A radial basis function neural network disturbance learning and adaptive terminal sliding mode double-loop control method for manned / unmanned aircraft cooperative formation

Abstract

The application discloses a radial basis function neural network disturbance learning and adaptive terminal sliding mode double-loop control method for manned aircraft / unmanned aircraft cooperative formation, adopts a distributed architecture in which a manned aircraft MAV only broadcasts a state and an unmanned aircraft UAV independently makes decisions; the UAV generates a desired reference trajectory based on the MAV broadcast state; an estimated value of a radial basis function neural network output is constructed; a position outer loop adaptive terminal sliding mode control law is designed, an equivalent translation control amount is output, a residual disturbance upper limit adaptive estimation is introduced to form a complementary mechanism of learning compensation and adaptive robustness; the equivalent translation control amount is analytically converted into a desired attitude angle and a total thrust instruction; an attitude inner loop adaptive terminal sliding mode control law is designed to track the desired attitude angle, and an attitude torque instruction is output; finally, a motor instruction is generated through a hybrid control module and is executed. The application reduces chattering, improves robustness and tracking accuracy, and has low calculation complexity and is easy to implement in engineering.

Description

Technical Field

[0001] This application belongs to the field of collaborative feedback control technology, specifically relating to a radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation. Background Technology

[0002] Manned / unmanned aircraft cooperative formation flight is an important development direction in the field of aircraft control. By grouping and coordinating manned aircraft with multiple unmanned aircraft, mission execution capabilities can be significantly expanded, and it has broad application prospects in civilian scenarios. Cooperative formation control requires that during manned aircraft-led maneuvers, each unmanned aircraft can maintain the desired relative geometric configuration while ensuring safe flight spacing. This places high demands on the accuracy, robustness, and real-time performance of the control system.

[0003] In existing technologies, research on manned / unmanned aircraft cooperative formation control mainly employs centralized or distributed architectures. Centralized methods involve a ground station or manned aircraft uniformly calculating control commands for all UAVs, resulting in a heavy computational burden and strong dependence on communication. Distributed methods, on the other hand, allow each UAV to make independent decisions based on information broadcast by the navigator, exhibiting strong scalability and fault tolerance. Regarding control algorithms, sliding mode control is widely used for formation flight control due to its invariance to matching disturbances. However, traditional sliding mode control suffers from chattering, which can easily lead to actuator wear and affect tracking accuracy. To suppress chattering, researchers have proposed higher-order sliding mode, adaptive sliding mode, and intelligent control methods based on neural network approximation. Among these, radial basis function neural networks, due to their simple structure and strong approximation ability, are used to estimate system uncertainties and external disturbances online, using the estimated values ​​as feedforward compensation to reduce sliding mode switching gain.

[0004] While existing methods can achieve formation control objectives under specific conditions, they still face the following challenges in manned-led cooperative formation scenarios: When the manned aircraft performs strong maneuvers, the equivalent disturbances caused by wind interference, parameter uncertainties, attitude-translation coupling residuals, and communication delays significantly increase for the UAVs, leading to decreased tracking accuracy; relying solely on sliding mode robust terms to suppress disturbances can amplify chattering, affecting control quality and flight safety; existing neural network learning methods do not fully utilize the characteristics of the cooperative formation structure and have limited learning capabilities for disturbances strongly correlated with the lead aircraft's maneuvers, making it difficult to effectively reduce reliance on large-amplitude robust terms; furthermore, under strong maneuvering conditions, dynamic changes in the UAV's reference trajectory may cause the actual distance to the manned aircraft to exceed the safe interval. Existing methods typically rely on online optimization to ensure constraints, resulting in high computational complexity and difficulty in meeting real-time control requirements. Therefore, a cooperative formation control scheme that can maintain high-precision tracking, suppress chattering, and ensure safe intervals under strong maneuvering and uncertain disturbance conditions is urgently needed. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this application provides a radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation. The technical problem to be solved by this application is achieved through the following technical solution: A radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation includes: S100, construct a cooperative formation system consisting of manned aircraft (MAV) and N unmanned aerial vehicles (UAV), wherein the MAV broadcasts its own status only in one direction and the UAV makes independent decisions; S200: Each UAV broadcasts its own status information unidirectionally based on the MAV, and combines it with the preset formation relative displacement vector to generate the expected position reference trajectory and its derivative with safety circle constraint correction. S300, Establish an equivalent disturbed model for the UAV. The equivalent disturbed model includes translational mechanics and attitude dynamics, wherein the translational mechanics is equivalent to a second-order system with a comprehensive disturbance term, and the attitude dynamics is described as a second-order form with an attitude disturbance term. S400 constructs a radial basis function neural network with local state and relative MAV state as input, learns online and outputs a comprehensive perturbation estimate; S500, based on the equivalent disturbance model and the comprehensive disturbance estimate, with the desired position reference trajectory and its derivative as the tracking target, designs a position outer loop adaptive terminal sliding mode control law that integrates radial basis function neural network feedforward compensation to output an equivalent translation control quantity; S600, the equivalent translation control quantity is analytically converted into the desired attitude angle and total thrust command; S700, design an attitude inner loop adaptive terminal sliding mode control law to track the desired attitude angle, thereby outputting attitude torque command; S800: Input the total thrust command and the attitude torque command into the hybrid control module to generate commands for each motor and send them out for execution.

[0006] Beneficial effects: This application discloses a radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation. It adopts a distributed architecture where the manned aircraft (MAV) only broadcasts its state, and the unmanned aircraft (UAV) makes independent decisions. The UAV generates a desired reference trajectory with safety circle constraint correction based on the MAV's broadcast state. A radial basis function neural network is constructed with the local state and the relative MAV state as inputs to learn and synthesize perturbations online and output estimates. An adaptive terminal sliding mode control law with feedforward compensation from the neural network is designed to output an equivalent translation control quantity. Simultaneously, an adaptive estimation of the upper bound of the residual perturbation is introduced to form a complementary mechanism of learning compensation and adaptive robustness. The equivalent translation control quantity is analytically converted into desired attitude angle and total thrust commands. An adaptive terminal sliding mode control law with an inner attitude loop is designed to track the desired attitude angle and output attitude torque commands. Finally, motor commands are generated and executed through a hybrid control module. This application solves the problems of decreased formation tracking accuracy, amplified sliding mode chattering, and difficulty in guaranteeing safety intervals under strong maneuvering and uncertain perturbations. It improves robustness and tracking accuracy while reducing chattering, and has low computational complexity, making it easy to implement in engineering.

[0007] The present application will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0008] Figure 1 This is a flowchart illustrating a radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation provided in this application; Figure 2 This is a schematic diagram of the control loop of the radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation provided in this application. Detailed Implementation

[0009] The present application will be described in further detail below with reference to specific embodiments, but the implementation of the present application is not limited thereto.

[0010] This application belongs to the field of aircraft cooperative control technology, specifically relating to a MAV / UAV cooperative formation flight method based on a dual-loop structure of radial basis function neural network (RBFNN) perturbation learning and adaptive terminal sliding mode control (ATS-MC). Addressing the problems of decreased tracking accuracy, amplified sliding mode chattering, and difficulty in uniformly guaranteeing safe intervals in cooperative formations with manned aircraft (MAV) leading and unmanned aircraft (UAV) following under strong maneuvering and uncertain perturbation conditions, this application proposes a distributed closed-loop control framework that emphasizes RBFNN perturbation learning. This method employs a collaborative architecture of "MAV broadcasting state only, UAV making independent decisions": the UAV outer loop is based on a translational equivalent model, incorporating wind disturbance, parameter uncertainty, attitude-translation coupling residuals, reference derivative errors, and communication delays into the integrated disturbance term; utilizing the formation collaborative structure characteristics, the RBFNN input is constructed as a combination of "local state + relative MAV state," learning the learnable part of the integrated disturbance that is strongly correlated with MAV maneuvering online, and embedding the outer loop ATS-MC in a feedforward compensation manner to reduce dependence on the robustness term for large-scale switching, thereby reducing chattering and improving steady-state error; simultaneously, the residual is compensated by adaptive estimation of the upper bound of the residual disturbance, realizing a complementary mechanism of "learning compensation + adaptive robustness." The attitude inner loop further constructs an ATS-MC isomorphic to the outer loop, achieving rapid and stable tracking of the desired attitude and thrust commands generated analytically by the outer loop. In the reference generation stage, analytical correction of the MAV-UAV safety circle constraints is introduced, and an analytical mapping interface between the outer and inner loops is established, achieving constraint-feasible collaborative formation closed-loop control without introducing optimization solutions.

[0011] Combination Figure 1 and Figure 2 This application provides a radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation, including: S100, construct a cooperative formation system consisting of manned aircraft (MAV) and N unmanned aerial vehicles (UAV), wherein the MAV broadcasts its own status only in one direction and the UAV makes independent decisions; S200: Each UAV broadcasts its own status information unidirectionally based on the MAV, and combines it with the preset formation relative displacement vector to generate the expected position reference trajectory and its derivative with safety circle constraint correction. S300, Establish an equivalent disturbed model for the UAV. The equivalent disturbed model includes translational mechanics and attitude dynamics, wherein the translational mechanics is equivalent to a second-order system with a comprehensive disturbance term, and the attitude dynamics is described as a second-order form with an attitude disturbance term. S400 constructs a radial basis function neural network with local state and relative MAV state as input, learns online and outputs a comprehensive perturbation estimate; S500, based on the equivalent disturbance model and the comprehensive disturbance estimate, with the desired position reference trajectory and its derivative as the tracking target, designs a position outer loop adaptive terminal sliding mode control law that integrates radial basis function neural network feedforward compensation to output an equivalent translation control quantity; S600, the equivalent translation control quantity is analytically converted into the desired attitude angle and total thrust command; S700, design an attitude inner loop adaptive terminal sliding mode control law to track the desired attitude angle, thereby outputting attitude torque command; S800: Input the total thrust command and the attitude torque command into the hybrid control module to generate commands for each motor and send them out for execution.

[0012] In one specific embodiment of this application, S100 includes: S110, Define the self-state of the MAV broadcast, which includes at least its position, speed and yaw angle; S120 defines that when the UAV side receives MAV broadcasts, it adopts the latest data retention strategy for communication delay and the communication strategy of retaining the previous valid data for short-term packet loss. S130 establishes a collaborative formation system that includes MAVs and N UAVs.

[0013] This application pertains to a manned aircraft (MAV) and A cooperative formation system consisting of unmanned aerial vehicles (UAVs). Let the index of the MAV be... UAV set is This application adopts a distributed architecture of "pilot broadcast - slave autonomy": the motion of the MAV is independently generated by the pilot or the existing flight control system, and the MAV is only generated by sampling period. Each UAV broadcasts its own status information unidirectionally as a formation reference and does not participate in any UAV control calculations or distribution. Each UAV independently generates a reference trajectory and solves for thrust and torque commands in a closed loop on its own side, thereby achieving a collaborative control mechanism of "independent decision-making on the UAV side." The purpose of this architecture is to reduce the coupling between centralized computing and communication, enabling the system to have scalability and fault tolerance, and ensuring that the MAV does not change its own operating logic due to participation in slave control.

[0014] To ensure the feasibility of the project, discrete control time is defined. Considering communication latency and packet loss, record the distance from MAV to UAV. i The equivalent communication delay is And make the boundedness assumption. in The upper bound is known. The UAV end adopts the latest-arriving data hold (zero-order hold) strategy: at time... Use the most recently received MAV state. It participates in the calculation; in the event of a short-term packet loss, it continues to use the previous valid data to maintain the continuity of the control link. The above processing does not introduce any iterative optimization or centralized synchronization module, which meets the basic constraint of low-complexity real-time implementation of this application.

[0015] This application establishes an inertial coordinate system. And for the first UAV building system in Take the UAV centroid or IMU mounting point; the MAV's system architecture is denoted as... The UAV attitude is represented using Euler angles. And define the rotation matrix from the machine system to the inertial frame as: in This is the standard rotation matrix. This convention will be used in the subsequent analytical transformation module so that the equivalent translation control quantity output by the outer loop can be mapped to the desired attitude and thrust.

[0016] For the first A UAV is deployed, and its position and velocity are defined in an inertial frame as follows: Attitude and angular velocity are defined as follows: The execution layer control inputs of a UAV are defined as total thrust and triaxial torque: To be consistent with the dual-loop control structure, the equivalent translation control quantity of the outer position loop is defined as follows: Its physical meaning is "desired translational acceleration (or equivalent resultant force acceleration) command". Subsequent steps will be based on translational mechanics... Convert to and And output by the attitude inner loop. Complete closed-loop control.

[0017] For MAV, the minimum set of its broadcast states is defined as follows: in For location, For speed, This is the heading angle. If engineering conditions permit, the broadcast set can also be expanded to include... Isoderine information is used to improve the estimation accuracy of the derivative of the reference trajectory.

[0018] To avoid operational ambiguities in terminal sliding mode control and RBFNN learning laws, a unified convention is first established for commonly used operators. Let... Define vector norm Define element-wise absolute value and element-wise exponentiation as Define element-wise symbolic functions To mitigate chattering in the sliding mode arrival law and ensure numerical realizability, a boundary layer continuity sign function is defined. in This is a small, adjustable constant. This continuous form will be used to implement the arrival laws for the outer position loop and the inner attitude loop, as well as the adaptive robust term.

[0019] Based on the above definitions, to ensure that the subsequent "reference generation-perturbation learning-adaptive terminal sliding mode" link is theoretically closed and practically feasible, the following general assumptions are made. First, the MAV broadcast state is bounded, that is, there exists a constant. , so that for any The UAV can obtain the derivative information required for reference trajectory generation. If the MAV does not directly broadcast the derivative, the UAV will... Obtained by differential filtering We use the same estimator and assume that the estimation error is bounded, i.e., there exists an upper bound. Each UAV It can be measured by sensors or obtained through conventional estimators, and the measurement / estimation error is bounded, thus ensuring that the control law can be calculated and executed in real time within each sampling period.

[0020] In one specific embodiment of this application, S200 includes: S210: Based on the position and yaw angle broadcast by the MAV, the preset formation relative displacement vector is rotated to the inertial frame and superimposed with the MAV position to generate the initial expected position reference; S220, calculate the relative distance between the initial expected position reference and the actual position of the MAV. When the relative distance is less than the preset safety radius, project the initial expected position reference radially to the safety boundary to obtain the corrected expected position reference and its derivative.

[0021] Based on the collaborative architecture and variable definitions of S100, this step presents a unified method for "generating the desired reference trajectory of each UAV from the MAV broadcast state". To describe the formation geometry, the desired relative displacement vector of each UAV relative to the MAV is first preset. in It can be a constant (fixed formation), or a piecewise constant or a time function (formation switching / task phase change). To ensure the subsequent control law's requirement for the reference derivative, it is required that... It is at least a piecewise quadratic differentiable signal, and its first and second derivatives are bounded within each piece; when a formation change occurs, a continuous transition (e.g., smooth interpolation within a finite time window) is preferred to avoid the reference excitation generating unnecessary high-frequency components.

[0022] Heading angle based on MAV broadcast Define the inertial frame of reference Rotation matrix of axis Therefore, the first The desired position reference definition for a UAV is defined as follows: in For reference of the UAV's expected location, Let be the position vector of MAV in the inertial frame. This indicates the relative displacement of the formation. The absolute offset obtained by rotating the "local configuration description aligned with the MAV heading" to the inertial frame. This definition allows the formation configuration to rotate naturally with the MAV heading, thus maintaining consistency in relative geometry when the MAV turns.

[0023] Meanwhile, to ensure consistent formation orientation and facilitate attitude transitions and inner-loop tracking, the desired yaw angle of the UAV is preferably defined as... That is, the UAV's desired heading is the same as the MAV's heading; if the mission requires maintaining a relative observation angle or formation pointing, then it can be done in... Based on this, a bounded bias term is added, but this bias term also needs to satisfy the requirements of differentiability and boundedness to ensure that the inner loop control law can be realized.

[0024] Since the outer loop control law of position usually requires a reference speed. With reference acceleration This step provides its analytical form and explains the source of the variables. Taking the derivative with respect to time, we get in As the reference velocity vector, For MAV speed, Let be the first derivative of the relative displacement of the formation. The derivative of the rotation matrix can be written as: in The yaw rate of the MAV. A constant antisymmetric matrix Further calculation of the second derivative yields the reference acceleration. in As a reference acceleration vector, For MAV acceleration, Let be the second derivative of the relative displacement of the formation. And... in For MAV yaw angle acceleration, Representation matrix The square of.

[0025] In engineering implementation, the above It can be obtained in two ways: firstly, by the MAV directly broadcasting the relevant derivative or equivalent measurable quantity; secondly, by the UAV receiving the data. , The estimator is obtained by difference and filtering. If the estimator is used in the calculation, the estimation error of the reference derivative can be regarded as a bounded uncertainty term, which will be suppressed together with the external disturbance in the subsequent "RBFNN perturbation learning + adaptive terminal sliding mode robust term", thus ensuring the closure of the derivation logic.

[0026] To ensure a safe distance between manned and unmanned aircraft in cooperative formation, this step introduces MAV-UAV safety circle constraints at the reference generation layer. Let the safety radius be... , requiring any The reference point satisfies in Denotes the Euclidean norm. The reference position generated for S200.1 The reference point is the actual position of the MAV. To avoid introducing model prediction, quadratic programming, or other iterative optimization modules, this application uses an analytical projection / saturation method to correct the reference point. The reference relative vector and its magnitude are defined as follows: in This represents the vector of the reference point relative to the MAV. This indicates the length of the vector. When Keep the reference unchanged; when At this time, the reference point is projected radially onto the safety boundary to obtain the corrected reference. in For the safety correction reference position, To avoid dividing by zero for extremely small positive numbers, subsequent steps will... Replace with (For brevity, it will still be written as) The outer loop is used as the tracking target, and its derivative is constructed accordingly. , This correction mechanism only involves norm, normalization, and linear operations, with a computational complexity of constant level, satisfying the overall constraint of "not increasing computational complexity".

[0027] Furthermore, to establish a logical connection between "reference safety" and "actual safety," the outer ring position tracking error is defined as... in for Actual location This is the corrected reference position. From the triangle inequality, we can obtain... Therefore, as long as the subsequent control design ensures After a finite time, entering a sufficiently small bounded set (a property supported by adaptive terminal sliding mode convergence and RBFNN perturbation compensation) can keep the actual MAV-UAV distance within a controllable margin outside the safe radius.

[0028] In one specific embodiment of this application, S300 includes: S310 describes the translational mechanics of UAV as a second-order form in which acceleration equals the sum of the equivalent translational control quantity and the comprehensive disturbance term; To facilitate the design of the position outer loop control without introducing complex optimizations or increasing the online computational burden, this step will... The translational mechanics of the UAV is equivalent to a second-order controlled system with unknown disturbances. Let... In inertial coordinate system The position below is in They represent In a three-axis inertial frame, define its velocity and acceleration as follows: and .

[0029] S320 describes the angular dynamics of each axis of the attitude channel as a second-order form of the sum of known coupling terms, controlled torque terms, and disturbance terms; S330, make boundedness assumptions on the integrated disturbance term and attitude disturbance term, and establish the equivalent disturbed model of the UAV.

[0030] Based on the fundamental force relationships of quadcopters / multirotors, translational acceleration can be expressed as "controllable equivalent acceleration term + comprehensive disturbance term", and the controllable part can be uniformly denoted as the outer loop equivalent control quantity. in They represent the outer ring at... The desired equivalent acceleration (or equivalent resultant force acceleration) command applied in three directions. Unmodeled terms such as external wind disturbances, aerodynamic disturbances, parameter uncertainties, coupling term residuals, and reference derivative estimation errors are uniformly incorporated into the synthesized disturbance vector. This yields the equivalent model of the outer ring location, i.e., the equivalent disturbed model: in This represents the combined disturbance acceleration term. These represent the perturbation components along the three axes. To ensure the rigor of the subsequent adaptive terminal sliding mode and RBFNN learning derivation, the following boundedness assumption is made: There exist positive constants. , so that for any satisfy in It is the Euclidean norm. This assumption corresponds to the engineering fact that wind disturbances and modeling errors have finite upper bounds within the flight envelope and can maintain bounded operation through airborne sensing and flight control.

[0031] It should be noted that the above equivalent model does not require the precise and explicit writing of all terms related to the thrust direction, attitude coupling, and mass parameters. Instead, it reduces the outer-loop design objective to "making..." Tracking the expected equivalent acceleration Then, through the subsequent parsing and conversion module, The model is mapped to the desired attitude and total thrust, thus forming a standard double-loop interface with the attitude inner loop. This modeling approach can theoretically maintain closed-loop analyzability while keeping the implementation low in complexity.

[0032] To achieve rapid and stable execution of the desired attitude and thrust generated by the outer loop at the airframe level, this step provides an angular dynamics description of the inner attitude loop and further clarifies the source of the disturbance term and its handling in the subsequent control structure. Let... Euler angles are in These are roll, pitch, and yaw angles, respectively; assuming the angular velocity of the aircraft system is... in These are the angular velocity components around the three axes of the aircraft body. Based on Euler's equations for rigid body rotation, each attitude angle channel can be written in a second-order form consisting of "known structural coupling terms + controlled terms + disturbance terms". Taking the roll channel as an example, we have... in For the body Moment of inertia of the shaft For rolling torque input, For the reason Coupling terms caused by inertia (which can be calculated when the inertia parameter is available or can be estimated). This represents the equivalent disturbance caused by unmodeled disturbances and parameter uncertainties. The pitch and yaw channels are similarly represented as... in They are respectively around the fuselage shaft and Moment of inertia of the shaft For pitch and yaw moment input, For coupling terms, This is a perturbation term. To ensure the stability derivation of the sliding mode at the inner loop of the attitude, it is assumed that there exists a constant. Make Furthermore, to highlight the application value of RBFNN in manned-unmanned cooperative formation, this application addresses the integrated disturbance of translational channels. A structured interpretation is provided. Considering the reference trajectory generation and derivative estimation process in S200, as well as the environmental and model uncertainties of actual flight, it can be... It can be understood as a combination of the following factors: in This represents the acceleration term of disturbances caused by the external wind field and gusts. This represents the equivalent error term caused by uncertainties in parameters such as mass, thrust coefficient, and damping. This represents the residual term resulting from attitude-translation coupling and modeling approximation. This represents the equivalent perturbation term introduced by the estimation error of the reference trajectory derivative, communication delay, and hold-up strategy.

[0033] Since the MAV serves as the reference point in the formation, its maneuvers (turning, acceleration, deceleration) will be directly entered. , , The structure of which makes It shows a significant correlation with "the state and rate of change of relative MAV". Based on this cooperative structural characteristic, RBFNN will be designed in the subsequent S400. RBFNN outputs during online learning. As a feedforward compensation term, it enters the outer-loop control law to reduce dependence on large sliding mode switching terms and reduce chattering; at the same time, the adaptive terminal sliding mode control in the subsequent S500 will introduce an estimate of the upper bound of the residual disturbance. Used for robust suppression The learning residuals form a complementary mechanism of "learning compensation + adaptive robustness", which ensures that the closed loop still has stability and convergence when the disturbance changes rapidly or learning error exists.

[0034] The given equivalent disturbed model in for Position vector in inertial coordinate system The equivalent translation control quantity designed for the outer loop of the position. This involves synthesizing the disturbance vector (including wind disturbance, parameter uncertainties, attitude-translation coupling residuals, reference derivative estimation errors, and equivalent terms caused by communication delays). The goal of this step is to construct an online learner to generate the disturbance estimate. This is used to offset the effect of "feedforward compensation" in the subsequent outer-loop control law of the S500. The main part of this reduces the magnitude of the residual entering the adaptive robust term significantly, thereby reducing sliding mode chattering and improving steady-state error while ensuring convergence and stability.

[0035] In one specific embodiment of this application, S400 includes: S410 defines the input vector, output, and architecture of the radial basis function neural network. The input vector is composed of the position and velocity of the local machine, as well as the relative position and relative velocity of the local machine and the MAV. The output is a comprehensive perturbation estimate, obtained by multiplying the adjustable weight matrix with the hidden layer output vector. The architecture contains multiple hidden layer nodes, and the hidden layer output is calculated by Gaussian radial basis functions. To reflect the structural information of "manned-unmanned cooperative formation" and improve the learnability of perturbations, this application preferably constructs the input vector of RBFNN as a combination of "local state + relative MAV state": in For network input, They are respectively Position and velocity, These represent the position and velocity of the MAV, respectively. and These represent the relative position and relative velocity of the UAV relative to the MAV, respectively. The key principle behind using this input lies in the reference trajectory generated by S200. Depend on and The construction, and the reference derivative obtained through broadcast information and estimation process, therefore the disturbance... (Refer to the derivative estimation error and communication delay equivalent) It is highly correlated with the relative state; injecting relative quantities into the input can enable the network to learn the "structural perturbations" in cooperative scenarios more effectively.

[0036] To ensure that the network input is a compact set in the theoretical analysis and satisfies the premise of the general approximation of RBFNN, we define the input reachable set. And assume that for any have .in It can be constrained by the flight envelope (speed / position range) and the safety circle. and relative formation configuration The scope is jointly determined.

[0037] For each Configure a containing A radial basis function neural network with n hidden layer nodes. The Gaussian radial basis functions are defined as follows: in For the first The output of each basis function Let be the center vector of the basis function. For width parameter, It is a Euclidean norm. The outputs of all basis functions are used to form the hidden layer vector. in This is the hidden layer output vector.

[0038] Due to disturbance Given a three-dimensional vector, an ideal weight matrix is ​​defined to ensure consistent output dimensions. And adopts a standard approximation form. in For the network's ideal approximation of the disturbance, Let be the approximation error vector. To support subsequent stability derivations, we make the boundedness assumption for the approximation error: there exists a constant vector. , making The inequality sign is interpreted according to the elements. This represents an element-wise absolute value vector.

[0039] The perturbation estimate of the online output of the network is defined as in To estimate the perturbation vector, This is an online adjustable weight matrix. The weight estimation error and the perturbation residual are defined as follows: in Here is the weight error matrix. To learn the residual perturbation, the residual decomposition can be obtained from the above definition. in This is the adjustable residual term caused by weighting error. This is the non-eliminable approximation error term. This decomposition will be used in the Lyapunov proof of S500 to connect the learning error with the robust design term, thus forming a strictly closed-loop theoretical chain.

[0040] S420 employs an online update law combining error-driven and leakage term-based approaches to adjust the adjustable weight matrix in real time, thereby outputting a comprehensive disturbance estimate in real time. Specifically, the online update law defines a weight change rate and updates the adjustable weight matrix in real time based on this rate, thus outputting the comprehensive disturbance estimate.

[0041] To make the network compact at input This application possesses excellent approximation capabilities for the center parameters. With width parameter Implementable setup principles are given. First, to reduce the impact of different dimensions (position, velocity, relative quantities) on distance measurement. The effect can be linearly scaled on the input, defining the scaled input. in For scaling input, It is a diagonal scaling matrix. For the first Dimensional scaling factor. Correspondingly, the distance term in the basis function definition is available. It means that, among them This is to scale the domain center. This process does not change the network structure; it is only used to improve numerical conditions and learning efficiency.

[0042] Secondly, the center vector Can be played offline The selection can be made by using methods such as uniform grid sampling or clustering to obtain a representative set of points. Width parameter It can be determined according to the center spacing, typically by making in The minimum distance or average nearest neighbor distance among adjacent centers in the central set. This is a scaling factor used to adjust the coverage of the basis functions. The purpose of this setting is to ensure that the basis functions cover the specified range. The activations have sufficient overlap to avoid learning blind spots caused by sparse activations or insufficient resolution caused by overly wide activations.

[0043] Next, initial weight values It can be a zero matrix or a small random matrix: in for Zero matrix. The significance of initializing to zero is that in the early stages of control, stability is mainly ensured by the adaptive terminal sliding mode robust terms of the S500. As the network learns gradually, the magnitude of the robust terms is reduced, thus achieving a "stability first, then optimization" performance evolution process. This strategy aligns with the priority requirements of safety and robustness in practical engineering.

[0044] To directly couple the learning process of the RBFNN with the outer loop tracking error and ensure bounded weights and low computational complexity, this application adopts an online update law of "error signal driving + leakage regularization". Let the position outer loop sliding mode variable constructed in S500 be... The weight update law is defined as follows: in The rate of change of weight. For learning rate, Leakage coefficient, It is the Euclidean norm. This is the outer product driving term. The outer product term prompts the weights to be updated along the correlation direction between the "basis function activation direction" and the "error signal direction," thereby reducing... Leakage terms are used to suppress parameter drift and ensure... Bounded, this applies to subsequent Lyapunov function construction (including...) (Item 1) is necessary.

[0045] In the discrete implementation, let the control period be... Euler discretization is used to obtain in Indicates time Weight estimation, Indicates in The update amount is calculated using the above formula. This implementation requires calculation per cycle. basis functions , forming vector Calculate the outer product And perform matrix addition, the overall complexity is O(n log n). It does not include any iterative optimization process and meets the requirements for low-complexity real-time control.

[0046] It should be further explained that this application adopts a complementary structure of "learning compensation + adaptive robustness" in its overall mechanism. Specifically, the S400 outputs... In the outer loop control law of S500, The formal compensation is incorporated into the nominal compensation term to offset the overall disturbance. The main part; at the same time, S500 will also introduce an upper bound estimator for residual perturbations. Construct robust terms to suppress The remaining impact. Due to It can be decomposed into ,in The amplitude of the robust term tends to decrease under the action of the update law, so the amplitude required by the robust term can be reduced as the learning process progresses. This effectively reduces sliding mode chattering and improves steady-state accuracy while ensuring stability and convergence, demonstrating the key contribution of RBFNN in MAV-UAV cooperative formation control.

[0047] In one specific embodiment of this application, S500 includes: S510, define position error and velocity error, which are obtained by subtracting the actual state of the UAV from the expected reference trajectory and its derivative; S520, constructs a position outer loop terminal sliding surface containing a linear error term and a regularized terminal nonlinear function; S530, based on the position outer loop terminal sliding surface, design the position outer loop adaptive terminal sliding control law, which includes a reference acceleration compensation term, an error dynamics compensation term, a comprehensive disturbance estimate feedforward compensation term, a sliding variable proportional term, a terminal arrival term, and an adaptive robust term. S540 introduces an adaptive estimation vector for the upper bound of the residual disturbance and updates it online according to the error-driven adaptive law, thereby outputting the equivalent translation control quantity.

[0048] The first is obtained from S200. Reference trajectory of UAV and its derivative , Position error and velocity error are defined as follows: in This is the position error vector. For the velocity error vector, and These represent the actual position and velocity of the UAV.

[0049] To introduce terminal convergence characteristics and avoid the problems of traditional terminal terms The strange problem that occurs at times, define a regularized terminal function. in For regularized terminal vectors, For element-wise absolute values, It is a very small positive number. The terminal exponent. For element-wise multiplication, Let be an element-wise sign function. Its corresponding derivative is written as . in for The derivative vector, because And being bounded ensures that the nominal compensation item can be realized.

[0050] Equivalent model of S300 Constructing the outer ring sliding mode variable in For sliding mode variables, and It is a positive definite diagonal gain matrix. , This is the gain constant. The sliding surface contains a linear error term and a terminal nonlinear term, when... The time-error dynamics contain a terminal term, thus exhibiting a faster convergence trend, and through... Guarantee differentiability and numerical stability.

[0051] To mitigate chattering caused by switching and maintain control continuity, a continuous sign function is defined. in For continuous symbol vectors, For boundary layer parameters, This is an element-wise absolute value vector. This operator is subsequently used for the continuous implementation of the terminal arrival law and the adaptive robustness term.

[0052] From the definition of error, we can obtain in For error acceleration, For reference acceleration. Differentiation yields The RBFNN perturbation estimate obtained from S400 is: in This is the disturbance estimation vector. For online weight matrix, Let be the hidden layer output vector. Define the learning residual perturbation as... in This refers to the residual disturbance that was not compensated by the network.

[0053] To form a complementary mechanism of "learning compensation + adaptive robustness" and ensure stability and convergence even with disturbance changes and learning errors, the outer-loop control law for position is designed as follows: in This is the equivalent control quantity for the outer loop. and It is a positive definite diagonal gain matrix. , It is the gain constant. For the terminal to reach the exponent, This is the adaptive estimation vector for the upper bound of the residual perturbation. This is a learning compensation term for RBFNN, used to offset the learnable part of the synthesized perturbation; and These are linear terms and terminal arrival terms, used to drive... Fast convergence; This is an adaptive robust term used to suppress the uncertainties caused by the learning residuals and approximation errors.

[0054] To estimate the upper bound of the residual perturbation online and avoid conservatively selecting the robust gain, an adaptive law is introduced. in To adaptively estimate the rate of change, For adaptive gain, Leakage coefficient, It is an element-wise absolute value vector.

[0055] Substitute the control law into Obtain closed-loop sliding mode dynamics in To learn the residual perturbation, and for stability analysis, the Lyapunov function is selected as a candidate. in For Lyapunov functions, The error vector is used to estimate the upper bound of the residual. The upper bound constant vector of the unknown but bounded residual perturbation (satisfying) ).right Differentiate and combine with inequalities And the adaptive law, can be obtained The upper bound satisfies in Representation matrix The smallest eigenvalue, For the reason The positive constants that are determined together with the boundary layer parameters. For boundary layer continuity RBFNN approximation error upper bound The bounded terms caused by equality. This inequality shows that... Enter a space with within a limited time. A proportionally adjustable small neighborhood; when Take the smallest and RBFNN learning makes As it decreases, the neighborhood can be further reduced. Because... and The relationship is given by the definition of the sliding surface, and therefore the positional error can be further derived. With speed error It also enters the bounded small neighborhood.

[0056] In one specific embodiment of this application, S600 includes: S610, The equivalent translation control quantity is superimposed with the gravitational acceleration to construct a combined acceleration command; S620, set the desired yaw angle to be consistent with the yaw angle broadcast by the MAV; S630, based on the combined acceleration command and the desired yaw angle, analytically calculates the desired pitch angle and desired roll angle through algebraic operations; S640 calculates the total thrust command based on the desired pitch angle, desired roll angle, and the vertical component of the resultant acceleration, thereby obtaining the desired attitude angle and total thrust command.

[0057] The equivalent translation control quantity of the outer loop output is obtained from S500. in for The outer ring equivalent acceleration command vector, Inertial coordinate system The equivalent acceleration components in the three axes. To enable the multi-rotor to perform this equivalent acceleration, it is necessary to... Mapped to attitude reference , , With total thrust This forms a parsing interface between the outer position loop and the inner attitude loop.

[0058] Define the resultant acceleration command vector as in To combine acceleration commands, The acceleration due to gravity is constant. Let be the unit vector in the vertical direction of the inertial frame. The physical meaning of this definition is: the thrust of a multi-rotor needs to simultaneously counteract gravity and generate the desired outer ring acceleration. Therefore, when analytically solving for the desired attitude and thrust, the resultant acceleration superimposed with the gravity compensation term should be used.

[0059] In manned-unmanned collaborative formation scenarios, to maintain consistent formation orientation and alignment with the S200 reference configuration, the yaw reference is taken as... in for Desired yaw angle The yaw angle for MAV broadcast.

[0060] make in These are combined acceleration commands. The three-axis components in an inertial coordinate system. (From...) achievable in This is the equivalent acceleration vector output by the outer loop of the S500. Its three-axis components, The acceleration due to gravity is constant. Let be the vertical unit vector of the inertial frame.

[0061] Given the desired yaw angle Then, based on the geometric relationship between the thrust direction and the resultant acceleration, the desired pitch angle is analytically obtained. in for The expected pitch angle, For the three-axis components of the resultant acceleration, for The expected yaw angle. Further analysis yields the expected roll angle. in for Expected roll angle The desired pitch angle is obtained from the above formula.

[0062] The total thrust command is obtained from the relationship between the vertical thrust component and the resultant acceleration scalar. in for Total thrust command, for Quality parameters, For the vertical component of the resultant acceleration, These are the desired roll angle and the desired pitch angle, respectively. To avoid... Too small a value leads to an excessively large calculated thrust, which is problematic in engineering implementation. , Set the upper limit of the tilt angle, for The maximum thrust limit is set; this limit is an execution-level feasibility constraint and does not change the control structure and theoretical derivation link of this application.

[0063] Finally, the reference signal required for the inner loop of the attitude output in this step is defined as follows: in for The expected Euler angle vector, This represents the expected total thrust. Subsequent S700s will use... To track the attitude of the target and output torque commands This achieves a complete closed-loop execution from the outer loop to the inner loop. The analytical transformation only involves algebraic operations and function calculations, without introducing model prediction or optimization solutions. The computational complexity per cycle is constant, meeting the requirements for low-complexity real-time implementation.

[0064] In one specific embodiment of this application, S700 includes: S710, define attitude angle error and angular velocity error, which are obtained by subtracting the actual attitude of the UAV from the desired attitude angle and its derivative; S720, constructs an attitude inner loop terminal sliding surface that includes a linear error term and a regularized terminal nonlinear function; S730, based on the attitude inner loop terminal sliding surface, design the attitude inner loop torque control law, which includes the desired attitude acceleration compensation term, coupling term compensation term, error dynamics compensation term, sliding variable proportional term, terminal arrival term, and attitude adaptive robust term. The S740 introduces an adaptive estimation vector for the upper bound of the attitude residual perturbation and updates it online according to the error-driven adaptive law, thereby outputting the attitude torque command.

[0065] The first is obtained from S600 The desired attitude reference for the UAV is in Let be the desired Euler angle vector. These are the desired roll angle, pitch angle, and yaw angle, respectively. The attitude angle tracking error and its derivative are defined as follows: in This is the attitude angle error vector. Let be the attitude angular velocity error vector. and Let be the actual Euler angles of the UAV and their derivatives, respectively.

[0066] To achieve finite-time convergence and avoid terminal term singularities, a regularized terminal function (defined element-wise) consistent with S500 is adopted: in This is the attitude channel regularized terminal vector. It is a very small positive number. The terminal exponent. It is an element-wise absolute value vector. This is element-wise multiplication. The corresponding derivative is... in for The time derivative, because And guarantee It is bounded, which facilitates the construction of subsequent nominal compensation terms.

[0067] Define the attitude inner loop terminal sliding mode variable as in Let be the attitude sliding mode variable vector. and It is a positive definite diagonal gain matrix. and This is the gain parameter. This sliding mode variable is consistent with the outer loop form of the S500, ensuring that the dual-loop design can be analyzed in a unified structural manner.

[0068] The second-order model of attitude angles given by S300 can be uniformly written in vector form. in The second derivative vector of the attitude angle. For a computable coupling term vector, For the input gain matrix, The moment of inertia is the rotation of the three axes. This is the attitude torque control input vector. This is the attitude channel integrated perturbation vector (see S300).

[0069] From the definition of error, we can obtain in Let be the vector of the second derivative of the attitude error. Let be the second derivative of the desired attitude angle. For Differentiation yields , in The derivative of the attitude sliding mode variable.

[0070] To reduce chattering and maintain continuity, a continuous sign function is introduced. in For continuous symbol vectors, For boundary layer parameters, It is an element-wise absolute value vector.

[0071] The design attitude inner loop torque control law is as follows: in This is the attitude torque command vector. The input gain inverse matrix, and It is a positive definite diagonal gain matrix. For the terminal to reach the exponent, This is the adaptive estimation vector for the upper bound of the attitude residual perturbation. The control law includes a nominal compensation term. Linear convergent term Terminal arrival item and adaptive robust terms Used for joint driving It converges and suppresses the effects of disturbances.

[0072] To estimate the upper bound of attitude channel residual perturbation online and avoid conservative gain selection, an adaptive law is introduced. in To adaptively estimate the rate of change, For adaptive gain, Leakage coefficient, This is an element-wise absolute value vector. This adaptive law enhances robust compensation when the sliding mode variable is large, and automatically reduces the magnitude of the robust term as the error decreases, thereby reducing chattering and energy consumption.

[0073] Substituting the attitude control law Obtain closed-loop sliding mode dynamics , in Let be the attitude channel synthesized perturbation vector. Assume there exists an unknown but bounded upper bound vector. Make The inequality sign is interpreted element-wise. The candidate Lyapunov function is selected as... in For Lyapunov functions, The error vector is used to estimate the upper bound of the residual. This is the adaptive gain constant. Combined with the inequality... And the adaptive law, can be obtained satisfy in for The smallest eigenvalue, For the reason The positive constants determined by the boundary layer parameters, For boundary layer continuity The bounded terms caused by the inequality. From this inequality, we know... Within a finite time, it enters an adjustable neighborhood, and the size of the neighborhood varies. It decreases as the quantity decreases. Because of this... and The relationship is given by the definition of the sliding surface, and the attitude error can be further derived. With attitude error derivative Similarly, it enters the bounded small neighborhood, thus ensuring the attitude inner loop is aligned. Stable tracking provides fast and stable attitude response support for the closed-loop execution of formation control.

[0074] In one specific embodiment of this application, S800 includes: S810, based on the UAV's rotor layout, geometry, and force efficiency characteristics, pre-establishes a hybrid control matrix; the hybrid control matrix is ​​used to realize the linear mapping of total thrust command and three-axis attitude torque command to the speed or thrust command of each motor; S820, in each control cycle, the total thrust command and the attitude torque command are input into the hybrid control module so that the hybrid control module can use the hybrid control matrix to calculate the commands of each motor and issue them for execution.

[0075] The total thrust command output by S600 Attitude torque command output by S700 The quadcopter's conventional hybrid control module receives speed / thrust commands from each motor and executes them. The hybrid control mapping can be represented as follows: in for Motor command vector, For the first The speed (or equivalent pulling force) command for each motor. This is a conventional hybrid control matrix for a quadcopter, determined by rotor layout, rotation direction, arm length, and thrust / anti-torque coefficients. This hybrid control module is part of the general engineering implementation and is only used to distribute the total thrust and torque commands to the actuators; it does not change the control law structure or theoretical derivation link of this application.

[0076] For each During the control cycle (Sampling period is) The following online processes are executed sequentially within the MAV to form a closed-loop control link from MAV broadcast to UAV actuator output: (1) Receive MAV broadcast status ,in For MAV position, For MAV speed, This is the MAV yaw angle; (2) Generate a reference trajectory based on S200 ,in for Reference position, and These are their first and second derivatives, respectively, and a safety-circle analytical correction is performed. (3) Collect local status superscript Indicates the measured value; (4) Calculate the outer loop error of the position based on S500. and sliding mode variables ,in , ; (5) Calculate the RBFNN basis function vector Update weights according to S400 And obtain the disturbance estimate ,in For online weight matrix, This is the disturbance estimation vector; (6) Update the upper bound estimate of the outer loop residuals according to the adaptive law of S500. The S500 outputs the outer loop equivalent control quantity. ; (7) Obtained through S600 parsing and conversion and ,in ; (8) Attitude torque output by S700 (and simultaneously update the inner loop adaptive value), and then the S800 hybrid control system obtains the motor command. The order was then issued and implemented, and the next cycle began. .

[0077] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of this application and should not be construed as limiting the specific implementation of this application to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of this application, and all such modifications or substitutions should be considered within the scope of protection of this application.

Claims

1. A radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation, characterized in that, include: S100, construct a cooperative formation system consisting of manned aircraft (MAV) and N unmanned aerial vehicles (UAV), wherein the MAV broadcasts its own status only in one direction and the UAV makes independent decisions; S200: Each UAV broadcasts its own status information unidirectionally based on the MAV, and combines it with the preset formation relative displacement vector to generate the expected position reference trajectory and its derivative with safety circle constraint correction. S300, Establish an equivalent disturbed model for the UAV. The equivalent disturbed model includes translational mechanics and attitude dynamics, wherein the translational mechanics is equivalent to a second-order system with a comprehensive disturbance term, and the attitude dynamics is described as a second-order form with an attitude disturbance term. S400 constructs a radial basis function neural network with local state and relative MAV state as input, learns online and outputs a comprehensive perturbation estimate; S500, based on the equivalent disturbance model and the comprehensive disturbance estimate, with the desired position reference trajectory and its derivative as the tracking target, designs a position outer loop adaptive terminal sliding mode control law that integrates radial basis function neural network feedforward compensation to output an equivalent translation control quantity; S600, the equivalent translation control quantity is analytically converted into the desired attitude angle and total thrust command; S700, design an attitude inner loop adaptive terminal sliding mode control law to track the desired attitude angle, thereby outputting attitude torque command; S800: Input the total thrust command and the attitude torque command into the hybrid control module to generate commands for each motor and send them out for execution.

2. The radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation as described in claim 1, characterized in that, S100 includes: S110, Define the self-state of the MAV broadcast, which includes at least its position, speed and yaw angle; S120 defines that when the UAV side receives MAV broadcasts, it adopts the latest data retention strategy for communication delay and the communication strategy of retaining the previous valid data for short-term packet loss. S130 establishes a collaborative formation system that includes MAVs and N UAVs.

3. The radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation as described in claim 1, is characterized in that... S200 includes: S210: Based on the position and yaw angle broadcast by the MAV, the preset formation relative displacement vector is rotated to the inertial frame and superimposed with the MAV position to generate the initial expected position reference; S220, calculate the relative distance between the initial expected position reference and the actual position of the MAV. When the relative distance is less than the preset safety radius, project the initial expected position reference radially to the safety boundary to obtain the corrected expected position reference and its derivative.

4. The radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation as described in claim 1, characterized in that, The S300 includes: S310 describes the translational mechanics of UAV as a second-order form in which acceleration equals the sum of the equivalent translational control quantity and the comprehensive disturbance term; S320 describes the angular dynamics of each axis of the attitude channel as a second-order form of the sum of known coupling terms, controlled torque terms, and disturbance terms; S330, make boundedness assumptions on the integrated disturbance term and attitude disturbance term, and establish the equivalent disturbed model of the UAV.

5. The radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation as described in claim 1, characterized in that, The S400 includes: S410 defines the input vector, output, and architecture of the radial basis function neural network. The input vector is composed of the position and velocity of the local machine, as well as the relative position and relative velocity of the local machine and the MAV. The output is a comprehensive perturbation estimate, obtained by multiplying the adjustable weight matrix with the hidden layer output vector. The architecture contains multiple hidden layer nodes, and the hidden layer output is calculated by Gaussian radial basis functions. The S420 employs an online update law that combines error-driven and leakage term-based adjustments to the adjustable weight matrix in real time, thereby outputting a comprehensive disturbance estimate in real time.

6. The radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation as described in claim 5, is characterized in that, The online update law is specifically defined as follows: a weight change rate is defined, and the adjustable weight matrix is ​​updated in real time according to the weight change rate, thereby outputting a comprehensive disturbance estimate.

7. The radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation as described in claim 1, characterized in that, The S500 includes: S510, define position error and velocity error, which are obtained by subtracting the actual state of the UAV from the expected reference trajectory and its derivative; S520, constructs a position outer loop terminal sliding surface containing a linear error term and a regularized terminal nonlinear function; S530, based on the position outer loop terminal sliding surface, design the position outer loop adaptive terminal sliding control law, which includes a reference acceleration compensation term, an error dynamics compensation term, a comprehensive disturbance estimate feedforward compensation term, a sliding variable proportional term, a terminal arrival term, and an adaptive robust term. S540 introduces an adaptive estimation vector for the upper bound of the residual disturbance and updates it online according to the error-driven adaptive law, thereby outputting the equivalent translation control quantity.

8. The radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation as described in claim 1, characterized in that, The S600 includes: S610, The equivalent translation control quantity is superimposed with the gravitational acceleration to construct a combined acceleration command; S620, set the desired yaw angle to be consistent with the yaw angle broadcast by the MAV; S630, based on the combined acceleration command and the desired yaw angle, analytically calculates the desired pitch angle and desired roll angle through algebraic operations; S640 calculates the total thrust command based on the desired pitch angle, desired roll angle, and the vertical component of the resultant acceleration, thereby obtaining the desired attitude angle and total thrust command.

9. The radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation as described in claim 1, characterized in that, The S700 includes: S710, define attitude angle error and angular velocity error, which are obtained by subtracting the actual attitude of the UAV from the desired attitude angle and its derivative; S720, constructs an attitude inner loop terminal sliding surface that includes a linear error term and a regularized terminal nonlinear function; S730, based on the attitude inner loop terminal sliding surface, design the attitude inner loop torque control law, which includes the desired attitude acceleration compensation term, coupling term compensation term, error dynamics compensation term, sliding variable proportional term, terminal arrival term, and attitude adaptive robust term. The S740 introduces an adaptive estimation vector for the upper bound of the attitude residual perturbation and updates it online according to the error-driven adaptive law, thereby outputting the attitude torque command.

10. The radial basis function neural network perturbation learning and adaptive terminal sliding mode dual-loop control method for manned / unmanned aircraft cooperative formation as described in claim 1, characterized in that, The S800 includes: S810, based on the UAV's rotor layout, geometry, and force efficiency characteristics, pre-establishes a hybrid control matrix; the hybrid control matrix is ​​used to realize the linear mapping of total thrust command and three-axis attitude torque command to the speed or thrust command of each motor; S820, in each control cycle, the total thrust command and the attitude torque command are input into the hybrid control module so that the hybrid control module can use the hybrid control matrix to calculate the commands of each motor and issue them for execution.

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