Distributed Fixed-Time Robust Formation Trajectory Tracking Control Method for Heterogeneous Cluster Systems

Abstract

This invention discloses a distributed fixed-time robust formation trajectory tracking control method for heterogeneous swarm systems, belonging to the field of formation control technology. The method includes the following steps: S1, establishing kinematic and dynamic models of a six-DOF quadrotor UAV and a three-DOF unmanned surface vessel; S2, determining the formation tracking error and velocity tracking error of the air-sea heterogeneous swarm system; S3, generating an error transformation function; S4, determining the fixed-time robust virtual control law and the distributed fixed-time robust controller; S5, determining the distributed fixed-time robust controller under a dynamic time-triggered mechanism; S6, completing the trajectory tracking control. Based on dynamic event triggering, this invention establishes a distributed fixed-time robust H∞ formation control method based on dynamic event triggering, reducing the controller update frequency and saving communication resources.

Description

Technical Field

[0001] This invention belongs to the field of formation control technology, specifically relating to a distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems. Background Technology

[0002] With the booming development of the marine economy and the continuous increase in maritime activities, the demand for tasks such as marine monitoring, resource exploration, and environmental protection is also showing a rapid growth trend. Traditional single-platform systems, limited by functionality and efficiency, often struggle to meet these complex task requirements. Heterogeneous swarm systems have emerged to address this need. These are swarm systems composed of multiple intelligent agents, including robots of various types, shapes, and capabilities. Among them, air-sea heterogeneous swarm systems, especially the formation tracking and control methods of quadcopter UAVs and unmanned surface vessels (USVs), provide innovative solutions for this field. UAVs, with their efficient aerial reconnaissance, surveillance, and strike capabilities, have become important tools in modern warfare and disaster response; while USVs, with their maneuverability and flexibility in the marine environment, play a crucial role in tasks such as marine monitoring, search and rescue, and logistics. Combining these two systems to form air-sea heterogeneous swarm systems not only fully leverages their respective advantages but also enables collaborative operations in more complex tasks and scenarios. Therefore, UAV and USV air-sea heterogeneous swarm systems are widely used in marine environmental protection, traffic management, scientific research, and marine resource exploration, providing important technical means for promoting the development of the marine industry and protecting the marine ecological environment.

[0003] However, research on formation tracking control methods for quadrotor UAVs and unmanned surface vessels (USVs) faces a series of technical challenges. The dynamic and unpredictable nature of the marine environment places high demands on the stability of unmanned systems. Factors such as ocean currents, wind speed, and weather changes can affect the navigation trajectory of USVs, while UAVs in the air need to cope with changes in wind force and airflow. Formation control algorithms must have a certain degree of anti-interference capability to handle these external disturbances. Meanwhile, in many application scenarios such as marine resource exploration, environmental monitoring, or emergency rescue, rapid response and timely execution are crucial for completing marine missions. A configurable, stable time control algorithm can ensure the system's immediacy and time determinism. Furthermore, in the harsh marine environment, improper use of communication resources in heterogeneous air-sea swarm systems of UAVs and USVs can lead to excessive waste, causing serious safety hazards and potentially reducing the system's stability at sea. Therefore, designing a reasonable formation controller to ensure that heterogeneous air-sea systems of quadrotor UAVs and USVs can perform trajectory tracking tasks smoothly and reliably in complex marine environments has significant research value and importance.

[0004] Formation tracking is crucial for ensuring the collaborative operation of heterogeneous swarm systems. Commonly used control algorithms include model predictive control, adaptive control, fuzzy control, and sliding mode control, all of which can guarantee formation within a finite time. However, the convergence time of finite-time control depends on the initial conditions of the system. For heterogeneous air-sea swarm systems of UAVs and unmanned surface vessels (USVs), the requirement for rapid and accurate formation to effectively complete various engineering tasks is particularly stringent. In this context, traditional finite-time control algorithms may not fully meet this requirement due to the uncertainty of their convergence time. Therefore, further exploration and research are needed to develop more efficient and stable control algorithms to ensure that heterogeneous air-sea swarm systems of UAVs and USVs can quickly and accurately achieve formation.

[0005] In the field of multi-agent control systems, techniques such as PID control, sliding mode control, and adaptive control have been widely adopted. PID control is renowned for its low requirements on the system model and reliable performance in various application scenarios. However, its limitations in anti-interference and fast response cannot be ignored, and the parameter tuning process is often cumbersome. Sliding mode control is highly regarded for its excellent fast response and robustness to system parameter fluctuations and external disturbances. However, chattering near the sliding surface can adversely affect the stability and performance of the system. Adaptive control strategies update control parameters in real time to adapt to dynamic changes in the system and external disturbances, but this method requires excessive parameter updates, thus increasing computational complexity.

[0006] In recent years, common approaches to controlling unmanned marine systems facing the uncertainties and complexities of the marine environment have included designing state observers or using various neural networks to approximate the system's behavior, followed by designing control laws to achieve trajectory tracking control and ensure global convergence of errors. However, the effectiveness of observers depends on observation gain; the computational complexity and limited online computing speed of neural networks lead to unavoidable problems such as numerous parameter updates, heavy computational burden potentially causing computational explosion, and the inability to guarantee system convergence within a finite timeframe. Another effective method for addressing external disturbances is H∞ control. H∞ control expresses the performance indicators in the control system design in the form of the H∞ norm. In an H∞ control system, the L2 gain of the closed-loop system is less than or equal to the set value, thus the controller exhibits strong robustness, effectively suppressing disturbances. Furthermore, the computational complexity is simpler than that of the aforementioned observers and neural networks, and the number of parameters requiring adjustment is significantly reduced. Therefore, H∞ control methods have been extensively studied in the field of control.

[0007] Data communication is a crucial component of swarm control in a cluster system, enabling information exchange between nodes. Data communication primarily involves two aspects: data interaction between controllers and actuators, and data interaction between robots. Under time-triggered control mechanisms, the continuous updating of control input signals can increase communication burden, thus affecting the overall system's communication efficiency and stability. In static event-triggered control, however, control input signals are only updated when a trigger condition is met, rather than continuously, thus reducing the controller update frequency and improving the utilization of communication resources. Introducing a dynamic variable into the static event-triggered control mechanism can more flexibly reduce the number of controller communications; this mechanism is called dynamic event-triggered control. When UAVs and unmanned surface vessels (USVs) operate in heterogeneous air-sea swarm systems, they often face harsh marine environments, making communication resources particularly valuable. Event-triggered mechanisms can effectively conserve these resources, thus holding significant importance in marine swarm systems.

[0008] Therefore, based on the above analysis, a distributed fixed-time robust H∞ formation control method based on specified performance and dynamic event triggering is proposed for a class of heterogeneous air-sea systems consisting of quadrotor UAVs and unmanned surface vessels. This method ensures that the tracking error of the system converges within a fixed time and is unaffected by the initial state of the system. The robust H∞ control improves the stability and robustness of the system in complex marine environments, and the combination of dynamic time triggering mechanism enhances the communication efficiency of the system and saves communication resources. Summary of the Invention

[0009] To address the above problems, this invention proposes a distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems.

[0010] The technical solution of this invention is: a distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems, comprising the following steps:

[0011] S1. Establish kinematic and dynamic models of a six-degree-of-freedom quadrotor UAV and a three-degree-of-freedom unmanned surface vessel;

[0012] S2. Based on the kinematic and dynamic models of the six-degree-of-freedom quadcopter UAV and the three-degree-of-freedom unmanned surface vessel, determine the formation tracking error and velocity tracking error of the air-sea heterogeneous swarm system;

[0013] S3. Construct a preset performance function and generate an error transformation function based on the formation tracking error and speed tracking error of the air-sea heterogeneous cluster system;

[0014] S4. Based on the error transformation function, determine the fixed-time robust virtual control law and the distributed fixed-time robust controller;

[0015] S5. Establish a dynamic event triggering mechanism and determine a distributed fixed-time robust controller under the dynamic time triggering mechanism;

[0016] S6. Trajectory tracking control is achieved using a distributed fixed-time robust controller based on a dynamic event triggering mechanism.

[0017] Furthermore, in S1, the expressions for the kinematic and dynamic models of the six-DOF quadcopter UAV are as follows:

[0018] ;

[0019] In the formula, The acceleration representing the roll angle of the drone. The acceleration representing the pitch angle of the drone. The acceleration representing the yaw angle of the drone. The acceleration representing the direction of the drone's movement. This represents the lateral acceleration of the drone. This represents the vertical acceleration of the drone. The velocity representing the drone's pitch angle The speed representing the yaw angle of the drone. The speed representing the roll angle of the drone. Indicates speed in the direction of travel. Indicates the velocity in the lateral direction. J represents the velocity in the vertical direction. xk J represents the first moment of inertia. yk J represents the second moment of inertia. zk J represents the third moment of inertia. rk The moment of inertia of the rotor. d represents the total remaining rotor angle. φk d represents the first aerodynamic damping coefficient. θk d represents the second aerodynamic damping coefficient. ψk The third aerodynamic damping coefficient, d yk The fourth aerodynamic damping coefficient, d zk U represents the fifth aerodynamic damping coefficient. φk Indicates the first controller to be designed, u θk This indicates the second controller to be designed, u ψk This indicates the third controller to be designed, u 1k This indicates the fourth controller to be designed, f φk Indicates the first time-varying unknown ocean disturbance, f θk Indicates the second time-varying unknown ocean disturbance, f kψ Indicates the third time-varying unknown ocean disturbance, f xkIndicates the fourth time-varying unknown ocean disturbance, f yk Indicates the fifth time-varying unknown ocean disturbance, f zk Indicates the sixth time-varying unknown ocean disturbance, η φk Indicates the roll angle, η θk η represents the pitch angle. ψk The yaw angle is represented by g, and the acceleration due to gravity is represented by m. a This indicates the quality of the drone.

[0020] Furthermore, in S1, the expressions for the kinematic and dynamic models of the three-degree-of-freedom unmanned surface vessel are:

[0021] ;

[0022] In the formula, This represents the velocity variable of the unmanned surface vessel in geodetic coordinates. ψ represents the acceleration variable of the unmanned surface vessel in the body coordinate system. sh J represents the yaw angle of the unmanned surface vessel. sh Let v represent the rotation matrix. sh Let u represent the velocity and angular velocity variables of the h-th unmanned surface vessel in the body coordinate system. sh f represents the control input to be designed for the h-th unmanned surface vessel. sh This represents the external disturbance of the h-th unmanned surface vessel. Represents the inertia matrix. Represents the Coriolis matrix as the centripetal matrix. This represents the damping matrix.

[0023] Furthermore, in S2, the formation tracking error includes UAV position loop tracking error, UAV attitude loop tracking error, and unmanned surface vessel tracking error;

[0024] The expression for the tracking error of the kth UAV position loop is:

[0025] ;

[0026] In the formula, e xk,1 e represents the tracking error in the direction of the UAV's movement. yk,1 e represents the tracking error in the lateral direction of the UAV. z,1 The vertical tracking error of the UAV is represented by N1, where N1 represents the number of UAVs in the UAV-USV system, and N2 represents the number of unmanned surface vessels in the UAV-USV system. k,j b represents the communication between the k-th drone and the j-th follower. kl η represents the communication between the k-th drone and the virtual leader. xk η represents the position indicating the direction of the drone's movement. yk η represents the lateral position of the drone.zk η represents the vertical position of the drone. xj η represents the position of the j-th follower in the direction of movement. yj η represents the horizontal position of the j-th follower. zj Let Δd represent the vertical position of the j-th follower. xk Δd represents the relative positional distance between the k-th drone and the virtual leader in their direction of travel. yk Δd represents the lateral relative distance between the k-th drone and the virtual leader. zk Δd represents the vertical relative distance between the k-th drone and the virtual leader. xj Indicates the first relative position between the follower and the virtual leader, Δd yj Δd represents the second relative position between the follower and the virtual leader. zj L represents the third relative position between the follower and the virtual leader. xd L represents the first expected trajectory information of the virtual leader. yd L represents the second expected trajectory information of the virtual leader. zd This represents the third expected trajectory information of the virtual leader, where j represents the follower number in the heterogeneous cluster system; when there is communication between the k-th drone and the j-th follower, a... k,j >0, otherwise a k,j =0, when the k-th drone communicates with the virtual leader, b kl >0, otherwise b kl =0;

[0027] The expression for the tracking error of the kth UAV attitude loop is:

[0028] ;

[0029] In the formula, e φk,1 e represents the tracking error of the UAV's roll angle. θk,1 e represents the tracking error of the UAV's pitch angle. ψk,1 η represents the tracking error of the UAV's yaw angle. φk Indicates the roll angle, η θk η represents the pitch angle. ψk η represents the yaw angle. ψj η represents the yaw angle of the j-th follower. φk.d η represents the desired roll angle of the drone. θk,d Δd represents the desired pitch angle of the UAV. ψk Δd represents the relative distance between the drone and the virtual leader, indicating the yaw angle. ψj L represents the fourth relative position between the follower and the virtual leader. ψdInformation representing the fourth expected trajectory of the virtual leader;

[0030] The expression for the tracking error of the unmanned surface vessel is:

[0031] ;

[0032] In the formula, e xh,1 e represents the tracking error in the forward direction of the unmanned surface vessel. yh,1 e represents the tracking error in the lateral direction of the unmanned surface vessel. ψh,1 The tracking error, a, represents the yaw angle of the UAV. h,j b represents the communication between the h-th drone and the j-th follower. hl η represents the communication between the k-th unmanned surface vessel and the virtual leader. xh η represents the position of the unmanned surface vessel in its direction of travel in geodetic coordinates. yh η represents the lateral position of the unmanned surface vessel in geodetic coordinates. ψh The unmanned surface vessel's yaw angle, Δd, represents its position in geodetic coordinates. xh Δd represents the relative distance between the unmanned surface vessel and the virtual leader in their directions of travel. yh Δd represents the lateral relative distance between the unmanned surface vessel and the virtual leader. ψh η represents the relative distance in the yaw direction between the unmanned surface vessel and the virtual leader. ψj Δd represents the yaw angle position of the j-th follower. ψj Let represent the yaw angle of the j-th follower and the relative distance between it and the virtual leader. a is defined as the distance between the h-th unmanned surface vessel and the j-th follower when there is communication between them. h,j >0, otherwise a h,j =0, when the h-th unmanned surface vessel communicates with the virtual leader, b hl >0, otherwise b hl =0.

[0033] Furthermore, in S2, the expression for the speed tracking error is:

[0034] ;

[0035] In the formula, e pk,2 e represents the velocity error variable of the UAV's position loop. ak,2 e represents the velocity error variable of the UAV attitude loop. sh,2 η represents the speed error variable of the unmanned surface vessel. pk,2 η represents the speed of the drone. ak,2 η represents the angular velocity of the drone. sh,2 α represents the speed of the unmanned surface vessel. pk Let α represent the first virtual control law to be designed. akα represents the second virtual control law that needs to be designed. sh This represents the virtual control law that needs to be designed for the third location.

[0036] Furthermore, in S3, the preset performance function β g The expression for (t) is:

[0037] ;

[0038] In the formula, β g,0 β represents the first-neighborhood parameter of the performance function. g,∞ The second-neighborhood parameter represents the performance function, exp(·) represents the exponential function, and t represents time. Represents the speed parameter of the performance function;

[0039] In S3, the expression for the error transformation function is:

[0040] ;

[0041] In the formula, This represents the position error transformation function for UAVs and unmanned surface vessels. The velocity error transformation function for UAVs and unmanned surface vessels, e g,1 e represents the positional error of drones and unmanned surface vessels. g,2 β represents the speed error of drones and unmanned surface vessels. g This represents the preset performance function, g represents the UAV position loop and attitude loop and the UAV position, pk represents the UAV position loop, ak represents the UAV attitude loop, and sh represents the UAV position.

[0042] Furthermore, in S4, the expression for the robust virtual control law is:

[0043] ;

[0044] In the formula, α pk Let α represent the virtual control law of the designed UAV position loop. ak Let α represent the virtual control law of the designed UAV attitude loop. sh e represents the virtual control law of the designed unmanned surface vessel. pk,1 e represents the position error of the UAV's position loop. ak,1 e represents the position error of the UAV attitude loop. sh,1 Λ represents the positional error of the unmanned surface vessel. pk The communication parameters representing the UAV's position loop, Λ ak The communication parameters representing the attitude loop of the UAV, Λ sh λ represents the communication parameters of the unmanned surface vessel. pk,1λ represents the first fixed-time gain parameter of the virtual control law of the UAV position loop. pk,2 λ represents the second fixed-time gain parameter of the virtual control law of the UAV position loop. ak,1 λ represents the first fixed-time gain parameter of the virtual control law of the UAV attitude loop. ak,2 λ represents the second fixed-time gain parameter of the virtual control law of the UAV attitude loop. sh,1 λ represents the first fixed-time gain parameter of the virtual control law of the unmanned surface vessel. sh,2 χ represents the second fixed-time gain parameter of the virtual control law of the unmanned surface vessel. pk,1 χ represents the time-varying coefficient of the position error transformation function of the UAV position loop. ak,1 χ represents the time-varying coefficient of the position error transformation function of the UAV attitude loop. sh,1 Ф represents the time-varying coefficient of the position error transformation function of the unmanned surface vessel. pk,1 Ф represents the position error transformation function vector of the UAV position loop. ak,1 Ф represents the position error transformation function vector of the UAV attitude loop. sh,1 κ represents the position error transformation function vector of the unmanned surface vessel. pk,1 κ represents the bias of the position error transformation function of the UAV position loop. ak,1 κ represents the bias of the position error transformation function of the UAV attitude loop. sh,1 Ξ represents the offset of the position error transformation function of the unmanned surface vessel. pk Ξ represents the position loop velocity error variable of the UAV. ak Ξ represents the attitude loop velocity error variable of the UAV. sh ∂ represents the speed error variable of the unmanned surface vessel. pk,1 The parameters representing the robust H∞ virtual control law for the UAV's position loop are ∂ ak,1 The parameters representing the robust virtual control law H∞ for the attitude loop of the UAV, ∂ sh,1 The parameters represent the robust H∞ virtual control law of the unmanned surface vessel, where σ represents the parameter of the first fixed-time exponential term. This represents the parameter of the second fixed-time exponent.

[0045] Furthermore, in S4, the expression for the distributed fixed-time robust controller is:

[0046] ;

[0047] In the formula, u pk This represents the distributed fixed-time robust H∞ controller for the designed UAV position loop, u ak This represents the distributed fixed-time robust H∞ controller for the designed UAV attitude loop, u sh This represents the designed distributed fixed-time robust H∞ controller for the unmanned surface vessel, epk,2 e represents the velocity error of the UAV's position loop. ak,2 e represents the velocity error of the UAV attitude loop. sh,2 Λ represents the speed error of the unmanned surface vessel. pk The communication parameters representing the UAV's position loop, Λ ak The communication parameters representing the attitude loop of the UAV, Λ sh λ represents the communication parameters of the unmanned surface vessel. pk,3 λ represents the first fixed-time gain parameter of the UAV position loop fixed-time robust H∞ controller. pk,4 λ represents the second fixed-time gain parameter of the UAV position loop fixed-time robust H∞ controller. ak,3 λ represents the first fixed-time gain parameter of the UAV attitude loop fixed-time robust H∞ controller. ak,4 λ represents the second fixed-time gain parameter of the UAV attitude loop fixed-time robust H∞ controller. sh,3 λ represents the first fixed-time gain parameter of the unmanned surface vessel's fixed-time robust H∞ controller. sh,4 χ represents the second fixed-time gain parameter of the unmanned surface vessel's fixed-time robust H∞ controller. pk,2 χ represents the time-varying coefficient of the velocity error transformation function of the UAV position loop. ak,2 χ represents the time-varying coefficient of the velocity error transformation function of the UAV attitude loop. sh,2 The time-varying coefficients, Ф, represent the velocity error transformation function of the unmanned surface vessel. pk,2 The vector representing the velocity error transformation function of the UAV's position loop, Ф ak,2 Ф represents the velocity error transformation function vector of the UAV attitude loop. sh,2 κ represents the velocity error transformation function vector of the unmanned surface vessel. pk,2 κ represents the bias of the velocity error transformation function in the UAV position loop. ak,2 κ represents the bias of the velocity error transformation function in the UAV attitude loop. sh,2 This indicates the bias of the speed error transformation function for the unmanned surface vessel. The derivative of the virtual control law for the UAV's position loop is given. The derivative of the virtual control law of the UAV attitude loop is given. Let A represent the derivative of the virtual control law of the unmanned surface vessel (USV), and let B represent the first model parameter of the USV and the second model parameter of the USV. This represents the first model parameter of the unmanned surface vessel. This represents the second model parameter of the unmanned surface vessel. This represents the third model parameter of the unmanned surface vessel. The velocity variable represents the position loop of the drone. The velocity variable represents the attitude loop of the drone. ∂ represents the velocity variable of the unmanned surface vessel in the geodetic coordinate system. pk,2 The first parameter, ∂, represents the fixed-time robust H∞ controller of the UAV position loop. ak,2 The first parameter, ∂, represents the fixed-time robust H∞ controller of the UAV attitude loop. sh,2 This represents the first parameter of the fixed-time robust H∞ controller for the unmanned surface vessel. The second parameter represents the fixed-time robust H∞ controller of the UAV position loop. The second parameter represents the fixed-time robust H∞ controller of the UAV attitude loop. The second parameter represents the fixed-time robust H∞ controller of the UAV position loop, and σ represents the first fixed-time exponential term parameter. This represents the parameter of the second fixed-time exponent.

[0048] Furthermore, in S5, the expression for the dynamic event triggering mechanism is:

[0049] ;

[0050] In the formula, u Eg (t) represents the controller that updates the event-triggered mechanism, g represents the UAV's position loop and attitude loop, and the UAV's position, and t represents time. Represents the control function, t k Indicates the time when the controller updates, t k+1 Let R represent the next moment after the event triggers the update, and let z represent the set of real numbers. g (t) represents the error of the event-triggered controller. Represents a time-varying function, o g The parameter that indicates when the event was triggered.

[0051] Furthermore, in S5, the expression for the distributed fixed-time robust grouping controller under the dynamic event triggering mechanism is:

[0052] ;

[0053] In the formula, This refers to the controller designed under the UAV position loop event triggering mechanism. This refers to the controller designed under the UAV attitude loop event triggering mechanism. This represents the controller designed under the unmanned surface vessel's event-triggered mechanism, where I3 represents a three-dimensional unit vector. This indicates the parameters that trigger the first event in the drone's position loop. This indicates the parameters that trigger the first event in the UAV attitude loop. This indicates the parameters that trigger the first event for the unmanned surface vessel. This indicates the parameters that trigger the second event in the drone's position loop. This indicates the parameters that trigger the second event in the UAV attitude loop. The parameter e represents the trigger condition for the second event of the unmanned surface vessel. pk,2 e represents the velocity tracking error of the UAV's position loop. ak,2 e represents the velocity tracking error of the UAV attitude loop. sh,2 χ represents the speed tracking error of the unmanned surface vessel. pk,2 χ represents the time-varying parameter of the velocity error transformation function of the UAV position loop. ak,2 χ represents the time-varying parameter of the velocity error transformation function of the UAV attitude loop. sh,2 The time-varying parameter u represents the velocity error transformation function of the unmanned surface vessel. pk This represents the distributed fixed-time robust H∞ controller for the designed UAV position loop, u ak This represents the distributed fixed-time robust H∞ controller for the designed UAV attitude loop, u sh This represents the distributed fixed-time robust H∞ controller of the designed unmanned surface vessel, q pk The parameter q represents the event triggering of the drone's position loop. ak The parameter q represents the event triggering of the drone's attitude loop. sh The parameter J represents the event triggering parameter for the unmanned surface vessel. sh Let M represent the rotation matrix. sh The parameters represent the model parameters of the unmanned surface vessel (USV), where A represents the first model parameter of the USV and B represents the second model parameter of the USV.

[0054] The beneficial effects of this invention are:

[0055] (1) The present invention limits the formation tracking error of the air-sea heterogeneous cluster system based on the functional characteristics of the performance function, and simultaneously constrains the speed tracking error. Compared with the method that only constrains the position error, the distributed time-varying constrained formation controller designed in this invention has better control performance.

[0056] (2) This invention targets a heterogeneous air-sea cluster system of UAVs and unmanned surface vessels with external interference. By using a fixed-time robust H∞ formation control method, the system can be guaranteed to converge within a fixed time and is independent of the initial state of the system, thereby improving the stability and robustness of the system.

[0057] (3) Based on dynamic time triggering, this invention determines a distributed fixed-time robust H∞ formation control method based on dynamic event triggering, which reduces the update frequency of the controller and saves communication resources. Attached Figure Description

[0058] Figure 1 A flowchart of a distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems;

[0059] Figure 2 Communication topology diagram of a heterogeneous air-sea cluster system for UAVs and unmanned surface vessels;

[0060] Figure 3 A 3D tracking diagram of an air-sea heterogeneous cluster system;

[0061] Figure 4 A two-dimensional tracking diagram of an air-sea heterogeneous cluster system;

[0062] Figure 5 Error diagram of unmanned surface vessels in an air-sea heterogeneous swarm system;

[0063] Figure 6 Error diagram of UAVs in air-sea heterogeneous swarm system;

[0064] Figure 7 The control input diagram for a drone and unmanned surface vessel swarm system;

[0065] Figure 8 The control input diagram for a drone and unmanned surface vessel swarm system;

[0066] Figure 9 This is a dynamic event triggering diagram for drone 1 and drone 2;

[0067] Figure 10 The dynamic event triggering diagram for unmanned surface vessel 1 and unmanned surface vessel 2;

[0068] Figure 11 This is a dynamic event triggering diagram for unmanned surface vessel 3 and unmanned surface vessel 4. Detailed Implementation

[0069] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0070] like Figure 1 As shown, this invention provides a distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems, comprising the following steps:

[0071] S1. Establish kinematic and dynamic models of a six-degree-of-freedom quadrotor UAV and a three-degree-of-freedom unmanned surface vessel;

[0072] S2. Based on the kinematic and dynamic models of the six-degree-of-freedom quadcopter UAV and the three-degree-of-freedom unmanned surface vessel, determine the formation tracking error and velocity tracking error of the air-sea heterogeneous swarm system;

[0073] S3. Construct a preset performance function and generate an error transformation function based on the formation tracking error and speed tracking error of the air-sea heterogeneous cluster system;

[0074] S4. Based on the error transformation function, determine the fixed-time robust virtual control law and the distributed fixed-time robust controller;

[0075] S5. Establish a dynamic event triggering mechanism and determine a distributed fixed-time robust controller under the dynamic time triggering mechanism;

[0076] S6. Trajectory tracking control is achieved using a distributed fixed-time robust controller based on a dynamic event triggering mechanism.

[0077] In this embodiment of the invention, in S1, the expressions for the kinematic and dynamic models of the six-degree-of-freedom quadcopter UAV are as follows:

[0078] ;

[0079] In the formula, The acceleration representing the roll angle of the drone. The acceleration representing the pitch angle of the drone. The acceleration representing the yaw angle of the drone. The acceleration representing the direction of the drone's movement. This represents the lateral acceleration of the drone. This represents the vertical acceleration of the drone. The velocity representing the drone's pitch angle The speed representing the yaw angle of the drone. The speed representing the roll angle of the drone. Indicates speed in the direction of travel. Indicates the velocity in the lateral direction. Represents the velocity in the vertical direction. J xk Represents the first moment of inertia. J yk Indicates the second moment of inertia. J zk J represents the third moment of inertia. rk The moment of inertia of the rotor. d represents the total remaining rotor angle. φk d represents the first aerodynamic damping coefficient. θk d represents the second aerodynamic damping coefficient. ψk The third aerodynamic damping coefficient, d yk The fourth aerodynamic damping coefficient, d zk U represents the fifth aerodynamic damping coefficient. φk Indicates the first controller to be designed, u θk This indicates the second controller to be designed, u ψk This indicates the third controller to be designed, u 1k This indicates the fourth controller to be designed, f φk Indicates the first time-varying unknown ocean disturbance, f θk Indicates the second time-varying unknown ocean disturbance, f kψ Indicates the third time-varying unknown ocean disturbance, fxk Indicates the fourth time-varying unknown ocean disturbance, f yk Indicates the fifth time-varying unknown ocean disturbance, f zk Indicates the sixth time-varying unknown ocean disturbance, η φk Indicates the roll angle, η θk η represents the pitch angle. ψk The yaw angle is represented by g, and the acceleration due to gravity is represented by m. a This indicates the quality of the drone.

[0080] In this embodiment of the invention, in S1, the expressions for the kinematic and dynamic models of the three-degree-of-freedom unmanned surface vessel are as follows:

[0081] ;

[0082] In the formula, This represents the velocity variable of the unmanned surface vessel in geodetic coordinates. ψ represents the acceleration variable of the unmanned surface vessel in the body coordinate system. sh J represents the yaw angle of the unmanned surface vessel. sh Let v represent the rotation matrix. sh Let u represent the velocity and angular velocity variables of the h-th unmanned surface vessel in the body coordinate system. sh f represents the control input to be designed for the h-th unmanned surface vessel. sh This represents the external disturbance of the h-th unmanned surface vessel. Represents the inertia matrix. Represents the Coriolis matrix as the centripetal matrix. This represents the damping matrix.

[0083] In this embodiment of the invention, in S2, the formation tracking error includes UAV position loop tracking error, UAV attitude loop tracking error, and unmanned surface vessel tracking error;

[0084] The expression for the tracking error of the kth UAV position loop is:

[0085] ;

[0086] In the formula, e xk,1 e represents the tracking error in the direction of the UAV's movement. yk,1 e represents the tracking error in the lateral direction of the UAV. z,1 The vertical tracking error of the UAV is represented by N1, where N1 represents the number of UAVs in the UAV-USV system, and N2 represents the number of unmanned surface vessels in the UAV-USV system. k,j b represents the communication between the k-th drone and the j-th follower. kl η represents the communication between the k-th drone and the virtual leader. xk η represents the position indicating the direction of the drone's movement. ykη represents the lateral position of the drone. zk η represents the vertical position of the drone. xj η represents the position of the j-th follower in the direction of movement. yj η represents the horizontal position of the j-th follower. zj Let Δd represent the vertical position of the j-th follower. xk Δd represents the relative positional distance between the k-th drone and the virtual leader in their direction of travel. yk Δd represents the lateral relative distance between the k-th drone and the virtual leader. zk Δd represents the vertical relative distance between the k-th drone and the virtual leader. xj Indicates the first relative position between the follower and the virtual leader, Δd yj Δd represents the second relative position between the follower and the virtual leader. zj L represents the third relative position between the follower and the virtual leader. xd L represents the first expected trajectory information of the virtual leader. yd L represents the second expected trajectory information of the virtual leader. zd This represents the third expected trajectory information of the virtual leader, where j represents the follower number in the heterogeneous cluster system; when there is communication between the k-th drone and the j-th follower, a... k,j >0, otherwise a k,j =0, when the k-th drone communicates with the virtual leader, b kl >0, otherwise b kl =0;

[0087] The expression for the tracking error of the kth UAV attitude loop is:

[0088] ;

[0089] In the formula, e φk,1 e represents the tracking error of the UAV's roll angle. θk,1 e represents the tracking error of the UAV's pitch angle. ψk,1 η represents the tracking error of the UAV's yaw angle. φk Indicates the roll angle, η θk η represents the pitch angle. ψk η represents the yaw angle. ψj η represents the yaw angle of the j-th follower. φk.d η represents the desired roll angle of the drone. θk,d Δd represents the desired pitch angle of the UAV. ψk Δd represents the relative distance between the drone and the virtual leader, indicating the yaw angle. ψj L represents the fourth relative position between the follower and the virtual leader.ψd Information representing the fourth expected trajectory of the virtual leader;

[0090] The expression for the tracking error of the unmanned surface vessel is:

[0091] ;

[0092] In the formula, e xh,1 e represents the tracking error in the forward direction of the unmanned surface vessel. yh,1 e represents the tracking error in the lateral direction of the unmanned surface vessel. ψh,1 The tracking error, a, represents the yaw angle of the UAV. h,j b represents the communication between the h-th drone and the j-th follower. hl η represents the communication between the k-th unmanned surface vessel and the virtual leader. xh η represents the position of the unmanned surface vessel in its direction of travel in geodetic coordinates. yh η represents the lateral position of the unmanned surface vessel in geodetic coordinates. ψh The unmanned surface vessel's yaw angle, Δd, represents its position in geodetic coordinates. xh Δd represents the relative distance between the unmanned surface vessel and the virtual leader in their directions of travel. yh Δd represents the lateral relative distance between the unmanned surface vessel and the virtual leader. ψh η represents the relative distance in the yaw direction between the unmanned surface vessel and the virtual leader. ψj Δd represents the yaw angle position of the j-th follower. ψj Let represent the yaw angle of the j-th follower and the relative distance between it and the virtual leader. a is defined as the distance between the h-th unmanned surface vessel and the j-th follower when there is communication between them. h,j >0, otherwise a h,j =0, when the h-th unmanned surface vessel communicates with the virtual leader, b hl >0, otherwise b hl =0.

[0093] In this embodiment of the invention, in S2, the expression for the speed tracking error is:

[0094] ;

[0095] In the formula, e pk,2 e represents the velocity error variable of the UAV's position loop. ak,2 e represents the velocity error variable of the UAV attitude loop. sh,2 η represents the speed error variable of the unmanned surface vessel. pk,2 η represents the speed of the drone. ak,2 η represents the angular velocity of the drone. sh,2 α represents the speed of the unmanned surface vessel. pk Let α represent the first virtual control law to be designed.ak α represents the second virtual control law that needs to be designed. sh This represents the virtual control law that needs to be designed in the third location. In S3, the preset performance function β... g The expression for (t) is:

[0096] ;

[0097] In the formula, β g,0 β represents the first-neighborhood parameter of the performance function. g,∞ The second-neighborhood parameter represents the performance function, exp(·) represents the exponential function, and t represents time. Represents the speed parameter of the performance function;

[0098] In S3, the expression for the error transformation function is:

[0099] ;

[0100] In the formula, This represents the position error transformation function for UAVs and unmanned surface vessels. The velocity error transformation function for UAVs and unmanned surface vessels, e g,1 e represents the positional error of drones and unmanned surface vessels. g,2 β represents the speed error of drones and unmanned surface vessels. g This represents the preset performance function, g represents the UAV position loop and attitude loop and the UAV position, pk represents the UAV position loop, ak represents the UAV attitude loop, and sh represents the UAV position.

[0101] In this embodiment of the invention, in S4, the expression of the robust virtual control law is:

[0102] ;

[0103] In the formula, α pk Let α represent the virtual control law of the designed UAV position loop. ak Let α represent the virtual control law of the designed UAV attitude loop. sh e represents the virtual control law of the designed unmanned surface vessel. pk,1 e represents the position error of the UAV's position loop. ak,1 e represents the position error of the UAV attitude loop. sh,1 Λ represents the positional error of the unmanned surface vessel. pk The communication parameters representing the UAV's position loop, Λ ak The communication parameters representing the attitude loop of the UAV, Λ sh λ represents the communication parameters of the unmanned surface vessel. pk,1 λ represents the first fixed-time gain parameter of the virtual control law of the UAV position loop. pk,2λ represents the second fixed-time gain parameter of the virtual control law of the UAV position loop. ak,1 λ represents the first fixed-time gain parameter of the virtual control law of the UAV attitude loop. ak,2 λ represents the second fixed-time gain parameter of the virtual control law of the UAV attitude loop. sh,1 λ represents the first fixed-time gain parameter of the virtual control law of the unmanned surface vessel. sh,2 χ represents the second fixed-time gain parameter of the virtual control law of the unmanned surface vessel. pk,1 χ represents the time-varying coefficient of the position error transformation function of the UAV position loop. ak,1 χ represents the time-varying coefficient of the position error transformation function of the UAV attitude loop. sh,1 Ф represents the time-varying coefficient of the position error transformation function of the unmanned surface vessel. pk,1 Ф represents the position error transformation function vector of the UAV position loop. ak,1 Ф represents the position error transformation function vector of the UAV attitude loop. sh,1 κ represents the position error transformation function vector of the unmanned surface vessel. pk,1 κ represents the bias of the position error transformation function of the UAV position loop. ak,1 κ represents the bias of the position error transformation function of the UAV attitude loop. sh,1 Ξ represents the offset of the position error transformation function of the unmanned surface vessel. pk Ξ represents the position loop velocity error variable of the UAV. ak Ξ represents the attitude loop velocity error variable of the UAV. sh ∂ represents the speed error variable of the unmanned surface vessel. pk,1 The parameters representing the robust H∞ virtual control law for the UAV's position loop are ∂ ak,1 The parameters representing the robust virtual control law H∞ for the attitude loop of the UAV, ∂ sh,1 The parameters represent the robust H∞ virtual control law of the unmanned surface vessel, where σ represents the parameter of the first fixed-time exponential term. This represents the parameter of the second fixed-time exponent.

[0104] In this embodiment of the invention, in S4, the expression for the distributed fixed-time robust controller is:

[0105] ;

[0106] In the formula, u pk This represents the distributed fixed-time robust H∞ controller for the designed UAV position loop, u ak This represents the distributed fixed-time robust H∞ controller for the designed UAV attitude loop, u sh This represents the designed distributed fixed-time robust H∞ controller for the unmanned surface vessel, e pk,2 e represents the velocity error of the UAV's position loop. ak,2e represents the velocity error of the UAV attitude loop. sh,2 Λ represents the speed error of the unmanned surface vessel. pk The communication parameters representing the UAV's position loop, Λ ak The communication parameters representing the attitude loop of the UAV, Λ sh λ represents the communication parameters of the unmanned surface vessel. pk,3 λ represents the first fixed-time gain parameter of the UAV position loop fixed-time robust H∞ controller. pk,4 λ represents the second fixed-time gain parameter of the UAV position loop fixed-time robust H∞ controller. ak,3 λ represents the first fixed-time gain parameter of the UAV attitude loop fixed-time robust H∞ controller. ak,4 λ represents the second fixed-time gain parameter of the UAV attitude loop fixed-time robust H∞ controller. sh,3 λ represents the first fixed-time gain parameter of the unmanned surface vessel's fixed-time robust H∞ controller. sh,4 χ represents the second fixed-time gain parameter of the unmanned surface vessel's fixed-time robust H∞ controller. pk,2 χ represents the time-varying coefficient of the velocity error transformation function of the UAV position loop. ak,2 χ represents the time-varying coefficient of the velocity error transformation function of the UAV attitude loop. sh,2 The time-varying coefficients, Ф, represent the velocity error transformation function of the unmanned surface vessel. pk,2 The vector representing the velocity error transformation function of the UAV's position loop, Ф ak,2 Ф represents the velocity error transformation function vector of the UAV attitude loop. sh,2 κ represents the velocity error transformation function vector of the unmanned surface vessel. pk,2 κ represents the bias of the velocity error transformation function in the UAV position loop. ak,2 κ represents the bias of the velocity error transformation function in the UAV attitude loop. sh,2 This indicates the bias of the speed error transformation function for the unmanned surface vessel. The derivative of the virtual control law for the UAV's position loop is given. The derivative of the virtual control law of the UAV attitude loop is given. Let A represent the derivative of the virtual control law of the unmanned surface vessel (USV), and let B represent the first model parameter of the USV and the second model parameter of the USV. This represents the first model parameter of the unmanned surface vessel. This represents the second model parameter of the unmanned surface vessel. This represents the third model parameter of the unmanned surface vessel. The velocity variable represents the position loop of the drone. The velocity variable represents the attitude loop of the drone. ∂ represents the velocity variable of the unmanned surface vessel in the geodetic coordinate system. pk,2The first parameter, ∂, represents the fixed-time robust H∞ controller of the UAV position loop. ak,2 The first parameter, ∂, represents the fixed-time robust H∞ controller of the UAV attitude loop. sh,2 This represents the first parameter of the fixed-time robust H∞ controller for the unmanned surface vessel. The second parameter represents the fixed-time robust H∞ controller of the UAV position loop. The second parameter represents the fixed-time robust H∞ controller of the UAV attitude loop. The second parameter represents the fixed-time robust H∞ controller of the UAV position loop, and σ represents the first fixed-time exponential term parameter. This represents the parameter of the second fixed-time exponent.

[0107] In this embodiment of the invention, in S5, the expression for the dynamic event triggering mechanism is:

[0108] ;

[0109] In the formula, u Eg (t) represents the controller that updates the event-triggered mechanism, g represents the UAV's position loop and attitude loop, and the UAV's position, and t represents time. Represents the control function, t k Indicates the time when the controller updates, t k+1 Let R represent the next moment after the event triggers the update, and let z represent the set of real numbers. g (t) represents the error of the event-triggered controller. Represents a time-varying function, o g The parameter that indicates when the event was triggered.

[0110] In this embodiment of the invention, in S5, the expression for the distributed fixed-time robust array controller under the dynamic event triggering mechanism is:

[0111] ;

[0112] In the formula, This refers to the controller designed under the UAV position loop event triggering mechanism. This refers to the controller designed under the UAV attitude loop event triggering mechanism. This represents the controller designed under the unmanned surface vessel's event-triggered mechanism, where I3 represents a three-dimensional unit vector. This indicates the parameters that trigger the first event in the drone's position loop. This indicates the parameters that trigger the first event in the UAV attitude loop. This indicates the parameters that trigger unmanned surface vessel (USV) events. This indicates the parameters that trigger the second event in the drone's position loop. This indicates the parameters that trigger the second event in the UAV attitude loop. The parameter e represents the trigger condition for the second event of the unmanned surface vessel. pk,2 e represents the velocity tracking error of the UAV's position loop. ak,2 e represents the velocity tracking error of the UAV attitude loop. sh,2 χ represents the speed tracking error of the unmanned surface vessel. pk,2 χ represents the time-varying parameter of the velocity error transformation function of the UAV position loop. ak,2 χ represents the time-varying parameter of the velocity error transformation function of the UAV attitude loop. sh,2 The time-varying parameter u represents the velocity error transformation function of the unmanned surface vessel. pk This represents the distributed fixed-time robust H∞ controller for the designed UAV position loop, u ak This represents the distributed fixed-time robust H∞ controller for the designed UAV attitude loop, u sh This represents the distributed fixed-time robust H∞ controller of the designed unmanned surface vessel, q pk The parameter q represents the event triggering of the drone's position loop. ak The parameter q represents the event triggering of the drone's attitude loop. sh The parameter J represents the event triggering parameter for the unmanned surface vessel. sh Let M represent the rotation matrix. sh The parameters represent the model parameters of the unmanned surface vessel (USV), where A represents the first model parameter of the USV and B represents the second model parameter of the USV.

[0113] To verify the effectiveness of the method of the present invention, a simulation experiment was conducted, as detailed below.

[0114] Simulation experiments were conducted using a heterogeneous air-sea swarm system of UAVs and unmanned surface vessels to verify the designed distributed fixed-time robust H-type system based on dynamic event triggering. ∞ The effectiveness of the formation control method. System parameters are shown in Table 1, and controller parameters are shown in Table 2.

[0115] Table 1

[0116]

[0117] Table 2

[0118]

[0119] The selected drone and unmanned surface vessel (USV) swarm system includes a virtual leader, two drones, and four USVs, with the relative quantities of the drone attitude subsystem being: The relative position vectors of the UAV and unmanned surface vessel (USV) heterogeneous air-sea swarm system can be selected as follows: The relative position vector of the UAV is: and The relative position vector of the unmanned surface vessel is: , , , The simulation results are as follows: Figure 2-11 As shown, where, Figure 2 This is a communication topology diagram of the UAV-USV system. Number 0 represents the virtual leader, numbers 1 and 2 represent drones, and numbers 3-6 represent unmanned surface vessels. Figure 3 This represents a three-dimensional trajectory diagram of the UAV-USV system. Figure 4 This represents a two-dimensional trajectory diagram of the UAV-USV system. Figure 5 The graph shows the results of the position and velocity tracking errors of the four unmanned surface vessels. Figure 6 This represents the position and velocity tracking error results for the position loop and attitude loop of the two UAVs. Figure 7 and Figure 8 This indicates the control inputs for unmanned surface vessels and drones. Figure 9 , Figure 10 and Figure 11 This represents the time interval for triggering events on drones and unmanned surface vessels. It demonstrates the distributed fixed-time robust H-type design. ∞ The formation controller can complete three-dimensional formation tracking and control of a heterogeneous air-sea swarm system of UAVs and unmanned surface vessels within a fixed time period, exhibiting good robustness, fast convergence speed, and independence from initial states. The designed distributed fixed-time robust H-type controller is based on dynamic event triggering. ∞ Formation control methods can effectively reduce the update frequency of the controller and save communication resources.

[0120] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems, characterized in that, Includes the following steps: S1. Establish kinematic and dynamic models of a six-degree-of-freedom quadrotor UAV and a three-degree-of-freedom unmanned surface vessel; S2. Based on the kinematic and dynamic models of the six-degree-of-freedom quadcopter UAV and the three-degree-of-freedom unmanned surface vessel, determine the formation tracking error and velocity tracking error of the air-sea heterogeneous swarm system; S3. Construct a preset performance function and generate an error transformation function based on the formation tracking error and speed tracking error of the air-sea heterogeneous cluster system; S4. Based on the error transformation function, determine the fixed-time robust virtual control law and the distributed fixed-time robust controller; S5. Establish a dynamic event triggering mechanism and determine a distributed fixed-time robust controller under the dynamic time triggering mechanism; S6. Trajectory tracking control is achieved using a distributed fixed-time robust controller based on a dynamic event triggering mechanism.

2. The distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems according to claim 1, characterized in that, In S1, the kinematic and dynamic model of the six-degree-of-freedom quadcopter UAV is expressed as follows: ； In the formula, The acceleration representing the roll angle of the drone. The acceleration representing the pitch angle of the drone. The acceleration representing the yaw angle of the drone. The acceleration representing the direction of the drone's movement. This represents the lateral acceleration of the drone. This represents the vertical acceleration of the drone. The velocity representing the drone's pitch angle The speed representing the yaw angle of the drone. The speed representing the drone's roll angle. Indicates speed in the direction of travel. Indicates the velocity in the lateral direction. J represents the velocity in the vertical direction. xk J represents the first moment of inertia. yk J represents the second moment of inertia. zk J represents the third moment of inertia. rk The moment of inertia of the rotor. d represents the total remaining rotor angle. φk d represents the first aerodynamic damping coefficient. θk d represents the second aerodynamic damping coefficient. ψk d represents the third aerodynamic damping coefficient. yk The fourth aerodynamic damping coefficient, d zk U represents the fifth aerodynamic damping coefficient. φk This represents the first controller to be designed, u θk This indicates the second controller to be designed, u ψk This indicates the third controller to be designed, u 1k This indicates the fourth controller to be designed, f φk Indicates the first time-varying unknown ocean disturbance, f θk Indicates the second time-varying unknown ocean disturbance, f kψ Indicates the third time-varying unknown ocean disturbance, f xk Indicates the fourth time-varying unknown ocean disturbance, f yk Indicates the fifth time-varying unknown ocean disturbance, f zk Indicates the sixth time-varying unknown ocean disturbance, η φk Indicates the roll angle, η θk η represents the pitch angle. ψk The yaw angle is represented by g, and the acceleration due to gravity is represented by m. a This indicates the quality of the drone.

3. The distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems according to claim 1, characterized in that, In S1, the kinematic and dynamic model of the three-degree-of-freedom unmanned surface vessel is expressed as follows: ； In the formula, This represents the velocity variable of the unmanned surface vessel in geodetic coordinates. ψ represents the acceleration variable of the unmanned surface vessel in the body coordinate system. sh J represents the yaw angle of the unmanned surface vessel. sh Let v represent the rotation matrix. sh Let u represent the velocity and angular velocity variables of the h-th unmanned surface vessel in the body coordinate system. sh f represents the control input to be designed for the h-th unmanned surface vessel. sh This represents the external disturbance of the h-th unmanned surface vessel. Represents the inertia matrix. Represents the Coriolis matrix as the centripetal matrix. This represents the damping matrix.

4. The distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems according to claim 1, characterized in that, In S2, the formation tracking error includes UAV position loop tracking error, UAV attitude loop tracking error and unmanned surface vessel tracking error; The expression for the tracking error of the kth UAV position loop is: ； In the formula, e xk,1 e represents the tracking error in the direction of the UAV's movement. yk,1 e represents the tracking error in the lateral direction of the UAV. z,1 The vertical tracking error of the UAV is represented by N1, where N1 represents the number of UAVs in the UAV-USV system, and N2 represents the number of unmanned surface vessels in the UAV-USV system. k,j b represents the communication between the k-th drone and the j-th follower. kl η represents the communication between the k-th drone and the virtual leader. xk η represents the position indicating the direction of the drone's movement. yk η represents the lateral position of the drone. zk η represents the vertical position of the drone. xj η represents the position of the j-th follower in the direction of movement. yj η represents the horizontal position of the j-th follower. zj Let Δd represent the vertical position of the j-th follower. xk Δd represents the relative positional distance between the k-th drone and the virtual leader in their direction of travel. yk Δd represents the lateral relative distance between the k-th drone and the virtual leader. zk Δd represents the vertical relative distance between the k-th drone and the virtual leader. xj Indicates the first relative position between the follower and the virtual leader, Δd yj Δd represents the second relative position between the follower and the virtual leader. zj L represents the third relative position between the follower and the virtual leader. xd L represents the first expected trajectory information of the virtual leader. yd L represents the second expected trajectory information of the virtual leader. zd The third expected trajectory information of the virtual leader is represented, and j represents the follower number in the heterogeneous cluster system; The expression for the tracking error of the kth UAV attitude loop is: ； In the formula, e φk,1 e represents the tracking error of the UAV's roll angle. θk,1 e represents the tracking error of the UAV's pitch angle. ψk,1 η represents the tracking error of the UAV's yaw angle. φk Indicates the roll angle, η θk η represents the pitch angle. ψk η represents the yaw angle. ψj η represents the yaw angle of the j-th follower. φk.d η represents the desired roll angle of the drone. θk,d Δd represents the desired pitch angle of the UAV. ψk Δd represents the relative distance between the drone and the virtual leader, indicating the yaw angle. ψj L represents the fourth relative position between the follower and the virtual leader. ψd Information representing the fourth expected trajectory of the virtual leader; The expression for the tracking error of the unmanned surface vessel is: ； In the formula, e xh,1 e represents the tracking error in the forward direction of the unmanned surface vessel. yh,1 e represents the tracking error in the lateral direction of the unmanned surface vessel. ψh,1 The tracking error, a, represents the yaw angle of the UAV. h,j b represents the communication between the h-th drone and the j-th follower. hl η represents the communication between the k-th unmanned surface vessel and the virtual leader. xh η represents the position of the unmanned surface vessel in its direction of travel in geodetic coordinates. yh η represents the lateral position of the unmanned surface vessel in geodetic coordinates. ψh The unmanned surface vessel's yaw angle, Δd, represents its position in geodetic coordinates. xh Δd represents the relative distance between the unmanned surface vessel and the virtual leader in their directions of travel. yh Δd represents the lateral relative distance between the unmanned surface vessel and the virtual leader. ψh η represents the relative distance in the yaw direction between the unmanned surface vessel and the virtual leader. ψj Δd represents the yaw angle position of the j-th follower. ψj This represents the yaw angle of the j-th follower and the relative distance between it and the virtual leader.

5. The distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems according to claim 1, characterized in that, In S2, the expression for the speed tracking error is: ； In the formula, e pk,2 e represents the velocity error variable of the UAV's position loop. ak,2 e represents the velocity error variable of the UAV attitude loop. sh,2 η represents the speed error variable of the unmanned surface vessel. pk,2 η represents the speed of the drone. ak,2 η represents the angular velocity of the drone. sh,2 α represents the speed of the unmanned surface vessel. pk Let α represent the first virtual control law to be designed. ak α represents the second virtual control law that needs to be designed. sh This represents the virtual control law that needs to be designed for the third location.

6. The distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems according to claim 1, characterized in that, In S3, the preset performance function β g The expression for (t) is: ； In the formula, β g,0 β represents the first-neighborhood parameter of the performance function. g,∞ The second-neighborhood parameter represents the performance function, exp(·) represents the exponential function, and t represents time. The speed parameter represents the performance function; In S3, the expression for the error transformation function is: ； In the formula, This represents the position error transformation function for UAVs and unmanned surface vessels. The velocity error transformation function for UAVs and unmanned surface vessels, e g,1 e represents the positional error of drones and unmanned surface vessels. g,2 β represents the speed error of drones and unmanned surface vessels. g This represents the preset performance function, g represents the UAV position loop and attitude loop and the UAV position, pk represents the UAV position loop, ak represents the UAV attitude loop, and sh represents the UAV position.

7. The distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems according to claim 1, characterized in that, In S4, the expression for the robust virtual control law is: ； In the formula, α pk Let α represent the virtual control law of the designed UAV position loop. ak Let α represent the virtual control law of the designed UAV attitude loop. sh e represents the virtual control law of the designed unmanned surface vessel. pk,1 e represents the position error of the UAV's position loop. ak,1 e represents the position error of the UAV attitude loop. sh,1 Λ represents the positional error of the unmanned surface vessel. pk The communication parameters representing the UAV's position loop, Λ ak The communication parameters representing the attitude loop of the UAV, Λ sh λ represents the communication parameters of the unmanned surface vessel. pk,1 λ represents the first fixed-time gain parameter of the virtual control law of the UAV position loop. pk,2 λ represents the second fixed-time gain parameter of the virtual control law of the UAV position loop. ak,1 λ represents the first fixed-time gain parameter of the virtual control law of the UAV attitude loop. ak,2 λ represents the second fixed-time gain parameter of the virtual control law of the UAV attitude loop. sh,1 λ represents the first fixed-time gain parameter of the virtual control law of the unmanned surface vessel. sh,2 χ represents the second fixed-time gain parameter of the virtual control law of the unmanned surface vessel. pk,1 χ represents the time-varying coefficient of the position error transformation function of the UAV position loop. ak,1 χ represents the time-varying coefficient of the position error transformation function of the UAV attitude loop. sh,1 Ф represents the time-varying coefficient of the position error transformation function of the unmanned surface vessel. pk,1 Ф represents the position error transformation function vector of the UAV position loop. ak,1 Ф represents the position error transformation function vector of the UAV attitude loop. sh,1 κ represents the position error transformation function vector of the unmanned surface vessel. pk,1 κ represents the bias of the position error transformation function of the UAV position loop. ak,1 κ represents the bias of the position error transformation function of the UAV attitude loop. sh,1 Ξ represents the offset of the position error transformation function of the unmanned surface vessel. pk Ξ represents the position loop velocity error variable of the UAV. ak Ξ represents the attitude loop velocity error variable of the UAV. sh ∂ represents the speed error variable of the unmanned surface vessel. pk,1 The parameters representing the robust H∞ virtual control law for the UAV's position loop are ∂ ak,1 The parameters representing the robust virtual control law H∞ for the attitude loop of the UAV, ∂ sh,1 Let σ represent the parameters of the robust H∞ virtual control law for the unmanned surface vessel, and let σ represent the parameter of the first fixed-time exponential term. This represents the parameter of the second fixed-time exponent.

8. The distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems according to claim 1, characterized in that, In S4, the expression for the distributed fixed-time robust controller is: ； In the formula, u pk This represents the distributed fixed-time robust H∞ controller for the designed UAV position loop, u ak This represents the distributed fixed-time robust H∞ controller for the designed UAV attitude loop, u sh This represents the designed distributed fixed-time robust H∞ controller for the unmanned surface vessel, e pk,2 e represents the velocity error of the UAV's position loop. ak,2 e represents the velocity error of the UAV attitude loop. sh,2 Λ represents the speed error of the unmanned surface vessel. pk The communication parameters representing the UAV's position loop, Λ ak The communication parameters representing the attitude loop of the UAV, Λ sh λ represents the communication parameters of the unmanned surface vessel. pk,3 λ represents the first fixed-time gain parameter of the UAV position loop fixed-time robust H∞ controller. pk,4 λ represents the second fixed-time gain parameter of the UAV position loop fixed-time robust H∞ controller. ak,3 λ represents the first fixed-time gain parameter of the UAV attitude loop fixed-time robust H∞ controller. ak,4 λ represents the second fixed-time gain parameter of the UAV attitude loop fixed-time robust H∞ controller. sh,3 λ represents the first fixed-time gain parameter of the unmanned surface vessel's fixed-time robust H∞ controller. sh,4 χ represents the second fixed-time gain parameter of the unmanned surface vessel's fixed-time robust H∞ controller. pk,2 χ represents the time-varying coefficient of the velocity error transformation function of the UAV position loop. ak,2 χ represents the time-varying coefficient of the velocity error transformation function of the UAV attitude loop. sh,2 The time-varying coefficients, Ф, represent the velocity error transformation function of the unmanned surface vessel. pk,2 The vector representing the velocity error transformation function of the UAV position loop, Ф ak,2 Ф represents the velocity error transformation function vector of the UAV attitude loop. sh,2 κ represents the velocity error transformation function vector of the unmanned surface vessel. pk,2 κ represents the bias of the velocity error transformation function in the UAV position loop. ak,2 κ represents the bias of the velocity error transformation function in the UAV attitude loop. sh,2 This indicates the bias of the speed error transformation function for the unmanned surface vessel. The derivative of the virtual control law for the UAV's position loop is given. The derivative of the virtual control law of the UAV attitude loop is given. Let A represent the derivative of the virtual control law of the unmanned surface vessel (USV), and let B represent the first model parameter of the USV and the second model parameter of the USV. This represents the first model parameter of the unmanned surface vessel. This represents the second model parameter of the unmanned surface vessel. This represents the third model parameter of the unmanned surface vessel. The velocity variable represents the position loop of the drone. The velocity variable represents the attitude loop of the drone. ∂ represents the velocity variable of the unmanned surface vessel in the geodetic coordinate system. pk,2 The first parameter, ∂, represents the fixed-time robust H∞ controller of the UAV position loop. ak,2 The first parameter, ∂, represents the fixed-time robust H∞ controller of the UAV attitude loop. sh,2 This represents the first parameter of the fixed-time robust H∞ controller for the unmanned surface vessel. The second parameter represents the fixed-time robust H∞ controller of the UAV position loop. The second parameter represents the fixed-time robust H∞ controller of the UAV attitude loop. The second parameter represents the fixed-time robust H∞ controller of the UAV position loop, and σ represents the first fixed-time exponential term parameter. This represents the parameter of the second fixed-time exponent.

9. The distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems according to claim 1, characterized in that, In S5, the expression for the dynamic event triggering mechanism is: ； In the formula, u Eg (t) represents the controller that updates the event-triggered mechanism, g represents the UAV's position loop and attitude loop, and the UAV's position, and t represents time. Represents the control function, t k Indicates the time when the controller updates, t k+1 Let R represent the next moment after the event triggers the update, and let z represent the set of real numbers. g (t) represents the error of the event-triggered controller. Represents a time-varying function, o g The parameter that indicates when the event was triggered.

10. The distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems according to claim 1, characterized in that, In S5, the expression for the distributed fixed-time robust grouping controller under the dynamic event triggering mechanism is: ； In the formula, This refers to the controller designed under the UAV position loop event triggering mechanism. This refers to the controller designed under the UAV attitude loop event triggering mechanism. This represents the controller designed under the unmanned surface vessel's event-triggered mechanism, where I3 represents a three-dimensional unit vector. This indicates the parameters that trigger the first event in the drone's position loop. This indicates the parameters that trigger the first event in the UAV attitude loop. This indicates the parameters that trigger the first event for the unmanned surface vessel. This indicates the parameters that trigger the second event in the drone's position loop. This indicates the parameters that trigger the second event in the UAV attitude loop. The parameter e represents the trigger condition for the second event of the unmanned surface vessel. pk,2 e represents the velocity tracking error of the UAV's position loop. ak,2 e represents the velocity tracking error of the UAV attitude loop. sh,2 χ represents the speed tracking error of the unmanned surface vessel. pk,2 χ represents the time-varying parameter of the velocity error transformation function of the UAV position loop. ak,2 χ represents the time-varying parameter of the velocity error transformation function of the UAV attitude loop. sh,2 The time-varying parameter u represents the velocity error transformation function of the unmanned surface vessel. pk This represents the distributed fixed-time robust H∞ controller for the designed UAV position loop, u ak This represents the distributed fixed-time robust H∞ controller for the designed UAV attitude loop, u sh This represents the distributed fixed-time robust H∞ controller of the designed unmanned surface vessel, q pk The parameter q represents the event triggering of the drone's position loop. ak The parameter q represents the event triggering of the drone's attitude loop. sh The parameter J represents the event triggering parameter for the unmanned surface vessel. sh Let M represent the rotation matrix. sh The parameters represent the model parameters of the unmanned surface vessel (USV), where A represents the first model parameter of the USV and B represents the second model parameter of the USV.

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