Multi-unmanned aerial vehicle adaptive target surrounding control method

Abstract

The invention discloses a multi-unmanned aerial vehicle adaptive target surrounding control method, and relates to the technical field of multi-unmanned aerial vehicle control, and the method comprises the steps: obtaining a kinetic model and a communication topology of an unmanned aerial vehicle; according to the dynamic model, based on a formation transformation operator, determining a formation pattern of the unmanned aerial vehicle; keeping the formation pattern of the unmanned aerial vehicles unchanged, adjusting the motion direction of the virtual unmanned aerial vehicles according to the motion state of the target until the distance between the target and the virtual unmanned aerial vehicles is smaller than a preset distance threshold, and obtaining a surrounding path; constructing a dual-channel event trigger function based on a dynamic event trigger mechanism according to the kinetic model; according to the triggering time, the communication topology and the surrounding path, constructing an unmanned aerial vehicle formation distributed dynamic event triggering target surrounding control law; according to the unmanned aerial vehicle formation distributed dynamic event, triggering a target surrounding control law to surround the target; according to the invention, the trigger threshold can be adjusted in the dynamic change process, and the optimal balance between the control performance and the communication efficiency is realized.

Description

Technical Field

[0001] This application relates to the field of multi-UAV control technology, and in particular to a multi-UAV adaptive target encirclement control method. Background Technology

[0002] Target encirclement control aims to enable multiple UAVs to form and maintain a stable internal configuration and move as a whole to follow the target trajectory in dynamic environments. Existing research has made significant progress in multi-UAV target encirclement control, but several key bottlenecks remain to be overcome. At the encirclement mechanism level, existing methods generally assume that UAVs need to move collaboratively around the target along a fixed orbital distance, lacking control design for time-varying encirclement distances. This fixed orbital distance constraint limits the flexibility and adaptability of swarms in handling complex mission scenarios, making it difficult to achieve dynamic switching from close-range fine surveillance to long-range safe tracking. A more fundamental limitation is that most studies treat formation control and target encirclement as two relatively independent problem domains. This separate design not only increases system complexity but may also trigger significant transient oscillations, convergence delays, or even configuration instability during mission transitions, thereby weakening the overall robustness and mission consistency of the system in dynamic and uncertain environments.

[0003] Regarding resource constraints, traditional cooperative control schemes often rely on periodic time-triggered mechanisms, requiring agents to maintain high-frequency, synchronous state interactions and control law updates. As cluster size increases, this continuous communication mode leads to network channel congestion, uneven computational load, and rapid depletion of onboard energy, severely limiting the scalability and practicality of the system in large-scale deployments and long-endurance missions. While event-triggered control provides a new approach to resource optimization through a "state-driven" discrete communication mechanism, existing triggering strategies mostly use fixed thresholds, lacking the ability to adaptively adjust to tracking errors, external disturbances, and time-varying network state characteristics in dynamic mission scenarios. Specifically, conservative threshold settings can lead to redundant communication events, while overly lenient thresholds may affect control accuracy.

[0004] Therefore, based on the above problems, there is an urgent need to provide a multi-UAV adaptive target encirclement control method that can adjust the trigger threshold during dynamic changes to achieve the best balance between control performance and communication efficiency. Summary of the Invention

[0005] The purpose of this application is to provide a multi-UAV adaptive target encirclement control method that can adjust the trigger threshold during dynamic changes to achieve the best balance between control performance and communication efficiency.

[0006] To achieve the above objectives, this application provides the following solution: This application provides a multi-UAV adaptive target encirclement control method, including: Obtain the dynamic model and communication topology of the drone; the drone includes: multiple virtual drones and multiple real drones; Based on the dynamic model and the formation transformation operator, the formation of the UAVs is determined; the formation transformation operator is determined by the scaling and rotation parameters of the UAVs. Keep the formation of the drones unchanged, and adjust the direction of movement of the virtual drones according to the movement state of the target until the distance between the target and the virtual drones is less than a preset distance threshold, thus obtaining the encirclement path; Based on the dynamic model and the dynamic event triggering mechanism, a dual-channel event triggering function is constructed; and the triggering time is determined according to the dual-channel event triggering function. Based on the triggering time, communication topology, and encirclement path, a target encirclement control law for UAV formation distributed dynamic event triggering is constructed; and the target is encircled according to the target encirclement control law for UAV formation distributed dynamic event triggering target encirclement.

[0007] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a multi-UAV adaptive target encirclement control method. Based on the UAV's dynamic model and communication topology, and using a formation transformation operator, the UAV formation is determined. Specifically, this method can dynamically adjust the UAV formation by adjusting the formation transformation operator, achieving smooth switching between multiple modes and improving the adaptability and execution capability of encirclement tasks. While maintaining the UAV formation, the method adjusts the motion direction of the virtual UAVs according to the target's motion state, unifying formation control and target encirclement within a single control framework. Based on the dynamic model and a dynamic event triggering mechanism, a dual-channel event triggering function is constructed, and a distributed dynamic event triggering target encirclement control law for UAV formation is further built to encircle the target, alleviating communication pressure between UAVs and solving the problem of frequent control update frequency. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 This is a schematic flowchart of a multi-UAV adaptive target encirclement control method in one embodiment of this application; Figure 2 This is a schematic diagram of a multi-UAV adaptive target encirclement control method module in one embodiment of this application; Figure 3 This is a schematic diagram of formation control and target encirclement in one embodiment of this application; Figure 4 This is a schematic diagram showing the changes in the relative orientation and relative distance of a UAV in one embodiment of this application. Figure 4 Part (a) is a schematic diagram of the relative orientation change. Figure 4 (Part (b) is a schematic diagram of the relative distance change). Figure 5 This is a schematic diagram of the formation in one embodiment of this application; Figure 6 This is a schematic diagram of the trajectory evolution process surrounding a uniformly moving target in one embodiment of this application; Figure 7 This is a schematic diagram illustrating the change in the relative distance between a virtual drone and a target over time when the target is surrounded by a target moving at a constant speed, according to one embodiment of this application. Figure 8 This is a schematic diagram illustrating the velocity changes of each UAV when surrounding a uniformly moving target in one embodiment of this application; Figure 9 This is a schematic diagram of the formation position error when surrounding a uniformly moving target in one embodiment of this application; Figure 10 This is a schematic diagram of the formation speed error when surrounding a uniformly moving target in one embodiment of this application; Figure 11 This is a schematic diagram of the phase distribution of each UAV relative to the target when surrounding a target moving at a constant speed in one embodiment of this application; Figure 12 This is a schematic diagram illustrating the changing trend of dynamic variables when surrounding a uniformly moving target in one embodiment of this application; Figure 13 This is a trigger distribution diagram when surrounding a uniformly moving target in one embodiment of this application; Figure 14 This is a schematic diagram illustrating the number of event triggers when surrounding a target moving at a constant speed in one embodiment of this application; Figure 15 This is a schematic diagram of the encirclement trajectory of an unmanned aerial vehicle (UAV) when encircling a maneuvering target in one embodiment of this application; Figure 16 This is a schematic diagram illustrating the relative distance between a virtual UAV and a moving target when surrounding a maneuvering target in one embodiment of this application; Figure 17 This is a schematic diagram illustrating the dynamic process of velocity changes of each UAV when surrounding a maneuvering target in one embodiment of this application; Figure 18 This is a schematic diagram of the positional error of a UAV formation when surrounding a maneuvering target in one embodiment of this application; Figure 19 This is a schematic diagram of the speed error of UAV formation when surrounding a maneuvering target in one embodiment of this application; Figure 20 This is a phase distribution diagram of a maneuvering target in one embodiment of this application; Figure 21 This is a schematic diagram illustrating the changes in dynamic variables when surrounding a maneuvering target in one embodiment of this application; Figure 22 This is a trigger distribution diagram when surrounding a moving target in one embodiment of this application; Figure 23 This is a schematic diagram illustrating the number of event triggers when surrounding a moving target in one embodiment of this application. Detailed Implementation

[0010] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0011] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0012] In one exemplary embodiment, such as Figure 1 and Figure 2 As shown, a multi-UAV adaptive target encirclement control method is provided, including the following S1 to S5. Wherein: S1: Obtain the dynamic model and communication topology of the UAV.

[0013] S1 specifically includes: S11 acquires the dynamic model of the UAV.

[0014] Specifically, assuming a multi-UAV collaborative control system includes Considering a set of real drones, and the internal stability control of each real drone, each real drone is treated as a point mass and described using the following kinematic model: ; in, For real drones exist time The derivative at position on the axis, For real drones exist time The derivative at position on the axis, , For real drones exist Location at any given moment For real drones exist time Position on the axis For real drones exist time Position on the axis For real drones exist The speed of time , For real drones exist time Speed ​​on the axis For real drones exist time Speed ​​on the axis For real drones exist The heading angle at any moment, For real drones exist The derivative of the velocity at time t, For real drones exist Time-based control input, , For real drones exist time Control inputs on the axis For real drones exist time Control inputs on the axis For real drones exist The derivative of the heading angle at any given time. for The control input, This is an index set for real drones.

[0015] To simplify controller design and focus on the cooperative strategy itself, the dynamics model is transformed into a more tractable dual integrator form using a dynamic feedback linearization method. The calculation formula for the dynamics model of a real UAV is as follows: ; in, For real drones exist The derivative of the position at time.

[0016] To clearly describe the cooperative task of encircling a formation target and to provide a unified reference framework for it, this application introduces two virtual unmanned aerial vehicles with specific functions. and That is, the drones in this application include multiple virtual drones and multiple real drones. The dynamic model calculation formula for the virtual drones is as follows: ; ; in, For virtual drones exist The derivative of the position at time, , For virtual drones exist time Position on the axis For virtual drones exist time Position on the axis For virtual drones exist Location at any given moment For virtual drones exist The speed of time , For virtual drones exist time Speed ​​on the axis For virtual drones exist time Speed ​​on the axis For virtual drones exist The derivative of the velocity at time t, For virtual drones exist Time-based control input, For virtual drones exist The derivative of the reference vector at time step, For virtual drones exist The baseline change at any given time. For virtual drones exist The derivative of the change in the time base. For virtual drones exist The baseline control quantity at any given time.

[0017] Virtual drone here Not a drone in the true sense of the word. For predetermined parameters, and by Control and Inaction here The actual position and velocity.

[0018] S12: Obtain the communication topology of the drone.

[0019] In multi-UAV cooperative control systems, information exchange is fundamental to achieving collaboration. This application employs graph theory to model the complex communication relationships within the multi-UAV cooperative control system. The guidance relationships between real UAVs are represented using an undirected graph. It means that among them This represents a collection of real drones, with each node corresponding to one real drone. The table represents the set of communication relationships between real drones. ,express and They are capable of two-way communication and refer to each other as neighboring drones. For real drones , For real drones , The set of adjacent drones can be represented as Define the adjacency matrix. To quantify the weights of communication connections, satisfying the following formula: ; in, For real drones Compared to real drones The weight of communication connections between them.

[0020] Based on this, we define an undirected graph. The Laplacian matrix is .in, in-degree matrix , Weighted in-degree .

[0021] The guidance relationship between real and virtual drones is achieved using a directed graph. It means that among them It includes all real and virtual drones; express and The set of communication relationships between them For virtual drones, ,when At that time, it was called Able to obtain from The information, and define the matrix. The calculation formula is as follows: ; in, For real drones With virtual drones The weight of communication connections between them.

[0022] S2: Based on the dynamic model and the formation transformation operator, determine the formation of the UAVs.

[0023] Unmanned aerial vehicle (UAV) swarm target encirclement, as an integrated cooperative mission approach, hinges on the organic integration of two similar sub-tasks: swarm control and target encirclement. However, current research typically treats these two issues as independent processes, neglecting the coordination of multiple UAVs from mission initiation to the encirclement phase. Swarm control requires the UAV swarm to form and maintain a specific spatial geometry during its movement; while target encirclement requires the UAV swarm to form a stable encirclement structure around the target, often requiring the maintenance of a specific relative phase to achieve cooperative surveillance or attack, such as... Figure 3 As shown. Although the two differ in their manifestations, with the former focusing on maintaining the formation in space and the latter on deploying and maintaining the formation around the target, their essence can be reduced to the problem of multiple UAVs coordinating their movements around a dynamic center in a specific pattern. That is, the dynamic center of formation control is the formation center, i.e., the leader, and the center surrounding the target is the target.

[0024] Furthermore, in the specific implementation of encirclement strategies, existing methods are mostly limited to fixed-distance encirclement, requiring all UAVs to maintain the same preset distance from the target, thus forming an encirclement circle with a fixed radius. While this strategy simplifies control design, its limitations in terms of fixed formation structure and insufficient flexibility become apparent when dealing with complex terrain, avoiding obstacles, or performing specific tasks. In contrast, this application can dynamically adjust the encirclement radius and formation geometry according to mission requirements and environmental changes, achieving smooth switching between various modes such as equidistant encirclement and variable-distance encirclement, significantly improving the adaptability and mission execution capability of the encirclement strategy.

[0025] S2 specifically includes: S21: Determine the set of geometric transformation parameters for the UAV based on the dynamic model.

[0026] like Figure 4As shown, the relative orientation method, after formation rotation, will result in a deviation between the actual and desired formation if the relative azimuth angles between the drones do not change in tandem. For example, if the relative azimuth between two drones is initially defined as... When the relative positions of the two undergo rotational motion, their relative orientations become... ,like If the formation deviates from the initially described formation, then the formation will also become distorted after scaling, especially if the distance is not adjusted according to a preset ratio. For example, if the relative distance between two drones is initially defined as... However, after scaling, the distance between them becomes... ,like If this happens, the formation will also deviate from the initially defined desired formation. The fundamental reason is that the formations defined by these methods are static and fail to take into account the geometric transformation rules that the formation as a whole should follow.

[0027] To address the aforementioned issues, this application considers the desired formation of the entire UAV formation as a result generated by uniform translation, rotation, and scaling transformations applied to a standard reference vector. This description method is compatible with the requirements of time-varying formations and enables control of the formation and target encirclement.

[0028] The geometric transformation parameter set includes the position and reference vector of the virtual UAV, as well as the scaling and rotation parameters of the real UAV. Geometric transformation parameter set as follows: ; in, For virtual drones exist Location at any given moment For virtual drones exist The reference vector at time t, For real drones Scaling parameters, For real drones The rotation parameters.

[0029] Furthermore, the formation of the entire formation It can be defined by the parameter set of all drones: ; in, The actual drone number, , This represents the total number of actual drones.

[0030] S22: In the geometric transformation parameter set, construct the formation transformation operator with the position of the virtual UAV as the formation center and reference vector.

[0031] In the geometric transformation parameter set The designated formation center is comprised of virtual drones. The position definition of the (virtual navigation drone) determines the overall translational movement of the formation in space and serves as the reference origin for all drone movements. As the reference vector, it is generated by the virtual drone. (Virtual reference drone) is defined as a directional reference on the unit circle, providing a common reference frame for the rotation and scaling of the formation. This determines the radial distance of the drone in the reference vector direction, controlling the shape and size of the formation; It is a two-dimensional identity orthogonal matrix that controls the rotational transformation of the UAV relative to the reference direction and determines the phase of the UAV on the circumference.

[0032] The above analysis shows that the geometric transformation parameter set includes three types of motion: rotation, scaling, and translation. Among them, the scaling motion is... Control, rotational motion is Control and translational movement depend on the formation center. The changes, and both scaling and rotational motions are relative. In other words, this is also to The reason for using it as a formation benchmark.

[0033] In all three sports, the formation of drones primarily depends on... and The changes, and both of them are based on As a baseline. To simplify calculations in subsequent controller design, scaling and rotation parameters acting on the same object are merged and defined as follows. Formation transformation operator for: .

[0034] S23: Determine the formation of the UAVs according to the formation transformation operator.

[0035] drone formation It can be equivalently represented as: .

[0036] like Figure 5 As shown, assuming the actual number of drones is... ,set up , , ,in, for phase angle, for The phase angle.

[0037] Obviously, The conditions are met. Consider this: For time invariance, assume ,Right now It can be observed that when Once confirmed, all drones in the formation will follow... Rotate counterclockwise angle They then arrived at their respective positions, demonstrating that the formation of the drone formation can be determined by... Definitions are generated.

[0038] This application unifies the traditionally separate tasks of formation control and target encirclement under a single control framework by assigning clear and complementary responsibilities to two virtual drones.

[0039] S3: Keep the formation of the drones unchanged, and adjust the movement direction of the virtual drones according to the movement state of the target until the distance between the target and the virtual drones is less than the preset distance threshold, so as to obtain the encirclement path; As a trajectory-guided drone for formation. Its primary function is to provide reference movement positions for UAV formation. In target encirclement missions, trajectory guidance aims to continuously bring the UAVs closer to the target. Considering that airborne sensors typically observe the target's state at each sampling point, this characteristic is leveraged... Surround the target. The motion rules for approaching the target are as follows: 1. Settings initial position Its initial velocity is defined as ,in Initial time The direction pointing to the target for The speed.

[0040] 2. In each control cycle, the target's motion state is estimated based on the current moment to determine... The current motion direction and control input are calculated using the following formulas: ; ; in, For virtual drones exist Direction of motion at any moment For the goal Location at any given moment , For virtual drones exist Location at any given moment for The control input, For time intervals, For the goal Location at any given moment For the goal The speed of time For virtual drones exist The speed of time.

[0041] 3. Repeat step 2 until... The distance to the target meets the set error tolerance, that is, it is less than the preset distance threshold.

[0042] In the multi-UAV target encirclement problem, it is usually required that each UAV maintains the same distance from the target, and that the phases of the UAVs need to be coordinated. Therefore, the formation transformation operator... The formulas for calculating the scaling and rotation parameters are as follows: ; ; in, The radius of the fixed-distance enclosure determines the size of the enclosing ring. for The phase angle ensures that the drones are evenly distributed on the encircling ring. , For an initially set arbitrary phase angle, for The rotational angular velocity is used to handle situations requiring formation changes, and can be defined as follows (unless otherwise specified). .

[0043] Its core responsibility is to generate and maintain the desired encirclement formation around the target. The baseline vector is designed as follows: ; in, for phase angle, , for The rotational angular velocity, which also represents the angular velocity of the drone formation's hovering motion, can be switched according to different stages of the encirclement mission to enhance strategic flexibility. The settings depend on Relative position to the target, when When the distance is less than the preset threshold, Tracking the target means forming a formation to surround it. , For tracking angle, The enclosing angle.

[0044] The above The definition considers the hovering angular velocities before and after the drone formation surrounds the target. Before surrounding the target, the speed of the drone formation depends on... Once the target is surrounded, the formation speed depends on the target's speed.

[0045] For any given initial state of the drone and If the desired formation is achieved, that is, if the formula is satisfied... At the same time, satisfy If so, it is said that by controlling the set of geometric transformation parameters, the formation is achieved to surround the target in the desired formation.

[0046] S4: Based on the dynamic model and the dynamic event triggering mechanism, construct a dual-channel event triggering function; and determine the triggering time based on the dual-channel event triggering function.

[0047] Whether during formation formation or target encirclement, UAVs require continuous communication and control input updates to maintain their formation. However, communication network bandwidth and computing resources are very limited. Therefore, reducing the communication pressure between UAVs during target encirclement is a pressing issue. This application addresses this problem by designing an intermittent communication mechanism with dynamic triggering characteristics to alleviate the communication pressure and frequent control updates between UAVs.

[0048] S4 specifically includes: S41: Based on the dynamic model and the dynamic event triggering mechanism, determine the formation error and measurement error of the UAVs.

[0049] Formation error includes formation position error and formation speed error, while measurement error includes position measurement error and speed measurement error.

[0050] Specifically, the formula for calculating formation error is as follows: ; ; in, For real drones exist The formation position error at any given moment, For real drones exist Location at any given moment For virtual drones exist Location at any given moment For real drones exist The formation transformation operator at time step, For virtual drones exist The reference vector at time t, For real drones exist The formation speed error at any given moment, For real drones exist The speed of time For virtual drones exist The speed of time For virtual drones exist The baseline change at any given time. For real drones exist The derivative of the time-varying formation transformation operator.

[0051] The aforementioned error measures the deviation between the real drone and the desired state defined by the virtual drone and the formation transformation operator; the control objective is the driving force. and It approaches 0.

[0052] For any and If there exists a bounded moment , making When, satisfy and And satisfy and Then it is said that the desired multi-drone formation is formed and maintained if the following conditions are met simultaneously: This means that the drone formation maintains the desired formation to surround the target, whereby... For real drones exist The formation speed error at any given moment, For real drones exist The formation position error at any given moment.

[0053] The formula for calculating measurement error is as follows: ; ; in, For real drones exist Position measurement error at any given time For real drones At the time of communication triggering Formation position error, The communication trigger time, The next communication trigger time, For real drones exist The speed measurement error at a given moment For real drones At the time of communication triggering The formation speed error.

[0054] S42: Construct a dual-channel event trigger function based on formation error and measurement error.

[0055] Design a dual-channel event trigger function based on position and velocity. The calculation formula is as follows: ; in, For real drones exist Position measurement error at any given time For real drones exist The speed measurement error at a given moment For real drones exist The formation position error at any given moment, The first trigger parameter, , For the second control gain, It is the smallest non-zero eigenvalue of the matrix. For Laplace matrix, For gain adjustment parameters, , , This is the second trigger parameter. , The first control gain, for State acquirer For trigger parameters, This is the third trigger parameter. , For real drones exist The formation speed error at any given moment, For internal dynamic variables, , , The derivative of the internal dynamic variable.

[0056] Dual-channel event triggering functions are used to determine the triggering time. , Internal dynamic variables The size can be adjusted according to the actual situation to balance the trade-off between control accuracy and communication consumption.

[0057] According to the triggering conditions, when When the event is triggered, it will then occur at intervals. Internally, the multi-UAV collaborative control system updates the state and measures the error through a zero-order hold. , If reset to 0, the internal dynamic variable... Satisfy the following formula: .

[0058] in, Further analysis reveals: .

[0059] Compared to static triggering (fixed threshold), dynamic variables A time-varying trigger threshold is introduced. When the error of the multi-UAV cooperative control system is large or the dynamics are drastic, the positive term dominates in the calculation process of the derivative of the internal dynamic variables. This increases the frequency of triggering, avoiding unnecessary and frequent activation; when the multi-UAV collaborative control system approaches a steady state, Exponential decay tightens the triggering conditions, thereby ensuring the final encirclement accuracy.

[0060] S5: Construct a target encirclement control law for UAV formations based on the triggering time, communication topology, and encirclement path; and encircle the target according to the target encirclement control law for UAV formations based on the distributed dynamic event triggering target encirclement control law.

[0061] In resource-constrained real-world systems, requiring continuous communication between UAVs for precise coordination is often impractical. To address this issue, this application proposes an intermittent communication control strategy based on dynamic event triggering. The core of this strategy is that each UAV only exchanges information and updates control commands with neighboring UAVs when its local state error accumulates to a certain level, sufficient to trigger communication conditions. This significantly conserves communication and computing resources while ensuring control performance.

[0062] Based on the above description, a distributed dynamic event-triggered target encirclement control law for UAV formations is constructed, and the calculation formula is as follows: ; in, For real drones exist Time-based control input, For real drones exist The feedforward compensation term at each time step is used to offset the desired dynamics caused by the virtual drones and formation changes, thereby simplifying the closed-loop system analysis. The actual total number of drones, For real drones Compared to real drones Communication connection weights between them The first control gain, For real drones At the time of communication triggering Formation speed error, For real drones At the time of communication triggering Formation speed error, For the second control gain, , For real drones At the time of communication triggering Formation position error, Real drones At the time of communication triggering Formation position error, For real drones With virtual drones Communication connection weights between them For real drones exist The formation speed error at any given moment, For real drones exist The formation position error at any given moment, For real drones exist The second derivative of the time-varying formation transformation operator, For virtual drones exist The reference vector at time t, For real drones exist The derivative of the time-varying formation transformation operator, For virtual drones exist The baseline change at any given time. For real drones exist The formation transformation operator at time step, Virtual drones exist The baseline control quantity at any given time. For virtual drones exist Time-based control input, for The At the moment an event is triggered, the drone only communicates at that moment until the next trigger moment. During this period, no communication or exchange of status information takes place, that is, in Inside, the drone status remains unchanged. The value at any given time remains unchanged.

[0063] After determining the target encirclement control law triggered by distributed dynamic events in the UAV formation, the target is encircled. This application enables the multi-UAV cooperative control system to achieve the desired formation and encircle the target, while ensuring that no Zeno behavior occurs during the mission. The stability and Zeno-free behavior of the multi-UAV cooperative control system are proven as follows: Proof of the stability of a multi-UAV collaborative control system.

[0064] For the following Lyapunov function: .

[0065] Taking its derivative, we get: .

[0066] After sorting, we can obtain: .

[0067] Therefore, we get: .

[0068] Further analysis yields: ; in, for Time of the first The number of adjacent drones, and satisfying the inequality , For the first A collection of adjacent drones.

[0069] because , According to Young's inequality, we can obtain: ; ; ; ; .

[0070] Further results were obtained: .

[0071] Organized .

[0072] Based on the triggering conditions: .

[0073] Pick We can obtain: .

[0074] Obviously, when the constant , , , When the corresponding requirements are met, it can be inferred that This demonstrates that drone swarms are capable of encircling targets in a desired formation.

[0075] Proof that the multi-UAV collaborative control system exhibited no Zeno behavior throughout the entire encirclement process.

[0076] When the triggering condition is met The event is activated, and we can obtain: .

[0077] Taking the Dini derivative of the left side of the equation, we get: .

[0078] according to and From the definition, we can obtain: .

[0079] make , , They represent , and In time interval The maximum value within, i.e. , , .

[0080] After sorting, we can obtain: .

[0081] because , Then the following inequality holds: .

[0082] Then when At that time, there were: ; when or At that time, obviously .when and At that time, due to Similarly, we can obtain Therefore, it can be concluded that there is a strict lower bound greater than 0 for any triggering time interval, meaning that the multi-UAV cooperative control system has no Zeno behavior.

[0083] In an exemplary embodiment, the effectiveness of the proposed solution is verified through simulation.

[0084] In Scenario 1, by changing the formation parameters, the control performance of multiple UAVs surrounding a uniformly moving target in a time-varying formation was verified; in Scenario 2, the feasibility of surrounding a maneuvering target in a variable-pitch rotating formation was verified.

[0085] Specifically, in scenario one, the control gain is set. Trigger parameters , , angular velocity of rotation The initial phase angle is The phase angle within 30 seconds is The enclosing radius is The phase angle from 31s to 50s is The enclosing radius is The phase angle from 51s to 60s is The enclosing radius is .

[0086] Simulation results are as follows Figures 6-14 As shown in the figure. The trajectory evolution process of multiple UAVs surrounding a uniformly moving target under time-varying formation control is as follows. Figure 6 As shown in the diagram, in the initial stage, the drones quickly assemble into a rectangular formation and approach the target; subsequently, under the control of preset formation parameters, the formation gradually transitions from a rectangle to a square, and then evolves into a rhomboid configuration, simultaneously completing the formation transformation and target encirclement tasks. The change in the relative distance between the virtual drone and the target over time is shown in the diagram. Figure 7 As shown, the distance gradually converges to zero, indicating that the virtual drone has achieved asymptotic tracking of the target. The dynamic process of the speed change of each drone is as follows: Figure 8As shown, this reflects that under the control strategy, the speeds of each aircraft tend to be consistent and eventually remain stable, demonstrating good coordination and consistency. The evolution process of formation position error and formation speed error is as follows: Figure 9 and Figure 10 As shown, both types of errors gradually converge over time. Especially after the formation switch, although a brief fluctuation occurs, it quickly decays to zero, verifying the effectiveness of the distributed dynamic event-triggered target encirclement control law for UAV formation in adjusting formation deviation and ensuring formation stability. The phase distribution of each UAV relative to the target is shown in the figure. Figure 11 As shown, the UAV maintained good phase coordination during the encirclement process, forming a uniformly distributed encirclement loop. The changing trends of the dynamic variables are as follows: Figure 12 As shown in the diagram, the trigger distribution is as follows: Figure 13 As shown, the triggering events are mainly concentrated in the initial adjustment phase, and the trigger interval gradually increases thereafter, indicating that the communication burden of the system is significantly reduced in the stable phase. The number of event trigger times for each UAV in the scene is as follows: Figure 14 As shown.

[0087] In scenario two, the target is set to use segmented maneuvers, within a timeframe of 0s-12s. Within 13s-60s, The initial phase angle is The subsequent phase angle update satisfies the formula The radius of the enclosure within 0s-30s angular velocity of rotation The radius of the enclosure within 31s-50s angular velocity of rotation The radius of the enclosure within 0s-30s angular velocity of rotation .

[0088] Simulation results are as follows Figures 15-23 As shown. The encirclement trajectory of the UAV around a maneuvering target in a variable-pitch rotating formation is as follows. Figure 15 As shown, despite the target's continuous maneuvering, the UAV was able to adjust its formation in real time and complete the encirclement, reflecting the good adaptability of the proposed control strategy to maneuvering targets. Figure 16 As shown, the relative distance between the virtual UAV and the target still converges to zero, indicating that the system has good robustness to target maneuvers. The dynamic process of the speed change of each UAV is as follows: Figure 17 As shown, this demonstrates that the drones maintain good consistency in tracking performance even in dynamic environments. The drone formation position error and formation speed error are as follows: Figure 18 and Figure 19As shown, during the target maneuver and the change in the radius of the encirclement loop, the error briefly increases, but the controller responds quickly and recovers to stability, demonstrating good disturbance suppression capability. The phase distribution diagram is shown below. Figure 20 As shown, this demonstrates that the UAV can maintain the desired phase structure under variable pitch conditions, verifying the rationality of the formation factor design. Figure 21 As shown, the changes in the dynamic variables are consistent with the performance of the triggering mechanism, indicating that the mechanism can still work effectively in complex scenarios. The event triggering statistics are as follows: Figure 22 and Figure 23 As shown, this demonstrates that despite the target's mobility, the drone formation can still achieve intermittent communication through a dynamic event-triggered mechanism, reducing communication pressure while ensuring the completion of the encirclement mission.

[0089] This application achieves autonomous adjustment of communication frequency by dynamically adjusting the trigger threshold. This mechanism increases the threshold to avoid frequent communication when the system is dynamically volatile, and tightens the threshold to ensure control accuracy when it approaches a steady state. This significantly reduces communication burden and computational load while strictly guaranteeing system performance, outperforming traditional fixed-threshold triggering strategies. Furthermore, this application rigorously proves the stability of the closed-loop system under a dynamic event triggering mechanism by constructing a suitable Lyapunov function and designing a control law with dual-channel triggering conditions. It also proves that there is no Zeno behavior in the system (i.e., it will not trigger an unlimited number of times within a finite time), ensuring the feasibility and reliability of the control strategy in practical systems. Finally, under a unified control framework, this application supports smooth switching between various encirclement modes, such as equidistant encirclement, variable-distance encirclement, and time-varying formations. It can dynamically adjust the encirclement radius and formation configuration according to task requirements and environmental changes, improving the system's adaptability and task execution capabilities in complex scenarios.

[0090] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0091] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A multi-UAV adaptive target encirclement control method, characterized in that, The multi-UAV adaptive target encirclement control method includes: Obtain the dynamic model and communication topology of the drone; the drone includes: multiple virtual drones and multiple real drones; Based on the dynamic model and the formation transformation operator, the formation of the UAVs is determined; the formation transformation operator is determined by the scaling and rotation parameters of the UAVs. Keep the formation of the drones unchanged, and adjust the direction of movement of the virtual drones according to the movement state of the target until the distance between the target and the virtual drones is less than a preset distance threshold, thus obtaining the encirclement path; Based on the dynamic model and the dynamic event triggering mechanism, a dual-channel event triggering function is constructed; and the triggering time is determined according to the dual-channel event triggering function. Based on the triggering time, communication topology, and encirclement path, a target encirclement control law for UAV formation distributed dynamic event triggering is constructed; and the target is encircled according to the target encirclement control law for UAV formation distributed dynamic event triggering target encirclement.

2. The multi-UAV adaptive target encirclement control method according to claim 1, characterized in that, The acquisition of the UAV's dynamic model and communication topology specifically includes: Using formula Determine the dynamic model of the real drone; Using formula and formula Determine the dynamic model of the virtual drone; Using formula Determine the communication topology between real drones; Using formula Determine the communication topology between the real drone and the virtual drone; in, For real drones exist The derivative of the position at time, For real drones exist The speed of time For real drones exist The derivative of the velocity at time t, For real drones exist Time-based control input, A collection of real drone indexes. For virtual drones exist The derivative of the position at time, For virtual drones exist The speed of time For virtual drones exist The derivative of the velocity at time t, For virtual drones exist Time-based control input, For virtual drones exist The derivative of the reference vector at time step, For virtual drones exist The baseline change at any given time. For virtual drones exist The derivative of the change in the time base. For virtual drones exist The baseline control quantity at any given time. For real drones Compared to real drones Communication connection weights between them For real drones , For real drones , This is a set of communication relationships between real drones. For real drones With virtual drones Communication connection weights between them , For virtual drones, This is a set of communication relationships between real drones and virtual drones.

3. The multi-UAV adaptive target encirclement control method according to claim 1, characterized in that, The process of determining the formation of UAVs based on the dynamic model and the formation transformation operator specifically includes: Based on the dynamic model, the geometric transformation parameter set of the real UAV is determined; the geometric transformation parameter set includes the position and reference vector of the virtual UAV and the scaling and rotation parameters of the real UAV. In the set of geometric transformation parameters, a formation transformation operator is constructed with the position of the virtual UAV as the formation center and reference vector; The formation of the UAVs is determined based on the formation transformation operator.

4. The multi-UAV adaptive target encirclement control method according to claim 3, characterized in that, The determination of the geometric transformation parameter set of the real UAV based on the dynamic model specifically includes: Using formula Determine the set of geometric transformation parameters for real UAVs ; in, For virtual drones exist Location at any given moment For virtual drones exist The reference vector at time t, For real drones Scaling parameters, For real drones rotation parameters, The actual drone number, , This represents the total number of actual drones.

5. The multi-UAV adaptive target encirclement control method according to claim 3, characterized in that, The formation transformation operator is constructed in the geometric transformation parameter set, using the position of the virtual UAV as the formation center and reference vector, specifically including: Using formula Construct formation transformation operators; in, For real drones exist The formation transformation operator at time step, For real drones Scaling parameters, For real drones The rotation parameters.

6. The multi-UAV adaptive target encirclement control method according to claim 1, characterized in that, Maintaining the formation of the drones unchanged, and adjusting the movement direction of the virtual drones according to the target's movement state until the distance between the target and the virtual drones is less than a preset distance threshold, thus obtaining an encirclement path, specifically includes: Using formula Adjust the direction of movement of the virtual drone; in, For virtual drones exist Direction of motion at any moment For the goal Location at any given moment For virtual drones exist The position at any given moment.

7. The multi-UAV adaptive target encirclement control method according to claim 1, characterized in that, Based on the dynamic model and the dynamic event triggering mechanism, a dual-channel event triggering function is constructed, specifically including: Based on the dynamic model and the dynamic event triggering mechanism, the formation error and measurement error of the UAV are determined; the formation error includes: formation position error and formation speed error; the measurement error includes: position measurement error and speed measurement error. Based on formation error and measurement error, a dual-channel event trigger function is constructed.

8. The multi-UAV adaptive target encirclement control method according to claim 7, characterized in that, The determination of UAV formation error and measurement error based on the dynamic model and dynamic event triggering mechanism specifically includes: Using formula Determine the formation position error of the drones; Using formula Determine the formation speed error of the drones; Using formula Determine the position measurement error of the UAV; Using formula Determine the speed measurement error of the drone; in, For real drones exist The formation position error at any given moment, For real drones exist Location at any given moment For virtual drones exist Location at any given moment For real drones exist The formation transformation operator at time step, For virtual drones exist The reference vector at time t, For real drones exist The formation speed error at any given moment, For real drones exist The speed of time For virtual drones exist The speed of time For virtual drones exist The baseline change at any given time. For real drones exist The derivative of the time-varying formation transformation operator, For real drones exist Position measurement error at any given time For real drones At the time of communication triggering Formation position error, The communication trigger time, The next communication trigger time, For real drones exist Error in velocity measurement at any given time For real drones At the time of communication triggering The formation speed error.

9. The multi-UAV adaptive target encirclement control method according to claim 7, characterized in that, The construction of a dual-channel event triggering function based on formation error and measurement error specifically includes: Using formula Construct a dual-channel event trigger function ; in, For real drones exist Position measurement error at any given time For real drones exist Error in velocity measurement at any given time For real drones exist The formation position error at any given moment, The first trigger parameter, This is the second trigger parameter. For real drones exist The formation speed error at any given moment, It is an internal dynamic variable.

10. The multi-UAV adaptive target encirclement control method according to claim 1, characterized in that, The step of constructing a distributed dynamic event-triggered target encirclement control law for UAV formations based on the triggering time, communication topology, and encirclement path specifically includes: Using formula Constructing a distributed dynamic event-triggered target encirclement control law for drone formations; in, For real drones exist Time-based control input, For real drones exist The feedforward compensation term at time, The actual total number of drones, For real drones Compared to real drones Communication connection weights between them The first control gain, For real drones At the time of communication triggering Formation speed error, For real drones At the time of communication triggering Formation speed error, For the second control gain, For real drones At the time of communication triggering Formation position error, Real drones At the time of communication triggering Formation position error, For real drones With virtual drones Communication connection weights between them For real drones exist The formation speed error at any given moment, For real drones exist The formation position error at any given moment, For real drones exist The second derivative of the time-varying formation transformation operator, For virtual drones exist The reference vector at time t, For real drones exist The derivative of the time-varying formation transformation operator, For virtual drones exist The baseline change at any given time. For real drones exist The formation transformation operator at time step, Virtual drones exist The baseline control quantity at any given time. For virtual drones exist Time-based control input.

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