Unmanned aerial vehicle network system phase point trajectory simulation modeling method and system, medium and software product

Abstract

The invention relates to the technical field of unmanned aerial vehicle cluster control, in particular to an unmanned aerial vehicle network system phase point trajectory simulation modeling method and system, a medium and a software product. The method comprises the steps of system analysis and task analysis, interaction rule matrix construction, state analysis and phase vector space construction, stability domain approximate calibration, limit impulse measurement, disturbance impulse injection simulation and data segmentation and transition area marking, and the closed-loop process from modeling to interference evaluation is achieved. Trajectory prediction is carried out through an NARX neural network, Gaussian white noise expansion and multi-round simulation are combined, stability domain approximate calibration and limit impulse judgment are achieved, and a structured trajectory data set is automatically output. According to the method, the modeling precision, the simulation efficiency and the system safety are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of unmanned aerial vehicle cluster control, and particularly relates to a method and system for simulating and modeling a phase point trajectory of an unmanned aerial vehicle network system, a medium and a software product. BACKGROUND

[0002] With the improvement of single unmanned aerial vehicle (UAV) performance and the continuous decline in cost, multi-vehicle formation is rapidly becoming a mainstream technical solution for search and rescue, disaster monitoring, material distribution, air communication relay, and confrontation exercises. Compared with traditional single unmanned aerial vehicles, multi-UAV network systems (Multi-UAV Network System, referred to as "unmanned aerial vehicle network system") have significant advantages in coverage area, task redundancy, robustness, and real-time response. However, the increase in the number of nodes and the complexity of cooperative behavior also brings new challenges in modeling, simulation, and control.

[0003] Existing research generally uses a cooperative control model based on graph theory or a distributed consensus model to describe the network topology and formation keeping logic. For example, the Vicsek model and its improved Boids model can produce swarm behavior with simple speed matching, position keeping, and collision avoidance rules; consensus algorithms describe global convergence characteristics through Laplacian matrices; and formation control often uses leader-follower, virtual structure, or behavior hierarchy to build mathematical models. These methods can reproduce group motion at the macro level, but they are difficult to uniformly depict multi-dimensional dynamic properties such as task phase switching, communication link failure, and node performance differences.

[0004] To address the above shortcomings, in recent years, scholars have begun to introduce multi-agent system (MAS) modeling and complex network theory, treating unmanned aerial vehicle individuals as attribute nodes and communication or perception links as directed / undirected edges, and using switched graph systems to describe task phase jumps. However, in existing work, "node attributes" usually only include a small number of continuous variables such as position, velocity, or power, lacking systematic management of discrete or semi-discrete variables such as member identity, real-time load, and sensor state; on the other hand, the network's overall connectivity matrix, connectivity state matrix, and interaction rule set are often statically assumed in algorithm derivation, ignoring the phased rule changes and intelligent decision logic in actual tasks.

[0005] In addition, in the theory of dynamical systems, a "state point" refers to the position of a system in a state space at a certain time; the curve formed by the evolution of the state point over time is called a "state point trajectory". For a UAV network, its state space can be high-dimensional, with tens or even hundreds of dimensions, and its trajectory contains comprehensive information about topological changes, node interactions, and external disturbances. Traditional research focuses on: 1. Linear state space model: approximate linearization for small range motion, stability analysis using pole distribution or state feedback; 2. Lyapunov function and invariant set: construct global or local stability domain criteria, but it is difficult to give an analytical expression in the case of discrete jumps or strong coupling of nonlinear systems; 3. Monte-Carlo simulation: evaluate the collision probability and convergence time through large-scale random sampling, but there is a lack of precise definition of "first boundary crossing" or "trajectory divergence threshold".

[0006] In recent years, data-driven modeling (such as autoregressive neural networks, time convolution networks, NARX networks, etc.) has been used to predict the future state of the system; Gaussian process regression and deep generative models are used to capture complex nonlinearities that are not explicitly shown. Although the prediction accuracy has been improved, how to combine the prediction results to quickly calibrate the stability domain boundary is still a problem to be solved: existing methods rely on manual thresholding or empirical settings, and lack a unified approximate calibration process.

[0007] In addition, multi-UAV tasks are often exposed to sudden wind gusts, GPS lock loss, link congestion, and even node failure disturbances, making researchers begin to focus on the system's limit bearing capacity for instantaneous impulse or sustained disturbance. Existing work usually adopts: 1. Incremental intensity scanning: gradually increase the disturbance intensity, record the changes in system performance indicators (such as average deviation, time consumption); 2. Robust control margin: based on μ-analysis or H∞ norm to obtain the worst-case gain, but it is difficult to consider discrete topology switching at the same time; 3. Limit load experiment: directly apply limit deflection or torque in hardware or simulation environment to test the system collapse threshold.

[0008] Such methods either only give a "bear / collapse" binary conclusion, or have a huge computational load and lack a systematic explanation of the coupling relationship between disturbance intensity and action step. There is no unified framework to automatically determine the limit impulse in one simulation process and further generate multi-round disturbance injection scripts to systematically evaluate the recovery performance and stability domain migration. SUMMARY

[0009] In order to solve the above technical problems, the unmanned aerial vehicle network system phase point trajectory simulation modeling method aims to provide an end-to-end closed loop process from system analysis, rule matrix construction, state analysis, stable domain approximation calibration to limit impulse determination and disturbance injection simulation, and realize high-quality, structured trajectory data set output through data segmentation and transition zone marking; realize simulation-control-evaluation integration, and provide a new technical means for robustness design, verification and real-time adjustment of multi-unmanned aerial vehicle system.

[0010] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows: An unmanned aerial vehicle network system phase point trajectory simulation modeling method, the method comprising the following steps: 1) System analysis and task analysis: dividing members of the target unmanned aerial vehicle network, collecting attributes, obtaining a static attribute model composed of member attribute set and system attribute set; 2) Interactive rule matrix construction: according to the task stage, the member interaction relationship of each stage is described, numbered and coded to obtain the interactive rule matrix of the corresponding stage; 3) State analysis: based on task stage division, the state variables capable of measuring network performance are extracted and their types are determined, and then the phase vector space is formed in each stage; 4) Stable domain approximation calibration: the original data of the phase point trajectory is expanded by linear Gaussian white noise, the NARX neural network time series model is used to predict the future trajectory of the phase point, and the stable domain center vector and radial vector are calculated combined with the observation window data; 5) Limit impulse determination: for the predetermined disturbance type, the determinator uses the strength decreasing-step increasing principle to obtain the maximum tolerable step, and outputs the limit impulse after determining the linear characteristic; 6) Disturbance impulse injection simulation: generate a disturbance strength-step length matrix within the limit impulse range, fix the initial state of the network system model and run to stable, record the phase point trajectory after each disturbance injection until the termination threshold is met; 7) Data segmentation and transition zone marking: according to the phase point-stable domain distance and threshold condition, the starting point and ending point of the transition zone are automatically marked and the labeled phase point trajectory data set is output, which is used for subsequent modeling or algorithm training.

[0011] As a preferred, the member attributes in step 1) include identity attributes, real-time information attributes and performance attributes, and the system attributes at least include interactive rule number information matrix, connectivity information matrix and connectivity state matrix.

[0012] As a preferred, the static attribute model static attribute model mdl SA is a member attribute set M and a system attribute setS a pair of tuples, i.e.: , , ; wherein the meaning of each symbol is: n m the number of member nodes in the network system; n ma the number of member attributes of the ith member node; n sa the number of system attributes of the network as a whole; M i the set of member attributes of the ith member node; o i k the kth element in the set of member attributes of the ith member node; s j the jth element in the set of system attributes.

[0013] As a preference, the network system is described by a pair of tuples mdl NS , which is composed of a static attribute model of the network system mdl SA and its interaction rule matrix RL n×n , i.e.: mdl NS ( mdl SA , RL n×n ); wherein the element in the ith row and jth column of RL n×n represents the set of attribute state change rules of the ith member node in the network system upon receiving the information from the jth member node. i r j r i r j r

[0014] As a preference, the element of the interaction rule matrix in step 2) is a set of rule numbers, and different interaction rule matrices are used in different task stages and the matrix replacement is triggered by stage switching.

[0015] As a preference, the state analysis in step 3) comprises the following steps: 3.1) listing each task stage of the network system in time sequence according to the task analysis result; ​​​​3.2) for each task stage, abstract the subtask requirements of the stage; 3.3) according to the subtask requirements, qualitatively describe the network state capable of reflecting the task completion situation; 3.4) for each network state, specify at least one scalar state variable for quantitatively describing the network state; the scalar satisfies that any two state variables in the same stage are independent of each other; 3.5) classify the state variables as continuous or discrete, and record them in the state analysis table; 3.6) fill in the task stage, task requirement, network state, state variable and its type into the state analysis table in turn, and construct the phase space according to the specific state variable.

[0016] As preferred, the method for approximating the stable domain in step 4) comprises the following steps: 4.1) collect the original trajectory data of the multi-dimensional phase points in the phase space within the continuous step length, and store them in the matrix format according to "the first behavior as the step sequence, and the rest as the dimensional position coordinates"; 4.2) judge whether the column number of the original data matrix is less than the preset data expansion threshold, if yes, execute the data expansion processing, otherwise skip the processing; 4.3) in the data expansion processing, uniformly insert a plurality of new data points between the adjacent step length data, and introduce Gaussian white noise to the inserted data to generate an expanded data matrix; 4.4) according to the preset prediction window size, input the original or expanded data matrix into the NARX dynamic neural network time series model to obtain a prediction matrix composed of prediction data points; 4.5) according to the preset observation window size, cut off the data in the rear columns of the original data matrix to form an observation matrix; 4.6) combine the observation data and the prediction data into a calibration data set, input it into the stable domain calibration model, and output the approximate values of the center vector and the radial vector of the target stable domain.

[0017] As preferred, the method for determining the limit impulse in step 5) comprises the following steps: 5.1) obtain the value range identifier of the interference intensity flg1 and the continuous characteristic identifier of the interference intensity flg2 , and set the determination times c ; 5.2) according to the logical combination of flg1 and flg2 , use the interference intensity extraction module to determine a group of interference intensity data, the interference intensity is sorted in descending order according to its absolute value of system disturbance; 5.3) Following the principles of decreasing intensity and increasing step size, use the measurement module to perform simulation experiments for each interference intensity and iteratively determine the maximum action step size that keeps the system stable in the phase space state dimension; 5.4) All interference intensity data and the corresponding maximum action step length data are input into the linear characteristic judgment module to determine whether the reciprocal absolute values ​​have a linear relationship; 5.5) If the linear relationship holds, the average value of the product of each interference intensity and the maximum step length is used as the limit impulse output; if not, the minimum interference intensity and the maximum step length product is output as the limit impulse value.

[0018] Preferably, the method for simulating the injection of disturbance impulses in step 6) includes the following steps: 6.1) Set the number of injections: preset a positive integer cnt , represents the number of interference injection rounds to be carried out in this experiment; 6.2) Generate interference parameter matrix: Construct a two-dimensional numerical matrix D σ , where the first row is the interference intensity of each round, and the second row is the corresponding action step length; 6.3) Prepare the network system model: Fix the initial state of the network system model, start the model, and let it run to a stable state; ensure that the network system model remains in the same stable state each time interference is injected; 6.4) The first part of the matrix of the injected interference intensity data i Column value: Set the disturbance intensity in the disturbance impulse injection module of the model to σ m , the action duration is sp m , so that the simulation model continues to run; 6.5) Record and observe phase point trajectory data: Monitor the changes of phase points in the phase vector space in real time in the phase point trajectory observation window; when it is observed that the change of phase point position is continuously sp end less than the termination threshold within the step e end When , terminate the network operation and go to step 6; otherwise, continue to execute step 5; 6.6) Save the phase point trajectory data of the mth injection experiment: Save the phase point trajectory data of the ith perturbation impulse injection experiment as (n+1)× spr m The numerical matrix of D trcm ,in spr m is the number of simulation steps from the time the disturbance is injected to the time it is fully recovered to the stable operating state; 6.7) Obtain perturbation impulse injection experiment data: obtain all numerical matrices from cnt perturbation impulse injection experiment D trcm ( m =1,…, cnt ) are saved into cell array D eo for subsequent data processing.

[0019] Further, the present application also discloses a UAV network system phase point trajectory simulation modeling system, which realizes the method and comprises: A) attribute modeling module, used for performing system analysis and task analysis, and generating a static attribute model; B) rule management module, used for performing natural language description, numbering, coding and establishing an interaction rule matrix on the interaction rules; C) state space construction module, used for extracting state variables, determining types and generating phase vector spaces of each stage; D) stable domain calibration module, used for expanding, predicting and outputting stable domain center vectors and radial vectors on the basis of the original phase point trajectory data; E) limit impulse measurement module, comprising an interference intensity extractor, a measurer and a linear characteristic determiner, and used for outputting limit impulses of each interference in the phase vector space dimension; F) impulse injection simulation module, used for generating an interference intensity-step length matrix according to the limit impulses, performing multiple rounds of simulation and collecting phase point trajectories; G) data processing module, used for marking and segmenting the phase point trajectories obtained through simulation, and forming a searchable data set; H) interaction interface module, used for providing phase point trajectory data and stable domain information to an upper design platform or a control algorithm.

[0020] Further, the present application also provides a computer readable storage medium, which stores a computer program, and the program enables a computer to realize the method when executed by a processor.

[0021] Further, the present application also provides a computer program product, which comprises a computer program or instructions, and the computer program or instructions realize the method when executed by a processor.

[0022] The present application has the following technical effects due to the adoption of the above technical scheme: 1. End-to-end integrated framework improves modeling integrity and accuracy The static attribute model and the interaction rule matrix are combined to uniformly describe continuous flight parameters, discrete identity / task attributes and network connection information in a single data structure, and heterogeneous nodes and stage switching rules are synchronously managed. Model errors (RMSE compared with high-fidelity physical simulation) are reduced by more than 20% on average; in the cross-stage switching scene, the maximum deviation of formation keeping is reduced by about 18%.

[0023] 2. Rapid approximation calibration of stability domain, efficiency and precision A coupling scheme of linear Gaussian white noise expansion and NARX time series prediction is adopted, and the approximate values of the stability domain center vector and the radius vector can be output in one inference without artificial experience threshold. In a typical 10-dimensional phase space test, the calibration error is controlled within ± 3% (relative to the Monte-Carlo true value), and the calculation time is shortened by 35%, ensuring the real-time performance of the simulation-control closed loop.

[0024] 3. Significant reduction in simulation cost by adaptive determination of limit impulse The joint search of "intensity decrease-step increase" and the self-checking algorithm of linear correlation can reduce 50-65% of simulation rounds while maintaining 1% accuracy. The limit impulse criterion directly outputs the quantitative value of the disturbance intensity-step product, providing executable boundaries for control law and safety margin design.

[0025] 4. Improved data quality by disturbance impulse injection and transition zone intelligent labeling The disturbance intensity-step matrix is generated and injected in one key, and the total time of multiple experiments is shortened by 40%; the trajectory data completely covers the whole process of "disturbance-transition-recovery". Combined with the automatic labeling of the transition zone based on the phase point-stability domain distance threshold, the label consistency rate (compared with manual labeling) reaches 97.6%, greatly improving the training efficiency of subsequent machine learning algorithms.

[0026] 5. Significant improvement in comprehensive robustness and safety performance The limit impulse quantitative result and stability domain migration analysis are coordinated to provide quantitative input for real-time fault tolerance, emergency decision and adaptive control. In the case of communication failure and wind array composite disturbance, the formation recovery time is reduced from 12.4s to 7.9s, and the average energy consumption is reduced by 11%; the task success rate is improved by 16-20%.

[0027] In summary, the present application not only realizes the "attribute-rule-state-trajectory" closed-loop modeling and efficient data generation of unmanned aerial vehicle network, but also significantly improves the simulation efficiency, evaluation accuracy and system robustness in engineering practice, providing practical technical support and quantitative evaluation means for the design, verification and online optimization of multi-unmanned aerial vehicle cluster. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1Basic flowchart for modeling the invention.

[0029] Figure 2 For the relationship between the key links in the modeling method.

[0030] Figure 3 For the task execution process chart of 3-UAV transport formation.

[0031] Figure 4 Step flowchart for constructing the interaction rule matrix.

[0032] Figure 5 Interaction rule matrix framework for 3-UAV transport formation example.

[0033] Figure 6 Matlab code example of interaction rule matrix and part of rule dictionary for 3-UAV transport formation example.

[0034] Figure 7 Method flowchart for stable domain approximation calibration.

[0035] Figure 8 Method flowchart for limit impulse determination.

[0036] Figure 9 Method flowchart for disturbance impulse injection simulation.

[0037] Figure 10 UAV network system performs formation flight task.

[0038] Figure 11 For cnctA and cnctS value examples, Figure 11 in (a) cnctA default value of the matrix, (b) cnctS value example of the matrix.

[0039] Figure 12 Two-stage diagram for UAV formation flight task.

[0040] Figure 13 Interaction rule matrix of UAV formation network in two task stages; Figure 13 (a) Interaction rule matrix in the team formation stage, (b) Interaction rule matrix in the formation flight stage.

[0041] Figure 14 UAV formation network simulation running process display; Figure 14 (a) Initial take-off area hovering, (b) In the team formation stage, (c) Complete team formation, (d) Enter the formation flight stage, (e) Fly according to the planned trajectory, (f) Complete trajectory after reaching the end point.

[0042] Figure 15 Desired position vector and actual position vector.

[0043] Figure 16 Phase space for different mission phases.

[0044] Figure 17 Wind intensity diagram.

[0045] Figure 18 Phase point trajectory for two mission phases. Figure 18 (a) Formation phase phase point trajectory, (b) formation flight phase phase point trajectory.

[0046] Figure 19 Formation phase phase point trajectory with wind disturbance injection.

[0047] Figure 20 Formation flight phase phase point trajectory with wind disturbance injection.

[0048] Figure 21 Injecting single UAV communication failure stress by setting connectivity information matrix.

[0049] Figure 22 Formation flight phase phase point trajectory with UAV communication failure stress injection disturbance. DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments will be described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work are within the protection scope of the present application.

[0051] As shown in Figure 1 A UAV network system phase point trajectory simulation modeling method includes three basic contents: first, network system model construction based on system analysis and mission analysis, second, phase vector space establishment based on state analysis, and third, disturbance impulse injection module establishment based on interference analysis. The goal of modeling is to build a phase point trajectory observation window. The relationship between the contents in the process is shown in Figure 1 .

[0052] The modeling process includes four "analyses", namely, system analysis to clarify network structure and properties, task analysis to divide mission phases, state analysis to define network states, and interference analysis to sort out interference types and strengths. Among them, the goals of system analysis and task analysis are to establish a network system model, the goal of state analysis is to build a network phase vector space, and the goal of interference analysis is to integrate a disturbance impulse injection module. The results of the four analyses are related to each other, with the acquisition of network system phase point trajectory as the final goal.Figure 2 The outputs of the analyses of the modeling process and the relationships between them are summarized.

[0053] To explain in detail Figure 1 the content, an example of a 3-UAV transport formation consisting of three UAVs is introduced. It is assumed that the UAV formation is required to complete a transport task, and the three UAVs constituting the formation must cooperate during the execution of the task and maintain a "triangle" formation at all times. At the same time, they must avoid obstacles during the transport process. Figure 3 The process of the UAV formation executing the entire transport task is shown.

[0054] The following will rely on the 3-UAV transport formation example to explain in detail the establishment method of the network system model and the phase point trajectory observation window in the modeling process.

[0055] I. Establishment method of the network system model The primary task of modeling is to establish the network system model of the research object. According to Definition 2, the network system model contains two key elements, namely the static attribute model of the network system and the rule matrix composed of the interaction rules between the members of the system. Therefore, when establishing the network system model of the research object, it is necessary to complete the construction of the static attribute model and the interaction rule matrix respectively.

[0056] Definition 1 (Static Attribute Model) The static attribute model is a binary tuple consisting of a member attribute set M and a system attribute set S, i.e.: mdl SA , , , ; wherein the meanings of the symbols are: nmthe number of member nodes in the network system; nma the number of member attributes of the i-th member node; nsa the number of system attributes of the network as a whole; Mi the member attribute set of the i-th member node; oik the k-th element in the member attribute set of the i-th member node; sj the j-th element in the system attribute set; Definition 2 (Network System Model) The network system is described by a binary tuple mdl NS , which is composed of the static attribute model mdl mdl SA of the network system and its interaction rule matrix RL n×n , i.e.: mdl NS =(mdl SA, RL n×n ); wherein RLn×n the first column of the matrix represents the i i r the first row of the matrix represents the i j r th member node in the network system, and the elements in the second column represent the set of attribute state change rules of the i r th member node after receiving the information of the i j r th member node. In particular, the elements on the diagonal of the matrix represent the attribute change rules of a certain member node itself, which do not require information provided by other member nodes. n×n

[0057] 1. Construction of static attribute model A clear system understanding is the basis for the construction of the static attribute model of the network system. In order to scientifically and efficiently understand the research object, a comprehensive system analysis of the network system is needed. System analysis is divided into two levels, the first is structure analysis, and the second is attribute analysis.

[0058] In structure analysis, first, the members that make up the network system are clarified, and the total number of members is determined. Members that may have the same attribute set are classified into one category. Second, the interaction activities between members that can be encountered are described in natural language and listed, and preliminary qualitative analysis of the interaction rules is completed.

[0059] In attribute analysis, the attributes of each category of members and the system as a whole are refined from identity, real-time information, and performance to form an attribute set. Among them, the connotations of identity attribute, real-time information attribute, and performance attribute are as follows: (1) Identity attribute: attribute that distinguishes member identity; (2) Real-time information attribute: attribute that represents member real-time state information; (3) Performance attribute: attribute that represents a certain characteristic and ability of the member.

[0060] Example: System analysis of 3-UAV transport formation example First, structure analysis is performed. The number of formation members is 3. Assuming that the three UAVs are of the same model, the three members of the system have the same attribute set, so they belong to the same category of members. The formation adopts the "long machine-squire" formation strategy, so the most important interaction behavior between members is that the follower updates its movement direction and speed in real time according to the real-time position information feedback by the leader and the specified relative position.

[0061] ​Secondly, attribute analysis is performed. The identity attribute of each member UAV is its name, such as "leader", "follwer_a" and "follwer_b" respectively. Their real-time position, real-time velocity and real-time acceleration are real-time information attributes that need to be concerned. The performance attributes that need to be considered can include the maximum allowed acceleration, the maximum sensing range, etc. The attribute of the whole formation system can be the connectivity state among the three member UAVs, which is a real-time information attribute.

[0062] The attribute set of the members and the attribute set of the system obtained by attribute analysis together constitute the static attribute model. The static attribute model is a continuously open model. At any stage of modeling, newly refined attributes can be added at any time, and attributes that are determined to be unnecessary can be deleted at any time.

[0063] 2. Construction of interaction rule matrix Generally, the construction of the interaction rule matrix includes four steps: task analysis, matrix framework construction, rule description, and rule coding. Rule coding needs to use the results of attribute analysis, as shown in Figure 4 .

[0064] (1) Task analysis Interaction rules are the product of specific task scenarios, so the construction of the interaction rule matrix of the network system must be based on reasonable task analysis.

[0065] The target system may need to go through multiple stages to complete a task, and different combinations of interaction rules may be needed to complete the sub-tasks of different stages. Therefore, the first necessary step of task analysis is to clearly define all the stages that the target system will go through in the task, and to reasonably divide these task stages. For example, in the example of the 3-UAV formation system, the entire transportation task can be divided into two main stages: formation assembly stage (stage 1) and formation flight stage (stage 2). In stage 1, the basic sub-tasks of the three UAVs are to take off from their respective parking positions and form a triangular formation. In stage 2, the sub-task of the whole system is to cruise to the destination in a triangular formation, and to avoid collisions with obstacles along the way.

[0066] (2) Interaction rule matrix framework construction and rule description After completing the stage division, the number of members involved in each stage needs to be determined. Then, a square matrix framework is generated for each stage, with the dimension of the square matrix being the number of participating members in the stage. Finally, the interaction mode between members is described in natural language and filled into the corresponding elements of the square matrix. These square matrices are the prototypes of the interaction rule matrix corresponding to each stage.

[0067] For the example of a 3-UAV transport formation, since all three UAVs will participate in subtasks in two phases, the dimension of the interaction rule matrix in phase 1 and phase 2 is 3. The established matrix framework is as follows: Figure 5 In phase 1, the three drones are required to move from their respective parking positions to the initial formation position without any cooperation. Therefore, they only have their own action rules. rl (1) , and appear on the diagonal position of the interaction rule matrix. In phase 2, the leader drone (leader) will cruise along the obstacle-avoiding route calculated in advance by the path planning center, while the two follower drones (follower_a and follower_b) will track the position of the leader drone in real time and maintain the formation. Therefore, the leader drone will act alone, and the action rule is recorded as rl (2) , is the element of the first row and first column of the rule matrix; the two follower drones must obtain the real-time position of the leader drone to complete the subtask of the formation flight phase, and the action rules they need to follow are recorded as rl (3) , which is the element of the 2nd row and 1st column and the 3rd row and 1st column of the interaction rule matrix, see Figure 5 .

[0068] The above three rules rl (1) 、 rl (2) and rl (3) The natural language description of is shown in Table 1.

[0069] Table 1 Description of the behavioral rules for controlling the formation flight of three UAVs

[0070] (3) Rule encoding Rule encoding involves translating interaction rules from natural language into computer-readable logic code. Specifically, each rule is assigned a numerical number, and each element in the interaction rule matrix is ​​replaced with a set of these numerical numbers. Then, using computer language, each rule is encapsulated into a callable function module and stored in a "rule dictionary." This allows computer programs to access specific rule commands in the rule dictionary (function) using the numerical number of the rule in the interaction rule matrix.

[0071] For example, given the rule rl (1) 、 rl (2) and rl (3)The assigned digital numbers are 1, 2 and 3 respectively. rl (3) A more specific explanation is given by way of example. It is assumed that the follower UAV acquires the real-time position of the leader UAV without time delay. Then the position of the follower UAV at the next time instant is equal to the position of the leader UAV at the current time instant plus the relative distance between the follower UAV and the leader UAV as specified by the formation. Figure 6 A Matlab code example of the above statement is given.

[0072] The process of rule coding is also a process of further dissecting the target system, during which more modeling details may emerge that were not perceived in the previous system analysis and task analysis sessions. Once this happens, it is necessary to add, delete or adjust members or system attributes in the static attribute model to continuously update and optimize the network system model of the target system.

[0073] 3. Method for establishing phase vector space The core of establishing the phase point trajectory observation window is to complete the construction of the network system phase vector space through state analysis. Therefore, reasonable state analysis is the basis for establishing the phase point trajectory observation window.

[0074] The state of the network system is meaningful only in a specific task scenario. For the same network system, the states that need to be concerned are different in different task requirements. For example, for a UAV cluster performing a search task, we pay more attention to the state change of the search result; if we ask the same UAV cluster to perform a transport task, the accuracy and timeliness of the transport may be the states that we pay more attention to. Therefore, the state analysis in the phase point trajectory modeling process is task-oriented state analysis, which needs to be based on the results of task analysis.

[0075] Table 2 State analysis sample table

[0076] The results of task analysis give a clear division of task phases. To use the results of task analysis for state analysis, it is necessary to first clarify the specific task requirements of each phase. For each task requirement, the corresponding network state is described qualitatively. Finally, a quantitative description method is defined for each network state. The present invention provides a sample table as shown in Table 2 to guide state analysis.

[0077] State analysis sample table filling instructions: The state analysis sample table shown in Table 2 contains 5 columns of information. The content of the first column comes from the results of task analysis, and the task phase names are written in this column in chronological order from top to bottom.

[0078] From the second column, comb and fill in the order from left to right, from top to bottom. Among them, the content of the second column is the condensation result of the specific requirements of the network system under each stage sub-task; the content of the third column is the network system state name that can reflect the completion of the task requirements; the fourth column fills in the state variable name corresponding to this network system state; the last column is the judgment result of the continuity of the state variable.

[0079] The state variable source of the fourth column can be a common physical variable or a self-defined variable. Among them, when defining the state variable, the following two conditions should be met: (1) The state variable is defined as a scalar; (2) Multiple state variables in the same stage are independent of each other, that is, state variables cannot be derived from each other.

[0080] Table 3 3-Status analysis table of unmanned aerial vehicle transport formation example

[0081] After completing the state analysis and filling in the state analysis table, construct the phasor space according to the specific state variable. Generally, the number and type of state variables corresponding to each task stage are different, so the phasor space of each task stage is also different, in other words, the phasor space is constructed in units of task stages. The specific construction method is to span the space of each dimension orthogonal corresponding to the state variable of each stage.

[0082] For example, the results of the state analysis of the 3-unmanned aerial vehicle transport formation example are shown in Table 3. As can be seen from the table, there is only one state variable "array shape variable" in the formation system in stage 1, so its phasor space in stage 1 is a one-dimensional space spanned by the array shape variable; similarly, the phasor space in stage 2 is a two-dimensional space spanned by the "array shape variable" and "cluster collision identifier variable".

[0083] 4、Establishment method of disturbance impulse injection module Disturbance analysis is the basis for establishing the disturbance impulse injection module, mainly including two contents: first, determine the disturbance type, second, define the strength of the disturbance.

[0084] 4.1 Determine the disturbance type for state variables When performing disturbance analysis, first, for each state variable, determine the main disturbance type by analyzing the disturbance source. The disturbance source can be combed from two angles of internal and external causes: (1) Endogenous disturbance refers to the disturbance to the state variables of the system caused by the performance constraints, performance degradation and faults of the members or the connection relationship between the members of the network system. For example, for the array shape variable of the 3-UAV transport formation in stage 2, the communication fault between the UAVs can cause the follower UAV to fail to perceive the position of the leader, thereby losing the required formation shape, causing the array shape variable to change. At this time, the communication fault between the 3 UAVs is a kind of disturbance.

[0085] (2) Exogenous disturbance refers to the environmental factors that cause disturbance to the state variables in the running environment of the network system. For example, for all UAV swarm networks running in the airspace of the earth, natural wind power is a non-negligible disturbance; for the UAV formation executing the confrontation task, the enemy's firepower attack is also a typical disturbance.

[0086] 4.2 Definition of disturbance intensity Since the disturbance in the network system phase point trajectory modeling is general, there is no direct and typical physical quantity to represent its intensity many times. For example, the communication fault between the UAVs as an example of the disturbance of the formation in stage 2, there is no physical quantity that can directly describe the degree of its influence. Therefore, after the type of disturbance is determined, the definition of the intensity of each type of disturbance needs to be given to provide a clear measurement method. The basic principle of self-defining the intensity of the disturbance is that the greater the influence of the disturbance on the state variables of the network system, the greater the intensity of the disturbance.

[0087] On the basis of the definition of the intensity of the disturbance, the action intensity and action time of the disturbance on the specific attributes in the network system model are described and coded, that is, the injection of the disturbance impulse is realized, and the establishment of the disturbance impulse injection module is completed.

[0088] For example, in the formation example, the disturbance of the communication fault between the UAVs can be reflected by the system attribute "the connection state between the UAVs": when a UAV has a communication fault, the connection state of the UAV with the other two UAVs changes to "unconnectable". The action time of the communication fault corresponds to the holding time of the "unconnectable" state.

[0089] 5. Approximate calibration of stable domain At present, at least the following three types of stable domains need to be calibrated in the phase point trajectory simulation of the prediction model of the UAV network system: (1) The initial stable domain where the phase point is located after the network system starts to run and reaches a stable state ; (2) The stable domain farthest from the initial stable domain reached by the phase point under the action of the disturbance impulse (The stable domain may be the maximum stable domain, at which time the network system is in a collapsed state); (3) After the action of the disturbance impulse stops, the phase point reenters the stable domain under the recovery mechanism .

[0090] The three types of stable domains of the network system phase point are very clear in some cases and can be obtained through state analysis or theoretical derivation. However, in other cases, the dynamics of the interaction between the nodes of the network system makes it difficult to obtain the accurate values of the center vector and the radius vector of the stable domain, and at this time, a reasonable approximation method is urgently needed.

[0091] In order to solve the problem that the accurate values of the center vector and the radius vector of the stable domain of the network system are difficult to obtain in some cases, the present application proposes a stable domain approximation calibration method. The stable domain calibration model in the method ensures a certain approximation accuracy. Under this accuracy, the deviation of the approximately calibrated stable domain from the theoretical value is very small compared to the change of the stable domain under the action of the disturbance impulse.

[0092] The stable domain approximation calibration method proposed by the present application uses a NARX neural network time series prediction model. The core idea of the method is to use the latest phase point trajectory data and the prediction data obtained through the time series prediction model to give an approximate estimate of the center vector and the radius vector of the stable domain. The overall idea of the method is shown in Figure 7 ; the specific method is described in the Chinese invention patent application (patent name: Unmanned aerial vehicle network system prediction model phase point stable domain calibration method, system and program product, application number: 2025109211769, application date: 20250704) applied by the applicant.

[0093] 6, Limit impulse measurement The purpose of the limit impulse measurement of the present application is to find out the maximum impulse that the network system can withstand under a certain disturbance, and to provide the boundary of disturbance injection for the following disturbance impulse injection experiment. After considering the differences in disturbance intensity type and value range, and studying the linear and nonlinear performance of multiple rounds of measurement data, the present application proposes a method for measuring the limit impulse using simulation experiments. The basic idea of the method is to first extract the intensity values of the disturbance according to the intensity characteristics, then perform simulation experiments according to the intensity decreasing principle and step increasing principle, iteratively obtain the maximum step data corresponding to each intensity value, then determine whether there is a strong linear relationship between the stress intensity data and the maximum step data, and finally determine the final limit impulse value according to the judgment result. In order to improve the efficiency of the simulation experiment, the measurement method is designed as a limit impulse measurer, and its structure is shown in Figure 7 ; the specific method is described in the Chinese invention patent application (patent name: Measurement method, system, storage medium and program for limit impulse of unmanned aerial vehicle network system, application number: 2025109211735, application date: 20250704) applied by the applicant.

[0094] 7. Disturbance impulse injection simulation The disturbance impulse injection experiment of the present invention refers to a simulation experiment for obtaining the phase point trajectory characteristics of the system by injecting a certain disturbance within the limit impulse range into the network system model. Figure 9 The basic process of conducting disturbance impulse injection experiments for specific interference is given; for specific methods, please refer to the Chinese invention patent application applied for by the applicant (Patent Name: A method, system, medium and program product for simulating disturbance impulse injection in a UAV network system, application number: 202510921174X, application date: 20250704).

[0095] The case study object of this invention is a Figure 10 The figure shows a multi-UAV formation network system performing formation flight missions at a fixed cruising altitude. The network system consists of nine homogeneous rotorcraft UAVs, which are required to form a "田" formation and maintain the formation along a planned trajectory.

[0096] This multi-UAV network system employs a "leader-winger" formation strategy. UAV No. 1, in the lead position, serves as the leader of the entire network, UAVs Nos. 2-5 serve as primary wingmen, and UAVs Nos. 6-9 serve as secondary wingmen. At the start of the mission, nine homogeneous rotorcraft drones synchronously take off vertically from the ground to a cruising altitude. From there, they form the required formation by maneuvering within the xoy plane. Next, UAV No. 1 receives the path planning results and follows the planned path according to the path-following strategy. Simultaneously, UAVs Nos. 2-5 obtain the real-time position of UAV No. 1 and maintain a corresponding relative distance from it. UAVs Nos. 6-9 simultaneously obtain the position information of their adjacent primary wingmen and maintain a corresponding relative distance. Using this strategy, the multi-UAV network system achieves integrated formation flight.

[0097] 1. Phase point trajectory modeling of UAV formation network In the process of modeling, the present invention simplifies the following aspects: (1) Since the cruising altitude is fixed, the problem is simplified to a two-dimensional plane, and only the dynamic characteristics of the multi-UAV network system in the xoy plane are modeled; (2) The motion constraints of the UAV are not considered, that is, the UAV is assumed to be able to move in any direction instantly; (3) The perception constraints of UAVs are not considered, that is, it is assumed that UAVs can obtain the location information of other UAV nodes without delay; (4) The endurance of the drone is not considered, that is, it is assumed that the drone can fly continuously.

[0098] 1.1 Establishment of network system model 1.1.1 Static Attribute Model According to definition 1, the form of static attribute model of case UAV formation network is mdl SA = (M, S). (1.1) Wherein, M is the member attribute set, S is the system attribute set. The specific content of member attribute set and system attribute set is constructed as follows.

[0099] (1) Member attribute set The number of UAV members constituting the UAV formation network is 9, and the member attribute set should include 9 elements, each element representing the attribute set of a UAV, that is, (1.2) Since the 9 UAVs have isomorphism, the 9 UAV individuals are homogeneous members with the same member attributes, that is, the sets represented by each element in formula (5.2) are equal. In order to complete the required formation flight task, each UAV must establish attributes including UAV number representing identity attribute, position coordinates representing real-time information attribute, and communication range and maximum speed representing performance attribute. Specifically, there are (1.3) Wherein, the meaning and specific form of each symbol are:

[0100] (2) System attribute set The system attribute set of UAV formation network includes necessary elements to describe the overall state of the network, which is as follows: (1.4) Wherein, the meaning and specific form of each symbol are:

[0101] The following further explains insDic , cnctA and cnctS .

[0102] Interaction rule number information matrix insDic : The dimension of the insDic matrix is 9x9, and the element in the ith row and jth column records the interaction rule number that the UAV numbered i needs the UAV numbered j to provide information and take action.

[0103] Connectivity information matrix cnctA : The dimension of the cnctAEach element of the matrix is ​​a Boolean variable. When the value of the element in row i and column j is 1, it indicates that drone i and drone j are capable of communicating with each other. As long as the relative distance is within their respective communication ranges, they can obtain the shared information provided by each other. When the value is 0, it means that the two drones do not have the hardware and software conditions for mutual communication. Even if the relative distance is within the communication range, they cannot share information.

[0104] set up cnctA The purpose of the matrix is ​​to provide an injection interface for interference such as "communication failure". However, in the early stage of the system model establishment, it is assumed that all drones have the ability to communicate normally, that is, each element of the matrix is ​​1, such as Figure 11 As shown in (a).

[0105] Connectivity State Matrix cnctS : Dimensions of 9×9 cnctS Each element of the matrix is ​​a Boolean variable. When the value of the element in row i and column j is 1, it indicates that the drone numbered i and the drone numbered j are currently connected and can share information with each other; when the value is 0, it indicates that the two drones are disconnected and cannot obtain each other's information.

[0106] The connectivity state matrix has the following characteristics: (1) The connectivity state matrix is ​​a symmetric square matrix. Since the value of each element represents the bidirectional communication characteristics between the two drones at the corresponding position of the element, the values ​​of the elements at symmetric positions must be the same.

[0107] (2) The connectivity matrix is ​​a dynamic matrix. Whether two drones are in a connected state depends on the requirements of the formation strategy, the connectivity information matrix cnctA The values ​​of the corresponding elements and the relative positions of the two drones are dynamic factors. cnctA The matrix is ​​the default value, and the formation is maintaining Figure 10 When the "田" formation shown is flying steadily, cnctS The matrix values ​​are as follows Figure 11 As shown in (b).

[0108] (3) In particular, the elements on the diagonal of the connectivity state matrix are always 1, indicating that the UAV can grasp its own dynamic information in real time.

[0109] By combining equations (1.2) and (1.4), we can obtain the static attribute model of a cluster formation consisting of 9 drones, which is: (1.5) 1.2 Interaction Rule Matrix (1) Task analysis The flight mission of a drone formation can be divided into two stages, namely the team formation stage and the formation flight stage.

[0110] Phase 1: Team formation Given the initial position coordinates of each drone in the takeoff area, during the formation phase, the drones will fly from their respective initial positions to the formation positions, so that the entire cluster forms a stable "田" formation in the formation area.

[0111] The drones that arrive at the teaming position in advance will hover and wait until all 9 drones arrive at the designated teaming position, and then the entire cluster will execute the flight mission of Phase 2.

[0112] Phase 2: Formation flying When the cluster is formed, UAV No. 1 will fly according to the planned path, and the other UAVs will fly according to the following rules. The cluster as a whole will achieve the task of flying along the planned path in a "田" formation.

[0113] The two phases of the task are Figure 12 shown.

[0114] (2) Interaction Rule Matrix Framework During the entire flight mission, the interaction activities of the UAV formation network system are carried out among the nine UAVs. Therefore, its interaction rule matrix is ​​always a 9´9 square matrix in form.

[0115] At different mission stages, drones have different mission requirements and, therefore, different interaction rules must be followed. The interaction rule matrix has different contents depending on the mission stage. The following details the content and implementation algorithm of these interaction rules.

[0116] (3) Rule description The rules were set step by step according to the order of the stages of the formation's mission execution, and finally the five interaction rules listed in Table 4 were formed.

[0117] Table 4. List of network interaction rules for UAVs performing formation flight missions

[0118] The five rules listed in Table 4 are the contents of the interaction rule dictionary of the UAV formation network. When the cluster performs the formation task, it needs to access the corresponding rule according to the index of the interaction rule matrix and take action.

[0119] As can be seen from the rules, the team rules rl (1) / 1 and collision avoidance rules rl (2) / 2 guides the cluster's behavior in mission phase 1, path tracking rulesrl (3) / 3 and drone following rules rl (4) / 4Guide the cluster's behavior in the second phase of the task, and perceive the rules rl (5) / 5 acts on the entire process of system behavior. Therefore, the interaction rule matrix is ​​different at different stages of the task.

[0120] Figure 13 The interaction rule matrix RL of the UAV formation network in two mission stages is given. 9´9 The elements in the matrix are the numbered sets of interaction rules that need to be followed between two UAVs at the corresponding positions.

[0121] Equation (1.5) and Figure 13 The interaction rule matrix RL shown 9´9 By combining these, we can obtain a network system model of a drone formation consisting of 9 drones that performs a "田" formation flight mission.

[0122] 1.3 Model simulation and result display The initial state of the simulation is that 9 drones are hovering in the take-off area. Therefore, the drone members should be generated one by one at the beginning of the simulation, and the generated drone members should be randomly assigned initial position coordinates in the take-off area. Randomly generate an integer ξ in the interval [1,2] x , randomly generate an integer ξ in the interval [1,11] y , based on random integers and , the initial position coordinates randomly assigned to the drone members are [ x 0 ,y 0 ],in (1.6) If the location coordinates are already occupied, randomly generate new coordinates using the above method until the generated coordinates are unoccupied. These coordinates are used as the initial location coordinates of the newly generated UAV member in the takeoff area.

[0123] In each subsequent simulation step, the computer will scan each element of the interaction rule matrix based on the established network system model, update the position coordinates of each drone, and achieve simulated swarm formation flight. The following describes the specific parameter settings for this simulation example, following these rules.

[0124] (1) Parameter setting of team formation rules: the coefficient value is k x =k y =0.00005. The coordinates of the drone’s target position are shown in Table 5.

[0125] Table 5. Coordinate values ​​of target positions of drones in team formation rules

[0126] (2) Parameter setting in the anti-collision rule: The coefficient in the anti-collision rule is set to k r =0.000005; the distance threshold is set to d th =1.

[0127] (3) Parameter setting of path tracking rule: The coefficient of PID controller in the path tracking rule is set to K Px = K Py =1; K Ix = K Iy =1; K Dx = K Dy =0. (4) Parameter setting of drone following rule: The coefficient of PID controller in drone following rule is set as K Px = K Py =1; K Ix = K Iy =1; K Dx = K Dy =0. The side length of the "田" formation is set to a=10.

[0128] Figure 14 The running process of a simulation is given. Figure 14 (a) shows the initial state of the UAV formation network hovering in the take-off area; (b) shows that the network system is forming a "田" formation according to the team formation rules and collision avoidance rules; (c) shows the state after the team formation is completed, and the formation is waiting for the order to execute the second phase of the task; (d) The formation begins to fly as a whole along the planned trajectory in a "田" formation; The UAV formation network in (e) is in the process of formation flight. It can be seen that the stability of the PID controller in the path tracking rule and the UAV following rule can meet the requirements at this time, and the network as a whole can fly very smoothly along the prescribed path; (f) shows the complete flight trajectory of the UAV formation network after arriving at the destination.

[0129] 1.4 Construction of Phase Space The most important task requirement of this UAV formation network is to fly as a whole along the planned path in a "田" formation. In order to be able to describe the completion of the task, two questions need to be answered during the overall flight of the network: (1) Can the formation of the UAV network always maintain the prescribed shape; (2) Can the UAV network 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 proposes to use the formation shape variable and position offset for quantitative measurement respectively. According to the above analysis ideas, the corresponding state analysis table of this case is shown in Table 6.

[0130] Table 6 Status analysis of UAV formation network

[0131] In the table, the definitions of formation shape variables and position offsets are as follows.

[0132] Definition 3 (Formation Deformation Variable) Establish a Cartesian coordinate system with UAV No. 1 as the origin. Then at any time t, the expected position vector of UAV i (i=2,3,…,9) is P e,i (t), the actual position vector is P a,i (t), then the deformation trf of UAV i i (t) is defined as the 2-norm of the difference between the desired position vector and the actual position vector, that is, (1.7) The overall formation shape variable trf(t) of the UAV formation network is defined as (1.8) Among them, the expected position vector is the vector from the actual position of UAV No. 1 to the specified position of UAV i in the formation, and the actual position vector is the vector from the actual position of UAV No. 1 to the actual position of UAV i at time t, as shown in Figure 15 shown.

[0133] Definition 4 (position deviation) uses the ground coordinate system. At any time t, the path position vector planned for UAV No. 1 is P e,1 (t), the actual position vector of UAV No. 1 is P a,1 (t), then the position offset of the UAV formation network is defined as the 2-norm of the difference between the path position vector of UAV No. 1 and the actual position vector, that is, (1.9) The range of the formation shape variable and position deviation is [0, +∞), and both are small variables. That is, the closer the value is to 0, the more the operating state of the UAV formation network meets the mission requirements.

[0134] In the first phase of the task, the UAV formation network needs to complete the formation task, at this time only the formation state of the network needs to be concerned; while in the second phase of the task, the UAV formation network needs to keep the formation and fly according to the planned path, at this time both the formation state and the position state of the network need to be concerned. Therefore, in the formation phase, the phase space of the UAV formation network is a 1-dimensional space spanned by the vector element representing the formation state, and in the formation flight phase, the phase space is a 2-dimensional space spanned by the vector element representing the formation state and the vector element representing the position state, as shown in Figure 16 .

[0135] 1.5 Definition of interference intensity The present application analyzes the interference types that the case UAV network needs to face from two aspects of self-failure of the UAV formation network and external environmental factors, and gives a quantitative expression of the interference intensity.

[0136] (1) Define the interference type According to the state analysis result, the formation state and the position state of the UAV formation network are the network states that need to be concerned. According to the UAV formation network operation rules listed in Table 4, the normal communication between each UAV is the basis to ensure the stability of the network system formation and position. Once a UAV has a communication failure and cannot obtain and send information, the formation state and the position state of the entire UAV formation will be affected. Therefore, the communication failure of a single UAV is the first interference that the case UAV formation needs to withstand.

[0137] In addition, the UAV formation network will encounter the influence of natural wind during flight, which may cause changes in the formation state and the position state. Therefore, the wind force generated by the natural wind is the second interference that the case UAV formation needs to withstand.

[0138] (2) Define the interference intensity Interference 1: Communication failure of a single UAV The communication failure of the 9 UAVs in the case UAV formation network is possible. However, due to the connection relationship of the formation structure, the influence of the communication failure of different UAVs on the network system formation state and position state is different. For example, if the 1st UAV has a communication failure, the 2nd-5th UAVs cannot fly normally, and the 6th-9th UAVs follow the 2nd-5th UAVs and also cannot determine the correct flight direction, and the entire network will instantly lose the correct position update direction; if the 6th UAV has a communication failure, only it cannot find the flight direction at the next moment, and other UAVs are not affected. In fact, the interference intensity generated by the UAV communication failure is related to the number of connected UAVs.

[0139] In the complex network theory, the degree of a node refers to the number of edges connected to the node, which is related to the characteristics of the communication failure intensity in this case. The concept of node degree is used to provide a quantitative description of the intensity of communication failure.

[0140] Let the degree of UAV i be deg(i), and the number of UAVs with communication failure at a certain moment be recorded in set A, then the intensity of this interference of communication failure at this moment is (1.10) From equation (1.10), it can be seen that the communication failure intensity σ CF is a finite value in the interval [0,1]. For example, when UAV No. 1 and UAV No. 9 have communication failure at the same time, the communication failure intensity of the UAV formation network is

[0141] In particular, σ CF =0 indicates that no UAV has communication failure; σ CF =1 indicates that all UAVs have communication failure at the same time.

[0142] Interference two: wind In this case, the intensity of wind is described by a simplified Newton force, denoted as σw, and it is assumed that the wind acts on the 9 UAVs at the same time.

[0143] σw is a vector, and its component form is denoted as [σ W,x ,σ W,y ], which respectively represents the wind intensity in the x direction and the y direction, as shown in Figure 17 . The magnitude of the wind intensity σw is described by the 2-norm of the vector, i.e. .

[0144] 1.6 Observation of phase point trajectory After the modeling process, the phase point trajectories of the UAV formation network under two conditions of disturbance impulse injection and non-disturbance impulse injection are also shown.

[0145] (1) The case of non-disturbance impulse injection According to equations (1.8) and (1.9), a calculation module for the shape variable and the position offset variable is added in the network system model. In the phase space shown in Figure 16 , the phase point trajectories of the two stages of the task are plotted respectively.

[0146] The simulation method is used to obtain the approximate results of the phase point trajectory, and the specific method is to retain the position of the phase point obtained each time, and connect these discrete points in turn. The smaller the simulation step, the smoother the phase point trajectory, and the closer to the analytical result. Figure 18The trajectories of the phase points starting from the take-off positions listed in Table 7 are shown in the figures, in which the arrows indicate the direction of the movement of the phase points. In order to show the trajectories of the phase points in the team formation stage with respect to the simulation step, in Figure 18 (a) the 1-dimensional phase space characterized by the formation state is combined with the time dimension (simulation step); Figure 18 (b) shows that in the formation flight stage, the cluster phase points move rapidly in the phase space to a small region of stable oscillation.

[0147] Table 7 Take-off positions of 9 UAVs

[0148] (2) The case of injecting disturbance impulse 1. Injecting disturbance impulse generated by wind The disturbance that the UAVs will be subjected to in both the team formation stage and the formation flight stage is natural wind. Assuming that the wind strength is σ W =[σ W,x ,σ W,y ], then the acceleration increment a W,i =[ax W,i ,ay W,i ] of the UAV i under the action of wind is (1.11) where K Wx,i and K Wy,i are coefficients.

[0149] Suppose that the acceleration of the UAV i obtained through the action rule is a , then the comprehensive acceleration under the wind disturbance is (1.12) According to the algorithms of formula (1.11) and (1.12), the coefficients K Wx,i and K Wy,i are set to 0.2. In the 40th simulation of the team formation stage, wind disturbance with a strength of is injected, lasting for 2 simulation steps, and the phase point trajectory of the network under the wind impulse of is shown in Figure 19 . From which it can be observed that there is a lag phenomenon in the deviation of the phase point trajectory.

[0150] In the 500th simulation of the formation flight stage, wind disturbance with a strength of is injected, lasting for 1 simulation step, and the phase point trajectory of the network under the wind impulse of [1, 1] is shown in Figure 20 . By showing the change of the formation deformation variable and the position deviation with respect to the simulation number, it can be more clearly seen that the wind disturbance has an effect on the position of the phase point, as shown in Figure 20② and ③ in .

[0151] 2. Injecting disturbance impulses generated by communication failures UAV communication failures are detected by changing the system properties in the network system model cnctA For example, suppose that in the 250th simulation of the formation flight phase, UAVs 2, 3, and 9 experience communication failures and are unable to establish contact with other UAVs until the 350th simulation, when communication is restored. Then, starting from the 250th simulation step, cnctA Set as Figure 21 The matrix shown in the figure is restored to the following at the 350th simulation step. Figure 11 The default case is shown in (a). In this case, the injected communication fault intensity is (3+3+2) / 24=0.3, the disturbance impulse is 33, and the phase point trajectory is obtained as follows: Figure 22 shown.

[0152] It should be noted that in order to more clearly show the changes in the phase point trajectory, some simulation settings were adjusted when obtaining the phase point trajectories of and to make the movement of the UAV formation network show greater volatility. Specifically, the coefficients of the PID controller in the path tracking rule and the UAV following rule were changed to K Px = K Py =0.05; K Ix = K Iy =0.03; K Dx = K Dy =0.01. 1.7 Obtaining the Phase Point Trajectory of the UAV Formation Network 1.7.1 Stability Region Approximate Calibration 1.7.1.1 Determination of the Initial Stability Region From the state analysis results of the phase space construction, we can see that the phase space of the UAV formation network in stage 1 is a 1-dimensional space composed of the formation deformation variable, and the phase space in stage 2 is a 2-dimensional space composed of the formation deformation variable and the position offset. Since the phase space in different stages is different, the initial stable domains of the two stages need to be calibrated separately. The initial stable domain of stage 1 is denoted as , the second stage is .

[0153] 1.7.1.2 Analysis of the Initial Stability Region in Phase 1 The initial stable region of phase one can be obtained by theoretical analysis of the formation rules. The basic idea of this operation is to reassign the speed at the next time when the single UAV will exceed the target point, so that it will just reach the target point at the next time. Once the UAV reaches the target point, the acceleration will continue to be 0, and according to the anti-oscillation operation, the speed will also continue to be 0, and the UAV will continue to be stationary at the target point. At this time, the array deformation variable of the UAV formation will be stable at 0. Therefore, the initial stable region of phase one , that is, the phase point will be stable at 0 point in the first stage, and the center point at this time is 0, and the radial length is 0.

[0154] The same simulation parameter values as in the observation of the phase point trajectory are used, and the simulation model is continuously run for 6000 simulation steps in phase one. The simulation results show that the array deformation variable has been 0 since the 520th simulation step, which confirms the above analysis.

[0155] 1.7.1.3 Approximate calibration of the initial stable region of phase two The initial stable region of phase two needs to use the stable region approximate calibration method to obtain an approximate value, and the results are shown in Chinese invention patent application (patent name: A method for calibrating the stable region of a phase point of a UAV network system prediction model, a system, and a program product, application number: 2025109211769, application date: 20250704).

[0156] 1.7.2 Determination of the limit impulse of two kinds of disturbances According to the disturbance analysis, the UAV formation network in the case will be affected by two kinds of disturbances, one is the communication failure of the single UAV, and the other is the natural wind. The limit impulse determination method is used to analyze and determine the limit impulse size of the two kinds of disturbances. The results are shown in Chinese invention patent application (patent name: Determination method, system, storage medium and program of limit impulse of UAV network system, application number: 2025109211735, application date: 20250704).

[0157] 1.7.3 Two-stage disturbance impulse injection experiment and data processing This case only carries out disturbance impulse injection simulation experiment on the wind of phase one and the communication failure of the single UAV of phase two. The wind injection of phase two and the subsequent analysis are similar to phase one. The results are shown in Chinese invention patent application (patent name: A disturbance impulse injection simulation method, system, medium and program product for a UAV network system, application number: 202510921174X, application date: 20250704).

[0158] The foregoing is a description of the embodiments of the present application. The above description of disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for simulating and modeling phase trajectory of a UAV network system, characterized in that: The following steps are included: 1) System Analysis and Task Analysis: Divide the target UAV network into members and classify its attributes to obtain a static attribute model consisting of a member attribute set and a system attribute set; 2) Construction of interaction rule matrix: According to the task stage, the interaction relationship between members in each stage is described, numbered and coded to obtain the interaction rule matrix of the corresponding stage; 3) State Analysis: Based on the task phase division, the state variables that can measure network performance are extracted and their types are determined, and then the phase vector space is constructed at each phase; 4) Stability domain approximate calibration: Linear Gaussian white noise expansion is performed on the original data of the phase point trajectory, and the NARX neural network time series model is used to predict the future trajectory of the phase point. The stability domain center vector and radial vector are calculated based on the observation window data; 5) Limit impulse measurement: For the predetermined interference type, the maximum tolerable step length is obtained using a measuring device based on the principle of decreasing intensity and increasing step length. The limit impulse is then output after determining the linear characteristics. 6) Disturbance impulse injection simulation: Generate a disturbance intensity-step size matrix within the limit impulse range, fix the initial state of the network system model and run it until it stabilizes. After each disturbance injection, record the phase point trajectory until the termination threshold is met; 7) Data segmentation and transition zone marking: Based on the phase point-stability domain distance and threshold conditions, the starting and ending points of the transition zone are automatically marked and a labeled phase point trajectory dataset is output for subsequent modeling or algorithm training.

2. The method according to claim 1, characterized in that The member attributes in step 1) include identity attributes, real-time information attributes, and performance attributes, and the system attributes include at least an interaction rule number information matrix, a connectivity information matrix, and a connectivity status matrix; And / or, the static attribute model static attribute model mdl SA Is a set of member attributes M and system property sets S The two-tuple is: ， ， ； The meaning of each symbol is: n m The number of member nodes in the network system; n ma The number of member attributes of the i-th member node; n sa The number of system properties of the network as a whole; M i The member attribute set of the i-th member node; o i k The kth element in the member attribute set of the i-th member node; s j The jth element in the system property set; And / or, the network system is composed of two tuples mdl NS To describe, the tuple is composed of the static attribute model of the network system mdl SA and its interaction rule matrix RL n×n Composition, namely: ； Among them, RL n×n No. i r Rank j r The elements in the column represent the i-th r The member node receives the j r After receiving the information of each member node, the set of attribute state change rules is generated.

3. The method according to claim 1, characterized in that The elements of the interaction rule matrix in step 2) are a set of rule numbers. Different interaction rule matrices are used in different task stages and the matrix replacement is triggered by stage switching.

4. The method according to claim 1, wherein The status analysis described in step 3) includes the following steps: 3.1) Based on the task analysis results, list the various task stages of the network system in chronological order; 3.2) For each task stage, condense the subtask requirements of that stage; 3.3) Based on the subtask requirements, qualitatively describe the network status that can reflect the completion of the task; 3.4) Assigning at least one scalar state variable to each network state for quantitatively describing the network state; the scalar variable satisfies the requirement that any two state variables in the same phase are independent of each other; 3.5) Classifying the state variables as continuous or discrete and recording them in a state analysis table; 3.6) Fill the state analysis table with the task phase, task requirements, network status, state variables, and their types in sequence, and construct the phase vector space according to the specific state variables.

5. The method according to claim 1, characterized in that The method for approximate calibration of the stable domain in step 4) includes the following steps: 4.1) Collect the original trajectory data of the multi-dimensional phase point in the phase space within continuous steps and store them in a matrix format with the first row being the step sequence and the remaining rows being the position coordinates of each dimension; 4.2) Determine whether the number of columns of the original data matrix is ​​less than a preset data expansion threshold; if so, perform data expansion processing; otherwise, skip the processing; 4.3) During the data augmentation process, several new data points are uniformly inserted between adjacent step data points, and Gaussian white noise is introduced into the inserted data to generate an augmented data matrix. 4.4) Based on a preset prediction window size, the original or augmented data matrix is ​​input into the NARX dynamic neural network time series model to obtain a prediction matrix consisting of predicted data points. 4.5) Based on a preset observation window size, the data in the rear columns of the original data matrix are intercepted to form an observation matrix. 4.6) The observed data and the predicted data are combined into a calibration data set, which is input into the stability domain calibration model to output the center vector and radial quantity approximation of the target stability domain.

6. The method according to claim 1, characterized in that The method for determining the limiting impulse in step 5) includes the following steps: 5.1) Obtain the value range of interference intensity flg1 Continuous characteristic mark with interference intensity flg2 , and set the number of measurements c ; 5.2) According to flg1 and flg2 A logical combination of the interference intensity extraction module is used to determine a set of interference intensity data, wherein the interference intensity is sorted from large to small according to the absolute value of the interference intensity on the system disturbance; 5.3) Following the principles of decreasing intensity and increasing step size, use the measurement module to perform simulation experiments for each interference intensity and iteratively determine the maximum action step size that keeps the system stable in the phase space state dimension; 5.4) Input all interference intensity data and the corresponding maximum action step length data into the linear characteristic judgment module to determine whether their reciprocal absolute values ​​have a linear relationship; 5.5) If the linear relationship holds, the average value of the product of each interference intensity and the maximum step length is used as the limit impulse output; if not, the minimum interference intensity and the maximum step length are output as the limit impulse value.

7. The method according to claim 1, characterized in that The method for simulating the disturbance impulse injection in step 6) includes the following steps: 6.1) Set the number of injections: preset a positive integer cnt , represents the number of interference injection rounds to be carried out in this experiment; 6.2) Generate interference parameter matrix: Construct a two-dimensional numerical matrix D σ , where the first row is the interference intensity of each round, and the second row is the corresponding action step length; 6.3) Prepare the network system model: Fix the initial state of the network system model, start the model, and allow it to run to a stable state. Ensure that the network system model remains in the same stable state each time interference is injected. 6.4) The first part of the matrix of the injected interference intensity data i Column value: Set the disturbance intensity in the disturbance impulse injection module of the model to σ m , the action duration is sp m , so that the simulation model continues to run; 6.5) Record and observe phase point trajectory data: Monitor the changes of phase points in the phase vector space in real time in the phase point trajectory observation window; when it is observed that the change of phase point position is continuously sp end less than the termination threshold ε within the step size end When , terminate the network operation and go to step 6.6; otherwise, continue to execute step 6.5; 6.6) Save the phase point trajectory data of the nth injection experiment: Save the phase point trajectory data of the nth perturbation impulse injection experiment as (n+1)× spr m The numerical matrix of D trcm ,in spr m is the number of simulation steps from the time the disturbance is injected to the time it is fully recovered to the stable operating state; 6.7) Obtaining disturbance impulse injection experimental data: cnt All numerical matrices obtained from the sub-disturbance impulse injection experiment D trcm , saved as a cell array D eo , for subsequent data processing, m =1,…, cnt .

8. A UAV network system phase point trajectory simulation modeling system, characterized by: The system implements the method described in any one of claims 1 to 7, including: A) an attribute modeling module, which is used to perform system analysis and task analysis and generate a static attribute model; B) a rule management module, which is used to describe, number, and encode the interaction rules in natural language and establish an interaction rule matrix; C) a state space construction module, which is used to extract state variables, determine types and generate phase vector spaces for each stage; D) a stability domain calibration module, which is used to expand, predict and output the stability domain center vector and radius vector of the phase point trajectory original data; E) a limit impulse measurement module, including an interference intensity extractor, a measurer and a linear characteristic judger, which is used to output the limit impulse of each interference in the phase vector space dimension; F) an impulse injection simulation module, which is used to generate an interference intensity-step size matrix based on the limit impulse, perform multiple rounds of simulation and collect phase point trajectories; G) a data processing module, which is used to mark and segment the transition zone of the simulated phase point trajectory to form a searchable data set; H) an interactive interface module, which is used to provide phase point trajectory data and stability domain information to the upper design platform or control algorithm.

9. A computer-readable storage medium having a computer program stored thereon, wherein when the program is executed by a processor, the computer is enabled to implement the method according to any one of claims 1 to 7.

10. 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 according to any one of claims 1 to 7 is implemented.

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