Control method and system of flexible joint robot under input delay

Abstract

The invention relates to a control method and system for a flexible joint robot under input delay, and the method comprises the steps: carrying out the modeling according to the motion state of the flexible joint robot, and introducing the input delay into a constructed model; according to the physical characteristics of the flexible joint robot, the constructed model is converted into a state equation; introducing a specified performance function with preset time into the state equation obtained by conversion; constructing an error conversion function, and converting a tracking error constraint problem in the control period of the flexible joint robot into a bounded problem by utilizing the error conversion function and a specified performance function; through an auxiliary system and coordinate transformation, the influence of input delay is eliminated, and a compensated tracking error signal is obtained; and defining a performance index function including an error index and a control input index, designing a virtual controller by taking the minimization of the performance index function as a target, and obtaining unknown parameters in the virtual controller by using a neural network.

Description

Technical Field

[0001] The present invention relates to the field of robot control technology, and in particular to a control method and system for a flexible joint robot under input delay. Background Art

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

[0003] In industrial production machinery, flexible robots have greatly improved production efficiency and product quality through their heavy-load and high-precision capabilities. Especially in the application scenarios of human-machine integration, flexible robots show their unique advantages. They can safely collaborate with human workers to complete delicate operations and complex tasks, greatly expanding the application range of robots. Flexible joint robots are a type of flexible robot with flexible joints, which are more flexible and suitable for complex tasks. For example, in the medical industry, flexible joint robots are used in minimally invasive surgery and rehabilitation treatment, improving surgical accuracy and patient rehabilitation effects.

[0004] Input delay is a critical issue in robot system control, which can seriously affect the stability of the system. Input delay is usually caused by the response time of signal transmission, data processing or actuators, which will lead to a time difference between control instructions and actual execution, thus causing system oscillation, increased tracking error and even instability.

[0005] For the input delay problem, we can use the predictive control method to build a system model to predict the future state, thereby compensating for the impact of the delay; we can also reduce the delay time by optimizing the signal processing process based on the filter design; in addition, we can also use adaptive control or robust control strategies to improve the system's tolerance to delay. However, most of the above methods focus on the stability analysis and delay compensation of the system, while ignoring the optimization of the system's output performance.

[0006] Prescribed performance control is a method that can effectively maintain the transient behavior and steady-state performance of the system and has been widely used in robotic systems. The core idea of ​​prescribed performance control is to limit the tracking error of the system to a preset range by designing a performance function, thereby ensuring that the system can meet the performance requirements both in the dynamic process and in the steady state. This method has shown significant advantages in the fields of industrial robots, drones, flexible joint robots, etc., especially in tasks that require high-precision tracking and stability.

[0007] Although the traditional prescribed performance control method ensures that the tracking error converges within the specified range, the time for error convergence cannot be pre-set. This limitation is particularly prominent in application scenarios that require fast response. For example, in the operation of flexible joint robots, fast response is the key to achieving efficient task execution, especially in scenarios such as high-speed assembly, dynamic grasping, or human-machine 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 a rapidly changing environment, thereby affecting the overall performance. Summary of the invention

[0008] In order to solve the technical problems existing in the above-mentioned background technology, the present invention provides a control method and system for a flexible joint robot under input delay, constructs an input delay compensation system, introduces a compensation signal through coordinate transformation and combines dynamic surface control with adaptive backstepping method to design a control signal, so as to eliminate the negative impact of input delay on the system; designs a performance function with a predetermined time to ensure that the tracking error converges to a specified range within a preset time; and designs an identification neural network update law by constructing a prediction error model to better approximate unknown nonlinear functions.

[0009] In order to achieve the above object, the present invention adopts the following technical solution:

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

[0011] Modeling is performed based on the motion state of the flexible joint robot, and input delay is introduced into 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 a 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 transformed into a bounded problem by using the error conversion function and the specified performance function.

[0015] Through auxiliary systems and coordinate transformation, the influence of input delay is eliminated and the compensated tracking error signal is obtained;

[0016] A performance indicator function including error indicator and control input indicator is defined, a virtual controller is designed with the goal of minimizing the performance indicator function, and a neural network is used to obtain the unknown parameters in the virtual controller. During this period, the unknown nonlinear function in the virtual controller is approximated by constructing a prediction error model, designing the update law for executing the neural network and evaluating the neural network weights, and identifying the update law of the network.

[0017] As a further implementation method, a model is built according to the motion state of the flexible joint robot, as shown in the following formula:

[0018]

[0019] in, denote the angular position and angular velocity of the connecting rod, respectively. They represent the angular position and angular velocity of the rotor respectively, M(q) represents the inertia matrix, represents the Coriolis force and the centripetal force, G(q)∈R m represents the gravity vector, represents the friction term.

[0020] As a further implementation method, input delay is introduced into the constructed model as shown in the following formula:

[0021]

[0022] in, denote the angular position and angular velocity of the connecting rod, respectively. Represent the angular position and angular velocity of the rotor respectively, and the positive definite diagonal matrix K∈R m×m ,J∈R m×m ,B∈R m×m They correspond to joint flexibility, actuator inertia and natural damping terms respectively, τ is the input delay, and the control input is u τ =u(t-τ)∈R m , t is the current time.

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

[0024]

[0025] in, denote the angular position and angular velocity of the connecting rod, respectively. They represent the angular position and angular velocity of the rotor respectively, and the control input is u 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, Λ(x1)=M -1 (x1)K, where the matrices M(x1), C(x1, x2), G(x2), F(x2), K, B, and J are all known parameters during modeling.

[0026] As a further implementation, a specified performance function with a predetermined time is shown in the following formula:

[0027]

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

[0029] As a further implementation method, the influence of input delay is eliminated through auxiliary system and coordinate transformation, and a compensated tracking error signal is obtained; as shown in the following formula:

[0030]

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

[0032] As a further implementation method, the performance indicator function is shown in the following formula:

[0033]

[0034] Among them, β1>0 represents the discount factor, α1, denote the controller and the transpose of the controller respectively.

[0035] A second aspect of the present invention provides a system for implementing the above method, comprising:

[0036] The model building module is configured to: model the motion state of the flexible joint robot and introduce input delay into the built model;

[0037] 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;

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

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

[0040] The error compensation module is configured to: eliminate the influence of input delay through the auxiliary system and coordinate transformation, and obtain a compensated tracking error signal;

[0041] The parameter solving module is configured to: define a performance indicator function including an error indicator and a control input indicator, design a virtual controller with the goal of minimizing the performance indicator function, and use a neural network to obtain the unknown parameters in the virtual controller; during this period, by constructing a prediction error model, designing the update law for executing the neural network and evaluating the weights of the neural network, and identifying the update law of the network, the unknown nonlinear function in the virtual controller is approximated.

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

[0043] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps in the control method of a flexible joint robot under input delay as described above.

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

[0045] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the control method of a flexible joint robot under input delay as described above are implemented.

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

[0047] 1. Taking into account the optimal control of the flexible joint robot, input delay, predetermined time specified performance control and other issues, an input delay compensation system was constructed. The compensation signal was introduced through coordinate transformation and the control signal was designed in combination with dynamic surface control and adaptive backstepping method to eliminate the negative impact of input delay on the system; the designed predetermined time specified performance function can ensure that the tracking error converges to the specified range within the preset time; by constructing a prediction error model, an identification neural network update law was designed to better approximate unknown nonlinear functions.

[0048] 2. An auxiliary system is designed to generate compensation signals, and these signals are introduced through coordinate transformation, which effectively eliminates the adverse effects of input delay on the system. Compared with other methods of processing delay, the method of designing an auxiliary system considers the output performance of the system more and makes the research on flexible joint robot system more valuable for practical application.

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

[0050] 4. An improved reinforcement learning strategy for identification-execution-evaluation neural network is proposed. This strategy simplifies the entire design process by adopting 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 includes the prediction error and the compensation tracking error, which can more effectively approximate the unknown function. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

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

[0053] Figure 2 is a reference signal x provided by one or more embodiments of the present invention d And the response curve of 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 invention;

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

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

[0057] Figure 6 is a bounded graph of weights of an execution neural network provided by one or more embodiments of the present invention;

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

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

[0060] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0061] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0062] The following embodiments provide a control method and system for a flexible joint robot under input delay, and propose a specified performance control method under input delay based on Lyapunov stability analysis. The method first constructs an input delay compensation system, introduces compensation signals through coordinate transformation, and combines dynamic surface control and adaptive backstepping to design control signals 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 a specified range within a preset time; in addition, by constructing a prediction error model, an identification neural network update law is designed to better approximate unknown nonlinear functions; finally, the Lyapunov stability theorem is used to prove that all signals of the closed-loop system are globally consistent and ultimately bounded, and the consistent tracking error converges to a compact set near the origin. The simple implementation of the formula is illustrated in the attached figure, but it does not represent a specific implementation, nor is it limited to this implementation.

[0063] Embodiment 1:

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

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

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

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

[0068] Step 4: construct an error conversion function to transform the tracking error constraint problem into a bounded problem;

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

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

[0071] This embodiment uses Figure 1 Take the flexible joint robot shown as an example, in which the driver (motor) drives the rotor to rotate, one end of the connecting rod (link) is connected and driven by the rotor to rotate, and the other end is suspended in the air, with the rotation point as the O point of the coordinate system XY, and the connecting rod and the rotor are connected by an elastic element (such as a spring or a harmonic reducer) to form a flexible joint.

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

[0073]

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

[0075] set up The matrix M(q) represents the inertia matrix, and Represents the Coriolis force and the centripetal force. The gravity vector is represented by G(q)∈R m , the friction term is expressed as Positive definite diagonal matrix K∈R m×m , J∈R m×m , B∈R m×m They correspond to 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 input delay is considered. The state equation of the system after conversion is:

[0077]

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

[0079] As a further implementation manner, in step 3, the designed predetermined time specified performance function is:

[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 moment. 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 traditional prescribed performance control method can ensure the ultimate 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 a rapidly changing environment in a timely manner, thus affecting the overall performance. However, 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 manner, in step 4, construct an error transformation function to transform the tracking error constraint problem into a boundedness problem. The constructed error transformation 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 connecting rod, x d represents the given objective function.

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

[0089] Take the time derivative of to obtain:

[0090] ​

[0091] In the above formula,

[0092] As a further implementation, step 5: constructing the coordinate transformation by utilizing the auxiliary system and the dynamic surface control technology, thereby avoiding the influence of input delay and solving the "complexity explosion" problem in the backstepping method.

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

[0094]

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

[0096] The tracking error signal after coordinate transformation and compensation is constructed as:

[0097]

[0098] In the above formula, 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, a virtual controller is designed and the unknown parameters of the system are estimated online by a neural network:

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

[0101]

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

[0103] Designing a virtual controller

[0104]

[0105] In the above formula, h1 is a positive design parameter. For the matrix The inverse matrix of For a given objective function x d The derivative of Use a neural network to approximate the unknown vector function P1, expressed as: is the ideal weight vector of the neural network is the transpose of , ε1 is the approximate error vector, and S1(N1) is the basis function vector.

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

[0107]

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

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

[0110]

[0111] In the above formula, η c1 is a normal number and satisfies

[0112] Since the matrix is positive semidefinite, and its eigenvalue is zero. Falling The training may terminate if the value of the zero eigenvector of is reached. To avoid this possibility, a correction term μI is introduced to ensure that the matrix is strictly positive definite, thus ensuring sufficient training. By adopting a simplified positive function to design the update law for the execution-evaluation neural network, the entire design process is simplified.

[0113] Step 6.2: The control method of this embodiment is designed based on the backstepping method. The traditional backstepping method needs to be implemented in the virtual controller. Repeated differentiation will lead to the problem of "differential 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 to generate a new state variable m i , which is used to replace the first virtual controller for subsequent calculations. The advantage of this processing method is that it reduces the number of independent variables and 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 get 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 the 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 unknown nonlinear systems, 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 third virtual controller as:

[0131]

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

[0133] The update law for executing the neural network and evaluating the neural network weights is designed as follows:

[0134]

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

[0136] Step 6.4, design the fourth controller as:

[0137]

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

[0139] Introducing prediction error Prediction Status The update is expressed as:

[0140]

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

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

[0143]

[0144] In the above formula, F2, γ Z2 , ω2 is a positive design parameter.

[0145] The update law for executing the neural network and evaluating the neural network weights is 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 in order to verify the effectiveness of the method, it can be assumed that τ = 0.01sin(t) + 0.01. According to the actual system, the relevant parameters are: the total mass of the connecting rod is n = 1kg, and the total moment of inertia of the connecting rod is J = 1kg·m 2 , the acceleration due to gravity is g = 10 m / s 2 , the distance from the joint axis to the center of mass is l = 1m, and the friction force is The joint flexibility is K=1, and the natural damping term is B=1.

[0150] The initial conditions of the simulation are: the 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 values ​​of the execution neural network and the evaluation neural network are chosen as:

[0152]

[0153] The simulation results are as follows Figures 2 to 8 shown. Figure 2 Shows the reference signal x d And the response curve of the system output signal x1. Figure 3It can be seen that compared with the adaptive feedback control method, the method proposed by us 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. Figure 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. Figure 6-7 The boundedness of the weights of the actor neural network and the critic neural network are demonstrated respectively. Figure 8 The control input trajectory of the flexible joint robot system is shown. Therefore, the numerical simulation proves the effectiveness of the proposed control method.

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

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

[0156] (2) A predetermined time specified performance technology is proposed. Different from the traditional specified performance control method, the proposed method not only ensures that the error remains within the predefined range, but also specifies its convergence time, which can significantly enhance the flexibility and accuracy 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. This strategy simplifies the entire design process by adopting 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 includes the prediction error and the compensation tracking error, which can more effectively approximate the unknown function.

[0158] Embodiment 2:

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

[0160] The model building module is configured to: model the motion state of the flexible joint robot and introduce input delay into the built 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 into the converted state equation;

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

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

[0165] The parameter solving module is configured to: define a performance indicator function including an error indicator and a control input indicator, design a virtual controller with the goal of minimizing the performance indicator function, and use a neural network to obtain the unknown parameters in the virtual controller; during this period, by constructing a prediction error model, designing the update law for executing the neural network and evaluating the weights of the neural network, and identifying the update law of the network, the unknown nonlinear function in the virtual controller is approximated.

[0166] Embodiment three:

[0167] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps in the control method of a flexible joint robot under input delay in the above-mentioned embodiment 1 are implemented.

[0168] Embodiment 4:

[0169] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the control method of a flexible joint robot under input delay in the above-mentioned embodiment 1 are implemented.

[0170] The steps or modules involved in the above embodiments 2 to 4 correspond to those in embodiment 1. For the specific implementation, please refer to the relevant description of embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0171] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A control method for a flexible joint robot under input delay, characterized in that: The following steps are involved: Modeling is performed based on the motion state of the flexible joint robot, and input delay is introduced into the constructed model; According to the physical characteristics of the flexible joint robot, the constructed model is converted into a state equation; In the converted state equation, 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 transformed into a bounded problem by using the error conversion function and the specified performance function. Through auxiliary systems and coordinate transformation, the influence of input delay is eliminated and the compensated tracking error signal is obtained; A performance indicator function including error indicator and control input indicator is defined, a virtual controller is designed with the goal of minimizing the performance indicator function, and a neural network is used to obtain the unknown parameters in the virtual controller. During this period, the unknown nonlinear function in the virtual controller is approximated by constructing a prediction error model, designing the update law for executing the neural network and evaluating the neural network weights, and identifying the update law of the network.

2. The control method of a flexible joint robot under input delay as claimed in claim 1, characterized in that: The model is built according to the motion state of the flexible joint robot, as shown in the following formula: in, denote the angular position and angular velocity of the connecting rod, respectively. They represent the angular position and angular velocity of the rotor respectively, M(q) represents the inertia matrix, represents the Coriolis force and the centripetal force, G(q)∈R m represents the gravity vector, represents the friction term.

3. The control method of a flexible joint robot under input delay as claimed in claim 1, characterized in that: Input delay is introduced into the constructed model as shown in the following equation: in, denote the angular position and angular velocity of the connecting rod, respectively. Represent the angular position and angular velocity of the rotor respectively, and the positive definite diagonal matrix K∈R m×m ,J∈R m×m ,B∈R m×m They correspond to joint flexibility, actuator inertia and natural damping terms respectively, τ is the input delay, and the control input is u τ =u(t-τ)∈R m , t is the current time.

4. The control method of a flexible joint robot under input delay as claimed in claim 1, characterized in that: According to the physical characteristics of the flexible joint robot, the constructed model is converted into a state equation; as shown in the following formula: Where x1 = q, x3=q m , denote the angular position and angular velocity of the connecting rod, respectively. They represent the angular position and angular velocity of the rotor respectively, and the control input is u 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, Λ(x1)=M -1 (x1)K, where the matrices M(x1), C(x1,x2), G(x2), F(x2), K, B, and J are all known parameters during modeling.

5. The control method of a flexible joint robot under input delay as claimed in claim 1, characterized in that: A specified performance function with a predetermined time is shown below: In the above formula, m and represents a positive design parameter and satisfies T represents the preset time, and t represents the current time.

6. The control method of a flexible joint robot under input delay as claimed in claim 1, characterized in that: Through the auxiliary system and coordinate transformation, the influence of input delay is eliminated and the compensated tracking error signal is obtained; as shown in the following formula: In the above formula, p i >0(i=1,2,3,4) is a positive constant, Δu=u τ -u, u τ is the control input, v i (i=1,2,3,4) is the compensated tracking error signal, m i (i=1,2,3,4) is the filter output.

7. The control method of a flexible joint robot under input delay as claimed in claim 1, characterized in that: The performance indicator function is shown in the following formula: Among them, β1>0 represents the discount factor.

8. A control system for a flexible joint robot with input delay, characterized in that: include: The model building module is configured to: model the motion state of the flexible joint robot and introduce input delay into the built model; 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; The specified performance function module is configured to: introduce a specified performance function with a predetermined time into the converted state equation; The error conversion module is configured to: construct an error conversion function, and convert the tracking error constraint problem during the control of the flexible joint robot into a boundedness problem using the error conversion function and the specified performance function; The error compensation module is configured to: eliminate the influence of input delay through the auxiliary system and coordinate transformation, and obtain a compensated tracking error signal; The parameter solving module is configured to: define a performance indicator function including an error indicator and a control input indicator, design a virtual controller with the goal of minimizing the performance indicator function, and use a neural network to obtain the unknown parameters in the virtual controller; during this period, by constructing a prediction error model, designing the update law for executing the neural network and evaluating the weights of the neural network, and identifying the update law of the network, the unknown nonlinear function in the virtual controller is approximated.

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

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in the method for controlling a flexible joint robot under input delay as claimed in any one of claims 1 to 7 are implemented.

Images