Control method and system for flexible joint robot under input delay

Abstract

The present application relates to a control method and system of a flexible joint robot under input delay, a model is established according to the motion state of the flexible joint robot, and input delay is introduced in the established model;The established model is converted into a state equation according to the physical characteristics of the flexible joint robot;In the state equation obtained by conversion, a specified performance function with a predetermined time is introduced;An error conversion function is constructed, and the tracking error constraint problem during the control of the flexible joint robot is converted into a boundedness problem by using the error conversion function and the specified performance function;The influence of input delay is eliminated through an auxiliary system and coordinate transformation, and a compensated tracking error signal is obtained;A performance index function containing error index and control input index is defined, a virtual controller is designed with the minimum performance index function as the target, and unknown parameters in the virtual controller are obtained by using a neural network.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot control, in particular to a control method and system for a flexible joint robot under input delay. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute the prior art.

[0003] In industrial production machinery, flexible robots greatly improve production efficiency and product quality through their heavy load and high precision capabilities. In particular, in human-robot coexistence application scenarios, flexible robots exhibit unique advantages. They can safely collaborate with human workers to perform delicate operations and complex tasks, greatly expanding the application range of robots. Flexible joint robots are a type of flexible robot, with flexible joint design, higher flexibility, and suitability for complex tasks. For example, in the medical industry, flexible joint robots are used for minimally invasive surgery and rehabilitation, improving surgical precision and patient rehabilitation outcomes.

[0004] Input delay is a key issue in robot system control, which can seriously affect system stability. Input delay is usually caused by signal transmission, data processing, or response time of the actuator, resulting in a time difference between control commands and actual execution, which can cause system oscillation, increased tracking error, and even instability.

[0005] To address the input delay problem, methods based on predictive control can predict future states by building system models to compensate for the effects of delay; methods based on filter design can reduce delay time by optimizing signal processing; and adaptive control or robust control strategies can be used to improve system tolerance to delay. However, the above methods mostly focus on system stability analysis and delay compensation, while ignoring system output performance optimization.

[0006] Specified performance control is a method that can effectively maintain system transient behavior and steady-state performance, and has been widely applied in robot systems. The core idea of specified performance control is to design a performance function to limit the tracking error of the system within a pre-set range, ensuring that the system meets performance requirements during dynamic processes and in steady state. This method has shown significant advantages in industrial robots, unmanned aerial vehicles, flexible joint robots, and other fields, especially in tasks requiring high precision tracking and stability.

[0007] Although the traditional prescribed performance control method ensures that the tracking error converges within the prescribed range, the time of error convergence cannot be set in advance. This limitation is particularly prominent in application scenarios that require fast response. For example, in the operation of a flexible joint robot, fast response is the key to achieving efficient task execution, especially in scenarios such as high-speed assembly, dynamic grasping, or human-robot collaboration. Although the traditional prescribed performance control method can ensure that the error eventually converges, its convergence speed depends on the system dynamic characteristics and controller parameters, and cannot be flexibly adjusted according to task requirements. This uncontrollable convergence time may cause the system to fail to reach the desired state in time in a rapidly changing environment, thereby affecting the overall performance. SUMMARY

[0008] To solve the technical problems in the background art, the present application provides a control method and system for a flexible joint robot under input delay, an input delay compensation system is constructed, a compensation signal is introduced through coordinate transformation, and a control signal is designed combining dynamic surface control and adaptive backstepping method to eliminate the negative impact of input delay on the system; a predetermined time specified performance function is designed to ensure that the tracking error converges within the specified range within the preset time; by constructing a prediction error model, an identification neural network update law is designed to better approximate the unknown nonlinear function.

[0009] To achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0010] The first aspect of the present application provides a control method for a flexible joint robot under input delay, comprising the following steps:

[0011] Modeling according to the motion state of the flexible joint robot, and introducing input delay in the constructed model;

[0012] According to the physical characteristics of the flexible joint robot, the constructed model is converted into a state equation;

[0013] In the converted state equation, a specified performance function with predetermined time is introduced;

[0014] An error conversion function is constructed, and the tracking error constraint problem during the control of the flexible joint robot is converted into a boundedness problem using the error conversion function and the specified performance function;

[0015] The influence of input delay is eliminated through an auxiliary system and coordinate transformation to obtain a compensated tracking error signal;

[0016] The performance index function including error index and control input index is defined, the virtual controller is designed aiming at minimizing the performance index function, and the unknown parameters in the virtual controller are obtained by using neural network; during the process, the unknown nonlinear function in the virtual controller is approximated by constructing a prediction error model, designing an execution neural network and an update law of evaluating neural network weight, and identifying an update law of network.

[0017] As a further implementation, the motion state of the flexible joint robot is modeled as follows:

[0018]

[0019] wherein, θ and θ respectively represent the angular position and angular velocity of the link, θ and θ respectively represent the angular position and angular velocity of the rotor, and M (q) represents an inertia matrix, C (q) represents the Coriolis force and centripetal force, and G (q) ∈ R m G represents a gravity vector, B represents a friction force term.

[0020] As a further implementation, an input delay is introduced in the constructed model as follows:

[0021]

[0022] wherein, θ and θ respectively represent the angular position and angular velocity of the link, θ and θ respectively represent the angular position and angular velocity of the rotor, and the positive definite diagonal matrix K ∈ R m×m J ∈ R m×m B ∈ R m×m respectively correspond to joint flexibility, actuator inertia and natural damping term, and τ is an input delay, and u represents a control input τ = u (t-τ) ∈ R m t represents a current time.

[0023] As a further implementation, the constructed model is converted into a state equation according to the physical characteristics of the flexible joint robot; as follows:

[0024]

[0025] wherein, θ and θ respectively represent the angular position and angular velocity of the link, θ and θ respectively represent the angular position and angular velocity of the rotor, and u represents a control input τ = u (t-τ) ∈ R m f1 = -M -1(x1) [C(x1, x2) + G(x2) + F(x2) + Kx1] and f2 = -J -1 [Bx4 + K(x3 - x1)] is an unknown smooth function, and Λ(x1) = M -1 (x1) K, wherein the matrix M(x1), C(x1, x2), G(x2), F(x2), K, B, J are known parameters during modeling.

[0026] As a further implementation, a specified performance function with a predetermined time is as follows:

[0027]

[0028] In the above formula, n and θ represent positive design parameters, and satisfy m > θ, T represents a preset time, and t represents a current time.

[0029] As a further implementation, the influence of input delay is eliminated through an auxiliary system and coordinate transformation to obtain a compensated tracking error signal; as follows:

[0030]

[0031] In the above formula, p i > 0 (i = 1, 2, 3, 4) is a normal number, and Δu = u τ -u, u τ is a control input, v i (i = 1, 2, 3, 4) is a compensated tracking error signal, m i (i = 1, 2, 3, 4) is a filter output, δ i (i = 1, 2, 3, 4) is a compensation signal, is the derivative of δ i (i = 1, 2, 3, 4).

[0032] As a further implementation, a performance index function is as follows:

[0033]

[0034] Wherein, β1> 0 represents a discount factor, α1, respectively represent a controller and a transpose of the controller.

[0035] The second aspect of the present application provides a system required for implementing the above method, comprising:

[0036] A model construction module is configured to model according to a motion state of the flexible joint robot, and introduce an input delay in the constructed model.

[0037] a state equation conversion module configured to convert the constructed model into a state equation according to physical characteristics of the flexible joint robot;

[0038] a specified performance function module configured to introduce a specified performance function with a predetermined time into the converted state equation;

[0039] an error conversion module configured to construct an error conversion function and convert a tracking error constraint problem during control of the flexible joint robot into a boundedness problem by using the error conversion function and the specified performance function;

[0040] an error compensation module configured to eliminate the influence of input delay by an auxiliary system and coordinate transformation to obtain a compensated tracking error signal;

[0041] a parameter solving module configured to define a performance index function containing an error index and a control input index, design a virtual controller with minimization of the performance index function as a target, and obtain unknown parameters in the virtual controller by using a neural network; during the process, an unknown nonlinear function in the virtual controller is approximated by constructing a prediction error model, designing an execution neural network and an update law for evaluating neural network weights, and identifying an update law for the network.

[0042] A third aspect of the present application provides a computer readable storage medium.

[0043] A computer readable storage medium having a computer program stored thereon, the program being executed by a processor to implement the steps in the control method for the flexible joint robot under input delay.

[0044] A fourth aspect of the present application provides a computer device.

[0045] A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor implementing the steps in the control method for the flexible joint robot under input delay when executing the program.

[0046] Compared with the prior art, the above one or more technical solutions have the following beneficial effects:

[0047] 1. The input delay compensation system is constructed by comprehensively considering the optimal control of the flexible joint robot, input delay, predetermined time specified performance control and other problems, a compensation signal is introduced by coordinate transformation, and a control signal is designed by combining dynamic surface control and adaptive backstepping method to eliminate the negative influence of input delay on the system; the predetermined time specified performance function can ensure that the tracking error converges to a specified range within a predetermined time; the identification neural network update law is designed by constructing a prediction error model, which can better approximate the unknown nonlinear function.

[0048] 2、Design of auxiliary system to generate compensation signals, and through coordinate transformation to introduce these signals, effectively eliminate the adverse effects of input delay on the system, compared with other processing delay method, the method of designing auxiliary system more consider the output performance of the system, and make the flexible joint robot system research more practical application value.

[0049] 3、Proposed predetermined time specified performance technology, unlike the traditional specified performance control method, the proposed method not only ensures that the error remains within the predefined range, but also specifies the convergence time, which can significantly enhance the flexibility and precision of flexible joint robot when performing complex tasks.

[0050] 4、Proposed improved reinforcement learning strategy of identification-execution-evaluation neural network. The strategy simplifies the update law of the execution-evaluation neural network by using a simplified positive function, thereby simplifying the entire design process. More importantly, by constructing a prediction error model, the update law of the identification neural network contains the prediction error and the compensation tracking error, which can more effectively approximate the unknown function. BRIEF DESCRIPTION OF DRAWINGS

[0051] The drawings accompanying the specification of this application form a part thereof, serve to provide further understanding of the present application, and together with the description of the exemplary embodiments of the present application, serve to explain the present application, and do not constitute an improper limitation on the present application.

[0052] Figure 1 is a structural schematic diagram of a flexible joint robot provided by one or more embodiments of the present application;

[0053] Figure 2 is a response curve diagram of the reference signal x d and the system output signal x1;

[0054] Figure 3 is a comparison diagram of the convergence effect of the tracking error provided by one or more embodiments of the present application;

[0055] Figure 4 is an effect diagram of the identification neural network approximating function f1 provided by one or more embodiments of the present application;

[0056] Figure 5 is an effect diagram of the identification neural network approximating function f2 provided by one or more embodiments of the present application;

[0057] Figure 6 is a bounded diagram of the execution neural network weight provided by one or more embodiments of the present application;

[0058] Figure 7is a bounded graph of neural network weights provided by one or more embodiments of the invention;

[0059] Figure 8 is a control input trajectory graph of a flexible joint robot system provided by one or more embodiments of the invention. DETAILED DESCRIPTION

[0060] The invention is further described below by way of example with reference to the accompanying drawings.

[0061] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the invention. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0062] The following embodiments give a control method and system of flexible joint robot under input delay, and propose a prescribed performance control method under input delay based on Lyapunov stability analysis. The method first constructs an input delay compensation system, introduces a compensation signal through coordinate transformation, and designs a control signal combining dynamic surface control and adaptive backstepping method to eliminate the negative impact of input delay on the system. Secondly, a predetermined time specified performance function is designed to ensure that the tracking error converges to the specified range within the preset time. In addition, by constructing a prediction error model, an identification neural network update law is designed to better approximate the unknown nonlinear function. Finally, the Lyapunov stability theorem is used to prove that all signals of the closed-loop system are globally uniformly ultimately bounded and the uniform tracking error converges to a compact set near the origin. The simple implementation of the formula is described in the accompanying drawings, but it does not represent the specific implementation and is not limited to this implementation.

[0063] Embodiment one:

[0064] The control method of flexible joint robot under input delay includes the following steps:

[0065] Step 1, model the flexible joint robot and consider the input delay;

[0066] Step 2, according to the physical characteristics of the flexible joint robot, convert the equation model obtained by modeling into a state equation;

[0067] Step 3, introduce a predetermined time specified performance function;

[0068] Step 4, construct an error conversion function to convert the tracking error constraint problem into a boundedness problem;

[0069] Step 5, construct an auxiliary system to eliminate the influence of input delay, and construct a coordinate transformation to obtain a compensated tracking error signal;

[0070] Step 6, define the optimal cost function, design the virtual controller, solve the "complexity explosion" problem of backstepping method by using dynamic surface control method, design the update law of the execution and evaluation neural network, and design the update law of the identification neural network by using the correction term and the prediction error.

[0071] The embodiment takes a flexible joint robot as shown in the figure as an example, wherein a motor drives a rotor to rotate, a link is connected to the rotor and is driven to rotate by the rotor, one end of the link is suspended, and the other end of the link is suspended, and the rotation point is taken as the O point of the coordinate system XY, and the link and the rotor are connected by an elastic element (such as a spring or a harmonic reducer) to form a flexible joint. Figure 1

[0072] As a further implementation, the system model of the flexible joint robot in step 1 is:

[0073]

[0074] In the above formula, respectively represent the angular position and angular velocity of the link. respectively represent the angular position and angular velocity of the rotor.

[0075] Let The matrix M(q) represents the inertia matrix, and represents the Coriolis force and the centripetal force. The gravity vector is represented as G(q) ∈ R m , and the friction term is represented as The positive definite diagonal matrix K ∈ R m×m , J ∈ R m×m , and B ∈ R m×m correspond to the joint flexibility, actuator inertia, and natural damping terms, respectively. Considering the input delay τ, the control input is u τ = u(t-τ) ∈ R m .

[0076] As a further implementation, according to the physical characteristics of the flexible joint robot, the equation obtained by modeling is converted into a state equation, and the influence of the input delay is considered. The converted state equation of the system is:

[0077]

[0078] In the above formula, f1 = -M -1 (x1)[C(x1, x2) + G(x2) + F(x2) + Kx1], and f2 = -J -1 [Bx4 + K(x3-x1)] are unknown smooth functions, and Λ(x1) = M -1 (x1)K. The matrices M(x1), C(x1, x2), G(x2), F(x2), K, B, and J are known. ​

[0079] As a further implementation, step 3, the predetermined time designated performance function is designed as:

[0080]

[0081] In the above formula, m and θ represent positive design parameters, and satisfy m> θ. T represents the preset time, and t represents the current time. The above formula needs to satisfy the following conditions:

[0082] 1). ζ is strictly decreasing on the interval [0, T], and satisfies ζ(0) = m, when t>T, ζ = θ;

[0083] 2). ζ and are smooth and bounded for all t≥0.

[0084] Although the conventional prescribed performance control method can guarantee the final convergence of the error, it cannot be flexibly adjusted according to the task requirements. This uncontrollable convergence time may cause the system to fail to reach the desired state in time in a rapidly changing environment, thereby affecting the overall performance. The prescribed performance function designed in this embodiment can flexibly set the preset time T, without relying on the system dynamic characteristics and controller parameters.

[0085] As a further implementation, step 4, an error conversion function is constructed to convert the tracking error constraint problem into a boundedness problem. The constructed error conversion function is:

[0086]

[0087] In the above formula, represents the transformed error vector, represents the tracking error, x1 = q represents the angular position of the link, x d represents a given target function.

[0088] Given the initial condition and using the designated performance function and the error conversion function, if is bounded for all t≥0, then it can be deduced that This means that satisfies According to the definition of ζ, it is further shown that as long as is bounded, for all T<t, there is Therefore, the tracking error constraint problem is effectively converted into a boundedness problem of ensuring .

[0089] Taking the time derivative of , we get:

[0090]

[0091] In the above equation,

[0092] As a further implementation, step 5: Coordinate transformation is constructed by using auxiliary system and dynamic surface control technique, which avoids the influence of input delay and solves the "complexity explosion" problem in backstepping method.

[0093] In order to eliminate the adverse effects of input delay of nonlinear system, an effective auxiliary system is constructed to obtain compensation signal δ i (i = 1, 2, 3, 4):

[0094]

[0095] In the above equation, p i > 0 (i = 1, 2, 3, 4) is a normal number, Δu = u τ -u, is the derivative of δ i (i = 1, 2, 3, 4).

[0096] The coordinate transformation is constructed to obtain the compensated tracking error signal:

[0097]

[0098] In the above equation, v i (i = 1, 2, 3, 4) is the compensated tracking error signal, m i (i = 1, 2, 3, 4) is the filter output.

[0099] As a further implementation, step 6, design a virtual controller and estimate the unknown parameters of the system online through a neural network:

[0100] Step 6.1, in order to achieve optimal control, the performance index function includes error index and control input index, through which the performance index function can be minimized. Define the optimal cost function as:

[0101]

[0102] In the above equation, β1> 0 represents the discount factor, α1, respectively represent the controller and the transpose of the controller.

[0103] Design a virtual controller

[0104]

[0105] In the above equation, h1is a positive design parameter. is the inverse matrix of matrix , is the derivative of the given objective function x d , approximates the unknown vector function P1 using a neural network, denoted as: is the transpose of the ideal weight vector of the neural network , and ε1 is the approximation error vector, and S1(N1) is the basis function vector.

[0106] The design of the neural network weight update law is:

[0107]

[0108] In the above formula, is a positive design parameter.

[0109] The update law of the evaluation network is designed as:

[0110]

[0111] In the above formula, η c1 is a positive constant, and satisfies

[0112] Since the matrix is semi-positive definite, its eigenvalue is zero. If the term falls on the value of the zero eigenvalue of , the training may terminate. In order to avoid this possibility, a correction term μI is introduced to ensure that the matrix is strictly positive definite, so that sufficient training can be guaranteed. By using a simplified positive function to implement the evaluation neural network design update law, the entire design process is simplified.

[0113] Step 6.2, the control method of the embodiment is designed based on backstepping method, and the traditional backstepping method needs to repeatedly differentiate the virtual controller in the implementation process, which will cause the problem of "differentiation explosion". In order to solve this problem, dynamic surface technology is introduced.

[0114] Specifically, the dynamic surface technology inputs the signal of the first virtual controller into a first-order low-pass filter, thereby generating a new state variable m i , which is used to replace the first virtual controller for subsequent calculation. The advantage of this processing method is that it reduces the number of independent variables, avoids the complexity of repeated differentiation, thereby significantly reducing the amount of calculation, while maintaining the stability and accuracy of the control system.

[0115] In this embodiment, the first virtual controller Input to the first first-order low-pass filter to obtain the new state variable m i , according to the new state variable m i Design the second error surface as:

[0116]

[0117] In the above formula,

[0118] Designing a second virtual controller for

[0119]

[0120] In the above formula, h2 is a positive design parameter. -1 (x1) is the inverse matrix of matrix Λ(x1). The unknown vector functions P2 and f1 are approximated by neural networks, which are expressed as: and are the ideal weight vectors of the neural network and The transpose of ε2 and ε f1 is the approximate error vector, and S2(N2) is the basis function vector.

[0121] In order to accurately approximate the dynamic characteristics of the unknown nonlinear system, a composite learning method is used to design the update law of the identification neural network and introduce the prediction error Prediction Status The updates are as follows:

[0122]

[0123] In the above formula, σ1>0 is a positive parameter.

[0124] Considering the prediction error z 1F , the update law of the identifier is designed as follows:

[0125]

[0126] In the above formula, γ Z1 , ω1, F1 are the positive constants to be designed.

[0127] The update law for executing the neural network and evaluating the neural network weights is designed as follows:

[0128]

[0129] In the above formula, is a positive parameter.

[0130] Step 6.3. Design the 3rd virtual controller as:

[0131]

[0132] In the above equation, h3 is a positive design parameter. is the transpose of the ideal weight vector of the neural network , ε3 is the approximation error vector, and S3(N3) is the basis function vector.

[0133] The update law of the neural network and the evaluation of the neural network weight are designed as follows:

[0134]

[0135] In the above equation, is a positive design parameter.

[0136] Step 6.4. Design the 4th controller as:

[0137]

[0138] In the above equation, h4 is a positive design parameter. The unknown vector functions P4 and f2 are approximated by neural networks, represented as: and is the transpose of the ideal weight vector of the neural network and , ε4 and ε f1 are the approximation error vectors, and S4(N4) is the basis function vector.

[0139] The prediction error is introduced to predict the state The update of the predicted state is represented as:

[0140]

[0141] In the above equation, σ2>0 is a positive design parameter.

[0142] The update law of the identification network is shown as follows:

[0143]

[0144] In the above equation, F2, γ Z2 , ω2 are positive design parameters.

[0145] The update law of the neural network and the evaluation of the neural network weight are designed as follows:

[0146]

[0147] In the above formula, is a positive design parameter.

[0148] Simulation experiment.

[0149] The control objective of the simulation experiment is to make the angular velocity of the connecting rod track the given trajectory signal x d = sin(0.3t), considering the system input delay, but assuming τ = 0.01 for the purpose of verifying the effectiveness of the method. According to the actual system, the relevant parameters are: the total mass of the connecting rod n = 1 kg, the total rotational inertia of the connecting rod J = 1 kg·m 2 , the acceleration of gravity g = 10 m / s 2 , the distance from the joint axis to the center of mass l = 1 m, and the friction force The joint compliance is K = 1, and the natural damping term is B = 1.

[0150] The simulation initial conditions are: the specified convergence time is set to T = 2. The values of the design parameters are determined as m = 0.8, θ = 0.05, μ = 0.007, h i = 30, p i = 0.1, and γ Zi = 0.1 (i = 1, 2). In addition, η a1 = 200, η a2 = 50, η a3 = 100, η a4 = 50, η c1 = 210, η c2 = 60, η c3 = 110, η c4 = 85. The initial state of the system is x i (0) = 0.5, δ i (0) = 0.01, (i = 1,..., 4), m i (0) = 0.01, (i = 2, 3, 4).

[0151] The initial value selection of the neural network is executed and evaluated as follows:

[0152]

[0153] The simulation results are shown in Figures 2-8 . Figure 2 The response curves of the reference signal x d and the system output signal x1 are shown. From Figure 3It can be seen that, compared with the adaptive feedback control method, the proposed method can make the error converge to the specified range within the specified time, thereby effectively ensuring the transient and steady-state performance of the system. Figures 4-5 The performance of the identifier neural network in approximating functions f1 and f2 is demonstrated, verifying the effectiveness of the proposed method in estimating unknown functions. Figures 6-7 The weight boundedness of the actor neural network and the critic neural network is respectively demonstrated. Figure 8 The control input trajectory of the flexible joint robot system is demonstrated. Therefore, the numerical simulation proves the effectiveness of the proposed control method.

[0154] In summary, the control method given in the embodiment has the following advantages:

[0155] (1) An auxiliary system is designed to generate compensation signals, and these signals are introduced through coordinate transformation, effectively eliminating the adverse effects of input delay on the system. Compared with other methods of handling delay, the method of designing an auxiliary system more considers the output performance of the system, and makes the research of the flexible joint robot system more practical.

[0156] (2) A predetermined time specified performance technique is proposed. Unlike traditional specified performance control methods, the proposed method not only ensures that the error remains within the predefined range, but also specifies the convergence time, which can significantly enhance the flexibility and precision of the flexible joint robot when performing complex tasks.

[0157] (3) An improved reinforcement learning strategy for the identification-execution-evaluation neural network is proposed. The strategy simplifies the design process by using a simplified positive function to design the update law for the execution-evaluation neural network. More importantly, by constructing a prediction error model, the update law of the identification neural network contains the prediction error and the compensation tracking error, which can more effectively approximate the unknown function.

[0158] Embodiment Two:

[0159] The system for implementing the above method comprises:

[0160] The model construction module is configured to model according to the motion state of the flexible joint robot, and introduce input delay in the constructed model;

[0161] The state equation conversion module is configured to convert the constructed model into a state equation according to the physical characteristics of the flexible joint robot;

[0162] The specified performance function module is configured to introduce a specified performance function with a predetermined time in the converted state equation;

[0163] The error conversion module is configured to construct an error conversion function, and convert a tracking error constraint problem during flexible joint robot control into a boundedness problem by using the error conversion function and a specified performance function.

[0164] The error compensation module is configured to eliminate the influence of input delay by an auxiliary system and coordinate transformation, and obtain a compensated tracking error signal.

[0165] The parameter solving module is configured to define a performance index function containing an error index and a control input index, design a virtual controller with the performance index function minimized as a target, and obtain unknown parameters in the virtual controller by using a neural network; during which, an unknown nonlinear function in the virtual controller is approximated by constructing a prediction error model, designing an execution neural network and an update law of neural network weight evaluation, and identifying an update law of the network.

[0166] Embodiment three:

[0167] The embodiment provides a computer readable storage medium, which stores a computer program, and the program is executed by a processor to implement steps in the control method of the flexible joint robot under input delay in the above embodiment one.

[0168] Embodiment four:

[0169] The embodiment provides a computer device, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements steps in the control method of the flexible joint robot under input delay in the above embodiment one when executing the program.

[0170] The steps or modules involved in the above embodiments two to four correspond to the embodiment one, and the specific embodiments can refer to the related description part of the embodiment one. The term "computer readable storage medium" should be understood as including a single medium or multiple media of one or more instruction sets; and should also be understood as including any medium capable of storing, encoding or carrying instruction sets for execution by a processor and causing the processor to execute any method in the present application.

[0171] The above only describes the preferred embodiments of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A control method for a flexible joint robot with input delay, characterized by: The method comprises the following steps: modeling according to the motion state of the flexible joint robot, introducing input delay in the constructed model; converting the constructed model into a state equation according to the physical characteristics of the flexible joint robot; in the converted state equation, introducing a specified performance function with a predetermined time; constructing an error conversion function, and using the error conversion function and the specified performance function to convert a tracking error constraint problem during control of the flexible joint robot into a boundedness problem; eliminating the influence of the input delay through auxiliary system and coordinate transformation to obtain a compensated tracking error signal; defining a performance index function containing an error index and a control input index, designing a virtual controller with minimization of the performance index function as the goal, and using a neural network to obtain unknown parameters in the virtual controller; during this process, an unknown nonlinear function in the virtual controller is approximated by constructing a prediction error model, designing an execution neural network and an update law for evaluating neural network weights, and an update law for identifying the network; modeling according to the motion state of the flexible joint robot, as shown in the following formula: ； wherein, θ and ω respectively represent the angular position and angular velocity of the connecting rod, θ and ω respectively represent the angular position and angular velocity of the rotor, I represents the inertia matrix, Fcor and Fcent represent the Coriolis force and centripetal force, g represents the gravity vector, Ffric represents the friction force term; eliminating the influence of the input delay through auxiliary system and coordinate transformation to obtain a compensated tracking error signal; as shown in the following formula: ； ； In the above equation, (0.5 ) is a constant, , is a control input (0.5 ) is a compensated tracking error signal, (0.5 ) is a filter output.

2. The control method of a flexible joint robot with input delay according to claim 1, characterized by, introducing input delay in the constructed model, as shown in the following formula: ； where denote the angular position and angular velocity of the link, respectively, denote the angular position and angular velocity of the rotor, respectively, and correspond to the joint flexibility, actuator inertia and natural damping terms, respectively, is the input delay, and the control input is , t is the current time instant.

3. The control method of a flexible joint robot with input delay according to claim 1, characterized by, converting the constructed model into a state equation according to the physical characteristics of the flexible joint robot; as shown in the following formula: ； wherein , respectively denote the angular position and angular velocity of the connecting rod, respectively denote the angular position and angular velocity of the rotor; ； ； the control input is: ； is an unknown smooth function, where the matrix are known parameters at the time of modeling.

4. The control method of a flexible joint robot with input delay according to claim 1, characterized by, the specified performance function with a predetermined time, as shown in the following formula: ； In the above formula, and denote positive design parameters, and satisfy , denotes a preset time, t denotes a current time.

5. The control method of a flexible joint robot with input delay according to claim 1, characterized by, the performance index function, as shown in the following formula: ； wherein represents a discount factor.

6. A control system of a flexible joint robot with input delay for implementing the control method of the flexible joint robot with input delay according to any one of claims 1 to 5, characterized in that, comprising: a model construction module configured to model according to the motion state of the flexible joint robot, and introduce input delay in the constructed model; a state equation conversion module configured to convert the constructed model into a state equation according to the physical characteristics of the flexible joint robot; a specified performance function module configured to introduce a specified performance function with a predetermined time in the converted state equation; an error conversion module configured to construct an error conversion function, and use the error conversion function and the specified performance function to convert a tracking error constraint problem during control of the flexible joint robot into a boundedness problem; an error compensation module configured to eliminate the influence of the input delay through auxiliary system and coordinate transformation to obtain a compensated tracking error signal; a parameter solving module configured to define a performance index function containing an error index and a control input index, design a virtual controller with minimization of the performance index function as the goal, and use a neural network to obtain unknown parameters in the virtual controller; during this process, an unknown nonlinear function in the virtual controller is approximated by constructing a prediction error model, designing an execution neural network and an update law for evaluating neural network weights, and an update law for identifying the network.

7. A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps in the control method of the flexible joint robot under input delay according to any one of claims 1-5.

8. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the control method of a flexible joint robot with input delay according to any one of claims 1-5 when executing the program.

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