Self-adaptive dynamic event triggering three-dimensional cooperative control method of air-sea cross-domain unmanned system

Abstract

The invention discloses a self-adaptive dynamic event triggering three-dimensional cooperative control method of an air-sea cross-domain unmanned system. Firstly, a cross-domain system model composed of an unmanned ship and an unmanned aerial vehicle and a path tracking error dynamic equation of the cross-domain system model are constructed. Thirdly, respectively designing sight distance guidance laws of the two and establishing a corresponding path following error kinematical equation; a unified air-sea cooperative control error system is constructed by defining cluster cooperative errors. Then, designing a total path parameter collaborative error of aperiodic communication, and establishing an error historical queue maintenance mechanism; and finally, designing a self-adaptive dynamic event triggering condition, driving a sight distance guidance law, and realizing cooperative control of the system. According to the invention, the air-sea cross-domain unmanned system can realize high-precision motion synchronization and path tracking in a complex marine environment. According to the provided self-adaptive event triggering mechanism, the triggering threshold value is dynamically adjusted through historical error analysis, the control precision is strictly guaranteed, meanwhile, the system communication load is remarkably reduced, the resource utilization efficiency and the overall robustness are improved, and an efficient and reliable solution is provided for practical application such as ocean monitoring and joint search and rescue.

Description

Technical Field

[0001] This invention relates to the field of cooperative control technology for unmanned systems, and in particular to an adaptive dynamic event-triggered three-dimensional cooperative control method for cross-domain unmanned systems operating in air and sea. Background Technology

[0002] With the deepening of marine resource development and environmental monitoring, the operational environment is becoming increasingly complex and the mission requirements increasingly diverse. Air-sea cross-domain unmanned systems have attracted widespread attention due to their unique collaborative advantages. These systems typically consist of heterogeneous platforms such as unmanned aerial vehicles (UAVs) and unmanned surface vessels (USVs), demonstrating significant application potential in tasks such as marine resource exploration, wide-area environmental monitoring, dynamic target search, and emergency search and rescue. UAVs offer advantages such as wide high-altitude visibility and maneuverability, but are limited in endurance and payload. USVs, on the other hand, possess strong endurance and payload capabilities, but their perception range is relatively limited due to low-angle observation. Therefore, in practical missions, USVs often carry UAVs to the mission area, and then collaborative operations are used to achieve complementary effectiveness, thereby constructing an integrated air-sea cross-domain collaborative operation system and significantly improving the execution capability of comprehensive maritime missions.

[0003] However, UAVs and unmanned surface vessels (USVs) exist in different spatial media and exhibit significant differences in motion characteristics, communication bandwidth, motion constraints, and mission roles. This presents a severe challenge to cross-domain collaborative control between the two. Particularly in complex air and sea environments, achieving accurate and robust collaborative path tracking between UAVs and USVs in three-dimensional space has become a key technical challenge in the field of air-sea cross-domain collaboration. Existing collaborative control methods often rely on periodic communication and fixed-time triggering control strategies, which are difficult to adapt to dynamic environments and resource-constrained maritime conditions. They also fall short in balancing system stability, control accuracy, and communication efficiency, with specific shortcomings as follows: (1) Most existing collaborative control methods are only applicable to homogeneous unmanned systems in the same operational space domain, and are difficult to handle collaborative control problems between air and sea cross-domain platforms; (2) The static event triggering mechanisms in the existing communication strategies all use fixed thresholds for communication, which cannot be dynamically adjusted according to the actual system state of the aircraft. This leads to excessively frequent communication triggers when the system state changes drastically due to large initial state deviations or large external disturbances; (3) Existing dynamic event triggering mechanisms usually require manual setting of trigger threshold parameters, which places high technical demands on operators. In addition, improper parameter selection may lead to a decrease in system performance or a waste of communication resources; (4) There is a lack of a unified three-dimensional cross-domain collaborative path tracking control method, making it difficult to achieve cross-domain collaborative control of air and sea platforms.

[0004] Therefore, how to design a collaborative path tracking control method that can adapt to changes in the marine environment and take into account both control performance and communication resource optimization has become a core issue that urgently needs to be addressed in the current research on collaborative technologies for cross-domain unmanned systems in the air and sea. Summary of the Invention

[0005] This invention provides an adaptive dynamic event-triggered three-dimensional cooperative control method for air-sea cross-domain unmanned systems to overcome the aforementioned technical problems.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: An adaptive dynamic event-triggered three-dimensional cooperative control method for an air-sea cross-domain unmanned system, comprising the following steps: S1. Construct an air-sea cross-domain unmanned system consisting of several unmanned surface vessels and unmanned aerial vehicles (UAVs), and construct the path tracking error dynamic equations for the unmanned surface vessels and UAVs based on the air-sea cross-domain unmanned system. S2. Design the line-of-sight guidance law for the unmanned surface vessel (USV) and the unmanned aerial vehicle (UAV) respectively. Based on the USV's line-of-sight guidance law and the USV's path tracking error dynamic equation, design the first path following error kinematic equation. Based on the UAV's line-of-sight guidance law and the UAV's path tracking error dynamic equation, design the second path tracking error kinematic equation. S3. Define the cluster coordination error, and construct an air-sea unmanned cluster coordination control error system based on the cluster coordination error, the kinematic equation of the first path following error, and the kinematic equation of the second path tracking error. S4. Construct the total path parameter coordination error for aperiodic communication based on the cluster coordination error; S5. Establish an error history queue maintenance mechanism, and design an adaptive trigger threshold decay mechanism based on the error history queue maintenance mechanism; S6. Based on the total path parameter coordination error and adaptive trigger threshold decay mechanism of the non-periodic communication, an adaptive dynamic event triggering condition is designed for the air-sea unmanned swarm collaborative control error system. Combined with the line-of-sight guidance law of unmanned surface vessels and unmanned aerial vehicles, adaptive dynamic event triggering three-dimensional collaborative control of the air-sea cross-domain unmanned system is realized.

[0007] Furthermore, in S1, the specific steps for constructing an air-sea cross-domain unmanned system composed of several unmanned surface vessels (USVs) and unmanned aerial vehicles (UAVs), and for constructing the path tracking error dynamic equations for USVs and UAVs based on the air-sea cross-domain unmanned system, include: Construct an air-sea cross-domain unmanned system consisting of N unmanned vehicles, where unmanned vehicles numbered 1 to M are unmanned surface vessels, and unmanned vehicles numbered M+1 to N are unmanned aerial vehicles (UAVs). Among them, the establishment of the first i The dynamic model of the unmanned surface vessel is as follows: ; in, and The unmanned surface vessel is in a fixed coordinate system { I The position within}; and These are the pitch speed and sway speed of the unmanned surface vessel, respectively. It is the yaw angle of the unmanned surface vessel; It is the yaw rate of the unmanned surface vessel; Establish the first based on the ship's coordinate system i The kinematic model of the unmanned surface vessel is as follows: ; in, This indicates the actual forward speed of the unmanned surface vessel. ; This refers to the actual operating direction of the unmanned surface vessel. , For the sideslip angle of the unmanned surface vessel, ,and ; N is established based on the body coordinate system. The first of the M drones i The five-degree-of-freedom kinematic model of the drone is as follows: ; in, The drone is in a fixed coordinate system { I The position within}; , These are the axes along the UAV's body coordinate system. speed; These are the pitch and yaw angles of the drone, respectively. These are the pitch rate and yaw rate of the drone, respectively. si In i express i ∈[1, M ], ai In i express ; Will The parameterized path of an unmanned surface vessel is represented as follows: ,in, and For path points at fixed coordinates The position in the middle; For the first Path parameters of an unmanned surface vessel; For in The position of An unmanned surface vessel (USV) tracks its longitudinal tracking error in a three-dimensional tangential coordinate system based on a parametric path. and lateral tracking error Represented as: ; in, The tangent angle given the path parameters of the unmanned surface vessel is expressed as: ; in, ; ; Longitudinal tracking error in the three-dimensional path tangential coordinate system and lateral tracking error Differentiating the equations yields the dynamic equation for the path tracking error of the unmanned surface vessel, which is expressed as: ; in, To parameterize the speed of the virtual guide reference point on the path, ; fluid coordinate system The total speed of the drone is expressed as The angle of attack and sideslip angle of the UAV are expressed as follows: and ,in ; Therefore, the first i The five-degree-of-freedom kinematic model of the drone is transformed into: ; in, and They represent the first The flight path climb angle and flight path azimuth angle of the drone; The first The parameterized path of the UAV is represented as ,in, If the path parameter is given, then the tangent angle of the UAV given the path parameter is expressed as: ; in, ; ; ; definition Let be the rotation matrix that transforms the 3D path tangential coordinate system {Fi} to the fixed coordinate system {I}, expressed as: ; Based on the tangent angle of the given path parameters of the UAV and Define cooperative path tracking error for: ; in, , , ,and, ; definition For the fluid coordinate system { A i} Tangential coordinate system of the three-dimensional path { F i The rotation matrix of the transformation is then: ; in, , , ; For the first A drone in a fluid coordinate system { A i The speed in} ; Forward sight distance; Differentiating the cooperative path tracking error yields: ; Combining the transformed first i Based on the five-degree-of-freedom kinematic model of the UAV, the dynamic equation for the UAV's path tracking error is derived, expressed as: ; in, It is the speed of the virtual guide reference point in the parameterized path. .

[0008] Furthermore, in S2, the specific steps for designing the line-of-sight guidance laws for the unmanned surface vessel (USV) and the unmanned aerial vehicle (UAV), designing the first path-following error kinematic equation based on the USV's line-of-sight guidance law and the USV's path-tracking error dynamic equation, and designing the second path-tracking error kinematic equation based on the UAV's line-of-sight guidance law and the UAV's path-tracking error dynamic equation include: Assuming that both unmanned surface vessels (USVs) and unmanned aerial vehicles (UAVs) can track guidance signals generated by motion controllers; Design No. The kinematic control laws of the unmanned surface vessel are as follows: ; in, For the first Yaw angle deviation of the unmanned surface vessel; and The first The actual yaw angle and guidance yaw angle of the unmanned surface vessel; The constant reference speed for the unmanned surface vessel; For the first Subsequent design variables for unmanned surface vessels; Based on the first The kinematic control law of the unmanned surface vessel will be the first i The line-of-sight guidance law of the unmanned surface vessel is designed as follows: ; in, ; in, U sir and r sir These are the guidance speed and guidance angular velocity of the unmanned surface vessel, respectively. ; ; ; It is the forward sight distance; , , k si4 and k si5 It is a positive number; Based on the i The line-of-sight guidance law and path tracking error dynamic equation of the unmanned surface vessel (USV) are designed. The first path following error kinematic equation is expressed as: ; Design No. i The kinematic control laws of the drone are as follows: ; in, and The first The trajectory angle deviation and azimuth angle deviation of the UAV; and The first The navigation trajectory angle and guidance azimuth angle of the unmanned aerial vehicle (UAV); , , ; The constant reference speed for the drone; For the first Subsequent design variables for the drone; The dynamic equation for the path tracking error of the UAV is then transformed into: ; in, , The first The guidance pitch rate and guidance yaw rate of the UAV; Based on the first iThe kinematic control law of the drone will be the first i The line-of-sight guidance law for this UAV is designed as follows: ; in, U aiU Indicates the first i The guidance speed of the drone; ; ; ; ; ;k ai1 k ai2 k ai3 , , and All are positive numbers; Based on the i Based on the line-of-sight guidance law of the UAV and the transformed path tracking error dynamic equation, the second path tracking error kinematic equation is designed, expressed as:

[0009] in, ; .

[0010] Furthermore, in S3, the swarm coordination error is defined. The specific steps for constructing the air-sea unmanned swarm coordinated control error system based on the swarm coordination error, the kinematic equation of the first path following error, and the kinematic equation of the second path tracking error include: Define the cluster cooperation error based on information from neighboring unmanned surface vessels and unmanned aerial vehicles. e i for: e i = ; in, ;when hour, ;when hour, ; e i The matrix form is represented as ,in ,and ; Represents the Laplacian matrix; Based on the kinematic equations of the first path tracking error, the kinematic equations of the second path following error, and the cluster coordination error e i The error system for collaborative control of air-sea unmanned swarms is constructed as follows: ; in, As a collaborative control term, it is designed as follows: ; in, µ i It is about controlling the gain. µ i >0, And when hour, and ;when hour, and .

[0011] Furthermore, in S4, the specific steps for constructing the total path parameter coordination error for aperiodic communication based on the cluster coordination error include: Definition of the first i Unmanned aerial vehicles, including drones and unmanned surface vessels, in t The structure of the communication data packet at any given time is as follows: ; At non-triggering time t>t i At that time, based on the last trigger time recorded in the communication data packet. t k j status And its derivative, the first is estimated using linear extrapolation. i The path parameter states of adjacent vehicles of an unmanned aerial vehicle are represented as follows: ; in, Indicates adjacent aircraft j The path parameter of its most recent event trigger time; t k j Indicates adjacent aircraft j Recent event trigger time, j ∈ , For adjacent aircraft groups; Using the first i An unmanned aerial vehicle in t The information contained in the communication data packet at time t defines the total path parameter coordination error of aperiodic communication as follows: ; in, ; in, fort k i The deviation between the cooperative estimation error of adjacent vessels at time and the cooperative estimation error of adjacent vessels at the current time; For the current moment, the first j The actual path parameters of the unmanned aerial vehicle and the first i The ship to the first j The deviation of the path parameters estimated by the unmanned aerial vehicle.

[0012] Furthermore, in S5, the specific steps for establishing an error history queue maintenance mechanism and designing an adaptive trigger threshold decay mechanism based on this mechanism include: S51. Establish an error history queue maintenance mechanism: Setting the first i Each unmanned aerial vehicle maintains a first-in-first-out queue. H i , is represented as: ; in, K This is the current queue length; L max It is the maximum length of the queue; The update rules for the first-in-first-out queue are designed as follows: 1) When the latest event is triggered, record its error norm as new data, denoted as: ; 2) Check the queue length to update the queue: If the current queue length K L max Then Add to the end of the queue and update the queue length. ; if K > L max , then delete H i The first record in will Add to the end of the queue to make the queue length K Keep as L max ; make ; S52. Calculate the rate of change based on historical data in the queue, and design an adaptive trigger threshold decay mechanism based on the rate of change, including: From queue H i Extract a number of historical data points. The number of historical data points extracted is: , is a positive integer; The average difference, or rate of change, is calculated based on the extracted historical data, using the following formula: ; The design incorporates an adaptive trigger threshold decay mechanism during non-trigger intervals, expressed as follows: ; in, This is the dynamic decay threshold, and ; It is a preset positive threshold used to prevent Decaying indefinitely to zero ensures system stability; Indicates time t Previous threshold parameters; It is based on the rate of change A dynamically adjusted adaptive attenuation factor, and: ; in, The initial attenuation rate, , These are positive tuning coefficients; It is the average historical error difference.

[0013] Furthermore, in S6, the specific steps for designing adaptive dynamic event triggering conditions for the air-sea unmanned swarm collaborative control error system based on the total path parameter coordination error and adaptive triggering threshold decay mechanism of the aperiodic communication include: Based on the total path parameter cooperative error and the adaptive trigger threshold decay mechanism, an adaptive dynamic event triggering condition is designed as follows: , in, For dynamic thresholds, ; For the first i The unmanned aerial vehicle at the most recent trigger time The error value stored at that time; Represented as: ; It is a mixed tolerance term of absolute tolerance and relative tolerance, expressed as:

[0014] in, It is the basic absolute tolerance. ; It is a relative tolerance; It is a constant adjustment parameter. .

[0015] Beneficial Effects: This invention addresses the cooperative path tracking control problem of cross-domain air-sea unmanned systems in complex marine environments. It proposes an adaptive dynamic event-triggered three-dimensional cooperative control method for cross-domain air-sea unmanned systems, resulting in the following benefits: First, it achieved high-precision cooperative motion of cross-domain heterogeneous unmanned systems. By constructing a unified air-sea cross-domain unmanned system model and error dynamic equations, and designing line-of-sight guidance laws for unmanned surface vessels and unmanned aerial vehicles (UAVs) respectively, it ensured that UAVs in the air and unmanned surface vessels on the sea could achieve precise motion synchronization and cooperative path tracking under different navigation dynamic environments, significantly improving the core capabilities of cross-domain swarms in performing collaborative tasks such as marine monitoring and joint search and rescue. Secondly, it significantly improves the system's communication efficiency and resource utilization. This invention creatively designs an adaptive dynamic event triggering control mechanism for non-periodic communication air-sea clusters. This mechanism includes two key technologies: first, it proposes an adaptive threshold decay strategy based on historical error change rate analysis, which can dynamically and intelligently adjust the trigger sensitivity according to real-time errors, avoiding unnecessary communication; second, it introduces a historical error queue maintenance mechanism, realizing intelligent balance adjustment between absolute accuracy and relative change in triggering conditions. This allows the system to communicate only when necessary, thereby significantly reducing the communication resource consumption of the entire cross-domain unmanned system while strictly ensuring path tracking control accuracy. Third, the system's adaptability and robustness in complex real-world environments are enhanced. This invention fully considers the complexity and uncertainty of the marine environment, as well as the resource-constrained nature of the unmanned platform itself. Through an adaptive event-triggered mechanism and a cooperative error system design, the control system's adaptability to communication delays, intermittent interruptions, and external disturbances is enhanced, thereby improving the dynamic performance and robustness of the entire cross-domain cooperative system.

[0016] In summary, this invention provides an efficient and reliable solution to the challenge of cross-domain collaborative control in resource-constrained scenarios. While ensuring high-precision collaborative performance, this method significantly optimizes communication overhead, demonstrating significant theoretical innovation and engineering application value. It offers a highly robust, low-communication-overhead solution for cross-domain collaborative tasks in resource-constrained scenarios, and has important engineering value in practical applications such as marine monitoring and joint search and rescue. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of an adaptive dynamic event-triggered three-dimensional cooperative control method for an air-sea cross-domain unmanned system according to the present invention; Figure 2 This is a three-dimensional trajectory comparison diagram of the preset path and the actual path in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the change of path variables over time in an embodiment of the present invention; Figure 4 Guidance speed in embodiments of the present invention U i A schematic diagram showing how it changes over time; Figures 5-7 The guidance angular velocity in this embodiment of the invention , and A schematic diagram showing how it changes over time; Figures 8-10 This refers to the cooperative path following error in the embodiments of the present invention. x ie , y ie and z ie A schematic diagram showing how it changes over time; Figure 11 This is a schematic diagram of the adaptive dynamic communication triggering events for three unmanned surface vessels in an embodiment of the present invention; Figure 12 This is a schematic diagram of the adaptive dynamic communication triggering events of three UAVs in an embodiment of the present invention; Figure 13 This is a schematic diagram of the dynamic communication triggering events of three unmanned surface vessels in an embodiment of the present invention; Figure 14 This is a schematic diagram illustrating the dynamic communication triggering events of three drones in an embodiment of the present invention; Figure 15 This is a schematic diagram of the communication triggering events of three unmanned surface vessels in an embodiment of the present invention; Figure 16 This is a schematic diagram of the communication triggering events of three drones in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] This embodiment provides an adaptive dynamic event-triggered three-dimensional cooperative control method for an air-sea cross-domain unmanned system, such as... Figure 1 As shown, the specific steps include: S1. Construct an air-sea cross-domain unmanned system consisting of several unmanned surface vessels and unmanned aerial vehicles (UAVs), and construct the path tracking error dynamic equations for the unmanned surface vessels and UAVs based on the air-sea cross-domain unmanned system. S2. Design the line-of-sight guidance law for the unmanned surface vessel (USV) and the unmanned aerial vehicle (UAV) respectively. Based on the USV's line-of-sight guidance law and the USV's path tracking error dynamic equation, design the first path following error kinematic equation. Based on the UAV's line-of-sight guidance law and the UAV's path tracking error dynamic equation, design the second path tracking error kinematic equation. S3. Define the cluster coordination error, and construct an air-sea unmanned cluster coordination control error system based on the cluster coordination error, the kinematic equation of the first path following error, and the kinematic equation of the second path tracking error. S4. Construct the total path parameter coordination error for aperiodic communication based on the cluster coordination error; S5. Establish an error history queue maintenance mechanism, and design an adaptive trigger threshold decay mechanism based on the error history queue maintenance mechanism; S6. Based on the total path parameter coordination error and adaptive trigger threshold decay mechanism of the non-periodic communication, an adaptive dynamic event triggering condition is designed for the air-sea unmanned swarm collaborative control error system. Combined with the line-of-sight guidance law of unmanned surface vessels and unmanned aerial vehicles, adaptive dynamic event triggering three-dimensional collaborative control of the air-sea cross-domain unmanned system is realized.

[0021] In a specific embodiment, S1 involves constructing an air-sea cross-domain unmanned system composed of several unmanned surface vessels (USVs) and unmanned aerial vehicles (UAVs), and then constructing the path tracking error dynamic equations for the USVs and UAVs based on the air-sea cross-domain unmanned system. The specific steps include: Construct an air-sea cross-domain unmanned system consisting of N unmanned vehicles, where unmanned vehicles numbered 1 to M are unmanned surface vessels (USVs), and unmanned vehicles numbered M+1 to N are unmanned aerial vehicles (UAVs). Among them, the establishment of the first i The dynamic model of the unmanned surface vessel is as follows: ; in, and The unmanned surface vessel is in a fixed coordinate system { I The position within}; and These are the pitch speed and sway speed of the unmanned surface vessel, respectively. It is the yaw angle of the unmanned surface vessel; It is the yaw rate of the unmanned surface vessel; Establish the first based on the ship's coordinate system i The kinematic model of the unmanned surface vessel is as follows: ; in, This indicates the actual forward speed of the unmanned surface vessel. ; This refers to the actual operating direction of the unmanned surface vessel. , For the sideslip angle of the unmanned surface vessel, ,and ; N is established based on the body coordinate system. The first of the M drones i The five-degree-of-freedom kinematic model of the drone is as follows: ; in, The drone is in a fixed coordinate system { I The position within}; , These are the axes along the UAV's body coordinate system. speed; These are the pitch and yaw angles of the drone, respectively. These are the pitch rate and yaw rate of the drone, respectively. si In i express i ∈[1, M ], ai In i express ; Specifically, this embodiment establishes a kinematic model of the unmanned surface vessel (USV) based on the ship's coordinate system and a kinematic model of the unmanned aerial vehicle (UAV) based on the body coordinate system, and sets their respective desired paths and desired velocities. By parameterizing the desired paths, the error between the actual position and the virtual guidance reference point is projected onto the three-dimensional path tangential coordinate system, and the dynamic equation of the path tracking error of the air-sea cross-domain unmanned system is obtained by solving partial differential equations.

[0022] Will The parameterized path of an unmanned surface vessel is represented as follows: ,in, and For path points at fixed coordinates The position in the middle; For the first Path parameters of an unmanned surface vessel; For in The position of An unmanned surface vessel (USV) tracks its longitudinal tracking error in a three-dimensional tangential coordinate system based on a parametric path. and lateral tracking error Represented as: ; in, The tangent angle given the path parameters of the unmanned surface vessel is expressed as: ; in, ; ; Longitudinal tracking error in the three-dimensional path tangential coordinate system and lateral tracking error Differentiating the equations yields the dynamic equation for the path tracking error of the unmanned surface vessel, which is expressed as: ; in, To parameterize the speed of the virtual guide reference point on the path, ; fluid coordinate system The total speed of the drone is expressed as The angle of attack and sideslip angle of the UAV are expressed as follows: and ,in ; Therefore, the first i The five-degree-of-freedom kinematic model of the drone is transformed into: ; in, and They represent the first The flight path climb angle and flight path azimuth angle of the drone; The first The parameterized path of the UAV is represented as ,in, If the path parameter is given, then the tangent angle of the UAV given the path parameter is expressed as: ; in, ; ; ; definition For the three-dimensional path tangential coordinate system { F i} To a fixed coordinate system { I The rotation matrix of the transformation is expressed as: ; Based on the tangent angle of the given path parameters of the UAV and Define cooperative path tracking error for: ; in, , , ,and, ; definition For the fluid coordinate system { A i} Tangential coordinate system of the three-dimensional path { F i The rotation matrix of the transformation is then: ; in, , , ; For the first A drone in a fluid coordinate system { A i The speed in} ; Forward sight distance; Differentiating the cooperative path tracking error yields: ; Combining the transformed first i Based on the five-degree-of-freedom kinematic model of the UAV, the dynamic equation for the UAV's path tracking error is derived, expressed as: ; in, It is the speed of the virtual guide reference point in the parameterized path. .

[0023] In a specific embodiment, in S2, the specific steps for designing the line-of-sight guidance laws for the unmanned surface vessel (USV) and the unmanned aerial vehicle (UAV), designing the first path-following error kinematic equation based on the USV's line-of-sight guidance law and the USV's path-tracking error dynamic equation, and designing the second path-tracking error kinematic equation based on the UAV's line-of-sight guidance law and the UAV's path-tracking error dynamic equation include: Assuming that both unmanned surface vessels (USVs) and unmanned aerial vehicles (UAVs) can perfectly track the guidance signals generated by the motion controller; Design No. The kinematic control laws of the unmanned surface vessel are as follows: ; in, For the first Yaw angle deviation of the unmanned surface vessel; and The first The actual yaw angle and guidance yaw angle of the unmanned surface vessel; The constant reference speed for the unmanned surface vessel; For the first Subsequent design variables for unmanned surface vessels; Based on the first The kinematic control law of the unmanned surface vessel will be the first i The line-of-sight guidance law of the unmanned surface vessel is designed as follows: ; in, ; in, U sir and r sir These are the guidance speed and guidance angular velocity of the unmanned surface vessel, respectively. ; ; ; It is the forward sight distance; , , k si4 and k si5 It is a positive number; Based on the i The line-of-sight guidance law and path tracking error dynamic equation of the unmanned surface vessel (USV) are designed. The first path following error kinematic equation is expressed as: ; Design No. i The kinematic control laws of the drone are as follows: ; in, and The first The trajectory angle deviation and azimuth angle deviation of the UAV; and The first The navigation trajectory angle and guidance azimuth angle of the unmanned aerial vehicle (UAV); , , ; The constant reference speed for the drone; For the first Subsequent design variables for the drone; The dynamic equation for the path tracking error of the UAV is then transformed into: ; in, , The first The guidance pitch rate and guidance yaw rate of the UAV; Based on the first i The kinematic control law of the drone will be the first i The line-of-sight guidance law for this UAV is designed as follows: ; in, U aiU Indicates the first i The guidance speed of the drone; ; ; ; ; ;k ai1 k ai2 k ai3 , , and All are positive numbers; Based on the i Based on the line-of-sight guidance law of the UAV and the dynamic equation of the converted UAV path tracking error, the second path tracking error kinematic equation is designed, expressed as:

[0024] in, ; .

[0025] Specifically, this embodiment designs line-of-sight guidance laws for UAVs and UAVs by using the track angle and azimuth angle errors of UAVs and the bow angle error of UAVs, so as to calculate the guidance speed and guidance angular velocity respectively; and establishes the kinematic equations of path tracking error for UAVs and UAVs, which include path tracking error and angle error, as cooperative control inputs.

[0026] In a specific embodiment, S3 defines a cluster coordination error. The specific steps for constructing an air-sea unmanned cluster coordinated control error system based on the cluster coordination error, the kinematic equation of the first path following error, and the kinematic equation of the second path tracking error include: When considering multi-vehicle (UAV + UAV) collaborative formation, the communication topology between the vehicles is as follows. can be It means that, among them: For a set of nodes, Each spacecraft corresponds to a node. ; For edge set, ,picture The adjacency matrix is ​​represented as ,when hour, In other cases, ;picture In and nodes Number of associated edges For the sake of measurement, The matrix formed by the degrees is the degree matrix. , represented as Based on this, the diagram The Laplacian matrix is ​​represented as ,and ; Define when hour, ;when hour, ; To achieve synchronized formation, this embodiment defines the cluster coordination error based on information from neighboring unmanned surface vessels and unmanned aerial vehicles. e i for: e i = ; in, ;when hour, ;when hour, ; e i The matrix form is represented as ,in ,and ; Based on the kinematic equations of the first path tracking error, the kinematic equations of the second path following error, and the cluster coordination error e i The error system for collaborative control of air-sea unmanned swarms is constructed as follows: ; in, As a collaborative control term, it is designed as follows: ; in, µ i It is about controlling the gain. µ i >0, And when hour, and ;when hour, and .

[0027] Specifically, this embodiment defines the cooperative error based on information from adjacent unmanned surface vessels (USVs) and constructs a unified cooperative control error system that includes USVs and UAVs; it designs a path parameter update rate based on path cooperative control terms. and This enables collaborative path tracking and control across domain platforms.

[0028] In a specific embodiment, S4 includes the following steps for constructing the total path parameter coordination error of aperiodic communication based on the cluster coordination error: Definition of the first i An unmanned aerial vehicle in t The structure of the communication data packet at any given time is as follows: ; At non-triggering time t>t i At that time, based on the last trigger time recorded in the communication data packet. t k j status And its derivative, the first is estimated using linear extrapolation. i The path parameter states of adjacent vehicles of an unmanned aerial vehicle are represented as follows: ; in, Indicates adjacent aircraft j The path parameter of its most recent event trigger time; t k j Indicates adjacent aircraft j Recent event trigger time, j ∈ , For adjacent aircraft groups; Specifically, no. i Each unmanned vehicle adjusts its current actual path parameters based on the latest information from its neighboring vehicles. With estimated state The sum of the deviations between them forms the basic evaluation quantity for triggering conditions.

[0029] Using the first i An unmanned aerial vehicle in t The information contained in the communication data packet at time t defines the total path parameter coordination error of aperiodic communication as follows: ; in, ; in, for t k i The deviation between the cooperative estimation error of adjacent vessels at time and the cooperative estimation error of adjacent vessels at the current time; For the current moment, the first j The actual path parameters of the unmanned aerial vehicle and the first i The ship to the first j The deviation of the path parameters estimated by the unmanned aerial vehicle.

[0030] In a specific embodiment, S5, the specific steps for establishing an error history queue maintenance mechanism and designing an adaptive trigger threshold decay mechanism based on the error history queue maintenance mechanism include: S51. Establish an error history queue maintenance mechanism: Setting the first i Each unmanned aerial vehicle maintains a first-in-first-out (FIFO) queue. H i , is represented as: ; in, K This is the current queue length; L max It is the maximum length of the queue; The update rules for the first-in-first-out queue are designed as follows: 1) When the latest event is triggered, record its error norm as new data, denoted as: ; 2) Check the queue length to update the queue: If the current queue length K L max Then Add to the end of the queue and update the queue length. ; if K > L max , then delete H i The first record in will Add to the end of the queue to make the queue length K Keep as L max ; make ; Specifically, each vehicle maintains a fixed-length first-in-first-out queue to record historical error data; when an event is triggered, the queue is updated. If the queue is not full, a new record is added; if the queue is full, the oldest record is removed and a new record is added. The average difference of the most recent records in the queue is calculated as the basis for adjusting the threshold decay factor to ensure the adaptability of the air-sea cross-domain unmanned system to the dynamic marine environment.

[0031] S52. Calculate the rate of change based on historical data in the queue, and design an adaptive trigger threshold decay mechanism based on the rate of change, including: From queue H i Extract a number of historical data points. The number of historical data points extracted is: , is a positive integer; The average difference, or rate of change, is calculated based on the extracted historical data, using the following formula: ; The design incorporates an adaptive trigger threshold decay mechanism during non-trigger intervals, expressed as follows: ; in, This is the dynamic decay threshold, and ; It is a preset positive threshold used to prevent Decaying indefinitely to zero ensures system stability; Indicates time t Previous threshold parameters; It is based on the rate of change A dynamically adjusted adaptive attenuation factor, and: ; in, The initial attenuation rate, , These are positive tuning coefficients; It is the average historical error difference, which can reflect the gradient of recent error changes. Its calculation depends on the error history queue maintained by the aircraft.

[0032] Specifically, if A smaller value indicates that the historical error has remained relatively stable. near The threshold decays slowly, and the event triggering conditions are strict at this time, so frequent triggering should be avoided in a stable state; if A large value indicates drastic changes in historical error. Increase The threshold decays faster as it decreases, making it easier to meet triggering conditions and enabling the system to respond more sensitively to dynamic changes.

[0033] Specifically, during the non-trigger interval, the dynamic threshold parameter decreases according to the adaptive decay factor; a preset positive lower threshold is designed to prevent infinite decay to zero; the adaptive decay factor is dynamically adjusted according to the average difference. Specifically, when the error changes drastically, the decay factor is increased to accelerate the threshold decay and improve sensitivity, and when the error changes steadily, the decay factor is decreased to slow down the decay and avoid over-triggering; the initial decay rate and positive tuning coefficient are used to adjust the response speed of the adaptive process.

[0034] In a specific embodiment, S6, the specific steps for designing adaptive dynamic event triggering conditions for the air-sea unmanned swarm collaborative control error system based on the total path parameter coordination error and adaptive triggering threshold decay mechanism of the aperiodic communication include: Based on the total path parameter cooperative error and the adaptive trigger threshold decay mechanism, an adaptive dynamic event triggering condition is designed as follows: , in, For dynamic thresholds, ; For the first i The unmanned aerial vehicle at the most recent trigger time The error value stored at that time; Represented as: ; It is a mixed tolerance term combining absolute and relative tolerances, used for fine-tuning trigger sensitivity, and is expressed as:

[0035] in, It is the basic absolute tolerance. ; It is a relative tolerance; It is a constant adjustment parameter. .

[0036] Specifically, communication is triggered when the cumulative deviation of the total path parameter coordination error exceeds the dynamic threshold. The unmanned vehicle broadcasts a communication data packet to its neighbors, which includes the current trigger time, its own path parameters, and the derivatives of the path parameters. The dynamic threshold consists of a hybrid tolerance term and a dynamic decay threshold parameter. The hybrid tolerance term includes a basic absolute tolerance and a relative tolerance proportional to the square of the error, and introduces a small constant adjustment parameter to prevent abnormal triggering caused by excessively small errors. The dynamic decay threshold parameter is updated in real time based on an adaptive trigger threshold decay mechanism to ensure the intelligent adjustment capability of the triggering conditions. The error value at the time of the most recent trigger is stored to calculate the cumulative deviation, realizing closed-loop control of event triggering.

[0037] To verify the effectiveness of the adaptive dynamic event-triggered cooperative path tracking control method for air-sea cross-domain unmanned systems proposed in this embodiment, a simulation experiment was conducted on an unmanned system cluster consisting of three unmanned surface vessels (USVs) and three unmanned aerial vehicles (UAVs). The UAVs took off from their respective USVs, and all three UAVs adopted a path-following strategy, forming a formation to perform cooperative tasks. The target area was set as a fan-shaped sea area. The controller parameters were set as follows: k ai1 = 0.5 ，k ai2 = 0.3 ，k ai3 = 0.2 ，k si4 = 0.5 ， k si1 = 0.2, τ iabs = 0.001. Initial positions: Unmanned surface vessel is located at (20,0,0), (20,40,0), (20,40,0); Unmanned aerial vehicle is located at (20,0,0), (20,40,0), (20,40,0). Figure 2 The cooperative path tracking performance of the air-sea cross-domain unmanned system was demonstrated, and the results showed that all three unmanned surface vessels and three unmanned aerial vehicles effectively tracked their predefined parameterized paths. Figure 3 The evolution of path variables in the air-sea cross-domain unmanned system is shown. It can be seen that after a period of time, the path parameters of the three unmanned surface vessels and three unmanned aerial vehicles tend to be synchronized, achieving parameter coordination. Figures 4 to 7 The guidance speeds of the drone and the unmanned surface vessel were displayed respectively. U i and guidance angular velocity p i , q i , r iAfter dynamic adjustments, the guidance velocity and angular velocity of the air-sea cross-domain unmanned system converged to a unified value, achieving synchronous tracking. Figures 8 to 10 The cooperative tracking error was shown. x ie , y ie , z ie As can be seen from the figure, these tracking errors gradually approach zero after the initial transient phase. Figure 11 and 12 The communication trigger events of three unmanned surface vessels (USVs) and three unmanned aerial vehicles (UAVs) based on an adaptive dynamic event triggering mechanism are displayed respectively (1 on the vertical axis represents an event triggered, and 0 represents no event triggered). For comparison, Figures 13 to 16 This paper demonstrates communication triggering events based on traditional Dynamic Event Triggered Communication (DETC) and Static Event Triggered Control (ETC). Experimental results show that in the initial stage of cross-domain unmanned system cooperation between air and sea, the communication events of traditional DETC and ETC methods are extremely dense and have a high triggering frequency. The Adaptive Dynamic Event Triggered Control (ADETC) strategy proposed in this embodiment significantly outperforms the other two strategies in this stage. After 200 seconds of simulation, the number of triggering events per agent using the ADETC strategy does not exceed 4, indicating that this communication strategy can minimize unnecessary communication resource consumption while ensuring the completion of cross-domain formation path tracking tasks in both the initial and stable cooperation phases.

[0038] Specifically, Table 1 shows the number of ADETC (Adaptive Dynamic Event Triggered Communication), DETC (Dynamic Event Triggered Communication), ETC (Static Event Triggered Communication), ACT (Average Communication Time), and OCT (Overall Communication Time) for the three unmanned surface vessels and three unmanned aerial vehicles (UAVs). As can be seen from Table 1, compared with the traditional DETC method, the ADETC-based air-sea cross-domain unmanned system reduces the number of ACTs by 37.1% and the number of OCTs by 36.5%. Compared with the ETC method, ACT is reduced by 43.6%, and OCT by 42.5%. This indicates that the proposed adaptive dynamic event triggered communication strategy significantly reduces the communication frequency.

[0039] Table 1:

[0040] In summary, this invention, through the design of a threshold decay strategy driven by historical errors and a hybrid tolerance mechanism (absolute + relative), significantly reduces the system's communication resource consumption while strictly ensuring path tracking accuracy. Theoretical analysis proves the global asymptotic stability of the closed-loop system and the absence of Zeno behavior. This invention significantly reduces the communication frequency and total communication volume of unmanned surface vessel / unmanned aerial vehicle (USV) formations, effectively solving the problems of collaborative instability caused by mismatched motion characteristics of cross-domain platforms (high maneuverability of UAVs / strong inertia of USVs), environmental disturbances (wind, waves, currents), and communication delays. It provides a highly robust and low-communication-overhead solution for cross-domain collaborative tasks in resource-constrained scenarios, and has significant engineering value in practical applications such as marine monitoring and joint search and rescue.

[0041] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive dynamic event-triggered three-dimensional cooperative control method for an air-sea cross-domain unmanned system, characterized in that, The specific steps include: S1. Construct an air-sea cross-domain unmanned system consisting of several unmanned surface vessels and unmanned aerial vehicles (UAVs), and construct the path tracking error dynamic equations for the unmanned surface vessels and UAVs based on the air-sea cross-domain unmanned system. S2. Design the line-of-sight guidance law for the unmanned surface vessel (USV) and the unmanned aerial vehicle (UAV) respectively. Based on the USV's line-of-sight guidance law and the USV's path tracking error dynamic equation, design the first path following error kinematic equation. Based on the UAV's line-of-sight guidance law and the UAV's path tracking error dynamic equation, design the second path tracking error kinematic equation. S3. Define the cluster coordination error, and construct an air-sea unmanned cluster coordination control error system based on the cluster coordination error, the kinematic equation of the first path following error, and the kinematic equation of the second path tracking error. S4. Construct the total path parameter coordination error for aperiodic communication based on the cluster coordination error; S5. Establish an error history queue maintenance mechanism, and design an adaptive trigger threshold decay mechanism based on the error history queue maintenance mechanism; S6. Based on the total path parameter coordination error and adaptive trigger threshold decay mechanism of the non-periodic communication, an adaptive dynamic event triggering condition is designed for the air-sea unmanned swarm collaborative control error system. Combined with the line-of-sight guidance law of unmanned surface vessels and unmanned aerial vehicles, adaptive dynamic event triggering three-dimensional collaborative control of the air-sea cross-domain unmanned system is realized.

2. The adaptive dynamic event-triggered three-dimensional cooperative control method for air-sea cross-domain unmanned systems according to claim 1, characterized in that, In S1, the specific steps for constructing an air-sea cross-domain unmanned system consisting of several unmanned surface vessels (USVs) and unmanned aerial vehicles (UAVs), and for constructing the path tracking error dynamic equations for the USVs and UAVs based on the air-sea cross-domain unmanned system, include: Construct an air-sea cross-domain unmanned system consisting of N unmanned vehicles, where unmanned vehicles numbered 1 to M are unmanned surface vessels, and unmanned vehicles numbered M+1 to N are unmanned aerial vehicles (UAVs). Among them, the establishment of the first i The dynamic model of the unmanned surface vessel is as follows: ； in, and The unmanned surface vessel is in a fixed coordinate system { I The position within}; and These are the pitch speed and sway speed of the unmanned surface vessel, respectively. It is the yaw angle of the unmanned surface vessel; It is the yaw rate of the unmanned surface vessel; Establish the first based on the ship's coordinate system i The kinematic model of the unmanned surface vessel is as follows: ； in, This indicates the actual forward speed of the unmanned surface vessel. ; This refers to the actual operating direction of the unmanned surface vessel. , For the sideslip angle of the unmanned surface vessel, ,and ; N is established based on the body coordinate system. The first of the M drones i The five-degree-of-freedom kinematic model of the drone is as follows: ； in, The drone is in a fixed coordinate system { I The position within}; , These are the axes along the UAV's body coordinate system. speed; These are the pitch and yaw angles of the drone, respectively. These are the pitch rate and yaw rate of the drone, respectively. si In i express i ∈[1, M ], ai In i express ; Will The parameterized path of an unmanned surface vessel is represented as follows: ,in, and For path points at fixed coordinates The position in the middle; For the first Path parameters of an unmanned surface vessel; For in The position of An unmanned surface vessel (USV) tracks its longitudinal tracking error in a three-dimensional tangential coordinate system based on a parametric path. and lateral tracking error Represented as: ； in, The tangent angle given the path parameters of the unmanned surface vessel is expressed as: ； in, ; ; Longitudinal tracking error in the three-dimensional path tangential coordinate system and lateral tracking error Differentiating the equation yields the dynamic equation for the path tracking error of the unmanned surface vessel, which is expressed as: ； in, To parameterize the speed of the virtual guide reference point on the path, ; fluid coordinate system The total speed of the drone is expressed as The angle of attack and sideslip angle of the UAV are expressed as follows: and ,in ; Therefore, the first i The five-degree-of-freedom kinematic model of the drone is transformed into: ； in, and They represent the first The flight path climb angle and flight path azimuth angle of the drone; The first The parameterized path of the UAV is represented as ,in, If the path parameter is given, then the tangent angle of the UAV given the path parameter is expressed as: ； in, ; ; ; definition Let be the rotation matrix that transforms the 3D path tangential coordinate system {Fi} to the fixed coordinate system {I}, expressed as: ； Based on the tangent angle of the given path parameters of the UAV and Define cooperative path tracking error for: ； in, , , ,and, ； definition For the fluid coordinate system { A i } Tangential coordinate system of the three-dimensional path { F i The rotation matrix of the transformation is then: ； in, , , ; For the first A drone in a fluid coordinate system { A i The speed in} ; Forward sight distance; Differentiating the cooperative path tracking error yields: ； Combining the transformed first i Based on the five-degree-of-freedom kinematic model of the UAV, the dynamic equation for the UAV's path tracking error is derived, expressed as: ； in, It is the speed of the virtual guide reference point in the parameterized path. .

3. The adaptive dynamic event-triggered three-dimensional cooperative control method for air-sea cross-domain unmanned systems according to claim 2, characterized in that, In S2, the line-of-sight guidance laws for the unmanned surface vessel (USV) and the unmanned aerial vehicle (UAV) are designed respectively. Based on the USV's line-of-sight guidance law and the dynamic equation of its path tracking error, the first path following error kinematic equation is designed. Based on the UAV's line-of-sight guidance law and the UAV's path tracking error dynamic equation, the second path tracking error kinematic equation is designed. The specific steps include: Assuming that both unmanned surface vessels (USVs) and unmanned aerial vehicles (UAVs) can track guidance signals generated by motion controllers; Design No. The kinematic control laws of the unmanned surface vessel are as follows: ； in, For the first Yaw angle deviation of the unmanned surface vessel; and The first The actual yaw angle and guidance yaw angle of the unmanned surface vessel; The constant reference speed for the unmanned surface vessel; For the first Subsequent design variables for unmanned surface vessels; Based on the first The kinematic control law of the unmanned surface vessel will be the first i The line-of-sight guidance law of the unmanned surface vessel is designed as follows: ； in, ； in, U sir and r sir These are the guidance speed and guidance angular velocity of the unmanned surface vessel, respectively. ; ; ; It is the forward sight distance; , , k si4 and k si5 It is a positive number; Based on the i The line-of-sight guidance law and the dynamic equation of the path tracking error of the unmanned surface vessel (USV) are designed. The first kinematic equation of the path following error is expressed as: ； Design No. i The kinematic control laws of the drone are as follows: ； in, and The first The trajectory angle deviation and azimuth angle deviation of the UAV; and The first The navigation trajectory angle and guidance azimuth angle of the unmanned aerial vehicle (UAV); , , ; The constant reference speed for the drone; For the first Subsequent design variables for the drone; The dynamic equation for the path tracking error of the UAV is then transformed into: ； in, , The first The guidance pitch rate and guidance yaw rate of the UAV; Based on the first i The kinematic control law of the drone will be the first i The line-of-sight guidance law for this UAV is designed as follows: ； in, U aiU Indicates the first i The guidance speed of the drone; ; ; ; ; ;k ai1 k ai2 k ai3 , , and All are positive numbers; Based on the i Based on the line-of-sight guidance law of the UAV and the transformed path tracking error dynamic equation, the second path tracking error kinematic equation is designed, expressed as: in, ; .

4. The adaptive dynamic event-triggered three-dimensional cooperative control method for air-sea cross-domain unmanned systems according to claim 3, characterized in that, In S3, the swarm coordination error is defined. The specific steps for constructing an air-sea unmanned swarm coordinated control error system based on the swarm coordination error, the kinematic equation of the first path following error, and the kinematic equation of the second path tracking error include: Define the cluster cooperation error based on information from neighboring unmanned surface vessels and unmanned aerial vehicles. e i for: e i = ； in, ;when hour, ;when hour, ; e i The matrix form is represented as ,in ,and ; Represents the Laplacian matrix; Based on the kinematic equations of the first path tracking error, the kinematic equations of the second path following error, and the cluster coordination error e i The error system for collaborative control of air-sea unmanned swarms is constructed as follows: ； in, As a collaborative control term, it is designed as follows: ； in, µ i It is about controlling the gain. µ i >0, And when hour, and ;when hour, and .

5. The adaptive dynamic event-triggered three-dimensional cooperative control method for air-sea cross-domain unmanned systems according to claim 4, characterized in that, In S4, the specific steps for constructing the total path parameter coordination error for aperiodic communication based on the cluster coordination error include: Definition of the first i Unmanned aerial vehicles, including drones and unmanned surface vessels, in t The communication data packet structure at any given time is as follows: ； At non-triggering time t>t i At that time, based on the last trigger time recorded in the communication data packet. t k j status And its derivative, the first is estimated using linear extrapolation. i The path parameter states of adjacent vehicles of an unmanned aerial vehicle are represented as follows: ； in, Indicates adjacent aircraft j The path parameter of its most recent event trigger time; t k j Indicates adjacent aircraft j Recent event trigger time, j ∈ , For adjacent aircraft groups; Using the first i An unmanned aerial vehicle in t The information contained in the communication data packet at time t defines the total path parameter coordination error of aperiodic communication as follows: ； in, ； in, for t k i The deviation between the cooperative estimation error of adjacent vessels at time and the cooperative estimation error of adjacent vessels at the current time; For the current moment j The actual path parameters of the unmanned aerial vehicle and the first i The ship to the first j The deviation of the path parameters estimated by the unmanned aerial vehicle.

6. The adaptive dynamic event-triggered three-dimensional cooperative control method for air-sea cross-domain unmanned systems according to claim 5, characterized in that, In S5, the specific steps for establishing an error history queue maintenance mechanism and designing an adaptive trigger threshold decay mechanism based on this mechanism include: S51. Establish an error history queue maintenance mechanism: Setting the first i Each unmanned aerial vehicle maintains a first-in-first-out queue. H i , represented as: ； in, K This is the current queue length; L max It is the maximum length of the queue; The update rules for the first-in-first-out queue are designed as follows: 1) When the latest event is triggered, record its error norm as new data, denoted as: ; 2) Check the queue length to update the queue: If the current queue length K L max Then Add to the end of the queue and update the queue length. ; if K > L max , then delete H i The first record in will Add to the end of the queue to make the queue length K Keep as L max ; make ; S52. Calculate the rate of change based on historical data in the queue, and design an adaptive trigger threshold decay mechanism based on the rate of change, including: From queue H i Extract a number of historical data points. The number of historical data points extracted is: , is a positive integer; The average difference, or rate of change, is calculated based on the extracted historical data, using the following formula: ； The design incorporates an adaptive trigger threshold decay mechanism during non-trigger intervals, expressed as follows: ； in, This is the dynamic decay threshold, and ; It is a preset positive threshold used to prevent Decaying indefinitely to zero ensures system stability; Indicates time t Previous threshold parameters; It is based on the rate of change A dynamically adjusted adaptive attenuation factor, and: ； in, The initial attenuation rate, , These are positive tuning coefficients; It is the average historical error difference.

7. The adaptive dynamic event-triggered three-dimensional cooperative control method for air-sea cross-domain unmanned systems according to claim 6, characterized in that, In S6, the specific steps for designing adaptive dynamic event triggering conditions for the air-sea unmanned swarm collaborative control error system based on the total path parameter coordination error and adaptive triggering threshold decay mechanism of the aforementioned aperiodic communication include: Based on the total path parameter cooperative error and the adaptive trigger threshold decay mechanism, an adaptive dynamic event triggering condition is designed as follows: ， in, For dynamic thresholds, ; For the first i The unmanned aerial vehicle at the most recent trigger time The error value stored at that time; Represented as: ； It is a mixed tolerance term of absolute tolerance and relative tolerance, expressed as: in, It is the basic absolute tolerance. ; It is a relative tolerance; It is a constant adjustment parameter. .

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