Data-driven pose tracking control method for micro / nano single-rotor helicopter

Abstract

The present application relates to the control technology of single rotor unmanned helicopter, in order to improve the accuracy of micro-nano single rotor helicopter model, through the design of nonlinear control strategy based on integral geometry control strategy, realize the high precision position and attitude tracking control of micro-nano single rotor unmanned helicopter.For this purpose, the technical scheme adopted by the present application is that the micro-nano single rotor unmanned helicopter pose tracking control method based on data driving is adopted, the system identification method based on deep convolutional neural network is used to establish the unmanned aerial vehicle dynamics model, the data driving method is used for micro-nano helicopter model identification, the attitude loop control law design and position loop control law design are carried out according to the identification result, and the automatic control of unmanned aerial vehicle is realized.The present application is mainly applied to the control design and control occasion of single rotor unmanned helicopter.

Description

Technical Field

[0001] This invention relates to control technology for single-rotor unmanned helicopters, specifically to a data-driven micro / nano single-rotor helicopter attitude tracking and control method. Background Technology

[0002] Current research on the control of single-rotor unmanned helicopters mostly focuses on medium-sized and micro-sized helicopters. Their fuselage weight is generally greater than 730g, and their fuselage length is greater than 0.7m. This chapter focuses on micro / nano single-rotor helicopters with a fuselage weight of less than 70g and a fuselage length of less than 0.25m. Compared to larger helicopters, micro / nano single-rotor helicopters, while possessing greater carrying capacity and higher maneuverability, are more sensitive to modeling uncertainties and unknown external disturbances, posing a significant challenge to high-precision flight control.

[0003] In recent years, deep neural network technology has matured and has been successfully applied to various fields such as machine learning, image processing, and system identification (Journal: IEEE Transactions on Cybernetics; Authors: Nguyen TT, Nguyen ND, Nahavandi S; Publication Date: September 2020; Article Title: Deep reinforcement learning for multiagent systems: A review of challenges, solutions, and applications; Pages: 3826–3839). Despite the complex aerodynamic characteristics of helicopter systems, the paper (Conference: IEEE International Conference on Robotics and Automation; Authors: Punjani A, Abbeel P; Publication Date: May 2015; Article Title: Deep learning helicopter dynamics models; Pages: 3223–3230) utilizes the superior high-dimensional regression properties of deep learning to achieve system identification. Experimental results show that the proposed ReLU network model significantly improves identification accuracy compared to other traditional system identification methods. Furthermore, the literature (Journal: IEEE Transactions on Neural Networks and Learning Systems; Authors: Kang Y, Chen S, Wang X, et al.; Publication date: February 2018; Article title: Deepconvolutional identifier for dynamic modeling and adaptive control of unmanned helicopter; Pages: 524–538) takes into account the correlation of neural network input data over time and optimizes the neural network model, resulting in better system identification results.

[0004] In summary, during agile flight, unmodeled dynamics of the unmanned helicopter are aroused and become more sensitive to external disturbances. Therefore, it is necessary to design a nonlinear control algorithm capable of estimating the unmodeled dynamics of the system online, while also exhibiting robustness to external disturbances, to ensure high-precision agile tracking control of the unmanned helicopter. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention aims to improve the accuracy of micro / nano single-rotor helicopter models. It achieves high-precision position and attitude tracking control of micro / nano single-rotor unmanned helicopters by designing a nonlinear control strategy based on integral geometry control. The technical solution adopted in this invention is a data-driven micro / nano single-rotor helicopter attitude tracking control method. This method employs a system identification method based on deep convolutional neural networks to establish a UAV dynamic model, utilizes data-driven methods to identify the micro / nano helicopter model, and designs attitude loop control laws and position loop control laws based on the identification results to achieve automatic control of the UAV.

[0006] The detailed steps are as follows:

[0007] 1) Establish a dynamic model of a tilt-rotor UAV.

[0008] First, define two coordinate systems as follows: Figure 1 As shown. Figure 1 in{I}={O I ,x I ,y I ,z I} and {B} = {O B ,x B ,y B ,z B} represent the inertial coordinate system with the origin at the ground and the body coordinate system with the body center, respectively, where the origin O is at the ground. I Located on the ground, z I Vertically downwards, y I Pointing east, x B Pointing to the front of the helicopter, y B Pointing to the right of the helicopter, z B If the vertical fuselage points downwards from the helicopter, and all mechanical components and their corresponding connections do not deform, then the kinematic and dynamic model of a single-rotor unmanned helicopter can be expressed as follows:

[0009]

[0010] where p(t) and v(t) ∈ R 3 Let R(t) represent the position and velocity vectors of the helicopter under {I}, m∈R represent the mass of the helicopter, and R(t)∈R 3×3 Let g denote the rotation matrix from {B} to {I}, g denote the gravitational acceleration constant, and J∈R. 3×3 Let w(t) ∈ R be the inertia matrix of the helicopter. 3×3 T represents the angular velocity of the helicopter in {B}. m (t)∈R and τ(t)∈R 3×3 This represents the main lift generated by the rotation of the main propeller and the impulse generated by the rotation of the main propeller and tail propeller, denoted by e3 = [0 0 1].T S(w) represents the vector w = [w1 w2 w3] T Zhang Cheng's antisymmetric matrix, i.e.

[0011]

[0012] 1.1 Main Rotor Dynamics

[0013] Define virtual control input v c (t)=[a s (t)b s (t)T t (t)] T ∈R 3 , where a s (t) and b s (t) represent the flapping angles in the roll and pitch directions of the helicopter's main rotor, respectively. t (t) represents the thrust generated by the tail rotor, then the control input τ(t) and T m The coupling relationship of (t) is expressed as:

[0014]

[0015] in and Indicates v c The transition matrix from τ(t) to τ(t) is expressed as follows:

[0016]

[0017]

[0018] in This represents the distance vector constant from the main propeller to the center of mass. K represents the distance vector constant from the tail rotor to the center of mass. β Q represents a constant coefficient related to the main propeller. m (T m The expression for ) is:

[0019]

[0020] Where C M and D M Represents constants related to helicopter aerodynamics;

[0021] The main rotor flapping dynamics model is written as follows:

[0022]

[0023] Where, τ f The time constant of the main rotor flapping motion, A cA lon and C lon The coupling constant coefficient between the main rotor's lateral flapping motion and lateral cyclic pitch, B d B lat and D lat The coupling constant coefficient between the longitudinal flapping motion and the longitudinal cyclic pitch of the main rotor is used, at which point the actual control input δ of the roll and pitch channels is... att (t)=[δ lon δ lat ]∈R 2×1 and virtual control input v c The transformation relationship between (t) can be simplified to:

[0024]

[0025] Where f1(·) and f2(·) are higher-order, difficult-to-measure coupling terms of the system state, let Equation (7) simplifies to

[0026]

[0027] On the other hand, helicopters generate main thrust T by driving the main rotor through the high-speed rotation of the main engine. m (t), assuming the time constant of the helicopter's attitude rotation dynamics is much larger than the time constant of the main rotor motor's response dynamics, then the actual control input δ col (t) and T m The transformation relationship between (t) can be rewritten as:

[0028] T m =K col δ col #(9)

[0029] Among them, K col It is a positive constant;

[0030] 1.2 Tail rotor dynamics

[0031] For δ ped (t) and the total lift T provided by the tail rotor rotation t The linear correlation between (t) yields:

[0032] T t =K ped δ ped #(10)

[0033] Where δ ped It is a positive constant;

[0034] The dynamic equations of a micro / nano single-rotor helicopter are written as follows:

[0035]

[0036] Where vectors p(t) and v(t) ∈ R 3×1 Let represent the position and velocity under {I}, respectively. Scalars m and g represent the mass of the micro / nano single-rotor helicopter and the local gravitational acceleration, respectively. The symbol e3 represents [0 0 1]. T T m (t) represents the main lift force generated by the rotation of the main propeller, Δ(η,ω,δ)∈R 3×1 Represents an unknown external disturbance acting on the position loop, R∈R 3×3 Represents the rotation from {B} to {I}, where vector ω(t)∈R 3×1 J represents the angular velocity under {B}, with the symbol J∈R. 3×3 The system inertial matrix, vector τ(t), and τ' represent the inertial matrix of the micro / nano helicopter system. d (t)∈R 3×1 Let Δ(η(t),ω(t),δ(t))∈R represent the control input torque and the unknown external disturbance acting on the attitude loop, respectively. 3×1 The vector δ(t) ∈ R represents the modeling uncertainty of the system state and control inputs of the micro / nano helicopter. 3×1 Represents the actual control input matrix, matrix A(T) m (t)∈R 3×3 and B(T) m (t)∈R 3×3 Indicates with T m (t) is the time-varying matrix related to E∈R 3×3 This represents the constant coefficient matrix from the actual control input δ(t) to τ(t);

[0037] 2) Pose tracking control design

[0038] To facilitate the training of the convolutional neural network model, the pose representation η(t) = [φ(t) θ(t)ψ(t)] based on Euler angles is used as the input data. The pose representation based on the rotation matrix is ​​defined as follows:

[0039]

[0040] Then there is

[0041]

[0042] 2.1 Data-driven identification of micro / nano helicopter models

[0043] The activation function for the deep neural network is ReLU, and the optimizer is the stochastic gradient descent (SGD) optimization method. The structure of the deep convolutional neural network is as follows:

[0044]

[0045] Where L represents the number of network layers, T is the total data acquisition time, σ(t)=[η(t),ω(t),δ(t)] is the input data of the neural network, and λ=[W 1 W 2 ,…,W L+1 ] represents the weight function of the neural network, ξ n (x) = max(0,x) is the ReLU activation function;

[0046] Spectral normalization is used to improve training effectiveness and the robustness of neural networks to input data. The mathematical expression of spectral normalization is written as:

[0047]

[0048] Where γ is a positive constant; the Lipschitz constant ∥f∥ is defined. Lip The smallest constant for K to satisfy the following inequality:

[0049]

[0050] Furthermore, for a differentiable function f(x), its Lipschitz constant can be chosen as the maximum value of the derivative spectrum norm, i.e. For composite functions Its Lipschitz constant satisfies Considering the spectral normalization method in equation (15) and the mathematical expression of the deep neural network in equation (14), the Lipschitz constant of the deep convolutional neural network satisfies the following inequality.

[0051]

[0052] Rewriting the equation concerning the modeling uncertainty in equation (11) yields the following equation:

[0053]

[0054] The state variables η(t), ψ(t), and δ(t) at consecutive moments on the left side of the equation are selected as inputs, and the calculation results on the right side of the equation are used as labels. The network parameters are optimized using the stochastic gradient descent method, and the network is spectrally normalized during training. Based on equation (17), it is ensured that the Lipschitz constant of the convolutional neural network is less than the constant γ, i.e.

[0055]

[0056] The system identification error calculation formula based on deep convolutional neural networks is selected as follows:

[0057]

[0058] Where y pred (t) represents the system identification output value, y label (t) represents the equivalent actual output value, and N represents the total number of samples;

[0059] 2.2 Attitude Loop Control Law Design

[0060] Based on the system identification results in 2.1, the dynamic model of the micro-nano helicopter can be rewritten as follows:

[0061]

[0062] in This represents the system identification error of the convolutional neural network. This represents the system's identification output value, defined as follows: External unknown disturbance τ d and identification error of system identification based on convolutional neural networks For uncertain nonlinear C 2 The function defines the attitude error e. R (t)∈R 3×1 Attitude angular velocity error e w (t)∈R 3 ×1 and auxiliary error function for

[0063]

[0064] Where R d ∈R 3×3 w d ∈R 3 Let I be the desired attitude angle and the desired attitude angular velocity. 3×3 Let be a 3×3 unit diagonal matrix, and tr(·) denote the trace of the matrix. Differentiating the second equation in equation (22) and multiplying both sides by J, we get:

[0065]

[0066] Combining the second formula in equation (21) with equation (23), we have:

[0067]

[0068] Design the attitude loop control law for a micro / nano single-rotor helicopter.

[0069]

[0070] Where K R K w K I ∈R+ The gain is adjustable and controllable.

[0071]

[0072] Where α is a positive adjustable gain;

[0073] 2.3 Position Loop Control Law Design

[0074] To facilitate subsequent control law design, the position loop tracking error e is defined. px (t)∈R 3×1 and velocity tracking error e pv (t)∈R 3×1 for

[0075]

[0076] Where x d For a given trajectory that is continuously and twice differentiable, define the integral filtering error e. i (t)∈R 3×1 for:

[0077]

[0078] Where ξ is the adjustable control gain, the position loop auxiliary function A(t)∈R is defined. 3×1 for:

[0079] A = -T m Re3#(29)

[0080] The position loop control law can then be designed as follows:

[0081]

[0082] Sat σ (·) is a saturated function with boundary σ, K x ,K v ,K I For adjustable gain, the actual control input T is... m (t) is solved by (29):

[0083]

[0084] Combining the second formulas (30) and (11), we get:

[0085]

[0086] Substituting (27) into (32), we obtain the dynamic equation of the closed-loop system as follows:

[0087]

[0088] The features and beneficial effects of this invention are:

[0089] This invention addresses the modeling uncertainties in micro / nano single-rotor helicopter system models by proposing a data-driven deep convolutional neural network-based system identification method. 2) It proposes a robust nonlinear position tracking control method based on geometric control. This method avoids the singularity introduced by Euler angles and the ambiguity introduced by quaternions, while also exhibiting robustness to external disturbances. 3) The proposed control algorithm is validated through actual flight testing on an experimental platform. Indoor full-degree-of-freedom flight experiments verify the effectiveness of the proposed control algorithm.

[0090] This invention addresses the sensitivity of micro / nano helicopters to unmodeled dynamics and unknown external disturbances. It leverages the ability of deep convolutional neural networks to effectively fit nonlinear functions, thus modeling the unmodeled dynamics (the mechanistic and dynamic aspects that are difficult to model in micro / nano unmanned helicopters). Subsequently, considering unknown external gust disturbances during flight, a nonlinear control strategy based on integral geometry control is designed. Finally, the effectiveness and robustness of the proposed control algorithm are verified through indoor full-degree-of-freedom flight experiments with the micro / nano helicopter, achieving high-precision position and attitude tracking control for the micro / nano single-rotor unmanned helicopter. Attached image description:

[0091] Figure 1 This is a schematic diagram of the coordinate system for a micro / nano single-rotor helicopter used in this invention;

[0092] Figure 2 This is a schematic diagram of the results of dynamic identification of the roll channel without modeling in the data-driven micro / nano helicopter system of this invention;

[0093] Figure 3 This is a schematic diagram of the results of dynamic identification of pitch channels without modeling in the data-driven micro / nano helicopter system of this invention;

[0094] Figure 4 This is a schematic diagram of the results of dynamic identification of yaw channels without modeling in the data-driven micro / nano helicopter system of the present invention;

[0095] Figure 5 This is a 3D image of UAV rectangular tracking after adopting integral geometric robust control law;

[0096] Figure 6 This is a diagram showing the rectangular tracking effect of the UAV after adopting the integral geometric robust control law;

[0097] Figure 7 This is a rectangular tracking error diagram of the UAV after adopting the integral geometric robust control law;

[0098] Figure 8 This is a 3D image of the UAV rectangular tracking after adopting the cascade PID control algorithm;

[0099] Figure 9 This is a diagram showing the rectangular tracking effect of a UAV after adopting a cascaded PID control algorithm.

[0100] Figure 10 This is a rectangular tracking error diagram of the UAV after adopting the cascade PID control algorithm. Detailed Implementation

[0101] This invention relates to the nonlinear control of micro / nano single-rotor helicopters weighing no more than 70 grams. To address the modeling uncertainties in the micro / nano single-rotor helicopter system model, a data-driven deep convolutional neural network-based system identification method is proposed. Furthermore, considering unknown external gust disturbances during flight, a robust nonlinear position tracking control method based on geometric control is proposed. This method avoids the singularity introduced by Euler angles and the ambiguity introduced by quaternions, achieving high-precision position and attitude tracking control of the micro / nano single-rotor unmanned helicopter while exhibiting robustness to external disturbances. Specifically, it involves the modeling of uncertainties and attitude tracking control of the micro / nano single-rotor helicopter.

[0102] The technical solution adopted in this invention is as follows: To address the modeling uncertainties in micro / nano single-rotor helicopter system models, a data-driven deep convolutional neural network-based system identification method is proposed. Furthermore, considering the unknown external gust disturbances during flight, a robust nonlinear position tracking control method based on geometric control is proposed. This includes the following steps:

[0103] 2) Establish a dynamic model of a tilt-rotor UAV.

[0104] To better describe the dynamics and kinematics of a micro / nano single-rotor helicopter, two coordinate systems are first defined as follows: Figure 1 As shown. Figure 1 in{I}={O I ,x I ,y I ,z I} and {B} = {O B ,x B ,y B ,z B Let O represent the inertial coordinate system with its origin at the ground and the body coordinate system with its origin at the center of the aircraft, respectively. I Located on the ground, z I Vertically downwards, y I Pointing east, x B Pointing to the front of the helicopter, y B Pointing to the right of the helicopter, zB The vertical fuselage points downwards from the helicopter. When describing the helicopter's kinematic model, it is assumed that the various mechanical components and their corresponding mechanical connections do not deform (Journal: IEEE Transactions on Control Systems Technology; Authors: Raptis IA, Valavanis KP, Moreno WA; Publication Date: March 2011; Article Title: A novel nonlinear backstepping controller design for helicopters using the rotation matrix; Pages: 465–473). Therefore, the kinematic and dynamic model of a single-rotor unmanned helicopter can be described as follows:

[0105]

[0106] where p(t) and v(t) ∈ R 3 Let R(t) represent the position and velocity vectors of the helicopter under {I}, m∈R represent the mass of the helicopter, and R(t)∈R 3×3 Let g denote the rotation matrix from {B} to {I}, g denote the gravitational acceleration constant, and J∈R. 3×3 Let w(t) ∈ R represent the inertia matrix of the helicopter. 3×3 Let T represent the angular velocity of the helicopter in {B}. m (t)∈R and τ(t)∈R 3×3 This represents the main lift generated by the rotation of the main propeller and the impulse generated by the rotation of the main propeller and tail propeller. Symbol e3 = [0 0 1] T S(w) represents the vector w = [w1 w2 w3] T Zhang Cheng's antisymmetric matrix, i.e.

[0107]

[0108] 1.1 Main Rotor Dynamics

[0109] A schematic diagram of the main rotor and swashplate of a small single-rotor unmanned helicopter is shown below. Figure 2 As shown. Due to the unique swashplate structure of helicopters, single-rotor helicopters adjust the flapping motion of the main rotor by changing the lateral and longitudinal periodic pitch, thereby altering the helicopter's real-time attitude. A virtual control input v is defined. c (t)=[a s (t)b s (t)T t (t)] T ∈R 3 , where a s (t) and b s(t) represent the flapping angles in the roll and pitch directions of the helicopter's main rotor, respectively. t (t) represents the thrust generated by the tail rotor. Then the control input τ(t) and T m The coupling relationship of (t) can be expressed as

[0110]

[0111] in and Indicates v c The transition matrix from τ(t) to τ(t). The specific expression is as follows:

[0112]

[0113]

[0114] in This represents the distance vector constant from the main propeller to the center of mass. K represents the distance vector constant from the tail rotor to the center of mass. β Q represents a constant coefficient related to the main propeller. m (T m The expression for ) is

[0115]

[0116] Where C M and D M Represents constant coefficients related to helicopter aerodynamics.

[0117] However, in practical applications, the aforementioned waving angle is difficult to measure directly. Typically, a lateral periodic pitch δ is used as the actual control input. lat (t) and longitudinal periodic pitch δ lon (t) drives the servo motor to move, thereby changing the swashplate plane to change the flapping angle. Therefore, it is necessary to find the conversion relationship between the main rotor flapping angle and the actual control input. The main rotor flapping dynamics model can be written as (Journal: Nonlinear Dynamics; Authors: Zhu B, Huo W; Publication Date: March 2013; Article Title: Robust nonlinear control for a model-scaled helicopter with parameter uncertainties; Pages: 1139–1154)

[0118]

[0119] Where, τ f The time constant of the main rotor flapping motion, A c Alon and C lon The coupling constant coefficient between the main rotor's lateral flapping motion and lateral cyclic pitch, B d B lat and D lat This is the coupling constant coefficient between the longitudinal flapping motion and the longitudinal cyclic pitch of the main rotor. At this point, the actual control input δ of the roll and pitch channels is... att (t)=[δ lon δ lat ]∈R 2×1 and virtual control input v c The transformation relationship between (t) can be simplified to:

[0120]

[0121] Where f1(·) and f2(·) are high-order coupling terms of the system state that are difficult to measure. For ease of subsequent control strategy design, it is assumed that the helicopter's waving motion changes slowly during flight, and that the waving motion time constant is relatively small. Therefore, let... Equation (7) can be simplified to

[0122]

[0123] On the other hand, helicopters generate main thrust T by driving the main rotor through the high-speed rotation of the main engine. m (t), assuming the time constant of the helicopter's attitude rotation dynamics is much larger than the time constant of the main rotor motor's response dynamics, then the actual control input δ col (t) and T m The transformation relationship between (t) can be rewritten as follows:

[0124] T m =K col δ col #(9)

[0125] Among them, K col It is a positive constant.

[0126] 1.2 Tail rotor dynamics

[0127] The tail rotor of a single-rotor UAV is mainly used to provide anti-torque and directional force, and is usually achieved in two ways: 1) a fixed tail rotor collective pitch, where the directional force is mainly adjusted by changing the rotational speed; 2) the tail rotor speed is linked to the main rotor speed through gear meshing and belt power transmission, where the directional force is mainly adjusted by changing the tail rotor collective pitch. However, regardless of which method is used for the helicopter tail rotor, the control input signal is transmitted through the δ... ped (t) The associated pulse modulation signal (PWM) is completed. Considering that the heading direction rotation speed is relatively slow in actual control design, δ ped(t) and the total lift T provided by the tail rotor rotation t The linear correlation between (t) is obtained by performing linear correlation processing on the relationship between them.

[0128] T t =K ped δ ped #(10)

[0129] Where δ ped It is a positive constant.

[0130] Based on the above, the dynamic equations of the micro / nano single-rotor helicopter can be written as:

[0131]

[0132] Where vectors p(t) and v(t) ∈ R 3×1 Let represent the position and velocity under {I}, respectively. Scalars m and g represent the mass of the micro / nano single-rotor helicopter and the local gravitational acceleration, respectively. The symbol e3 represents [0 0 1]. T T m Δ(t) represents the main lift force generated by the rotation of the main propeller, where Δ(t) ∈ R. 3×1 This represents an unknown external perturbation acting on the position loop. On the other hand, R∈R 3×3 Represents the rotation from {B} to {I}, where vector ω(t)∈R 3×1 J represents the angular velocity under {B}, with the symbol J∈R. 3×3 The system inertial matrix, vector τ(t), and τ' represent the inertial matrix of the micro / nano helicopter system. d (t)∈R 3×1 Let Δ(η(t),ω(t),δ(t))∈R represent the control input torque and the unknown external disturbance acting on the attitude loop, respectively. 3×1 This represents the modeling uncertainty regarding the system state and control inputs of the micro / nano helicopter. Vector δ(t)∈R 3×1 Represents the actual control input matrix (corresponding to lateral cyclic pitch, longitudinal cyclic pitch, and tail rotor collective pitch, respectively), matrix A(T) m (t)∈R 3×3 and B(T) m (t)∈R 3×3 Indicates with T m (t) is the time-varying matrix related to E∈R 3×3 This represents the constant coefficient matrix from the actual control input δ(t) to τ(t).

[0133] 2) Pose tracking control design

[0134] To facilitate the training of the convolutional neural network model, the pose representation η(t) = [φ(t) θ(t)ψ(t)] based on Euler angles is used as the input data. The pose representation based on the rotation matrix is ​​defined as follows:

[0135]

[0136] Then there is

[0137]

[0138] 2.1 Data-driven identification of micro / nano helicopter models

[0139] Assuming the dynamic model of the helicopter yaw channel has a small coupling with the roll and pitch channels, from an experimental perspective, the roll and pitch channel data are treated as a single data packet for system identification, while the yaw channel data is extracted separately for system identification. The proposed deep convolutional neural network structure is shown in Table 1, and a schematic diagram is shown below. Figure 3 As shown. To accelerate convergence and avoid the vanishing gradient problem, the activation function of the deep neural network is ReLU, and the optimizer is the stochastic gradient descent (SGD) optimization method. Furthermore, the deep convolutional neural network structure proposed in this section can be written as...

[0140]

[0141] Where L represents the number of network layers, T is the total data acquisition time, σ(t)=[η(t),ω(t),δ(t)] is the input data of the neural network, and λ=[W 1 W 2 ,…,W L+1 ] represents the weight function of the neural network, ξ n (x) = max(0,x) is the ReLU activation function.

[0142] Because deep neural networks are highly sensitive to noise in their input data, spectral normalization is used to improve training performance and the network's robustness to noise. The mathematical expression for spectral normalization can be written as:

[0143]

[0144] Where γ is a positive constant.

[0145] Define the Lipschitz constant ∥f∥ Lip The smallest constant K that satisfies the following inequality:

[0146]

[0147] Furthermore, for a differentiable function f(x), its Lipschitz constant can be chosen as the maximum value of the derivative spectrum norm, i.e. For composite functions Its Lipschitz constant satisfies Considering the spectral normalization method in equation (15) and the mathematical expression of the deep neural network in equation (14), the Lipschitz constant of the deep convolutional neural network satisfies the following inequality.

[0148]

[0149] By rewriting the equation concerning the modeling uncertainty in equation (11), we can obtain the following equation.

[0150]

[0151] The state variables η(t), ω(t), and δ(t) at consecutive moments on the left side of the equation are selected as inputs, and the calculation results on the right side of the equation are used as labels. The network parameters are optimized using stochastic gradient descent, and the network is spectrally normalized during training. Based on equation (17), it can be guaranteed that the Lipschitz constant of the convolutional neural network is less than the constant γ, i.e.

[0152]

[0153] Data-driven dynamic identification results of micro / nano helicopter systems without modeling, such as... Figure 4 , 5 As shown in Figure 6, the system identification error calculation formula based on deep convolutional neural networks is selected as follows:

[0154]

[0155] Where y pred (t) represents the system identification output value, y label (t) represents the equivalent actual output value, and N represents the total sample size.

[0156] Sample size.

[0157] 2.2 Attitude Loop Control Law Design

[0158] Based on the system identification results in 2.1, the dynamic model of the micro-nano helicopter can be rewritten as follows:

[0159]

[0160] in This represents the system identification error of the convolutional neural network. This represents the system's identified output value. Furthermore, to facilitate subsequent control law design and expression, we define... External unknown disturbance τ d and identification error of system identification based on convolutional neural networks For uncertain nonlinear C 2 Function. Define attitude error e. R(t)∈R 3×1 Attitude angular velocity error e w (t)∈R 3×1 and auxiliary error function for

[0161]

[0162] Where R d ∈R 3×3 w d ∈R 3 Let I be the desired attitude angle and the desired attitude angular velocity. 3×3 Let be a 3×3 unit diagonal matrix, and tr(·) denote the trace of the matrix. Differentiating the second equation in equation (22), multiplying both sides by J yields...

[0163]

[0164] Combining the second formula in equation (21) with equation (23), we have:

[0165]

[0166] Design the attitude loop control law for a micro / nano single-rotor helicopter.

[0167]

[0168] Where K R K w K I ∈R + The gain is adjustable and controllable.

[0169]

[0170] Where α is a positive adjustable gain.

[0171] 2.3 Position Loop Control Law Design

[0172] To facilitate subsequent control law design, the position loop tracking error e is defined. px (t)∈R 3×1 and velocity tracking error e pv (t)∈R 3×1 for

[0173]

[0174] Where x d Given a continuously differentiable trajectory. Define the integral filtering error e. i (t)∈R 3×1 for

[0175]

[0176] Where ξ is the adjustable control gain. Define the position loop auxiliary function A(t)∈R. 3×1 for

[0177] A = -T m Re3#(29)

[0178] The position loop control law can then be designed as follows:

[0179]

[0180] Sat σ (·) is a saturated function with boundary σ, K x ,K v ,K I The gain is adjustable. At this point, the actual control...

[0181] Enter T m (t) can be solved using (29).

[0182]

[0183] Combining the second formulas (30) and (11), we can obtain

[0184]

[0185] Substituting (27) into (32), we obtain the dynamic equation of the closed-loop system as follows:

[0186]

[0187] The following is a specific implementation example:

[0188] I. Introduction to the Experimental Platform

[0189] The micro-nano single-rotor unmanned helicopter has a fuselage length of 260mm, a height of 83mm, a main rotor diameter of 275mm, and a fuselage weight of 68.9g. The flight control board utilizes a high-performance STM32F745VGH6 microcontroller with a main frequency of 216MHz and dimensions of 33x26x6mm. Furthermore, the flight control software system is a secondary development based on the ChibiOS lightweight real-time system framework. It includes attitude control mode, position control mode, and safety degradation control strategies, all designed to meet actual safe flight requirements, providing reliable safety assurance for the indoor full-degree-of-freedom flight experiment of the micro-nano single-rotor unmanned helicopter presented in this paper. Additionally, a high-precision full-degree-of-freedom flight platform was constructed by integrating an indoor motion capture system. Considering the limited carrying capacity of the micro-nano single-rotor unmanned helicopter, real-time interaction with the ground station data is achieved through the wireless network module. The data content includes: (1) position and attitude data obtained from the motion capture system ground station software, with an update frequency of 50Hz; (2) the drone unlock status, remote controller data, fused position and attitude, etc., obtained through the drone general communication protocol, with an update frequency of 5Hz; (3) sending commands such as unlock, lock, and mode switching to the drone.

[0190] II. Flight Test Results

[0191] To further verify the effectiveness of the data-driven trajectory tracking nonlinear control algorithm proposed in this chapter, a corresponding indoor flight experiment was designed based on a micro-nano helicopter full-degree-of-freedom flight platform. Simultaneously, a visual ground station auxiliary system was independently designed on a PC using Python 3. The ground station auxiliary system features a modular design for both front-end and back-end. The front-end primarily displays necessary flight parameters (including attitude angles, control variables, flight modes, and neural network prediction results), while the back-end mainly handles convolutional neural network model prediction, data interaction with the flight controller via a wireless network, and data interaction with the onboard motion capture system via a wireless transmission protocol. A circular trajectory tracking experiment based on a cascaded PID control strategy was selected for comparison.

[0192] Due to the unique cross-shaped linkage structure of the actuator in micro / nano single-rotor helicopters, attitude changes in both the roll and pitch channels require the coordinated action of three servos. Therefore, the roll and pitch channels exhibit strong system coupling. Furthermore, in a circular flight trajectory, the setpoints for both channels change synchronously over time, posing a significant challenge to high-precision flight tracking. In this experiment, a circular reference trajectory radius of 0.5m and a period of 18s were selected. The control gain parameter was set to K during the experiment. x =5,K v =4,K i =0.2,K R =4.5,K w =0.15,KI =1.66.

[0193] Experiment 1: Circular Trajectory Tracking Control Experiment

[0194] Experimental results are as follows Figure 5-7 As shown. From Figure 5 and Figure 6 It can be seen that, under the control compensation of the identification model, the nonlinear control strategy proposed in this chapter has high position tracking accuracy. At the same time, its tracking speed is also good, and the real-time trajectory closely matches the given trajectory. From... Figure 7 It can be seen that, affected by mechanical vibration and feedback delay of the actuator, small-amplitude high-frequency jitter still exists, but the steady-state error of position tracking in the x, y, and z directions is still maintained within ±0.1m. The micro-nano single-rotor helicopter has achieved good tracking of circular trajectory.

[0195] Experiment 2: Comparative Experiment of Circular Trajectory Tracking Control

[0196] A position-linear velocity P-PID control structure is used in the position loop, and an attitude-attitude angular velocity P-PID control structure is used in the attitude loop. The experimental parameters are shown below. Position loop: k p =1.5; Linear velocity loop: k vp =1.5,k vi =0.1,k vd =0.5; Angle ring: k q =4.5; Angular velocity loop: k wp =0.1508,k wi =1.66,k wd =0.001. Experimental results are as follows Figure 8-10 As shown. From Figure 8 and 9 It can be seen that due to the structure of the inner and outer loops of the cascade PID control, the micro / nano UAV based on the cascade PID control law exhibits a certain phase lag in circular trajectory tracking, which leads to a relatively large tracking error. From Figure 10 As can be seen, the steady-state error in the x-direction fluctuates between -0.1m and 0.3m, the steady-state error in the y-direction fluctuates between -0.2m and 0.25m, and the steady-state error in the z-direction fluctuates between -0.2m and 0.1m due to the influence of integration.

[0197] In summary, the data-driven high-precision pose tracking control method for micro / nano helicopters proposed in this invention has high control accuracy and good feasibility.

[0198] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A data-driven attitude tracking and control method for micro / nano single-rotor helicopters, characterized in that, A system identification method based on deep convolutional neural networks is used to establish a dynamic model of the UAV. A data-driven method is used to identify the micro-nano helicopter model. Based on the identification results, attitude loop control law and position loop control law are designed to achieve automatic control of the UAV. The detailed steps are as follows: 1) Establish a dynamic model of a tilt-rotor UAV. First, define two coordinate systems. and Represent the inertial coordinate system with the origin at the ground and the body coordinate system with the body center, respectively. Located on the ground, Vertically downwards, Pointing east, Pointing towards the front of the helicopter, Pointing to the right of the helicopter, If the vertical fuselage points downwards from the helicopter, and all mechanical components and their corresponding connections do not deform, then the kinematic and dynamic model of a single-rotor unmanned helicopter can be expressed as follows: in and Indicates the helicopter is in The position and velocity vectors below, Indicates the mass of the helicopter. Indicates from arrive The rotation matrix, Represents the gravitational acceleration constant. The inertia matrix of the helicopter. Indicates the helicopter is in angular velocity in and The symbols represent the main lift generated by the rotation of the main propeller and the impulse generated by the rotation of the main propeller and tail propeller. , Represents vector Zhang Cheng's antisymmetric matrix, i.e. 1-1 Main Rotor Dynamics Define virtual control input ,in and These represent the flapping angles in the roll and pitch directions of the helicopter's main rotor, respectively. The control input represents the thrust generated by the tail rotor. and The coupling relationship is expressed as: in and express arrive The transition matrix is ​​expressed as follows: in This represents the distance vector constant from the main propeller to the center of mass. This represents the distance vector constant from the tail rotor to the center of mass. This represents constant coefficients related to the main propeller. The expression is: in and Represents constants related to helicopter aerodynamics; The main rotor flapping dynamics model is written as follows: in, The time constant of the main rotor flapping motion, , and The coupling constant coefficient between the lateral flapping motion and the lateral cyclic pitch of the main rotor. , and The coupling constant coefficient between the longitudinal flapping motion and the longitudinal cyclic pitch of the main rotor is the actual control input of the roll and pitch channels at this time. and virtual control input The conversion relationship between them can be simplified as follows: in , Let the higher-order, less measurable coupling terms of the system state be... = =0, equation (7) simplifies to On the other hand, helicopters generate main thrust by driving the main rotor through the high-speed rotation of the main engine. Assuming the time constant of the helicopter's attitude rotation dynamics is much larger than the time constant of the main rotor motor's response dynamics, then the actual control input... and The conversion relationship between them can be rewritten as follows: in, It is a positive constant; 1-2 Tail Rotor Dynamics right Total lift provided by tail rotor rotation Linear correlation analysis of the relationship between them yields: in It is a positive constant; The dynamic equations of a micro / nano single-rotor helicopter are written as follows: Where vector and They represent in Position and velocity, scalar and Representing the mass of the micro / nano single-rotor helicopter and the local gravitational acceleration, respectively, with symbols... express , This represents the main lift generated by the rotation of the main propeller. This represents an unknown external disturbance acting on the position loop. Indicates from arrive rotation, vector express Angular velocity at the bottom, symbol The system inertial matrix and vector representation of a micro / nano helicopter. and These represent the control input torque and the unknown external disturbance acting on the attitude loop, respectively. The vector represents the modeling uncertainty of the system state and control inputs of the micro / nano helicopter. Represents the actual control input matrix, matrix and Indicates and The relevant time-varying matrix, Indicates the actual control input arrive The constant coefficient matrix; 2) Pose tracking control design To facilitate the training of convolutional neural network models, pose representation based on Euler angles is adopted. As input data, the pose expression based on the rotation matrix is ​​defined as follows: Then there is 2-1 Data-Driven Identification of Micro / Nano Helicopter Models The activation function for the deep neural network is ReLU, and the optimizer is the stochastic gradient descent (SGD) optimization method. The structure of the deep convolutional neural network is as follows: in Indicates the number of network layers. The total length of data collection time. For the input data of the neural network, The weight function of a neural network. It is the ReLU activation function; Spectral normalization is used to improve training effectiveness and the robustness of neural networks to input data. The mathematical expression of spectral normalization is written as: Where γ is a positive constant; the Lipschitz constant is defined. The smallest constant for K to satisfy the following inequality: At the same time, for differentiable functions Its Lipschitz constant can be chosen as the maximum value of the derivative spectrum norm, i.e. For composite functions Its Lipschitz constant satisfies Considering the spectral normalization method in equation (15) and the mathematical expression of deep neural networks in equation (14), the Lipschitz constant of deep convolutional neural networks satisfies the following inequality. Rewriting the equation concerning the modeling uncertainty in equation (11) yields the following equation: Select the state quantities at consecutive times on the left side of the equation. , , As input, the calculation result on the right side of the equation is used as the label. The network parameters are optimized using stochastic gradient descent. During training, the network is spectral normalized. Based on equation (17), the Lipschitz constant of the convolutional neural network is guaranteed to be less than the constant. ,Right now The system identification error calculation formula based on deep convolutional neural networks is selected as follows: in This indicates the system's identification output value. This represents the equivalent actual output value. Indicates the total number of samples; 2-2 Attitude Loop Control Law Design Based on the system identification results in 2.1, the dynamic model of the micro-nano helicopter can be rewritten as follows: in This represents the system identification error of the convolutional neural network. This represents the system's identification output value, defined as follows: Unknown external disturbances and identification error of system identification based on convolutional neural networks Uncertain nonlinear Function, defining attitude error Attitude angular velocity error and auxiliary error function for in , Let the desired attitude angle and desired attitude angular velocity be... It is a 3×3 unit diagonal matrix. The trace of the matrix is ​​determined by differentiating the second equation in equation (22) and multiplying both sides of the equation by . have to: Combining the second formula in equation (21) with equation (23), we have: Design the attitude loop control law for a micro / nano single-rotor helicopter. in , , The gain is adjustable, and in A positive adjustable gain; 2-3 position loop control law design To facilitate subsequent control law design, the position tracking error of the position loop is defined. and speed tracking error for in For a given trajectory that is continuously and twice differentiable, define the integral filtering error. for: in To enable adjustable control gain, define a position loop auxiliary function. for: The position loop control law can then be designed as follows: in For the boundary The saturation function, , , For adjustable gain, the actual control input at this time... Solving through (29) yields: Combining the second formulas (30) and (11), we get: Substituting (27) into (32), we obtain the dynamic equation of the closed-loop system as follows:

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