Fixed-wing unmanned aerial vehicle predetermined time cooperative path following formation control method

Abstract

The invention discloses a fixed-wing unmanned aerial vehicle predetermined time cooperative path following formation control method, and relates to an unmanned aerial vehicle technology. A multi-unmanned aerial vehicle cooperative path following control strategy based on preset time stability, neural network adaptive control and preset performance control is provided; according to the method, the multiple fixed-wing unmanned aerial vehicles can realize preset time convergence of path following errors and preset time preset performance convergence of control signal tracking errors under the conditions of external disturbance and actuator faults, so that a high-precision and quick-response cooperative path following formation control task is completed; and meanwhile, the control precision and robustness are improved.

Description

Technical Field

[0001] The invention relates to unmanned aerial vehicle technology, and in particular to a method for controlling a fixed-wing unmanned aerial vehicle to follow a coordinated path at a predetermined time. Background Art

[0002] In recent years, drone technology has been increasingly used in modern society, involving military and civilian fields such as reconnaissance, logistics, crop monitoring, and environmental monitoring. In these applications, innovations in drone technology have promoted the realization of a variety of tasks, especially in remote monitoring and long-term flight missions, where fixed-wing drones are particularly prominent due to their longer endurance and larger flight range. Compared with rotary-wing drones, fixed-wing drones have higher speeds and ranges, and can better complete long-distance, long-term, and complex tasks.

[0003] In cooperative missions of UAVs, path following is a commonly used control method that can effectively guide UAVs to fly along a predetermined path. Path following does not require strict time synchronization, which makes the method more flexible in mission scenarios at different times, allowing UAVs to flexibly arrange relative geometric positions when performing cooperative missions, such as complex tasks such as group formations. Collaborative path following can be divided into two layers: the upper layer includes the design of path parameter consistency protocol and guidance law, and the lower layer involves the design of control law. Among the existing guidance methods, line of sight guidance is widely used and is often used in path following, strike and other tasks of aircraft such as UAVs and missiles.

[0004] In many practical application scenarios, fast response and high-precision execution are crucial. Traditional asymptotically stable guidance laws may cause the system to perform poorly in tasks that require fast response, and the accuracy and efficiency of path following cannot be effectively guaranteed. In order to improve the accuracy and efficiency of path following, researchers 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 can make the system reach a stable state within a limited time, while fixed-time control ensures that the convergence time of the system does not depend on the initial conditions, which improves the practicality of the algorithm. In order to further improve the convergence speed and facilitate parameter adjustment, the predefined-time control (PTC) method was proposed and applied to a variety of tasks. Predetermined time control not only makes the convergence time of the system independent of the initial conditions, but also can predetermine the upper limit of the convergence time during the design process, thereby simplifying the parameter adjustment process and improving the control accuracy of the system and the reliability of task execution. This method has been successfully applied to a variety of control scenarios, especially in the field of aircraft attitude control, showing its significant advantages.

[0005] For the control system of UAV, in addition to the design of path following, it is also necessary to deal with uncertainties and disturbances during flight, such as sensor errors, external interference, actuator wear, and temperature changes. These uncertainties will significantly affect the control accuracy and stability of UAVs, especially in high-speed flight and complex environments. Because neural networks have good nonlinear approximation capabilities, when facing the above problems, adaptive control methods based on neural networks show good uncertainty approximation and compensation effects (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 use neural networks to approximate the unknown dynamics of the system, thereby improving control accuracy and system robustness. In the control tasks of complex systems, scheduled time control combined with the nonlinear approximation capabilities of neural networks provides an efficient and robust solution.

[0006] In addition, when designing a control algorithm, it is necessary to consider both the transient and steady-state performance of the algorithm, and these indicators are often difficult to take into account. In order to achieve better results, researchers proposed a preset performance control (PPC) method, which constructs a control law based on the error system after equivalent transformation, constrains the error within a preset performance envelope, and enables 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] Based on the above analysis, the existing technology still has many shortcomings in terms of multi-dimensional path following of UAVs, control system convergence time, and compensation for disturbances. The traditional asymptotically stable guidance law cannot meet the requirements of the task for rapid response, and the existing methods still rely heavily on system parameters, increasing the complexity of controller design. At the same time, although the existing preset performance control methods can effectively constrain errors, most of them fail to provide a clear convergence time, limiting the scope of their real-time control applications. Summary of the invention

[0008] The purpose of the present invention is to provide a method for controlling a fixed-wing UAV coordinated path following formation within a predetermined time in view of the above problems existing in the prior art. A multi-UAV coordinated path following control strategy based on predetermined time stability, neural network adaptive control and preset performance control is proposed. This method can enable multiple fixed-wing UAVs to achieve the predetermined time convergence of path following errors and the predetermined time preset performance convergence of control signal tracking errors in the face of external disturbances and actuator failures, thereby completing high-precision and fast-response coordinated path following formation control tasks, while improving the accuracy and robustness of control.

[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 to follow a coordinated path at a predetermined time, comprising the following steps:

[0011] 1) Construct a mathematical model of fixed-wing UAV, simulate the effectiveness decline and deviation of actuators by introducing the residual actuator effectiveness diagonal matrix and deviation fault vector, use hyperbolic tangent function (HTF) to deal with physical constraints, and define summary uncertainty;

[0012] 2) Given the expected path of each UAV, the formation configuration is determined; by defining the expected path for each fixed-wing UAV, it is ensured that the UAV can accurately follow the predetermined path during the collaborative flight, and the constraints of path following error, speed error and path parameter error are set;

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

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

[0015] 5) Design a predetermined time LOS guidance law, introduce the Serret-Frenet coordinate system to describe the three-dimensional motion of the UAV, and construct a three-dimensional guidance law based on adaptive LOS in this coordinate system. Construct a Lyapunov function to ensure that the UAV converges to the reference path within the predetermined time and the UAV path following error converges to 0;

[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 impact of state constraints to ensure that the control input can stably achieve the control target under the existence of constraints;

[0017] 7) Design a preset performance control law 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 and obtain the control instructions acting on the fixed-wing UAV to achieve 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, the collaborative path following task of n fixed-wing UAVs is modeled; 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 , 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 the 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 decline and deviation failure of the actuator, and the expression is 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. 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 drone 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 by 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 are non-negative constants such that

[0038] The control objective is to design a collaborative path following controller for multiple fixed-wing UAVs so that the UAVs can 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 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 path parameters and realize path parameter synchronization are as follows: in order to realize the collaborative path following task of multiple UAVs, each UAV must realize the synchronization of path parameters under the distributed communication topology to ensure that the change rate of the path parameters can converge to the change rate of the virtual leader; for this purpose, a predefined time distributed observer is designed so that each UAV can obtain the path parameters and their change rate of the virtual leader 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 change 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 drones 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:

[0046]

[0047] Among them, s i is the path parameter of the i-th UAV, Through this consistency 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. In order 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, and the path following error of the UAV is dynamically adjusted to ensure that the UAV converges 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 angle 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 values ​​of the sight distance, 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 tasks.

[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] The uncertainty is approximated and compensated by a self-organizing neural network estimator, and the impact of state constraints is compensated by input auxiliary systems. 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 the neural network can be dynamically adjusted according to the operating state of the system, and the number of neurons can be increased or decreased 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 invalid neurons are reduced through pruning strategies 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 , the neuron splits; 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 through 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 neuron will be pruned;

[0070] Dynamic Threshold Adjustment:

[0071] Improvement of the fixed splitting 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 split 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 Dynamic adjustment 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 Update of Neural Networks:

[0075] 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:

[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 The optimal weight vectors are defined respectively. 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 the 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 normal number, 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 amount 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 so that the tracking error of the UAV for the guidance speed and angle is kept 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, 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 how far the error is 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 began to design the speed and attitude control laws of each UAV. The Lyapunov function of the speed controller is constructed as follows: 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 guidance speed and angle of the UAV 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, so as to realize the motion control of the UAV. Specifically, the control law designed is solved to obtain the control instructions acting on the fixed-wing UAV, so as 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 , thereby realizing the motion control of the drone;

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

[0103] When the guidance command 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, so as to actually drive 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 the prior art 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 introduces a predetermined time control strategy to ensure that the path following error can converge within the time set in the design stage. 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 the collaborative control of multiple UAVs. Compared with the prior art, the present invention has the following significant advantages:

[0109] First: Although the 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 preset 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 a high accuracy and response speed throughout the 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 uncertainty 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, which can dynamically adjust the number and structure of neurons according to the size of the system error, thereby achieving online approximation and compensation for uncertainty 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. The present invention ensures that under distributed communication conditions, UAVs can achieve rapid synchronization of path parameters within a predetermined time by designing a predetermined time distributed observer and a path parameter consistency protocol, ensuring that all UAVs can maintain a relatively consistent formation, thereby improving the system's collaborative efficiency and the accuracy of task completion. In addition, by introducing a consistency control method based on a predetermined time, the present invention effectively solves the problems of slow convergence speed and susceptibility to communication delays in traditional consistency control methods under complex network topologies.

[0112] Fourth: Traditional path following control systems often use simple switching logic or saturation controllers when dealing with actuator failures and state constraints, which makes it difficult to maintain the control performance of the system in complex mission environments. The present invention, by combining input auxiliary systems and adaptive control strategies, can effectively deal with the control problems of drones 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 a variety of constraints and disturbances, and has strong robustness, which can effectively avoid 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 a control system proposed in an embodiment of the present invention.

[0114] Figure 2 The figure is a flow chart of the method described in the 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 the 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] Fig. 9 This is the path following error diagram of the drone in Experiment 2. DETAILED DESCRIPTION

[0122] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following embodiments will further illustrate the present invention in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. On the contrary, the present invention covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present invention as defined by the claims.

[0123] With the widespread application of UAVs in military and civilian fields, the three-dimensional path following tasks of fixed-wing UAVs face increasingly complex operating environments and higher control accuracy requirements. In actual tasks, UAVs often encounter a variety of uncertain factors, including state constraints, external disturbances, and actuator failures, all of which pose huge challenges to the coordinated control of UAVs. Although the existing path following control methods can solve these problems to a certain extent, they usually rely on the initial conditions or parameter adjustments of the system, and it is difficult to ensure the error convergence within the predetermined time under complex conditions. In addition, in multi-UAV collaborative tasks, the consistency of path parameters and the collaborative communication between UAVs also put forward higher requirements on the stability and control accuracy of the system. In view of these problems, the present invention proposes a multi-fixed-wing UAV collaborative three-dimensional path following control method based on adaptive predefined-time prescribed performance control (PTPPC), which consists of a guidance law, a distributed observer, a path parameter coordination law, a disturbance estimator, an input auxiliary system, and a preset performance control law. It can ensure that the path following error converges within the predetermined time under the conditions of state constraints, actuator failures and disturbances, and realize 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; 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 the UAVs are rapidly 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 command 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 and ensure 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 of a fixed-wing UAV and sets a reference path for each UAV. By parameterizing the path, the calculation formula of the path parameters and the path tangent angle is defined to determine the direction and position of the UAV along the path. By designing a distributed observer and a consistency protocol with a predetermined time, each UAV can synchronize the path parameters under a distributed communication topology, thereby ensuring the coordination of the formation.

[0125] On this basis, a three-dimensional line-of-sight guidance law with a predetermined time is designed, so that the UAV converges to the reference path within the predetermined time, and estimates the uncertainty and external disturbance in the system through an adaptive neural network, thereby improving the accuracy of path following. By introducing an adaptive preset time preset performance controller, the path following error is precisely controlled to ensure that the speed and attitude following instructions of the UAV meet the preset performance requirements of the system within the predetermined time.

[0126] Specifically, the system includes upper-level path parameter consistency control and guidance control, as well as lower-level speed and attitude control. In the upper-level path following, the path parameter consistency protocol ensures that the path parameters of all drones are synchronized to keep them in formation. The guidance law provides speed and angular velocity instructions to the drones based on the current path parameters and the reference path. The lower-level control, based on these instructions and combined with the input auxiliary system, handles the actuator failures and state constraint problems of the drones to ensure that the drones accurately follow the guidance instructions.

[0127] The purpose of the present invention is to provide a control method and system that can realize the coordinated path following of multiple fixed-wing UAVs under distributed communication conditions, while improving the control accuracy and robustness. In order to make the purpose, features and advantages of the present invention clearer, the present invention is described in detail below in conjunction with a flow chart and specific implementation methods.

[0128] like Figure 2 As shown, an embodiment of a method for controlling a fixed-wing UAV to coordinate a path following formation at a predetermined time according to the present invention comprises 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, gravity acceleration, thrust, lift, and drag, and consider the actuator failure model. Deal with actuator failures, and simulate the effectiveness degradation and deviation of the actuator by introducing the residual actuator effectiveness diagonal matrix and deviation fault vector. Define virtual control inputs, use hyperbolic tangent function (HTF) to handle physical constraints, and define summary uncertainty. Specifically:

[0130] The collaborative path following task of n fixed-wing UAVs is modeled. 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 , 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. 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 the unknown input disturbances, and the control input is u i :=[T i ,L i ,μ i ] T , where the thrust T i Controlled by 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 decline and deviation failure of the actuator, and the expression is 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. 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 expected path of 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 drone accurately follows the given parameterized path within the predetermined time, and set constraints on path following error, speed error, and path parameter error. Specifically:

[0145] The present invention defines an expected path for each drone to ensure that the drones can accurately follow the predetermined path during the collaborative flight. The reference path of the i-th drone 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 by 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 are non-negative constants such that

[0150] The control objective is to design a collaborative path following controller for multiple fixed-wing UAVs so that the UAVs can 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 s are three small bounded positive constants used to constrain the path following error, velocity error, and path parameter error.

[0153] Step 3: Use the predefined time observer to obtain the path parameters of the virtual leader. In order to realize the collaborative path following task of multiple UAVs, each UAV must synchronize the path parameters under the 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 so that each UAV can obtain the path parameters and their change rate of the virtual leader 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 change 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.

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

[0158]

[0159] Among them, s iis the path parameter of the i-th UAV, Through this consistency 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 a 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 drone. 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 Respectively represent the longitudinal, lateral and vertical following errors of the UAV, Δ i is the line of sight distance of the i-th UAV, ψ LOS and Respectively represent the yaw angle and pitch angle of the line of sight of the i-th UAV. 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 the 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] where γ 1 >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, γ 2 >0 is an adjustable parameter, T cg is the scheduled convergence time.

[0170] By introducing these auxiliary variables, the LOS azimuth and pitch angle 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 values ​​of the sight distance, 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 tasks.

[0175] Step 6: Approximate and compensate for uncertainty through a self-organizing neural network estimator, and compensate for the impact 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 estimate the uncertainty in the system online. 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, SSNN can increase the network complexity by splitting neurons to enhance the approximation ability; when the system error is small, the invalid neurons are reduced through pruning strategies 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 ι s (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 through 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 The design of the dynamic error adjustment strategy 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 dynamic adjustment threshold calculation formula 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 Update 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, the Lyapunov function is first constructed. Based on this, the following speed control auxiliary system is constructed:

[0195]

[0196] Among them, k u is a normal number, 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 amount Δ Vi The problem of input saturation in speed control can be effectively solved. Next, similar to the auxiliary system of speed control, the heading angle ψ of the i-th UAV can also be calculated. iand pitch angle Design auxiliary systems respectively. 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 tracking error of the UAV on the guidance speed and angle within the performance envelope. To ensure that the fixed-wing UAV can quickly converge and remain within the desired performance range during the path following process, design a preset performance control law for a predetermined time. First, in order to ensure that the tracking error is always within the desired envelope, design the following preset performance function:

[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 It is a schematic diagram of the relationship between the preset performance function and the error convergence coefficient, which shows 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 influence of the error convergence coefficient on the system performance is revealed. Figure 5 It is a schematic diagram of the relationship between the preset performance function and the convergence time, showing 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 =ψi -ψ di , Introducing the error constraint function h ki To measure how far the error is relative to a preset performance envelope:

[0203]

[0204] in, Used to determine whether the error satisfies 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 began 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 guidance speed and angle of the UAV is always kept within the preset performance envelope within the predetermined time, which greatly improves the control accuracy and robustness of the system.

[0213] Step 8: Solve the control law and apply it to the UAV. According to the control instructions of the guidance speed and angle, calculate the control quantities such as thrust, lift and roll angle actually applied to the UAV. Drive the movement of the UAV through control input so that it can accurately follow the predetermined path and attitude target to achieve UAV 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 drone. Definition Among them, μ i represents the roll angle, and They are the control inputs for heading and pitch angle respectively.

[0215] When the guidance command 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 Through these formulas, 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.

[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] In order to verify the effectiveness of the multi-UAV cooperative path following control system proposed in the present invention, the present invention uses MATLAB to conduct a series of simulation experiments on the control scheme. The simulation environment includes five fixed-wing UAVs, and the control system parameters and initial conditions are detailed in Table 1, Table 2, and Table 3. For the sake of simplicity, only the flight trajectories of Experiment 1 and Experiment 2 and the corresponding path following error convergence are shown.

[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 / s2 , 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 trajectory of all drones within the predetermined time p 1 ~p 5 All closely follow the predetermined expected path p d1 ~p d5 , indicating that the UAV system has good path tracking ability. The UAVs maintain a stable formation during the flight, indicating that the coordinated control between them is good. The curves of different colors represent the trajectories of the five UAVs. It can be observed that the path error gradually converges to near zero during the flight. There is no obvious deviation or jitter in the trajectory, which further verifies the stability and control accuracy of the UAV system.

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

[0230] Through the simulation results of the above embodiments, the collaborative path following control system designed by the present invention can effectively control multiple drones to collaboratively complete the path following task. In Experiment 1 and Experiment 2, the path following error of each drone can converge 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 cannot 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 present invention.

Claims

1. A method for controlling a fixed-wing UAV to follow a coordinated path at a predetermined time, characterized in that The following steps are involved: 1) Construct a mathematical model of a fixed-wing UAV, simulate the effectiveness degradation and deviation of the actuator by introducing the residual actuator effectiveness diagonal matrix and the deviation fault vector, use the hyperbolic tangent function to handle the physical constraints, and define the summary uncertainty; 2) Given the expected path of each UAV, the formation configuration is determined; by defining the expected path for each fixed-wing UAV, it is ensured that the UAV can accurately follow the predetermined path during the collaborative flight, and the constraints of path following error, speed error and path parameter error are set; 3) Design a predefined time observer, use the predefined time observer to obtain the virtual leader path parameters, and realize path parameter synchronization; 4) Based on the estimation of the virtual leader, a path parameter consistency control law is designed to synchronize the path parameters of all UAVs with the path parameters of the virtual leader step by step and converge within the predetermined time; 5) Design a predetermined time LOS guidance law, introduce the Serret-Frenet coordinate system to describe the three-dimensional motion of the UAV, and construct a three-dimensional guidance law based on adaptive LOS in this coordinate system. Construct a Lyapunov function to ensure that the UAV converges to the reference path within the predetermined time and the UAV path following error converges to 0; 6) Design a self-organizing neural network estimator to approximate and compensate for uncertainty, and design an input auxiliary system to compensate for the impact of state constraints to ensure that the control input can stably achieve the control target under the existence of constraints; 7) Design a preset performance control law 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 and obtain the control instructions acting on the fixed-wing UAV to achieve motion control of the UAV.

2. A method for controlling a fixed-wing UAV formation with a predetermined time coordinated path following as claimed in claim 1, characterized in that In step 1), the specific steps of constructing the mathematical model of the fixed-wing UAV are: The collaborative path following task of n fixed-wing UAVs is modeled; 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 , 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 drone respectively; assuming the lift L i is known; the disturbance terms of the system include w Vi 、w ψi and They represent the unknown input disturbances, and the control input is u i :=[T i ,L i ,μ i ] T , where the thrust T i Controlled by 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 decline and deviation failure of the actuator, and the expression is 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, the following dynamics model with actuator failure is obtained: 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. 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 coordinated path following as claimed in 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 drone 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 ) is derived to obtain: 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 by 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 are non-negative constants such that The control objective is to design a collaborative path following controller for multiple fixed-wing UAVs so that the UAVs can 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 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 coordinated path following as claimed in claim 1, characterized in that In step 3), the specific steps of using the predefined time observer to obtain the virtual leader path parameters and realize path parameter synchronization are as follows: in order to realize the collaborative path following task of multiple UAVs, each UAV must realize the synchronization of path parameters under the distributed communication topology to ensure that the change rate of the path parameters can converge to the change rate of the virtual leader; for this purpose, a predefined time distributed observer is designed so that each UAV can obtain the path parameters and their change rate of the virtual leader 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 change 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 coordinated path following as claimed in claim 1, characterized in that In step 4), the path parameters of all drones 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: Among them, s i is the path parameter of the i-th UAV, Through this consistency control law, the path parameters of all UAVs will be gradually synchronized 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 coordinated path following as claimed in claim 1, characterized in that In step 5), the predetermined time LOS guidance law is designed. In order 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, and the path following error of the UAV is dynamically adjusted to ensure that the UAV converges 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 values ​​of the sight distance, 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 tasks.

7. A method for controlling a fixed-wing UAV formation with a predetermined time coordinated path following as claimed in 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: The uncertainty is approximated and compensated by the self-organizing neural network estimator, and the influence of the state constraint is compensated by the input auxiliary system. In order to improve the control performance of the system, the self-organizing neural network SSNN is used to estimate the uncertainty in the system online. The structure of the neural network can be dynamically adjusted according to the operating state of the system, and the number of neurons can be increased or decreased to balance the computational burden and control performance. When the system error is large, the SSNN increases the network complexity by splitting the neurons to enhance the approximation ability. When the system error is small, the invalid neurons are reduced through the pruning strategy 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 , the neuron splits; 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 through pruning strategies; use the attenuation parameter 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 neuron will be pruned; Dynamic Threshold Adjustment: Improvement of the fixed splitting 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 split 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 Dynamic adjustment 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 Update of Neural Networks: 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: 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 The optimal weight vectors are defined respectively. 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 the 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 normal number, 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 amount 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 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 coordinated path following as claimed in claim 1, characterized in that In step 7), the preset performance control law for the predetermined time is designed so that the tracking error of the UAV for the guidance speed and angle is kept 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, 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 how far the error is 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 get the transformed error, and take its derivative with respect to time to get: After obtaining the reconstructed error variables and their derivatives, we began to design the speed and attitude control laws of each UAV. The Lyapunov function of the speed controller is constructed as follows: 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 guidance speed and angle of the UAV 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 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, so as to realize the motion control of the UAV. Specifically, the control law designed is solved to obtain the control instructions acting on the fixed-wing UAV, so as 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 , thereby realizing the motion control of the drone; First, define Among them, μ i represents the roll angle, and They are the control inputs for heading and pitch angle respectively; When the guidance command 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 can accurately follow the predetermined path and attitude target.

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