A Fixed-Time Neural Adaptive Formation Control Method for Multi-UAVs Resistant to Aerodynamic Disturbances

Abstract

This invention relates to the field of multi-UAV cooperative control technology and discloses a fixed-time neural adaptive formation control method for multi-UAVs to resist aerodynamic disturbances. A hierarchical controller architecture is constructed, with an outer loop of a distributed reference generation and safety tracking controller and an inner loop of a fixed-time terminal sliding mode controller with a cubic non-singular smooth switching mechanism. A fixed-time sliding mode surface with a cubic non-singular smooth switching mechanism is configured to achieve deterministic convergence. An adaptive RBF neural network is used to actively compensate for aerodynamic disturbances, and a safety mechanism based on obstacle functions is combined to constrain the UAV states within a safe set. Lyapunov analysis verifies the fixed-time stability of the system. Simulation results of six UAVs in formation show that the proposed method improves convergence speed by 29.6%, exhibits better robustness, and can achieve safe, accurate, and fast formation control of multiple UAVs under complex aerodynamic disturbances.

Description

Technical Field

[0001] This invention relates to the field of multi-UAV cooperative control technology, specifically a fixed-time neural adaptive formation control method for multi-UAVs that resists aerodynamic disturbances. Background Technology

[0002] Multi-UAV (UAV) systems, composed of multiple UAVs, exhibit significant advantages in flexibility, fault tolerance, and robustness, supporting various application scenarios such as aerial surveillance, collaborative transport, and electronic warfare. In the cooperative control of multi-UAV systems, formation control is the core and the foundation for critical tasks requiring strict spatial coordination.

[0003] Significant progress has been made in the field of multi-drone formation control over the past few decades, with mainstream strategies including behavior-based methods, virtual structure methods, and leader-follower methods. However, these traditional strategies can only achieve asymptotic stability, meaning that the formation error converges to zero as time approaches infinity, making them unsuitable for time-critical tasks such as military interception and emergency rescue.

[0004] While existing finite-time control techniques can ensure convergence within a finite time, their settling time depends on the system's initial state. When the initial formation error is large, the convergence time is too long, making it impossible to pre-plan a precise mission schedule. The emergence of fixed-time stability theory overcomes this dependency. Its settling time is limited by a constant value independent of the initial conditions. This characteristic is crucial for multi-UAV systems, ensuring deterministic convergence time under large initial disturbances.

[0005] Furthermore, in real-world flight environments, UAVs are inevitably affected by complex coupled aerodynamic uncertainties such as gusts, wake vortices, and unmodeled aerodynamic coefficients. These uncertainties are nonlinear, state-dependent, and coupled between roll, pitch, and yaw channels, posing significant challenges to controller design. Neural networks, due to their general approximation capabilities, are used to compensate for unmodeled dynamics. However, existing neural network-based control techniques suffer from a key flaw in approximation effectiveness: most methods rely on the strong assumption that the UAV state always remains within a predefined compact set. Without explicit constraints, intense maneuvers or large disturbances during formation flight can drive the state outside the compact set, causing neural network approximation failure and even system instability.

[0006] In summary, existing multi-UAV formation control technologies face the combined effects of aerodynamic uncertainties and strict time window constraints. There is an urgent need for a formation control method that can achieve deterministic convergence, effectively compensate for aerodynamic disturbances, and ensure the effectiveness of neural network approximation. Summary of the Invention

[0007] The purpose of this invention is to provide a fixed-time neural adaptive formation control method for multiple unmanned aerial vehicles (UAVs) that is resistant to aerodynamic disturbances, so as to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, the present invention provides the following technical solution: a fixed-time neural adaptive formation control method for multiple unmanned aerial vehicles (UAVs) to resist aerodynamic disturbances, comprising the following steps:

[0009] Step S1: Construct a hierarchical control architecture consisting of an outer ring formation controller and an inner ring attitude / velocity controller; determine the three-dimensional nonlinear dynamic model and spatially varying wind field model of the multi-UAV system; define the multi-UAV formation control objective as making the tracking error converge quickly from any initial conditions to a small neighborhood of the origin and strictly constrained to a predefined constant safety region.

[0010] Step S2: Design the outer ring formation controller, including distributed reference generation and robust tracking controller design: First, based on the distributed consensus algorithm of the communication topology, define the position offset of the UAV relative to the reference trajectory and the binary restraint parameters, design a distributed update protocol to generate the local reference position of each UAV, then define the local tracking error, and design the virtual velocity control input as a combination of linear stable term, neural adaptive term, robust damping term and obstacle safety term. Among them, the neural adaptive term uses a radial basis function neural network to approximate the unknown lumped uncertainty and derives the adaptive update law of the weight matrix. The robust damping term handles the residual approximation error of the neural network. The obstacle safety term constructs the obstacle potential field based on the improved obstacle function and defines the safety boundary through the decay specified performance function.

[0011] Step S3, perform kinematic inversion and dynamic reconstruction: First, convert the virtual control vector in the inertial coordinate system output by the outer loop into airspeed, track tilt angle and track azimuth angle commands for use by the inner loop tracking. Then, reconstruct the six-degree-of-freedom nonlinear particle dynamics of the UAV into a control affine form, determine the state vector, inner loop control input, and derive the system matrix and control efficiency matrix.

[0012] Step S4: Design the inner loop attitude / velocity controller, using an improved non-singular fixed-time sliding mode control protocol with a cubic non-singular smooth switching mechanism. First, define the inner loop tracking error vector, design the sliding mode surface vector, construct the cubic non-singular smooth switching mechanism, define the improved nonlinear function, configure the dynamic exponent and derive the correlation coefficient to ensure the continuity of the function value and its first derivative at the switching boundary, and that the second derivative of the nonlinear term disappears at the origin. Then, differentiate the sliding mode surface, use a preset reaching law, and combine it with the reconstructed control affine dynamics to derive the inner loop control law, ensuring the realizability of the controller.

[0013] Step S5: Based on the above hierarchical control architecture, realize fixed-time neural adaptive formation control of multiple UAVs under coupled aerodynamics and spatiotemporal wind disturbances.

[0014] Preferably, the three-dimensional nonlinear dynamic model of the UAV in step S1 is a six-degree-of-freedom nonlinear particle dynamic model, which defines the position of the UAV in the inertial coordinate system, with the Y-axis as the vertical axis, and includes parameters related to airspeed, track tilt angle, track azimuth angle, UAV mass, gravitational acceleration, environmental wind disturbance, generalized longitudinal control force, generalized maneuvering force, and aerodynamic drag. The aerodynamic drag is modeled as an expression that includes air density, reference wing area, and zero-lift drag coefficient.

[0015] Preferably, the spatially varying wind field model in step S1 is a deterministic spatiotemporal wind field model. Combining spatial shear and vortex-like coupling, the wind disturbance vector is modeled as a harmonic background field dependent on the UAV's spatial coordinates, including average wind speed, spatial oscillation amplitude, and characteristic wavelength parameters along each axis. The vertical component includes nonlinear cross-coupling terms to simulate vortex-induced updrafts.

[0016] Preferably, the outer-loop formation controller in step S2 consists of two coupling layers, one of which generates a local reference trajectory using the communication topology. A distributed estimator, and a driver for drone positioning. Security tracking A robust tracking controller, in which the distributed estimator is designed for the first... The drone generates a local reference position. ,make , indicating the first The drone relative to the reference trajectory The specified position offset, where It is the dimension symbol. This indicates that the variable is Vehicular drones and drones The expected relative formation vector between them is defined as , , , They represent drones With drones The relative distances in the x / y / z directions satisfy:

[0017]

[0018] Further define binary restraint parameters ,in Indicates the first The drone can directly access the reference trajectory ,but The distributed update protocol is designed as follows:

[0019]

[0020] in Let the adjacency weight be , and This represents the coupling gain.

[0021] Preferably: the robust tracking controller of the outer loop formation controller in step S2 defines the local tracking error as based on the generated reference signal. Next, input the virtual speed control. Designed as a combination of five items:

[0022] .

[0023] in, It is a linearly stable term. For neural adaptive terms, For robust damping term and For obstacle safety items, This is the update protocol for the local reference trajectory.

[0024] Preferably, the kinematic inversion and dynamic reconstruction process in step S3 specifically includes obtaining the virtual control vector from the outer ring formation controller. This represents the desired velocity vector in the inertial coordinate system, which is then converted into airspeed, track inclination, and track azimuth commands. The inverse kinematic logic is derived as follows:

[0025]

[0026]

[0027]

[0028] The affine dynamics reconstruction reconstructs the aforementioned nonlinear particle dynamics of the UAV into a control affine form, specifically by letting the state vector be... The dynamics can be expressed as:

[0029]

[0030] in, Indicating the inner-loop control input, the system matrix... (Representing undriven internal dynamics) and control performance matrix The derivation is as follows:

[0031]

[0032] in, Represents a diagonal matrix. , , These represent airspeed, track inclination, and track azimuth, respectively. Indicates the first The quality of the drone For gravitational acceleration, the term The environmental wind disturbance in the inertial coordinate system is represented in the dynamic equations. This represents the generalized longitudinal control force (including engine thrust and active braking force), while and Represents generalized mobility (related to lift and lateral force components), term This indicates aerodynamic drag.

[0033] Preferably, the design process of the inner loop attitude / velocity controller in step S4 is as follows: First, the inner loop tracking error vector is defined as... ,in Next, an improved non-singular fixed-time sliding mode control protocol with a three-stage smoothing mechanism is designed, and the sliding mode surface vector is... Designed as follows:

[0034]

[0035] in, For sliding mode surface gain, a nonlinear function and Configured to when the system reaches the sliding surface Ensures fixed-time convergence; for the th The improved nonlinear function is defined as having elements:

[0036]

[0037]

[0038] in For a user-defined smaller boundary layer constant, dynamic exponent and Configured to switch based on error magnitude:

[0039]

[0040] The basic index satisfies and ,coefficient and Through rigorous derivation, the function value is strictly guaranteed. and its first derivative (Jacobi matrix) at the switching boundary Continuity at point:

[0041] .

[0042] Compared with the prior art, the beneficial effects of this invention are as follows:

[0043] Deterministic convergence and smooth control: A fixed-time sliding mode mechanism with a cubic nonsingular smooth switching law is proposed, which solves the singularity or chattering problem of traditional fixed-time methods and ensures the global nonsingularity and smoothness of the control input. The formation error can converge to a small neighborhood of the origin within a user-defined time, and the convergence time is strictly independent of the initial position, achieving deterministic convergence and facilitating accurate task planning.

[0044] Adaptive aerodynamic disturbance compensation: The radial basis function (RBF) neural network is used to approximate the unknown coupled aerodynamics online. The weights are updated in real time through an adaptive adjustment law. No precise model knowledge and offline training are required. It can effectively suppress the influence of aerodynamic disturbances such as wind shear and wake vortex, and the compensation effect is good.

[0045] Ensuring flight safety and neural network effectiveness: Integrating a hierarchical safety mechanism based on an improved obstacle function, the formation error is strictly constrained within a predetermined performance envelope, preventing the system state from escaping the effective approximation domain of the neural network. This achieves collision-free formation keeping and ensures flight safety, while also mathematically verifying the effectiveness of the neural network approximation and avoiding system instability caused by approximation failure.

[0046] Improved robustness and convergence speed: Lyapunov analysis confirms the fixed-time stability of the system. Simulation results of a formation of six UAVs show that compared with the traditional method, the convergence speed of this method is improved by 29.6%, and the formation can still be well maintained under strong wind disturbances with spatial variations, demonstrating better robustness. Attached Figure Description

[0047] Figure 1 This is a flowchart of the method of the present invention;

[0048] Figure 2 This is a curve showing the wind field changing over time.

[0049] Figure 3 This is a graph showing the variation of the wind field vector along a preset trajectory.

[0050] Figure 4 A formation trajectory diagram of 6 drones;

[0051] Figure 5 To control the curve of how the quantity changes over time;

[0052] Figure 6This is an envelope diagram showing the relationship between the position error of the UAV and the preset performance function.

[0053] Explanation of reference numerals in the attached figures: Figure 4 In the diagram, Reference represents the virtual navigator trajectory, while UAV1-UAV6 represent the trajector trajectories of six follower drones. Figure 6 In the diagram, Envelope is the preset performance envelope, and Bound... (t) represents the safety boundary, and UAV1-UAV6 represent the positional errors of the six UAVs. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] Example

[0056] Please see Figure 1 The illustrated method for fixed-time neural adaptive formation control of multiple unmanned aerial vehicles (UAVs) to resist aerodynamic disturbances includes the following steps:

[0057] Step S1: Construct a hierarchical control architecture consisting of an outer ring formation controller and an inner ring attitude / velocity controller; determine the three-dimensional nonlinear dynamic model and spatially varying wind field model of the multi-UAV system; define the multi-UAV formation control objective as making the tracking error converge quickly from any initial conditions to a small neighborhood of the origin and strictly constrained to a predefined constant safety region.

[0058] Step S2: Design the outer ring formation controller, including distributed reference generation and robust tracking controller design: First, based on the distributed consensus algorithm of the communication topology, define the position offset of the UAV relative to the reference trajectory and the binary restraint parameters, design a distributed update protocol to generate the local reference position of each UAV, then define the local tracking error, and design the virtual velocity control input as a combination of linear stable term, neural adaptive term, robust damping term and obstacle safety term. Among them, the neural adaptive term uses a radial basis function neural network to approximate the unknown lumped uncertainty and derives the adaptive update law of the weight matrix. The robust damping term handles the residual approximation error of the neural network. The obstacle safety term constructs the obstacle potential field based on the improved obstacle function and defines the safety boundary through the decay specified performance function.

[0059] Step S3, perform kinematic inversion and dynamic reconstruction: First, convert the virtual control vector in the inertial coordinate system output by the outer loop into airspeed, track tilt angle and track azimuth angle commands for use by the inner loop tracking. Then, reconstruct the six-degree-of-freedom nonlinear particle dynamics of the UAV into a control affine form, determine the state vector, inner loop control input, and derive the system matrix and control efficiency matrix.

[0060] Step S4: Design the inner loop attitude / velocity controller, using an improved non-singular fixed-time sliding mode control protocol with a cubic non-singular smooth switching mechanism. First, define the inner loop tracking error vector, design the sliding mode surface vector, construct the cubic non-singular smooth switching mechanism, define the improved nonlinear function, configure the dynamic exponent and derive the correlation coefficient to ensure the continuity of the function value and its first derivative at the switching boundary, and that the second derivative of the nonlinear term disappears at the origin. Then, differentiate the sliding mode surface, use a preset reaching law, and combine it with the reconstructed control affine dynamics to derive the inner loop control law, ensuring the realizability of the controller.

[0061] Step S5: Based on the above hierarchical control architecture, realize fixed-time neural adaptive formation control of multiple UAVs under coupled aerodynamics and spatiotemporal wind disturbances.

[0062] A three-dimensional nonlinear dynamic model of a UAV is considered, consisting of... A multi-UAV system consisting of 3 UAVs is configured to operate in a three-dimensional workspace. drones The motion is controlled by six-degree-of-freedom (6-DOF) nonlinear particle dynamics, making The position of the UAV in the inertial coordinate system is represented by the Y-axis, which is defined as the vertical axis (height). The state equation is described as follows:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] Here, , , These represent airspeed, track inclination, and track azimuth, respectively. Indicates the first The quality of the drone For gravitational acceleration, the term The environmental wind disturbance in the inertial coordinate system is represented in the dynamic equations. This represents the generalized longitudinal control force (including engine thrust and active braking force), while and Represents generalized mobility (related to lift and lateral force components), term The aerodynamic drag is represented by the following model:

[0070]

[0071] in air density, For reference wing area, It is a zero-lift drag coefficient.

[0072] To rigorously evaluate the system's robustness, a deterministic spatiotemporal wind field model is employed. This model combines spatial shear and eddy-like coupling, configured to simulate complex flight environments, with wind disturbance vectors... Depends on the spatial coordinates of the UAV It is modeled as a harmonic background field:

[0073]

[0074]

[0075]

[0076] in, , and (for These represent the average wind speed, spatial oscillation amplitude, and characteristic wavelength along their respective axes, specifically the vertical component. It includes a nonlinear cross-coupling term configured to simulate complex vortex-induced updrafts that depend on changes in two horizontal coordinates, thus ensuring that the disturbance is bounded while exhibiting rapid spatial variation and strong interaxial coupling.

[0077] The main control objective of this invention is to design a distributed control scheme configured to ensure stable formation holding under coupled aerodynamics and spatiotemporal wind disturbances. Specifically, the controller aims to ensure that the tracking error converges rapidly from any initial conditions to a small neighborhood of the origin. Furthermore, the tracking error must be strictly constrained within a predefined constant safety region to ensure operational safety during dynamic formation.

[0078] The hierarchical controller design achieves the control objective through a hierarchical architecture consisting of an outer-loop formation controller and an inner-loop attitude / velocity controller. The outer-loop formation controller is configured to generate virtual velocity commands to satisfy formation constraints, while the inner-loop controller is configured to generate forces and torques to track the commands over a fixed time period.

[0079] The outer loop control is a distributed reference generation and safe tracking mechanism. The outer loop formation controller consists of two coupled layers: one that generates a local reference trajectory using the communication topology. A distributed estimator, and a driver for drone positioning. Security tracking The robust tracking controller, the first layer of the outer loop formation controller is designed for the first... The drone generates a local reference position. This variable, serving as an intermediate tracking target, is generated by a distributed consensus algorithm for the communication topology. To formally describe the desired geometric configuration, let... Indicates the first The drone relative to the reference trajectory The specified position offset, therefore, the drone and drones The expected relative formation vector between them is defined as , , , They represent drones With drones The relative distances in the x / y / z directions satisfy:

[0080]

[0081] Further define binary restraint parameters ,in Indicates the first The drone can directly access the reference trajectory , The distributed update protocol is designed as follows:

[0082]

[0083] in Let the adjacency weight be , and This represents the coupling gain.

[0084] The tracking controller design is based on the generated reference signal, defining the local tracking error as... To achieve robust tracking with strict safety guarantees, virtual velocity control input is used. Designed as a combination of five items:

[0085]

[0086] The detailed design descriptions of each component are as follows:

[0087] 1) Linear stability term Employing a proportional feedback term provides baseline exponential stability for error dynamics.

[0088]

[0089] in For feedback gain.

[0090] 2) Neural Adaptive Term To compensate for the uncertainty of the unknown aggregate (Including wind disturbance and dynamic hysteresis), a radial basis function neural network (RBFNN) is used:

[0091]

[0092] weight matrix The adaptive update law is configured to minimize the approximation error:

[0093]

[0094] in The basis function vector is usually chosen to be a Gaussian function. ,in As the sample center, This refers to the sample range.

[0095] 3) Robust damping term To handle the residual approximation error of the neural network, a robust feedback term is designed as follows:

[0096]

[0097] in For robustness gain, Represents standard symbolic functions, The adaptive estimate of the uncertainty upper limit has the following online update law:

[0098]

[0099] 4) Obstacle Safety Items This key item enforces safety constraints to ensure that tracking errors are strictly kept within the dynamic safety region (i.e., The obstacle potential field is constructed as follows:

[0100]

[0101] in For obstacle gain, the safety boundary The performance function defined by the attenuation is:

[0102]

[0103] in The initial buffer and convergence speed are determined by the design parameters.

[0104] Furthermore, the obstacle term functions by generating a repulsive velocity command, when When the instruction approaches infinity, the initial error satisfies... This mechanism guarantees that for all The error trajectory will never escape the safe set. .

[0105] Kinematic inversion and dynamic reconstruction are performed, and instructions are used to generate a virtual control vector obtained from the outer loop. This represents the desired velocity vector in the inertial coordinate system. To drive the UAV, this vector must be converted into airspeed, trajectory tilt, and trajectory azimuth commands. For use in inner-loop tracking, the kinematic inverse logic is derived as follows:

[0106]

[0107]

[0108]

[0109] To facilitate the subsequent design of the inner-loop controller, the nonlinear particle dynamics of the UAV described in the above equation are reconstructed into a control affine form, with the state vector being... The dynamics can be expressed as:

[0110]

[0111] in, Representing the inner-loop control input, based on the above full-scale model, the system matrix... (Representing undriven internal dynamics) and control performance matrix The derivation is as follows:

[0112]

[0113] in, Represents a diagonal matrix. , , These represent airspeed, track inclination, and track azimuth, respectively. Indicates the first The quality of the drone For gravitational acceleration, the term The environmental wind disturbance in the inertial coordinate system is represented in the dynamic equations. This represents the generalized longitudinal control force (including engine thrust and active braking force), while and Represents generalized mobility (related to lift and lateral force components), term This indicates aerodynamic drag.

[0114] and The construction strictly follows the physical constraints provided by the above formula. It should be noted that when the UAV operates within its effective flight envelope, it can naturally avoid... The singularity in (i.e., when) or (The situation at that time).

[0115] Inner loop control: Fixed-time terminal sliding mode control with a cubic smoothing mechanism, the inner loop tracking error vector is defined as follows. ,in To systematically address the inherent singularity of terminal sliding mode while ensuring fixed-time convergence, an improved non-singular fixed-time sliding mode control (MNFTSMC) protocol with a cubic smoothing mechanism is proposed, where the sliding surface vector... Designed as follows:

[0116]

[0117] in, For sliding mode surface gain, a nonlinear function and Configured to when the system reaches the sliding surface This ensures the convergence characteristic at a fixed time.

[0118] To address the inherent singularity problem in fractional power control laws and reduce control stiffness near the equilibrium point, this invention proposes a cubic nonsingular smooth switching mechanism. This differs from conventional mechanisms that only guarantee... Unlike traditional quadratic splicing methods that rely on continuity, the proposed cubic formula introduces a high-order polynomial structure within the boundary layer. For the th... The improved nonlinear function is defined as having elements:

[0119]

[0120]

[0121] in For a user-defined smaller boundary layer constant, dynamic exponent and Configured to switch based on error magnitude to ensure global fixed-time convergence:

[0122]

[0123] The basic index satisfies and ,coefficient and Through rigorous derivation, the function value is strictly guaranteed. and its first derivative (Jacobi matrix) at the switching boundary Continuity at point:

[0124]

[0125] Introducing the cubic term Compared to linear or quadratic approximation, it has significant structural advantages, ensuring that the second derivative of the nonlinear term vanishes at the origin (i.e., This provides a more "smooth" dynamic distribution, which effectively reduces the derivative gain sensitivity to measurement noise near the equilibrium point, thereby suppressing steady-state chattering and improving the lifespan of the actuator.

[0126] The derivative of the sliding surface in the derivation of the control law is as follows:

[0127]

[0128] in, express To drive the sliding variable to the origin within a fixed time, given the identity matrix, the following convergence law is used:

[0129]

[0130] in To approach the gain, the exponent satisfies and , For robust gain used to suppress disturbances, let Representing the non-singular auxiliary matrix, substituting affine dynamics into sliding dynamics, the final inner-loop control law is derived as follows:

[0131]

[0132] in This indicates the nominal approach dynamics.

[0133] matrix As the denominator in the control law, thanks to the triple splicing mechanism proposed in this invention, even when... hour, It remains bounded and non-zero, thus ensuring the realizability of the controller.

[0134] See Figures 2-6 To verify the effectiveness and superiority of the proposed distributed control scheme (protocol), this invention conducted extensive numerical simulation verification on a formation system composed of multiple UAVs. The experiment aimed to verify the effects of three key technologies: the feasibility of the overall system, the necessity of the performance specification mechanism (PPC) in the outer loop, and the superior convergence speed of the fixed-time controller in the inner loop.

[0135] Simulation environment and parameter settings: The multi-agent system includes one virtual navigator and... A follower drone was used, with a total simulation duration of 150 seconds and a fixed time step of 0.001 seconds.

[0136] The follower was modeled as a drone with the same physical properties as the drone in the initial configuration. Key inertial and aerodynamic parameters are shown in Table I.

[0137] Table I: Physical Parameters of the UAV

[0138]

[0139] To verify the ability of this invention to achieve convergence from dispersed locations, all UAVs were initialized with zero velocity and zero attitude angle (i.e., ), initial position matrix The coordinates are relatively scattered.

[0140] Environmental Disturbances and Reference Trajectory: This embodiment configures a harmonic wind field incorporating spatial shear and eddy-like coupling to rigorously evaluate the system's robustness. Average wind speed is set. for m / s, the virtual navigator is configured to track an outward-expanding spiral trajectory. The ultimate goal is to form a star-shaped formation geometry centered on a virtual navigator, with followers maintaining a fixed relative distance from the navigator.

[0141] Formation tracking performance (Scenario 1)

[0142] 1. Controller Configuration and Overall Performance The key parameter settings for the outer-loop distributed controller are as follows: Proportional Gain Robust gain Consistency gain Barrier gain (Baseline is 0), Number of hidden layer nodes in RBFNN Data Center It includes three channels: X, Y, and Z axes. The center node set of the X-axis channel is set as follows: The center node set of the Y-axis channel is set as follows: The center node set of the Z-axis channel is set as follows: The data range Simulation results show that despite strong wind disturbances with spatial variations, the star formation was well maintained, and the tracking errors of all UAVs were strictly constrained within the exponentially decaying performance envelope (PPC), ensuring transient and steady-state performance. Meanwhile, the control signal generated by the inner-loop scheme proposed in this invention is smooth and bounded, effectively suppressing the high-frequency chattering phenomenon commonly found in traditional sliding mode control.

[0143] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0144] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A fixed-time neural adaptive formation control method for multiple unmanned aerial vehicles (UAVs) to resist aerodynamic disturbances, characterized in that, Includes the following steps: Step S1: Construct a hierarchical control architecture consisting of an outer ring formation controller and an inner ring attitude / velocity controller; determine the three-dimensional nonlinear dynamic model and spatially varying wind field model of the multi-UAV system; define the multi-UAV formation control objective as making the tracking error converge quickly from any initial conditions to a small neighborhood of the origin and strictly constrained to a predefined constant safety region. Step S2: Design the outer ring formation controller, including distributed reference generation and robust tracking controller design: First, based on the distributed consensus algorithm of the communication topology, define the position offset of the UAV relative to the reference trajectory and the binary restraint parameters, design a distributed update protocol to generate the local reference position of each UAV, then define the local tracking error, and design the virtual velocity control input as a combination of linear stable term, neural adaptive term, robust damping term and obstacle safety term. Among them, the neural adaptive term uses a radial basis function neural network to approximate the unknown lumped uncertainty and derives the adaptive update law of the weight matrix. The robust damping term handles the residual approximation error of the neural network. The obstacle safety term constructs the obstacle potential field based on the improved obstacle function and defines the safety boundary through the decay specified performance function. Step S3, perform kinematic inversion and dynamic reconstruction: First, convert the virtual control vector in the inertial coordinate system output by the outer loop into airspeed, track tilt angle and track azimuth angle commands for use by the inner loop tracking. Then, reconstruct the six-degree-of-freedom nonlinear particle dynamics of the UAV into a control affine form, determine the state vector, inner loop control input, and derive the system matrix and control efficiency matrix. Step S4: Design the inner loop attitude / velocity controller, using an improved non-singular fixed-time sliding mode control protocol with a cubic non-singular smooth switching mechanism. First, define the inner loop tracking error vector, design the sliding mode surface vector, construct the cubic non-singular smooth switching mechanism, define the improved nonlinear function, configure the dynamic exponent and derive the correlation coefficient to ensure the continuity of the function value and its first derivative at the switching boundary, and that the second derivative of the nonlinear term disappears at the origin. Then, differentiate the sliding mode surface, use a preset reaching law, and combine it with the reconstructed control affine dynamics to derive the inner loop control law, ensuring the realizability of the controller. Step S5: Based on the above hierarchical control architecture, realize fixed-time neural adaptive formation control of multiple UAVs under coupled aerodynamics and spatiotemporal wind disturbances.

2. The method for fixed-time neural adaptive formation control of multiple unmanned aerial vehicles (UAVs) to resist aerodynamic disturbances according to claim 1, characterized in that: The three-dimensional nonlinear dynamic model of the UAV in step S1 is a six-degree-of-freedom nonlinear particle dynamic model. It defines the position of the UAV in the inertial coordinate system, with the Y-axis as the vertical axis. It includes parameters related to airspeed, track tilt angle, track azimuth angle, UAV mass, gravitational acceleration, environmental wind disturbance, generalized longitudinal control force, generalized maneuvering force, and aerodynamic drag. The aerodynamic drag is modeled as an expression that includes air density, reference wing area, and zero-lift drag coefficient.

3. The method for fixed-time neural adaptive formation control of multiple unmanned aerial vehicles (UAVs) to resist aerodynamic disturbances according to claim 2, characterized in that: The spatially varying wind field model in step S1 is a deterministic spatiotemporal wind field model. Combining spatial shear and vortex-like coupling, the wind disturbance vector is modeled as a harmonic background field dependent on the UAV's spatial coordinates, including average wind speed, spatial oscillation amplitude, and characteristic wavelength parameters along each axis. The vertical component includes nonlinear cross-coupling terms to simulate vortex-induced updrafts.

4. The multi-UAV fixed-time neural adaptive formation control method for resisting aerodynamic disturbances according to claim 3, characterized in that: The outer-loop formation controller in step S2 consists of two coupling layers, one of which generates a local reference trajectory using the communication topology. A distributed estimator, and a driver for drone positioning. Security tracking A robust tracking controller, in which the distributed estimator is designed for the first... The drone generates a local reference position. , It is the dimension symbol. This indicates that the variable is Wei, Ling Indicates the first The drone relative to the reference trajectory The specified position offset, then the drone and drones The expected relative formation vector between them is defined as ,satisfy: ， Further define binary restraint parameters ,in Indicates the first The drone can directly access the reference trajectory ,but The distributed update protocol is designed as follows: ， in Let the adjacency weight be , and This represents the coupling gain.

5. The method for fixed-time neural adaptive formation control of multiple unmanned aerial vehicles (UAVs) to resist aerodynamic disturbances according to claim 4, characterized in that: The robust tracking controller of the outer loop formation controller in step S2 defines the local tracking error based on the generated reference signal. Next, input the virtual speed control. Designed as a combination of five items: ， in, It is a linearly stable term. For neural adaptive terms, For robust damping term and For obstacle safety items, This is the update protocol for the local reference trajectory.

6. The multi-UAV fixed-time neural adaptive formation control method for resisting aerodynamic disturbances according to claim 5, characterized in that: The kinematic inversion and dynamic reconstruction process in step S3 specifically includes obtaining the virtual control vector from the outer ring formation controller. This represents the desired velocity vector in the inertial coordinate system, which is then converted into airspeed, track inclination, and track azimuth commands. The inverse kinematic logic is derived as follows: ， ， ， The affine dynamics reconstruction reconstructs the aforementioned nonlinear particle dynamics of the UAV into a control affine form, specifically by letting the state vector be... The dynamics can be expressed as: ， in, Indicating the inner-loop control input, the system matrix... and control performance matrix The derivation is as follows: ， in, Represents a diagonal matrix. , , These represent airspeed, track inclination, and track azimuth, respectively. Indicates the first The quality of the drone For gravitational acceleration, the term The environmental wind disturbance in the inertial coordinate system is represented in the dynamic equations. This represents generalized longitudinal control, while and Representing generalized kinetic energy, item This indicates aerodynamic drag.

7. The method for fixed-time neural adaptive formation control of multiple unmanned aerial vehicles (UAVs) to resist aerodynamic disturbances according to claim 6, characterized in that: The design process of the inner loop attitude / velocity controller in step S4 is as follows: First, the inner loop tracking error vector is defined as... ,in Next, an improved non-singular fixed-time sliding mode control protocol with a three-stage smoothing mechanism is designed, and the sliding mode surface vector is... Designed as follows: ， in, For sliding mode surface gain, a nonlinear function and Configured to when the system reaches the sliding surface Ensures fixed-time convergence characteristics; for the first... The improved nonlinear function is defined as having elements: ， ， in For a user-defined smaller boundary layer constant, dynamic exponent and Configured to switch based on error magnitude: ， The basic index satisfies and ,coefficient and Through rigorous derivation, the function value is strictly guaranteed. and its first derivative Switching boundaries Continuity at point: 。

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