Radial basis function neural network control method of multi-flapping-wing unmanned aerial vehicle system based on input limitation

Abstract

The invention discloses a radial basis function neural network control method of a multi-flapping-wing unmanned aerial vehicle system based on input limitation, and aims to solve the problems of flexible wing vibration suppression, input nonlinearity and multi-system consistency control of a multi-flapping-wing unmanned aerial vehicle. The method comprises the following steps: firstly, constructing a kinetic model containing a rigid-flexible coupled wing, then considering input saturation, a dead zone and unknown parameter influence, defining a virtual input function, combining a backstepping method and a radial basis function neural network to design a controller, verifying system stability by constructing a Lyapunov function, and finally optimizing parameters through simulation. The method can effectively suppress vibration, improves the consistency of multiple unmanned aerial vehicles, is high in robustness and easy to implement, provides theoretical reference for cooperative control of the flapping-wing unmanned aerial vehicles, and has high engineering value. Simulation shows that the vibration amplitude can be reduced by more than 60%, and the multi-machine attitude synchronization time is shortened to be within 30 seconds.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cooperative control of multi-flapping wing unmanned aerial vehicles, and in particular to a radial basis function neural network control method for a multi-flapping wing unmanned aerial vehicle system based on input restriction. BACKGROUND

[0002] Miniature flapping wing unmanned aerial vehicles have important application value in low-altitude reconnaissance, environmental monitoring and other scenarios due to their strong bionics, high aerodynamic efficiency and good concealment. However, the existing technology has the following key problems, which restrict its engineering application: 1. The rigid-flexible coupled wings of flapping wing unmanned aerial vehicles, as shown in Figure 1 , are prone to large vibrations due to airflow interference and structural resonance when high-frequency flapping, and existing active control or boundary control methods are difficult to adapt to their complex dynamic characteristics; 2. The actuators have input saturation (control signal exceeding the physical limit) and dead zone (small signal non-response) characteristics, as shown in Figure 2 , which leads to distortion of the control command, and existing methods do not compensate for such nonlinearities; 3. When multiple flapping wing unmanned aerial vehicles work cooperatively, synchronization (consistency) of attitude and vibration state needs to be achieved, but the existing technology does not solve the problem of cooperative control under input restriction and unknown parameters, resulting in large dispersion of multiple machines, as shown in Figures 7-8 , and . SUMMARY

[0003] In view of the deficiencies in the prior art, the present application provides a radial basis function neural network control method for a multi-flapping wing unmanned aerial vehicle system based on input restriction, which solves the vibration suppression and consistency problem of the multi-flapping wing unmanned aerial vehicle system in input nonlinearity, parameter uncertainty and multi-machine cooperative control.

[0004] In order to achieve the above purpose, the present application adopts the following technical scheme: A radial basis function neural network control method for a multi-flapping wing unmanned aerial vehicle system based on input restriction, comprising the following steps: S1. Constructing a multi-flapping wing unmanned aerial vehicle system according to the dynamics model of a flapping wing unmanned aerial vehicle with rigid-flexible coupled wings; S2. Defining a "virtual input function" to simulate the nonlinear input and unknown parameters in the system; S3. Designing a controller using backstepping method and radial basis function neural network control method, and sequentially performing backstepping compensation for the uncertainty of the system to make the system stable; S4. Constructing a Lyapunov candidate function, the expression of which is: ; wherein is the energy term, is the additional term, is the cross term; S5, constructing Lyapunov candidate function, and proving the stability of the system by verifying its positive definiteness and the negative definiteness of the derivative; S6, if the simulation results do not meet the expectations, adjusting the controller gain parameters and re-simulating until the stability requirements are met.

[0005] Further, in the S1 step, the dynamic model is derived by Hamilton equation, and the expression is: ; wherein: is the vibration displacement of the flexible wing, is the torsion displacement of the flexible wing, is the flapping displacement of the flapping wing, is the attitude angle of the rigid link, is the attitude angle of the flexible wing, and are the boundary control inputs of the system applied by the rigid link and the flexible wing respectively, and represent the length of the entire rigid link and the length of the entire wing respectively, represent the unit density of the flexible wing and the rigid rod respectively, is the polar moment of inertia of each unit span of the wing, represents the inertia moment of the actuator at the joint, represents the rotational inertia of the rigid link, represents the mass of the connected joint, are the bending stiffness and the torsional stiffness of the flexible wing respectively, are the distances between the center of mass, the aerodynamic center and the shear center of the flexible wing respectively, is the damping coefficient.

[0006] Further, in the S1 step, the is introduced, and the following is generated by transformation: .

[0007] Further, in the S2 step, the controller and the neural network control rate are: ; ; wherein: are N-1 order column vectors, are N-1 dimensional diagonal matrices with as elements, is a matrix related to Laplacian matrix, is virtual control.

[0008] Further, in the S2 step, respectively, ; .

[0009] Further, in the S2 step, a radial basis function neural network is defined to approximate the nonlinear input and unknown parameters: ; Therefore, the adaptive rate of the neural network is as follows: ; is used to compensate for the nonlinear input and unknown parameters of the system, where is the ideal weight of the neural network, is the estimate of the ideal weight , is a radial basis function, is the approximation error of the neural network.

[0010] Further, in the S3 step, , , respectively, ; ; .

[0011] Further, the system stability verification includes the following steps: By verifying the positive definiteness of the Lyapunov function and the negative definiteness of the derivative, it is proved that the system is uniformly bounded stable in the sense of Lyapunov; If the simulation result does not meet the expectation, the controller gain parameter is corrected and the stability is verified again.

[0012] Further, the simulation verification is realized by MATLAB software, including the following contents: Comparison of the vibration amplitude of the multi-flapping wing unmanned aerial vehicle system without control action and the vibration amplitude with control action; Analysis of the change of the attitude angle.

[0013] Further, the backstepping method is used to design the controller by layer-by-layer recursion to compensate for the uncertainty of the system, and finally realizes the convergence of the output tracking error to zero.

[0014] Compared with the prior art, the present application has the following beneficial effects: 1. By using the radial basis function neural network to adaptively approximate the nonlinearity and unknown parameters, the bending deformation variable of the flexible wing is reduced from ±1.0 m (see Figure 5 ) to ±0.15 m (see Figure 9 ), and the torsional deformation variable is narrowed from ±0.4 rad (see Figure 6 ) to ±0.05 rad (see Figure 10 ); 2. For the input nonlinearity shown in Figure 2 , the controller compensates through a "virtual input function", and remains stable when the parameters fluctuate, and has strong anti-interference ability; 3. Based on the communication topology of Figure 4 , the rigid link attitude angle of the multiple unmanned aerial vehicles is converged from a dispersion of >1.5 rad (see Figure 7 ) to ±0.2 rad (see Figure 11 ) without control, and the synchronous deviation of the flexible wing attitude angle is reduced from 0.6 rad (see Figure 8 ) to <0.1 rad (see Figure 12 ); 4. The control algorithm has small calculation amount, can be realized based on an STM32H743 microcontroller, and is suitable for miniaturized flapping wing unmanned aerial vehicles. BRIEF DESCRIPTION OF DRAWINGS

[0015] The present application will be further described below in combination with the drawings and embodiments: Figure 1 is a profile view of a rigid-flexible coupled wing model; Figure 2 is a nonlinear input dead zone diagram; Figure 3 is a nonlinear input saturation diagram; Figure 4 is a communication topology diagram in the simulation example; Figure 5 is the bending deformation variable of the four flapping wing unmanned aerial vehicles without control ; Figure 6 is the torsional deformation variable of the four flapping wing unmanned aerial vehicles without control ; Figure 7 is the attitude angle of the rigid link of the four flapping wing unmanned aerial vehicles without control ; Figure 8 is the attitude angle of the flexible wing of the four flapping wing unmanned aerial vehicles without control ; Figure 9 is the bending deformation variable of the four flapping wing unmanned aerial vehicles under neural network control ; Figure 10 For the twist deformation variable of four flapping wing unmanned aerial vehicle under neural network control ; Figure 11 For the attitude angle of rigid link of four flapping wing unmanned aerial vehicle under neural network control ; Figure 12 For the attitude angle of flexible wing of four flapping wing unmanned aerial vehicle under neural network control . DETAILED DESCRIPTION

[0016] The technical solutions in the present application will be further described below with reference to the drawings and embodiments.

[0017] The application discloses a radial basis function neural network control method for a multi-flapping wing unmanned aerial vehicle system based on input limitation, and comprises the following steps: According to a flapping wing unmanned aerial vehicle dynamics model with rigid-flexible coupling wings, a multi-flapping wing unmanned aerial vehicle system is constructed; While considering the influence of input saturation and dead zone and unknown system parameters on the system, a "virtual input function" is defined to simulate the nonlinear input and unknown parameters in the system, a backstepping method and a radial basis function neural network control method are used to design a controller of the system, and the system uncertainty is compensated from inside to outside in sequence to stabilize the system; According to the multi-flapping wing unmanned aerial vehicle system and the controller, a corresponding Lyapunov candidate function is constructed; The stability of the system is verified according to the Lyapunov function; If the designed neural network controller meets the required stability requirement, digital simulation verification is further carried out by using simulation software, and a result is obtained; If the obtained result meets the expectation, the gain parameters of the designed radial basis function neural network controller are reserved, and the operation is ended, and if the result does not meet the expectation, the radial basis function neural network controller is modified and re-simulated.

[0018] In the application, the multi-flapping wing unmanned aerial vehicle system dynamics model includes kinetic energy, potential energy and non-conservative force work of the system, the model is brought into a Hamilton equation, and a system dynamics model is obtained:

[0019] In the application, the multi-flapping wing unmanned aerial vehicle system dynamics model includes kinetic energy, potential energy and non-conservative force work of the system, the model is brought into a Hamilton equation, and a system dynamics model is obtained: The vibration offset of the flexible wing. The twist offset of the flexible wing. The flapping displacement of the flapping wing. The attitude angle of the rigid link. The attitude angle of the flexible wing. And are the boundary control inputs applied by the system on the rigid link and the flexible wing respectively. and represent the length of the entire rigid link and the length of the entire wing respectively. denote the unit density of the flexible wing and the rigid rod, is the polar moment of inertia per unit span of the wing, represents the moment of inertia of the actuator at the joint, represents the moment of inertia of the rigid link, Indicates the quality of the connected joint. are the bending stiffness and torsional stiffness of the flexible wing, respectively. are the distances between the center of mass, aerodynamic center and shear center of the flexible wing, is the damping coefficient. . Introduce the following transformation:

[0020] The controller and neural network control rate are obtained from the above control equations:

[0021]

[0022] in: are all N-1 order column vectors, All are based on is an N-1 dimensional diagonal matrix of elements, is the matrix related to the Laplace matrix, Is a virtual control: ; ; Define a radial basis function neural network to approximate nonlinear input and unknown parameters: ; Based on this, the neural network adaptation rate is proposed as follows: ; Used to compensate for the nonlinear input and unknown parameters of the system, where is the ideal weight of the neural network, For the ideal weight Estimates. is the radial basis function, is the neural network approximation error.

[0023] On this basis, the Lyapunov function is constructed as follows: ; wherein is an energy term, is an additional term, is a cross term, respectively as follows: ; ; .

[0024] Further, according to the proposed Lyapunov function, the stability of the described multi-flapping wing unmanned aerial vehicle system is verified, specifically as follows: By verifying the positive definiteness of the Lyapunov function and the negative definiteness of the first-order derivative of the Lyapunov function, it is concluded that the described multi-flapping wing unmanned aerial vehicle system is uniformly bounded stable in the sense of Lyapunov; Next, if the simulation results obtained do not meet the expectations, the gain parameters of the controller are corrected, and digital simulation is performed again. According to the gain parameters, the positive definiteness of the Lyapunov function and the negative definiteness of the first-order derivative of the Lyapunov function are verified, and the multi-flapping wing unmanned aerial vehicle system is digitally simulated using MATLAB simulation software. The simulation results include the vibration amplitude of the multi-flapping wing unmanned aerial vehicle system without control action and the vibration amplitude with control action, as well as the change of the attitude angle.

[0025] Next, taking a multi-agent system composed of four flapping wing unmanned aerial vehicles as an example, the implementation process of the present application is described in detail.

[0026] Step 1: Constructing a multi-flapping wing unmanned aerial vehicle system The flexible wing is made of carbon fiber composite material with a thickness of 0.1 mm and a length L_2=0.3 m. The rigid link is made of aluminum alloy with a length L_1=0.2 m. The actuator is selected as a DS3235 rudder with a maximum torque of 25 kg·cm, corresponding to Figure 2 The medium saturation gain k=0.9 and the dead zone width b=0.1 V. Based on the Hamilton principle, the kinetic energy, potential energy and damping force of the rigid-flexible coupled wing are substituted into the above Hamilton equation, wherein the parameter values are: =1.2 kg / m, EI=0.5 N·m 2 , GJ=0.3 N·m 2 , =0.1 N·s / m.

[0027] Step 2: Designing a controller Virtual input function: according to its definition, the input characteristics of Figure 2 , Figure 3 the rudder are simulated; Radial basis function neural network: define radial basis function neural network to approximate nonlinear input and unknown parameters; Backstepping design: define error variable as required, realize "from inside to outside" uncertainty compensation.

[0028] Step 3: stability verification and multi-machine communication Lyapunov function verification: construct , wherein is an energy term, is an additional term, is a cross term, calculate whether it satisfies positive definiteness and first-order derivative negativity, and verify the consistent bounded stability of the system in the sense of Lyapunov; Multi-machine communication topology: as shown in Figure 4 , four unmanned aerial vehicles form a connected network with a virtual leader as the center, and the Laplacian matrix ensures that there is no isolated node in information interaction, providing a topological basis for consensus control.

[0029] Step 4: simulation verification and result analysis Simulation parameters: MATLAB / Simulink is used, the sampling time is 0.01s, the simulation time is 100s, and the initial attitude angle of the multi-unmanned aerial vehicle is randomly distributed in ±1 rad; Result comparison Vibration suppression: the bending vibration of the flexible wing does not decay without control (see Figure 5 ), and tends to be stable within 30s after control (see Figure 9 ); the torsional vibration amplitude is reduced by 87.5% (see Figure 6 and Figure 10 ); Consensus: the attitude angle of the rigid connecting rod converges to ±0.2 rad within 40s (see Figure 11 ), and the attitude angle of the flexible wing synchronization deviation is less than 0.1 rad (see Figure 12 ), which is 80% lower than that without control (see Figures 7-8 ).

[0030] Finally, it should be pointed out that the above examples are only used to illustrate the technical solutions of the present application and are not limiting. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced by equivalents without departing from the spirit and scope of the present application, and they should be included in the scope of the claims of the present application.

Claims

1. A radial basis function neural network control method for a multi-flapping wing UAV system based on input constraints, characterized in that: The following steps are involved: S1. Construct a multi-flapping wing UAV system based on the dynamic model of a flapping wing UAV with rigid-flexible coupled wings. S2. Define a "virtual input function" to simulate nonlinear inputs and unknown parameters in the system; S3. Design a controller using backstepping and radial basis function neural network control methods, and then backstep to compensate for the uncertainty of the system to make the system stable. S4. Construct the Lyapunov candidate function, the expression is: ； in is the energy term, For additional items, is a cross term; S5. Construct a candidate Lyapunov function and prove the stability of the system by verifying its positive definiteness and the negative definiteness of its derivative; S6. If the simulation results do not meet expectations, adjust the controller gain parameters and re-simulate until the stability requirements are met.

2. The radial basis function neural network control method for a multi-flapping wing UAV system based on input constraints according to claim 1, characterized in that: In the step S1, the dynamic model is derived by the Hamiltonian equation, and the expression is: ； in: is the vibration offset of the flexible wing, is the torsional offset of the flexible wing, is the flapping displacement of the wing, is the attitude angle of the rigid link, is the attitude angle of the flexible wing, and are the boundary control inputs applied by the system on the rigid link and the flexible wing, and denote the length of the entire rigid link and the length of the entire wing, respectively. denote the unit density of the flexible wing and the rigid rod, is the polar moment of inertia per unit span of the wing, represents the moment of inertia of the actuator at the joint, represents the moment of inertia of the rigid link, Indicates the quality of the connected joints, are the bending stiffness and torsional stiffness of the flexible wing, are the distances between the center of mass, aerodynamic center and shear center of the flexible wing, is the damping coefficient.

3. The radial basis function neural network control method for a multi-flapping wing UAV system based on input constraints according to claim 2, characterized in that: In the S1 step, the , generated by transformation: 。 4. The radial basis function neural network control method for a multi-flapping wing UAV system based on input constraints according to claim 1, characterized in that: In the step S2, the controller and the neural network control rate are: ； ； in: are all N-1 order column vectors, All are based on is an N-1 dimensional diagonal matrix of elements, is the matrix related to the Laplace matrix, It is virtual control.

5. The radial basis function neural network control method for a multi-flapping wing UAV system based on input constraints according to claim 4, characterized in that: In the step S2, They are: ； 。 6. The radial basis function neural network control method for a multi-flapping wing UAV system based on input constraints according to claim 5, characterized in that: In the S2 step, a radial basis function neural network is defined to approximate nonlinear inputs and unknown parameters: ； Based on this, the neural network adaptation rate is proposed as follows: ； Used to compensate for the nonlinear input and unknown parameters of the system, where is the ideal weight of the neural network, For the ideal weight Estimates, is the radial basis function, is the neural network approximation error.

7. The radial basis function neural network control method for a multi-flapping wing UAV system based on input constraints according to claim 1, characterized in that: In the S3 step, 、 、 They are: ； ； 。 8. The radial basis function neural network control method for a multi-flapping wing UAV system based on input constraints according to claim 1, characterized in that: The system stability verification includes the following steps: By verifying the positive definiteness of the Lyapunov function and the negative definiteness of its derivative, it is proved that the system is uniformly bounded and stable in the Lyapunov sense. If the simulation results do not meet expectations, modify the controller gain parameters and re-verify the stability.

9. The radial basis function neural network control method for a multi-flapping wing UAV system based on input constraints according to claim 8, characterized in that: The simulation verification is implemented by MATLAB software, including the following contents: Comparison of the vibration amplitude of a multi-flapping wing UAV system with and without control. Analysis of changes in attitude angle.

10. The radial basis function neural network control method for a multi-flapping wing UAV system based on input constraints according to claim 1, characterized in that: The backstepping method designs a controller by recursively designing it layer by layer, thereby compensating for the uncertainty of the system and ultimately achieving the convergence of the output tracking error to zero.

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