Flexible joint dynamic surface controller design method, medium and electronic equipment

Abstract

The invention discloses a flexible joint dynamic surface controller design method, a medium and electronic equipment, and the method comprises the steps: building a rigid-flexible coupling dynamic model of a flexible joint, and defining a first composite error sliding mode surface of a connecting rod end of the flexible joint; designing a first Lyapunov function according to the first composite error sliding mode surface, and obtaining a first virtual control quantity; estimating first non-matching interference based on a first radial basis function neural network model, and substituting the first non-matching interference into the first virtual control quantity; a second-order low-pass filter with a first virtual control quantity as input is introduced, and a second composite error sliding mode surface is obtained; designing a second Lyapunov function according to the second composite error sliding mode surface, and designing an actual control law of the flexible joint; and estimating second non-matching interference based on a second radial basis function neural network model, and substituting the second non-matching interference into an actual control law of the flexible joint. According to the invention, the adjustment process of controller parameters is simplified.

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 of 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 the flexible joint manipulator is affected by matching interference and non-matching interference. Although the controller designed based on the backstepping method can effectively handle the non-matching interference in the flexible joint system, there is a "differential explosion" phenomenon of the virtual control item, so Swaroop et al. introduced the dynamic surface control method. This method introduces a first-order low-pass filter in each backstepping design process, thereby avoiding multiple derivatives of the virtual control item, 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 robot. The patent has four major steps: Step 1: Analysis and construction of the flexible joint robot system model; Step 2: Design of the dynamic surface controller of the flexible joint robot; Step 3: Tracking performance test and parameter adjustment; Step 4: End of design. This invention is aimed at the control system model of the flexible joint robot, gradually designs virtual control, and introduces a first-order low-pass filter at each step, and finally derives the dynamic surface controller of the flexible robot, which overcomes the "differential explosion" phenomenon of the backstepping control, can ensure the semi-global stability of the closed-loop control system, and at the same time realizes the fast and accurate tracking of the flexible joint robot link angle to 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. In order to achieve high-precision control of a flexible robotic arm, the invention combines adaptive RBF neural networks and dynamic surface technology to design a position controller. First, the approximation ability of RBF neural networks to 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 controller design. Finally, simulations verify 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 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 back-stepping step. Therefore, the traditional method for designing a flexible joint control law based on dynamic surface control requires four back-stepping 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, three filter errors are introduced, 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 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 black box without a model. Since the neural network needs to be trained in the early stage to 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 invention object, 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 according to 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 that makes the derivative of the first Lyapunov function less than or equal to 0;

[0011] 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 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 surface;

[0013] S6, designing a second Lyapunov function according to the second composite error sliding surface, and designing an actual control law of the flexible joint so that the 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 an 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 connecting rod end velocity of the flexible joint, I1 is the connecting rod end inertia, B1 is the viscous damping of the connecting rod end inertia J1 during the movement, x1 is the connecting rod end position, 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 an expected motion trajectory of the connecting rod end, defining a first tracking error of the connecting rod end according to the expected motion trajectory and the position of the connecting rod end, 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 according to the first tracking error and the derivative of the first tracking error. The first composite error sliding mode surface is expressed as:

[0026]

[0027] Wherein, λ1 is a positive real number.

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

[0029] S31, defining the first Lyapunov function according to the first composite error sliding surface, wherein 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] Said 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 It is expressed as:

[0036]

[0037] Among them, a1 is a positive constant, It 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 represented 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 It is 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 It is expressed as:

[0045]

[0046] Among them, c i =[c i1 , c i2 , c i3 , c i4 ] T is 1i The center vector of i is 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 quantity and 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 surface is expressed as:

[0055]

[0056] Where λ2 is a positive constant.

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

[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] Said 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] Among them, a2 is a positive constant, A second non-matching interference estimated from a second radial basis function neural network model.

[0066] In a preferred embodiment, in 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 It is 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 It is expressed as:

[0073]

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

[0075] On the other hand, the present invention further discloses a readable storage medium, in which a computer program is stored. When the computer program is executed, 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 the memory stores a computer program, 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 beneficial effects of the present invention are at least:

[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. Compared with the traditional method of directly using the neural network model to fit the system information, the 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 drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative work.

[0081] Figure 1 is a schematic diagram of the architecture of a flexible joint dynamic surface controller in 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 It is a schematic diagram of control energy of artificially injecting time-varying friction torque into the control object in an embodiment of the invention;

[0084] Figure 4It is a schematic diagram of control energy of 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 tracking error of the connecting rod end trajectory in the 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 only exemplary of the present invention, which can be embodied in various forms. Therefore, the specific functional details disclosed herein should not be interpreted as limiting, but only as the basis of the claims and as a representative basis for teaching those skilled in the art to adopt the present invention in different ways in virtually any appropriate detailed embodiment.

[0088] Taking the flexible joints of collaborative robots as an example, a control architecture for the design method of dynamic surface controllers for the 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. 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 subject to viscous damping B during 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 in 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 a gradually decreasing amplitude and a gradually increasing frequency at the motor end of the flexible joint, the position control of the flexible joint is realized based on the current loop of the motor. 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, and 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 surface according to the first tracking error.

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

[0100] S21, defining an expected motion trajectory of the connecting rod end, defining a first tracking error of the connecting rod end according to the expected motion trajectory and the position of the connecting rod end, 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] By differentiating the above equation, the derivative of the first tracking error can be obtained as:

[0104]

[0105] S22, defining the first composite error sliding mode surface according to the first tracking error and the derivative of the first tracking error, wherein 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, S3 includes:

[0110] S31, defining the first Lyapunov function according to the first composite error sliding surface, wherein 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 non-matching 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 normal constant, Γ1=diag(10000×[3 3 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 1i The center vector of i is 1i The width, b i =600.

[0129] 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, combining 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 variable, 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] Further, the second tracking error e2 is defined as:

[0133] e2=x3-x 3d ;

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

[0135]

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

[0137]

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

[0139] S6. Design a second Lyapunov function according to the second composite error sliding 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] Said 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, A second non-matching interference estimated from a 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 an 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 normal number, 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 2j The center vector, b j is 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 joints in Matlab's Simulink environment.

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

[0162] 3). Compare 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 the present invention;

[0163] The comparison between the traditional dynamic surface controller and the second-order dynamic surface controller proposed in this invention is shown in the figure. Figure 5 As shown, 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 brings 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, only brings 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. 2. Compared with the traditional method which directly uses the neural network model to fit the system information, and the 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.

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

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

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

[0172] More specific examples of readable storage media (a non-exhaustive list) include the following: an electrical connection with one or more wirings (electronic devices), a portable computer disk case (magnetic devices), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the readable storage medium may even be a paper or other suitable medium on which the program is printed, since the program may 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 the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated 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 aspects and are not intended to limit the present invention, the scope of the present invention is defined only 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 claimed invention.

[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 according to 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 that makes the derivative of the first Lyapunov function less than or equal to 0; 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 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 surface; S6, designing a second Lyapunov function according to the second composite error sliding surface, and designing an actual control law of the flexible joint so that the 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 an 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 dynamics model is expressed as: τ j =K(x3 / N-x1)+D(x4 / N-x2). Among them, E1 is the non-matching disturbance in the flexible joint, E2 is the matching disturbance in the flexible joint, x2 is the connecting rod end velocity of the flexible joint, J1 is the connecting rod end inertia, B1 is the viscous damping of the connecting rod end inertia J1 during the movement, x1 is the connecting rod end position, 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. A method for designing a flexible joint dynamic surface controller according to claim 2, characterized in that: In S2, the process of defining the first composite error sliding surface includes: S21, defining an expected motion trajectory of the connecting rod end, defining a first tracking error of the connecting rod end according to the expected motion trajectory and the position of the connecting rod end, 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 according to the first tracking error and the derivative of the first tracking error. The first composite error sliding mode surface is expressed as: Wherein, 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, defining the first Lyapunov function according to the first composite error sliding surface, wherein 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: Said It is expressed by the following formula: S33, in order to make the derivative of the first Lyapunov function The first virtual control amount It is expressed as: Where a1 is a positive constant, It is the first non-matching interference estimated by the first radial basis neural network model.

5. A 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: 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; The estimated weight parameter vector It is 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 It is expressed as: Among them, c i =[c i1 , c i2 , c i3 , c i4 ] T is 1i The center vector, b i is 1i Width.

6. A 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 quantity and 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 surface is expressed as: Where λ2 is a positive constant.

7. A 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: Said 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: Among them, a2 is a positive constant, The second non-matching interference is estimated from the second radial basis neural network model.

8. A method for designing a flexible joint dynamic surface controller according to claim 1, characterized in that: In S7, the second non-matching interference The second radial basis function neural network model is expressed as: 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; The estimated weight parameter vector It is expressed as: where Γ2 is a positive definite diagonal matrix, is a normal number. The output ψ of the hidden layer Gaussian basis function 2j It is expressed as: Among them, c j =[c j1 , c j2 , c j3 , c j4 ] T is 2j The center vector, b j is 2j Width.

9. A readable storage medium, characterized in that: The readable storage medium stores a computer program, and when the computer program is executed, the steps in 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 comprises a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps in 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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