Distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster system

Abstract

The invention discloses a distributed fixed time robust formation trajectory tracking control method for a heterogeneous cluster system, and belongs to the technical field of formation control, and the method comprises the following steps: S1, building kinematics and dynamics models of a six-degree-of-freedom four-rotor unmanned plane and kinematics and dynamics models of a three-degree-of-freedom unmanned ship; s2, determining a formation tracking error and a speed tracking error of the air-sea heterogeneous cluster system; s3, generating an error conversion function; s4, determining a fixed time robust virtual control law and a distributed fixed time robust controller; s5, determining a distributed fixed time robust controller under the dynamic time triggering mechanism; and S6, completing trajectory tracking control. On the basis of dynamic event triggering, the distributed fixed-time robust H-infinity formation control method based on dynamic event triggering is determined, the updating frequency of the controller is reduced, and communication resources are saved.

Description

Technical Field

[0001] The present invention belongs to the technical field of formation control, and in particular relates to a distributed fixed-time robust formation trajectory tracking control method for a heterogeneous cluster system. Background Art

[0002] With the vigorous 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 has also shown a rapid growth trend. Traditional single-platform systems are often difficult to meet these complex task requirements due to their limited functions and efficiency. Heterogeneous cluster systems have emerged as the times require. They are a group system composed of multiple intelligent agents, including robots of various types, shapes and capabilities. Among them, the air-sea heterogeneous cluster system, especially the formation tracking control method of quad-rotor drones and unmanned boats, provides innovative solutions for this field. UAVs have become an important tool in modern warfare and disaster response with their efficient aerial reconnaissance, surveillance and strike capabilities; while unmanned boats have played an important role in tasks such as marine monitoring, search and rescue, and logistics with their maneuverability and flexibility in the marine environment. Combining these two systems to form an air-sea heterogeneous cluster system can not only give full play to their respective advantages, but also realize collaborative operations in more complex tasks and scenarios. Therefore, the air-sea heterogeneous cluster system of drones and unmanned boats is widely used in the fields of marine environmental protection, traffic management, scientific research, marine resource exploration, etc., providing an important technical means to promote the development of the marine industry and protect the marine ecological environment.

[0003] However, the research on formation tracking control methods for quadrotor drones and unmanned boats 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 speeds, and weather changes will affect the navigation trajectory of unmanned boats, while drones in the air need to cope with changes in wind and airflow. The formation control algorithm must have a certain anti-interference ability to handle these external disturbances. At the same time, in many application scenarios such as marine resource exploration, environmental monitoring, or emergency rescue, the rapid response and timely execution of the system are the key to completing marine missions. The settable stable time control algorithm can ensure the immediacy and time certainty of the system. In addition, the air-sea heterogeneous cluster system of drones and unmanned boats working in harsh marine environments, if the communication resources are improperly used and excessively wasted, will not only cause serious safety hazards, but may also reduce the stability of the system in marine operations. Therefore, it is of great research value and significance to design a reasonable formation controller to ensure that the quadrotor drones and unmanned boats of the air-sea heterogeneous system can smoothly and reliably perform trajectory tracking tasks in complex marine environments.

[0004] Formation trajectory tracking is the key to ensure the collaborative work of heterogeneous cluster systems. Currently, the commonly used control algorithms include model predictive control, adaptive control, fuzzy control and sliding mode control. These control methods can ensure that the formation is achieved within a limited time. However, the convergence time of finite-time control depends on the initial conditions of the system. For UAV and unmanned boat air and sea heterogeneous cluster systems, since they need to quickly and accurately reach the predetermined formation to effectively complete various engineering tasks, the requirements for the system convergence speed are particularly strict. In this case, the traditional finite-time control algorithm may not be able to fully meet this requirement due to the uncertainty of its convergence time. Therefore, it is necessary to further explore and study more efficient and stable control algorithms to ensure that UAV and unmanned boat air and sea heterogeneous cluster systems can quickly and accurately complete the formation.

[0005] In the field of multi-agent control systems, technologies such as PID control, sliding mode control, and adaptive control have been widely adopted. PID control is known for its low requirements on system models and reliable performance in a variety of application scenarios. However, its limitations in anti-interference and fast response cannot be ignored, and the parameter adjustment process is often cumbersome. Sliding mode control technology is highly praised for its excellent fast response and robustness to system parameter fluctuations and external disturbances. However, its chattering phenomenon near the sliding surface may have an adverse effect on the stability and performance of the system. The adaptive control strategy updates the control parameters in real time to adapt to the dynamic changes of the system and external disturbances, but this method requires too many parameter updates and increases the computational complexity.

[0006] In recent years, the common method for controlling the uncertainty and complexity of the marine environment faced by marine unmanned systems is usually to design a state observer or use various neural networks to approximate, and then design a control law so that the system can achieve trajectory tracking control and ensure the global convergence of the error. However, the observation effect of the observer depends on the observation gain; the computational complexity of the neural network and the limited online calculation speed lead to some inevitable problems, such as a large number of parameter updates, a large system calculation burden, which may cause a calculation explosion problem, and the system cannot be guaranteed to converge within a limited time. In addition, there is another effective method to solve external disturbances, namely H∞ control. H∞ control refers to expressing the performance indicators in the control system design in the form of H∞ norms. In the H∞ control system, the L2 gain of the closed-loop system is less than or equal to the set value, so the controller has strong robustness, can well suppress disturbances, and the calculation amount is simpler than the observer and neural network mentioned above, and the parameters that need to be adjusted are also greatly reduced. Therefore, the H∞ control method has been widely studied in the control field.

[0007] Data communication is a key link in the formation control of cluster systems, which is used to realize information exchange between various nodes. Data communication mainly involves two aspects: one is the data interaction between the controller and the actuator; the other is the data interaction between robots. The continuous and uninterrupted update of the control input signal under the time-triggered control mechanism may lead to an increase in the communication burden, which in turn affects the communication efficiency and stability of the entire system. In static event-triggered control, the control input signal is updated only when the trigger condition is triggered, rather than continuously updating the control signal, thereby reducing the controller update frequency and improving the utilization of communication resources. In the static event-triggered control mechanism, the introduction of a dynamic variable can more flexibly reduce the number of controller communications, and this mechanism is called dynamic event-triggered control. When UAVs and unmanned boats are operating at sea, they often face harsh marine environments. At this time, communication resources are particularly valuable, and the event-triggered mechanism can effectively save these resources. Therefore, it is of great significance in cluster systems in the marine field.

[0008] Therefore, through the above analysis, a distributed fixed-time robust H∞ formation control method based on specified performance and dynamic event triggering is proposed for a type of quadrotor UAV and unmanned boat air-sea heterogeneous system. The tracking error of the system is guaranteed to converge within a fixed time and is not affected by the initial state of the system. The robust H∞ control improves the stability and robustness of the system in complex marine environments. The combination of dynamic time triggering mechanism improves the communication efficiency of the system and saves communication resources. Summary of the invention

[0009] In order to solve the above problems, the present invention proposes a distributed fixed-time robust formation trajectory tracking control method for a heterogeneous cluster system.

[0010] The technical solution of the present invention is: a distributed fixed-time robust formation trajectory tracking control method for a heterogeneous cluster system comprises the following steps:

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

[0012] S2. Determine the formation tracking error and velocity tracking error of the air-sea heterogeneous cluster system based on the kinematic and dynamic models of the six-degree-of-freedom quad-rotor drone and the three-degree-of-freedom unmanned boat;

[0013] S3, constructing a preset performance function, and generating an error conversion function according to the formation tracking error and speed tracking error of the air-sea heterogeneous cluster system;

[0014] S4. Determine a fixed-time robust virtual control law and a distributed fixed-time robust controller according to the error conversion function;

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

[0016] S6. Use the distributed fixed-time robust controller under the dynamic event trigger mechanism to complete trajectory tracking control.

[0017] Furthermore, in S1, the expressions of the kinematic and dynamic models of the six-degree-of-freedom quadrotor drone are:

[0018] ;

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

[0020] Furthermore, in S1, the kinematic and dynamic models of the three-degree-of-freedom unmanned boat are expressed as:

[0021] ;

[0022] In the formula, represents the speed variable of the unmanned boat in the geodetic coordinates, represents the acceleration variable of the unmanned boat in the body coordinates, ψ sh represents the yaw angle of the unmanned boat, J sh represents the rotation matrix, v sh represents the velocity variable and angular velocity variable of the hth unmanned boat in the body coordinates, u sh represents the control input to be designed for the hth unmanned boat, f sh represents the external disturbance of the hth unmanned boat, represents the inertia matrix, represents the Coriolis matrix centripetal matrix, represents the damping matrix.

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

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

[0025] ;

[0026] In the formula, e xk,1 Represents the tracking error of the UAV’s forward direction, e yk,1 represents the tracking error in the lateral direction of the UAV, e z,1 represents the tracking error of the UAV in the vertical direction, N1 represents the number of UAVs in the UAV-USV system, N2 represents the number of unmanned boats in the UAV-USV system, and a k,j represents the communication between the kth UAV and the jth follower, b kl represents the communication between the kth UAV and the virtual leader, η xk Indicates the position of the UAV's forward direction, η yk represents the lateral position of the drone, ηzk represents the vertical position of the UAV, η xj represents the position of the jth follower's forward direction, η yj represents the horizontal position of the jth follower, η zj represents the vertical position of the jth follower, Δd xk Indicates the relative position distance between the kth UAV and the virtual leader in the forward direction, Δd yk represents the relative position distance between the kth UAV and the virtual leader in the lateral direction, Δd zk represents the relative vertical distance between the kth UAV and the virtual leader, Δd xj represents the first relative position of the follower to the virtual leader, Δd yj represents the second relative position of the follower to the virtual leader, Δd zj represents the third relative position of the follower to the virtual leader, L xd represents the first expected trajectory information of the virtual leader, L yd represents the second expected trajectory information of the virtual leader, L zd represents the third expected trajectory information of the virtual leader, j represents the follower number in the heterogeneous cluster system; when there is communication between the kth UAV and the jth follower, a k,j >0, otherwise a k,j = 0, when the kth UAV has communication with the virtual leader, b kl >0, otherwise b kl =0;

[0027] The expression of the k-th UAV attitude loop tracking error is:

[0028] ;

[0029] In the formula, e φk,1 Represents the tracking error of the UAV’s roll angle, e θk,1 represents the tracking error of the UAV pitch angle, e ψk,1 Represents the tracking error of the UAV yaw angle, η φk is the roll angle, η θk represents the pitch angle, η ψk represents the yaw angle, η ψj represents the yaw angle of the jth follower, η φk.d represents the expected angle of the drone's roll angle, η θk,d Denotes the desired pitch angle of the drone, Δd ψk Represents the relative distance of the yaw angle between the UAV and the virtual leader, Δd ψj represents the fourth relative position of the follower to the virtual leader, L ψdrepresents the fourth desired trajectory information of the virtual leader;

[0030] The expression of unmanned boat tracking error is:

[0031] ;

[0032] In the formula, e xh,1 represents the tracking error of the unmanned boat’s forward direction, e yh,1 represents the tracking error of the unmanned boat in the lateral direction, e ψh,1 Represents the tracking error of the UAV yaw angle, a h,j represents the communication between the h-th UAV and the j-th follower, b hl represents the communication between the kth unmanned boat and the virtual leader, η xh represents the position of the unmanned boat in the direction of travel in the geodetic coordinates, η yh represents the lateral position of the unmanned boat in the geodetic coordinates, η ψh represents the yaw angle position of the unmanned boat in geodetic coordinates, Δd xh Indicates the relative distance between the unmanned boat and the virtual leader in the forward direction, Δd yh represents the relative distance in the lateral direction between the unmanned boat and the virtual leader, Δd ψh represents the relative distance between the unmanned boat and the virtual leader in the yaw angle direction, η ψj represents the yaw angle position of the jth follower, Δd ψj represents the relative distance between the jth follower’s yaw angle and the virtual leader. When there is communication between the hth unmanned boat and the jth follower, a h,j >0, otherwise a h,j = 0, when the hth unmanned boat has communication with the virtual leader, b hl >0, otherwise b hl =0.

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

[0034] ;

[0035] In the formula, e pk,2 represents the velocity error variable of the drone position loop, e ak,2 represents the velocity error variable of the UAV attitude loop, e sh,2 represents the speed error variable of the unmanned boat, η pk,2 represents the speed of the drone, η ak,2 represents the angular velocity of the drone, η sh,2 represents the speed of the unmanned boat, α pk represents the first virtual control law to be designed, α akrepresents the second virtual control law to be designed, α sh Represents the third virtual control law that needs to be designed.

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

[0037] ;

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

[0039] In S3, the expression of the error conversion function is:

[0040] ;

[0041] In the formula, Represents the position error conversion function of the UAV and the unmanned boat, represents the speed error conversion function between the UAV and the unmanned boat, e g,1 represents the position error of the UAV and the unmanned boat, e g,2 represents the speed error between the UAV and the unmanned boat, β g represents the preset performance function, g represents the position loop and attitude loop of the UAV and the position of the unmanned boat, pk represents the position loop of the UAV, ak represents the attitude loop of the UAV, and sh represents the position of the unmanned boat.

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

[0043] ;

[0044] In the formula, α pk represents the virtual control law of the designed UAV position loop, α ak represents the virtual control law of the designed UAV attitude loop, α sh represents the virtual control law of the designed unmanned boat, e pk,1 represents the position error of the drone position loop, e ak,1 represents the position error of the UAV attitude ring, e sh,1 represents the position error of the unmanned boat, Λ pk represents the communication parameters of the UAV position loop, Λ ak represents the communication parameters of the UAV attitude loop, Λ sh represents the communication parameters of the unmanned boat, λ pk,1represents the first fixed time gain parameter of the virtual control law of the UAV position loop, λ pk,2 represents the second fixed time gain parameter of the virtual control law of the UAV position loop, λ ak,1 represents the first fixed time gain parameter of the virtual control law of the UAV attitude loop, λ ak,2 represents the second fixed time gain parameter of the virtual control law of the UAV attitude loop, λ sh,1 represents the first fixed time gain parameter of the virtual control law of the unmanned boat, λ sh,2 represents the second fixed time gain parameter of the virtual control law of the unmanned boat, χ pk,1 represents the time-varying coefficient of the position error transfer function of the UAV position loop, χ ak,1 represents the time-varying coefficient of the position error transfer function of the UAV attitude loop, χ sh,1 represents the time-varying coefficient of the position error conversion function of the unmanned boat, Ф pk,1 Represents the position error conversion function vector of the UAV position loop, Ф ak,1 Represents the position error conversion function vector of the UAV attitude loop, Ф sh,1 represents the position error conversion function vector of the unmanned boat, κ pk,1 represents the position error transfer function bias of the UAV position loop, κ ak,1 represents the position error transfer function bias of the UAV attitude loop, κ sh,1 represents the position error conversion function bias of the unmanned boat, Ξ pk represents the velocity error variable of the UAV position loop, Ξ ak represents the velocity error variable of the UAV attitude loop, Ξ sh represents the speed error variable of the unmanned boat, ∂ pk,1 represents the parameters of the robust H∞ virtual control law for the UAV position loop, ∂ ak,1 represents the parameters of the robust H∞ virtual control law of the UAV attitude loop, ∂ sh,1 represents the parameters of the robust H∞ virtual control law of the unmanned boat, σ represents the first fixed time exponential term parameter, Represents the second fixed time index term parameter.

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

[0046] ;

[0047] In the formula, u pk represents the distributed fixed-time robust H∞ controller of the designed UAV position loop, u ak represents the distributed fixed-time robust H∞ controller of the designed UAV attitude loop, u sh represents the distributed fixed-time robust H∞ controller of the designed unmanned boat, epk,2 represents the velocity error of the drone position loop, e ak,2 represents the velocity error of the drone attitude loop, e sh,2 represents the speed error of the unmanned boat, Λ pk represents the communication parameters of the UAV position loop, Λ ak represents the communication parameters of the UAV attitude loop, Λ sh represents the communication parameters of the unmanned boat, λ pk,3 represents the first fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV position loop, λ pk,4 represents the second fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV position loop, λ ak,3 represents the first fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV attitude loop, λ ak,4 represents the second fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV attitude loop, λ sh,3 represents the first fixed-time gain parameter of the fixed-time robust H∞ controller of the unmanned boat, λ sh,4 represents the second fixed-time gain parameter of the fixed-time robust H∞ controller of the unmanned boat, χ pk,2 represents the time-varying coefficient of the velocity error conversion function of the UAV position loop, χ ak,2 represents the time-varying coefficient of the velocity error transfer function of the UAV attitude loop, χ sh,2 represents the time-varying coefficient of the speed error conversion function of the unmanned boat, Ф pk,2 Represents the velocity error conversion function vector of the UAV position loop, Ф ak,2 Represents the velocity error conversion function vector of the UAV attitude loop, Ф sh,2 represents the speed error conversion function vector of the unmanned boat, κ pk,2 represents the velocity error transfer function bias of the UAV position loop, κ ak,2 represents the velocity error transfer function bias of the UAV attitude loop, κ sh,2 represents the speed error conversion function bias of the unmanned boat, represents the derivative of the virtual control law of the UAV position loop, represents the derivative of the virtual control law of the UAV attitude loop, represents the derivative of the virtual control law of the unmanned boat, A represents the first model parameter of the unmanned boat, B represents the second model parameter of the unmanned boat, represents the first model parameter of the unmanned boat, represents the second model parameter of the unmanned boat, represents the third model parameter of the unmanned boat, represents the velocity variable of the drone position loop, represents the velocity variable of the drone attitude loop, represents the velocity variable of the unmanned boat in the geodetic coordinate system, ∂ pk,2 represents the first parameter of the fixed-time robust H∞ controller of the UAV position loop, ∂ ak,2 represents the first parameter of the fixed-time robust H∞ controller of the UAV attitude loop, ∂ sh,2 represents the first parameter of the fixed-time robust H∞ controller of the unmanned boat, represents the second parameter of the fixed-time robust H∞ controller of the UAV position loop, represents the second parameter of the fixed-time robust H∞ controller of the UAV attitude loop, represents the second parameter of the fixed-time robust H∞ controller of the UAV position loop, σ represents the first fixed-time exponential term parameter, Represents the second fixed time index term parameter.

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

[0049] ;

[0050] In the formula, u Eg (t) represents the controller updated by the event trigger mechanism, g represents the position loop and attitude loop of the UAV and the position of the UAV, t represents time, represents the control function, t k Indicates the time when the controller is updated, t k+1 represents the next moment when the event triggers the update, R represents a real number set, z g (t) represents the error of the event-triggered controller, represents a time-varying function, o g Indicates the parameters of the event trigger.

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

[0052] ;

[0053] In the formula, represents the controller designed under the UAV position loop event trigger mechanism, It represents the controller designed under the UAV attitude loop event trigger mechanism. represents the controller designed under the unmanned boat event trigger mechanism, I3 represents the three-dimensional unit vector, Indicates the trigger condition parameter of the first event of the drone position loop. Indicates the trigger condition parameters of the first event of the drone attitude loop. Indicates the trigger condition parameter of the first event of the unmanned boat. Indicates the trigger condition parameter of the second event of the drone position loop. Indicates the trigger condition parameter of the second event of the drone attitude loop. Indicates the trigger condition parameter of the second event of the unmanned boat, e pk,2 represents the velocity tracking error of the UAV position loop, e ak,2 represents the velocity tracking error of the UAV attitude loop, e sh,2 represents the speed tracking error of the unmanned boat, χ pk,2 represents the time-varying parameter of the velocity error transfer function of the UAV position loop, χ ak,2 represents the time-varying parameter of the velocity error transfer function of the UAV attitude loop, χ sh,2 represents the time-varying parameter of the speed error conversion function of the unmanned boat, u pk represents the distributed fixed-time robust H∞ controller of the designed UAV position loop, u ak represents the distributed fixed-time robust H∞ controller of the designed UAV attitude loop, u sh represents the distributed fixed-time robust H∞ controller of the designed unmanned boat, q pk Indicates the parameters of the event trigger of the drone position loop, q ak Indicates the parameters of the event trigger of the drone attitude loop, q sh Indicates the parameters of the unmanned boat event trigger, J sh represents the rotation matrix, M sh represents the model parameters of the unmanned boat, A represents the first model parameters of the unmanned aerial vehicle, and B represents the second model parameters of the unmanned aerial vehicle.

[0054] The beneficial effects of the present invention are:

[0055] (1) The present invention limits the tracking error of the air-sea heterogeneous cluster system formation according to the functional characteristics of the performance function, and constrains the speed tracking error at the same time. Compared with the method of only constraining the position error, the distributed time-varying constrained formation controller designed by the present invention has better control performance;

[0056] (2) The present invention aims at the air-sea heterogeneous cluster system of unmanned aerial vehicles and unmanned boats with external interference. By using the fixed-time robust H∞ formation control method, the system is ensured to converge within a fixed time and is not dependent on the initial state of the system, thereby improving the stability and robustness of the system.

[0057] (3) Based on dynamic time triggering, the present 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. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0059] Figure 2 The communication topology diagram of the air-sea heterogeneous cluster system of UAVs and unmanned boats;

[0060] Figure 3 It is a three-dimensional tracking diagram of the air-sea heterogeneous cluster system;

[0061] Figure 4 It is a two-dimensional tracking diagram of the air-sea heterogeneous cluster system;

[0062] Figure 5 This is the error diagram of the unmanned boat in the air-sea heterogeneous swarm system;

[0063] Figure 6 This is the error diagram of UAVs in the air-sea heterogeneous swarm system;

[0064] Figure 7 This is the control input diagram for the UAV and unmanned boat swarm system;

[0065] Figure 8 This is the control input diagram for the UAV and unmanned boat swarm system;

[0066] Fig. 9 The dynamic event trigger diagram of UAV 1 and UAV 2;

[0067] Fig.10 It is the dynamic event trigger diagram of unmanned boat 1 and unmanned boat 2;

[0068] Fig.11 This is the dynamic event trigger diagram of unmanned boat 3 and unmanned boat 4. DETAILED DESCRIPTION

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

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

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

[0072] S2. Determine the formation tracking error and velocity tracking error of the air-sea heterogeneous cluster system based on the kinematic and dynamic models of the six-degree-of-freedom quad-rotor drone and the three-degree-of-freedom unmanned boat;

[0073] S3, constructing a preset performance function, and generating an error conversion function according to the formation tracking error and speed tracking error of the air-sea heterogeneous cluster system;

[0074] S4. Determine a fixed-time robust virtual control law and a distributed fixed-time robust controller according to the error conversion function;

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

[0076] S6. Use the distributed fixed-time robust controller under the dynamic event trigger mechanism to complete trajectory tracking control.

[0077] In the embodiment of the present invention, in S1, the expressions of the kinematic and dynamic models of the six-degree-of-freedom quad-rotor drone are:

[0078] ;

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

[0080] In the embodiment of the present invention, in S1, the kinematic and dynamic models of the three-degree-of-freedom unmanned boat are expressed as follows:

[0081] ;

[0082] In the formula, represents the speed variable of the unmanned boat in the geodetic coordinates, represents the acceleration variable of the unmanned boat in the body coordinates, ψ sh represents the yaw angle of the unmanned boat, J sh represents the rotation matrix, v sh represents the velocity variable and angular velocity variable of the hth unmanned boat in the body coordinates, u sh represents the control input to be designed for the hth unmanned boat, f sh represents the external disturbance of the hth unmanned boat, represents the inertia matrix, represents the Coriolis matrix centripetal matrix, represents the damping matrix.

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

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

[0085] ;

[0086] In the formula, e xk,1 Represents the tracking error of the UAV’s forward direction, e yk,1 represents the tracking error in the lateral direction of the UAV, e z,1 represents the tracking error of the UAV in the vertical direction, N1 represents the number of UAVs in the UAV-USV system, N2 represents the number of unmanned boats in the UAV-USV system, and a k,j represents the communication between the kth UAV and the jth follower, b kl represents the communication between the kth UAV and the virtual leader, η xk Indicates the position of the UAV's forward direction, η ykrepresents the lateral position of the drone, η zk represents the vertical position of the UAV, η xj represents the position of the jth follower's forward direction, η yj represents the horizontal position of the jth follower, η zj represents the vertical position of the jth follower, Δd xk Indicates the relative position distance between the kth UAV and the virtual leader in the forward direction, Δd yk represents the relative position distance between the kth UAV and the virtual leader in the lateral direction, Δd zk represents the relative vertical distance between the kth UAV and the virtual leader, Δd xj represents the first relative position of the follower to the virtual leader, Δd yj represents the second relative position of the follower to the virtual leader, Δd zj represents the third relative position of the follower to the virtual leader, L xd represents the first expected trajectory information of the virtual leader, L yd represents the second expected trajectory information of the virtual leader, L zd represents the third expected trajectory information of the virtual leader, j represents the follower number in the heterogeneous cluster system; when there is communication between the kth UAV and the jth follower, a k,j >0, otherwise a k,j = 0, when the kth UAV has communication with the virtual leader, b kl >0, otherwise b kl =0;

[0087] The expression of the k-th UAV attitude loop tracking error is:

[0088] ;

[0089] In the formula, e φk,1 Represents the tracking error of the UAV’s roll angle, e θk,1 represents the tracking error of the UAV pitch angle, e ψk,1 Represents the tracking error of the UAV yaw angle, η φk is the roll angle, η θk represents the pitch angle, η ψk represents the yaw angle, η ψj represents the yaw angle of the jth follower, η φk.d represents the expected angle of the drone's roll angle, η θk,d Denotes the desired pitch angle of the drone, Δd ψk Represents the relative distance of the yaw angle between the UAV and the virtual leader, Δd ψj represents the fourth relative position of the follower to the virtual leader, Lψd represents the fourth desired trajectory information of the virtual leader;

[0090] The expression of unmanned boat tracking error is:

[0091] ;

[0092] In the formula, e xh,1 represents the tracking error of the unmanned boat’s forward direction, e yh,1 represents the tracking error of the unmanned boat in the lateral direction, e ψh,1 Represents the tracking error of the UAV yaw angle, a h,j represents the communication between the h-th UAV and the j-th follower, b hl represents the communication between the kth unmanned boat and the virtual leader, η xh represents the position of the unmanned boat in the direction of travel in the geodetic coordinates, η yh represents the lateral position of the unmanned boat in the geodetic coordinates, η ψh represents the yaw angle position of the unmanned boat in geodetic coordinates, Δd xh Indicates the relative distance between the unmanned boat and the virtual leader in the forward direction, Δd yh represents the relative distance in the lateral direction between the unmanned boat and the virtual leader, Δd ψh represents the relative distance between the unmanned boat and the virtual leader in the yaw angle direction, η ψj represents the yaw angle position of the jth follower, Δd ψj represents the relative distance between the jth follower’s yaw angle and the virtual leader. When there is communication between the hth unmanned boat and the jth follower, a h,j >0, otherwise a h,j = 0, when the hth unmanned boat has communication with the virtual leader, b hl >0, otherwise b hl =0.

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

[0094] ;

[0095] In the formula, e pk,2 represents the velocity error variable of the drone position loop, e ak,2 represents the velocity error variable of the UAV attitude loop, e sh,2 represents the speed error variable of the unmanned boat, η pk,2 represents the speed of the drone, η ak,2 represents the angular velocity of the drone, η sh,2 represents the speed of the unmanned boat, α pk represents the first virtual control law to be designed, αak represents the second virtual control law to be designed, α sh In S3, the preset performance function β g The expression of (t) is:

[0096] ;

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

[0098] In S3, the expression of the error conversion function is:

[0099] ;

[0100] In the formula, Represents the position error conversion function of the UAV and the unmanned boat, represents the speed error conversion function between the UAV and the unmanned boat, e g,1 represents the position error of the UAV and the unmanned boat, e g,2 represents the speed error between the UAV and the unmanned boat, β g represents the preset performance function, g represents the position loop and attitude loop of the UAV and the position of the unmanned boat, pk represents the position loop of the UAV, ak represents the attitude loop of the UAV, and sh represents the position of the unmanned boat.

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

[0102] ;

[0103] In the formula, α pk represents the virtual control law of the designed UAV position loop, α ak represents the virtual control law of the designed UAV attitude loop, α sh represents the virtual control law of the designed unmanned boat, e pk,1 represents the position error of the drone position loop, e ak,1 represents the position error of the UAV attitude ring, e sh,1 represents the position error of the unmanned boat, Λ pk represents the communication parameters of the UAV position loop, Λ ak represents the communication parameters of the UAV attitude loop, Λ sh represents the communication parameters of the unmanned boat, λ pk,1 represents the first fixed time gain parameter of the virtual control law of the UAV position loop, λ pk,2represents the second fixed time gain parameter of the virtual control law of the UAV position loop, λ ak,1 represents the first fixed time gain parameter of the virtual control law of the UAV attitude loop, λ ak,2 represents the second fixed time gain parameter of the virtual control law of the UAV attitude loop, λ sh,1 represents the first fixed time gain parameter of the virtual control law of the unmanned boat, λ sh,2 represents the second fixed time gain parameter of the virtual control law of the unmanned boat, χ pk,1 represents the time-varying coefficient of the position error transfer function of the UAV position loop, χ ak,1 represents the time-varying coefficient of the position error transfer function of the UAV attitude loop, χ sh,1 represents the time-varying coefficient of the position error conversion function of the unmanned boat, Ф pk,1 Represents the position error conversion function vector of the UAV position loop, Ф ak,1 Represents the position error conversion function vector of the UAV attitude loop, Ф sh,1 represents the position error conversion function vector of the unmanned boat, κ pk,1 represents the position error transfer function bias of the UAV position loop, κ ak,1 represents the position error transfer function bias of the UAV attitude loop, κ sh,1 represents the position error conversion function bias of the unmanned boat, Ξ pk represents the velocity error variable of the UAV position loop, Ξ ak represents the velocity error variable of the UAV attitude loop, Ξ sh represents the speed error variable of the unmanned boat, ∂ pk,1 represents the parameters of the robust H∞ virtual control law for the UAV position loop, ∂ ak,1 represents the parameters of the robust H∞ virtual control law of the UAV attitude loop, ∂ sh,1 represents the parameters of the robust H∞ virtual control law of the unmanned boat, σ represents the first fixed time exponential term parameter, Represents the second fixed time index term parameter.

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

[0105] ;

[0106] In the formula, u pk represents the distributed fixed-time robust H∞ controller of the designed UAV position loop, u ak represents the distributed fixed-time robust H∞ controller of the designed UAV attitude loop, u sh represents the distributed fixed-time robust H∞ controller of the designed unmanned boat, e pk,2 represents the velocity error of the drone position loop, e ak,2represents the velocity error of the UAV attitude loop, e sh,2 represents the speed error of the unmanned boat, Λ pk represents the communication parameters of the UAV position loop, Λ ak represents the communication parameters of the UAV attitude loop, Λ sh represents the communication parameters of the unmanned boat, λ pk,3 represents the first fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV position loop, λ pk,4 represents the second fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV position loop, λ ak,3 represents the first fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV attitude loop, λ ak,4 represents the second fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV attitude loop, λ sh,3 represents the first fixed-time gain parameter of the fixed-time robust H∞ controller of the unmanned boat, λ sh,4 represents the second fixed-time gain parameter of the fixed-time robust H∞ controller of the unmanned boat, χ pk,2 represents the time-varying coefficient of the velocity error conversion function of the UAV position loop, χ ak,2 represents the time-varying coefficient of the velocity error transfer function of the UAV attitude loop, χ sh,2 represents the time-varying coefficient of the speed error conversion function of the unmanned boat, Ф pk,2 Represents the velocity error conversion function vector of the UAV position loop, Ф ak,2 Represents the velocity error conversion function vector of the UAV attitude loop, Ф sh,2 represents the speed error conversion function vector of the unmanned boat, κ pk,2 represents the velocity error transfer function bias of the UAV position loop, κ ak,2 represents the velocity error transfer function bias of the UAV attitude loop, κ sh,2 represents the speed error conversion function bias of the unmanned boat, represents the derivative of the virtual control law of the UAV position loop, represents the derivative of the virtual control law of the UAV attitude loop, represents the derivative of the virtual control law of the unmanned boat, A represents the first model parameter of the unmanned boat, B represents the second model parameter of the unmanned boat, represents the first model parameter of the unmanned boat, represents the second model parameter of the unmanned boat, represents the third model parameter of the unmanned boat, represents the velocity variable of the drone position loop, represents the velocity variable of the drone attitude loop, represents the velocity variable of the unmanned boat in the geodetic coordinate system, ∂ pk,2represents the first parameter of the fixed-time robust H∞ controller of the UAV position loop, ∂ ak,2 represents the first parameter of the fixed-time robust H∞ controller of the UAV attitude loop, ∂ sh,2 represents the first parameter of the fixed-time robust H∞ controller of the unmanned boat, represents the second parameter of the fixed-time robust H∞ controller of the UAV position loop, represents the second parameter of the fixed-time robust H∞ controller of the UAV attitude loop, represents the second parameter of the fixed-time robust H∞ controller of the UAV position loop, σ represents the first fixed-time exponential term parameter, Represents the second fixed time index term parameter.

[0107] In the embodiment of the present invention, in S5, the expression of the dynamic event trigger mechanism is:

[0108] ;

[0109] In the formula, u Eg (t) represents the controller updated by the event trigger mechanism, g represents the position loop and attitude loop of the UAV and the position of the UAV, t represents time, represents the control function, t k Indicates the time when the controller is updated, t k+1 represents the next moment when the event triggers the update, R represents a real number set, z g (t) represents the error of the event-triggered controller, represents a time-varying function, o g Indicates the parameters of the event trigger.

[0110] In the embodiment of the present invention, in S5, the expression of the distributed fixed-time robust formation controller under the dynamic event trigger mechanism is:

[0111] ;

[0112] In the formula, represents the controller designed under the UAV position loop event trigger mechanism, It represents the controller designed under the UAV attitude loop event trigger mechanism. represents the controller designed under the unmanned boat event trigger mechanism, I3 represents the three-dimensional unit vector, Indicates the trigger condition parameter of the first event of the drone position loop. Indicates the trigger condition parameters of the first event of the drone attitude loop. Indicates the trigger condition parameters of the unmanned boat event. Indicates the trigger condition parameter of the second event of the drone position loop. Indicates the trigger condition parameter of the second event of the drone attitude loop. Indicates the trigger condition parameter of the second event of the unmanned boat, e pk,2 represents the velocity tracking error of the UAV position loop, e ak,2 represents the velocity tracking error of the UAV attitude loop, e sh,2 represents the speed tracking error of the unmanned boat, χ pk,2 represents the time-varying parameter of the velocity error transfer function of the UAV position loop, χ ak,2 represents the time-varying parameter of the velocity error transfer function of the UAV attitude loop, χ sh,2 represents the time-varying parameter of the speed error conversion function of the unmanned boat, u pk represents the distributed fixed-time robust H∞ controller of the designed UAV position loop, u ak represents the distributed fixed-time robust H∞ controller of the designed UAV attitude loop, u sh represents the distributed fixed-time robust H∞ controller of the designed unmanned boat, q pk Indicates the parameters of the event trigger of the drone position loop, q ak Indicates the parameters of the event trigger of the drone attitude loop, q sh Indicates the parameters of the unmanned boat event trigger, J sh represents the rotation matrix, M sh represents the model parameters of the unmanned boat, A represents the first model parameters of the unmanned aerial vehicle, and B represents the second model parameters of the unmanned aerial vehicle.

[0113] In order to verify the effectiveness of the method of the present invention, a simulation experiment was carried out, as follows.

[0114] The simulation experiment is carried out using the air-sea heterogeneous cluster system of unmanned aerial vehicles and unmanned boats to verify the designed distributed fixed-time robust H based on dynamic event triggering. ∞ The effectiveness of the formation control method. The system parameters are shown in Table 1, and the controller parameters are shown in Table 2.

[0115] Table 1

[0116]

[0117] Table 2

[0118]

[0119] The selected UAV and unmanned boat cluster system includes a virtual leader, 2 UAVs and 4 unmanned boats, among which the relative amount of the UAV attitude subsystem is , the relative position vectors of the UAV and unmanned boat air-sea heterogeneous cluster system can be selected as follows: The relative position vector of the UAV is: and , the relative vector of the unmanned boat position is: , , , The simulation results are as follows: Figure 2-11 As shown, Figure 2 This is the communication topology diagram of the UAV-USV system. Number 0 represents the virtual leader, numbers 1 and 2 represent UAVs, and numbers 3-6 represent unmanned boats. Figure 3 It shows the three-dimensional trajectory diagram of the UAV-USV system. Figure 4 It shows the two-dimensional trajectory diagram of the UAV-USV system. Figure 5 The result diagram showing the position and velocity tracking errors of the four unmanned boats. Figure 6 It shows the position and velocity tracking error results of the position loop and attitude loop of the two UAVs. Figure 7 and Figure 8 Represents the control input of the unmanned boat and the drone. Fig. 9 , Fig.10 and Fig.11 represents the time interval of the event triggering of the UAV and the unmanned boat. The distributed fixed-time robust H ∞ The formation controller can complete the three-dimensional formation tracking control of the air-sea heterogeneous cluster system of UAVs and unmanned boats within a fixed time, has good robustness, fast convergence speed and is independent of the initial state. ∞ The formation control method can effectively reduce the update frequency of the controller and save communication resources.

[0120] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A distributed fixed-time robust formation trajectory tracking control method for heterogeneous cluster systems, characterized in that: The following steps are involved: S1. Establish the kinematic and dynamic models of the six-degree-of-freedom quadrotor UAV and the kinematic and dynamic models of the three-degree-of-freedom unmanned boat; S2. Determine the formation tracking error and velocity tracking error of the air-sea heterogeneous cluster system based on the kinematic and dynamic models of the six-degree-of-freedom quad-rotor drone and the three-degree-of-freedom unmanned boat; S3, constructing a preset performance function, and generating an error conversion function according to the formation tracking error and speed tracking error of the air-sea heterogeneous cluster system; S4. Determine a fixed-time robust virtual control law and a distributed fixed-time robust controller according to the error conversion function; S5. Establish a dynamic event trigger mechanism and determine a distributed fixed-time robust controller under the dynamic time trigger mechanism; S6. Use the distributed fixed-time robust controller under the dynamic event trigger mechanism to complete trajectory tracking control.

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

3. The method for trajectory tracking control of a distributed fixed-time robust formation of a heterogeneous cluster system according to claim 1 is characterized in that: In S1, the kinematic and dynamic models of the three-degree-of-freedom unmanned boat are expressed as follows: ； In the formula, represents the speed variable of the unmanned boat in the geodetic coordinates, represents the acceleration variable of the unmanned boat in the body coordinates, ψ sh represents the yaw angle of the unmanned boat, J sh represents the rotation matrix, v sh represents the velocity variable and angular velocity variable of the hth unmanned boat in the body coordinates, u sh represents the control input to be designed for the hth unmanned boat, f sh represents the external disturbance of the hth unmanned boat, represents the inertia matrix, represents the Coriolis matrix centripetal matrix, represents the damping matrix.

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

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

6. The method for trajectory tracking control of a distributed fixed-time robust formation of a heterogeneous cluster system according to claim 1, characterized in that: In S3, the preset performance function β g The expression of (t) is: ； In the formula, β g,0 represents the first domain parameter of the performance function, β g,∞ represents the second domain parameter of the performance function, exp(·) represents the exponential function, t represents time, Represents the speed parameter of the performance function; In S3, the expression of the error conversion function is: ； In the formula, Represents the position error conversion function of the UAV and the unmanned boat, represents the speed error conversion function between the UAV and the unmanned boat, e g,1 represents the position error of the UAV and the unmanned boat, e g,2 represents the speed error between the UAV and the unmanned boat, β g represents the preset performance function, g represents the position loop and attitude loop of the UAV and the position of the unmanned boat, pk represents the position loop of the UAV, ak represents the attitude loop of the UAV, and sh represents the position of the unmanned boat.

7. The method for trajectory tracking control of a distributed fixed-time robust formation of a heterogeneous cluster system according to claim 1, characterized in that: In S4, the expression of the robust virtual control law is: ； In the formula, α pk represents the virtual control law of the designed UAV position loop, α ak represents the virtual control law of the designed UAV attitude loop, α sh represents the virtual control law of the designed unmanned boat, e pk,1 represents the position error of the drone position loop, e ak,1 represents the position error of the UAV attitude ring, e sh,1 represents the position error of the unmanned boat, Λ pk represents the communication parameters of the UAV position loop, Λ ak represents the communication parameters of the UAV attitude loop, Λ sh represents the communication parameters of the unmanned boat, λ pk,1 represents the first fixed time gain parameter of the virtual control law of the UAV position loop, λ pk,2 represents the second fixed time gain parameter of the virtual control law of the UAV position loop, λ ak,1 represents the first fixed time gain parameter of the virtual control law of the UAV attitude loop, λ ak,2 represents the second fixed time gain parameter of the virtual control law of the UAV attitude loop, λ sh,1 represents the first fixed time gain parameter of the virtual control law of the unmanned boat, λ sh,2 represents the second fixed time gain parameter of the virtual control law of the unmanned boat, χ pk,1 represents the time-varying coefficient of the position error transfer function of the UAV position loop, χ ak,1 represents the time-varying coefficient of the position error transfer function of the UAV attitude loop, χ sh,1 represents the time-varying coefficient of the position error conversion function of the unmanned boat, Ф pk,1 Represents the position error conversion function vector of the UAV position loop, Ф ak,1 Represents the position error conversion function vector of the UAV attitude loop, Ф sh,1 represents the position error conversion function vector of the unmanned boat, κ pk,1 represents the position error transfer function bias of the UAV position loop, κ ak,1 represents the position error transfer function bias of the UAV attitude loop, κ sh,1 represents the position error conversion function bias of the unmanned boat, Ξ pk represents the velocity error variable of the UAV position loop, Ξ ak represents the velocity error variable of the UAV attitude loop, Ξ sh represents the speed error variable of the unmanned boat, ∂ pk,1 represents the parameters of the robust H∞ virtual control law for the UAV position loop, ∂ ak,1 represents the parameters of the robust H∞ virtual control law of the UAV attitude loop, ∂ sh,1 represents the parameters of the robust H∞ virtual control law of the unmanned boat, σ represents the first fixed time exponential term parameter, Represents the second fixed time index term parameter.

8. The method for trajectory tracking control of a distributed fixed-time robust formation of a heterogeneous cluster system according to claim 1, characterized in that: In S4, the expression of the distributed fixed-time robust controller is: ； In the formula, u pk represents the distributed fixed-time robust H∞ controller of the designed UAV position loop, u ak represents the distributed fixed-time robust H∞ controller of the designed UAV attitude loop, u sh represents the distributed fixed-time robust H∞ controller of the designed unmanned boat, e pk,2 represents the velocity error of the drone position loop, e ak,2 represents the velocity error of the UAV attitude loop, e sh,2 represents the speed error of the unmanned boat, Λ pk represents the communication parameters of the UAV position loop, Λ ak represents the communication parameters of the UAV attitude loop, Λ sh represents the communication parameters of the unmanned boat, λ pk,3 represents the first fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV position loop, λ pk,4 represents the second fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV position loop, λ ak,3 represents the first fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV attitude loop, λ ak,4 represents the second fixed-time gain parameter of the fixed-time robust H∞ controller of the UAV attitude loop, λ sh,3 represents the first fixed-time gain parameter of the fixed-time robust H∞ controller of the unmanned boat, λ sh,4 represents the second fixed-time gain parameter of the fixed-time robust H∞ controller of the unmanned boat, χ pk,2 represents the time-varying coefficient of the velocity error conversion function of the UAV position loop, χ ak,2 represents the time-varying coefficient of the velocity error transfer function of the UAV attitude loop, χ sh,2 represents the time-varying coefficient of the speed error conversion function of the unmanned boat, Ф pk,2 Represents the velocity error conversion function vector of the UAV position loop, Ф ak,2 Represents the velocity error conversion function vector of the UAV attitude loop, Ф sh,2 represents the speed error conversion function vector of the unmanned boat, κ pk,2 represents the velocity error transfer function bias of the UAV position loop, κ ak,2 represents the velocity error transfer function bias of the UAV attitude loop, κ sh,2 represents the speed error conversion function bias of the unmanned boat, represents the derivative of the virtual control law of the UAV position loop, represents the derivative of the virtual control law of the UAV attitude loop, represents the derivative of the virtual control law of the unmanned boat, A represents the first model parameter of the unmanned boat, B represents the second model parameter of the unmanned boat, represents the first model parameter of the unmanned boat, represents the second model parameter of the unmanned boat, represents the third model parameter of the unmanned boat, represents the velocity variable of the drone position loop, represents the velocity variable of the drone attitude loop, represents the velocity variable of the unmanned boat in the geodetic coordinate system, ∂ pk,2 represents the first parameter of the fixed-time robust H∞ controller of the UAV position loop, ∂ ak,2 represents the first parameter of the fixed-time robust H∞ controller of the UAV attitude loop, ∂ sh,2 represents the first parameter of the fixed-time robust H∞ controller of the unmanned boat, represents the second parameter of the fixed-time robust H∞ controller of the UAV position loop, represents the second parameter of the fixed-time robust H∞ controller of the UAV attitude loop, represents the second parameter of the fixed-time robust H∞ controller of the UAV position loop, σ represents the first fixed-time exponential term parameter, Represents the second fixed time index term parameter.

9. The method for trajectory tracking control of a distributed fixed-time robust formation of a heterogeneous cluster system according to claim 1, characterized in that: In S5, the expression of the dynamic event triggering mechanism is: ； In the formula, u Eg (t) represents the controller updated by the event trigger mechanism, g represents the position loop and attitude loop of the UAV and the position of the UAV, t represents time, represents the control function, t k Indicates the time when the controller is updated, t k+1 represents the next moment when the event triggers the update, R represents a real number set, z g (t) represents the error of the event-triggered controller, represents a time-varying function, o g Indicates the parameters of the event trigger.

10. The method for trajectory tracking control of a distributed fixed-time robust formation of a heterogeneous cluster system according to claim 1, characterized in that: In S5, the expression of the distributed fixed-time robust formation controller under the dynamic event trigger mechanism is: ； In the formula, represents the controller designed under the UAV position loop event trigger mechanism, It represents the controller designed under the UAV attitude loop event trigger mechanism. represents the controller designed under the unmanned boat event trigger mechanism, I3 represents the three-dimensional unit vector, Indicates the trigger condition parameter of the first event of the drone position loop. Indicates the trigger condition parameters of the first event of the drone attitude loop. Indicates the trigger condition parameter of the first event of the unmanned boat. Indicates the trigger condition parameter of the second event of the drone position loop. Indicates the trigger condition parameter of the second event of the drone attitude loop. Indicates the trigger condition parameter of the second event of the unmanned boat, e pk,2 represents the velocity tracking error of the UAV position loop, e ak,2 represents the velocity tracking error of the UAV attitude loop, e sh,2 represents the speed tracking error of the unmanned boat, χ pk,2 represents the time-varying parameter of the velocity error transfer function of the UAV position loop, χ ak,2 represents the time-varying parameter of the velocity error transfer function of the UAV attitude loop, χ sh,2 represents the time-varying parameter of the speed error conversion function of the unmanned boat, u pk represents the distributed fixed-time robust H∞ controller of the designed UAV position loop, u ak represents the distributed fixed-time robust H∞ controller of the designed UAV attitude loop, u sh represents the distributed fixed-time robust H∞ controller of the designed unmanned boat, q pk Indicates the parameters of the event trigger of the drone position loop, q ak Indicates the parameters of the event trigger of the drone attitude loop, q sh Indicates the parameters of the unmanned boat event trigger, J sh represents the rotation matrix, M sh represents the model parameters of the unmanned boat, A represents the first model parameters of the unmanned aerial vehicle, and B represents the second model parameters of the unmanned aerial vehicle.

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