Mechanical arm residual vibration control method, device and equipment based on non-singular fast terminal sliding mode, medium and product

Abstract

The invention discloses a mechanical arm residual vibration control method and device based on a non-singular fast terminal sliding mode, equipment, a medium and a product, and relates to the field of industrial robot motion control. A non-singular sliding mode surface and a control law are constructed by taking a position error and a speed error between displacement of residual vibration at the tail end of the flexible part of the mechanical arm and a preset track as input, a non-singular fast terminal sliding mode controller is determined based on the non-singular sliding mode surface and the control law, the residual vibration acceleration at the tail end of the flexible part is collected, and the position error and the speed error of the residual vibration are determined; inputting the position error and the speed error into the optimized non-singular fast terminal sliding mode controller to obtain a residual vibration control law; solving joint driving angles of the first arm and the second arm of the mechanical arm according to the residual vibration control law and the mechanical arm kinematic model, and controlling the mechanical arm to move based on the joint driving angles. The residual vibration of the mechanical arm can be effectively restrained, and the control precision is improved.

Description

Technical Field

[0001] This application relates to the field of industrial robot motion control, and in particular to a method, device, equipment, medium and product for controlling residual vibration of a robotic arm based on non-singular fast end-of-line sliding mode. Background Technology

[0002] High-speed, high-load robotic arms perform tasks such as rapid sorting or assembly of targets through planar motion. They are widely used in food packaging, automotive parts assembly, electronics, and metal processing. The robotic arm has a simple overall structure, high rigidity in the vertical direction, smooth horizontal movement, coordinated joint movement, and overall compliant motion. It also features high-speed movement and high repeatability. However, in actual production environments, due to environmental uncertainties and the influence of the robotic arm's flexible components, vibrations are inevitable after high-speed operation, which will inevitably affect the accuracy of control and positioning. Summary of the Invention

[0003] The purpose of this application is to provide a method, device, equipment, medium, and product for controlling residual vibration of a robotic arm based on non-singular fast terminal sliding mode, which can effectively suppress residual vibration of the robotic arm and improve control accuracy.

[0004] To achieve the above objectives, this application provides the following solution:

[0005] In a first aspect, this application provides a method for controlling residual vibration of a robotic arm based on non-singular fast terminal sliding mode, including:

[0006] Construct a kinematic model of the robotic arm;

[0007] A non-singular sliding surface is constructed using the position and velocity errors between the displacement of the residual vibration at the end of the flexible component of the robotic arm and the preset trajectory as inputs, and a control law is designed with the aim of achieving the desired stability of the non-singular sliding surface.

[0008] A non-singular fast terminal sliding mode controller is determined based on the non-singular sliding surface and control law, and the parameters of the non-singular fast terminal sliding mode controller are optimized using a particle swarm optimization algorithm.

[0009] Collect residual vibration acceleration at the end of the flexible component;

[0010] The position and velocity errors of the residual vibration are determined based on the residual vibration acceleration and the preset trajectory.

[0011] The position and velocity errors of the residual vibration are input into the optimized non-singular fast terminal sliding mode controller to obtain the residual vibration control law;

[0012] The joint drive angles of the first and second arms of the robotic arm are solved based on the residual vibration control law and the kinematic model of the robotic arm, and the movement of the robotic arm is controlled based on the joint drive angles.

[0013] Secondly, this application provides a residual vibration control device for a robotic arm based on non-singular fast terminal sliding mode, comprising:

[0014] The first building module is used to build the kinematic model of the robotic arm;

[0015] The second construction module is used to construct a non-singular sliding surface with the position error and velocity error between the displacement of the residual vibration at the end of the flexible component of the robotic arm and the preset trajectory as input, and to design a control law with the aim of achieving the desired stability of the non-singular sliding surface.

[0016] The parameter optimization module is used to determine the non-singular fast terminal sliding mode controller based on the non-singular sliding surface and the control law, and to optimize the parameters of the non-singular fast terminal sliding mode controller using the particle swarm optimization algorithm.

[0017] The acquisition module is used to acquire the residual vibration acceleration at the end of the flexible component;

[0018] An error determination module is used to determine the position error and velocity error of the residual vibration based on the residual vibration acceleration and the preset trajectory.

[0019] The control law output module is used to input the position error and velocity error of the residual vibration into the optimized non-singular fast terminal sliding mode controller to obtain the residual vibration control law.

[0020] The residual vibration control module is used to solve the joint drive angles of the first and second arms of the robotic arm according to the residual vibration control law and the kinematic model of the robotic arm, and to control the movement of the robotic arm based on the joint drive angles.

[0021] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the robotic arm residual vibration control method based on non-singular fast terminal sliding mode as described above.

[0022] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the robotic arm residual vibration control method based on non-singular fast terminal sliding mode as described above.

[0023] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the robotic arm residual vibration control method based on non-singular fast terminal sliding mode as described above.

[0024] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0025] This application provides a method, device, equipment, medium, and product for controlling residual vibration of a robotic arm based on non-singular fast terminal sliding mode. The method suppresses residual vibration of the robotic arm by designing a non-singular fast terminal sliding mode controller. The controller includes a non-singular sliding surface and a control law designed to achieve the desired stability of the non-singular sliding surface. The non-singular sliding surface design and control law ensure strong convergence in the residual vibration control process, enabling rapid suppression of residual vibration. Furthermore, a particle swarm optimization algorithm is used to optimize the parameters of the non-singular fast terminal sliding mode controller, maximizing the control effect of residual vibration of the robotic arm and thus improving control accuracy. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is an application environment diagram of a robotic arm residual vibration control method based on non-singular fast terminal sliding mode in one embodiment of this application;

[0028] Figure 2 A flowchart illustrating a method for controlling residual vibration of a robotic arm based on non-singular fast terminal sliding mode, provided in an embodiment of this application;

[0029] Figure 3 A schematic diagram of the horizontal projection of a three-dimensional model of a robotic arm provided in an embodiment of this application;

[0030] Figure 4 A simplified schematic diagram of the first and second arms in a robotic arm provided in an embodiment of this application;

[0031] Figure 5 This is a schematic diagram showing the changes of various parameters at the end of the second arm over time when the robotic arm performs planar motion along a circular trajectory according to an embodiment of this application; wherein, (a) is the jerk curve, (b) is the acceleration curve, (c) is the velocity curve, and (d) is the displacement curve.

[0032] Figure 6 A schematic diagram of a closed-loop feedback control loop for residual vibration of a robotic arm provided in an embodiment of this application;

[0033] Figure 7 A functional module schematic diagram of a robotic arm residual vibration control device for a non-singular rapid terminal sliding mode provided in another embodiment of this application;

[0034] Figure 8 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0035] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0036] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] The residual vibration control method for robotic arms based on non-singular fast terminal sliding mode provided in this application can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up independently, integrated into server 104, or placed in the cloud or on another server. Terminal 102 can send the residual vibration acceleration of the flexible component's end to server 104. Server 104 receives the residual vibration acceleration and determines the position and velocity errors of the residual vibration based on the residual vibration acceleration and the preset trajectory. The position and velocity errors of the residual vibration are input to an optimized non-singular fast terminal sliding mode controller to obtain the residual vibration control law. Based on the residual vibration control law and the manipulator's kinematic model, the joint drive angles of the first and second arms of the manipulator are solved, and the manipulator's movement is controlled based on these joint drive angles. Server 104 can feed back the obtained drive angles to terminal 102. In addition, in some embodiments, the residual vibration control method of the robotic arm based on non-singular fast terminal sliding mode can also be implemented by the server 104 or the terminal 102 alone. For example, the terminal 102 can directly perform residual vibration control processing on the residual vibration acceleration of the end of the flexible component to be processed, or the server 104 can obtain the residual vibration acceleration of the end of the flexible component from the data storage system and then perform residual vibration control processing.

[0038] The terminal 102 can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle devices. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 104 can be implemented using a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.

[0039] In one exemplary embodiment, such as Figure 2 As shown, a method for controlling residual vibration of a robotic arm based on non-singular fast terminal sliding mode is provided. This method is executed by a computer device, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the explanation includes the following steps 201 to 207. Wherein:

[0040] Step 201: Construct the kinematic model of the robotic arm. The kinematic model of the robotic arm includes the forward kinematic model and the inverse kinematic model.

[0041] The robotic arm includes a first arm, a second arm, and a flexible component. The flexible component is fixed to the end of the second arm. The other end of the second arm is movably connected to one end of the first arm, and the other end of the first arm is fixed to a base. Figure 3 and Figure 4 As shown, Figure 3 The horizontal projection of the 3D model of the robotic arm. Figure 4 for Figure 3 A simplified diagram of the connection relationships between the various arms of the robotic arm is shown. A global fixed coordinate system {O:X,Y} is established with the center point O of the base as the origin. A moving coordinate system {O1:X1,Y1} for the first arm is established with the center point O1 of the rotary joint connecting the first arm to the base as the origin. The first joint is the rotary joint connecting the first arm to the base. A moving coordinate system {O2:X2,Y2} for the second arm is established with the center point O2 of the rotary joint connecting the second arm to the first arm as the origin. The second joint is the rotary joint connecting the second arm to the first arm. The pose transformation matrix of the end effector of the second arm can be obtained using the improved DH rule. Assuming the coordinates of the end effector of the second arm relative to the global fixed coordinate system are (x,y), the forward kinematics model of the robotic arm is obtained, and its expression is:

[0042]

[0043] The pose transformation matrix of the end effector of the robotic arm's second arm is:

[0044]

[0045] When the trajectory coordinates (x, y) of the second arm end effector of the robotic arm and the joint drive angle have a solution set, the inverse kinematics model of the robotic arm can be obtained by using geometric methods and the four-quadrant arctangent function. The expression of the inverse kinematics model of the robotic arm is as follows:

[0046]

[0047] k1=L1+L2 cosθ2(4);

[0048] k2=L2 sinθ2(5);

[0049]

[0050] Where L1 is the length of the first arm, L2 is the length of the second arm, θ1 and θ2 are the joint drive angles of the first and second arms respectively, and d1 and d2 are the offsets of the first and second joints respectively.

[0051] Step 202: Construct a non-singular sliding surface using the position error and velocity error between the displacement of the residual vibration at the end of the flexible component of the robotic arm and the preset trajectory as input, and design a control law with the aim of achieving the desired stability of the non-singular sliding surface.

[0052] In one exemplary embodiment, the robotic arm performs planar motion along a circular preset trajectory. This example illustrates the design process of the non-singular sliding surface and control law. Preset trajectories of other shapes are also possible, but this embodiment does not limit the specific trajectories.

[0053] A preset trajectory is generated using a double S-shaped smooth velocity planning algorithm, such as... Figure 5 As shown, the curves of the parameters at the end of the second arm changing with time when the robotic arm moves in a planar motion along a circular trajectory are displayed. Figure 5 (a) in the figure is the jerk curve. Figure 5 (b) in the figure is the acceleration curve. Figure 5 (c) in the figure represents the velocity curve. Figure 5 In the figure, (d) represents the displacement curve. The traditional S-shaped curve is modified to create a double S-shaped velocity curve, and the motion is divided into 7 stages. Constraints are set based on the motion parameters, and the time for each stage is determined by relevant factors. Furthermore, parameters need to be adjusted during real-time planning to address situations such as insufficient displacement. In the experiment, the robotic arm moves along a set circular trajectory. After trajectory discretization, the trajectory position of the second arm's end is obtained, and time synchronization is achieved using a control card contour mode.

[0054] Let t be any time interval during the movement of the robotic arm. [t0, t1] represents the acceleration ramp-up phase, [t1, t2] represents the constant acceleration phase, [t2, t3] represents the acceleration ramp-down phase, [t3, t4] represents the uniform motion phase, [t4, t5] represents the negative acceleration ramp-up phase, [t5, t6] represents the constant negative acceleration phase, and [t6, t7] represents the negative acceleration ramp-down phase. The duration of each phase is T. i i = 1, 2, ..., 7; the displacement value at the end of each motion stage is S. i ,i=1,2,…,7.

[0055] The mathematical model for acceleration in double S-shaped smooth velocity programming is as follows:

[0056]

[0057] The trajectory position of the end of the second arm is:

[0058]

[0059] Where j(t) is the jerk at time t, J max The maximum jerk is T, and the total motion time is T.

[0060] The residual vibration model of the flexible end of the robotic arm is approximated as an ideal second-order standard underdamped system. Its corresponding differential equation is obtained through the inverse Laplace transform. The input variables of the residual vibration model are the position and acceleration of the flexible end, i.e., let x1 = y(t). The state-space equations are further simplified to obtain the state-space equations. Taking the position and velocity errors between the displacement of the residual vibration at the end of the flexible component and the preset trajectory as inputs, a non-singular sliding surface is constructed through Lyapunov stability. The time derivative of the non-singular sliding surface is then calculated.

[0061] An ideal second-order standard underdamped system is:

[0062]

[0063] Where, ω n Let y(x) be the natural frequency, ξ be the damping ratio, x be the input, and y(x) be the output.

[0064] The corresponding differential equation is:

[0065]

[0066] The state-space equations are:

[0067]

[0068] in, and These are the first and second derivatives of y(t), respectively.

[0069] The expression for the non-singular sliding surface is:

[0070] S=e2+C1e1 α +C2e1 β (15);

[0071] The expression for the control law is:

[0072]

[0073] Where S is a non-singular sliding surface, e2 is the velocity error, e1 is the position error, u is the control law, and y d The target position in the preset trajectory, y d The first and second derivatives, C1, C2, α, β, k and γ are the parameters of the non-singular fast terminal sliding mode controller, u1 and h(t) are variables in the calculation process, and t is time.

[0074] In the actual calculation process, the position error and velocity error between the displacement of the residual vibration at the end of the flexible component and the preset trajectory are calculated using the absolute values ​​of the position error and velocity error.

[0075] Step 203: Determine a non-singular fast terminal sliding mode controller based on the non-singular sliding surface and control law, and optimize the parameters of the non-singular fast terminal sliding mode controller using a particle swarm optimization algorithm.

[0076] In an exemplary embodiment, before optimizing the parameters of the NFTSMC (Non-singular Fast Terminal Sliding Mode Controller), it is necessary to train an Extreme Learning Machine (ELM) surrogate model with the parameters of the NFTSMC as input and the amplitude of the residual vibration as output, thereby establishing an input-output relationship.

[0077]

[0078] Where f is the output value of the ELM proxy model, N is the number of hidden layer nodes, and ω i Let b be the random weights for the input layer and the i-th hidden layer node. i For the bias of the i-th hidden layer node, β i Let g be the weights of the i-th hidden layer node and the output layer, and g() be the activation function.

[0079] like Figure 6 As shown, 130 sets of data consisting of NFTSMC parameters and corresponding residual vibration amplitudes were obtained from the database. During the training of the ELM surrogate model, 116 sets of data were randomly selected as the training set, and the remaining 14 sets were used as the test set.

[0080] The parameters of the non-singular fast terminal sliding mode controller are optimized using the particle swarm optimization algorithm, specifically including:

[0081] A particle swarm optimization algorithm is employed, aiming to minimize the amplitude of residual vibrations, to optimize the parameters of the non-singular fast terminal sliding mode controller (NTS-SMA). The optimized STS-SMA parameters are obtained by searching within the feasible region of the STS-SMA. A trained ELM surrogate model is used to predict the amplitude of the residual vibrations for each particle during the optimization process. The combination of the STS-SMA parameters C1, C2, α, β, k, and γ is used as the particle. The input to the ELM surrogate model is the STS-SMA parameters, and the output is the amplitude of the residual vibrations. The optimization process includes:

[0082] 1) Within a feasible region of D dimensions, let the particle population size be N, and represent the i-th particle using a D-dimensional vector:

[0083] X i =(x i1 x i2 , ...x iD ), i = 1, 2...N(19);

[0084] 2) The particle's velocity:

[0085] V i =(v i1 , v i2 ,...v iD ), i = 1, 2...N(20);

[0086] 3) The optimal position that the particle can find is called the individual extreme value:

[0087] P best =(p i1 , p i2 ...p iD )(twenty one);

[0088] 4) The optimal position found by the entire particle swarm is called the global extremum:

[0089] G best =(g i1 g i2 ...g iD )(twenty two);

[0090] Once these two optimal values ​​are found, the particle updates its velocity and position using equations (23) and (24):

[0091]

[0092] x i (t+1)=x i (t)+v i (t+1)(24);

[0093] Among them, v i (t+1) and v i (t) represents the velocities of the i-th particle at time t+1 and time t, respectively. ij (t) represents the historical best position of the i-th particle, g i (t) represents the global optimal position of the i-th particle, x i (t+1) and x i (t) represents the position of the i-th particle at time t+1 and time t, respectively, r1 and r2 are uniform random numbers in [0,1], j = 1,2,...,D, and c1 and c2 are learning factors.

[0094] Step 204: Collect the residual vibration acceleration at the end of the flexible component.

[0095] like Figure 6 As shown, a closed-loop feedback control loop for residual vibration of a robotic arm is designed, with a non-singular fast end-of-arm sliding mode controller as the main controller. An accelerometer A is installed at the end of the flexible component. Accelerometer A is used to collect the residual vibration acceleration f(t) at the end of the flexible component after the robotic arm has moved along a preset trajectory. Step 205: Based on the residual vibration acceleration and the preset trajectory, the position error and velocity error of the residual vibration are determined. Specifically, this includes steps 301-304:

[0096] Step 301: Filter the residual vibration acceleration f(t) to obtain the filtered residual vibration acceleration f. a (t).

[0097] Step 302: Analyze the filtered residual vibration acceleration using Fast Fourier Transform (FFT) to obtain the frequency ξ of the residual vibration.

[0098] Specifically, the frequency and amplitude of the residual vibration can be obtained by analyzing the filtered residual vibration acceleration using the Fast Fourier Transform.

[0099] Step 303: Determine the vibration displacement at the end of the flexible component based on the frequency and amplitude curve of the residual vibration.

[0100] Step 304: Determine the position error and velocity error based on the vibration displacement and the preset trajectory.

[0101] Before step 205, an open-loop control for the robotic arm to move along a preset trajectory needs to be designed, obtained from the residual vibration amplitude curve of the robotic arm, specifically including steps 401-402:

[0102] Step 401: After the robotic arm executes the preset trajectory, the end of the flexible component of the robotic arm vibrates. The vibration acceleration data of the end of the flexible component during the vibration process is collected until the vibration disappears.

[0103] Step 402: Solve for the residual vibration amplitude curve based on the vibration acceleration data.

[0104] Specifically, the residual vibration frequency is obtained by using a fast Fourier transform based on the vibration acceleration data, and the residual vibration amplitude curve is further obtained by nonlinear fitting.

[0105] The expression for the residual vibration amplitude curve is:

[0106] f(t+Δt)=a*e bξt sin(cξ(t+Δt))(23);

[0107] Where a, b, and c are constants, ξ is the residual vibration frequency, f(t+Δt) is the residual vibration amplitude, t is the time, and Δt is the delay time.

[0108] Step 206: Input the position error and velocity error of the residual vibration into the optimized non-singular fast terminal sliding mode controller to obtain the residual vibration control law.

[0109] Step 207: Solve the joint drive angles of the first and second arms of the robotic arm according to the residual vibration control law and the kinematic model of the robotic arm, and control the movement of the robotic arm based on the joint drive angles.

[0110] Implementing steps 201 to 207 effectively suppresses the residual vibration of the robotic arm. This process utilizes a non-singular sliding surface design to provide good robustness, rapidly bringing the residual vibration model to the desired state within a finite time, exhibiting strong convergence. When large errors exist, it possesses strong fast convergence capability, quickly returning to the non-singular sliding surface; while for smaller errors, it accelerates towards zero, demonstrating strong convergence ability. Furthermore, by optimizing the parameters of the non-singular fast terminal sliding mode controller using a particle swarm optimization algorithm, the residual vibration control effect of the robotic arm can be maximized.

[0111] Based on the same inventive concept, this application also provides a device for implementing the above-mentioned residual vibration control of a robotic arm based on non-singular fast end-sliding mode. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the residual vibration control method for a robotic arm based on non-singular fast end-sliding mode provided below can be found in the above-described limitations of the residual vibration control device for a robotic arm based on non-singular fast end-sliding mode, and will not be repeated here.

[0112] In one exemplary embodiment, such as Figure 7 As shown, a residual vibration control device for a robotic arm based on non-singular fast terminal sliding mode is provided, comprising:

[0113] The first building module 71 is used to build the kinematic model of the robotic arm.

[0114] The second construction module 72 is used to construct a non-singular sliding surface with the position error and velocity error between the displacement of the residual vibration at the end of the flexible component of the robotic arm and the preset trajectory as input, and to design a control law with the aim of achieving the desired stability of the non-singular sliding surface.

[0115] The parameter optimization module 73 is used to determine the non-singular fast terminal sliding mode controller based on the non-singular sliding surface and the control law, and to optimize the parameters of the non-singular fast terminal sliding mode controller using the particle swarm optimization algorithm.

[0116] The acquisition module 74 is used to acquire the residual vibration acceleration at the end of the flexible component.

[0117] The error determination module 75 is used to determine the position error and velocity error of the residual vibration based on the residual vibration acceleration and the preset trajectory.

[0118] The control law output module 76 is used to input the position error and velocity error of the residual vibration to the optimized non-singular fast terminal sliding mode controller to obtain the residual vibration control law.

[0119] The residual vibration control module 77 is used to solve the joint drive angles of the first and second arms of the robotic arm according to the residual vibration control law and the kinematic model of the robotic arm, and to control the movement of the robotic arm based on the joint drive angles.

[0120] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 8As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores the residual vibration acceleration at the end of the flexible component. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a residual vibration control method for a robotic arm based on non-singular fast end-effector sliding mode.

[0121] Those skilled in the art will understand that Figure 8 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0122] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0123] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0124] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0125] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0126] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0127] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0128] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0129] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for controlling residual vibration of a robotic arm based on non-singular fast end-effector sliding mode, the robotic arm comprising a first arm, a second arm, and a flexible component, characterized in that, include: Construct a kinematic model of the robotic arm; A non-singular sliding surface is constructed using the position and velocity errors between the displacement of the residual vibration at the end of the flexible component of the robotic arm and the preset trajectory as inputs, and a control law is designed with the aim of achieving the desired stability of the non-singular sliding surface. A non-singular fast terminal sliding mode controller is determined based on the non-singular sliding surface and control law, and the parameters of the non-singular fast terminal sliding mode controller are optimized using a particle swarm optimization algorithm. Collect residual vibration acceleration at the end of the flexible component; The position and velocity errors of the residual vibration are determined based on the residual vibration acceleration and the preset trajectory. The position and velocity errors of the residual vibration are input into the optimized non-singular fast terminal sliding mode controller to obtain the residual vibration control law; The joint drive angles of the first and second arms of the robotic arm are solved based on the residual vibration control law and the kinematic model of the robotic arm, and the movement of the robotic arm is controlled based on the joint drive angles.

2. The method for controlling residual vibration of a robotic arm based on non-singular fast terminal sliding mode according to claim 1, characterized in that, The robotic arm kinematic model includes: a forward kinematic model of the robotic arm and a reverse kinematic model of the robotic arm; The expression for the forward kinematics model of the robotic arm is: The expression for the inverse kinematics model of the robotic arm is: Where (x, y) are the coordinates of the end of the second arm, L1 is the length of the first arm, L2 is the length of the second arm, θ1 and θ2 are the joint driving angles of the first and second arms, respectively; k1 = L1 + L2cosθ2, k2 = L2sinθ2.

3. The method for controlling residual vibration of a robotic arm based on non-singular fast terminal sliding mode according to claim 1, characterized in that, The robotic arm performs planar motion along a preset circular trajectory. The expression for the non-singular sliding surface is: S=e2+C1e1 α +C2e1 β ; The expression for the control law is: Where S is a non-singular sliding surface, e2 is the velocity error, e1 is the position error, u is the control law, and ω n Let y be the natural frequency, ξ be the damping ratio, and y be the frequency. d The target position in the preset trajectory, y d The first and second derivatives, C1, C2, α, β, k and γ are the parameters of the non-singular fast terminal sliding mode controller, u1 and h(t) are variables in the calculation process, and t is time.

4. The method for controlling residual vibration of a robotic arm based on non-singular fast terminal sliding mode according to claim 3, characterized in that, Before determining the position and velocity errors of the residual vibration based on the residual vibration acceleration and the preset trajectory, the method further includes: After the robotic arm executes the preset trajectory, the end of the flexible component of the robotic arm vibrates. The vibration acceleration data of the end of the flexible component is collected during the vibration until the vibration disappears. The residual vibration amplitude curve is calculated based on the vibration acceleration data.

5. The method for controlling residual vibration of a robotic arm based on non-singular fast terminal sliding mode according to claim 4, characterized in that, The position and velocity errors of the residual vibration are determined based on the residual vibration acceleration and the preset trajectory, specifically including: The residual vibration acceleration is filtered to obtain the filtered residual vibration acceleration; The filtered residual vibration acceleration was analyzed using Fast Fourier Transform to obtain the frequency of the residual vibration. The vibration displacement at the end of the flexible component is determined based on the frequency and amplitude curve of the residual vibration. The position error and velocity error are determined based on the vibration displacement and the preset trajectory.

6. The method for controlling residual vibration of a robotic arm based on non-singular fast terminal sliding mode according to claim 1, characterized in that, The parameters of the non-singular fast terminal sliding mode controller are optimized using the particle swarm optimization algorithm, specifically including: A particle swarm optimization algorithm is employed to minimize the amplitude of residual vibrations within the feasible region of the parameters of the non-singular fast terminal sliding mode controller (NTS-SMA). The optimized parameters of the NTS-SMA are obtained. A trained extreme learning machine (ELM) surrogate model is used to predict the amplitude of the residual vibrations of each particle during the optimization process. The combination of the NTS-SMA parameters C1, C2, α, β, k, and γ is used as the particle. The input to the ELM surrogate model is the parameters of the NTS-SMA, and the output is the amplitude of the residual vibrations.

7. A residual vibration control device for a robotic arm based on non-singular fast terminal sliding mode, characterized in that, include: The first building module is used to build the kinematic model of the robotic arm; The second construction module is used to construct a non-singular sliding surface with the position error and velocity error between the displacement of the residual vibration at the end of the flexible component of the robotic arm and the preset trajectory as input, and to design a control law with the aim of achieving the desired stability of the non-singular sliding surface. The parameter optimization module is used to determine the non-singular fast terminal sliding mode controller based on the non-singular sliding surface and the control law, and to optimize the parameters of the non-singular fast terminal sliding mode controller using the particle swarm optimization algorithm. The acquisition module is used to acquire the residual vibration acceleration at the end of the flexible component; An error determination module is used to determine the position error and velocity error of the residual vibration based on the residual vibration acceleration and the preset trajectory. The control law output module is used to input the position error and velocity error of the residual vibration into the optimized non-singular fast terminal sliding mode controller to obtain the residual vibration control law. The residual vibration control module is used to solve the joint drive angles of the first and second arms of the robotic arm according to the residual vibration control law and the kinematic model of the robotic arm, and to control the movement of the robotic arm based on the joint drive angles.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the residual vibration control method for a robotic arm based on non-singular fast terminal sliding mode as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the residual vibration control method for a robotic arm based on non-singular fast terminal sliding mode as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the residual vibration control method for a robotic arm based on non-singular fast terminal sliding mode as described in any one of claims 1-6.

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