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

Abstract

This invention relates to the field of unmanned aerial vehicle (UAV) swarm control technology, and more particularly to a method, system, medium, and software product for simulating and modeling phase trajectory of a UAV network system. The method includes system and task analysis, construction of interaction rule matrices, state analysis and phase vector space construction, approximate calibration of the stability domain, determination of the ultimate impulse, simulation of disturbance impulse injection, and data segmentation and transition zone marking, realizing a closed-loop process from modeling to disturbance assessment. Trajectory prediction is performed using a NARX neural network, combined with Gaussian white noise augmentation and multi-round simulation to achieve approximate calibration of the stability domain and determination of the ultimate impulse, and automatically outputs a structured trajectory dataset. This invention improves modeling accuracy, simulation efficiency, and system security.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) swarm control technology, and in particular to a method, system, medium, and software product for simulating and modeling the phase trajectory of a UAV network system. Background Technology

[0002] With the improvement of individual UAV (Unmanned Aerial Vehicle) performance and the continuous decline in cost, multi-UAV swarms are rapidly becoming the mainstream technical solution for tasks such as search and rescue, disaster monitoring, material delivery, aerial communication relay, and combat exercises. Compared with traditional single UAVs, multi-UAV network systems (MWNs) have significant advantages in coverage area, mission redundancy, robustness, and real-time response. However, the increase in the number of nodes and the complexity of cooperative behavior also bring new challenges in modeling, simulation, and control.

[0003] Existing research generally employs graph-based cooperative control models or distributed consensus models to describe network topology and formation maintenance logic. For example, the Vicsek model and its improved Boids model can generate swarm behavior using simple velocity matching, position maintenance, and collision avoidance rules; consensus algorithms characterize global convergence properties using the Laplace matrix; and formation control often utilizes ideas such as leader-follower, virtual structures, or behavioral hierarchies to construct mathematical models. While these methods can reproduce group movement at a macroscopic level, they struggle to uniformly characterize multi-dimensional dynamic attributes such as task phase transitions, communication link failures, and node performance differences.

[0004] To address these shortcomings, scholars have recently begun to introduce Multi-Agent System (MAS) modeling and complex network theory, treating individual UAVs as attributed nodes and abstracting communication or sensing links as directed / undirected edges, using switched graph systems to describe task phase transitions. However, in existing work, "node attributes" typically only include a few continuous variables such as position, speed, or battery level, lacking systematic management of discrete or semi-discrete variables such as member identity, real-time load, and sensor status. On the other hand, the overall network connectivity matrix, connectivity state matrix, and set of interaction rules are often statically assumed in algorithm derivation, ignoring the phased rule changes and intelligent decision-making logic in actual tasks.

[0005] Furthermore, in dynamical systems theory, a "state point" refers to the position of a system in the state space at a given moment; the curve formed by the evolution of a state point over time is called the "state point trajectory." For unmanned aerial vehicle (UAV) networks, their state space can be high-dimensional, reaching tens or even hundreds of dimensions, and their trajectories contain comprehensive information about topological changes, node interactions, and external disturbances. Traditional research focuses on:

[0006] 1. Linear state-space model: Approximates linearization of small-range motion and uses pole distribution or state feedback for stability analysis;

[0007] 2. Lyapunov functions and invariant sets: They can be used to construct global or local stability criteria, but it is difficult to provide analytical expressions for discrete jumps or strongly coupled nonlinear scenarios.

[0008] 3. Monte Carlo simulation: It evaluates collision probability and convergence time through large-scale random sampling, but lacks precise definition of "first cross-boundary" or "trajectory divergence threshold".

[0009] In recent years, data-driven modeling (such as autoregressive neural networks, temporal convolutional networks, and NARX networks) has been used to predict the future state of systems; Gaussian process regression and deep generative models are used to capture complex nonlinearities that are not explicitly stated. Although prediction accuracy has been improved, how to quickly calibrate the boundary of the stable region by combining the prediction results remains an urgent problem to be solved: existing methods mostly rely on manual thresholds or empirical settings, and lack a unified approximate calibration process.

[0010] Furthermore, multi-UAV missions are often exposed to disturbances such as sudden wind gusts, GPS loss of lock, link congestion, and even node failures, leading researchers to focus on the system's extreme tolerance to instantaneous impulses or sustained disturbances. Existing work typically employs:

[0011] 1. Incremental intensity scanning: Gradually increase the interference intensity and record the changes in system performance indicators (such as average deviation and time consumption);

[0012] 2. Robust control margin: The worst-case gain is obtained based on μ-analysis or the H∞ paradigm, but it is difficult to consider discrete topology switching at the same time.

[0013] 3. Ultimate load test: Apply ultimate deflection or torque directly in hardware or simulation environment to test the system's collapse threshold.

[0014] These methods either only provide a binary "endurance / collapse" conclusion, or they involve enormous computational costs and lack a systematic explanation of the coupling relationship between disturbance intensity and action step size. There is currently no unified framework that can automatically determine the limiting impulse in a single simulation process and further generate multi-round disturbance injection scripts to systematically evaluate recovery performance and stability domain migration. Summary of the Invention

[0015] To address the aforementioned technical problems, the present invention aims to provide a method for simulating and modeling the phase trajectory of unmanned aerial vehicle (UAV) network systems. This method follows an end-to-end closed-loop process, from system analysis, rule matrix construction, state analysis, and approximate calibration of the stability domain to the determination of the ultimate impulse and the simulation of disturbance injection. It also achieves high-quality, structured trajectory dataset output through data segmentation and transition zone marking. This method integrates simulation, control, and evaluation, providing a new technical means for the robust design, verification, and real-time adjustment of multi-UAV systems.

[0016] To achieve the above objectives, the present invention adopts the following technical solution:

[0017] A method for simulating and modeling the phase point trajectory of an unmanned aerial vehicle (UAV) network system, comprising the following steps:

[0018] 1) System analysis and task analysis: The target UAV network is divided into members and its attributes are collected to obtain a static attribute model composed of member attribute sets and system attribute sets;

[0019] 2) Construction of interaction rule matrix: According to the task stage, the member interaction relationship of each stage is described, numbered and encoded to obtain the interaction rule matrix of the corresponding stage;

[0020] 3) State analysis: Based on the task phase division, extract state variables that can measure network performance and determine their types, and then span the phase vector space in each phase.

[0021] 4) Approximate calibration of the stable domain: The original phase point trajectory data is augmented with linear Gaussian white noise, and the future trajectory of the phase point is predicted using a NARX neural network time series model. The center vector and radius vector of the stable domain are calculated in combination with the observation window data.

[0022] 5) Limit impulse measurement: For a predetermined type of interference, the maximum tolerable step size is obtained by a measuring device based on the principle of decreasing intensity and increasing step size. After determining the linearity, the limit impulse is output.

[0023] 6) Disturbance impulse injection simulation: Generate the disturbance intensity-step matrix within the limit impulse range, fix the initial state of the network system model and run it until it is stable, and record the phase point trajectory until the termination threshold is met after each disturbance injection.

[0024] 7) Data segmentation and transition zone labeling: Based on the phase point-stability region distance and threshold conditions, the start and end points of the transition zone are automatically labeled and a labeled phase point trajectory dataset is output for subsequent modeling or algorithm training.

[0025] Preferably, 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 state matrix.

[0026] Preferably, the static attribute model mdl SA It is a set of member attributes M and system attribute set S The resulting binary pair is:

[0027] ,

[0028] ,

[0029] ;

[0030] The meanings of each symbol are as follows: 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 attributes of the network as a whole; M i The set of member attributes of the i-th member node; o i k The k-th element in the member attribute set of the i-th member node; s j The j-th element in the system attribute set.

[0031] Preferably, the network system consists of binary tuples. mdl NS To describe this, the binary tuple is derived from the static attribute model of the network system. mdl SA and its interaction rule matrix RL n×n Composition, namely:

[0032] mdl NS =( mdl SA , RL n×n );

[0033] Among them, RL n×n The i r Line number j r The elements of the column represent the first element in the network system. i r The member node receives the firstj r The set of rules governing the change of attribute states of each member node.

[0034] Preferably, the elements of the interaction rule matrix in step 2) are a set of rule numbers, and different interaction rule matrices are used in different task stages and replaced by a stage switching trigger matrix.

[0035] Preferably, the state analysis in step 3) includes the following steps:

[0036] 3.1) Based on the task analysis results, list the various task stages of the network system in chronological order;

[0037] 3.2) For each task phase, refine the sub-task requirements for that phase;

[0038] 3.3) Based on the requirements of the sub-tasks, qualitatively describe the network status that reflects the task completion status;

[0039] 3.4) Assign at least one scalar state variable for each network state to quantitatively describe the network state; the scalar satisfies that any two state variables are independent within the same stage;

[0040] 3.5) Classify the state variables as either continuous or discrete and record the classification in the state analysis table;

[0041] 3.6) Fill in the task stage, task requirements, network status, state variables and their types into the state analysis table in sequence, and construct the phase space according to the specific state variables.

[0042] Preferably, the method for approximate calibration of the stability region in step 4) includes the following steps:

[0043] 4.1) Collect the original trajectory data of multidimensional phase points in phase space within continuous step lengths and store them in a matrix format with "the first row being the step length sequence and the remaining rows being the position coordinates of each dimension".

[0044] 4.2) Determine whether the number of columns in the original data matrix is ​​less than a preset data expansion threshold. If so, perform data expansion processing; otherwise, skip this processing.

[0045] 4.3) In the data augmentation process, several new data points are uniformly inserted between adjacent step size data, and Gaussian white noise is introduced into the inserted data to generate an augmented data matrix;

[0046] 4.4) Based on the preset prediction window size, input the original or expanded data matrix into the NARX dynamic neural network time series model to obtain the prediction matrix composed of the prediction data points;

[0047] 4.5) Based on the preset observation window size, extract the data from the last column of the original data matrix to form the observation matrix;

[0048] 4.6) Merge the observed data and predicted data into a calibration dataset, input the stable domain calibration model, and output the center vector and radial approximation values ​​of the target stable domain.

[0049] Preferably, the method for determining the ultimate impulse in step 5) includes the following steps:

[0050] 5.1) Obtain the range identifier of interference intensity. flg1 Continuous characteristic identification of interference intensity flg2 And set the number of measurements. c ;

[0051] 5.2) According to flg1 and flg2 The logical combination of the interference intensity extraction module determines a set of interference intensity data, which is sorted from largest to smallest according to the absolute value of its disturbance to the system.

[0052] 5.3) Following the principle of decreasing intensity and increasing step size, the measurement module is used to conduct simulation experiments on each disturbance intensity, and the maximum action step size that keeps the system stable in the phase vector space state dimension is determined iteratively.

[0053] 5.4) Input all interference intensity data and the corresponding maximum action step size data into the linear characteristic judgment module to determine whether their reciprocal absolute values ​​have a linear relationship;

[0054] 5.5) If the linear relationship holds, the average value of the product of each interference intensity and the maximum step size is used as the limit impulse output; if it does not hold, the minimum product of the interference intensity and the maximum step size is output as the limit impulse value.

[0055] Preferably, the method for simulating the disturbance impulse injection in step 6) includes the following steps:

[0056] 6.1) Set the number of injections: Preset a positive integer. cnt This represents the number of interference injection rounds to be performed in this experiment;

[0057] 6.2) Generate the interference parameter matrix: Construct a two-dimensional numerical matrix D σ The first row represents the interference intensity for each round, and the second row represents the corresponding action step size.

[0058] 6.3) Prepare the network system model: Fix the initial state of the network system model and start the model to run to a stable state; ensure that the network system model remains in the same stable state every time interference is injected;

[0059] 6.4) The first part of the injected interference intensity data matrix i Column values: Set the disturbance intensity in the model's disturbance impulse injection module to [value]. σ m The duration of action is sp m This allows the simulation model to continue running;

[0060] 6.5) Record and observe phase point trajectory data: Monitor the changes of phase points in the phase vector space in real time within the phase point trajectory observation window; when the change in phase point position is observed during the network system recovery phase, sp end Within a certain step, the value is less than the termination threshold. e end If the network fails, terminate the operation and proceed to step 6; otherwise, continue executing step 5.

[0061] 6.6) Save the phase trajectory data of the m-th injection experiment: Save the phase trajectory data of the i-th disturbance impulse injection experiment as (n+1)× spr m numerical matrix D trcm ,in spr m The number of simulation steps from the start of the disturbance injection to the point of complete recovery to a stable operating state;

[0062] 6.7) Obtain experimental data on disturbance impulse injection: cnt All numerical matrices obtained from the secondary perturbation impulse injection experiment D trcm ( m =1,…, cnt Save as a cell array D eo This is so that data processing can be done later.

[0063] Furthermore, this invention also discloses a phase trajectory simulation modeling system for an unmanned aerial vehicle (UAV) network system, which implements the method described, including:

[0064] A) The attribute modeling module is used to perform system analysis and task analysis and generate static attribute models;

[0065] B) Rule management module, used to describe, number, and encode interaction rules in natural language and establish an interaction rule matrix;

[0066] C) State space construction module, used to extract state variables, determine types, and generate phase vector spaces for each stage;

[0067] D) Stability domain calibration module, used to expand, predict and output the stability domain center vector and radius vector of the original phase point trajectory data;

[0068] E) Limit impulse measurement module, including interference intensity extractor, measuring device and linearity characteristic judge, used to output the limit impulse of each interference in the phase vector space dimension.

[0069] F) The impulse injection simulation module is used to generate an interference intensity-step matrix based on the ultimate impulse, perform multiple rounds of simulation, and collect phase point trajectories.

[0070] G) Data processing module, used to mark and segment the phase point trajectories obtained from simulation, forming a searchable dataset;

[0071] H) Interactive interface module, used to provide phase point trajectory data and stability domain information to the upper-level design platform or control algorithm.

[0072] Furthermore, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, causes the computer to implement the method described thereon.

[0073] Furthermore, the present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the method.

[0074] The present invention, by adopting the above-described technical solution, has the following technical effects:

[0075] 1. End-to-end integrated framework improves modeling completeness and accuracy

[0076] It pioneered a binary description of "static attribute model + interaction rule matrix," unifying continuous flight parameters, discrete identity / mission attributes, and network connectivity information into a single data structure, enabling synchronous management of heterogeneous nodes and phased rule switching. The model error (RMSE compared with high-fidelity physical simulation) decreased by an average of over 20%; in cross-phase switching scenarios, the maximum deviation in formation maintenance was reduced by approximately 18%.

[0077] 2. Fast approximate calibration in the stability region, balancing efficiency and accuracy.

[0078] A coupled scheme of linear white Gaussian noise augmentation and NARX time-series prediction is adopted, which can output approximate values ​​of the center vector and radial vector of the stable domain in a single inference without the need for manual empirical thresholds. In typical 10-dimensional phase vector space tests, the calibration error is controlled within ±3% (relative to the Monte Carlo true value), the calculation time is reduced by 35%, and the real-time performance of the simulation-control closed loop is guaranteed.

[0079] 3. Adaptive determination of ultimate impulse significantly reduces simulation costs.

[0080] The joint search algorithm of "intensity decreasing - step size increasing" and the linear correlation self-checking algorithm can reduce the number of simulation rounds by 50-65% while maintaining 1% accuracy. The limit impulse criterion directly outputs the quantitative value of the disturbance intensity-step size product, providing an executable boundary for the design of control laws and safety margins.

[0081] 4. Improved data quality through disturbance impulse injection and smart labeling in the transition zone.

[0082] One-click generation of disturbance intensity-step size matrix and batch injection reduces the overall time of multi-round experiments by 40%; trajectory data fully covers the entire process of "disturbance-transition-recovery". Combined with 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.

[0083] 5. Significantly improved overall robustness and safety performance

[0084] The quantification results of the ultimate impulse, combined with the stability domain migration analysis, provide quantitative input for real-time fault tolerance, emergency decision-making, and adaptive control. In a case involving combined disturbances of communication failure and wind gusts, the formation recovery time was reduced from 12.4s to 7.9s, and the average energy consumption was reduced by 11%; the mission success rate was improved by 16-20%.

[0085] In summary, this invention not only achieves closed-loop modeling and efficient data generation of UAV networks based on "attributes-rules-states-trajectories," but also significantly improves simulation efficiency, evaluation accuracy, and system robustness in engineering practice, providing practical technical support and quantitative evaluation methods for the design, verification, and online optimization of multi-UAV swarms. Attached Figure Description

[0086] Figure 1 The basic flowchart for modeling this invention.

[0087] Figure 2 This refers to the relationships between key components in the modeling method.

[0088] Figure 3 This is a diagram illustrating the mission execution process of a 3-drone transport formation.

[0089] Figure 4 A flowchart illustrating the steps involved in constructing the interaction rule matrix.

[0090] Figure 5 An interactive rule matrix framework for a 3-drone transport formation example.

[0091] Figure 6 This is a sample Matlab code for the interaction rule matrix and part of the rule dictionary for a 3-drone transport formation example.

[0092] Figure 7 A flowchart of the method for approximate calibration in the stability region.

[0093] Figure 8 This is a flowchart of the method for determining the ultimate impulse.

[0094] Figure 9 Flowchart of the method for injecting disturbance impulses into simulation.

[0095] Figure 10 To perform formation flight missions for unmanned aerial vehicle (UAV) network systems.

[0096] Figure 11 for cnctA and cnctS Examples of possible values, Figure 11 (a) cnctA The default values ​​for the matrix, (b) cnctS Examples of possible values ​​for a matrix.

[0097] Figure 12 This diagram illustrates the two phases of a drone formation flight mission.

[0098] Figure 13 The interaction rule matrix for the drone formation network in the two mission phases; Figure 13 (a) Interaction rule matrix for the formation phase, (b) Interaction rule matrix for the formation flight phase.

[0099] Figure 14 Demonstrates the simulation operation process of drone swarm network; Figure 14 (a) Hovering in the initial takeoff area, (b) During the formation phase, (c) Formation completed, (d) Entering the formation flight phase, (e) Flying according to the planned trajectory, (f) The complete trajectory after reaching the destination.

[0100] Figure 15 The desired position vector and the actual position vector.

[0101] Figure 16 This represents the phase space for different task phases.

[0102] Figure 17 This is a diagram illustrating wind force intensity.

[0103] Figure 18 The phase trajectories of the two task phases; Figure 18 (a) Phase trajectory during the formation phase, (b) Phase trajectory during the formation flight phase.

[0104] Figure 19 The phase trajectory of the formation phase to inject wind interference.

[0105] Figure 20 The phase trajectory of the formation flight phase to inject wind interference.

[0106] Figure 21 Inject individual UAV communication failure stress into the setup of the connectivity information matrix.

[0107] Figure 22 The phase trajectory of the formation flight phase to inject communication fault stress interference from UAVs. Detailed Implementation

[0108] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention.

[0109] like Figure 1 As shown, a phase trajectory simulation modeling method for an unmanned aerial vehicle (UAV) network system includes three basic components: first, the construction of a network system model based on system and task analysis; second, the establishment of a phase vector space based on state analysis; and third, the establishment of a disturbance impulse injection module based on interference analysis. The goal of the modeling is to establish a phase trajectory observation window. The relationship between these components in the workflow is as follows: Figure 1 As shown.

[0110] The modeling process includes four "analyses": system analysis to clarify the network structure and attributes, task analysis to divide the task phases, state analysis to define the network state, and interference analysis to identify interference types and intensities. The goal of system and task analysis is to build a network system model, the purpose of state analysis is to construct the network's phase space, and the purpose of interference analysis is to integrate a disturbance impulse injection module. The results of these four analyses are interrelated, with the ultimate goal of obtaining the phase trajectory of the network system. Figure 2 The outputs of each analytical task in the modeling process and the relationships between them are summarized.

[0111] To explain in detail Figure 1 The content introduces a 3-drone transport formation example consisting of three drones. Suppose this drone formation is required to complete a transport task; the three drones forming the formation must cooperate throughout the mission while maintaining a "triangle" formation. Simultaneously, they must avoid obstacles along the way. Figure 3 The demonstration showcased the entire transportation mission carried out by the drone formation.

[0112] The following section will use this 3-UAV transport formation example to explain in detail the methods for establishing the network system model and the phase point trajectory observation window during the modeling process.

[0113] I. Methods for Establishing Network System Models

[0114] The primary task of modeling is to establish a network system model of the research object. According to Definition 2, a network system model contains two key elements: the static attribute model of the network system and the rule matrix consisting of the interaction rules between the system members. Therefore, when establishing a network system model of the research object, it is necessary to construct both the static attribute model and the interaction rule matrix.

[0115] Definition 1 (Static Property Model) describes the static property model. mdl SA It is a binary tuple consisting of a set of member attributes M and a set of system attributes S, namely:

[0116] ,

[0117] ,

[0118] ;

[0119] The symbols represent the following: the number of member nodes in the nm network system; the number of member attributes of the i-th member node in nma; the number of system attributes of the entire nsa network; the set of member attributes of the i-th member node in Mi; the k-th element in the set of member attributes of the i-th member node in oik; and the j-th element in the set of system attributes of sj.

[0120] Definition 2 (Network System Model) describes a network system consisting of binary tuples. mdl NS To describe this, the binary tuple is derived from the static attribute model of the network system. mdl SA and its interaction rule matrix RL n×n Composition, namely:

[0121] mdl NS =(mdl SA, RL n×n );

[0122] Among them, RL n×n The i r Line number j r The elements of the column represent the i-th element in the network system. r The member node receives the first j r The set of rules governing the attribute state changes of each member node, after providing information about that node. Specifically, RL... n×n The elements on the diagonal represent the attribute change rules of a member node itself, and these changes do not require information from other member nodes.

[0123] 1. Construction of the static attribute model

[0124] A clear understanding of the system is the foundation for constructing a static attribute model of a network system. To understand the research object scientifically and efficiently, a comprehensive system analysis of the network system is necessary. System analysis consists of two levels: structural analysis and attribute analysis.

[0125] In structural analysis, the first step is to clearly identify the members that make up the network system, determine the total number of members, and group members that may have the same set of attributes together. Secondly, the foreseeable interactions between members are described and listed using natural language, and a preliminary qualitative analysis of the interaction rules is conducted.

[0126] In attribute analysis, attributes are extracted for each type of member and the system as a whole from three perspectives: identity, real-time information, and performance, forming an attribute set. The meanings of the identity attribute, real-time information attribute, and performance attribute are as follows:

[0127] (1) Identity attributes: attributes that distinguish the identity of members;

[0128] (2) Real-time information attributes: attributes that characterize the real-time status information of members;

[0129] (3) Performance attributes: attributes that characterize a member’s certain characteristics and abilities.

[0130] Example: System analysis of a 3-drone transport convoy example

[0131] First, a structural analysis is conducted. The formation consists of three members. Assuming the three drones are of the same model, the three members of the system share the same set of attributes and therefore belong to the same category. The formation employs a "leader-wingman" strategy; therefore, the primary interaction among the members is that the followers update their direction and speed in real time based on the real-time position information fed back by the navigator and the predetermined relative position.

[0132] Next, attribute analysis is performed. The identity attribute of each member drone is its name; for example, drones can be named "Leader," "Follower A," and "Follower B" to distinguish them. Their individual real-time position, real-time velocity, and real-time acceleration are essential real-time information attributes that need to be monitored. Performance attributes to consider may include the maximum allowable acceleration and maximum sensing range. The overall attribute of the formation system can be the connectivity status between the three member drones, which is a real-time information attribute.

[0133] The set of member attributes and the set of system attributes obtained from attribute analysis together constitute the static attribute model. The static attribute model is a continuously open model; newly extracted attributes can be added to it at any stage of modeling, and attributes that are determined to be unnecessary can be deleted at any time.

[0134] 2. Construction of the interaction rule matrix

[0135] In summary, constructing the interaction rule matrix involves four steps: task analysis, matrix framework building, rule description, and rule encoding. Rule encoding requires utilizing the results of attribute analysis, such as... Figure 4 As shown.

[0136] (1) Task Analysis

[0137] Interaction rules are products of specific task scenarios; therefore, the construction of the network system interaction rule matrix must be based on reasonable task analysis.

[0138] A target system may need to go through multiple stages to complete a task, and completing the sub-tasks of different stages may require different combinations of interaction rules. Therefore, the first necessary step in task analysis is to identify all the stages the target system will go through in the task and to rationally divide these task stages. For example, in the example of a 3-UAV formation system, the entire transportation task can be divided into two main stages: the formation stage (stage 1) and the formation flight stage (stage 2). In stage 1, the basic sub-task of the three UAVs is to take off from their respective parking positions and form a triangular formation according to the settings. In stage 2, the sub-task of the entire system is to cruise to the destination in a triangular formation, avoiding collisions with obstacles along the way.

[0139] (2) Construction of the interaction rule matrix framework and rule description

[0140] After completing the phase division, it is necessary to determine the number of members participating in each phase. Then, a matrix framework is generated for each phase, with the dimension of the matrix corresponding to the number of members participating in that phase. Finally, the interaction patterns between members are described in natural language and filled into the corresponding elements of the matrix. These matrices then serve as the prototype of the interaction rule matrix for each phase.

[0141] In the example of a 3-drone transport formation, since all three drones will participate in sub-tasks in both phases, the interaction rule matrices for phase 1 and phase 2 both have a dimension of 3. The established matrix framework is as follows: Figure 5 As shown. In Phase 1, the three drones are required to move from their respective parking positions to their initial formation positions without any coordination. Therefore, they only have their own rules of action. rl (1)And it appears on the diagonal of the interaction rule matrix. In Phase 2, the leader drone will cruise along a route pre-calculated by the path planning center to avoid obstacles, while the two follower drones (follower_a and follower_b) will track the leader drone's position in real time and maintain formation. Therefore, the leader drone will act independently, and the action rule is denoted as follows. rl (2) , is the element in the first row and first column of the rule matrix; and the two follower drones must obtain the real-time position of the leader drone to complete the sub-tasks of the formation flight phase, and the action rules they need to follow are denoted as rl (3) It is also an element in the 2nd row, 1st column and the 3rd row, 1st column of the interaction rule matrix, see details. Figure 5 .

[0142] The above three rules rl (1) , rl (2) and rl (3) The natural language descriptions are shown in Table 1.

[0143] Table 1. Description of the behavioral rules for controlling the formation flight of three drones.

[0144]

[0145] (3) Rule coding

[0146] Rule encoding refers to translating interaction rules from natural language into logical code that computers can understand. Specifically, firstly, 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, each rule is encapsulated into a callable function module using a computer language and stored in a "rule dictionary," so that computer programs can retrieve specific rule commands from the rule dictionary (functions) using the numerical numbers of the rules in the interaction rule matrix.

[0147] For example, give rules rl (1) , rl (2) and rl (3) The assigned numbers are 1, 2, and 3. Here, we only use... rl (3) To illustrate this more specifically, let's assume the follower drone acquires the real-time position of the navigator drone without delay. Then, the follower drone's position at the next moment is equal to the sum of the navigator drone's current position and the relative distance between the follower and navigator drones as defined in the formation. Figure 6The Matlab code example for the above statement is given.

[0148] The rule coding process is also a process of further in-depth analysis of the target system. During this process, more modeling details may emerge that may not have been noticed in the previous system and task analysis stages. Once this happens, it is necessary to add, delete, or adjust member or system attributes in the static attribute model to continuously update and optimize the network system model of the target system.

[0149] 3. Methods for establishing the phase space

[0150] The core of establishing a phase trajectory observation window is to construct the phase vector space of the network system through state analysis. Therefore, reasonable state analysis is the foundation for establishing a phase trajectory observation window.

[0151] The state behavior of a network system is only meaningful within a specific task scenario. For the same network system, the states that need to be focused on differ depending on the task requirements. For example, for a drone swarm performing a search task, we are more concerned with the state changes of its search results; while if the same drone swarm is performing a transportation task, we may be more concerned with the accuracy and timeliness of the transportation. Therefore, the state analysis in the phase trajectory modeling process is task-oriented state analysis and needs to be conducted based on the results of task analysis.

[0152] Table 2 Sample Table for Status Analysis

[0153]

[0154] The task analysis results provide a clear division of task phases. To utilize these results for state analysis, it is necessary to first clarify the specific task requirements for each phase. For each task requirement, a qualitative description of the corresponding network state is provided. Finally, a quantitative description method is defined for each network state. This invention provides a sample table as shown in Table 2 to guide state analysis.

[0155] Instructions for filling out the status analysis sample form:

[0156] Table 2 shows a sample status analysis table containing five columns of information. The first column contains information derived from the task analysis results, listing the task phase names in chronological order from top to bottom.

[0157] Starting from the second column, organize and fill in the information in a left-to-right, top-to-bottom order. The second column contains a summary of the specific requirements of the network system under each stage of the sub-task; the third column contains the name of the network system state that reflects the completion status of the task requirements; the fourth column contains the name of the state variable corresponding to this network system state; and the last column is the result of judging the continuity of the state variables.

[0158] The source of the state variables in the fourth column can be common physical variables or user-defined variables. When defining user-defined state variables, the following two conditions must be met:

[0159] (1) State variables must be defined as scalars;

[0160] (2) Multiple state variables in the same stage are independent of each other, meaning that state variables cannot be derived from each other.

[0161] Table 3.3 - Status Analysis Table for Example of Unmanned Aerial Vehicle Transport Formation

[0162]

[0163] After completing the state analysis and filling in the state analysis table, a phase space is constructed based on the specific state variables. Generally, the number and type of state variables differ for each task stage; therefore, the phase space for each task stage is also different. In other words, the phase space is constructed on a task-stage basis. Specifically, the construction method involves spanning the state variables corresponding to each stage into a space where all dimensions are orthogonal.

[0164] For example, the results of the state analysis of the 3-UAV transport formation example are shown in Table 3. As can be seen from the table, the formation system has only one state variable, "formation shape variable", in phase 1. Therefore, its phase space in phase 1 is a one-dimensional space spanned by the formation shape variable. Similarly, in phase 2, the phase space is a two-dimensional space spanned by the "formation shape variable" and the "swarm collision identifier variable".

[0165] 4. Method for establishing the disturbance impulse injection module

[0166] Interference analysis is the foundation for establishing the disturbance impulse injection module, and mainly includes two parts: first, determining the type of interference, and second, defining the intensity of the interference.

[0167] 4.1 Determining the type of disturbance based on state variables

[0168] When conducting interference analysis, the first step should be to identify the main types of interference for each state variable by analyzing the sources of interference. The sources of interference can be analyzed from both internal and external perspectives:

[0169] (1) Interference caused by internal factors refers to the interference on the system state variables caused by performance constraints, performance degradation, and faults of the members or the connections between members of the network system. For example, for the formation shape of a 3-UAV transport formation in phase 2, communication failure between UAVs can cause follower UAVs to be unable to perceive the position of the leader, thereby losing the required formation and causing a change in the formation shape. In this case, the communication failure between the 3 UAVs is a kind of interference.

[0170] (2) External interference refers to environmental factors that cause interference to state variables in the network system's operating environment. For example, for all UAV swarm networks operating in Earth's airspace, natural wind is a non-negligible interference; for UAV formations performing combat missions, enemy firepower is also a typical interference.

[0171] 4.2 Define Interference Intensity

[0172] Because interference in network system phase trajectory modeling is generalized, there are often no direct, typical physical quantities to represent its intensity. For example, communication failures between UAVs, as an example of interference in phase 2 of a formation, do not have a physical quantity that can directly describe the magnitude of their impact. Therefore, after identifying the type of interference, it is necessary to define the intensity of each type of interference to provide a clear measurement method. The basic principle for defining interference intensity is: the greater the impact of the interference on the network system's state variables, the greater the interference intensity.

[0173] Based on the definition of interference intensity, the intensity and duration of the interference effect on specific attributes in the network system model are described and encoded, thereby realizing the injection of disturbance impulse and completing the establishment of the disturbance impulse injection module.

[0174] For example, in the formation example, interference from communication failures between drones can be reflected through the system property "Connectivity Status Between Drones": when a drone experiences a communication failure, its connectivity status with the other two drones changes to "Unconnectable". The duration of the communication failure corresponds to the duration of the "Unconnectable" state.

[0175] 5. Approximate calibration in the stability region

[0176] Currently, at least the following three types of stability regions need to be calibrated in the phase point trajectory simulation of the prediction model of the UAV network system:

[0177] (1) The initial stability region of a phase point after the network system starts operating and reaches a stable state. ;

[0178] (2) The stability region that the phase point reaches farthest from the initial stability region under the action of the disturbance impulse. (This stability region may be a maximally stable region, at which point the network system is in a state of collapse.)

[0179] (3) The stable region that the phase point re-enters under the recovery mechanism after the disturbance impulse stops. .

[0180] In some cases, the three types of stability regions of a network system's nodes are quite clear and can be obtained through state analysis or theoretical derivation. However, in other cases, the dynamic interaction between nodes in the network system makes it difficult to obtain the precise values ​​of the center vector and radius vector of the stability region. In such cases, a reasonable approximate alternative method is urgently needed.

[0181] To address the difficulty in obtaining precise values ​​for the center vector and radius vector of the stability domain in some cases, this invention proposes an approximate stability domain calibration method. The stability domain calibration model in this method ensures a certain level of approximation accuracy. At this accuracy, the deviation between the approximate calibrated stability domain and the theoretical value is very small compared to the change in the stability domain under the influence of disturbance impulses.

[0182] The stability region approximation calibration method proposed in this invention utilizes the NARX neural network time series prediction model. The core idea of ​​this method is to use the most recent phase trajectory data and the predicted data obtained through the time series prediction model to provide approximate estimates of the center vector and radial vector of the stability region. The overall approach of the method is as follows: Figure 7 As shown; for specific methods, please refer to the applicant's Chinese invention patent application (Patent title: A method, system and program for calibrating the phase point stability domain of a UAV network system prediction model, application number: 2025109211769, application date: 20250704).

[0183] 6. Limiting impulse determination

[0184] The purpose of this invention is to determine the maximum impulse that a network system can withstand under certain disturbances, thus providing a boundary for disturbance injection experiments. Considering the differences in disturbance intensity types and value ranges, and studying the linear and nonlinear characteristics of multi-round measurement data, this invention proposes a method for determining the maximum impulse using simulation experiments. The basic idea of ​​this method is to first extract the intensity values ​​of the disturbance according to its characteristics, then conduct simulation experiments according to the principle of decreasing intensity and increasing step size, iteratively obtaining the maximum step size data corresponding to each intensity value. Next, it is determined whether there is a strong linear relationship between the stress intensity data and the maximum step size data, and finally, the final maximum impulse value is determined based on the judgment result. To improve the efficiency of the simulation experiment, the measurement method is designed as a maximum impulse measuring device, the structure of which is as follows: Figure 7As shown; for specific methods, please refer to the applicant's Chinese invention patent application (Patent title: Method, system, storage medium and program for measuring the ultimate impulse of a UAV network system, application number: 2025109211735, application date: 20250704).

[0185] 7. Simulation of Disturbance Impulse Injection

[0186] The disturbance impulse injection experiment of this invention refers to a simulation experiment that obtains the trajectory characteristics of system phase points by injecting a certain disturbance within the limit impulse range into the network system model. Figure 9 The basic process for conducting disturbance impulse injection experiments for specific interference is given; for the specific method, please refer to the applicant's Chinese invention patent application (Patent title: A simulation method, system, medium and program product for disturbance impulse injection in UAV network system, application number: 202510921174X, application date: 20250704).

[0187] The case study object of this invention is a such Figure 10 The diagram shows a multi-UAV formation network system performing formation flight missions at a fixed cruising altitude. The network system consists of nine isomorphic rotary-wing UAVs, which are required to form a "T" formation and maintain the formation along a planned trajectory.

[0188] This multi-UAV network system employs a "leader-wingman" formation strategy. The lead UAV (UAV 1) acts as the leader of the entire network, UAVs 2-5 are primary wingmen, and UAVs 6-9 are secondary wingmen. At the start of the mission, the nine isomorphic rotary-wing UAVs synchronously take off vertically from the ground to their cruising altitude. Then, at this altitude, they form the required formation by moving within the xoy plane. Next, UAV 1 receives the path planning results and flies along the planned path according to the path tracking strategy. Simultaneously, UAVs 2-5 acquire the real-time position information of UAV 1 and maintain a corresponding relative distance; while UAVs 6-9 simultaneously acquire the position information of their adjacent primary wingmen and maintain a corresponding relative distance. Under this strategy, the multi-UAV network system achieves overall formation flight.

[0189] 1. Phase trajectory modeling of UAV formation networks

[0190] In the modeling process of this invention, the following aspects will be simplified.

[0191] (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;

[0192] (2) The motion constraints of the UAV are not considered, that is, it is assumed that the UAV can move in any direction instantly;

[0193] (3) The perception constraints of the UAV are not considered, that is, it is assumed that the UAV can obtain the location information of other UAV nodes without delay;

[0194] (4) The problem of drone endurance is not considered, that is, it is assumed that drones can fly continuously.

[0195] 1.1 Establishment of Network System Model

[0196] 1.1.1 Static Attribute Model

[0197] According to Definition 1, the static attribute model of the case-specific UAV swarm network takes the form of:

[0198] mdl SA =(M,S).(1.1)

[0199] Where M is the set of member attributes and S is the set of system attributes. The following details the construction of the member attribute set and the system attribute set.

[0200] (1) Member attribute set

[0201] The drone swarm network consists of 9 drones, and each member's attribute set should include 9 elements, where each element represents a drone's attribute set.

[0202] (1.2)

[0203] Since the nine drones are isomorphic, they are all members of the same class, possessing the same membership attributes; that is, the sets represented by each element in equation (5.2) are equal. To complete the required formation flight mission, each drone must establish the following attributes: drone number representing its identity, position coordinates representing real-time information, and communication range and maximum speed representing performance attributes. Specifically, there are...

[0204] (1.3)

[0205] The meaning and specific form of each symbol are as follows:

[0206]

[0207] (2) System attribute set

[0208] The system attribute set of the drone swarm network includes the necessary elements to describe the overall state of the network, as follows:

[0209] (1.4)

[0210] The meaning and specific form of each symbol are as follows:

[0211]

[0212] The following is about insDic , cnctA and cnctS To provide further explanation.

[0213] Interaction rule number information matrix insDic :

[0214] 9x9 insDic The matrix contains the element in the i-th row and j-th column, which records the interaction rule number that drone number i needs drone number j to provide information and take action.

[0215] Connectivity Information Matrix cnctA :

[0216] 9x9 cnctA Each element of the matrix is ​​a Boolean variable. When the element in the i-th row and j-th column is 1, it indicates that the drone numbered i and the drone numbered j have the ability to communicate with each other. As long as the relative distance is within their respective communication range, 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 to communicate with each other. Even if the relative distance is within the communication range, the two cannot share information.

[0217] set up cnctA The purpose of the matrix is ​​to provide an injection interface for interference such as "communication failures." However, in the initial stage of system model building, 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).

[0218] Connectivity state matrix cnctS :

[0219] 9x9 cnctS Each element of the matrix is ​​a Boolean variable. When the element in the i-th row and j-th column is 1, it indicates that drone i and drone 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 information from each other.

[0220] The connected state matrix has the following characteristics:

[0221] (1) The connected state matrix is ​​a symmetric square matrix. Since the value of each element represents the bidirectional communication characteristics between the two UAVs at the corresponding position, the values ​​of elements at symmetric positions must be the same.

[0222] (2) The connectivity status matrix is a dynamic matrix. Whether two UAVs are in a connected state depends on dynamic factors such as the requirements including the formation strategy, the value of the corresponding elements in the connectivity information matrix cnctA and the relative position between the two UAVs. For example, when cnctA the matrix takes the default value and the formation is maintaining Figure 10 the stable "square" formation as shown, cnctS the value of the matrix is as Figure 11 shown in (b) of.

[0223] (3) Specifically, the elements on the diagonal of the connectivity status matrix always take the value of 1, indicating that the UAV can grasp its own dynamic information in real time.

[0224] Combining equations (1.2) - (1.4), the static attribute model of the cluster formation composed of 9 UAVs is obtained, which is

[0225] (1.5)

[0226] 1.2 Interaction rule matrix

[0227] (1) Task analysis

[0228] The flight tasks of the UAV formation can be divided into two stages, namely the teaming stage and the formation flight stage.

[0229] Stage 1: Teaming stage

[0230] The initial position coordinates of each UAV in the take-off area are given. In the teaming stage, the UAVs will fly from their respective initial positions to the teaming positions, so that the entire cluster forms a stable "square" formation in the teaming area.

[0231] The UAVs that arrive at the teaming positions in advance will hover and wait until all 9 UAVs reach the designated teaming positions, and then the entire cluster will execute the flight tasks in Stage 2.

[0232] Stage 2: Formation flight stage

[0233] After the cluster completes teaming, UAV No. 1 will fly along the planned path, and the other UAVs will fly according to the following rules, and the entire cluster will achieve the task of flying along the planned path in the "square" formation.

[0234] The two stages of the task are as Figure 12 shown.

[0235] (2) Interaction rule matrix framework

[0236] Throughout the flight mission, the interaction activities of the drone swarm network system take place among the nine drones. Therefore, its interaction rule matrix is ​​always a 9×9 square.

[0237] The mission requirements of drones differ at different mission stages, therefore, the interaction rules they need to follow also differ. The interaction rule matrix varies depending on the mission stage. The content and implementation algorithms of these interaction rules are explained in detail below.

[0238] (3) Rule description

[0239] The rules were set up step by step according to the phase sequence of the formation's mission, and the five interaction rules listed in Table 4 were finally formed.

[0240] Table 4. List of Network Interaction Rules for UAVs Performing Formation Flight Missions

[0241]

[0242] Table 4 lists five rules that constitute the interaction rule dictionary of the case-based UAV formation network. When the cluster performs formation tasks, it needs to access the corresponding rule according to the index of the interaction rule matrix to take action.

[0243] As can be seen from the rule description, the team formation rules rl (1) / 1 and collision avoidance rules rl (2) / 2 Guides the cluster's behavior during task phase one, path tracing rules rl (3) / 3 and drone follow rules rl (4) / 4 Guides the cluster's behavior in task phase two, perceiving rules rl (5) / 5 applies to the entire process of system behavior. Therefore, the interaction rule matrix differs at different stages of the task.

[0244] Figure 13 The interaction rule matrix RL of the case drone formation network is given in two task phases. 9´9 The elements in the matrix represent the set of numbers of the interaction rules that need to be followed between two drones at corresponding positions.

[0245] Equation (1.5) and Figure 13 The interaction rule matrix RL shown 9´9 By combining these models, a network system model of a drone formation consisting of nine drones performing a "T" formation flight mission can be obtained.

[0246] 1.3 Model Simulation and Result Display

[0247] The initial state of the simulation is that 9 drones are hovering in the takeoff area. Therefore, at the start of the simulation, drone members should be generated one by one, and their initial position coordinates in the takeoff area should be randomly assigned. An integer ξ is randomly generated in the interval [1,2]. x A random integer ξ is generated in the interval [1, 11]. y Based on random integers, the initial position coordinates randomly assigned to the drone crew are [ x 0 ,y 0 ],in

[0248] (1.6)

[0249] If the coordinates are already occupied, regenerate the coordinates randomly using the method described above until the generated coordinates are unoccupied. Use this coordinate value as the initial position coordinates of the newly generated drone crew member in the takeoff area.

[0250] 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 realize the simulated flight of the swarm formation. The specific parameter settings for this case study are given below, following the rules.

[0251] (1) Parameter settings for team formation rules: The coefficient is k x =k y =0.00005. The target location coordinates of the UAV are shown in Table 5.

[0252] Table 5. Coordinates of UAV Target Positions in Team Formation Rules

[0253]

[0254] (2) Parameter settings in collision avoidance rules: The coefficients in the collision avoidance rules are set to k. r =0.000005; Distance threshold set to d th =1.

[0255] (3) Parameter settings for path tracing rules: The coefficients of the PID controller in the path tracing rules are set to...

[0256] K Px = K Py =1; K Ix = K Iy =1; K Dx = K Dy =0.

[0257] (4)Parameter settings for the UAV following rule: The coefficients of the PID controller in the UAV following rule are set as

[0258] K Px = K Py = 1; K Ix = K Iy = 1; K Dx = K Dy = 0.

[0259] The side length of the "cross" formation is set as a = 10.

[0260] Figure 14 The running process of one simulation is given. Among them, Figure 14 (a) in it shows the initial state where the UAV formation network hovers in the take-off area; (b) shows that the network system is forming a "cross" formation according to the teaming rules and collision avoidance rules; (c) shows the state after teaming up, and the formation is waiting for the order to execute the second-stage task; (d) shows that the formation starts to fly as a whole along the planned trajectory in a "cross" formation; (e) shows that the UAV formation network is in the process of formation flight. It can be seen that at this time, the stability of the path tracking rule and the PID controller in the UAV following rule can meet the requirements, and the network as a whole can fly very smoothly along the specified path; (f) shows the complete flight trajectory after the UAV formation network reaches the destination.

[0261] 1.4 Construction of the phase vector space

[0262] The most important task requirement of this UAV formation network is to fly as a whole along the planned path in a "cross" formation. 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 amount and position offset amount for quantitative measurement. According to the above analysis idea, the corresponding state analysis table of this case is shown in Table 6.

[0263] Table 6 State analysis table of the UAV formation network

[0264]

[0265] In the table, the definitions of the formation deformation amount and position offset amount are as follows.

[0266] Definition 3 (Formation Deformation): Establish a Cartesian coordinate system with UAV 1 as the origin. Then, at any time t, let P be the desired position vector of UAV i (i=2,3,…,9). e,i (t), the actual position vector is P a,i (t), then the deformation of UAV i is trf i (t) is defined as the 2-norm of the difference between the desired position vector and the actual position vector, i.e.

[0267] (1.7)

[0268] The overall formation shape variable trf(t) of the UAV formation network is defined as follows:

[0269] (1.8)

[0270] Wherein, the expected position vector is the vector pointing from the actual position of UAV 1 to the specified position of UAV i in the formation, and the actual position vector is the vector pointing from the actual position of UAV 1 to the actual position of UAV i at time t, such as... Figure 15 As shown.

[0271] Definition 4 (Position Deviation): Using a ground coordinate system, let P be the path position vector planned by UAV 1 at any time t. 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 and the actual position vector of UAV 1, i.e.

[0272] (1.9)

[0273] The values ​​of the array shape variable and the position deviation are both in the range of [0, +∞), and both are small variables. That is, the closer the value is to 0, the more the operation of the UAV formation network meets the mission requirements.

[0274] In the first phase of the mission, the UAV formation network needs to complete the formation task, at which point only the network's formation state needs to be monitored. However, in the second phase, the UAV formation network is required to maintain its formation while also flying along the planned path, requiring simultaneous monitoring of both its formation and position states. Therefore, in the formation phase, the phase space of this UAV formation network is a 1-dimensional space spanned by vector elements representing the formation state; in the formation flight phase, the phase space is a 2-dimensional space spanned by vector elements representing both the formation and position states, as follows... Figure 16 .

[0275] 1.5 Definition of Interference Intensity

[0276] This invention analyzes the types of interference that the UAV formation network faces from two aspects: its own faults and external environmental factors, and provides a quantitative expression of the interference intensity.

[0277] (1) Identify the type of interference

[0278] Based on the state analysis results, the formation and position status of the drone swarm network are the network states that require attention. According to the drone swarm network operation rules listed in Table 4, normal communication between drones is fundamental to ensuring the stability of the network system's formation and position. If a drone experiences a communication failure and is unable to acquire or transmit information, the formation and position status of the entire drone swarm will inevitably be affected. Therefore, communication failure of a single drone is the first type of interference that the drone swarm in this case needs to withstand.

[0279] In addition, drone swarms encounter natural winds during flight, which can alter their formation and position. Therefore, wind force is the second type of interference experienced by the drone swarm in this case study.

[0280] (2) Define the interference intensity

[0281] Interference 1: Communication failure of a single drone

[0282] In this case study of a drone swarm network, all nine drones could potentially experience communication failures. However, due to the interconnectedness of the swarm structure, the impact of communication failures on the network's formation and position status varies depending on the drone. For instance, during formation flight, if drone number 1 experiences a communication failure, drones 2-5 will be unable to fly normally, and drones 6-9, following drones 2-5, will also be unable to determine the correct flight direction, causing the entire network to momentarily lose its correct position update direction. However, if drone number 6 experiences a communication failure, only it will be unable to determine its next flight direction, while the other drones will be unaffected. In reality, the interference intensity caused by drone communication failures is related to the number of drones connected to it.

[0283] In complex network theory, the degree of a node refers to the number of edges connected to that node, and is related to the strength of the communication failure. This case study uses the concept of node degree to provide a quantitative expression of the strength of the communication failure.

[0284] Let deg(i) be the degree of drone i. The drone numbers that experience communication failures at a certain moment are recorded in set A. Then, the intensity of this interference at that moment is:

[0285] (1.10)

[0286] As can be seen from equation (1.10), the communication fault intensity σCF It represents a finite number of values ​​within the interval [0,1]. For example, when UAV 1 and UAV 9 simultaneously experience a communication failure, the communication failure strength experienced by the UAV formation network is...

[0287]

[0288] In particular, σ CF =0 indicates that no drone communication failure occurred; σ CF =1 indicates that all drones experienced a communication failure simultaneously.

[0289] Interference 2: Wind

[0290] This case study uses a simplified Newtonian force to describe the intensity of the wind, denoted as σw, and assumes that the wind force acts on 9 drones simultaneously.

[0291] σw is a vector whose components are denoted as [σ W,x ,σ W,y ] represent the wind intensity in the x and y directions, respectively, such as Figure 17 As shown. The magnitude of the wind force σw is described by the 2-norm of the vector, i.e. .

[0292] 1.6 Observation of phase point trajectories

[0293] This invention also demonstrates the phase point trajectories of the UAV formation network under both unperturbed impulse injection and perturbed impulse injection scenarios after the aforementioned modeling process.

[0294] (1) Case of no disturbance impulse injection

[0295] Following equations (1.8) and (1.9), a module for calculating the lattice deformation and position offset is added to the network system model. Figure 16 In the phase space shown, the phase point trajectories of the two phases of the task are drawn respectively.

[0296] This invention uses simulation to obtain approximate results of phase point trajectories. Specifically, it retains the phase point positions obtained from each simulation and connects these discrete points sequentially. The smaller the simulation step size, the smoother the phase point trajectory will be, and the closer it will be to the analytical result. Figure 18 The diagram shows the simulated phase point trajectory of the UAV starting from the takeoff positions listed in Table 7. The arrows in the diagram indicate the direction of movement of the phase points. Specifically, to represent the change of the phase point trajectory during the formation phase with the number of simulation steps, [further details are needed]. Figure 18 In (a), the 1-dimensional phase space characterized by the formation state is combined with the time dimension (simulation steps); Figure 18 (b) shows that during the formation flight phase, the cluster phase point moves rapidly in phase space to a small region of stable oscillation.

[0297] Table 7. Takeoff positions of the 9 UAVs

[0298]

[0299] (2) Case of injecting disturbance impulse

[0300] 1. The disturbance impulse generated by the injected wind power

[0301] The disturbance encountered during both the formation and formation flight phases is natural wind. Let the wind force be σ. W =[σ W,x ,σ W,y If the acceleration increment a of drone i under wind force is given, then... W,i =[ax W,i ,ay W,i ]for

[0302] (1.11)

[0303] Among them, K Wx,i and K Wy,i is a coefficient.

[0304] Let the acceleration of drone i obtained through the action rules be... The combined acceleration under wind interference is:

[0305] (1.12)

[0306] According to the algorithms in equations (1.11) and (1.12), the coefficient K is... Wx,i and K Wy,i Set to 0.2. The injection strength was set to [value] during the 40th simulation in the team formation phase. The network was subjected to wind interference for two simulation steps to obtain the network's response time when the wind impulse was... The phase point trajectory below is as follows Figure 19 As shown, the hysteresis phenomenon of phase point trajectory offset can be observed.

[0307] In the 500th simulation during the formation flight phase, the injection size was... The wind interference was investigated for one simulation step, and the phase trajectory of the network in the wind impulse [1,1] was obtained as follows. Figure 20 As shown, the variations in array deformation and position offset with the number of simulations are displayed, providing a clearer view of the impact of wind disturbances on the phase point position. Figure 20 ② and ③ in the text.

[0308] 2. Injecting disturbance impulses generated by communication failures

[0309] Unmanned aerial vehicle (UAV) communication failures alter system properties in the network system model. cnctA The specific values ​​of the (connectivity information matrix) are injected. 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 follows Figure 21 The matrix shown is restored to its original state at the 350th simulation step. Figure 11 The default case is shown in (a). In this case, the injected communication fault strength is (3+3+2) / 24=0.3, the disturbance impulse is 33, and the obtained phase trajectory is as follows. Figure 22 As shown.

[0310] It should be noted that, in order to more clearly demonstrate the changes in the phase point trajectories, some simulation settings were adjusted when obtaining the phase point trajectories of and , making the motion of the UAV formation network exhibit greater volatility. Specifically, the coefficients of the PID controller in the path tracking rule and the UAV following rule were changed to .

[0311] K Px = K Py =0.05; K Ix = K Iy =0.03; K Dx = K Dy =0.01.

[0312] 1.7 Acquisition of Phenomenon Trajectories in UAV Formation Networks

[0313] 1.7.1 Approximate calibration of the stability region

[0314] 1.7.1.1 Determination of the initial stability region

[0315] The state analysis results from the construction of the phase space show that the phase space of the UAV formation network in stage one is a 1-dimensional space composed of formation deformation variables, while the phase space in stage two is a 2-dimensional space spanned by formation deformation variables and position offsets. Since the phase spaces are different in different stages, the initial stability regions for each stage must be calibrated separately. Let the initial stability region of stage one be denoted as... Phase Two is .

[0316] 1.7.1.2 Analysis of the initial stability region in stage one

[0317] The initial stable region of Phase 1 can be obtained through theoretical analysis of the formation rules. The basic idea is to reallocate the velocity of a single drone as it approaches the target point in the next moment, ensuring it reaches the target point just in the next moment. Once the drone reaches the target point, its acceleration will remain zero, and according to the anti-oscillation operation, its velocity will also remain zero. The drone will remain stationary at the target point, and the formation deformation of the drone formation will stabilize at zero. Therefore, the initial stable region of Phase 1... That is, the phase point will stabilize at point 0 in the first stage, at which point the center point is 0 and the diameter is 0.

[0318] Using the same simulation parameter values ​​as those observed in the phase point trajectory, the simulation model was run continuously for 6000 simulation steps in Phase 1. The simulation results show that from the 520th simulation step onwards, the array deformation remains at 0, confirming the above analysis.

[0319] 1.7.1.3 Approximate calibration of the initial stable region in stage two

[0320] The initial stable domain of Phase 2 needs to be approximated using a stable domain approximation calibration method, as shown in the Chinese invention patent application (Patent title: A method, system and program for calibrating the phase point stable domain of a UAV network system prediction model, application number: 2025109211769, application date: 20250704).

[0321] 1.7.2 Determination of the limiting impulse for two types of interference

[0322] According to interference analysis, the case study's UAV swarm network is affected by two types of interference: communication failure of individual UAVs and natural wind. The extreme impulse measurement method was used to analyze and determine the magnitude of the extreme impulse corresponding to each type of interference. The results are shown in the Chinese invention patent application (Patent title: Method, System, Storage Medium and Program for Determining Extreme Impulse of UAV Network System, Application No.: 2025109211735, Application Date: 20250704).

[0323] 1.7.3 Two-stage disturbance impulse injection experiment and data processing

[0324] This case study only conducted disturbance impulse injection simulation experiments for wind force in Phase 1 and communication failure of a single UAV in Phase 2. The wind force injection and subsequent analysis in Phase 2 are similar to those in Phase 1. The results are shown in the Chinese invention patent application (Patent title: A simulation method, system, medium and program product for disturbance impulse injection in a UAV network system, application number: 202510921174X, application date: 20250704).

[0325] The foregoing description of embodiments of the present invention, through which those skilled in the art are able to implement or use the present invention, will be readily apparent to those skilled in the art. Various modifications to these embodiments will be readily apparent to those skilled in the art. The general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novelty disclosed herein.

Claims

1. A method for simulating and modeling the trajectory of a phase point in an unmanned aerial vehicle (UAV) network system, characterized in that, It includes the following steps: 1) System analysis and task analysis: The target UAV network is divided into members and its attributes are collected to obtain a static attribute model composed of member attribute sets and system attribute sets; 2) Construction of interaction rule matrix: According to the task stage, the member interaction relationship of each stage is described, numbered and encoded to obtain the interaction rule matrix of the corresponding stage; 3) State analysis: Based on the task phase division, extract state variables that can measure network performance and determine their types, and then span the phase vector space in each phase. 4) Approximate calibration of the stable domain: The original phase point trajectory data is augmented with linear Gaussian white noise, and the future trajectory of the phase point is predicted using a NARX neural network time series model. The center vector and radius vector of the stable domain are calculated in combination with the observation window data. 5) Limit impulse measurement: For a predetermined type of interference, the maximum tolerable step size is obtained by a measuring device based on the principle of decreasing intensity and increasing step size. After determining the linearity, the limit impulse is output. 6) Disturbance impulse injection simulation: Generate the disturbance intensity-step matrix within the limit impulse range, fix the initial state of the network system model and run it until it is stable, and record the phase point trajectory until the termination threshold is met after each disturbance injection. 7) Data segmentation and transition zone labeling: Based on the phase point-stability region distance and threshold conditions, the start and end points of the transition zone are automatically labeled 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. The system attributes include at least an interaction rule number information matrix, a connectivity information matrix, and a connectivity state matrix. And / or, the static attribute model mdl SA It is a set of member attributes M and system attribute set S The resulting binary pair is: ， ， ； The meanings of each symbol are as follows: 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 attributes of the network as a whole; M i The set of member attributes of the i-th member node; o i k The k-th element in the member attribute set of the i-th member node; s j The j-th element in the system attribute set; And / or, the network system consists of binary tuples mdl NS To describe this, the binary tuple is derived from 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 The i r Line number j r The elements of the column represent the i-th element in the network system. r The member node receives the first j r The set of rules governing the change of attribute states of each member node.

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

4. The method according to claim 1, characterized in that, The state 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 phase, refine the sub-task requirements for that phase; 3.3) Based on the requirements of the sub-tasks, qualitatively describe the network status that reflects the task completion status; 3.4) Assign at least one scalar state variable for each network state to quantitatively describe the network state; the scalar satisfies that any two state variables are independent within the same stage; 3.5) Classify the state variables as either continuous or discrete and record the classification in the state analysis table; 3.6) Fill in the task stage, task requirements, network status, state variables and their types into the state analysis table in sequence, and construct the phase space according to the specific state variables.

5. The method according to claim 1, characterized in that, Step 4) involves the following steps for approximate calibration of the stability region: 4.1) Collect the original trajectory data of multidimensional phase points in phase space within a continuous step size, and store them in a matrix format with "the first row being the step size sequence and the remaining rows being the position coordinates of each dimension". 4.2) Determine whether the number of columns in the original data matrix is ​​less than the preset data expansion threshold. If so, perform data expansion processing; otherwise, skip this process. 4.3) In the data augmentation process, several new data points are uniformly inserted between adjacent step-size data, and Gaussian white noise is introduced into the inserted data to generate an augmented data matrix; 4.4) According to the 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 composed of predicted data points; 4.5) According to the preset observation window size, the data in the last column of the original data matrix is ​​extracted to form an observation matrix; 4.6) The observation data and the prediction data are merged into a calibration dataset, input into the stable domain calibration model, and the center vector and radial approximation values ​​of the target stable domain are output.

6. The method according to claim 1, characterized in that, Step 5) The method for determining the ultimate impulse includes the following steps: 5.1) Obtain the range identifier of interference intensity. flg1 Continuous characteristic identification of interference intensity flg2 And set the number of measurements. c ; 5.2) According to flg1 and flg2 The logical combination of the interference intensity extraction module determines a set of interference intensity data, which is sorted from largest to smallest according to the absolute value of its disturbance to the system. 5.3) Following the principle of decreasing intensity and increasing step size, the measurement module is used to conduct simulation experiments on each disturbance intensity, and the maximum action step size that keeps the system stable in the phase vector space state dimension is determined iteratively. 5.4) Input all interference intensity data and the corresponding maximum action step size 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 of the product of each interference intensity and the maximum step size is used as the limit impulse output; if it does not hold, the minimum interference intensity and the maximum step size product is output as the limit impulse value.

7. The method according to claim 1, characterized in that, Step 6) involves the following steps in simulating the disturbance impulse injection: 6.1) Set the number of injections: Preset a positive integer. cnt This represents the number of interference injection rounds to be performed in this experiment; 6.2) Generate the interference parameter matrix: Construct a two-dimensional numerical matrix D σ The first row represents the interference intensity for each round, and the second row represents the corresponding action step size. 6.3) Prepare the network system model: Fix the initial state of the network system model and start the model to run to a stable state; ensure that the network system model remains in the same stable state every time interference is injected; 6.4) The first part of the injected interference intensity data matrix i Column values: Set the disturbance intensity in the model's disturbance impulse injection module to [value]. σ m The duration of action is sp m This allows the simulation model to continue running; 6.5) Record and observe phase point trajectory data: Monitor the changes of phase points in the phase vector space in real time within the phase point trajectory observation window; when the change in phase point position is observed during the network system recovery phase, sp end Within each step, the value is less than the termination threshold ε. end If the network fails, terminate the operation and proceed to step 6.6; otherwise, continue executing step 6.

5. 6.6) Save the phase trajectory data of the nth injection experiment: Save the phase trajectory data of the nth disturbance impulse injection experiment as (n+1)× spr m numerical matrix D trcm ,in spr m The number of simulation steps from the start of the disturbance injection to the point of complete recovery to a stable operating state; 6.7) Obtain experimental data on disturbance impulse injection: cnt All numerical matrices obtained from the secondary perturbation impulse injection experiment D trcm Save as a cell array D eo This is so that data processing can be done later. m =1,…, cnt .

8. A simulation modeling system for phase point trajectories in an unmanned aerial vehicle (UAV) network system, characterized in that, The system implements the method described in any one of claims 1-7, comprising: A) an attribute modeling module for performing system analysis and task analysis, and generating a static attribute model; B) a rule management module for describing, numbering, and encoding interaction rules in natural language, and establishing an interaction rule matrix; C) a state space construction module for extracting state variables, determining their types, and generating phase vector spaces for each stage; D) a stability domain calibration module for expanding and predicting the original phase trajectory data and outputting the stability domain center vector and radial vector; E) a limit impulse determination module, including an interference intensity extractor, a measuring device, and a linear characteristic judge, for outputting the limit impulse of each interference in the phase vector space dimension; F) an impulse injection simulation module for generating an interference intensity-step matrix based on the limit impulse, performing multiple rounds of simulation, and collecting phase trajectory data; G) a data processing module for marking and segmenting the phase trajectory obtained from the simulation to form a searchable dataset; and H) an interaction interface module for providing phase trajectory data and stability domain information to the upper-level design platform or control algorithm.

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

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the method of any one of claims 1-7.

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