A method, system and program product for calibrating the phase point stability domain of a prediction model of an unmanned aerial vehicle network system

Abstract

The present invention relates to the technical field of unmanned aerial vehicle (UAV) cluster modeling and system stability analysis, and in particular to a method, system, and program product for calibrating the phase point stability domain of a UAV network system prediction model. The method comprises: collecting phase point trajectory data, determining whether the data scale meets the modeling requirements, and if insufficient, expanding the data through linear interpolation and Gaussian perturbation; then using the NARX dynamic neural network to perform time series prediction on the trajectory evolution; combining the latest observation data with the prediction results to construct a calibration data set, and finally outputting the center vector and radial quantity approximation of the stability domain. The present invention also provides a corresponding system structure and computer program product, which have the advantages of high computational efficiency, high precision, and strong adaptability, and can adapt to a variety of typical scenarios such as initial steady state, extreme offset, and recovery of steady state, and is widely applicable to stability assessment and control decision support for swarm UAVs.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) cluster modeling and system stability analysis, and in particular to a method, system and program product for calibrating the phase point stability domain of a UAV network system prediction model. Background Art

[0002] With the development of intelligent and swarming unmanned systems, drone network systems have shown tremendous potential in missions such as search and rescue, regional monitoring, material transportation, and combat drills. In particular, in multi-drone collaborative operations, the interaction patterns between nodes and the overall dynamic behavior of the system become key factors affecting mission efficiency and safety. Therefore, building accurate network system models and understanding their spatiotemporal evolution are crucial for ensuring the stability and robustness of mission execution.

[0003] In the network system modeling process, phase point trajectories, as a spatial representation of the system state evolution, can more intuitively reflect the behavioral changes of network node clusters in the time domain. Therefore, the modeling and analysis of phase point trajectories has gradually become an important research direction for network system performance evaluation, control strategy verification, and anti-interference capability testing. For multi-node distributed drone network systems, during mission execution, due to the collaborative dependencies between members, the system state is affected by various factors such as individual behavioral disturbances, environmental interference, and communication interruptions, which can easily lead to problems such as sudden state changes and system performance degradation.

[0004] However, under the complex interaction mechanisms of network systems, the stability domain of the system state is often difficult to clearly define through theoretical analysis, especially during the disturbance response phase of the system's nonlinear evolution. Therefore, existing methods face the following major challenges in accurately calibrating the stability domain of UAV network systems:

[0005] 1. High system modeling complexity: Traditional methods focus on node control algorithms or path planning strategies, while ignoring the impact of inter-node collaboration and cluster behavior evolution on overall stability. As a result, the system model cannot fully depict the actual state evolution process.

[0006] 2. The stability domain cannot be directly solved: In actual flight missions, the stable region of a drone cluster usually changes in a high-dimensional state space and is affected by time series driving factors. Traditional analytical methods cannot effectively determine the center position and boundary shape of the stability domain.

[0007] 3. Lack of dynamic modeling methods: Some methods have attempted to use simulation to track and analyze system status. However, due to the lack of a generalizable predictive model, it is difficult to extract the stability evolution law from a limited sample, which in turn affects the effectiveness of subsequent interference injection experiments and control algorithm optimization.

[0008] To address these technical challenges, current research is exploring data-driven approaches to system state prediction. Time series modeling tools, such as neural networks, have demonstrated promising performance. The nonlinear autoregressive external input model (NARX) has garnered significant attention in the field of time series data analysis due to its simple structure, high prediction accuracy, and adaptability to multidimensional input and output characteristics. By combining the NARX model with the dynamic evolution of phase point trajectories, it is possible to approximate the stability domain of the system without analytical expressions, thereby enabling the assessment of the stability performance of UAV network systems.

[0009] The paper "Simulation of the NARX Model Tracking Algorithm Based on Kalman Filtering" published by RswtPerl combines autoregressive and exogenous inputs to approximate arbitrary continuous mappings within a low-order network structure, and has been widely used for UAV attitude and trajectory prediction. "Drone Motion Prediction from Flight Data: A Nonlinear Timeseries Approach" published by Shuyan Dong et al. utilizes a three-layer NARX network to achieve 1-second advance prediction with an average error of 0.23 meters. In the paper "Online Prediction of Time Series Based on Combined Neural Networks," the team led by Xiang Jinwu of Beihang further proposed a combined FD-IWPD-NARX model for online prediction of wind speed series for tiltrotor flight platforms. Although NARX strikes a balance between accuracy and computational complexity, previous studies have generally overlooked the impact of sample size on model generalization. The limited number of trajectories available for field flight sampling leads to model overfitting, and the approach to approximating the stability domain when the sample size is insufficient has not been discussed.

[0010] Chinese invention patent CN106774436B proposes a vision-based target tracking system for rotary-wing UAVs, using image-IMU fusion to stabilize the trajectory, but does not address the estimation of the stability domain of a multi-aircraft network. Chinese invention patent CN106054931A discloses a fixed-point flight control system that uses visual positioning to correct GPS drift, but lacks a description of the concept of "multi-aircraft coordination / stability domain." This disclosure focuses on attitude / trajectory control for a single UAV, but has yet to address the "UAV network system - phase point stability domain - data-driven approximate calibration" system.

[0011] Furthermore, during the operational phase of a multi-UAV network system, the randomness of external environmental interference and the uncertainty of collaboration among internal members can lead to sudden changes in the system state. Therefore, in addition to calibrating the initial stability domain, dynamically identifying the system's extreme state under interference and the stability domain it reenters through recovery mechanisms becomes crucial for system robustness assessment and control strategy design. Therefore, developing a highly accurate and adaptable stability domain approximate calibration method is not only of great significance for network system simulation modeling but also provides theoretical support and engineering reference for the deployment, control, and fault-tolerant design of actual UAV formation systems. Summary of the Invention

[0012] In order to solve the above technical problems, the purpose of the present invention is to provide a method for calibrating the phase point stability domain of a UAV network system prediction model. The method utilizes the NARX neural network time series prediction model, and uses the recent phase point trajectory data and the prediction data obtained by the time series prediction model to give approximate estimates of the center vector and radial vector of the stability domain.

[0013] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions:

[0014] A method for calibrating a phase point stability domain of a prediction model of an unmanned aerial vehicle network system, the method comprising the following steps:

[0015] 1) Collect the original trajectory data of multi-dimensional phase points in phase space within continuous steps D , and stored in a matrix format of "the first line is the step sequence, and the remaining lines are the position coordinates of each dimension";

[0016] 2) determining whether the number of columns of the original data matrix is ​​less than a preset data expansion threshold; if so, performing data expansion processing; otherwise, skipping the processing;

[0017] 3) In the data expansion process, several new data points are uniformly inserted between adjacent step data, and Gaussian white noise is introduced into the inserted data to generate an expanded data matrix ,make ;

[0018] 4) Predict window size based on preset , input the original or expanded data matrix into the NARX dynamic neural network time series model, and obtain the The prediction matrix composed of prediction data points ;

[0019] 5) According to the preset observation window size , after intercepting the original data matrix Column data, forming the observation matrix ;

[0020] 6) Combine the observed data and predicted data into a calibration data set , input the stability domain calibration model, and output the center vector and radial quantity approximation of the target stability domain.

[0021] As a preference, in step 1), it is assumed that the time span of the acquired data is step size, the dimension of the phase space is , then the acquired phase point trajectory data is stored in The first row of the matrix is ​​the step sequence , lines 2 to 3 The rows place the position coordinates of each dimension of the phase point at the corresponding step size in sequence.

[0022] As a preference, in step 2), when the number of columns of the original data matrix of the phase point trajectory is less than When ; The original data matrix needs to be expanded; the data expansion threshold It should be no less than 10,000, and expansion is triggered only when the original data is insufficient to train a neural network that meets the accuracy requirements.

[0023] As a preference, in step 3), the original data matrix of the phase point trajectory is expressed as ;

[0024] in, is the step vector, and its components are recorded as:

[0025] ,

[0026] For the phase point in dimension The time series position vector on , its components are recorded as:

[0027] ;

[0028] When the data expansion conditions are met, p j and p j+1 between and ps i，j and ps i，j+1 Increase between ( x -1) data point, ;

[0029] Recorded in sequence and , where the data points and The formula for determining the value of is:

[0030] ,

[0031] ;

[0032] in, , The multiple by which the data is expanded; is a random Gaussian white noise with a standard deviation The value of is:

[0033]

[0034] is a coefficient related to the dispersion of noise intensity.

[0035] Preferably, the NARX neural network model in step 4) is:

[0036] ;

[0037] Where y(t) is the system output at the current time t; y(td) is the historical output value sequence of the system at the previous d times; f(.) is a nonlinear mapping function learned by the neural network model;

[0038] The NARX neural network consists of an input layer, a hidden layer, an output layer, and input and output delays. The input of the NARX dynamic neural network is a step sequence, and the output is the position of phase points in each dimension. The number of hidden layers can be set between 10 and 100 layers according to the accuracy requirements.

[0039] As a preference, in step 5), the starting position and the ending position of the observation window are set to be and ; Since the observation window only captures the last Data, the end position of the observation window ;

[0040] Observation window starting position The method is as follows:

[0041] make If there is such j , and satisfy the following three conditions at the same time:

[0042] ;

[0043] So, If this Does not exist, then ;

[0044] in, It is the change threshold, which needs to be set in advance;

[0045] is the minimum value of the observation window, which is set to ; is a differential sequence that stores the information of the degree of phase point change, and there is

[0046] .

[0047] As a preference, in step 6), the obtained calibration data matrix is ​​set to ,in:

[0048] ,

[0049] ;

[0050] make , Then the stability region of the approximate calibration is The central vector of is:

[0051] ;

[0052] The radius vector is:

[0053] .

[0054] Preferably, the method is applicable to any of the following three types of stable domains:

[0055] a) The initial stable region after the system reaches steady state;

[0056] b) The farthest stable region where the system is affected by the disturbance impulse;

[0057] c) The stable region that the system re-enters during the recovery phase after the disturbance stops.

[0058] Furthermore, the present invention also provides a UAV network system phase point stability domain approximate calibration system, which implements the method described above, including:

[0059] a) a data acquisition unit, used to collect and matrix the original trajectory data of the phase point;

[0060] b) a data expansion unit, configured to perform linear Gaussian white noise expansion when insufficient original data is detected;

[0061] c) prediction unit, configured with a NARX dynamic neural network, for generating future prediction data;

[0062] d) a window interception unit, used to intercept the tail segment of the original data according to the observation window size;

[0063] e) Calibration unit, used to combine the observed data with the predicted data and output the approximate values ​​of the center vector and radial quantity of the stability domain.

[0064] Furthermore, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which enables a computer to implement the method when the program is executed by a processor.

[0065] Furthermore, the present invention also provides a computer program product, comprising a computer program or instructions, which implement the method when executed by a processor.

[0066] The present invention adopts the above-mentioned technical solution, based on the trajectory data-driven modeling and dynamic prediction mechanism, which breaks through the limitations of the traditional stable domain analytical solution method in high-dimensional complex network systems and has the following significant technical effects:

[0067] 1. High-precision stability domain calibration in small sample scenarios: By performing linear-Gaussian white noise augmentation on the original trajectory data, the sample size can be quickly expanded from thousands to ≥10,000, significantly improving the adequacy and generalization capabilities of the NARX network training. Under the premise that the augmented noise amplitude is adaptively constrained by the Euclidean distance between trajectory points, overfitting and random drift are effectively avoided, achieving an average calibration error of less than 3% for the stability domain center vector and radius vector.

[0068] 2. Prediction-observation fusion mechanism with both real-time and robustness: using the “near-end observation window w o +Forward prediction window w p "Dual window fusion: The observation window ensures that the calibration process is sensitive to the latest system state, and the prediction window offsets the instantaneous fluctuations caused by occasional measurement noise. When the external disturbance causes the phase point to deviate from the steady state, the system can be p The updated stability region approximation is re-output within the step size to gain time margin for online fault-tolerant control.

[0069] 3. Unified adaptation of three key stability domains to support full life cycle assessment: The method of the present invention can perform one-time, same-format calibration on three typical areas: "initial steady-state domain, extreme offset steady-state domain, and recovery steady-state domain." In the interference injection test, it can automatically switch between different observation windows and threshold settings to ensure that the calibration accuracy is maintained without degradation under ±8dB interference intensity changes.

[0070] 4. Low computational overhead and embeddable implementation: The NARX network requires only 10–30 hidden layers to achieve two-dimensional state prediction for a 9-UAV formation. The supporting matrix operations and threshold judgments can run in real time (>60Hz update rate) on low-power single-board processors such as the ARM Cortex-A53. Calibration and parameter updates are performed by calculating the matrix mean and norm, with a time complexity of O(n·m), and linear scalability with the expansion of the formation size.

[0071] In summary, the present invention has achieved significant improvements in accuracy, real-time performance, robustness, computational efficiency, and engineering feasibility, providing strong technical support for online health assessment, anti-disturbance control, and adaptive mission planning of multi-UAV network systems, and has broad application prospects and promotion value. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 This is the overall process of the stability domain approximate calibration method.

[0073] Figure 2 This is an example of the original data format of the phase point trajectory, where: Figure 2 (a) Phase point trajectory example, Figure 2 (b) The original data of the phase point trajectory.

[0074] Figure 3 For example, data expansion is performed, Figure 3 In (a), Gaussian white noise is added to both dimensions. Figure 3 (b) only in Add Gaussian white noise to the dimension.

[0075] Figure 4 This is the basic structure of the NARX neural network.

[0076] Figure 5 For example, the neural network model Dimensional test results.

[0077] Figure 6 For example, the neural network model Dimensional test results.

[0078] Figure 7 Perform formation flying missions for drone network systems.

[0079] Figure 8 There are two stages of the UAV formation flight mission.

[0080] Figure 9 is the phase space of different task stages.

[0081] Figure 10 are the original phase point trajectory and the phase point trajectory after data expansion. DETAILED DESCRIPTION

[0082] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0083] At present, in the simulation of phase point trajectories of the UAV network system prediction model, at least the following three types of stability domains need to be calibrated:

[0084] (1) After the network system starts to operate and reaches a stable state, the initial stable domain where the phase point is located ;

[0085] (2) The stable region farthest from the initial stable region that the phase point reaches under the action of the disturbance impulse (This stable region may be a maximum stable region, at which point the network system is in a collapsed state);

[0086] (3) After the disturbance impulse stops, the phase point re-enters the stable domain under the recovery mechanism .

[0087] In some cases, the three types of stability regions for network system phase points are very clear and can be obtained through state analysis or theoretical derivation. However, in other cases, the dynamic nature of the interactions between network system nodes makes it difficult to obtain the exact values ​​of the stability region center vector and radius vector. In these cases, a reasonable approximate alternative method is urgently needed.

[0088] To address the difficulty in obtaining precise values ​​for the center and radial vectors of a network system's stability domain in some situations, this paper proposes an approximate stability domain calibration method. The stability domain calibration model in this method ensures a certain level of approximate accuracy. With this accuracy, the deviation between the approximate calibration stability domain and the theoretical value is significantly smaller than the change in the stability domain under the influence of a disturbance impulse.

[0089] The stability domain approximate calibration method proposed in this paper utilizes the NARX neural network time series prediction model. The core idea of ​​this method is to use the recent phase point trajectory data and the predicted data obtained by the time series prediction model to give an approximate estimate of the center vector and radial vector of the stability domain. The overall idea of ​​the method is as follows Figure 1 shown.

[0090] The execution steps of the method of the present invention are as follows:

[0091] Step 1. Obtain the raw data of the phase point trajectory and organize it into a specified matrix format to obtain the raw data matrix D. The raw data acquisition range varies with the type of calibrated stability domain, see Table 1. The specified data format is shown in Note 1.1;

[0092] Table 1. The acquisition range of raw data

[0093]

[0094] Step 2. Check whether the original data meets the expansion conditions: If yes, go to step 3; if not, let , and go to step 4;

[0095] Step 3. Put the original data matrix of the phase point trajectory into the linear Gaussian white noise data expansion model to obtain the expanded data matrix of the phase point trajectory ,make ;

[0096] Step 4. Set the prediction window size to , put the data matrix into the NARX neural network model, and obtain The prediction matrix composed of prediction data points ;

[0097] Step 5. Set the observation window size to , after intercepting the original data matrix Column data, forming the observation matrix ;

[0098] Step 6. Combine the observation matrix and the prediction matrix to obtain calibration data , and used as the input of the stable domain calibration model to obtain the approximate calibration value of the stable domain.

[0099] Note 1.1 stipulates that the acquired phase point trajectory data is stored in the form of a matrix. Assume that the time span of the acquired data is step size, the dimension of the phase space is , then the acquired phase point trajectory data is stored in The first row of the matrix is ​​the step sequence , lines 2 to 3 The rows place the position coordinates of each dimension of the phase point at the corresponding step size in sequence.

[0100] For example, in a two-dimensional phase space, the positions that a phase point passes through in steps 1-5 are as follows: Figure 2 As shown in (a), at this time, the original data of the phase point trajectory is Figure 2 The matrix shown in b).

[0101] like Figure 1 As shown in Figure 2, the overall concept of the stability domain approximate calibration method includes three core models: a linear Gaussian white noise data augmentation model, a neural network model, and a stability domain calibration model. The linear Gaussian white noise data augmentation model addresses the issue of insufficient raw data to improve the prediction accuracy of the neural network prediction model. The neural network model is used to predict the phase point position for future simulation steps. The stability domain calibration model integrates the raw and predicted data to ultimately output approximate calibration values ​​for the stability domain center vector and radial vector.

[0102] 1. Linear Gaussian white noise data augmentation model

[0103] (1) Data expansion judgment conditions

[0104] When implementing the stability domain approximate calibration method proposed in this invention, it is not necessary to expand the original data of the phase point trajectory. It is only necessary to expand the original data when the sample size of the original data is too small to train a neural network model that meets the accuracy requirements. The formal expression of the data expansion judgment condition is as follows:

[0105] When the number of columns of the original data matrix of the phase point trajectory is less than When (i.e. ), the original data matrix needs to be expanded. Among them, is the data expansion threshold. Based on the training experience of the neural network model, it is recommended that this value is not less than 10000. .

[0106] (2) Data expansion method

[0107] The original data matrix of the phase point trajectory is expressed as ;

[0108] in, is the step vector, and its components are recorded as:

[0109] ,

[0110] For the phase point in dimension The time series position vector on , its components are recorded as:

[0111] ;

[0112] When the data expansion conditions are met, p j and p j+1 between and ps i，j and ps i，j+1 Increase between ( x -1) data point, , ;

[0113] Recorded in sequence and , where the data points and The formula for determining the value of is:

[0114] ,

[0115] ; (1.1)

[0116] in, , The multiple by which the data is expanded; is a random Gaussian white noise with a standard deviation The value of is:

[0117] (1.2)

[0118] is a coefficient related to the dispersion of noise intensity. The default value of this coefficient in the present invention is .

[0119] In the above data augmentation method, the insertion position of the augmented data is uniform and linear, and the distribution of the random items of the augmented data adopts Gaussian distribution. Therefore, this method is called a linear Gaussian white noise data augmentation model.

[0120] Example. According to the model of formula (1.1)-(1.2), Figure 3 The numerical example shown needs to be expanded by a factor of , that is, 1999 new data points need to be added between every two data points in the 5 groups of data points. For example, the first two data points in the second row of the data matrix and The first data point added between The value of is:

[0121] (1.3)

[0122] in, The random number generated according to the Gaussian distribution is 0.0011, so the value of the added data point is According to this algorithm, the numerical calculation of each expanded data is completed, and the expanded phase point trajectory is obtained as follows Figure 3 As shown in (a).

[0123] In this example, we can also add Gaussian white noise to only one dimension of the phase space. Figure 3 (b) is only for the dimension Result of adding white Gaussian noise.

[0124] It should be noted that in order to more clearly present the Gaussian white noise on the linear trajectory of the original phase point caused by data expansion, the expansion process in the example does not fully adopt the data expansion threshold. and noise intensity dispersion coefficient The default value of Figure 3 The annotation in .

[0125] 2. Neural Network Model

[0126] (1) Model framework

[0127] The stability domain approximate calibration method proposed in this paper uses a neural network time series model to predict the trajectory of future phase points. There are many types of neural network models, among which the NARX dynamic neural network is a simple neural network with memory capabilities. Its original architecture can be easily and effectively applied to the prediction of univariate time series, and therefore has been widely used to solve problems related to time series prediction.

[0128] In the phase point trajectory prediction problem, first, the phase point trajectory is a time series. Second, the variable in this problem is the step data, and the target variable is the phase point position data. It is a single variable problem. Therefore, the NARX neural network model is suitable for the phase point trajectory prediction problem.

[0129] The NARX neural network model used in the present invention is:

[0130] (1.4)

[0131] That is, the output predicted by the neural network is only related to the historical value of the input. The structure of the neural network is as follows Figure 4 As shown in Figure 1, it mainly consists of input layer, hidden layer, output layer and input and output delay.

[0132] like Figure 4 As stated, It is the predictor variable input of the neural network. In the present invention, the step length data is substituted, i.e., the first row of the phase point trajectory data matrix; is the response output of the neural network. In the present invention, the position data of the phase point in each dimension in the phase space is substituted, that is, the second to the second dimension of the phase point trajectory data matrix. n In actual calculations, each dimension of the phase point position data is trained once to obtain the corresponding neural network model.

[0133] (2) Model effectiveness

[0134] Continue to use Figure 2 The numerical examples show the effectiveness of the NARX neural network model.

[0135] Will Figure 3 Middle (b) Middle Dimensionally and The expanded data in the dimension are put into the NARX neural network with 10 hidden layers and 100 hidden layers respectively to train the respective neural network models. Then the 51 data points from 730 to 780 are used for testing respectively. The test results are as follows Figure 5 and Figure 6 shown.

[0136] As can be seen, the MSE (Mean Square Error) values ​​during model training, validation, and testing were close to 0, and the R values ​​were all 1, indicating that the training resulted in a relatively ideal model. Further testing showed that the model's predicted output values ​​were very close to the target values, confirming the effectiveness of the NARX neural network model in phase point trajectory prediction.

[0137] 3. Stable domain calibration model

[0138] (1) Calibration data and window size setting

[0139] from Figure 1 As can be seen, the input of the stable domain calibration model is a calibration data set composed of a portion of the original phase point trajectory data intercepted through the observation window and the predicted data obtained under the prediction window. The number of data in the calibration data set depends on the size of the observation window and the prediction window. Reasonable window size setting can minimize the error of the stable domain approximate calibration, so it is very important. The prediction window size is given below. and observation window size How to set it up.

[0140] The size of the prediction window is mainly determined by the prediction ability of the time series prediction model. The NARX neural network model used in this method recommends that the number of future prediction points is 5, so the default value of the prediction window size in this paper is .

[0141] The setting of the observation window size is related to the original data of the phase point trajectory. Assume that the starting position and the ending position of the observation window are and Since the observation window only captures the last data, so the end position of the observation window .

[0142] When the phase point trajectory changes very slowly, it means that the network system is very close to a stable operating state, and the slowly changing phase point trajectory data can be used to calibrate the stability domain. Based on this idea, the following method is given to determine the starting position of the observation window: method.

[0143] make If there is such , and satisfy the three conditions in formula (1.5)

[0144] (1.5)

[0145] So, If this Does not exist, then .

[0146] in, It is the change threshold, which needs to be set in advance; is the minimum value of the observation window, which is set to ; is a differential sequence that stores the information of the degree of phase point change, and there is

[0147] (1.6)

[0148] In practice, the starting position of the observation window is the first step position after which the phase point's change in all dimensions of phase space is less than the change threshold. If this position does not exist, it indicates that the raw data of the phase point trajectory has not yet reached the stability requirement specified by the change threshold. In this case, if it is determined that the change threshold cannot be changed or more phase point trajectory data cannot be obtained, the starting position of the observation window is set to the minimum observation window.

[0149] (2) Calibration method

[0150] Assume that the obtained calibration data matrix is ,in

[0151]

[0152] make , Then the stability region of the approximate calibration is The central vector of is:

[0153] ;

[0154] The radius vector is:

[0155] .

[0156] The case study object of this invention is a multi - UAV formation network system that performs formation flight tasks at a fixed cruise altitude as Figure 7 shown. This network system consists of 9 homogeneous rotor UAVs, which are required to complete the formation of a "cross" shape and maintain this formation to fly along the planned trajectory.

[0157] This multi - UAV network system adopts a "leader - follower" formation strategy. The No. 1 UAV in the leader position is the leader of the entire network system, the No. 2 - 5 UAVs are the first - level followers, and the No. 6 - 9 UAVs are the second - level followers. At the beginning of the mission, the 9 homogeneous rotor UAVs take off vertically from the ground synchronously to the cruise altitude, and then form the required formation shape by moving in the xoy plane at this altitude. Then, the No. 1 UAV receives the path planning result and flies along the planned path according to the path - tracking strategy. At the same time, the No. 2 - 5 UAVs obtain the real - time position information of the No. 1 UAV and maintain the corresponding relative distance; while the No. 6 - 9 UAVs obtain the position information of the adjacent first - level followers at the same time and maintain the corresponding relative distance. Under the above strategy, this multi - UAV network system realizes the overall formation flight.

[0158] The flight mission of the UAV formation can be divided into two stages, namely the formation stage and the formation - flight stage.

[0159] Stage 1: Formation stage

[0160] The initial position coordinates of each UAV in the take - off area are given. In the formation stage, the UAVs will fly from their respective initial positions to the formation positions, so that the entire cluster forms a stable "cross" shape in the formation area.

[0161] The UAVs that arrive at the formation positions in advance will hover and wait until all 9 UAVs reach the designated formation positions, and then the entire cluster will execute the flight mission of the second stage.

[0162] Stage 2: Formation - flight stage

[0163] When the cluster completes the formation, the No. 1 UAV will fly according to the planned path, and other UAVs will fly according to the following rules, and the entire cluster realizes the task of flying along the planned path in a "cross" shape.

[0164] The two stages of the mission are as Figure 8As shown in the figure. The most important task requirement of this UAV formation network is to fly as a "square" formation along the planned path as a whole. In order to describe the task completion effect, two questions need to be answered during the overall flight of the network: (1) Whether the formation of the UAV network can always maintain the specified shape; (2) Whether the UAV network can always fly on the planned path. The first question focuses on the formation state of the UAV formation network, and the second question focuses on the position state of the UAV formation network. For the formation state and position state, this case respectively proposes to use the formation deformation quantity and the position offset quantity for quantitative measurement. According to the above analysis idea, the corresponding state analysis table of this case is shown in Table 2.

[0165] Table 2 State Analysis Table of UAV Formation Network

[0166]

[0167] In the first stage of the task, the UAV formation network needs to complete the teaming task. At this time, only the formation state of the network needs to be concerned; while in the second stage of the task, it is required that the UAV formation network not only maintains the formation but also flies along the planned path. At this time, both the formation state and the position state of the network need to be concerned. Therefore, in the teaming stage, the phase space of this UAV formation network is a 1D space spanned by the vector elements representing the formation state. In the formation flight stage, the phase space is a 2D space spanned by the vector elements representing the formation state and the vector elements representing the position state, as Figure 9 . Since the phase vector spaces in different stages are different, the initial stable domains of the two stages need to be calibrated separately. Denote the initial stable domain of the first stage as , and that of the second stage as . The present invention is applicable to the approximate calibration of the initial stable domain of the second stage.

[0168] Step 1. Obtain the original phase point trajectory data.

[0169] Let the simulation model continuously run for 9000 simulation steps in the second stage to obtain the phase point trajectory data and form a matrix with a size of .

[0170] Step 2. Data augmentation

[0171] Take the default value of the data augmentation threshold as 10000. Since the number of columns of the original data matrix is less than this threshold (9000 < 10000), data augmentation is required. The number of data to be added between each column of data is

[0172]

[0173] According to the linear Gaussian white noise data expansion model of formula (4.1), a data point is added between each column of the original phase point trajectory data matrix. The original phase point trajectory and the phase point trajectory after data expansion are as follows: Figure 10 shown.

[0174] Step 3. Phase point trajectory prediction

[0175] Set the prediction window size to The NARX neural network models for the formation shape variable trf time series and the position offset dvt time series were trained respectively, and the trained models were used to predict the data values ​​of the next 10 points. The prediction results are shown in Table 3.

[0176] Table 3 Predicted values ​​of formation shape and position offset

[0177]

[0178] The five groups of predicted values ​​of formation shape variables and position offsets corresponding to simulation steps 9001, 9002, 9003, 9004 and 9005 are taken out as predicted data.

[0179] Step 4. Stable Region Approximate calibration of

[0180] Set the change threshold to The starting point of the observation window determined by the method of formula (1.5)-(1.6) is the 7880th simulation step, that is, the size of the observation window is Combined with the five sets of predicted data in Table 3, the phase point trajectory data matrix from the 7880th to the 9055th simulation steps is obtained.

[0181] Get the minimum value in the second row of the merged matrix , maximum value ; Get the minimum value in the third row of the merged matrix , maximum value The stability domain of the approximate calibration is The components of the central vector are

[0182]

[0183] The components of the radius vector are in the form

[0184]

[0185] Path length

[0186]

[0187] The above is a description of the embodiments of the present invention. The above description of the disclosed embodiments will enable professionals in the field to implement or use the present invention. Various modifications to these embodiments will be apparent to professionals in the field. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but should conform to the widest scope consistent with the principles and novel features disclosed herein.

[0188] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0189] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0190] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0191] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0192] In a typical configuration, a computing device includes one or more processors (CPUs), input / output interfaces, network interfaces, and memory.

[0193] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0194] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can be implemented using any method or technology for information storage. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase-change RAM (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices, or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory computer-readable media, such as modulated data signals and carrier waves.

Claims

1. A method for calibrating the phase point stability domain of a UAV network system prediction model, characterized in that: The method comprises the following steps: 1) Collect the original trajectory data of multi-dimensional phase points in phase space within continuous steps D , and stored in a matrix format of "the first line is the step sequence, and the remaining lines are the position coordinates of each dimension"; 2) determining whether the number of columns of the original data matrix is ​​less than a preset data expansion threshold; if so, performing data expansion processing; otherwise, skipping the processing; 3) In the data expansion process, several new data points are uniformly inserted between adjacent step data, and Gaussian white noise is introduced into the inserted data to generate an expanded data matrix ,make ; 4) Predict window size based on preset , input the original or expanded data matrix into the NARX dynamic neural network time series model, and obtain the The prediction matrix composed of prediction data points ;5) According to the preset observation window size , after intercepting the original data matrix Column data, forming the observation matrix ; 6) Combine the observed data and predicted data into a calibration data set , input the stability domain calibration model, and output the center vector and radial quantity approximation of the target stability domain; In step 1), it is assumed that the time span of the acquired data is sp The dimension of the phase space is n, so the acquired phase point trajectory data is stored in (n+1)× sp The first row of the matrix is ​​the step sequence , lines 2 to 3 The position coordinates of each dimension of the phase point under the corresponding step length are placed in the rows in sequence; in the step 2), when the number of columns of the original data matrix of the phase point trajectory is less than When ; The original data matrix needs to be expanded; the data expansion threshold Not less than 10,000, and expansion is triggered only when the original data is insufficient to train a neural network that meets the accuracy requirements; In step 3), the original data matrix of the phase point trajectory is expressed as ; in, is the step vector, and its components are recorded as: ， ps i The phase point is s i The temporal position vector in dimension, i=1,2,...,n, has its components recorded as: ; When the data expansion conditions are met, p j and p j+1 between and ps i，j and ps i，j+1 Increase between ( x -1) data point, ， ； Recorded in sequence and , where the data points and The formula for determining the value of is: ， ； in, , The multiple by which the data is expanded; is a random Gaussian white noise with a standard deviation The value of is: ； is a coefficient related to the dispersion of noise intensity.

2. The method for calibrating the phase point stability domain of the UAV network system prediction model according to claim 1 is characterized in that: The NARX neural network model described in step 4) is: ； Where y(t) is the system output at the current time t; y(td) is the historical output value sequence of the system at the previous d times; f(.) is a nonlinear mapping function learned by the neural network model; The NARX neural network consists of an input layer, a hidden layer, an output layer, and input and output delays. The input of the NARX dynamic neural network is a step sequence, and the output is the position of phase points in each dimension. The number of hidden layers can be set between 10 and 100 layers according to the accuracy requirements.

3. The method for calibrating the phase point stability domain of the UAV network system prediction model according to claim 1 is characterized in that: In step 5), the starting position and ending position of the observation window are and ; Since the observation window only captures the last Data, the end position of the observation window ; Observation window starting position The method is as follows: If there is such j , and satisfy the following three conditions at the same time: ； So, If this Does not exist, then ; in, is the change threshold, is the minimum value of the observation window, ; is a differential sequence that stores the information of the degree of phase point change, and there is ， 。 4. The method for calibrating the phase point stability domain of the UAV network system prediction model according to claim 3 is characterized in that: In step 6), the obtained calibration data matrix is ​​assumed to be ,in: ， ； make , Then the stability region of the approximate calibration is The central vector of is: ； The radius vector is: 。 5. The method for calibrating the phase point stability domain of the UAV network system prediction model according to claim 1 is characterized in that: This method is applicable to any of the following three types of stable domains: a) The initial stable region after the system reaches steady state; b) The farthest stable region where the system is affected by the disturbance impulse; c) The stable region that the system re-enters during the recovery phase after the disturbance stops.

6. A UAV network system phase point stability domain approximate calibration system, characterized by: The system implements the method for calibrating the phase point stability domain of the UAV network system prediction model according to any one of claims 1 to 5, comprising: a) a data acquisition unit, used to collect and matrix the original trajectory data of the phase point; b) a data expansion unit, configured to perform linear Gaussian white noise expansion when insufficient original data is detected; c) prediction unit, configured with a NARX dynamic neural network, for generating future prediction data; d) a window interception unit, used to intercept the tail segment of the original data according to the observation window size; e) Calibration unit, used to combine the observed data with the predicted data and output the approximate values ​​of the center vector and radial quantity of the stability domain.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that when the program is executed by a processor, the computer implements the method for calibrating the phase point stability domain of the drone network system prediction model according to any one of claims 1 to 5.

8. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the method for calibrating the phase point stability domain of the drone network system prediction model described in any one of claims 1 to 5 is implemented.

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