Multi-rotor unmanned aerial vehicle adaptive distributed cooperative control method, medium and equipment

Abstract

The invention relates to the technical field of unmanned aerial vehicle control, and discloses a multi-rotor unmanned aerial vehicle adaptive distributed cooperative control method, a medium and equipment. The method comprises the following steps: constructing a spectrum normalization Lagrangian neural network for uncertainty identification of a multi-rotor unmanned aerial vehicle model; constructing a multi-fidelity Lagrangian identifier based on the Lagrangian neural network and a multi-fidelity learning strategy, and utilizing a training data set containing high-fidelity data and low-fidelity data to identify the uncertainty of the multi-rotor unmanned aerial vehicle model; and training a multi-fidelity Lagrange identifier by minimizing a multi-objective loss function, and designing an adaptive control law based on the trained multi-fidelity Lagrange identifier in combination with a predetermined performance function and a distributed synchronization error to generate a control instruction. According to the method, the model stability and the physical interpretability are guaranteed, the dependence on expensive high-fidelity data is reduced, and the tracking precision and the system reliability of the multi-rotor unmanned aerial vehicle cluster under the condition that the model is uncertain are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of unmanned aerial vehicle control, and particularly relates to a multi-rotor unmanned aerial vehicle adaptive distributed cooperative control method, medium and equipment. BACKGROUND

[0002] Multi-rotor unmanned aerial vehicles have become an indispensable device in modern emergency rescue due to their excellent maneuverability and versatility, and play a key role in mountain missing person search and rescue, urban debris life detection, and sea distress target positioning. Multi-rotor unmanned aerial vehicle cooperative operation can overcome the functional and performance limitations of single unmanned aerial vehicle, play the emergence of the whole system, improve the efficiency of task completion, and expand the task execution ability through the coordination and cooperation between unmanned aerial vehicles. Distributed cooperative control is not only the key to supporting multi-rotor unmanned aerial vehicle cooperative operation, but also a bottleneck that needs to be broken through, and is crucial to improving the effect of multi-rotor unmanned aerial vehicle cooperative operation.

[0003] Early multi-unmanned aerial vehicle cooperative control mainly considers centralized control, and although this kind of method is simple in design, it has heavy communication burden and is not easy to expand. At present, researchers pay more attention to multi-unmanned aerial vehicle cooperative control under distributed control, mainly including behavior-based method, virtual structure-based method and artificial potential field-based method. The behavior-based method is easy to implement, but cannot analyze system stability. The virtual structure-based method can realize precise control of formation due to formation feedback, but the design is too complex. The artificial potential field-based method has natural advantages for obstacle avoidance, but the design of artificial potential function is difficult.

[0004] Since the multi-rotor unmanned aerial vehicle is a complex high-order, time-varying, nonlinear system, the internal state space has hidden states that cannot be observed, and in actual rescue operations, the model of the multi-rotor unmanned aerial vehicle has great uncertainty due to the interaction of air flow disturbance, electromagnetic interference and vibration. These model uncertainties are not known and difficult to obtain accurately, and the traditional method often does not apply to the assumption of known model or accurate modeling, so a more complex control strategy is needed to deal with it.

[0005] The core difficulty of distributed cooperative control of multi-rotor unmanned aerial vehicles is accurate approximation of the model uncertainty of multi-rotor unmanned aerial vehicles. The latest method uses a deep neural network to mine hidden states from flight data to describe the model uncertainty, but the "black box" network structure lacks physical mechanism support and has the risk of "unknown model mechanism", which is difficult to meet the stringent requirements of stability and controllability of unmanned aerial vehicles in emergency rescue scenarios. Although the existing physical-inspired neural network has the advantages of clear structure and strong physical consistency, it still faces two challenges when directly applied to the description of the model uncertainty of multi-rotor unmanned aerial vehicles: first, the deep neural network that describes the correlation coefficient of physical prior knowledge lacks reliability, making it difficult for the controller designed based on the model to verify the system stability through traditional theory; second, the modeling accuracy of existing methods depends on a large amount of high-fidelity data, but the actual cost is high. Furthermore, traditional distributed cooperative control methods often perform poorly in the face of model uncertainty and disturbances of multi-rotor unmanned aerial vehicles.

[0006] The present application aims to overcome the shortcomings of the prior art and provide a deep neural network that has physical interpretability and stability and controllability and can reduce the dependence on high-fidelity data for describing the uncertainty of multi-rotor unmanned aerial vehicles, and on this basis, a multi-agent cooperative tracking control method with strong adaptability is designed. SUMMARY

[0007] To solve the above technical problems, the present application provides a multi-rotor unmanned aerial vehicle adaptive distributed cooperative control method, medium and equipment.

[0008] To solve the above technical problems, the present application adopts the following technical solutions: In a first aspect, the present application provides a multi-rotor unmanned aerial vehicle adaptive distributed cooperative control method, comprising: Constructing a spectral normalized Lagrangian neural network for multi-rotor unmanned aerial vehicle model uncertainty identification: based on the Lagrangian mechanics framework, defining the Lagrangian function according to the kinetic energy and potential energy of the unmanned aerial vehicle, and constructing a parameterized dynamics function based on the Euler-Lagrange equation, and imposing spectral normalization constraints on the weights of each layer of the Lagrangian neural network; Constructing a multi-fidelity Lagrangian identifier based on the Lagrangian neural network and a multi-fidelity learning strategy, using a training data set containing high-fidelity data and low-fidelity data, and training the multi-fidelity Lagrangian identifier by minimizing a multi-objective loss function, the multi-objective loss function including at least a low-fidelity data fitting loss, a high-fidelity data prediction loss, and an energy conservation constraint loss; For each unmanned aerial vehicle node in the multi-rotor unmanned aerial vehicle cluster, based on the trained multi-fidelity Lagrangian identifier, combining a predetermined performance function and a distributed synchronization error, designing an adaptive control law to generate control instructions.

[0009] In one embodiment, the Lagrangian mechanics framework is used to define a Lagrangian function based on the kinetic and potential energy of the UAV, including: The kinetic energy of the UAV includes translational kinetic energy and rotational kinetic energy The translational kinetic energy is calculated based on linear velocity The total kinetic energy of the UAV ; The potential energy of the UAV is calculated based on the vertical height of the UAV in the NECS with the ground as the zero potential energy surface ; According to Lagrangian mechanics, the Lagrangian function is defined as the kinetic energy minus the potential energy : .

[0010] In one embodiment, the translational kinetic energy is: where is the mass of the UAV, and are the north, east, and down linear velocity components recorded in the database, respectively. The rotational kinetic energy of the UAV with a symmetric octo-copter configuration and uniform mass distribution is:

[0011] where is the inertia tensor of the UAV, and are the moments of inertia of the UAV about the body coordinate system axes, and is the angular velocity vector, and are the components of in the body coordinate system axes, and correspond to the roll, pitch, and yaw angular velocities of the UAV, respectively. The potential energy of the UAV is: where is the gravitational acceleration. The Lagrangian function is: .

[0012] In one of the embodiments, the parameterized dynamics function is constructed based on Euler-Lagrange equation, specifically comprising: ; ; wherein, represents a generalized coordinate describing the attitude of the UAV, represents a generalized velocity, and are gradient operators on the generalized velocity and the generalized coordinate respectively; the time derivative is expanded by using the chain rule to obtain: ; ; is an angular acceleration; the acceleration is integrated by using the fourth-order Runge-Kutta method to realize state updating: ; ; ; ; wherein, is a state vector of the UAV at the current time, , represent a roll angle, a pitch angle and a yaw angle respectively, is a state change rate calculation function, is an intermediate calculation quantity, is a numerical integration step; the updated dynamics parameters of the UAV are obtained : .

[0013] In one of the embodiments, the spectral normalization constraint is imposed on the weights of each layer of the Lagrangian neural network, specifically comprising: ; ; wherein, L is referred to as a Poincare constant, is an original weight matrix of each layer of the Lagrangian neural network, is a spectral norm of the weight matrix, is a weight matrix of each layer of the Lagrangian neural network after imposing the spectral normalization constraint, is a norm of a vector x, is a maximum singular value of the weight matrix .

[0014] In one embodiment, the construction of the multi-fidelity Lagrange discriminator based on the Lagrange neural network and the multi-fidelity learning strategy specifically includes: Multi-fidelity Lagrange identifiers include low-fidelity prediction networks, high-fidelity linear association networks, high-fidelity nonlinear association networks, and Lagrange neural networks: The low-fidelity prediction network is used to perform low-fidelity prediction based on the input UAV state vector; the high-fidelity linear correlation network and the high-fidelity nonlinear correlation network are used to learn the linear and nonlinear mapping relationship between the low-fidelity prediction results and the high-fidelity data, and output correction terms; the Lagrange neural network is used to fuse the correction terms and fit the Lagrange quantity.

[0015] In one embodiment, the multi-objective loss function for: ; in: ; ; ; High-fidelity linear correlation network and high-fidelity nonlinear correlation networks Integrating into a high-fidelity prediction network , They represent low-fidelity prediction networks respectively. High-fidelity prediction network Lagrange neural networks Network output, respectively The corresponding actual data value The loss values ​​for low-fidelity data fitting are, in order: Calculation and high-fidelity data prediction loss Calculation and energy conservation constraint loss The number of samples calculated For regularization loss, As weight.

[0016] In one embodiment, the adaptive control law is designed based on the trained multi-fidelity Lagrange discriminator, combined with a predetermined performance function and distributed synchronization error, to generate control commands, specifically including: Design an exponentially decreasing predetermined performance function:

[0017] in, These correspond to the roll angle, pitch angle, and yaw angle error channels of the UAV, respectively. This is the upper bound of the initial error. Upper bound of steady-state error Here is the convergence rate parameter; the function satisfies For all Established, and ; Indicates the first The first drone The predetermined performance function for each error channel. Indicates the serial number of the drone node; Based on the characteristics of directed communication topology, the distributed synchronization error of UAV node i is defined, which integrates the state deviation of neighboring UAV nodes and the state deviation of the leader: ; Indicates drone node No. Distributed synchronization error of each error channel For drone nodes The neighborhood group, For elements of the adjacency matrix, Indicates drone node Leaders who can be accessed directly , , Each is a drone node Neighboring drone nodes The leader's first Channel status; The constrained synchronization error is transformed into an unconstrained optimization variable, and the transformation error is defined as follows: ; Its inverse transformation is: ; in, , All are positive numbers, used to adjust the sensitivity of the error transformation; For drone nodes The predetermined performance function value of the P-th channel at time t; The transformation error is unconstrained; the derivative of the transformation error is taken to obtain the error dynamic characteristics: ; in, The derivative of the predetermined performance function reflects the rate of change of the error boundary. To integrate the dynamic characteristics of transformation error, a metric error is defined. This reflects the transformation error from first order to... Overall deviation of the order: ; Expanded to: ; in, This is the error dynamic adjustment coefficient. Let be the system order. The m-th derivative of the transformation error; Then the control input signal of UAV node i The expression is: ; in, Let i be the known control input matrix of UAV node i. To control the gain, Let i be the metric error of UAV node i. These are the estimated weights of a Lagrange neural network. It is the activation function vector of the Lagrange neural network. Let be the weighted in-degree of drone node i in the communication topology, which is the sum of the communication weights of all its neighboring nodes for that node. For the leader connection identifier parameter of drone node i, Let i be the auxiliary matrix for UAV node i. It is a higher-order dynamic adjustment coefficient for the transformation error of UAV node i. For the transformation error of UAV node i reciprocal of order; To track changes in unknown dynamics in real time, an adaptive update rule for the weights of a Lagrange neural network is designed: ; in, Let be the estimated weights of the L-th layer network for drone node i. It is a positive definite gain matrix. Let be the basis function vector of UAV node i. Let i be the auxiliary matrix for UAV node i. For topology-related weights, Let i be the external disturbance compensation term for UAV node i. For the leader connection identifier parameter of drone node i, This is the weight decay coefficient.

[0018] In a second aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method of any embodiment of the first aspect.

[0019] Thirdly, the present invention provides a computer device including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the method of any embodiment of the first aspect.

[0020] Compared with the prior art, the beneficial technical effects of the present invention are: 1. This invention proposes a spectral normalized Lagrange neural network architecture for uncertainty identification in multi-rotor UAVs, which solves the problem that traditional physics-inspired deep neural networks are not reliable enough and cannot analyze system stability when used for cooperative control.

[0021] 2. This invention proposes a multi-fidelity learning strategy for Lagrange deep neural networks, which solves the problem of insufficient model generalization caused by the scarcity of high-fidelity data.

[0022] 3. This invention proposes an adaptive distributed cooperative optimization strategy based on a predetermined performance function and error transformation to solve the problem of uncontrollable transient and steady-state performance of traditional adaptive distributed cooperative control. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method in an embodiment of the present invention; Figure 2 This is an architectural diagram of a multi-fidelity Lagrange identifier in an embodiment of the present invention. Detailed Implementation

[0024] A preferred embodiment of the present invention will now be described in detail with reference to the accompanying drawings.

[0025] like Figure 1 As shown, this invention provides an adaptive distributed cooperative control method for multi-rotor unmanned aerial vehicles (UAVs), comprising the following steps: S1. Construct a spectral normalized Lagrange neural network for uncertainty identification of multi-rotor UAV models: Based on the Lagrange mechanics framework, define the Lagrange function according to the kinetic and potential energy of the UAV, and construct a parameterized dynamic function based on the Euler-Lagrange equation, and apply spectral normalization constraints to the weights of each layer of the Lagrange neural network. S2, Construct a multi-fidelity Lagrange identifier based on a Lagrange neural network and a multi-fidelity learning strategy. Use a training dataset containing high-fidelity data and low-fidelity data to train the multi-fidelity Lagrange identifier by minimizing a multi-objective loss function. The multi-objective loss function includes at least low-fidelity data fitting loss, high-fidelity data prediction loss, and energy conservation constraint loss. S3. For each drone node in the multi-rotor drone swarm, based on the trained multi-fidelity Lagrange identifier, combined with a predetermined performance function and distributed synchronization error, an adaptive control law is designed to generate control commands.

[0026] In this invention, high-fidelity data refers to high-precision state and control data that are collected based on the AirSim high-fidelity simulation platform and reflect the real dynamic characteristics of UAVs, while low-fidelity data is simulation data with lower precision but lower acquisition cost.

[0027] The present invention will be described in detail below in several parts.

[0028] 1. Data preparation and preprocessing.

[0029] Data collection was accomplished using the AirSim software package, which provides a physical simulation environment based on Unreal Engine. It uses a central processing unit (CPU) for logical operations and a graphics processing unit (GPU) for scene rendering, and defines the drone's characteristics through a unified drone parameter configuration interface.

[0030] The drone model used in this invention is the DJI Spreading Wings S1000+, an octocopter drone with a frame weight of 4.4 kg and fuselage dimensions of 460×511×305 mm. This drone provides rich expansion interfaces, adaptable to professional gimbals, GPS modules, and IMU unit components. Within the AirSim framework, the mass, inertial characteristics, physical constants, and frame structure shape of this model are described through a multi-rotor parameter configuration interface. Multiple flight experiments were conducted, and position data was collected during flight. linear velocity Euler angles angular velocity and control quantity The data included, among which , For roll angle, The pitch angle, The yaw angle is set at a sampling frequency of at least 100Hz. Random disturbances acting on the UAV's center of mass and the propellers are also added to simulate environmental noise during real flight.

[0031] The collected dataset was divided into training, validation, and test sets in a 6:2:2 ratio. Data smoothing, outlier removal, and normalization were performed to eliminate the influence of units and accelerate model convergence.

[0032] 2. Construct a multi-rotor UAV model based on a multi-fidelity Lagrange identifier.

[0033] The nonlinear dynamic model of UAV node i is as follows: ; in, For drone nodes of first state, For drone nodes of The first derivative of a state describes the rate of change of that state over time. For unknown nonlinear dynamics, Given the control input matrix, To control the input, this invention introduces a Lagrangian mechanics framework, defining the Lagrangian function. Then, by using the Euler-Lagrange equations and automatic differentiation, the angular acceleration is derived, and a parameterized dynamic function is constructed. .

[0034] (1) Construct a spectral normalized Lagrange mechanical framework.

[0035] First, for a coordinate of Classical physical systems, from their initial state To the final state There are many possible movement paths. These represent the system's generalized coordinates and generalized velocity, respectively. Lagrange mechanics uses the concept of "action" to determine the system's actual path of motion. Action Defined as a functional: ; in, Represents the kinetic energy of the system. This represents potential energy. The actual path of motion is... The path that takes the minimum value, i.e. To satisfy this condition, a Lagrange quantity is defined. The difference between kinetic energy and potential energy, i.e. .

[0036] The kinetic energy of the drone consists of translational kinetic energy. and rotational kinetic energy It consists of two parts. The translational kinetic energy is calculated based on the linear velocity, and the expression is: ; in, For the quality of drones, These are the linear velocity components in the north, east, and ground directions recorded in the database.

[0037] Rotational kinetic energy is related to angular velocity and moment of inertia. This UAV adopts a symmetrical octocopter layout with uniform mass distribution. The expression is: ; in, For the inertial tensor of the drone, Let angular velocity vector be the total kinetic energy of the UAV. It comprehensively reflects the energy state during the motion process.

[0038] Select the vertical altitude of the UAV in the northeast coordinate system Calculate the gravitational potential energy. Taking the ground as the zero potential energy surface, the potential energy expression is: ; in, It is the acceleration due to gravity. This refers to the vertical altitude of the drone.

[0039] According to Lagrange mechanics, the Lagrange function kinetic energy and potential energy Substituting, we get: ; Secondly, by automatically differentiating and solving the Euler-Lagrange equations, the angular acceleration is derived. Construct a parameterized dynamic function and output dynamic prediction results that conform to physical laws, specifically as follows: ; ; in, These are generalized coordinates describing the attitude of the drone. It is speed in a general sense. and These are the gradient operators for generalized velocity and generalized coordinates, respectively. Expanding the time derivative using the chain rule, we obtain: ; .

[0040] The fourth-order Runge-Kutta method (RK4) is used to integrate the acceleration to achieve state updates. First, the following calculations are performed: ; ; ; .

[0041] in, The state vector of the drone at the current moment is as follows: , The function for calculating the rate of change of state. , , , This is an intermediate computational resource used to gradually approximate the changes in the state. This is the numerical integration step size.

[0042] Then update the status: .

[0043] Finally, a spectral normalization constraint is introduced for the weight matrices of each layer of the network. The spectral norm is modified to satisfy the preset constraints, specifically as follows: ; .

[0044] Where L is called the Lipschitz constant. Here are the original weight matrices for each layer of the Lagrange neural network. Let be the spectral norm of the weight matrix. Let x be the norm of vector x. The maximum singular value of the weight matrix. In practical implementation, since directly calculating the spectral norm of a large-scale matrix is ​​computationally expensive, this invention uses a power iteration method to approximate the solution for the maximum singular value, that is, by iteratively optimizing vectors u and v to satisfy: ; After iterative convergence, use Approximate spectral norm This reduces computational complexity while maintaining accuracy.

[0045] (2) Construct a multi-fidelity Lagrange identifier.

[0046] The identifier constructed in this invention comprises four core modules: a low-fidelity prediction network, a high-fidelity linear association network, a high-fidelity nonlinear association network, and a Lagrange neural network, with the specific structure as follows: Low-fidelity prediction networks The network model consists of an input layer (Input), a fully connected layer (Fc1), a fully connected layer (Fc2), and an output layer (Output) from top to bottom. The input layer (Input) obtains the 6-dimensional state vector of the UAV. The system imports input data into the model; fully connected layers Fc1 and Fc2 are used together to extract basic features from the input data. Linear transformations of neurons and the Tanh activation function are used to initially fit the state change patterns. The weights of both fully connected layers are spectral normalized to ensure network stability. The output layer outputs a low-fidelity prediction of the state at the next time step. This completes the initial extraction of basic features. The fully connected layer Fc1 has 200 neurons, the fully connected layer Fc2 has 100 neurons, and the output layer has a dimension of 6, consistent with the input state dimension.

[0047] High-fidelity linear correlation network The network model consists of an input layer (Input), a fully connected layer (Linear_Fc), and an output layer (Output) from top to bottom. The input layer (Input) acquires high-fidelity data. Compared with low-fidelity prediction results The concatenated vector, with a dimension of 12, is used to import dual-input data. The fully connected layer Linear_Fc performs a linear transformation on the input vector, capturing the linear mapping relationship between the low-fidelity prediction results and the high-fidelity data. The output layer Output outputs the linear correction term. Specifically, it is expressed as: ; in, for The parameters are set, and the weights of this layer are spectral normalized.

[0048] High-fidelity nonlinear correlation networks with hyperbolic tangent activation function The network model consists of an input layer (Input), fully connected layers (Nonlinear_Fc1 and Nonlinear_Fc2), and an output layer (Output) from top to bottom. The input layer (Input) uses the same input as in a high-fidelity linear relational network. The fully connected layers (Nonlinear_Fc1 and Nonlinear_Fc2) learn high-fidelity data using the hyperbolic tangent activation function (Tanh). Compared with low-fidelity prediction results The complex nonlinear relationship between them, and the weights of both fully connected layers are spectral normalized, with the output layer outputting a nonlinear correction term. Specifically, it is expressed as: ; in, for The parameters are as follows. The number of neurons in the fully connected layer Nonlinear_Fc1 and the fully connected layer Nonlinear_Fc2 are 200 and 100 respectively, and the output layer dimension is 6.

[0049] Lagrange neural networks The network model consists of an input layer (Input), a fully connected layer (Lagrange_Fc1), a fully connected layer (Lagrange_Fc2), and an output layer (Output) from top to bottom. The input layer obtains the fused features by superimposing the linear and nonlinear correction terms. The feature dimension is 6, specifically represented as follows: ; ; ; This represents the fused feature vector resulting from the superposition of linear and nonlinear correction terms. The feature fusion operator is represented by two fully connected layers, Lagrange_Fc1 and Lagrange_Fc2, which are fitted with the Lagrangian quantity using the Softplus activation function. The weights of both fully connected layers are spectral normalized. The output layer, Output, outputs the Lagrangian quantity. Both fully connected layers Lagrange_Fc1 and Lagrange_Fc2 have 400 neurons, and the output layer has a dimension of 1.

[0050] (3) Construct a multi-objective loss function.

[0051] To achieve low-fidelity prediction networks High-fidelity linear correlation network High-fidelity nonlinear correlation networks Lagrange neural networks The collaborative optimization of the four sub-networks, the multi-fidelity Lagrange identifier adopts a multi-objective global loss function, the mathematical expression of which is: ; in: ; ; ; High-fidelity linear correlation network and high-fidelity nonlinear correlation networks Integrating into a high-fidelity prediction network , They represent low-fidelity prediction networks respectively. High-fidelity prediction network Lagrange neural networks Network output, respectively The corresponding actual data value The loss values ​​for low-fidelity data fitting are, in order: Calculation and high-fidelity data prediction loss Calculation and energy conservation constraint loss The number of samples calculated For regularization loss, As weight.

[0052] 3. Model training and optimization.

[0053] A gradient optimization method combined with an adaptive learning rate adjustment strategy was adopted to ensure that the multi-fidelity Lagrange discriminator could effectively converge during training and avoid overfitting. Based on the principle of gradient descent, the model parameter update formula is as follows: ; In the formula, Let represent the model parameters at the t-th iteration, and α be the learning rate used to control the step size of each parameter update. It is the gradient vector of the loss function at t.

[0054] The Adam optimizer was used to co-optimize the network parameters, with a learning rate of 0.001, a weight decay of 2e-05, and a batch size of 128. JAX was used as the automatic differential library to calculate gradients, and the network weights were iteratively optimized using a multi-objective loss function until the model converged. After training, a UAV dynamic model satisfying Lipschitz stability was output, which can be directly used for subsequent controller design and stability analysis.

[0055] 4. Design of predetermined performance functions and acquisition of error dynamic characteristics.

[0056] To constrain the transient and steady-state performance of the synchronization error and ensure that the error convergence rate, overshoot, and steady-state accuracy meet preset requirements, an exponentially decreasing predetermined performance function is designed: ; in, These correspond to the roll angle, pitch angle, and yaw angle error channels, respectively. This is the upper bound of the initial error. Upper bound of steady-state error This is the convergence rate parameter. The function satisfies... For all Established, and It can systematically guide the error from the initial large set to the steady-state small set.

[0057] Based on the characteristics of directed communication topology, the distributed synchronization error of UAV node i is defined. By fusing the state deviations of neighboring UAV nodes and the leader's state deviation, distributed cooperative tracking is achieved, expressed as: ; in, For drone nodes The neighborhood group, For elements of the adjacency matrix, Indicates drone node Leaders can be accessed directly. , , Each is a drone node ,Neighbor The leader's first Channel status.

[0058] The constrained synchronization error is transformed into an unconstrained optimization variable, eliminating the limitations imposed by error boundary constraints on controller design and facilitating the subsequent analytical derivation of the control law. The transformed error is defined as follows: .

[0059] Its inverse transformation is: ; in, , It is a positive number, used to adjust the sensitivity of the error transformation; For drone nodes The predetermined performance function value of the P-th channel at time t; This is an unconstrained transformation error, whose value range is not limited and can be directly used for subsequent control law design.

[0060] Furthermore, the derivative of the transformation error is calculated to obtain the dynamic characteristics of the error: ; in, It is the derivative of the predetermined performance function, reflecting the rate of change of the error boundary.

[0061] 5. Design an adaptive distributed neural control strategy based on a multi-fidelity Lagrange identifier.

[0062] To integrate the dynamic characteristics of transformation error, a metric error is defined. This reflects the transformation error from first order to... The overall deviation of the order is specifically expressed as: ; Expanded to: ; in, This is the error dynamic adjustment coefficient. Let be the system order. Let be the m-th derivative of the transformation error.

[0063] Then the control input signal of UAV node i The expression is: ; in, Let i be the known control input matrix of UAV node i. To control the gain, Let i be the metric error of UAV node i. These are the estimated weights of a Lagrange neural network. It is the activation function vector of the Lagrange neural network. Let be the weighted in-degree of drone node i in the communication topology, which is the sum of the communication weights of all its neighboring nodes for that node. For the leader connection identifier parameter of drone node i, Let i be the auxiliary matrix for UAV node i. It is a higher-order dynamic adjustment coefficient for the transformation error of UAV node i. For the transformation error of UAV node i Reciprocal of the order.

[0064] To track changes in unknown dynamics in real time, an adaptive update rule for the weights of a Lagrange neural network is designed: ; in, Let i be the estimated weight of the Lth layer network for UAV node i. It is a positive definite gain matrix. Let be the basis function vector of UAV node i. Let i be the auxiliary matrix for UAV node i. For topology-related weights, Let be the weighted in-degree of drone node i in the communication topology, which is the sum of the communication weights of all its neighboring nodes for that node. For the leader connection identifier parameter of drone node i, This is the weight decay coefficient.

[0065] 6. System stability analysis.

[0066] To prove the stability of the multi-agent system and ensure that the synchronization error meets the predetermined performance constraints, a Lyapunov candidate function is constructed, specifically expressed as: ; in, For the measurement error of multi-agent systems, It is a positive definite diagonal matrix. It is the weight bias of the neural network. It is a positive definite gain matrix. This is the auxiliary parameter matrix.

[0067] Differentiating the Lyapunov candidate function and analyzing its negative definiteness in conjunction with error dynamics, weight update rules, and control laws, we first... Taking the derivative and substituting it into the dynamic and control law of the measurement error, we get: ; in, The control gain moments for each agent are... The preset positive gain coefficient, Let be the activation function vector of the neural network. As a preset constant vector, The control gain constant, This is the diagonal matrix used to construct the damping term of the system. For auxiliary matrix, For the adjustment coefficient vector, It is a higher-order minterm vector.

[0068] Secondly, for Taking the derivative and substituting it into the weight update rule, we get: ; Finally, for Taking the derivative and combining it with the dynamics of the auxiliary parameters, we can obtain: ; in, The attenuation coefficient is... This is an auxiliary vector.

[0069] Based on the above derivative analysis, combined with the Cauchy-Schwarz inequality, the singular value property of matrices, and pre-defined parameter constraints, it can be proven that there exists a constant. When the control gain satisfy At that time, the following conditions are met: ; in, All are constants. According to Lyapunov stability theory, the global metric error of the system is... Neural network weight bias All are consistent and eventually bounded.

[0070] Furthermore, by combining the characteristics of the error transformation relationship and the predetermined performance function, the synchronization error can be derived. Always satisfied That is, the transient and steady-state performance of the synchronization error strictly meets the preset constraints.

[0071] This invention incorporates a multi-fidelity module into existing physics-inspired deep neural networks. This module can uncover the true mapping relationship between a small amount of real flight high-fidelity and low-fidelity data, thereby reducing the model's dependence on high-fidelity data during training while ensuring the generalization of dynamic predictions in practical applications. This invention introduces spectral normalization constraints into the physics-inspired deep neural network to ensure the model satisfies Lipschitz stability, which can be used for stability analysis of subsequent cooperative control strategies. This invention introduces a predetermined performance function to constrain the convergence process of synchronization errors, achieving dual controllability of transient and steady-state performance.

[0072] In one embodiment, the present invention provides a computer-readable storage medium storing computer program code thereon, which, when called and executed by a processor, can drive the processor to complete all the steps of the adaptive distributed cooperative control method for multi-rotor UAVs of the present invention.

[0073] In one embodiment, the present invention provides a computer device including a storage module, a computing module, and a communication module. The storage module is used to store the computer program code. The computing module executes model calculations, control command generation, and stability verification of a multi-fidelity Lagrange identifier by calling the program code in the storage module. The communication module realizes data interaction with the UAV cluster, sensors, and control terminal, and finally completes the adaptive distributed cooperative control of the multi-rotor UAV.

[0074] The technical solution of this invention can be implemented through software, hardware, firmware, or any combination thereof. If implemented in software, the core algorithm and control logic of the multi-fidelity Lagrange multiplier can be encapsulated into a computer program product. The instructions contained therein can be stored in a readable storage medium or transmitted and deployed between different devices—for example, via wired links (such as gigabit Ethernet, industrial buses) or wireless links (such as 5G private networks, drone-specific data transmission radios)—to complete transmission between websites, servers, data centers, or airborne equipment. The computer-readable storage medium can be any non-transitory carrier capable of storing instructions, including magnetic storage media (such as hard disk drives, magnetic tape storage), optical storage media (such as optical discs, Blu-ray discs), semiconductor storage media (such as solid-state drives, flash memory modules), or composite storage devices integrating multiple media (such as distributed storage arrays).

[0075] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0076] It should be understood that although the steps in the flowcharts of the accompanying drawings are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some of the steps in the flowcharts of the accompanying drawings may include multiple steps or stages, which are not necessarily completed at the same time, but may be executed at different times, and the execution order of these steps or stages is not necessarily sequential, but may be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0077] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0078] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0079] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. An adaptive distributed cooperative control method for multi-rotor unmanned aerial vehicles, characterized in that, include: Constructing a spectral normalized Lagrange neural network for uncertainty identification of multi-rotor UAV models: Based on the Lagrange mechanics framework, the Lagrange function is defined according to the kinetic and potential energy of the UAV, and a parameterized dynamic function is constructed based on the Euler-Lagrange equation. Spectral normalization constraints are applied to the weights of each layer of the Lagrange neural network. A multi-fidelity Lagrange identifier is constructed based on a Lagrange neural network and a multi-fidelity learning strategy. The multi-fidelity Lagrange identifier is trained by minimizing a multi-objective loss function using a training dataset containing high-fidelity data and low-fidelity data. The multi-objective loss function includes at least low-fidelity data fitting loss, high-fidelity data prediction loss, and energy conservation constraint loss. For each UAV node in a multi-rotor UAV swarm, an adaptive control law is designed based on the trained multi-fidelity Lagrange identifier, combined with a predetermined performance function and distributed synchronization error, to generate control commands.

2. The adaptive distributed cooperative control method for a multi-rotor unmanned aerial vehicle according to claim 1, characterized in that, The Lagrangian function, defined based on the Lagrangian mechanics framework and the kinetic and potential energy of the UAV, specifically includes: The kinetic energy of a drone includes translational kinetic energy. and rotational kinetic energy It consists of two parts; translational kinetic energy Based on linear velocity calculation, rotational kinetic energy The total kinetic energy of the UAV is related to angular velocity and moment of inertia. ; Taking the ground as the zero potential energy surface, the vertical height of the UAV in the northeast coordinate system is selected. Calculate gravitational potential energy ; According to Lagrange mechanics, the Lagrange function kinetic energy and potential energy Substitute: 。 3. The adaptive distributed cooperative control method for a multi-rotor unmanned aerial vehicle according to claim 2, characterized in that, Translational kinetic energy for: ;in, For the quality of drones, These are the linear velocity components in the north, east, and ground directions recorded in the database, respectively. The drone adopts a symmetrical octocopter layout with uniform mass distribution and rotational kinetic energy. for: in, For the inertial tensor of the drone, These are the coordinate systems of the UAV around its body. axis, axis, Moment of inertia of the shaft, It is the angular velocity vector. They are respectively In the body coordinate system axis, axis, The components on the axis correspond to the roll, pitch, and yaw angular velocities of the UAV; gravitational potential energy for: , It is the acceleration due to gravity; Then the Lagrange function for 。 4. The adaptive distributed cooperative control method for a multi-rotor unmanned aerial vehicle according to claim 3, characterized in that, The construction of parameterized dynamic functions based on the Euler-Lagrange equations specifically includes: ； ； in, Represents the generalized coordinates describing the attitude of the UAV. Represents generalized speed. and These are the gradient operators for generalized velocity and generalized coordinates, respectively; expanding the time derivative using the chain rule, we obtain: ； ； The acceleration is angular; the fourth-order Runge-Kutta method is used to integrate the acceleration to achieve state update: ； ； ； ； in, Let be the state vector of the drone at the current moment. , These represent the roll angle, pitch angle, and yaw angle, respectively. The function for calculating the rate of change of state. This is for intermediate calculations. The numerical integration step size is used to obtain the updated dynamic parameters of the UAV. : 。 5. The adaptive distributed cooperative control method for a multi-rotor unmanned aerial vehicle according to claim 1, characterized in that, The application of spectral normalization constraints to the weights of each layer of the Lagrange neural network specifically includes: ； ； Where L is called the Pushtz constant, Here are the original weight matrices for each layer of the Lagrange neural network. Let be the spectral norm of the weight matrix. The weight matrices of each layer of the Lagrange neural network after applying spectral normalization constraints. Let x be the norm of vector x. Weight matrix The maximum singular value.

6. The adaptive distributed cooperative control method for a multi-rotor unmanned aerial vehicle according to claim 1, characterized in that, The construction of the multi-fidelity Lagrange discriminator based on the Lagrange neural network and multi-fidelity learning strategy specifically includes: Multi-fidelity Lagrange identifiers include low-fidelity prediction networks, high-fidelity linear association networks, high-fidelity nonlinear association networks, and Lagrange neural networks: The low-fidelity prediction network is used to perform low-fidelity prediction based on the input UAV state vector; the high-fidelity linear correlation network and the high-fidelity nonlinear correlation network are used to learn the linear and nonlinear mapping relationship between the low-fidelity prediction results and the high-fidelity data, and output correction terms; the Lagrange neural network is used to fuse the correction terms and fit the Lagrange quantity.

7. The adaptive distributed cooperative control method for a multi-rotor unmanned aerial vehicle according to claim 1, characterized in that, The multi-objective loss function for: ； in: ； ； ； High-fidelity linear correlation network and high-fidelity nonlinear correlation networks Integrating into a high-fidelity prediction network , They represent low-fidelity prediction networks respectively. High-fidelity prediction network Lagrange neural networks Network output, respectively The corresponding actual data value The loss values ​​for low-fidelity data fitting are, in order: Calculation and high-fidelity data prediction loss Calculation and energy conservation constraint loss The number of samples calculated For regularization loss, As weight.

8. The adaptive distributed cooperative control method for a multi-rotor unmanned aerial vehicle according to claim 1, characterized in that, Based on the trained multi-fidelity Lagrange identifier, and combined with a predetermined performance function and distributed synchronization error, an adaptive control law is designed to generate control commands, specifically including: Design an exponentially decreasing predetermined performance function: in, These correspond to the roll angle, pitch angle, and yaw angle error channels of the UAV, respectively. This is the upper bound of the initial error. Upper bound of steady-state error Here is the convergence rate parameter; the function satisfies For all Established, and ; Indicates the first The first drone The predetermined performance function for each error channel. Indicates the serial number of the drone node; Based on the characteristics of directed communication topology, the distributed synchronization error of UAV node i is defined, which integrates the state deviation of neighboring UAV nodes and the state deviation of the leader: ； Indicates drone node No. Distributed synchronization error of each error channel For drone nodes The neighborhood group, For elements of the adjacency matrix, Indicates drone node Leaders who can be accessed directly , , Each is a drone node Neighboring drone nodes The leader's first Channel status; The constrained synchronization error is transformed into an unconstrained optimization variable, and the transformation error is defined as follows: ； Its inverse transformation is: ； in, , All are positive numbers, used to adjust the sensitivity of the error transformation; For drone nodes The predetermined performance function value of the P-th channel at time t; The transformation error is unconstrained; the derivative of the transformation error is taken to obtain the error dynamic characteristics: ； in, The derivative of the predetermined performance function reflects the rate of change of the error boundary. To integrate the dynamic characteristics of transformation error, a metric error is defined. This reflects the transformation error from first order to... Overall deviation of the order: ； Expanded to: ； in, This is the error dynamic adjustment coefficient. Let be the system order. The m-th derivative of the transformation error; Then the control input signal of UAV node i The expression is: ； in, Let i be the known control input matrix of UAV node i. To control the gain, Let i be the metric error of UAV node i. These are the estimated weights of a Lagrange neural network. It is the activation function vector of the Lagrange neural network. Let be the weighted in-degree of drone node i in the communication topology, which is the sum of the communication weights of all its neighboring nodes for that node. For the leader connection identifier parameter of drone node i, Let i be the auxiliary matrix for UAV node i. It is a higher-order dynamic adjustment coefficient for the transformation error of UAV node i. For the transformation error of UAV node i reciprocal of order; To track changes in unknown dynamics in real time, an adaptive update rule for the weights of a Lagrange neural network is designed: ； in, Let be the estimated weights of the L-th layer network for drone node i. It is a positive definite gain matrix. Let be the basis function vector of UAV node i. Let i be the auxiliary matrix for UAV node i. For topology-related weights, Let i be the external disturbance compensation term for UAV node i. For the leader connection identifier parameter of drone node i, This is the weight decay coefficient.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 8.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 8.

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