths and simple control algorithms, 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 cyber attacks, resulting in the loss of coordination of the formation and ultimately affecting the completion of the mission. In addition, most of the existing formation control algorithms are based on distributed control strategies. In distributed control, each drone can make decisions independently, which can theoretically enhance the flexibility of the formation. However, when the communication of the drone formation is attacked by complex network attacks, the lack of effective coordination mechanism interferes with the information transmission between drones, leading to information asymmetry and decision-making errors, which in turn exacerbates the instability of the drone formation. Individual drones may respond inappropriately to emergencies, causing the drone formation to become chaotic or even completely out of control. Summary of the invention

[0004] In order to solve the problem of drone formation chaos caused by network attack on drone formation communication, the purpose of the present invention is to provide a method for recovering formation control of quad-rotor drones under network attack. By analyzing the label signal from the leading drone to the following drone and the directed path of the neighboring drone, the OR logic operation is used to determine whether the following drone can receive the information of the leading drone, and the quad-rotor drones are classified as healthy or harmful. The corresponding quad-rotor drone recovery formation control method is constructed respectively. The stability and autonomous recovery ability of the quad-rotor drone formation in the situation of network attack on drone formation communication can be improved, so that the drones can perform formation control more efficiently and accurately under network attack, and the execution and response capabilities of the formation in complex environments are improved.

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

[0006] The present invention discloses a method for recovering formation control of a quad-rotor drone under network attack, which realizes the judgment of the status of the follower drone by analyzing the tag signal between the leader drone and the follower drone and the directed path of the neighbor drone. If the follower drone can receive the information of the leader drone, it is judged as a healthy quad-rotor drone; on the contrary, if the follower drone cannot receive the information of the leader drone, it is judged as a harmful quad-rotor drone.

[0007] For healthy quadrotors, a cooperative flight based on a distributed control strategy is adopted, which only requires local information exchange between neighboring drones, rather than relying on global information of the communication graph. In addition, compared with the traditional control strategy that requires full access to the reference acceleration or control acceleration of neighboring drones, this control strategy only introduces an upper limit for the control of the leader drone, and satisfies the Lyapunov stability condition through the design of the control strategy, ensuring that the position error of each drone converges to zero when the formation is completed.

[0008] For harmful quad-rotor drones, an LSTM neural network model for quad-rotor drone trajectory prediction is constructed, and the historical trajectory information of the quad-rotor drone is used as training data, wherein the historical trajectory data of n time steps is used as the input feature sequence in a sliding window manner, and the trajectory data of m time steps in the future is used as the output feature sequence, and the LSTM neural network model is trained using the training data; the trajectory data of n time steps of each harmful quad-rotor drone is input into the trained LSTM neural network model, and the trajectory data of m time steps in the future of each harmful quad-rotor drone is output, and flight control is performed in combination with the proportional differential PD control strategy. The present invention can cope with the uncertainty caused by the network attack on the communication of the quad-rotor drone, so that the quad-rotor drone formation communication can quickly restore its formation state when it is attacked by the network, and ensure the continuity and safety of the task.

[0009] Therefore, the present invention significantly improves the stability and autonomous recovery capability of the quad-rotor UAV formation in the UAV formation communication under network attack scenarios, enables the UAVs to complete the formation tasks more efficiently and accurately, and enhances the execution and response capabilities of the formation in complex environments.

[0010] The present invention discloses a method for restoring formation control of a quad-rotor drone under a network attack, comprising the following steps:

[0011] Step 1: The quadrotor formation includes a leader drone and N follower drones. The leader drone has known position and speed information and is responsible for transmitting status information to one of the follower drones. The remaining follower drones can only communicate locally with their neighboring follower drones to form an interconnected network. For the communication of quadrotor formation, a directed graph is defined, in which the nodes represent each quadrotor in the quadrotor formation, and the edges represent the communication relationship between the quadrotors. A label signal is introduced as the status information transmitted by the leader drone to the follower drones. When the communication of the quadrotor formation is attacked by the network, the status of the follower drone is judged by analyzing the label signal between the leader drone and the follower drone and the directed path of the neighbor drone. If the follower drone can receive the information of the leader drone, it is judged as a healthy quadrotor drone and proceeds to step 2; otherwise, if the follower drone cannot receive the information of the leader drone, it is judged as a harmful quadrotor drone and proceeds to step 4.

[0012] In order to distinguish whether a quadcopter under a network DoS attack is healthy or harmful to its neighboring drones, a logic detection algorithm is constructed to determine whether the following drone can obtain the status information of the leader drone. The label signal between the leader drone and the following drone is introduced, and the directed path between the following drone and the neighboring drone is combined to realize the judgment of the status of the following drone. When the communication of the quadcopter formation is attacked by the network, there is a path from the leader drone to the n neighboring drones. o The nodes and edges of the directed graph of the quadcopter formation are defined as and in definition is the neighbor set of node i. As a tag signal passed from the leader drone to the follower drones. Detection information through The logic detection algorithm constructed based on formula (1) can timely identify and isolate harmful quadrotor drones, effectively adjust the control strategy to prevent them from posing potential threats to formation missions or other quadrotor drones, and maintain the stability and safety of the quadrotor drone formation:

[0013]

[0014] Where ∨ is the OR logic operation, Obviously, indicates that there is a directed path from the leader UAV to the follower UAV i, where This means that the following drone i is healthy for its neighbor drones. Otherwise, when When , it means there is no directed path from the leader UAV to the follower UAV i, where It shows that following drone i is harmful to its neighboring drones.

[0015] Step 2: For healthy quadrotor drones, a cooperative flight mode based on a distributed control strategy is adopted. Each quadrotor drone coordinates and adjusts its own control strategy by sharing the status information of the leader drone and the data of its neighbor drones in real time, thereby achieving efficient collective movement. During the cooperative formation flight of quadrotor drones, each quadrotor drone calculates the tracking error between itself and its neighbor drones, including position error and speed error. The former represents the difference between the current position of the quadrotor drone and the target position, and the latter represents the difference between the current flight speed of the quadrotor drone and the expected speed. Based on the tracking error and introducing real-time feedback on the error, each quadrotor drone can generate appropriate control force, so that the quadrotor drone can not only maintain coordination with the leader drone and neighbor drones, but also make dynamic adjustments according to real-time status information. In addition, a dynamic adjustment mechanism for the error is introduced in the control strategy to ensure that the quadrotor drone can quickly respond to environmental changes and state changes of other quadrotors. The response speed of the error is adjusted by introducing a positive constant to ensure the stability and flexibility of the quadrotor drone formation. Compared with the traditional quad-rotor UAV formation control strategy, the control strategy of the present invention only needs to exchange local information with neighboring UAVs, rather than relying on the global information of the communication graph. In addition, compared with the traditional control strategy that requires full access to the reference acceleration or the control acceleration of the neighboring UAVs, the control strategy of the present invention only introduces the upper limit of the control of the leading UAV, and satisfies the Lyapunov stability condition through the design of the control strategy, ensuring that the tracking error of each UAV converges to zero when the formation is completed, thereby effectively reducing the communication burden between quad-rotor UAVs, improving the control efficiency, and ensuring the stability and reliability of the quad-rotor UAV formation.

[0016] The kinematic model of the quadrotor drone is expressed as Equation (2) and Equation (3):

[0017]

[0018] Among them, p is the center of gravity of the drone, v is the speed of the drone, and T is the applied control force. g is the acceleration of gravity, Assume that the leader's control u0 is bounded, that is, in is a normal number.

[0019] For healthy quad-rotor drones, a collaborative flight mode based on distributed control strategy is adopted. In this mode, each drone coordinates and adjusts its own flight path by sharing the status information of the leader drone and the data of its neighbor drones in real time, thus achieving efficient quad-rotor drone formation flight. This not only enhances the overall flexibility of the quad-rotor drone formation, but also improves the ability to respond to emergencies in complex environments. Define the normalization function Used to deal with the directional problem of the state vector of the quadrotor drone. This function can standardize any non-zero vector to maintain directional consistency in the control algorithm. if but The position error and velocity error of the quadrotor drone are defined as and Design the control force as shown in formula (4) to reduce the communication burden between quadrotor drones, improve control efficiency, and ensure the stability and reliability of the quadrotor drone formation:

[0020]

[0021] in:

[0022]

[0023] where κ β and is a positive constant, and

[0024] Step 3: For harmful quadrotor drones, an LSTM neural network model for quadrotor drone trajectory prediction is constructed, and the historical position information and historical speed information of the quadrotor drone are used as training data respectively. The historical position data or speed data of n time steps are used as input feature sequence in a sliding window manner, and the position data or speed data of m time steps in the future are used as output feature sequence. The LSTM neural network model is trained separately using the training data; the n time step position data and speed data of each harmful quadrotor drone are input into the trained LSTM neural network model respectively, and the future m time step position data and speed data of each harmful quadrotor drone are output, and the flight control is performed in combination with the proportional differential PD control strategy, which can cope with the uncertainty caused by the network attack on the quadrotor drone communication, so that the quadrotor drone formation communication can quickly restore its formation state when it is attacked by the network, thereby ensuring the continuity and safety of the mission.

[0025] Step 3.1: In the trajectory prediction task of harmful quadcopters, since the motion characteristics of each dimension may be different, in order to improve the prediction accuracy and model flexibility, an independent LSTM neural network model for quadcopter trajectory prediction is constructed for each dimension, while allowing targeted optimization and tuning of each neural network to better capture the dynamic changes and trends of each dimension. Specifically, for each dimension, the sliding window technology is used to extract the position data or velocity data of the first n time steps of each training sample in the training data set as the input feature sequence, and the position data or velocity data of the next m time steps are extracted as the output feature sequence, where the size of the sliding window n and the prediction step size m are crucial. The setting of the two parameters will directly affect the performance of the model and the accuracy of the prediction.

[0026] For the three dimensions of the x-axis, y-axis, and z-axis of the harmful quadrotor drone, the sliding window technique is used to convert the position data of the first n time steps of each training sample in the training data set {p i (t-n+1),p i (t-n+2),…,p i (t)} and speed data {v i (t-n+1),v i (t-n+2),…,v i (t)}, i = x, y, z are extracted as input feature sequences respectively, and the position data of the next m time steps {p i (t+1),…,p i (t+m)} and speed 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 the prediction of harmful quadcopter trajectories. 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 inputs the feature sequence in the training data set to the LSTM layer. The LSTM network submodel is a long short-term memory network. By modeling the input feature sequence in time series, it fully explores the motion law of the quadcopter at different time steps. When processing the trajectory data at the current moment, the LSTM layer can use the past trajectory information to perform serialized feature fusion, so as to better characterize the dynamic relationship between the current trajectory and the historical trajectory, and enhance the LSTM network model's ability to predict the trajectory of the drone. The dropout layer randomly discards a certain proportion of neurons to prevent the overfitting phenomenon of the LSTM neural network model and ensure the generalization ability of the model during the training process. Its output will be 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. The ReLU activation layer is added to the fully connected layer to introduce nonlinear features, so that the LSTM neural network model can better learn complex trajectory patterns. The regression layer is used to output the prediction results, map the output of the fully connected layer to the target value space, and generate the prediction results of the future trajectory of the drone. The trajectory of harmful quad-rotor drones is predicted through the LSTM neural network model to improve the accuracy and reliability of the LSTM neural network model prediction.

[0028] An LSTM neural network model for harmful quadrotor drone trajectory prediction is constructed, wherein the LSTM network model includes an input layer, an LSTM layer, a discard layer, a fully connected layer, a ReLU activation layer, and a regression layer.

[0029] The input layer converts the feature sequence {p 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 into the LSTM layers of different LSTM neural network models.

[0030] The LSTM layer introduces a gating mechanism to solve the problem of quadcopter trajectory prediction based on long-term historical data. Its internal structure includes input gate, forget gate and output gate. The gating unit can dynamically adjust the transmission and storage of information related to the quadcopter movement, thereby capturing the complex patterns and timing relationships between different time steps. For time t, the processing process of the LSTM module 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 is the input at the current moment and the hidden layer state at the previous moment [h t-1 ,x t ] weight parameter matrix, b f 、b i 、b C 、b o is the bias parameter matrix, σ(·) is the Sigmoid function, and ⊙ represents 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 quadrotor drone position signal or new high speed and the historical quadrotor drone position signal or speed signal.

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

[0039] h ic =W fc ·h i +b fc (13)

[0040] Among them, W fc represents the weight matrix of the fully connected layer, b fc 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:

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

[0042] The regression layer is based on the output y of the ReLU activation layer ReLU , map the feature vector to the prediction value space and generate the trajectory prediction result of the quadcopter in the future time step:

[0043] y=W reg ·r ReLU +b reg (15)

[0044] Among them, W reg and b reg They represent the weights and biases of the regression layer.

[0045] Step 3.3: For the LSTM neural network for the prediction of harmful quad-rotor drone trajectories constructed in step 3.2, respectively configure the parameters required for model training, set the learning rate, number of hidden layers, discard rate and number of iterations; use the constructed training data set to train the LSTM neural network model for drone trajectory prediction, and use the trained LSTM neural network model to construct a nonlinear relationship between the current drone historical trajectory data and its corresponding future trajectory. The 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. The trained LSTM neural network model is used in step 4 to predict the trajectory of harmful quad-rotor drones.

[0046] For the LSTM neural network model for harmful quadrotor drone trajectory prediction built in step 3.2, configure the parameters required for model training, set the learning rate, number of hidden layers, dropout rate, and number of iterations.

[0047] For the x-axis, y-axis, and z-axis dimensions of the harmful quadrotor drone, use the training dataset {p 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, use the Adam parameter optimization algorithm to determine the optimal model parameters, and obtain a trained LSTM neural network model. The nonlinear relationship between the current UAV historical trajectory data and its corresponding future trajectory is constructed through the trained LSTM 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.

[0048] Step 4: For harmful quadrotor drones, the trajectory data of the first n time steps are respectively input into the trained LSTM neural network model, and the prediction results of each drone's trajectory are output, including the predicted position information and speed information; the output prediction results are used as the expected position and expected speed of the drone, and the expected trajectory is tracked and controlled in combination with the proportional differential PD control strategy to obtain the control force of the harmful quadrotor drone. The problem that the harmful quadrotor drone cannot indirectly obtain the status of the leading drone is solved based on the control force, thereby improving the stability and reliability of the quadrotor drone formation.

[0049] For the three dimensions of the x-axis, y-axis, and z-axis of the harmful quadrotor drone, 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 (t)}, i = x, y, z are input into the trained LSTM neural network model respectively, and the prediction result of the harmful quadrotor drone trajectory is output

[0050] The output prediction results are used as the future expected trajectory of the harmful quadrotor drone, including three-dimensional position information Combined with the proportional differential PD control strategy, the control force u is designed as shown in formula (16): i , which solves the problem that harmful quadrotor drones cannot indirectly obtain the status of the leading drone, and improves the stability and reliability of the quadrotor drone formation.

[0051]

[0052] Among them, K p is the proportional gain, which determines the influence of the error on the control signal; K d is the differential gain, which determines the degree of influence of the error change rate on the control signal. is the expected value of the position predicted at time T = t + j, p i is the current position value at time T = t + j, is the expected value of the position predicted at time T = t + j, v i It is the current position value at time T = t + j, j = 1, 2, ..., m. This enables harmful quadrotor drones to form a formation effectively without the information of the leading drone, thus improving the stability and accuracy of the quadrotor drone formation flight.

[0053] Beneficial effects:

[0054] 1. The present invention discloses a method for restoring formation control of a quad-rotor drone under a network attack, constructs a logic detection algorithm for determining whether a follower drone can obtain the status information of a leader drone, introduces a tag signal between the leader drone and the follower drone, and combines the directed path between the follower drone and the neighboring drone to achieve the determination of the status of the follower drone. If the follower drone can receive the information of the leader drone, it is determined to be a healthy quad-rotor drone; conversely, if the follower drone cannot receive the information of the leader drone, it is determined to be a harmful quad-rotor drone. Furthermore, by timely identifying and isolating harmful quad-rotor drones, the control strategy can be effectively adjusted to prevent them from posing a potential threat to formation tasks or other quad-rotor drones, maintaining the stability and security of the quad-rotor drone formation, thereby achieving formation flight of quad-rotor drones when the quad-rotor drone formation communication is under network attack.

[0055] 2. The present invention discloses a method for restoring formation control of a quad-rotor drone under a network attack. For healthy quad-rotor drones, a distributed control strategy is constructed. The control strategy only needs to exchange local information with neighboring drones, rather than relying on the global information of the communication graph. In addition, compared with the traditional control strategy that requires full access to the reference acceleration or the control acceleration of neighboring drones, the control strategy only introduces the upper limit of the leading drone control, and satisfies the Lyapunov stability condition through the design of the control strategy, ensuring that the position error of each drone converges to zero when the formation is completed, thereby effectively reducing the communication burden between quad-rotor drones, improving control efficiency, and ensuring the stability and reliability of the quad-rotor drone formation.

[0056] 3. The present invention discloses a method for restoring formation control of a quad-rotor drone under a network attack. For harmful quad-rotor drones, the present invention discloses an LSTM neural network model for trajectory prediction of quad-rotor drones, and uses the historical trajectory information of harmful quad-rotor drones as training data, wherein the historical trajectory data of n time steps is used as the input feature sequence in a sliding window manner, and the trajectory data of m time steps in the future is used as the output feature sequence, and the LSTM neural network model is trained using the training data; the trajectory data of n time steps of each harmful quad-rotor drone is input into the trained LSTM neural network model, and the trajectory data of m time steps in the future of each harmful quad-rotor drone is output, and the flight control is performed in combination with the proportional differential PD control strategy, thereby realizing effective monitoring and control of harmful quad-rotor drones to prevent them from posing potential threats to formation tasks or other quad-rotor drones. In addition, combined with the PD control strategy, dynamic tracking and control of harmful drones can be achieved to ensure the safety and stability of the formation in a complex environment, thereby ensuring the continuity and safety of the quad-rotor drone formation mission. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Schematic diagram of the coordinate system setting of a quadrotor drone.

[0058] Figure 2 Schematic diagram of the principle of long short-term memory neural network.

[0059] Figure 3 A flow chart of a method for recovering formation control of a quad-rotor drone under a network attack according to the present invention. DETAILED DESCRIPTION

[0060] In order to overcome the shortcomings of the prior art, the present invention aims to propose a method for recoverable formation control of quadcopters under network attacks, so as to optimize and improve the formation control method of drones under network attacks. The technical solutions adopted by the present invention are mainly aimed at two aspects: first, a fully distributed control strategy is adopted, which only requires the upper limit of the leader control; second, the trajectory of the drone is predicted through LSTM, and the proportional differential (PD) control strategy is used to independently generate the control information of the force.

[0061] like Figure 1 As shown, the present embodiment discloses a method for restoring formation control of a quad-rotor drone under a network attack, and the specific steps are as follows:

[0062] Step 1: The quadrotor formation consists of a leader drone and four follower drones. The leader drone has known position and speed information and is responsible for transmitting status information to one of the follower drones. The remaining follower drones can only communicate locally with their neighboring follower drones to form an interconnected network. For quadrotor formation communication, a directed graph is defined, in which the nodes represent each quadrotor in the quadrotor formation, and the edges represent the communication relationship between the quadrotors.

[0063] We designed different scenarios under different network attack conditions. First, the drone flew for 40 seconds without being attacked. Then, it experienced the first network attack, which lasted for 5 seconds, and the network recovered for 20 seconds. Then, the drone encountered the second network attack, which also lasted for 5 seconds, and the recovery time was 60 seconds. Finally, the drone faced a third network attack of 5 seconds. The changes in the communication graph are shown in Equations (19) to (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] Among them, cal_A1 is the communication graph before the attack; cal_A2 is the communication graph after the first attack, and the communication between node 2 and node 3 is affected; cal_A3 is the communication graph after the second attack, and the communication between node 2 and node 3 is affected, and the communication between node 2 and the leader is affected; cal_A4 is the communication graph after the third attack, and the communication between node 4 and the leader is affected.

[0069] In order to distinguish whether a quadrotor drone is healthy or harmful to its neighboring drones under a network DoS attack, a logical detection algorithm is constructed to determine whether the follower drone can obtain the status information of the leader drone. The label signal between the leader drone and the follower drone is introduced, and the directed path between the follower drone and the neighboring drone is combined to realize the judgment of the status of the follower drone. When the communication of the quadrotor drone formation is attacked by the network, there is a directed path from the leader drone to the four follower drones. The nodes and edges of the quadrotor drone formation directed graph are defined as and in definition is the neighbor set of node i. As a tag signal passed from the leader drone to the follower drones. Detection information through The logic detection algorithm constructed based on formula (23) can timely identify and isolate harmful quadrotor drones, effectively adjust the control strategy to prevent them from posing potential threats to formation missions or other quadrotor drones, and maintain the stability and safety of the quadrotor drone formation:

[0070]

[0071] Where ∨ is the OR logic operation, Obviously, indicates that there is a directed path from the leader UAV to the follower UAV i, where This means that the following drone i is healthy for its neighbor drones. Otherwise, when When , it means there is no directed path from the leader UAV to the follower UAV i, where It shows that following drone i is harmful to its neighboring drones.

[0072] like Figure 3 As shown, if the follower drone can receive the information of the leading drone, it is determined as a healthy quadrotor drone and proceeds to step two; conversely, if the follower drone cannot receive the information of the leading drone, it is determined as a harmful quadrotor drone and proceeds to step four.

[0073] Step 2: For healthy quadrotors, a collaborative flight mode based on a distributed control strategy is adopted. Each quadrotor shares the status information of the leader drone and the data of its neighbor drones in real time, coordinates and adjusts its own control strategies, and thus achieves efficient collective movement.

[0074] The kinematic model of the quadrotor drone is expressed as Equation (24) and Equation (25):

[0075]

[0076] Among them, p is the center of gravity of the drone, v is the speed of the drone, T is the applied control force, g is the acceleration of gravity, Assume that the leader's control u0 is bounded, that is, in is a normal number.

[0077] Determine the mass of the drone as m = 0.85*[0.5, 1.2, 0.8, 1.3] kg, and bring the above physical quantities into the quadrotor drone dynamics model.

[0078] For healthy quad-rotor drones, a collaborative flight mode based on distributed control strategy is adopted. In this mode, each drone coordinates and adjusts its own flight path by sharing the status information of the leader drone and the data of its neighbor drones in real time, thus achieving efficient quad-rotor drone formation flight. This not only enhances the overall flexibility of the quad-rotor drone formation, but also improves the ability to respond to emergencies in complex environments. Define the normalization function Used to deal with the directional problem of the state vector of the quadrotor drone. This function can normalize any non-zero vector to maintain directional consistency in the control algorithm. if but Set its reference trajectory to 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 quadrotor drone as and The control force shown in formula (22) is designed to reduce the communication burden between quadrotor drones, improve control efficiency, and ensure the stability and reliability of the quadrotor drone formation:

[0079]

[0080] in:

[0081]

[0082] where k β and is a positive constant, and

[0083] Determine the control parameters as κ β =5, And bring the above parameters into the healthy quadrotor drone control force design.

[0084] Step 3: For harmful quadrotor drones, an LSTM neural network model for quadrotor drone trajectory prediction is constructed, and the historical position information and historical speed information of the quadrotor drone are used as training data respectively. The historical position data or speed data of 6 time steps are used as input feature sequence in a sliding window manner, and the position data or speed data of 1 time step in the future is used as output feature sequence. The LSTM neural network model is trained separately using the training data; the 6 time step position data and speed data of each harmful quadrotor drone are input into the trained LSTM neural network model respectively, and the position data and speed data of 1 time step in the future of each harmful quadrotor drone are output. The flight control is performed in combination with the proportional differential PD control strategy, which can cope with the uncertainty brought by the network attack on the quadrotor drone communication, so that the quadrotor drone formation communication can quickly restore its formation state when it is attacked by the network, thereby ensuring the continuity and safety of the mission.

[0085] Step 3.1: In the trajectory prediction task of harmful quadrotor drones, since the motion characteristics of each dimension may be different, in order to improve the prediction accuracy and model flexibility, an independent LSTM neural network model for quadrotor drone trajectory prediction is constructed for each dimension, while allowing targeted optimization and tuning of each neural network to better capture the dynamic changes and trends of each dimension. Specifically, for each dimension, the sliding window technology is used to extract the position data or velocity data of the first 6 time steps of each training sample in the training data set as the input feature sequence, and the position data or velocity data of the next 1 time step is extracted as the output feature sequence.

[0086] For the three dimensions of the x-axis, y-axis, and z-axis of the harmful quadrotor drone, the sliding window technique is used to convert the position data of the first 6 time steps of each training sample in the training data set into i (t-5),p i (t-4),…,p i (t)} and speed data {v i (t-5),v i (t-4),…,v i(t)}, i = x, y, z are extracted as input feature sequences respectively, and the position data of the next time step {p i (t+1)} and speed 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 the prediction of harmful quadcopter trajectories. The LSTM network model includes an input layer, an LSTM layer, a discard layer, a fully connected layer, a ReLU activation layer, and a regression layer. The input layer inputs the feature sequence in the training data set to the LSTM layer. The LSTM network sub-model is a long short-term memory network. By performing time series modeling on the input feature sequence, it fully explores the motion patterns of the quadcopter at different time steps. When processing the trajectory data at the current moment, such as Figure 2 As shown in the figure, the LSTM layer can use the past trajectory information to perform serialized feature fusion, so as to better characterize the dynamic relationship between the current trajectory and the historical trajectory, and improve the LSTM network model's ability to predict the trajectory of the drone. The discard layer randomly discards a certain proportion of neurons to prevent the overfitting phenomenon of the LSTM neural network model and ensure the generalization ability of the model during the training process. Its output will be 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. After the ReLU activation layer is added to the fully connected layer, it introduces nonlinear features so that the LSTM neural network model can better learn complex trajectory patterns. The regression layer is used to output the prediction results, map the output of the fully connected layer to the target value space, and generate the prediction results of the drone's future trajectory. The trajectory prediction of harmful quadrotor drones is carried out through the LSTM neural network model to improve the accuracy and reliability of the LSTM neural network model prediction.

[0088] Step 3.3: For the LSTM neural network for the prediction of harmful quad-rotor drone trajectories constructed in step 3.2, respectively configure the parameters required for model training, set the learning rate, number of hidden layers, discard rate and number of iterations; use the constructed training data set to train the LSTM neural network model for drone trajectory prediction, and use the trained LSTM neural network model to construct a nonlinear relationship between the current drone historical trajectory data and its corresponding future trajectory. The 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. The trained LSTM neural network model is used in step 4 to predict the trajectory of harmful quad-rotor drones.

[0089] For the LSTM neural network model for harmful quadcopter trajectory prediction built in step 3.2, configure the parameters required for model training, set the learning rate, number of hidden layers, drop 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 x-axis, y-axis, and z-axis dimensions of the harmful quadrotor drone, use the training dataset {p 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, respectively train the LSTM neural network model constructed in step 3.2, use the Adam parameter optimization algorithm to determine the optimal model parameters, and obtain a trained LSTM neural network model. The nonlinear relationship between the current UAV historical trajectory data and its corresponding future trajectory is constructed through the trained LSTM 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.

[0091] Step 4: For harmful quadrotor drones, the trajectory data of the first 6 time steps are respectively input into the trained LSTM neural network model, and the prediction results of each drone trajectory at the next moment are output, including the predicted position information and speed information; the output prediction results are used as the expected position and expected speed of the drone, and the expected trajectory is tracked and controlled in combination with the proportional differential PD control strategy to obtain the control force of the harmful quadrotor drone. The problem that the harmful quadrotor drone cannot indirectly obtain the status of the leading drone is solved based on the control force, thereby improving the stability and reliability of the quadrotor drone formation.

[0092] For the three dimensions of the x-axis, y-axis, and z-axis of the harmful quadrotor drone, 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 i(t)}, i = x, y, z are input into the trained LSTM neural network model respectively, and the prediction result of the harmful quadrotor drone trajectory is output

[0093] The output prediction result is used as the future expected trajectory of the harmful quadrotor drone, including three-dimensional position information Combined with the proportional differential PD control strategy, the control force u is designed as shown in formula (25): i , which solves the problem that harmful quadrotor drones cannot indirectly obtain the status of the leading drone, and improves the stability and reliability of the quadrotor drone formation.

[0094]

[0095] Among them, K p is the proportional gain, which determines the influence of the error on the control signal; K d is the differential gain, which determines the degree of influence of the error change rate on the control signal. is the expected value of the position predicted at time T = t + 1, p i is the current position value at time T = t + 1, is the expected value of the position predicted at time T = t + 1, v i It is the current position value at time T=t+1, which enables harmful quadrotor drones to effectively form a formation without the information of the leading drone, thereby improving the stability and accuracy of the quadrotor drone formation flight.

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

[0097] From this specific implementation, the quadcopter can perform formation control under network attacks, track the reference trajectory well, and have a small position error. The applied force can also be well adjusted within the control range, with a short convergence time and good formation tracking performance.

[0098] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above 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 in the scope of protection of the present invention.

Claims

1. A method for restoring formation control of a quad-rotor drone under a network attack, characterized in that: The following steps are included: Step 1: A quadrotor UAV formation includes a leader UAV and N follower UAVs, where the position information and speed information of the leader UAV is known and it is responsible for transmitting status information to one of the follower UAVs. The remaining follower UAVs can only communicate locally with their neighboring follower UAVs to form an interconnected network. For quadrotor UAV formation communication, a directed graph is defined, in which the nodes represent each quadrotor UAV in the quadrotor UAV formation, and the edges represent the communication relationship between the quadrotor UAVs. A label signal is introduced as the status information transmitted by the leader UAV to the follower UAVs. When the quadrotor UAV formation communication is attacked by the network, the status of the follower UAV is judged by analyzing the label signal between the leader UAV and the follower UAV and the directed path of the neighbor UAV. If the follower UAV can receive the information of the leader UAV, it is judged as a healthy quadrotor UAV and proceeds to step 2. On the contrary, if the follower UAV cannot receive the information of the leader UAV, it is judged as a harmful quadrotor UAV and proceeds to step 4. Step 2: For healthy quadrotor drones, a collaborative flight mode based on a distributed control strategy is adopted. Each quadrotor drone coordinates and adjusts its own control strategy by sharing the status information of the leader drone and the data of its neighbor drones in real time, thereby achieving efficient collective movement. During the collaborative formation flight of quadrotor drones, each quadrotor drone calculates the tracking error between it and its neighbor drones, including position error and speed error. The former represents the difference between the current position of the quadrotor drone and the target position, and the latter represents the difference between the current flight speed of the quadrotor drone and the expected speed. Based on tracking errors and introducing real-time feedback on the errors, each quadrotor drone can generate appropriate control force, so that the quadrotor drone can not only maintain coordination with the leader drone and neighbor drones, but also make dynamic adjustments based on real-time status information; in addition, a dynamic adjustment mechanism for the error is introduced into the control strategy to ensure that the quadrotor drone can quickly respond to environmental changes and status changes of other quadrotors. The error response speed is adjusted by introducing a positive constant to ensure the stability and flexibility of the quadrotor drone formation; Step 3: For harmful quad-rotor drones, an LSTM neural network model for quad-rotor drone trajectory prediction is constructed, and the historical position information and historical speed information of the quad-rotor drone are used as training data respectively, wherein the historical position data or speed data of n time steps are used as input feature sequences in a sliding window manner, and the position data or speed data of m time steps in the future are used as output feature sequences, and the LSTM neural network model is trained separately using the training data; the position data and speed data of n time steps of each harmful quad-rotor drone are respectively input into the trained LSTM neural network model, and the position data and speed data of m time steps in the future of each harmful quad-rotor drone are output, and the flight control is performed in combination with the proportional differential PD control strategy, which can cope with the uncertainty caused by the network attack on the communication of the quad-rotor drone, so that the quad-rotor drone formation communication can quickly restore its formation state when it is attacked by the network, thereby ensuring the continuity and safety of the mission; Step 4: For harmful quadrotor drones, the trajectory data of the first n time steps are respectively input into the trained LSTM neural network model, and the prediction results of each drone's trajectory are output, including the predicted position information and speed information; the output prediction results are used as the expected position and expected speed of the drone, and the expected trajectory is tracked and controlled in combination with the proportional differential PD control strategy to obtain the control force of the harmful quadrotor drone. The problem that the harmful quadrotor drone cannot indirectly obtain the status of the leading drone is solved based on the control force, thereby improving the stability and reliability of the quadrotor drone formation.

2. The method for recovering formation control of a quad-rotor drone under a network attack as claimed in claim 1, characterized in that: In step one, In order to distinguish whether a quadrotor drone is healthy or harmful to its neighboring drones under a network DoS attack, a logical detection algorithm is constructed to determine whether the following drone can obtain the status information of the leader drone. The label signal between the leader drone and the following drone is introduced, and the directed path between the following drone and the neighboring drone is combined to realize the judgment of the status of the following drone. When the communication of the quadrotor drone formation is attacked by the network, there is a path from the leader drone to the neighboring drones. o The nodes and edges of the directed graph of the quadcopter formation are defined as follows: and in definition is the neighbor set of node i; As a tag signal passed from the leader drone to the follower drone; Detection information through Provided; A logical detection algorithm constructed based on formula (1) can timely identify and isolate harmful quadrotor drones, adjust the control strategy to prevent them from posing potential threats to formation missions or other quadrotor drones, and maintain the stability and safety of the quadrotor drone formation: Where ∨ is the OR logic operation, Obviously, indicates that there is a directed path from the leader UAV to the follower UAV i, where This means that following drone i is healthy for its neighboring drones; otherwise, when When , it means there is no directed path from the leader UAV to the follower UAV i, where It shows that following drone i is harmful to its neighboring drones.

3. The method for recovering formation control of a quad-rotor drone under a network attack as claimed in claim 2, characterized in that: In step 2, The kinematic model of the quadrotor drone is expressed as Equation (2) and Equation (3): Among them, p is the center of gravity of the drone, v is the speed of the drone, T is the applied control force; g is the acceleration of gravity, Assume that the leader's control u0 is bounded, that is, in is a positive constant; For healthy quadrotor drones, a collaborative flight mode based on distributed control strategy is adopted. In this mode, each drone coordinates and adjusts its own flight path by sharing the status information of the leader drone and the data of its neighbor drones in real time, so as to achieve efficient quadrotor drone formation flight. This not only enhances the overall flexibility of the quadrotor drone formation, but also improves the ability to deal with emergencies in complex environments. Define the normalization function Used to deal with the directional problem of the state vector of the quadrotor drone. This function can standardize any non-zero vector to maintain directional consistency in the control algorithm. if but The position error and velocity error of the quadrotor drone are defined as and Design the control force as shown in formula (4) to reduce the communication burden between quadrotor drones, improve control efficiency, and ensure the stability and reliability of the quadrotor drone formation: in: where κ β and is a positive constant, and 4. The method for recovering formation control of a quad-rotor drone under a network attack as claimed in claim 3, characterized in that: The implementation method of step three is: Step 3.1: In the trajectory prediction task of harmful quadrotor drones, since the motion characteristics of each dimension may be different, in order to improve the prediction accuracy and model flexibility, an independent LSTM neural network model for quadrotor drone trajectory prediction is constructed for each dimension, while allowing targeted optimization and tuning of each neural network to better capture the dynamic changes and trends of each dimension; specifically, for each dimension, the sliding window technology is used to extract the position data or speed data of the first n time steps of each training sample in the training data set as the input feature sequence, and the position data or speed data of the next m time steps are extracted as the output feature sequence, where the selection of the sliding window size n and the prediction step size m is crucial, and the setting of the two parameters will directly affect the performance of the model and the accuracy of the prediction; For the three dimensions of the x-axis, y-axis, and z-axis of the harmful quadrotor drone, the sliding window technique is used to convert the position data of the first n time steps of each training sample in the training data set {p i (t-n+1),p i (t-n+2),…,p i (t)} and speed data {v i (t-n+1),v i (t-n+2),…,v i (t)}, i = x, y, z are extracted as input feature sequences respectively, and the position data of the next m time steps {p i (t+1),…,p i (t+m)} and speed 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 harmful quadcopter trajectories, the LSTM network model includes an input layer, an LSTM layer, a discard layer, a fully connected layer, a ReLU activation layer and a regression layer; the input layer inputs the feature sequence in the training data set into the LSTM layer; the LSTM network sub-model is a long short-term memory network, which fully explores the motion law of the quadcopter at different time steps by performing time series modeling on the input feature sequence; when processing the trajectory data at the current moment, the LSTM layer can use the past trajectory information to perform serialized feature fusion, so as to better characterize the dynamic relationship between the current trajectory and the historical trajectory, and enhance the LSTM network model's ability to predict the trajectory of the drone; the discard layer randomly discards a certain proportion of neurons to prevent the overfitting phenomenon of the LSTM neural network model, ensure the generalization ability of the model during the training process, and its output will be 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; The ReLU activation layer is added after the fully connected layer to introduce nonlinear features, enabling the LSTM neural network model to better learn complex trajectory patterns; The regression layer is used to output the prediction results, map the output of the fully connected layer to the target value space, and generate the prediction results of the future trajectory of the drone. The trajectory of the harmful quadrotor drone is predicted through the LSTM neural network model to improve the accuracy and reliability of the LSTM neural network model prediction. Constructing an LSTM neural network model for trajectory prediction of harmful quadrotor drones, the LSTM network model includes an input layer, an LSTM layer, a discard layer, a fully connected layer, a ReLU activation layer, and a regression layer; The input layer converts the feature sequence {p 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 input into the LSTM layers of different LSTM neural network models respectively; The LSTM layer introduces a gating mechanism to solve the problem of quadrotor trajectory prediction based on long-term historical data. Its internal structure includes input gate, forget gate and output gate. The gating unit can dynamically adjust the transmission and storage of information related to the quadrotor motion, thereby capturing the complex patterns and timing relationships between different time steps. For time t, the processing process of the LSTM module 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 is the input at the current moment and the hidden layer state at the previous moment [h t-1 ,x t ] weight parameter matrix, b f , b i , b C , b o 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 quadrotor drone position signal or new high speed and the historical quadrotor drone position signal or speed signal; The dropout layer is used to prevent overfitting. The output of the LSTM layer is randomly set to zero with probability p, making the LSTM neural network model more robust during the training process. The output feature sequence of the dropout layer is input into the fully connected layer to generate the feature vector of the future trajectory of the quadcopter: h ic =W fc ·h i +b fc (13) Among them, W fc represents the weight matrix of the fully connected layer, b fc 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 , map the feature vector to the prediction value space and generate the trajectory prediction result of the quadcopter in the future time step: y=W reg ·y ReLU +b reg (15) Among them, W reg and b reg They represent the weights and biases of the regression layer; Step 3.3: For the LSTM neural network for trajectory prediction of harmful quadrotor drones constructed in step 3.2, respectively configure the parameters required for model training, set the learning rate, number of hidden layers, discard rate and number of iterations; use the constructed training data set to train the LSTM neural network model for drone trajectory prediction, and use the trained LSTM neural network model to construct a nonlinear relationship between the current drone historical trajectory data and its corresponding future trajectory. The 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 quadrotor drones; For the LSTM neural network model for harmful quadrotor drone trajectory prediction built in step 3.2, configure the parameters required for model training, set the learning rate, number of hidden layers, dropout rate, and number of iterations; For the x-axis, y-axis, and z-axis dimensions of the harmful quadrotor drone, use the training dataset {p 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, use the Adam parameter optimization algorithm to determine the optimal model parameters, and obtain a trained LSTM neural network model; construct a nonlinear relationship between the current UAV historical trajectory data and its corresponding future trajectory through the trained LSTM network model, and 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 recovering formation control of a quad-rotor drone under a network attack as claimed in claim 4, characterized in that: In step four, For the x-axis, y-axis, and z-axis dimensions of the harmful quadrotor drone, the trajectory data of the first n time steps are The results are respectively input into the trained LSTM neural network model, and the prediction results of harmful quadrotor drone trajectories are output. The output prediction result is used as the future expected trajectory of the harmful quadrotor drone, including three-dimensional position information Combined with the proportional differential PD control strategy, the control force u is designed as shown in formula (16): i , solve the problem that harmful quadrotor drones cannot indirectly obtain the status of the leading drone, and improve the stability and reliability of the quadrotor drone formation; Among them, K p is the proportional gain, which determines the influence of the error on the control signal; K d is the differential gain, which determines the degree of influence of the error change rate on the control signal; is the expected value of the position predicted at time T = t + j, p i is the current position value at time T = t + j, is the expected value of the position predicted at time T = t + j, v i It is the current position value at time T = t + j, j = 1, 2, ..., m, so that the harmful quadrotor drones can still form a formation effectively without the information of the leading drone, thereby improving the stability and accuracy of the quadrotor drone formation flight.

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