A design method, medium and electronic device for a flexible joint dynamic surface controller

Abstract

The present invention discloses a design method, medium, and electronic device for a flexible joint dynamic surface controller. The method includes establishing a rigid-flexible coupling dynamic model of the flexible joint, defining a first composite error sliding mode surface at the connecting rod end of the flexible joint; designing a first Lyapunov function based on the first composite error sliding mode surface and obtaining a first virtual control variable; estimating a first non-matching disturbance based on a first radial basis function neural network model and substituting the first virtual control variable into the first virtual control variable; introducing a second-order low-pass filter with the first virtual control variable as input to obtain a second composite error sliding mode surface; designing a second Lyapunov function based on the second composite error sliding mode surface and designing an actual control law for the flexible joint; and estimating a second non-matching disturbance based on a second radial basis function neural network model and substituting the second non-matching disturbance into the actual control law for the flexible joint. The present invention simplifies the controller parameter adjustment process.

Description

Technical Field

[0001] The present invention belongs to the field of artificial intelligence and control technology, and specifically relates to a design method, medium and electronic equipment for a flexible joint dynamic surface controller for a collaborative robot. Background Art

[0002] The integrated joint module of a collaborative robot usually integrates components such as motors, incremental encoders, absolute encoders, harmonic reducers, and torque sensors. The flexibility of the harmonic reducer and torque sensor reduces the stiffness of the collaborative robot, posing a challenge to the high-precision control of the flexible joints of the collaborative robot. The control of flexible joint manipulators is affected by matching interference and non-matching interference. Although the controller designed based on the backstepping method can effectively handle non-matching interference in the flexible joint system, there is a "differential explosion" phenomenon of virtual control items. Therefore, Swaroop et al. introduced the dynamic surface control method. This method avoids multiple derivations of virtual control items by introducing a first-order low-pass filter in each backstepping design process, greatly reducing the complexity of the flexible joint control law and avoiding the "differential explosion" caused by the design of the flexible joint control law based on the backstepping method.

[0003] Invention patent CN102566417A discloses a method for dynamic surface control of a flexible joint manipulator. The patent has four major steps: Step 1: Analysis and construction of the flexible joint manipulator system model; Step 2: Design of the dynamic surface controller of the flexible joint manipulator; Step 3: Tracking performance testing and parameter adjustment; Step 4: Design completion. This invention is based on the flexible joint manipulator control system model, gradually designs virtual control, and introduces a first-order low-pass filter at each step, ultimately deriving a dynamic surface controller for the flexible manipulator. This overcomes the "differential explosion" phenomenon of backstepping control, ensures the semi-global stability of the closed-loop control system, and simultaneously enables the flexible joint manipulator's link angle to quickly and accurately track the predetermined trajectory. It has broad application prospects in the field of automatic control technology.

[0004] Invention patent CN 109465825 A discloses an RBF neural network adaptive dynamic surface control method for flexible joints of a robotic arm. To achieve high-precision control of a flexible robotic arm, this invention combines adaptive RBF neural networks and dynamic surface technology to design a position controller. First, the RBF neural network's ability to approximate nonlinear functions is utilized to avoid the need to obtain a high-precision dynamic model of the robotic arm. The dynamic surface control method is used to avoid multiple derivatives of virtual terms in backstepping control, reducing the complexity of the controller design. Finally, simulations verified that the controller can ensure that the joint effectively tracks the output trajectory signal, and the tracking error can converge within a certain range, and all signals are semi-globally uniformly bounded.

[0005] However, the above-mentioned patent for designing a flexible joint position controller based on a dynamic surface control method requires the introduction of a first-order low-pass filter in each backstepping step. Therefore, the traditional method for designing a flexible joint control law based on dynamic surface control requires four backstepping steps and the introduction of three first-order low-pass filters. Each introduction of a low-pass filter brings a low-pass filter error, that is, it introduces three filter errors, and there is a time constant that needs to be adjusted in each low-pass filter, which also increases the complexity of controller parameter adjustment. In addition, the above-mentioned invention patent CN 109465825 A uses an RBF neural network model to directly fit a nonlinear model, which is equivalent to treating the flexible joint as a model-free black box. Since the neural network needs to be trained in the early stage to more accurately output the flexible joint characteristics, this will result in poor transient performance of the neural network. Summary of the Invention

[0006] The main purpose of the present invention is to provide a flexible joint dynamic surface controller design method, medium and electronic equipment that reduce the complexity of controller parameter design.

[0007] To achieve the aforementioned object of the invention, the technical solution adopted by the present invention includes: a method for designing a flexible joint dynamic surface controller, comprising:

[0008] S1, establish the rigid-flexible coupling dynamic model of the flexible joint;

[0009] S2, defining a first tracking error of the flexible joint link end, and defining a first composite error sliding mode surface based on the first tracking error;

[0010] S3, designing a first Lyapunov function according to the first composite error sliding surface, and obtaining a first virtual control variable such that a derivative of the first Lyapunov function is less than or equal to 0;

[0011] S4, estimating a first mismatching interference based on a first radial basis function neural network model, and substituting the first virtual control variable into the first virtual control variable;

[0012] S5, introducing a second-order low-pass filter with the first virtual control variable as input, obtaining a second tracking error by the second-order low-pass filter, and combining the second tracking error with its derivative to obtain a second composite error sliding mode surface;

[0013] S6, designing a second Lyapunov function based on the second composite error sliding mode surface, and designing an actual control law for the flexible joint such that a derivative of the second Lyapunov function is less than or equal to 0;

[0014] S7, estimating a second non-matching disturbance based on a second radial basis function neural network model, and substituting the second non-matching disturbance into the actual control law of the flexible joint.

[0015] In a preferred embodiment, in S1, the rigid-flexible coupling dynamic model is expressed as:

[0016]

[0017] τ j =K(x3 / N-x1)+D(x4 / N-x2).

[0018] Among them, E1 is the non-matching disturbance in the flexible joint, E2 is the matching disturbance in the flexible joint, x2 is the speed of the connecting rod end of the flexible joint, I1 is the inertia of the connecting rod end, B1 is the viscous damping of the inertia of the connecting rod end J1 during the movement, x1 is the position of the connecting rod end, τ j is the torque of the flexible joint, x4 is the motor end speed of the flexible joint, J m is the motor end inertia, B m is the motor end inertia J m The viscous damping during the motion, τ m is the torque generated by the permanent magnet torque motor at the motor end, N is the reduction ratio of the harmonic reducer, K is the joint flexibility, x3 is the motor end position, D is the joint damping, and the inertia J at the motor end m and the connecting rod end inertia J1 are separated by the joint flexibility K and the joint damping D.

[0019] In a preferred embodiment, in S2, the process of defining the first composite error sliding mode surface includes:

[0020] S21, defining a desired motion trajectory of the connecting rod end, defining a first tracking error of the connecting rod end based on the desired motion trajectory and the position of the connecting rod end, and differentiating the first tracking error to obtain a derivative of the first tracking error; the first tracking error is defined as:

[0021] e1=x1-x 1d ;

[0022] Among them, x 1d is the desired motion trajectory of the connecting rod end, x1 is the position of the connecting rod end;

[0023] The derivative of the first tracking error is:

[0024]

[0025] S22: Define a first composite error sliding mode surface based on the first tracking error and the derivative of the first tracking error. The first composite error sliding mode surface is expressed as:

[0026]

[0027] Where λ1 is a positive real number.

[0028] In a preferred embodiment, the S3 includes:

[0029] S31: Define the first Lyapunov function according to the first composite error sliding surface. The first Lyapunov function is expressed as:

[0030]

[0031] Wherein, z1 is the first composite error sliding surface;

[0032] S32, deriving the first Lyapunov function to obtain the derivative of the first Lyapunov function:

[0033] described It is expressed by the following formula:

[0034]

[0035] S33, in order to make the derivative of the first Lyapunov function The first virtual control amount Expressed as:

[0036]

[0037] Where a1 is a positive constant, is the first non-matching interference estimated by the first radial basis neural network model.

[0038] In a preferred embodiment, in S4, the first non-matching interference is expressed by the first radial basis function neural network model as:

[0039]

[0040] where ξ1 = [x1, x2, x3, x4] T is the input of the first radial basis function neural network model, is the estimated weight parameter vector, is the total number of nodes in the hidden layer, is the output of the hidden layer Gaussian basis function;

[0041] The estimated weight parameter vector Expressed as:

[0042]

[0043] where Γ1 is a positive definite diagonal matrix, is a positive constant;

[0044] The output ψ of the hidden layer Gaussian basis function1i Expressed as:

[0045]

[0046] Among them, c i =[c i1 , c i2 , c i3 , c i4 ] T is ψ 1i The center vector, b i is ψ 1i width.

[0047] In a preferred embodiment, in S5, the second-order low-pass filter is expressed as:

[0048]

[0049] Among them, τ c is the time constant of the second-order low-pass filter, x 3d is the output of the second-order low-pass filter, is the first virtual control variable, which is the input of the second-order low-pass filter;

[0050] The second tracking error e2 is expressed as:

[0051] e2=x3-x 3d ;

[0052] The derivative of the second tracking error e2 is expressed as:

[0053]

[0054] The second composite error sliding mode surface is expressed as:

[0055]

[0056] Where λ2 is a positive constant.

[0057] In a preferred embodiment, the S6 includes:

[0058] S61: Define the second Lyapunov function according to the second composite error sliding surface. The second Lyapunov function is expressed as:

[0059]

[0060] S62, deriving the second Lyapunov function to obtain the derivative of the second Lyapunov function:

[0061] described It is expressed by the following formula:

[0062]

[0063] S63, in order to make the derivative of the second Lyapunov function The actual control law of the flexible joint is obtained by the following formula:

[0064]

[0065] Where a2 is a positive constant, The second non-matching interference is estimated from the second radial basis function neural network model.

[0066] In a preferred embodiment, in said S7, the second non-matching interference The second radial basis function neural network model is expressed as:

[0067]

[0068] where ξ2 = [x1, x2, x3, x4] T is the input of the second radial basis function neural network model, is the estimated weight parameter vector, is the total number of nodes in the hidden layer, is the output of the hidden layer Gaussian basis function;

[0069] The estimated weight parameter vector Expressed as:

[0070]

[0071] where Γ2 is a positive definite diagonal matrix, is a positive constant;

[0072] The output ψ of the hidden layer Gaussian basis function 2j Expressed as:

[0073]

[0074] Among them, c j =[c j1 , c j2 , c j3 , c j4 ] T is ψ 2j The center vector, b j is ψ 2j width.

[0075] On the other hand, the present invention further discloses a readable storage medium, wherein the readable storage medium stores a computer program, and when the computer program is run, the steps in the above-mentioned flexible joint dynamic surface controller design method are executed.

[0076] On the other hand, the present invention also discloses an electronic device, which includes a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is run by the processor, the steps in the above-mentioned flexible joint dynamic surface controller design method are executed.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] 1. Compared with the traditional flexible joint dynamic surface controller design which requires four steps of backstepping, introduces three first-order low-pass filters, and brings about three filtering errors, the flexible joint dynamic surface controller designed by the present invention only requires two steps of backstepping and introduces only one second-order low-pass filter, which only brings about one filtering error; and compared with the traditional method which requires three time constants, the second-order dynamic surface proposed by the present invention has only one time constant, which simplifies the adjustment process of the controller parameters.

[0079] 2. Unlike the traditional method of directly using a neural network model to fit system information, a black box model without dynamic parameter information will lead to poor initial training effect of the neural network. The controller of the present invention is based on the identified dynamic parameters, and the introduced dual radial basis function neural network is only used to estimate the non-matching interference and matching interference in the flexible joint. The introduction of model information can reduce the transient error caused by the initial learning of the neural network. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0081] Figure 1 Schematic diagram of the architecture of a flexible joint dynamic surface controller according to an embodiment of the present invention;

[0082] Figure 2 is a reference trajectory diagram of the connecting rod end in an embodiment of the present invention;

[0083] Figure 3 This is a schematic diagram of control energy for artificially injecting a time-varying friction torque into a control object in an embodiment of the invention;

[0084] Figure 4This is a schematic diagram of control energy for artificially injecting a time-varying external torque into a control object in an embodiment of the invention;

[0085] Figure 5 is a comparison diagram of the connecting rod end trajectory tracking error in an embodiment of the present invention;

[0086] Figure 6 It is a flow chart of a method for designing a flexible joint dynamic surface controller according to an embodiment of the present invention. DETAILED DESCRIPTION

[0087] The present invention will be more fully understood through the following detailed description, which should be read in conjunction with the accompanying drawings. Detailed embodiments of the present invention are disclosed herein; however, it should be understood that the disclosed embodiments are merely exemplary of the present invention, which can be embodied in various forms. Therefore, the specific functional details disclosed herein should not be construed as limiting, but rather as a basis for the claims and as a representative basis for teaching those skilled in the art to employ the present invention in various ways in virtually any appropriately detailed embodiment.

[0088] Taking the flexible joints of collaborative robots as an example, a control architecture for the design method of dynamic surface controller of flexible joints of collaborative robots is proposed. Figure 1 As shown, it includes: a second-order dynamic surface controller and a dual radial basis function neural network controller. Figure 6 As shown, the specific design method mainly includes the following steps:

[0089] S1, establish the rigid-flexible coupling dynamic model of the flexible joint.

[0090] Specifically, the dynamics of the flexible joint is mainly divided into three parts: motor, joint flexibility and load. Among them, the torque generated by the permanent magnet torque motor at the motor end is defined as τ m Motor end inertia J m and the connecting rod end inertia J1 are separated by the joint flexibility K and the joint damping D, τ j is the torque of the flexible joint. In addition, J m J1 and J2 will also be affected by viscous damping B during the movement m The reduction ratio of the harmonic reducer is N, the motor end position is represented by x3, the motor end speed of the flexible joint is represented by x4, the connecting rod end position is represented by x1, and the connecting rod end speed of the flexible joint is represented by x2. Therefore, the rigid-flexible coupling dynamic model of the integrated joint can be expressed as:

[0091]

[0092] τ j =K(x3 / N-x1)+D(x4 / N-x2).

[0093] Among them, E1 is the non-matching interference in the flexible joint, and E2 is the matching interference in the flexible joint.

[0094] Since the dynamic model parameters of the flexible joint are unknown, a frequency sweep identification method is required to obtain the dynamic parameters of the joint. By inputting a sinusoidal current with gradually decreasing amplitude and increasing frequency into the flexible joint motor, the position control of the flexible joint is achieved based on the motor's current loop. The absolute position encoder at the connecting rod end of the flexible joint can obtain the position signal of the connecting rod output end. Then, based on the Matlab identification toolbox, the input current signal and the output connecting rod end position signal are imported into the identification toolbox. The obtained flexible joint dynamic model parameters are shown in Table 1 below:

[0095]

[0096]

[0097] Table 1 Identified integrated joint dynamic parameters

[0098] S2, defining a first tracking error of the flexible joint link end, and defining a first composite error sliding mode surface according to the first tracking error.

[0099] Specifically, the process of defining the first composite error sliding mode surface includes:

[0100] S21, defining a desired motion trajectory of the connecting rod end, defining a first tracking error of the connecting rod end based on the desired motion trajectory and the position of the connecting rod end, and differentiating the first tracking error to obtain a derivative of the first tracking error; the first tracking error is defined as:

[0101] e1=x1-x 1d ;

[0102] Among them, x 1d is the expected motion trajectory of the connecting rod end, and x1 is the measured position signal of the connecting rod end;

[0103] Differentiating the above equation, we can get the derivative of the first tracking error:

[0104]

[0105] S22: Define a first composite error sliding mode surface based on the first tracking error and the derivative of the first tracking error. The first composite error sliding mode surface z1 is expressed as:

[0106]

[0107] Wherein, λ1 is a set positive real number, λ1=10.

[0108] S3, designing a first Lyapunov function (i.e., Lyapunov function) according to the first composite error sliding surface, and obtaining a first virtual control variable that makes the derivative of the first Lyapunov function less than or equal to 0

[0109] Specifically, the S3 includes:

[0110] S31: Define the first Lyapunov function according to the first composite error sliding surface. The first Lyapunov function V1 is expressed as:

[0111]

[0112] Wherein, z1 is the first composite error sliding surface;

[0113] S32, deriving the first Lyapunov function V1 to obtain the derivative of the first Lyapunov function for:

[0114] Due to the It can be expressed by the following formula:

[0115]

[0116] S33, in order to make the derivative of the first Lyapunov function Then the first virtual control quantity It can be expressed as:

[0117]

[0118] Among them, a1 is a positive constant, a1=550, It is the first mismatching interference estimated by the first radial basis neural network model for compensation.

[0119] S4, estimating a first non-matching interference based on a first radial basis function neural network model, and substituting the first virtual control variable into the first non-matching interference.

[0120] Specifically, since the radial basis neural network model has the ability to universally approximate any nonlinear function, the first non-matching interference The first radial basis function neural network model can be expressed as:

[0121]

[0122] where ξ1 = [x1, x2, x3, x4] T is the input of the first radial basis function neural network model, is the estimated weight parameter vector, is the total number of nodes in the hidden layer, is the output of the hidden layer Gaussian basis function;

[0123] Furthermore, the estimated weight parameter vector It can be expressed as:

[0124]

[0125] where Γ1 is a positive definite diagonal matrix, is a set positive constant, Γ1=diag(10000×[33 3 3 3 3 3]);

[0126] Furthermore, the output ψ of the hidden layer Gaussian basis function 1i It can be expressed as:

[0127]

[0128] Among them, c i =[c i1 , c i2 , c i3 , c i4 ] T is ψ 1i The center vector, b i is ψ 1i The width, b i =600.

[0129] S5. Introduce a second-order low-pass filter with the first virtual control variable as input, obtain a second tracking error by the second-order low-pass filter, and combine the second tracking error with its derivative to obtain a second composite error sliding surface.

[0130] Specifically, in this step, a single second-order low-pass filter is introduced, and the time constant of the second-order low-pass filter is set to τ c =0.04, is the first virtual control quantity, which is the input of the second-order low-pass filter, x 3d is the output of a second-order low-pass filter, which can be designed as follows:

[0131]

[0132] Furthermore, the second tracking error e2 is defined as:

[0133] e2=x3-x 3d ;

[0134] Furthermore, the derivative of the second tracking error e2 is expressed as:

[0135]

[0136] Furthermore, the second composite error sliding mode surface is defined as:

[0137]

[0138] Here, λ2 is a positive constant, and λ2=450 is set.

[0139] S6. Design a second Lyapunov function based on the second composite error sliding mode surface, and design an actual control law for the flexible joint so that the derivative of the second Lyapunov function is less than or equal to 0.

[0140] Specifically, the S6 includes:

[0141] S61: Define the second Lyapunov function according to the second composite error sliding surface. The second Lyapunov function is expressed as:

[0142]

[0143] S62, deriving the second Lyapunov function to obtain the derivative of the second Lyapunov function:

[0144] described It is expressed by the following formula:

[0145]

[0146] S63, in order to make the derivative of the second Lyapunov function The actual control law of the flexible joint is obtained by the following formula:

[0147]

[0148] Where a2 is a positive constant, set a2 = 50, The second non-matching interference is estimated from the second radial basis function neural network model.

[0149] S7, estimating a second non-matching disturbance based on a second radial basis function neural network model, and substituting the second non-matching disturbance into the actual control law of the flexible joint.

[0150] Specifically, in S7, the second non-matching interference The second radial basis function neural network model can be expressed as:

[0151]

[0152] where ξ2 = [x1, x2, x3, x4] T is the input of the second radial basis function neural network model, is the estimated weight parameter vector, is the total number of nodes in the hidden layer, is the output of the hidden layer Gaussian basis function;

[0153] Furthermore, the estimated weight parameter vector It can be expressed as:

[0154]

[0155] Where Γ2 is a positive definite diagonal matrix, set Γ2 = diag(0.0001×[3 3 3 3 3 3 3}), is a positive constant, set

[0156] The output ψ of the hidden layer Gaussian basis function 2j It can be expressed as:

[0157]

[0158] Among them, c j =[c j1 , c j2 , c j3 , c j4 ] T is ψ 2j The center vector, b j is ψ 2j width, set b j =300.

[0159] In Simulink, the second-order dynamic surface and dual radial basis function neural network controller proposed in the present invention is compared with the traditional dynamic surface and dual radial basis function neural network controller to verify the superiority of the controller proposed in the present invention.

[0160] 1). Use the identified controller parameters to build a virtual control object of the collaborative robot's flexible joint in the Simulink environment of Matlab.

[0161] 2). If Figure 3 and Figure 4 As shown in Figure 1, time-varying friction torque and external torque are artificially injected into the control object as interference to the control object in practice.

[0162] 3) Comparison of the tracking accuracy of the flexible joint link end based on the traditional dynamic surface (SDC) + dual radial basis function neural network controller and the second-order dynamic surface (SDSC) + dual radial basis function neural network controller proposed in this invention;

[0163] The comparison between the traditional dynamic surface controller and the second-order dynamic surface controller proposed in this invention is as follows: Figure 5 As shown in Table 2, the maximum, mean and root mean square error indicators of the tracking errors of the two controllers are shown in Table 2:

[0164]

[0165]

[0166] Table 2: Comparison of tracking errors of two position controllers

[0167] It can be seen from the position tracking error that no matter the maximum value, mean value or variance index, the position controller proposed in the present invention achieves the best tracking effect, thereby verifying the superiority of the position controller proposed in the scheme of the present invention.

[0168] The present invention has the following advantages: 1. Compared with the traditional flexible joint dynamic surface controller design which requires four steps of back-stepping, introduces three first-order low-pass filters, and causes three filtering errors, the flexible joint dynamic surface controller designed by the present invention only requires two steps of back-stepping and introduces only one second-order low-pass filter, that is, it only causes one filtering error; and compared with the traditional method which requires three time constants, the second-order dynamic surface proposed by the present invention has only one time constant, which simplifies the controller parameter adjustment process. 2. Compared with the traditional method which directly uses a neural network model to fit system information, and a black box model without dynamic parameter information will lead to poor initial neural network training effect, the controller of the present invention is based on identified dynamic parameters, and the introduced dual radial basis function neural network is only used to estimate the non-matching interference and matching interference in the flexible joint. The introduction of model information can reduce the transient error caused by the initial learning of the neural network.

[0169] On the other hand, the present invention further provides a readable storage medium having a computer program stored thereon, which implements the steps in the controller design method provided in the above embodiment when the program is executed.

[0170] On the other hand, the present invention further provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is run by the processor, the steps in the above controller design method are executed.

[0171] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0172] More specific examples (a non-exhaustive list) of readable storage media include the following: an electrical connection with one or more wires (electronic device), a portable computer disk cartridge (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disk read-only memory (CDROM). In addition, the readable storage medium may even be paper or other suitable medium on which the program is printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0173] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0174] The various aspects, embodiments, features and examples of the present invention should be considered as illustrative in all respects and are not intended to limit the present invention, the scope of which is defined solely by the claims. Other embodiments, modifications and uses will be apparent to those skilled in the art without departing from the spirit and scope of the invention as claimed.

[0175] The use of headings and sections in this disclosure is not meant to limit the disclosure; each section may apply to any aspect, embodiment, or feature of the disclosure.

Claims

1. A method for designing a flexible joint dynamic surface controller, characterized in that: include: S1, establish the rigid-flexible coupling dynamic model of the flexible joint; S2, defining a first tracking error of the flexible joint link end, and defining a first composite error sliding mode surface based on the first tracking error; S3, designing a first Lyapunov function according to the first composite error sliding surface, and obtaining a first virtual control variable such that a derivative of the first Lyapunov function is less than or equal to 0; S4, estimating a first mismatching interference based on a first radial basis function neural network model, and substituting the first virtual control variable into the first virtual control variable; S5, introducing a second-order low-pass filter with the first virtual control variable as input, obtaining a second tracking error by the second-order low-pass filter, and combining the second tracking error with its derivative to obtain a second composite error sliding mode surface; S6, designing a second Lyapunov function based on the second composite error sliding mode surface, and designing an actual control law for the flexible joint such that a derivative of the second Lyapunov function is less than or equal to 0; S7, estimating a second non-matching disturbance based on a second radial basis function neural network model, and substituting the second non-matching disturbance into the actual control law of the flexible joint.

2. A method for designing a flexible joint dynamic surface controller according to claim 1, characterized in that: In S1, the rigid-flexible coupling dynamic model is expressed as: τ j =K(x3 / N-x1)+D(x4 / N-x2)? Among them, E1 is the non-matching interference in the flexible joint, E2 is the matching interference in the flexible joint, x2 is the speed of the connecting rod end of the flexible joint, J1 is the inertia of the connecting rod end, B1 is the viscous damping of the connecting rod end inertia J1 during the movement, x1 is the position of the connecting rod end, τ j is the torque of the flexible joint, x4 is the motor end speed of the flexible joint, J m is the motor end inertia, B m is the motor end inertia J m The viscous damping during the motion, τ m is the torque generated by the permanent magnet torque motor at the motor end, N is the reduction ratio of the harmonic reducer, K is the joint flexibility, x3 is the motor end position, D is the joint damping, and the inertia J at the motor end m and the connecting rod end inertia J1 are separated by the joint flexibility K and the joint damping D.

3. The method for designing a flexible joint dynamic surface controller according to claim 2, wherein: In S2, the process of defining the first composite error sliding mode surface includes: S21, defining a desired motion trajectory of the connecting rod end, defining a first tracking error of the connecting rod end based on the desired motion trajectory and the position of the connecting rod end, and differentiating the first tracking error to obtain a derivative of the first tracking error; the first tracking error is defined as: e1=x1-x 1d ; Among them, x 1d is the desired motion trajectory of the connecting rod end, x1 is the position of the connecting rod end; The derivative of the first tracking error is: S22: Define a first composite error sliding mode surface based on the first tracking error and the derivative of the first tracking error. The first composite error sliding mode surface is expressed as: Where λ1 is a positive real number.

4. A method for designing a flexible joint dynamic surface controller according to claim 3, characterized in that: The S3 includes: S31: Define the first Lyapunov function according to the first composite error sliding surface. The first Lyapunov function is expressed as: Wherein, z1 is the first composite error sliding surface; S32, deriving the first Lyapunov function to obtain the derivative of the first Lyapunov function: described It is expressed by the following formula: S33, in order to make the derivative of the first Lyapunov function The first virtual control amount Expressed as: Where a1 is a positive constant, is the first non-matching interference estimated by the first radial basis neural network model.

5. The method for designing a flexible joint dynamic surface controller according to claim 4, characterized in that: In S4, the first non-matching interference is expressed by the first radial basis function neural network model as follows: where ξ1 = [x1, x2, x3, x4] T is the input of the first radial basis neural network model, is the estimated weight parameter vector, is the total number of nodes in the hidden layer, is the output of the hidden layer Gaussian basis function; The estimated weight parameter vector Expressed as: where Γ1 is a positive definite diagonal matrix, is a positive constant; The output ψ of the hidden layer Gaussian basis function 1i Expressed as: Among them, c i =[c i1 , c i2 , c i3 , c i4 ] T is ψ 1i The center vector, b i is ψ 1i width.

6. The method for designing a flexible joint dynamic surface controller according to claim 5, characterized in that: In S5, the second-order low-pass filter is expressed as: Among them, τ c is the time constant of the second-order low-pass filter, x 3d is the output of the second-order low-pass filter, is the first virtual control variable, which is the input of the second-order low-pass filter; The second tracking error e2 is expressed as: e2=x3-x 3d ; The derivative of the second tracking error e2 is expressed as: The second composite error sliding mode surface is expressed as: Where λ2 is a positive constant.

7. The method for designing a flexible joint dynamic surface controller according to claim 6, characterized in that: The S6 includes: S61: Define the second Lyapunov function according to the second composite error sliding surface. The second Lyapunov function is expressed as: S62, deriving the second Lyapunov function to obtain the derivative of the second Lyapunov function: described It is expressed by the following formula: S63, in order to make the derivative of the second Lyapunov function The actual control law of the flexible joint is obtained by the following formula: Where a2 is a positive constant, The second non-matching interference is estimated from the second radial basis function neural network model.

8. The method for designing a flexible joint dynamic surface controller according to claim 1, wherein: In S7, the second non-matching interference The second radial basis neural network model is expressed as: where ξ2 = [x1, x2, x3, x4] T is the input of the second radial basis neural network model, is the estimated weight parameter vector, is the total number of nodes in the hidden layer, is the output of the hidden layer Gaussian basis function; The estimated weight parameter vector Expressed as: where Γ2 is a positive definite diagonal matrix, is a positive constant; The output ψ of the hidden layer Gaussian basis function 2j Expressed as: Among them, c j =[c j1 , c j2 , c j3 , c j4 ] T is ψ 2j The center vector, b j is ψ 2j width.

9. A readable storage medium, characterized in that: The readable storage medium stores a computer program, and when the computer program is run, the steps of the method for designing a flexible joint dynamic surface controller according to any one of claims 1 to 8 are executed.

10. An electronic device, characterized in that: The electronic device includes a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is run by the processor, the steps of the method for designing a flexible joint dynamic surface controller according to any one of claims 1 to 8 are executed.

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