A method for controlling a fixed-wing UAV's scheduled time cooperative path-following formation

Abstract

A method for coordinated path-following formation control of fixed-wing UAVs within a predetermined timeframe is presented, which relates to UAV technology. A coordinated path-following control strategy for multiple UAVs based on predetermined time stability, neural network adaptive control, and preset performance control is proposed. This method enables multiple fixed-wing UAVs to achieve predetermined time convergence of path-following errors and predetermined time-preset performance convergence of control signal tracking errors, even in the face of external disturbances and actuator failures. This method enables highly accurate and fast-response coordinated path-following formation control tasks, while also improving control accuracy and robustness.

Description

Technical Field

[0001] The present invention relates to UAV technology, and in particular to a method for controlling a fixed-wing UAV formation following a coordinated path at a predetermined time. Background Art

[0002] In recent years, drone technology has been increasingly used in modern society, encompassing a wide range of military and civilian applications, including reconnaissance, logistics, crop monitoring, and environmental monitoring. Within these applications, innovations in drone technology are driving the realization of diverse missions. Fixed-wing drones, particularly in remote monitoring and long-duration missions, excel due to their longer endurance and greater flight range. Compared to rotary-wing drones, fixed-wing drones offer greater speed and range, making them better suited to completing complex, long-distance, and extended-duration missions.

[0003] Path following is a commonly used control method for collaborative UAV missions, effectively guiding them along a predetermined path. Path following does not require strict time synchronization, making it more flexible for mission scenarios at different times. This allows UAVs to flexibly arrange their relative geometric positions when collaborating on missions, such as complex tasks like swarm formations. Collaborative path following can be divided into two layers: the upper layer includes the design of path parameter consistency protocols and guidance laws, while the lower layer involves the design of control laws. Among existing guidance methods, line-of-sight guidance is the most widely used, often used for path following and strike missions for aircraft such as UAVs and missiles.

[0004] In many practical applications, fast response and high-precision execution are crucial. Traditional asymptotically stable guidance laws can lead to poor performance in tasks requiring rapid response, and path following accuracy and efficiency cannot be effectively guaranteed. To improve path following accuracy and efficiency, researchers have proposed finite-time and fixed-time guidance laws (S. Wang, et al., “Predictor-based fixed-time LOS path following control of underactuated USV with unknown disturbances,” IEEE Transactions on Intelligent Vehicles, vol. 8, no. 3, pp. 2088–2096, 2023). Finite-time control enables the system to reach a stable state within a limited time, while fixed-time control ensures that the system's convergence time is independent of initial conditions, improving the algorithm's practicality. To further improve convergence speed and facilitate parameter adjustment, predefined-time control (PTC) methods have been proposed and applied to various tasks. Predetermined time control not only makes the system's convergence time independent of initial conditions but also allows the upper bound of the convergence time to be predetermined during the design process, simplifying parameter adjustment and improving system control accuracy and mission reliability. This method has been successfully applied to various control scenarios, particularly in areas such as aircraft attitude control, demonstrating significant advantages.

[0005] In addition to designing path-following algorithms, UAV control systems must also address uncertainties and disturbances during flight, such as sensor errors, external interference, actuator wear, and temperature variations. These uncertainties can significantly impact the control accuracy and stability of UAVs, especially at high speeds and in complex environments. Due to the excellent nonlinear approximation capabilities of neural networks, adaptive control methods based on neural networks have demonstrated excellent uncertainty approximation and compensation for these challenges (S. Ullah, et al., “Neuro-adaptive fast integral terminal sliding mode control design with variable gain robust exact differentiator for under-actuated quadcopter UAV,” ISA transactions, vol. 120, pp. 293–304, 2022). These methods utilize neural networks to approximate the unknown dynamics of the system, thereby improving control accuracy and system robustness. In complex system control tasks, scheduled time control, combined with the nonlinear approximation capabilities of neural networks, provides an efficient and robust solution.

[0006] Furthermore, when designing a control algorithm, it is necessary to consider both the transient and steady-state performance of the algorithm, which are often difficult to balance. To achieve better results, researchers have proposed a method called Prescribed-Performance Control (PPC). This method constructs a control law based on the error system after equivalent transformation, constraining the error within a preset performance envelope. This allows the system to take into account both transient and steady-state performance (W. Gong, et al. “Prescribed-time extended state observer and prescribed performance control of quadrotor UAVs against actuator faults,” Aerospace Science and Technology, vol. 138, p. 108322, 2023).

[0007] In summary, existing technologies still have many shortcomings in areas such as multi-dimensional UAV path following, control system convergence time, and disturbance compensation. Traditional asymptotically stable guidance laws cannot meet the rapid response requirements of missions, and existing methods still rely heavily on system parameters, increasing the complexity of controller design. Furthermore, while existing preset performance control methods can effectively constrain errors, most fail to provide a clear convergence time, limiting their scope for real-time control applications. Summary of the Invention

[0008] The present invention aims to address the aforementioned issues in the prior art by providing a method for coordinated path-following formation control within a predetermined timeframe for fixed-wing UAVs. This method proposes a multi-UAV coordinated path-following control strategy based on predetermined time stability, neural network adaptive control, and preset performance control. This method enables multiple fixed-wing UAVs to achieve predetermined time convergence of path-following errors and predetermined time-preset performance convergence of control signal tracking errors, even in the face of external disturbances and actuator failures. This method enables highly accurate and fast-response coordinated path-following formation control tasks, while also improving control accuracy and robustness.

[0009] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions.

[0010] A method for controlling a fixed-wing UAV formation with a predetermined time and coordinated path following includes the following steps:

[0011] 1) Construct a mathematical model of a fixed-wing UAV. By introducing the residual actuator effectiveness diagonal matrix and the deviation fault vector, the actuator effectiveness degradation and deviation are simulated. The hyperbolic tangent function (HTF) is used to handle physical constraints and define the summary uncertainty.

[0012] 2) Given the desired path for each UAV, the formation configuration is determined. By defining the desired path for each fixed-wing UAV, the UAVs are ensured to accurately follow the predetermined path during the collaborative flight, and constraints are set on path following error, velocity error, and path parameter error.

[0013] 3) designing a predefined time observer, wherein the predefined time observer is used to obtain the virtual leader path parameters and realize path parameter synchronization;

[0014] 4) Based on the virtual leader’s estimation, a path parameter consistency control law is designed to synchronize the path parameters of all UAVs with those of the virtual leader and converge within a predetermined time.

[0015] 5) Design a guidance law with a predetermined time loss of orbit (LOS). The Serret-Frenet coordinate system is introduced to describe the three-dimensional motion of the UAV. In this coordinate system, a three-dimensional guidance law based on adaptive LOS is constructed. A Lyapunov function is constructed to ensure that the UAV converges to the reference path within the predetermined time and that the UAV path following error converges to zero.

[0016] 6) Design a self-organizing neural network estimator to approximate and compensate for uncertainty, and design an input auxiliary system to compensate for the effects of state constraints, ensuring that the control input can stably achieve the control target under the constraints;

[0017] 7) Design a control law with preset performance at a predetermined time so that the tracking error of the UAV for the guidance speed and angle remains within the desired envelope and gradually converges to the specified range over time;

[0018] 8) Solve the control law to obtain the control instructions acting on the fixed-wing UAV and realize the motion control of the UAV.

[0019] In step 1), the specific steps of constructing the mathematical model of the fixed-wing UAV may be:

[0020] First, a collaborative path following task is modeled for n fixed-wing UAVs; the dynamic model of each UAV can be described as follows:

[0021]

[0022] Among them, p i =[x i ,y i ,z i ] T Represents the position vector of the drone in the inertial coordinate system, V i , ψ i and are the speed, yaw angle and pitch angle of the drone, μ i is the roll angle of the drone, m i is the mass of the drone, g is the acceleration due to gravity, T i , L i 、D i Represent the thrust, lift and drag of the UAV respectively; in order to simplify the design process, it is assumed that the lift L i is known; the disturbance terms of the system include δ Vi , δ ψi and They represent unknown input disturbances, and the control input is u i :=[T i ,L i ,μ i ] T , where the thrust T i Controlled by the throttle, lift L i Controlled by the elevator, the roll angle μ i Controlled by ailerons;

[0023] In order to improve the flight safety of cooperative path following of multiple fixed-wing UAVs, the model also considers the effectiveness degradation and deviation failure of the actuators, as expressed as follows:

[0024]

[0025] Among them, u i is the actual application control signal, ui0 is the control input of the design, is the diagonal matrix of the remaining actuator efficiencies, is the deviation fault vector.

[0026] Substituting the actuator failure model into the UAV dynamics model, we can obtain the following dynamics model with actuator failure:

[0027]

[0028] in, Define the virtual control input as At the same time, the aggregate uncertainty is defined as in:

[0029]

[0030] In order to cope with the physical constraints in the actual path following task, the hyperbolic tangent function (HTF) is used to constrain the upper and lower bounds of the virtual control input, and let Δ τi =sat H (τ i0 )-τ i0 , then the constrained input is denoted as τ i =τ i0 +Δ τi , where sat H For the HTF function:

[0031]

[0032] Among them, τ mi represents the absolute value of the upper bound of the constraint, 0<κ mi <1. Then we have:

[0033] In step 2), the expected path of each drone is given and the formation configuration is determined. Specifically, by defining the expected path for each drone, it is ensured that the drones can accurately follow the predetermined path during the collaborative flight process; the reference path of the i-th drone is defined as p ri (s i )=[x ri (s i ),y ri (s i ),z ri (s i )] T , where s i (t) is the path parameter of the UAV, which determines its current target position on the reference path. ri (s i) Taking the derivative we get:

[0034]

[0035] in, is the current tangent vector of the reference path, satisfying ||τ si (s i )||≡1; The tangent angle of the reference path can be calculated using the following formula:

[0036]

[0037] In order to ensure the smoothness and followability of the path, it is assumed that the reference path p ri Have sufficient smoothness and are all bounded quantities, that is, there exists a non-negative constant such that

[0038] The control objective is to design a cooperative path-following controller for multiple fixed-wing UAVs so that the UAVs accurately follow a given time-independent parameterized path within a predetermined time. The specific control objective formula is as follows:

[0039]

[0040] Among them, T cr and T cs is the bounded convergence time designed by the user, ζ pr ,ζ v and ζ s are three small bounded positive constants used to constrain the path following error, velocity error, and path parameter error.

[0041] In step 3), the specific steps of using the predefined time observer to obtain the virtual leader's path parameters and achieve path parameter synchronization can be as follows: in order to achieve the collaborative path following task of multiple UAVs, each UAV must synchronize its path parameters under a distributed communication topology to ensure that the change rate of the path parameters can converge to the change rate of the virtual leader; to this end, a predefined time distributed observer is designed to enable each UAV to obtain the virtual leader's path parameters and their change rate through communication with neighboring UAVs and some nodes connected to the virtual leader;

[0042] For the i-th UAV, the design of the distributed observer is as follows:

[0043]

[0044] in, and are the estimated values ​​of the path parameters and their changing rates of the virtual leader by the i-th UAV, and is the estimation error; through this distributed observer, the UAV can obtain the path information of the virtual leader in a limited communication topology and achieve accurate estimation of the path parameters within the predetermined time.

[0045] In step 4), the path parameters of all UAVs are gradually synchronized with the path parameters of the virtual leader. Specifically, based on the estimation of the virtual leader, the path parameter consistency control law is designed as follows:

[0046]

[0047] Among them, s i is the path parameter of the i-th UAV, Through this consensus control law, the path parameters of all UAVs will gradually synchronize with the path parameters of the virtual leader and converge within the predetermined time.

[0048] In step 5), the predetermined time LOS guidance law is designed. To simplify the design of the three-dimensional collaborative path following controller, the Serret-Frenet coordinate system is introduced to more effectively describe the three-dimensional motion of the UAV. In this coordinate system, a three-dimensional guidance law based on adaptive LOS is constructed. By dynamically adjusting the UAV's path following error, the UAV is ensured to converge to the reference path within the predetermined time.

[0049] The path following error of the i-th UAV relative to the reference path is defined as:

[0050]

[0051] in, For {F i} coordinate system to the inertial coordinate system {I}; To ensure error convergence, construct the Lyapunov function The adaptive linear line of sight (ALOS) three-dimensional guidance law is designed as follows:

[0052]

[0053] Among them, V di is the guidance speed, V i is the current velocity, ψ LOSi and They are the LOS azimuth and elevation angles, which are dynamically adjusted through auxiliary variables to adapt to the actual path error;

[0054] The auxiliary variables are defined as:

[0055]

[0056] By introducing these auxiliary variables, the LOS azimuth and pitch angles of the UAV can be adaptively adjusted to ensure that the path error is gradually reduced;

[0057] In order to ensure the flexible approach process of the UAV on the path, the time-varying line-of-sight distance Δ 2i and Δ 3i To dynamically adjust the guidance angle, it is defined as follows:

[0058]

[0059] Among them, Δ min ,Δ max are the minimum and maximum viewing distances, respectively, K Δ Adjust the gain for viewing distance.

[0060] Through the scheduled time three-dimensional LOS guidance law, it is ensured that the UAV path following error can converge to 0 within the scheduled time, meeting the high-precision path following requirements in UAV collaborative missions.

[0061] In step 6), the self-organizing neural network estimator is designed to approximate and compensate for uncertainty, and the input auxiliary system is designed to compensate for the influence of state constraints. The specific steps may be:

[0062] A self-organizing neural network estimator is used to approximate and compensate for uncertainty, and an auxiliary input system is used to compensate for the effects of state constraints. To improve the control performance of the system, a self-organizing neural network (SSNN) is used to estimate the uncertainty in the system online. The structure of this neural network can be dynamically adjusted according to the operating state of the system, by increasing or decreasing the number of neurons to balance the computational burden and control performance. When the system error is large, the SSNN can increase the network complexity by splitting neurons to enhance the approximation ability. When the system error is small, a pruning strategy is used to reduce invalid neurons to reduce the computational burden.

[0063] Structural adjustment mechanism of neural network:

[0064] 1. Neuron splitting mechanism: When the output of the neural network is small and the approximation effect is poor, it means that the current network structure is not enough to accurately estimate the uncertainty of the system; at this time, the neuron splitting operation will be triggered, and new neurons will be added to enhance the approximation ability of the network; the splitting threshold is set to ι s (e), when When , neurons are split; the parameters of the newly split neurons are:

[0065]

[0066] Among them, xM is the input value, c M and σ M are the center and variance parameters of the selected neurons, c * and σ * is the parameter of the new neuron, W * is the weight of the new neuron;

[0067] 2. Neuron pruning mechanism: When the activation level of some neurons is low, their effect is small, and the computational burden can be reduced by pruning strategies; using attenuation parameters To determine whether pruning is needed, the specific expression is:

[0068]

[0069] Among them, λ d is the attenuation coefficient, ι d (e) is the pruning threshold; when When , the corresponding neurons will be pruned;

[0070] Dynamic threshold adjustment:

[0071] Improve the fixed split threshold ι in the traditional SSNN algorithm s and pruning threshold ι d Based on the design of the proposed strategy, a strategy based on dynamic error adjustment is proposed. When the system error is large, the splitting threshold is increased to allow more neurons to participate in the fitting. When the error is small, the pruning threshold is reduced to quickly prune invalid neurons. The calculation formula of the dynamically adjusted threshold is as follows:

[0072]

[0073] Among them, κ s and κ d Dynamically adjust the coefficients; through this dynamic adjustment strategy, the network can split neurons faster to improve approximation ability, and quickly prune when the error is small to reduce the computational burden;

[0074] Adaptive updates of neural networks:

[0075] In order to further improve the approximation accuracy of SSNN, an adaptive weight update law is designed; let is the optimal weight vector approximated by the neural network, is the weight estimation error, and the adaptive update law of the weight is as follows:

[0076]

[0077] Among them, Γ wV ,λ wV >0 is a normal number, β ViThis will be further explained later; Proj(·) is a projection operator used to ensure that the weight value does not exceed the preset range;

[0078] For the heading angle ψ i and pitch angle , respectively define the optimal weight vector and And order and The adaptive update laws are:

[0079]

[0080] in, β ψi , This will be further explained later; through these update laws, the neural network can adaptively adjust the weights while ensuring approximation accuracy, thereby improving the robustness and accuracy of the control system;

[0081] In order to compensate for the influence of state constraints on system control, an input auxiliary system is designed to ensure that the control input can stably achieve the control target under the existence of constraints; for the speed control of the i-th UAV, the Lyapunov function is first constructed Based on this, the following speed control auxiliary system is constructed:

[0082]

[0083] Among them, κ u is a positive constant, Used to dynamically adjust the control input, Δ τVi Indicates the saturation compensation amount, φ g Is the trigger condition, when |φ Vi |≥φ g When saturation compensation Δ τVi It takes effect, thus effectively dealing with the problem caused by input saturation in speed control;

[0084] Next, similar to the auxiliary system of speed control, the heading angle ψ of the i-th UAV can also be i and pitch angle Design auxiliary systems separately; based on Lyapunov function and The following auxiliary system is obtained:

[0085]

[0086] In the above auxiliary system, and The control inputs used to dynamically adjust the heading angle and pitch angle, Δ τψi and are the corresponding saturation compensation amounts respectively; through these auxiliary systems, the saturation problem of control input can be effectively compensated and the control performance of the UAV under state constraints can be improved.

[0087] In step 7), the preset performance control law for the predetermined time is designed to keep the tracking error of the UAV for the guidance speed and angle within the desired envelope. Specifically, in order to ensure that the fixed-wing UAV can quickly converge and remain within the desired performance range during the path following process, the preset performance control law for the predetermined time is designed. First, in order to ensure that the tracking error is always within the desired envelope, the following preset performance function is designed:

[0088]

[0089] Among them, c ρ1 is the error convergence coefficient, T f is the convergence time, and ε is the final convergence region; the function is to make the error gradually converge to the range of ε over time, while ensuring that the rate of change of the error is controlled; the properties of this function include: ρ(0)=∞, ρ(t)>0, And when t>T f When ρ(t)=ε; the performance envelope obtained by different parameters;

[0090] By defining the tracking error of the current guidance speed and angle of the UAV as e Vi =V i -V di , e ψi =ψ i -ψ di , Introducing the error constraint function h ki To measure the distance of the error relative to a preset performance envelope:

[0091]

[0092] in, Used to determine whether the error meets the constraints; when Y ki When (t)>0, the error is within the preset performance envelope;

[0093] By transforming the error, we get a new variable And process its time derivative to get the transformed error, and take its derivative with respect to time to get:

[0094]

[0095] After obtaining the reconstructed error variables and their derivatives, we begin to design the speed and attitude control laws for each UAV. The Lyapunov function for constructing the speed controller is: Then we get the speed control law of the i-th UAV:

[0096]

[0097] in, is the control gain, is the weight of the neural network used to estimate the combined disturbance in the velocity channel;

[0098] Similarly, for the control of heading angle and pitch angle, the corresponding Lyapunov function is designed and The following heading angle control law and pitch angle control law are obtained respectively:

[0099]

[0100] Through the preset performance control law at the above-mentioned predetermined time, combined with the input auxiliary system and the adaptive update law, it can be ensured that the tracking error of the UAV's guidance speed and angle is always kept within the preset performance envelope within the predetermined time, greatly improving the control accuracy and robustness of the system.

[0101] In step 8), the control law is solved to obtain the control instructions acting on the fixed-wing UAV, thereby realizing the motion control of the UAV. Specifically, the control law is solved to obtain the control instructions acting on the fixed-wing UAV, thereby realizing the motion control of the UAV. After obtaining the control instructions of the guidance speed and angle, the control input u actually applied to the fixed-wing UAV is obtained by calculation. i , thereby realizing the motion control of the UAV;

[0102] First, define Among them, μ i represents the roll angle, and are the control inputs for heading and pitch angle respectively;

[0103] When the guidance instruction τ i After the calculation is completed, the control law is converted into actual UAV control input using the following formula:

[0104]

[0105] Among them, T i is the thrust, L i is the lift, μ i is the roll angle; through these formulas, the control variables such as thrust, lift and roll angle can be calculated according to the output of the control law, thereby actually driving the movement of the UAV so that it can accurately follow the predetermined path and attitude target.

[0106] By designing and solving various control laws, not only can the path following control of fixed-wing UAVs be achieved, but also high control accuracy and robustness can be maintained in complex flight environments.

[0107] Compared with the prior art, the present invention has the following advantages:

[0108] The present invention aims at the problem of collaborative path following control of multiple fixed-wing UAVs, proposes a path following control framework based on predetermined time, and combines adaptive neural networks and distributed consistency control protocols, aiming to solve the limitations of existing technologies in terms of actuator failure, state constraints and path following error convergence time. In view of the high dynamic characteristics of UAVs, the present invention adopts a more flexible control model and method, and ensures that the path following error can converge within the time set in the design stage by introducing a predetermined time control strategy. In addition, the present invention enhances the system's online adaptability and compensation capabilities for uncertainties and external disturbances through the improvement of the adaptive self-organizing neural network, effectively improving the efficiency and robustness of multi-UAV collaborative control. Compared with the existing technology, the present invention has the following significant advantages:

[0109] First: Although existing finite-time or fixed-time path following control algorithms can ensure that the system converges within a finite or fixed time, their convergence time often depends on the initial state, and complex parameter adjustments are required according to specific system characteristics in different application scenarios, which has great limitations in actual use. The present invention is based on the theory of predetermined time stability to ensure that the path following error converges within a pre-set time, and the convergence time is not affected by the initial conditions of the system. In addition, the preset performance controller of the predetermined time can ensure that the control error is always constrained within the performance envelope defined by the user, ensuring that the control system always maintains high accuracy and response speed throughout the entire control process.

[0110] Second: Although the neural networks and robust control methods widely used in existing control systems have shown a certain adaptability in the face of system uncertainties and external disturbances, they usually require the pre-setting of a fixed structure of the neural network, resulting in limited adaptability and approximation capabilities of the network, especially when dealing with dynamic and complex environments. The present invention introduces an adaptive self-organizing neural network that can dynamically adjust the number and structure of neurons according to the size of the system error, thereby achieving online approximation and compensation for uncertainties and external disturbances. When the initial error of the system is large, the neural network can quickly increase the number of neurons to improve the fitting accuracy of the system; when the system error decreases, the number of neurons will decrease, reducing the computational burden and ensuring the optimal performance of the system at different time periods.

[0111] Third: In multi-UAV collaborative tasks, existing distributed control methods can usually only achieve local path parameter consistency, and the convergence time is uncertain. By designing a scheduled time distributed observer and a path parameter consistency protocol, the present invention ensures that under distributed communication conditions, UAVs can achieve rapid synchronization of path parameters within a scheduled time, ensuring that all UAVs can maintain a relatively consistent formation, improving the system's collaborative efficiency and the accuracy of task completion. In addition, by introducing a scheduled time-based consistency control method, the present invention effectively solves the problems of traditional consistency control methods such as slow convergence speed in complex network topologies and susceptibility to communication delays.

[0112] Fourth: Traditional path-following control systems often use simple switching logic or saturation controllers to deal with actuator failures and state constraints, making it difficult to maintain the system's control performance in complex mission environments. The present invention, by combining an input-assisted system with an adaptive control strategy, can effectively address UAV control issues in complex environments such as actuator failure, actuator degradation, and state constraints. This method can ensure that the system maintains high control accuracy and stability under various constraints and disturbances, and has strong robustness, effectively avoiding the problem of decreased control performance caused by actuator failure or state constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0113] Figure 1 This is a framework diagram of the control system proposed in an embodiment of the present invention.

[0114] Figure 2 The figure is a flow chart of the method according to an embodiment of the present invention.

[0115] Figure 3 Schematic diagram of inertial coordinate system and Serret-Frenet coordinate system.

[0116] Figure 4 Schematic diagram of the relationship between the preset performance function and the error convergence coefficient.

[0117] Figure 5 Schematic diagram of the relationship between the preset performance function and convergence time.

[0118] Figure 6 This is the trajectory diagram of the drone in Experiment 1.

[0119] Figure 7 This is the path following error diagram of the drone in Experiment 1.

[0120] Figure 8 This is the trajectory diagram of the drone in Experiment 2.

[0121] Figure 9 This is the path following error diagram of the drone in Experiment 2. DETAILED DESCRIPTION

[0122] To make the objectives, technical solutions, and advantages of the present invention more clearly understood, the following embodiments will be further described with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention. On the contrary, the present invention encompasses any alternatives, modifications, equivalent methods, and solutions made within the spirit and scope of the present invention as defined by the claims.

[0123] With the widespread application of drones in both military and civilian fields, three-dimensional path following tasks for fixed-wing drones are facing increasingly complex operating environments and higher control precision requirements. In practical missions, drones often encounter a variety of uncertainties, including state constraints, external disturbances, and actuator failures. These issues pose significant challenges to the coordinated control of drones. While existing path following control methods can address these issues to a certain extent, they typically rely on system initial conditions or parameter adjustments, making it difficult to ensure error convergence within a predetermined time under complex conditions. Furthermore, in multi-UAV collaborative missions, path parameter consistency and inter-UAV collaborative communication also place higher demands on system stability and control precision. To address these issues, the present invention proposes a collaborative three-dimensional path following control method for multiple fixed-wing drones based on adaptive predefined-time prescribed performance control (PTPPC). This method comprises a guidance law, a distributed observer, a path parameter coordination law, a disturbance estimator, an input assistance system, and a predefined performance control law. This method ensures that the path following error converges within a predetermined time under state constraints, actuator failures, and disturbances, achieving fast and accurate collaborative path following. In this method, a three-dimensional adaptive scheduled time line-of-sight guidance law is designed to ensure that the system can accurately follow a given path within a predetermined time without relying on the initial state conditions; a distributed scheduled time observer and path parameter consistency control law are designed to achieve rapid consistency convergence of path parameters in multi-UAV collaborative tasks, ensuring that the relative geometric positions of UAVs are quickly stabilized; in response to actuator failures and external disturbances, an adaptive neural network estimator is designed based on a self-organizing neural network to online estimate and compensate for system uncertainties and disturbances to ensure high-precision control performance; in response to the impact of state constraints on stability, an input auxiliary system is designed to ensure the stability of the system when state constraints exist; in order to ensure the transient and steady-state convergence performance of the guidance instruction tracking error, a preset performance control law is designed to ensure that the tracking error is constrained within a predetermined performance envelope. In the face of complex actuator failures and state constraints, the input auxiliary system and adaptive control strategy of the present invention can effectively guarantee the stability and robustness of the system, ensuring that the task is successfully completed under restricted conditions. The control system framework proposed in the present invention is as follows: Figure 1 shown.

[0124] The control method and system of the present invention first defines a three-dimensional path model for fixed-wing UAVs and sets a reference path for each UAV. By parameterizing the path, a calculation formula for path parameters and path tangent angles is defined to determine the UAV's direction and position along the path. By designing a timed distributed observer and a consensus protocol, each UAV can synchronize path parameters within a distributed communication topology, thereby ensuring formation coordination.

[0125] On this basis, a time-scheduled 3D line-of-sight guidance law is designed to enable the UAV to converge to a reference path within a predetermined timeframe. An adaptive neural network is used to estimate system uncertainties and external disturbances, thereby improving path-following accuracy. By introducing an adaptive time-scheduled preset performance controller, precise control of path-following errors is achieved, ensuring that the UAV's speed and attitude follow commands within the predetermined timeframe, meeting the system's preset performance requirements.

[0126] Specifically, the system comprises upper-level path parameter consistency control and guidance control, as well as lower-level speed and attitude control. In the upper-level path following, a path parameter consistency protocol ensures the synchronization of path parameters for all drones, keeping them in formation. The guidance law provides velocity and angular velocity commands to the drones based on the current path parameters and the reference path. Based on these commands, the lower-level control, combined with input assistance systems, addresses actuator failures and state constraints, ensuring that the drones accurately follow the guidance commands.

[0127] The purpose of the present invention is to provide a control method and system that can achieve coordinated path following of multiple fixed-wing UAVs under distributed communication conditions, while improving the accuracy and robustness of control. To make the purpose, features, and advantages of the present invention more clear, the present invention is described in detail below with reference to flowcharts and specific implementation methods.

[0128] like Figure 2 As shown, an embodiment of a method for controlling a fixed-wing UAV formation with a predetermined time and coordinated path following according to the present invention includes the following steps:

[0129] Step 1: Construct a mathematical model of the fixed-wing UAV. Define the position and attitude of the UAV, and use position vector, velocity, yaw angle, pitch angle, and roll angle to describe the state of the UAV. Establish a dynamic model, including factors such as mass, gravitational acceleration, thrust, lift, and drag, and consider the actuator failure model. Deal with actuator failures by introducing the residual actuator effectiveness diagonal matrix and deviation fault vector to simulate the effectiveness decline and deviation of the actuator. Define virtual control inputs, use hyperbolic tangent function (HTF) to handle physical constraints, and define summary uncertainty. Specifically:

[0130] Modeling a collaborative path following task for n fixed-wing UAVs. The dynamic model of each UAV can be described as follows:

[0131]

[0132] Among them, p i =[x i ,y i ,z i ] T Represents the position vector of the drone in the inertial coordinate system, V i , ψ i and are the speed, yaw angle and pitch angle of the drone, μ i is the roll angle of the drone, m i is the mass of the drone, g is the acceleration due to gravity, T i , L i 、D i Represent the thrust, lift and drag of the UAV respectively. In order to simplify the design process, it is assumed that the lift L i is known. The disturbance terms of the system include w Vi 、w ψi and They represent unknown input disturbances, and the control input is u i :=[T i ,L i ,μ i ] T , where the thrust T i Controlled by the throttle, lift L i Controlled by the elevator, the roll angle μ i Controlled by ailerons.

[0133] In order to improve the flight safety of cooperative path following of multiple fixed-wing UAVs, the model also considers the effectiveness degradation and deviation failure of the actuators, as expressed as follows:

[0134]

[0135] Among them, u i is the actual application control signal, u i0 is the control input of the design, is the diagonal matrix of the remaining actuator efficiencies, is the deviation fault vector.

[0136] Substituting the actuator failure model into the UAV dynamics model, we can obtain the following dynamics model with actuator failure:

[0137]

[0138] Define the virtual control input as in:

[0139]

[0140] In order to cope with the physical constraints in the actual path following task, the hyperbolic tangent function (HTF) is used instead of the traditional saturation function, and the input τ i =sat H (τ i0 ) can be expressed as:

[0141] τ i =τ i0 +Δ τi

[0142] Define the aggregate uncertainty as in:

[0143]

[0144] Step 2: Given the desired path for each drone, determine the formation configuration. Set a parameterized path for each drone and calculate the path tangent angle. Assume that the reference path is sufficiently smooth and the relevant variables are bounded. Ensure that the drones accurately follow the given parameterized path within the predetermined time, and set constraints on path following error, velocity error, and path parameter error. Specifically:

[0145] The present invention defines an expected path for each UAV to ensure that the UAVs can accurately follow the predetermined path during the collaborative flight process. The reference path of the i-th UAV can be expressed as

[0146]

[0147] Among them, s i (t) represents the path parameter of the UAV, p ri (s i )=[x ri (s i ),y ri (s i ),z ri (s i )] T is the position information in the inertial coordinate system corresponding to the path parameter, τ s (s) is the tangent vector of the reference path, satisfying ||τ s (s)||≡1. The tangent angle of the reference path can be calculated using the following formula:

[0148]

[0149] In order to ensure the smoothness and followability of the path, it is assumed that the reference path p ri Have sufficient smoothness and are all bounded quantities, that is, there exists a non-negative constant such that

[0150] The control objective is to design a collaborative path-following controller for multiple fixed-wing UAVs so that the UAVs accurately follow a given time-independent parameterized path within a predetermined time. The specific control objective formula is as follows:

[0151]

[0152] Among them, T cr and T cs is the bounded convergence time designed by the user, ζ pr ,ζ v and ζ s are three small bounded positive constants used to constrain the path following error, velocity error, and path parameter error.

[0153] Step 3: Use a predefined-time observer to obtain the virtual leader's path parameters. To achieve collaborative path-following tasks for multiple UAVs, each UAV must synchronize its path parameters within a distributed communication topology to ensure that the rate of change of the path parameters converges to that of the virtual leader. To this end, a predefined-time distributed observer is designed, enabling each UAV to obtain the virtual leader's path parameters and their rate of change through communication with neighboring UAVs and some nodes connected to the virtual leader.

[0154] For the i-th UAV, the design of the distributed observer is as follows:

[0155]

[0156] in, and are the estimated values ​​of the path parameters and their changing rates of the virtual leader by the i-th UAV, and is the estimation error. Through this distributed observer, the UAVs can obtain the path information of the virtual leader in a limited communication topology and achieve accurate estimation of the path parameters within the predetermined time.

[0157] Step 4: Design a path parameter consistency control law to synchronize the path parameters of all UAVs with the path parameters of the virtual leader. Based on the virtual leader's estimation, the path parameter consistency control law is designed as follows:

[0158]

[0159] Among them, s iis the path parameter of the i-th UAV, Through this consensus control law, the path parameters of all UAVs will gradually synchronize with the path parameters of the virtual leader and converge within the predetermined time.

[0160] Step 5: Design the predetermined time LOS guidance law to make the UAV path following error converge to 0. In order to simplify the design of the three-dimensional collaborative path following controller, the present invention introduces the Serret-Frenet coordinate system, such as Figure 3 As shown in the figure, in order to more effectively describe the three-dimensional motion of the UAV. i} and {F i} respectively represent the inertial coordinate system, the body coordinate system of the i-th UAV and the Serret-Frenet coordinate system, p di is the current target position of the i-th UAV, e 1i , e 2i and e 3i Represent the longitudinal, lateral and vertical following errors of the UAV, Δ i is the sight distance of the i-th UAV, ψ LOS and Denote the yaw and pitch angles of the line of sight of the i-th UAV, respectively. In this coordinate system, a three-dimensional guidance law based on adaptive LOS is constructed to ensure that the UAV converges to the reference path within a predetermined time by dynamically adjusting the path following error of the UAV.

[0161] The path following error of the i-th UAV relative to the reference path is defined as:

[0162]

[0163] in, For {F i} coordinate system to the inertial coordinate system {I}. To ensure error convergence, construct the Lyapunov function The adaptive linear line of sight (ALOS) three-dimensional guidance law is designed as follows:

[0164]

[0165]

[0166] Among them, γ1>0 is an adjustable parameter, T cg is the predetermined convergence time, N=12n+3 is a constant, n is the number of drones, V di is the guidance speed, V i is the current velocity, ψ LOSi and They are the LOS azimuth and elevation angles, which are dynamically adjusted through auxiliary variables to adapt to the actual path error.

[0167] The auxiliary variables are defined as:

[0168]

[0169] Among them, γ2>0 is an adjustable parameter, T cg The scheduled convergence time.

[0170] By introducing these auxiliary variables, the LOS azimuth and pitch angles of the UAV can be adaptively adjusted to ensure that the path error is gradually reduced.

[0171] In order to ensure the flexible approach process of the UAV on the path, the time-varying line-of-sight distance Δ 2i and Δ 3i To dynamically adjust the guidance angle, it is defined as follows:

[0172]

[0173] where Δ min ,Δ max are the minimum and maximum viewing distances, respectively, K Δ Adjust the gain for viewing distance.

[0174] Through the scheduled time three-dimensional LOS guidance law, it is ensured that the UAV path following error can converge to 0 within the scheduled time, meeting the high-precision path following requirements in UAV collaborative missions.

[0175] Step 6: Approximate and compensate for uncertainty through a self-organizing neural network estimator, and compensate for the effects of state constraints through input auxiliary systems. In order to improve the control performance of the system, the present invention uses a self-organizing neural network (SSNN) to perform online estimation of the uncertainty in the system. The structure of the neural network can be dynamically adjusted according to the operating state of the system, by increasing or decreasing the number of neurons to balance the computational burden and control performance. When the system error is large, the SSNN can increase the network complexity by splitting neurons to enhance the approximation ability; when the system error is small, the pruning strategy is used to reduce invalid neurons to reduce the computational burden.

[0176] Structural adjustment mechanism of neural network:

[0177] 1. Neuron splitting mechanism: When the output of the neural network is small and the approximation effect is poor, it means that the current network structure is not sufficient to accurately estimate the uncertainty of the system. At this time, the neuron splitting operation will be triggered, and new neurons will be added to enhance the approximation ability of the network. Set the splitting threshold to ιs (e), when When , the neuron splits. The parameters of the newly split neurons are:

[0178]

[0179] Among them, x M is the input value, c M and σ M are the center and variance parameters of the selected neurons, c * and σ * is the parameter of the new neuron, W * is the weight of the new neuron.

[0180] 2. Neuron pruning mechanism: When the activation level of some neurons is low, their effect is small, and the computational burden can be reduced by pruning strategies. Use the attenuation parameter To determine whether pruning is needed, the specific expression is:

[0181]

[0182] Among them, λ d is the attenuation coefficient, ι d (e) is the pruning threshold. , the corresponding neurons will be pruned.

[0183] Dynamic threshold adjustment:

[0184] The present invention improves the fixed splitting threshold ι in the traditional SSNN algorithm s and pruning threshold ι d Based on the design of the proposed method, a strategy based on dynamic error adjustment is proposed. When the system error is large, the splitting threshold is increased to allow more neurons to participate in the fitting; when the error is small, the pruning threshold is reduced to quickly prune invalid neurons. The formula for calculating the dynamically adjusted threshold is as follows:

[0185]

[0186] Among them, κ s and κ d is the dynamic adjustment coefficient. Through this dynamic adjustment strategy, the network can split neurons faster to improve the approximation ability, and quickly prune when the error is small to reduce the computational burden.

[0187] Adaptive updates of neural networks:

[0188] In order to further improve the approximation accuracy of SSNN, an adaptive weight update law is designed. is the optimal weight vector approximated by the neural network, is the weight estimation error, and the adaptive update law of the weight is as follows:

[0189]

[0190] Among them, Γ wV ,λ wV >0 is a normal number, β Vi This will be further explained later. Proj(·) is a projection operator used to ensure that the weight value does not exceed the preset range.

[0191] For the heading angle ψ i and pitch angle The optimal weight vectors are defined respectively. and And order and The adaptive update laws are:

[0192]

[0193] in, β ψi , This will be further explained later. Through these update laws, the neural network can adaptively adjust the weights while ensuring the approximation accuracy, thereby improving the robustness and accuracy of the control system.

[0194] In order to compensate for the influence of state constraints on system control, the present invention designs an input auxiliary system to ensure that the control input can stably achieve the control target under the existence of constraints. For the speed control of the i-th UAV, first construct the Lyapunov function Based on this, the following speed control auxiliary system is constructed:

[0195]

[0196] Among them, k u is a positive constant, Used to dynamically adjust the control input, Δ τVi Indicates the saturation compensation amount, φ g Is the trigger condition, when |φ Vi |≥φ g When saturation compensation Δ Vi The problem of input saturation in speed control is effectively handled. Next, similar to the auxiliary system of speed control, the heading angle ψ of the i-th UAV can also be i and pitch angle Design auxiliary systems separately. Based on Lyapunov function and The following auxiliary system is obtained:

[0197]

[0198] In the above auxiliary system, and The control inputs used to dynamically adjust the heading angle and pitch angle, Δ τψi and These auxiliary systems can effectively compensate for the saturation problem of control input and improve the control performance of the UAV under state constraints.

[0199] Step 7: Design a preset performance control law for a predetermined time to keep the UAV's tracking error for the guidance speed and angle within the performance envelope. To ensure that the fixed-wing UAV can quickly converge and maintain the desired performance range during the path following process, a preset performance control law for a predetermined time is designed. First, to ensure that the tracking error is always within the desired envelope, the following preset performance function is designed:

[0200]

[0201] Among them, c ρ1 is the error convergence coefficient, T f is the convergence time, and ε is the final convergence region. The function is to make the error gradually converge to the range of ε over time, while ensuring that the rate of change of the error is controlled. The properties of this function include: ρ(0)=∞, ρ(t)>0, And when t>T f When ρ(t)=ε. The performance envelope obtained by different parameters is as follows Figure 4 and 5 shown. Figure 4 This is a schematic diagram of the relationship between the preset performance function and the error convergence coefficient, showing how the preset performance function changes with the change of the error convergence coefficient. By comparing the performance envelope under different error convergence coefficients, the impact of the error convergence coefficient on system performance is revealed. Figure 5 This is a schematic diagram of the relationship between the preset performance function and the convergence time. It shows the relationship between the preset performance function and the convergence time. By comparing the performance envelope under different convergence times, it reveals how the convergence time affects the convergence speed and final convergence state of the system.

[0202] By defining the tracking error of the current guidance speed and angle of the UAV as e Vi =V i -V di , e ψi =ψ i -ψ di , Introducing the error constraint function h ki To measure the distance of the error relative to a preset performance envelope:

[0203]

[0204] in, Used to determine whether the error meets the constraints. ki When (t)>0, the error is within the preset performance envelope.

[0205] By transforming the error, we get a new variable And process its time derivative to get the transformed error, and take its derivative with respect to time to get:

[0206]

[0207] After obtaining the reconstructed error variables and their derivatives, we begin to design the speed and attitude control laws for each UAV. The Lyapunov function for constructing the speed controller is: Then we get the speed control law of the i-th UAV:

[0208]

[0209] in, is the control gain, are the weights of the neural network used to estimate the combined disturbance in the velocity channel.

[0210] Similarly, for the control of heading angle and pitch angle, the corresponding Lyapunov function is designed and The following heading angle control law and pitch angle control law are obtained respectively:

[0211]

[0212] Through the preset performance control law at the above-mentioned predetermined time, combined with the input auxiliary system and the adaptive update law, it can be ensured that the tracking error of the UAV's guidance speed and angle is always kept within the preset performance envelope within the predetermined time, greatly improving the control accuracy and robustness of the system.

[0213] Step 8: Solve the control law and apply it to the drone. Based on the guidance speed and angle control instructions, calculate the actual thrust, lift, roll angle and other control variables applied to the drone. Drive the drone's motion through control inputs, making it accurately follow the predetermined path and attitude target, thus achieving drone motion control. Specifically:

[0214] By solving the designed control law, the control instructions acting on the fixed-wing UAV are obtained to realize the motion control of the UAV. After obtaining the control instructions of the guidance speed and angle, the control input u actually applied to the fixed-wing UAV is obtained by calculation. i , to achieve motion control of the UAV. Definition Among them, μi represents the roll angle, and are the control inputs for heading and pitch angle respectively.

[0215] When the guidance instruction τ i After the calculation is completed, the control law is converted into actual UAV control input using the following formula:

[0216]

[0217] Among them, T i is the thrust, L i is the lift, μ i is the roll angle. Through these formulas, control variables such as thrust, lift, and roll angle can be calculated based on the output of the control law, thereby actually driving the movement of the UAV so that it accurately follows the predetermined path and attitude target.

[0218] By designing and solving various control laws, the present invention can not only realize path following control of fixed-wing UAVs, but also maintain high control accuracy and robustness in complex flight environments.

[0219] Simulation experiment:

[0220] To verify the effectiveness of the proposed multi-UAV collaborative path-following control system, we conducted a series of simulation experiments using MATLAB. The simulation environment included five fixed-wing UAVs. The control system parameters and initial conditions are detailed in Tables 1, 2, and 3. For brevity, only the flight trajectories and corresponding path-following error convergence for Experiments 1 and 2 are presented.

[0221] In Experiment 1, the initial positions and velocities of the five drones are set as shown in Table 1. The target flight speed of each drone is V di =30m / s, the velocity change rate is constrained by τ 1i ∈[-τ 1max ,τ 1max ], angular velocity change rate τ 2i ∈[-τ 2max ,τ 2max ], and τ 3i ∈[-τ 3max ,τ 3max ], where τ 1max =30m / s 2 , τ 2max =5π / 9,τ 3max =5π / 6.

[0222] Table 1 Parameter settings

[0223]

[0224] Table 2 Initial conditions of Experiment 1

[0225]

[0226] Table 3 Initial conditions of Experiment 2

[0227]

[0228] Figure 6 and Figure 8 The flight trajectories of the five drones in Experiment 1 and Experiment 2 are shown respectively. Different colors are used to distinguish the trajectories of different drones. The dotted line is the target path and the solid line is the actual flight trajectory. It can be seen that the trajectories p1 to p5 of all drones within the predetermined time closely follow the predetermined expected path p d1 ~p d5 , demonstrating that the drone system has excellent path tracking capabilities. The drones maintained a stable formation during flight, demonstrating effective coordinated control. The different colored curves represent the trajectories of the five drones. It can be observed that the path errors gradually converged to near zero during flight. The trajectories showed no significant deviation or jitter, further verifying the stability and control accuracy of the drone system.

[0229] Figure 7 and Figure 9 The graph shows the convergence of the path-following errors in the x, y, and z directions for five drones from two experiments. The path-following errors for all drones converged quickly to near zero within the predetermined time, verifying the effectiveness of the control law. The excellent convergence speed and stability of the errors in the x, y, and z directions demonstrate the excellent control performance of the drone system in all three dimensions.

[0230] The simulation results from the above examples demonstrate that the collaborative path-following control system designed by the present invention can effectively control multiple drones to collaboratively complete path-following tasks. In Experiments 1 and 2, the path-following errors of each drone converged to near zero within the predetermined time, verifying the effectiveness and robustness of the control law proposed by the present invention.

[0231] The above embodiments are only preferred embodiments of the present invention and should not be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent of the present invention.

Claims

1. A method for controlling a fixed-wing UAV formation with a predetermined time and coordinated path following, characterized in that The following steps are involved: 1) Construct a mathematical model of a fixed-wing UAV. By introducing the residual actuator effectiveness diagonal matrix and the deviation fault vector, the actuator effectiveness degradation and deviation are simulated. The hyperbolic tangent function is used to handle physical constraints and define the summary uncertainty. 2) Given the desired path for each UAV, the formation configuration is determined. By defining the desired path for each fixed-wing UAV, the UAVs are ensured to accurately follow the predetermined path during the collaborative flight, and constraints are set on path following error, velocity error, and path parameter error. 3) Design a predefined time observer and use it to obtain the virtual leader path parameters to achieve path parameter synchronization; 4) Based on the virtual leader’s estimation, a path parameter consistency control law is designed to synchronize the path parameters of all UAVs with those of the virtual leader and converge within a predetermined time. 5) Design a guidance law with a predetermined time loss of orbit (LOS). The Serret-Frenet coordinate system is introduced to describe the three-dimensional motion of the UAV. In this coordinate system, a three-dimensional guidance law based on adaptive LOS is constructed. A Lyapunov function is constructed to ensure that the UAV converges to the reference path within the predetermined time and that the UAV path following error converges to zero. 6) Design a self-organizing neural network estimator to approximate and compensate for uncertainty, and design an input auxiliary system to compensate for the effects of state constraints, ensuring that the control input can stably achieve the control target under the constraints; 7) Design a control law with preset performance at a predetermined time so that the tracking error of the UAV for the guidance speed and angle remains within the desired envelope and gradually converges to the specified range over time; 8) Solve the control law to obtain the control instructions acting on the fixed-wing UAV and realize the motion control of the UAV.

2. A method for controlling a fixed-wing UAV formation with a predetermined time and coordinated path following according to claim 1, characterized in that In step 1), the specific steps of constructing the mathematical model of the fixed-wing UAV are: Model the collaborative path following task of n fixed-wing UAVs; the dynamic model of each UAV is described as follows: Among them, p i =[x i ,y i ,z i ] T Represents the position vector of the drone in the inertial coordinate system, V i , ψ i and are the speed, yaw angle and pitch angle of the drone, μ i is the roll angle of the drone, m i is the mass of the drone, g is the acceleration due to gravity, T i 、L i 、D i They represent the thrust, lift and drag of the UAV respectively; assuming the lift L i is known; the disturbance terms of the system include w Vi 、w ψi and They represent unknown input disturbances, and the control input is u i :=[T i ,L i ,μ i ] T , where the thrust T i Controlled by the throttle, lift L i Controlled by the elevator, the roll angle μ i Controlled by ailerons; In order to improve the flight safety of cooperative path following of multiple fixed-wing UAVs, the model also considers the effectiveness degradation and deviation failure of the actuators, as expressed as follows: Among them, u i is the actual application control signal, u i0 is the control input of the design, is the diagonal matrix of the remaining actuator efficiencies, is the deviation fault vector; Substituting the actuator failure model into the UAV dynamics model, we obtain the following dynamics model with actuator failure: in, Define the virtual control input as At the same time, the aggregate uncertainty is defined as in: In order to cope with the physical constraints in the actual path following task, the hyperbolic tangent function HTF is used to constrain the upper and lower bounds of the virtual control input, and let Δ τi =sat H (τ i0 )-τ i0 , then the constrained input is denoted as τ i =τ i0 +Δ τi , where sat H For the HTF function: where τ mi represents the absolute value of the upper bound of the constraint, make Then we have:

3. A method for controlling a fixed-wing UAV formation with a predetermined time and coordinated path following according to claim 1, characterized in that In step 2), the expected path of each drone is given and the formation configuration is determined. Specifically, by defining the expected path for each drone, it is ensured that the drones can accurately follow the predetermined path during the collaborative flight process; the reference path of the i-th drone is defined as p ri (s i )=[x ri (s i ),y ri (s i ),z ri (s i )] T , where s i (t) is the path parameter of the UAV, which determines its current target position on the reference path. ri (s i ) and we get: in, is the current tangent vector of the reference path, satisfying ||τ si (s i )||≡1; The tangent angle of the reference path is calculated using the following formula: In order to ensure the smoothness and followability of the path, it is assumed that the reference path p ri Have sufficient smoothness and are all bounded quantities, that is, there exists a non-negative constant such that The control objective is to design a cooperative path-following controller for multiple fixed-wing UAVs so that the UAVs accurately follow a given time-independent parameterized path within a predetermined time. The specific control objective formula is as follows: Among them, T cr and T cs is the bounded convergence time designed by the user, ζ pr ,ζ v and ζ s are three small bounded positive constants used to constrain the path following error, velocity error, and path parameter error.

4. A method for controlling a fixed-wing UAV formation with a predetermined time and coordinated path following according to claim 1, characterized in that In step 3), the specific steps of using a predefined time observer to obtain the virtual leader's path parameters and achieve path parameter synchronization are as follows: To achieve the collaborative path following task of multiple UAVs, each UAV must synchronize its path parameters under a distributed communication topology to ensure that the rate of change of the path parameters can converge to the rate of change of the virtual leader; to this end, a predefined time distributed observer is designed so that each UAV can obtain the virtual leader's path parameters and their rate of change through communication with neighboring UAVs and some nodes connected to the virtual leader; For the i-th UAV, the design of the distributed observer is as follows: in, and are the estimated values ​​of the path parameters and their changing rates of the virtual leader by the i-th UAV, and is the estimation error; through this distributed observer, the UAV can obtain the path information of the virtual leader in a limited communication topology and achieve accurate estimation of the path parameters within the predetermined time.

5. A method for controlling a fixed-wing UAV formation with a predetermined time and coordinated path following according to claim 1, characterized in that In step 4), the path parameters of all UAVs are gradually synchronized with the path parameters of the virtual leader. Specifically, based on the estimation of the virtual leader, the path parameter consistency control law is designed as follows: Among them, s i is the path parameter of the i-th UAV, Through this consensus control law, the path parameters of all UAVs will gradually synchronize with the path parameters of the virtual leader and converge within the predetermined time.

6. A method for controlling a fixed-wing UAV formation with a predetermined time and coordinated path following according to claim 1, characterized in that In step 5), the predetermined time LOS guidance law is designed. To simplify the design of the three-dimensional collaborative path following controller, the Serret-Frenet coordinate system is introduced to more effectively describe the three-dimensional motion of the UAV. In this coordinate system, a three-dimensional guidance law based on adaptive LOS is constructed. By dynamically adjusting the UAV's path following error, the UAV is ensured to converge to the reference path within the predetermined time. The path following error of the i-th UAV relative to the reference path is defined as: in, For {F i } coordinate system to the inertial coordinate system {I}; To ensure error convergence, construct the Lyapunov function The adaptive linear line-of-sight ALOS three-dimensional guidance law is designed as follows: Among them, V di is the guidance speed, V i is the current velocity, ψ LOSi and They are the LOS azimuth and elevation angles, which are dynamically adjusted through auxiliary variables to adapt to the actual path error; The auxiliary variables are defined as: By introducing these auxiliary variables, the LOS azimuth and pitch angles of the UAV are adaptively adjusted to ensure that the path error is gradually reduced; In order to ensure the flexible approach process of the UAV on the path, the time-varying line-of-sight distance Δ 2i and Δ 3i To dynamically adjust the guidance angle, it is defined as follows: where Δ min ,Δ max are the minimum and maximum viewing distances, respectively, K Δ Adjust gain for viewing distance; Through the scheduled time three-dimensional LOS guidance law, it is ensured that the UAV path following error can converge to 0 within the scheduled time, meeting the high-precision path following requirements in UAV collaborative missions.

7. A method for controlling a fixed-wing UAV formation with a predetermined time and coordinated path following according to claim 1, characterized in that In step 6), the self-organizing neural network estimator is designed to approximate and compensate for uncertainty, and the input auxiliary system is designed to compensate for the influence of state constraints. The specific steps are: Uncertainty is approximated and compensated for using a self-organizing neural network estimator, while the impact of state constraints is compensated by inputting auxiliary systems. To improve the system's control performance, a self-organizing neural network (SSNN) is used to estimate uncertainty online. The structure of this neural network can be dynamically adjusted according to the system's operating state, balancing computational burden and control performance by increasing or decreasing the number of neurons. When the system error is large, the SSNN increases network complexity by splitting neurons to enhance approximation capabilities. When the system error is small, a pruning strategy is used to reduce ineffective neurons to reduce the computational burden. Structural adjustment mechanism of neural network:

1. Neuron splitting mechanism: When the output of the neural network is small and the approximation effect is poor, it means that the current network structure is not enough to accurately estimate the uncertainty of the system; at this time, the neuron splitting operation will be triggered, and new neurons will be added to enhance the approximation ability of the network; the splitting threshold is set to ι s (e), when When , neurons are split; the parameters of the newly split neurons are: Among them, x M is the input value, c M and σ M are the center and variance parameters of the selected neurons, c * and σ * is the parameter of the new neuron, W * is the weight of the new neuron; 2. Neuron pruning mechanism: When the activation level of some neurons is low, their effect is small, and the computational burden is reduced by pruning strategies; using attenuation parameters To determine whether pruning is needed, the specific expression is: Among them, λ d is the attenuation coefficient, ι d (e) is the pruning threshold; when When , the corresponding neurons will be pruned; Dynamic threshold adjustment: Improve the fixed split threshold ι in the traditional SSNN algorithm s and pruning threshold ι d Based on the design of the proposed method, a strategy based on dynamic error adjustment is proposed. When the system error is large, the splitting threshold is increased to allow more neurons to participate in the fitting. When the error is small, the pruning threshold is reduced to quickly prune invalid neurons. The calculation formula of the dynamically adjusted threshold is as follows: Among them, κ s and κ d Dynamically adjust the coefficients; through this dynamic adjustment strategy, the network can split neurons faster to improve approximation ability, and quickly prune when the error is small to reduce the computational burden; Adaptive updates of neural networks: In order to further improve the approximation accuracy of SSNN, an adaptive weight update law is designed; let is the optimal weight vector approximated by the neural network, is the weight estimation error, and the adaptive update law of the weight is as follows: Among them, Γ wV ,λ wV >0 is a normal number, β Vi This will be further explained later; Proj(·) is a projection operator used to ensure that the weight value does not exceed the preset range; For the heading angle ψ i and pitch angle , respectively define the optimal weight vector and And order and The adaptive update laws are: in, β ψi , This will be further explained later; through these update laws, the neural network can adaptively adjust the weights while ensuring approximation accuracy, thereby improving the robustness and accuracy of the control system; In order to compensate for the influence of state constraints on system control, an input auxiliary system is designed to ensure that the control input can stably achieve the control target under the existence of constraints; for the speed control of the i-th UAV, the Lyapunov function is first constructed Based on this, the following speed control auxiliary system is constructed: Among them, k u is a positive constant, Used to dynamically adjust the control input, Δ τVi Indicates the saturation compensation amount, φ g Is the trigger condition, when |φ Vi |φ g When saturation compensation Δ τVi It takes effect, thus effectively dealing with the problem caused by input saturation in speed control; Similar to the auxiliary system of speed control, it also provides the heading angle ψ of the i-th UAV i and pitch angle Design auxiliary systems separately; based on Lyapunov function and The following auxiliary system is obtained: In the above auxiliary system, and The control inputs used to dynamically adjust the heading angle and pitch angle, Δ τψi and are the corresponding saturation compensation amounts respectively; these auxiliary systems can effectively compensate for the saturation problem of the control input and improve the control performance of the UAV under state constraints.

8. A method for controlling a fixed-wing UAV formation with a predetermined time and coordinated path following according to claim 1, characterized in that In step 7), the preset performance control law for the predetermined time is designed to keep the tracking error of the UAV for the guidance speed and angle within the desired envelope. Specifically, in order to ensure that the fixed-wing UAV can quickly converge and remain within the desired performance range during the path following process, the preset performance control law for the predetermined time is designed. First, in order to ensure that the tracking error is always within the desired envelope, the following preset performance function is designed: Among them, c ρ1 is the error convergence coefficient, T f is the convergence time, and ε is the final convergence region; the function is to make the error gradually converge to the range of ε over time, while ensuring that the rate of change of the error is controlled; the properties of this function include: ρ(0)=∞, ρ(t)>0, And when t>T f When ρ(t)=ε; the performance envelope obtained by different parameters; By defining the tracking error of the current guidance speed and angle of the UAV as e Vi =V i -V di , e ψi =ψ i -ψ di , Introducing the error constraint function h ki To measure the distance of the error relative to a preset performance envelope: in, Used to determine whether the error meets the constraints; when Y ki When (t)>0, the error is within the preset performance envelope; By transforming the error, we get a new variable And process its time derivative to obtain the transformed error, and take its derivative with respect to time to obtain: After obtaining the reconstructed error variables and their derivatives, we begin to design the speed and attitude control laws for each UAV. The Lyapunov function for constructing the speed controller is: Then we get the speed control law of the i-th UAV: in, is the control gain, is the weight of the neural network used to estimate the combined disturbance in the velocity channel; Similarly, for the control of heading angle and pitch angle, the corresponding Lyapunov function is designed and The following heading angle control law and pitch angle control law are obtained respectively: Through the preset performance control law at the above-mentioned predetermined time, combined with the input auxiliary system and the adaptive update law, it is ensured that the tracking error of the UAV's guidance speed and angle is always kept within the preset performance envelope within the predetermined time, greatly improving the control accuracy and robustness of the system.

9. A method for controlling a fixed-wing UAV formation with a predetermined time and coordinated path following as claimed in claim 1, characterized in that In step 8), the control law is solved to obtain the control instructions acting on the fixed-wing UAV, thereby realizing the motion control of the UAV. Specifically, the control law is solved to obtain the control instructions acting on the fixed-wing UAV, thereby realizing the motion control of the UAV. After obtaining the control instructions of the guidance speed and angle, the control input u actually applied to the fixed-wing UAV is obtained by calculation. i , thereby realizing the motion control of the UAV; First, define Among them, μ i represents the roll angle, and are the control inputs for heading and pitch angle respectively; When the guidance instruction τ i After the calculation is completed, the control law is converted into actual UAV control input using the following formula: Among them, T i is the thrust, L i is the lift, μ i is the roll angle; through these formulas, the thrust, lift and roll angle are calculated according to the output of the control law, thereby actually driving the movement of the UAV so that it accurately follows the predetermined path and attitude target.

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