Unmanned aerial vehicle network system phase point trajectory modeling accuracy analysis method, system and software product

Abstract

The invention relates to the technical field of unmanned aerial vehicle network system modeling, in particular to an unmanned aerial vehicle network system phase point trajectory modeling accuracy analysis method and system and a software product. According to the method, a three-layer seven-node equilateral triangle topology model with an analytic solution is constructed, a unified PI controller is adopted to set a node following rule, a time domain trajectory analytic expression of each node is derived through Laplace transformation, error comparison with a multi-step numerical simulation result is carried out, and a maximum absolute error, a mean square error and an L2 norm are calculated. And when the error is lower than a preset threshold value, judging that the established model has simulation accuracy. The system can automatically output an error evaluation report, supports precision evaluation under complex topology and disturbance conditions, and improves the modeling verification efficiency and credibility of the unmanned aerial vehicle cluster.

Description

Technical Field

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

[0002] With the improvement of individual UAV 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 (MWS) 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] The applicant's earlier Chinese patent application (application number: 2025109865683, application date: 20250717) provides a method for simulating and modeling the phase trajectory of an unmanned aerial vehicle (UAV) network system. This method is an end-to-end closed-loop process from system analysis, rule matrix construction, state analysis, stability domain approximation calibration to limit impulse determination and disturbance injection simulation. It also achieves high-quality, structured trajectory dataset output through data segmentation and transition zone marking. It realizes the integration of simulation, control, and evaluation, and provides a new technical means for the robust design, verification, and real-time adjustment of multi-UAV systems.

[0005] However, existing technologies have not yet provided a solution to the accuracy of the aforementioned modeling process itself. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a method for analyzing the accuracy of phase trajectory modeling in UAV network systems. This method constructs a hierarchical triangular formation-PI control closed-loop analytical model, using formation deformation / position offset as the core state. It derives analytical solutions through Laplace inversion, and then evaluates the modeling accuracy and robustness through multi-step numerical simulation, error statistics, and extreme impulse disturbance experiments. This solves the problems of existing technologies being unable to quantitatively describe modeling errors and lacking a unified evaluation framework.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for analyzing the accuracy of phase point trajectory modeling in an unmanned aerial vehicle (UAV) network system includes the following steps: 1) Construct a three-layer network topology consisting of n UAV nodes in a simulation environment. The topology is composed of multiple nested equilateral triangle units. 2) Set the desired trajectory of the first layer node number #1 as x1(t), y1(t), where t is the time variable, and set the initial position, velocity, and acceleration of each node to zero in the x and y directions. 3) Configure PI controllers with proportional gain Kp=1 and integral gain Ki=1 for all nodes except node #1; based on the geometric relationship of equilateral triangles, use the output of the upper-level node as the target input of the lower-level node through the weight matrix; 4) Using the trajectory of node #1 as the system input, and based on the closed-loop transfer function formula of the negative feedback system, the analytical solutions x in the x and y directions of each node are obtained sequentially through Laplace transform. i (t),y i (t), i = 2 - n, where n is a positive integer greater than 2; 5) Calculate the array deformation of the network system in the x and y directions; 6) Run the discrete simulation model using at least two different time steps Δt to obtain the numerical solution for each node; compare the numerical solution with the analytical solution obtained in step 4), and calculate the maximum absolute error, mean square error and L2 norm; when the error is lower than the preset threshold, determine that the modeling method has the required accuracy.

[0008] Preferably, in step 2), the desired trajectory of the first-layer node number #1 is set as follows: - .

[0009] Preferably, the weight matrix in step 3) takes values ​​of ±2 within a triangle with a side length of 4 and ±1 within a triangle with a side length of 2.

[0010] As a preferred embodiment, the transfer function in step 4) is as follows: , The transfer function is solved using a block negative feedback structure. First, a block negative feedback structure is established for each follower node: , And use the following formula: , Derive the closed-loop response; Where s is the Laplace domain complex frequency variable, G(s) is the forward transfer function, H(s) is the unity feedback channel, and Φ i (s) is the closed-loop transfer function of the system.

[0011] Preferably, in step 4), x2(t) can be considered as the output of a negative feedback system; the input signal of this system is r(t) = t - 4, and the forward transfer function is G(s) = (s + 1) / s. 2 The transfer function of the feedback path is H(s)=1; Based on the closed-loop transfer function formula of a negative feedback system, performing a Laplace transform on the input r(t) = t - 4 yields: ; The Laplace transform of the output is: ; Performing an inverse Laplace transform on the above equation, we obtain the time-domain analytical expression of the output: ; Following the method described above, calculate x in the x and y directions sequentially. i (t),y i The analytical expression for (t) is given by i = 2 - n. in, [.] represents the Laplace transform operator, R(s) is the Laplace transform of the input signal r(t) = t - 4, X2(s) is the Laplace domain representation of node #2 in the x-direction, and e -t / 2 : Decay exponent.

[0012] Preferably, the time step Δt in step 6) includes at least 0.01s and 0.05s to simultaneously evaluate the model accuracy in high-fidelity and fast simulation scenarios.

[0013] Preferably, the calculation results of the error index in step 6) are used to automatically generate a simulation accuracy report, which includes an error-step relationship curve.

[0014] Preferably, the preset threshold in step 6) is set by the user according to the task requirements, and the threshold range is 10. -4 Up to 10 -2 .

[0015] Furthermore, the present invention also provides an unmanned aerial vehicle (UAV) network system for implementing the method, the system comprising: a) Topology configuration module, used to generate a three-layer, seven-node equilateral triangle network topology; b) Trajectory input module, used to inject the baseline trajectory x1(t), y1(t) into node #1; c) Controller management module, used to assign PI controllers to each follower node and write Kp, Ki parameters; d) Analytical computation module, used to perform Laplace transform and inverse transform, outputting analytical solution x. i (t),y i (t); e) Simulation execution module, used to run discrete simulations at a given time step and output numerical solutions; f) Error analysis module, used to compare analytical solutions with numerical solutions and generate error indices; g) Result determination module, used to output modeling accuracy conclusions based on error indicators and thresholds.

[0016] 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.

[0017] 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.

[0018] By employing the above-mentioned technical solution, and through analytical derivation and multi-step error evaluation of the multi-node hierarchical formation model, this invention achieves the following significant technical effects: 1. Establish analytical benchmarks and absolute quantization error By using a three-layer, seven-node equilateral triangle topology and a unified PI control law, a closed-form analytical solution network model is constructed, enabling a multi-UAV system to obtain a full-node time-domain analytical solution for the first time under a given input. Using the analytical solution as the "true value" reference, the absolute error quantification of numerical solutions under any simulation solver and any time step setting can be performed, avoiding the drawbacks of traditional empirical methods that can only make relative comparisons or rely on subjective thresholds.

[0019] 2. Provide the step size and error evaluation curves to determine the reliable simulation step size range. Numerical solutions are computed in parallel under various discrete step sizes. "Step size and error" curves are plotted using indicators such as maximum absolute error, mean square error, and L2L_2L2 norm. The "high-fidelity zone, transition zone, and distortion zone" are clearly defined, providing an objective basis for engineers to select the minimum acceptable step size. This can significantly reduce simulation time and computing power consumption while ensuring accuracy.

[0020] 3. Robustness and accuracy assessment under multiple disturbance conditions Under typical disturbance scenarios such as communication link failure and external pulse wind field, the upper bound of the model error and recovery time are analyzed, and the output error and disturbance intensity are mapped; a quantitative baseline is provided for control law tuning and fault-tolerant strategy design, thereby improving the reliability of the system in complex environments.

[0021] 4. Integration of simulation, control, and evaluation shortens the development iteration cycle. The system's modular integration of topology generation, PI control configuration, analytical solution, simulation execution, and error analysis enables researchers to complete model building and accuracy verification on the same platform, reducing the workload of cross-tool data migration and repetitive modeling.

[0022] 5. Automated generation of accuracy reports enhances repeatability and traceability. The software product can output PDF / HTML reports containing error curves, statistical tables, and threshold judgment results with one click, which facilitates project archiving and third-party review. With fixed inputs, fixed topology, and unified evaluation indicators, external teams can reproduce the testing process and achieve cross-institutional model accuracy comparison.

[0023] In summary, this invention solves the problem that existing technologies cannot quantitatively evaluate the modeling accuracy of multi-UAV networks by combining analytical benchmarks with multi-dimensional error metrics. It significantly improves simulation efficiency, result reliability, and model reproducibility, and has important value for research and engineering applications in the field of UAV swarm control. Attached Figure Description

[0024] Figure 1 A basic flowchart of the method for simulating and modeling the phase trajectory of an unmanned aerial vehicle (UAV) network system.

[0025] Figure 2 This is a diagram illustrating the mission execution process of a 3-drone transport formation.

[0026] Figure 3 To verify the stable topology of the example.

[0027] Figure 4 Block diagram of the PI controller for the following members.

[0028] Figure 5 The diagram shows the input-output x-direction relationship of the entire network system in the example.

[0029] Figure 6 The diagram shows the input-output y-direction relationship of the entire network system in the example.

[0030] Figure 7 For calculation x 2 ( t The negative feedback block diagram.

[0031] Figure 8 The desired position vector and the actual position vector.

[0032] Figure 9 The absolute error between the simulation step size model results and the analytical solution at integer time points.

[0033] Figure 10 for Figure 9 A magnified view of the area within the red box in the x-axis diagram.

[0034] Figure 11 for Figure 9 A magnified view of the area within the red box in the y-direction plot.

[0035] Figure 12 The simulation step size and absolute error exhibit a linear relationship in the logarithmic coordinate system. Detailed Implementation

[0036] 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.

[0037] like Figure 1As shown, referring to the applicant's previous Chinese patent application (application number: 2025109865683, application date: 20250717), a method for simulating and modeling the phase trajectory of an unmanned aerial vehicle (UAV) network system includes three basic components: 1) System analysis and task analysis: dividing the target UAV network into members and aggregating its attributes to obtain a static attribute model composed of member attribute sets and system attribute sets; 2) Construction of interaction rule matrix: describing, numbering, and encoding the member interaction relationships in each task stage to obtain the corresponding interaction rule matrix; 3) State analysis: extracting state variables that can measure network performance and determining their types based on the task stage division, and then spanning the phase vector space in each stage; 4) Approximate calibration of the stability domain: applying the original phase trajectory data... The process involves: 1) Linear Gaussian white noise augmentation; 2) Predicting future phase trajectories using a NARX neural network time series model; 3) Calculating the center vector and radial vector of the stable domain using observation window data; 4) Limit impulse determination: For a predetermined disturbance type, obtaining the maximum tolerable step size using a measuring device based on the principle of decreasing intensity and increasing step size, and outputting the limit impulse after determining linear characteristics; 5) Disturbance impulse injection simulation: Generating a disturbance intensity-step size matrix within the limit impulse range, fixing the initial state of the network system model and running it until stability, recording the phase trajectory after each disturbance injection until the termination threshold is met; 6) Data segmentation and transition zone labeling: Automatically labeling the start and end points of the transition zone based on the phase-stable domain distance and threshold conditions, and outputting a labeled phase trajectory dataset for subsequent modeling or algorithm training. The relationship between each component in the process is as follows: Figure 1 As shown.

[0038] 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.

[0039] 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 2 The demonstration showcased the entire transportation mission carried out by the drone formation.

[0040] To verify the accuracy of the proposed modeling method, this invention... Figure 2Using the structure shown as the basic unit, a computational example was designed to obtain analytical solutions for the array deformation. Using the analytical solutions as a reference, the accuracy of the modeling method was verified by comparing the errors between the numerical and analytical solutions of the simulation model under different simulation step sizes.

[0041] The topology of the example in the steady state is a 3-layer network system consisting of 7 member nodes, containing a total of 3 Figure 2 The triangular structure shown is as follows: Figure 3 As shown in the diagram, the member nodes are numbered from 1 to 7.

[0042] The initial state of the network system is that the position, velocity, and acceleration of all member nodes are all [0,0] in the [x,y] direction. The dynamic rules for member #1 are: (1.1) Members #2-1 and #2-2 follow member #1 to form an equilateral triangle structure with a side length of 4; members #3-1 and #3-2 and members #3-3 and #3-4 follow members #2-1 and #2-2 respectively to form an equilateral triangle structure with a side length of 2.

[0043] The following rules for each triangular structure are designed as PI controllers. With both the proportional gain and integral gain of the controller set to 1, the input-output relationship of each following member can be expressed as follows: Figure 4 The block diagram shown, Figure 4 In, i=2,3…7.

[0044] Using equation (1.1) as the input to the example network system, according to Figure 4 The motion rules, the overall input-output relationship of the network system can be determined by... Figure 5 , Figure 6 describe. Figure 5 , Figure 6 middle, x 1 ( t )and y 1 ( t ), x 2 ( t )and y 2 ( t ), x 3 ( t )and y 3 ( t ), x 4 ( t )and y4 ( t ), x 5 ( t )and y 5 ( t ), x 6 ( t )and y 6 ( t ), x 7 ( t )and y 7 ( t ) represent the actual positions of member nodes 1-7 in the x and y directions, respectively.

[0045] according to Figure 5 , Figure 6 The input and output relationships shown can be derived sequentially. x 1 ( t )and y 1 ( t ), x 2 ( t )and y 2 ( t ), x 3 ( t )and y 3 ( t ), x 4 ( t )and y 4 ( t ), x 5 ( t )and y 5 ( t ), x 6 ( t )and y 6 ( t ), x 7 ( t )and y 7 ( t The analytical expression of ).

[0046] The following is based onx 2 ( t The derivation process will be explained in detail using an example. x 2 ( t This can be seen as... Figure 7 The diagram shows the output of a negative feedback system. The input signal of this system is r(t) = t - 4, and the forward path transfer function is G(s) = (s + 1) / s. 2 The transfer function of the feedback path is H(s)=1.

[0047] According to the formula for the closed-loop transfer function of a negative feedback system, the transfer function of this system is: (1.2) Taking the Laplace transform of the input r(t) = t - 4, we get: (1.3) Therefore, the Laplace transform of the output is: (1.4) Performing an inverse Laplace transform on equation (1.4), the time-domain analytical expression of the output is obtained as follows: (1.5) Using the same method, it can be found that... x i ( t ), y i ( t The analytical expression for i=2,3…7.

[0048] Referring to the formula for calculating the formation deformation given in Definition 1, the analytical expressions for the formation deformation in the x and y directions are respectively... (1.6) (1.7) in, and It is a two-column array. x(i) and y(i) This represents the i-th element of the array from left to right; d x,i (t) and d y,i (t) This represents the absolute distance between the actual position of each member node and the target position.

[0049] Definition 1 (Formation Deformation): Establish a Cartesian coordinate system with UAV 1 as the origin. Then, at any time t, let the desired position vector of UAVs i=2,3…7 be [formula missing].P e,i (t) The actual position vector is P a,i (t) Then the deformation of UAV i trf i (t) Defined as the 2-norm of the difference between the desired position vector and the actual position vector, i.e. (1.8) Overall formation deformation of drone swarm networks trf(t) Defined as: (1.9); 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 8 As shown.

[0050] By combining equations (1.6), (1.7), and the equations in Table 1, the analysis of the example network system can be obtained.

[0051] According to such Figure 1 The modeling method shown in the Chinese invention patent application (application number: 2025109865683, application date: 20250717) was used to establish the network system model for this example. The simulation step size stp was set to 10. 0 s, 10 -1 s, 10 -2 s, 10 -3 s and 10 -4 The simulation was performed continuously for 50 seconds, obtaining simulation data of the array deformation of the example network system at five discrete time points. At integer time points (1s, 2s, ..., 50s), the absolute error at each time point under each simulation step size was obtained by subtracting the value obtained by the analytical expression from the simulation data value. Figure 9 The results from 1 second to 16 seconds are shown. After 16 seconds, the absolute error of each data set tends to 0.

[0052] The absolute errors at 50 integer time points are averaged to obtain... x direction and y The average absolute error under five simulation step size settings in the direction is shown in Table 1.

[0053] Table 1. Relationship between step size and mean absolute error

[0054] Take the logarithm of the step size and the absolute value of the mean absolute error in Table 1, and plot them separately.x direction and y Five points in a logarithmic coordinate system are used to fit a linear curve, such as... Figure 12 As shown.

[0055] observe Figure 12 It can be seen that in the logarithmic coordinate system, there is a linear relationship between the simulation step size and the absolute error. The slope of the linear curve represents the rate at which the simulation error increases as the order of magnitude of the simulation step size increases. For example, in x In the direction, the simulation error increases at a rate of approximately 1.078. y The direction is approximately 1.112.

[0056] The above pattern implies that as the simulation step size decreases, the absolute error of the simulation also decreases. Therefore, by controlling the simulation step size, the simulation results can achieve the required accuracy, and this modeling method has controllable accuracy.

[0057] 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 analyzing the accuracy of phase point trajectory modeling in an unmanned aerial vehicle (UAV) network system, characterized in that, Includes the following steps: 1) Construct a three-layer network topology consisting of n UAV nodes in a simulation environment. The topology is composed of multiple nested equilateral triangle units. 2) Set the desired trajectory of the first layer node number #1 as x1(t), y1(t), where t is the time variable, and set the initial position, velocity, and acceleration of each node to zero in the x and y directions. 3) Configure PI controllers with proportional gain Kp=1 and integral gain Ki=1 for all nodes except node #1; based on the geometric relationship of equilateral triangles, use the output of the upper-level node as the target input of the lower-level node through the weight matrix; 4) Using the trajectory of node #1 as the system input, and based on the closed-loop transfer function formula of the negative feedback system, the analytical solutions x in the x and y directions of each node are obtained sequentially through Laplace transform. i (t),y i (t), i = 2 - n, where n is a positive integer greater than 2; 5) Calculate the array deformation of the network system in the x and y directions; 6) Run the discrete simulation model using at least two different time steps Δt to obtain the numerical solution for each node; compare the numerical solution with the analytical solution obtained in step 4), and calculate the maximum absolute error, mean square error and L2 norm; when the error is lower than the preset threshold, determine that the modeling method has the required accuracy.

2. The method according to claim 1, characterized in that, In step 2), the desired trajectory of node #1 in the first layer is set as follows: 。 3. The method according to claim 1, characterized in that, In step 3), the weight matrix takes values ​​of ±2 within a triangle with a side length of 4 and ±1 within a triangle with a side length of 2.

4. The method according to claim 1, characterized in that, The transfer function in step 4) is as follows: ， The transfer function is solved using a block negative feedback structure. First, a block negative feedback structure is established for each follower node: ， And use the following formula: ， Derive the closed-loop response; Where s is the Laplace domain complex frequency variable, G(s) is the forward transfer function, H(s) is the unity feedback channel, and Φ i (s) is the closed-loop transfer function of the system.

5. The method according to claim 4, characterized in that, In step 4), x2(t) can be considered as the output of a negative feedback system; the input signal of this system is r(t) = t - 4, and the forward transfer function is G(s) = (s + 1) / s. 2 The transfer function of the feedback path is H(s)=1; Based on the closed-loop transfer function formula of a negative feedback system, performing a Laplace transform on the input r(t) = t - 4 yields: ； The Laplace transform of the output is: ； Performing an inverse Laplace transform on the above equation, we obtain the time-domain analytical expression of the output: ； Following the method described above, calculate x in the x and y directions sequentially. i (t),y i The analytical expression for (t) is given by i = 2 - n. in, [.] represents the Laplace transform operator, R(s) is the Laplace transform of the input signal r(t) = t - 4, X2(s) is the Laplace domain representation of node #2 in the x-direction, and e -t / 2 : Decay exponent.

6. The method according to claim 1, characterized in that, In step 5), the array deformation of the network system in the x and y directions is calculated according to the following formula: ， 。 7. The method according to claim 1, characterized in that, The time step Δt mentioned in step 6) includes at least 0.01s and 0.05s to simultaneously evaluate the model accuracy in high-fidelity and fast simulation scenarios; and / or, the calculation results of the error index are used to automatically generate a simulation accuracy report, which includes an error-step relationship curve; and / or, the preset threshold is set by the user according to task requirements, and the threshold range is 10. -4 Up to 10 -2 .

8. A drone network system for implementing the method of any one of claims 1-7, characterized in that, The system includes: a) Topology configuration module, used to generate a three-layer, seven-node equilateral triangle network topology; b) Trajectory input module, used to inject the baseline trajectory x1(t), y1(t) into node #1; c) Controller management module, used to assign PI controllers to each follower node and write Kp,Ki parameters; d) Analytical computation module, used to perform Laplace transform and inverse transform, outputting analytical solution x. i (t),y i (t); e) Simulation execution module, used to run discrete simulations at a given time step and output numerical solutions; f) Error analysis module, used to compare analytical solutions with numerical solutions and generate error indices; g) Result determination module, used to output modeling accuracy conclusions based on error indicators and thresholds.

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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