A six-axis industrial robot pose-dependent stiffness identification method, device and medium

Abstract

The application discloses a six-axis industrial robot posture-related stiffness identification method, equipment and medium, and belongs to the technical field of industrial robot vibration suppression. The method comprises the following steps: S1, a flexible joint dynamics model of a six-axis industrial robot is established; S2, an analytical function relationship between a robot posture and a target joint stiffness is established; S3, a set of robot postures that minimize the dynamic coupling effect between the target joint and non-target joints is determined; S4, under the robot postures determined in step S3, a multi-frequency sinusoidal signal excitation is applied to the target joint, and motor speed and torque data in the excitation process are collected by using a motor servo driver; S5, a cascade identification strategy is used to identify model parameters corresponding to different postures; and S6, after the stiffness parameters in different postures identified in step S5, unknown coefficient fitting is performed on the posture-stiffness analytical function established in step S2, so that analytical calculation of the target joint posture-related stiffness is realized.

Description

Technical Field

[0001] This invention relates to the field of industrial robot vibration suppression technology, and in particular to a method for identifying the configuration-related stiffness of a six-axis industrial robot. Background Technology

[0002] When industrial robots perform tasks such as heavy-load handling or high-precision welding, their inherent mechanical flexibility (including joint transmission flexibility and link elasticity) can induce significant residual vibrations under high-speed motion excitation, severely affecting positioning accuracy and settling time. Although feedforward control based on dynamic models is the mainstream solution for suppressing vibration, balancing model accuracy and computational efficiency remains a significant challenge. Traditional simplified flexible joint models often treat stiffness as constant, ignoring the nonlinear characteristics of equivalent stiffness changing with robot configuration, resulting in insufficient fidelity across the entire workspace. While high-dimensional extended models can improve accuracy, their enormous computational burden makes them difficult to deploy in real-time in standard industrial controllers. Furthermore, common flexibility identification methods heavily rely on external precision measuring instruments or joint-end sensors, resulting in high hardware costs and limited applicability. In methods that only utilize motor-end data for identification, the identification process is easily trapped in local optima due to limitations of nonlinear optimization algorithms, making it difficult to obtain physically consistent parameter solutions.

[0003] Therefore, how to construct a computationally efficient and accurate lightweight flexible joint dynamic model that can characterize pose-related properties, and how to achieve model parameter identification that relies solely on motor feedback, is a pressing challenge to improve the dynamic performance of industrial robots.

[0004] In view of this, the present invention is hereby proposed. Summary of the Invention

[0005] The purpose of this invention is to provide a method, device, and medium for identifying the configuration-related stiffness of a six-axis industrial robot. Based on a lightweight flexible joint dynamics model, it describes the nonlinear mapping relationship between robot configuration and stiffness through analytical functions. By combining a decoupling identification strategy and a cascaded identification process, it achieves robust identification of model parameters using only feedback data from the motor end, thereby solving the aforementioned technical problems in the prior art.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A method for identifying the configuration-related stiffness of a six-axis industrial robot includes:

[0008] Step S1: Use a dual inertia model to describe the dynamic characteristics of the identified flexible joint of the six-axis industrial robot and establish a lightweight flexible joint dynamic model.

[0009] Step S2: Select the main flexible joint as the target joint for identification in the flexible joint dynamic model in step S1, and establish the configuration-stiffness analytical function between the robot configuration and the stiffness of the target joint.

[0010] Step S3: Establish a set of robot configurations that decouples the dynamics between joints through robot configuration optimization. Under this set of configurations, decouple the target subsystem containing only the target joint from the flexible joint dynamics model in step S1.

[0011] Step S4: Under the robot configuration in the configuration set in step S3, apply multi-frequency sinusoidal signal excitation to the target joint, and use the motor servo driver of the target joint to collect the speed and torque data of the motor during the excitation process.

[0012] Step S5: Based on the speed and torque data of the motor collected in step S4, the target subsystem obtained in step S3 is parameter identified using a cascaded identification strategy to obtain the estimated value of the frequency response function and the initial value of the model parameters, and finally the refined identification parameters.

[0013] Step S6: Extract joint stiffness values ​​under different configurations from the refined identification parameters in step S5, fit the unknown coefficients of the configuration-stiffness analytical function established in step S2, and complete the analytical calculation of the stiffness related to the target joint configuration.

[0014] A processing apparatus, comprising:

[0015] At least one memory for storing one or more programs;

[0016] At least one processor is capable of executing one or more programs stored in the memory, such that when the processor executes one or more programs, the processor can implement the method of the present invention.

[0017] A readable storage medium storing a computer program that, when executed by a processor, enables the implementation of the methods described in this invention.

[0018] Compared with existing technologies, the six-axis industrial robot configuration-related stiffness identification method, equipment, and medium provided by this invention have the following advantages:

[0019] By establishing a pose-related stiffness model in the form of a configuration-stiffness analytical function between the robot's configuration and the target joint stiffness, the dynamic characteristics changes within the entire workspace can be accurately captured. The cascaded identification process combining vector fitting and nonlinear programming effectively solves the problem of the identification process easily getting trapped in local optima. Parameter identification can be completed using only the encoder data from the robot's own motor end, resulting in low implementation costs. The proposed lightweight dynamic model has low computational cost and can be directly deployed on standard industrial controllers to achieve robot vibration suppression. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 The overall flowchart of the six-axis industrial robot configuration-related stiffness identification method provided in the embodiments of the present invention is shown.

[0022] Figure 2 A flowchart illustrating the parameter identification steps of the configuration-related stiffness identification method for a six-axis industrial robot provided in this embodiment of the invention.

[0023] Figure 3 A schematic diagram of the overall kinematic structure of a six-axis industrial robot provided in an embodiment of the present invention.

[0024] Figure 4 This is a schematic diagram of a dual-inertia model of a flexible joint of a six-axis industrial robot provided in an embodiment of the present invention.

[0025] Figure 5 This is a schematic diagram illustrating the influence of the link elasticity on the stiffness of the first joint of a six-axis industrial robot provided in an embodiment of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them, and do not constitute a limitation on the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0027] First, the following explanations are provided for the terms that may be used in this article:

[0028] The term "and / or" means that either or both can be achieved simultaneously. For example, X and / or Y means that it includes both "X" or "Y" as well as the three cases of "X and Y".

[0029] The terms "comprising," "including," "containing," "having," or other similar semantic descriptions should be interpreted as non-exclusive inclusion. For example, including a technical feature element (such as raw material, component, ingredient, carrier, dosage form, material, size, part, component, mechanism, device, step, process, method, reaction conditions, processing conditions, parameter, algorithm, signal, data, product or article of manufacture, etc.) should be interpreted as including not only the expressly listed technical feature element, but also other technical feature elements that are not expressly listed and are well-known in the art.

[0030] The term "composed of" excludes any technical features not expressly listed. When used in a claim, it closes the claim to exclude all technical features other than those expressly listed, except for associated conventional impurities. If the term appears only in a clause of a claim, it limits the claim to the elements expressly listed in that clause; elements recited in other clauses are not excluded from the overall claim.

[0031] Unless otherwise explicitly specified or limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this document according to the specific circumstances.

[0032] The terms “center,” “longitudinal,” “lateral,” “length,” “width,” “thickness,” “up,” “down,” “front,” “back,” “left,” “right,” “vertical,” “horizontal,” “top,” “bottom,” “inner,” “outer,” “clockwise,” and “counterclockwise” indicate the current orientation or positional relationship, and are only for the convenience and simplification of description, and do not explicitly or implicitly suggest that the device or component referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this document.

[0033] The technical solution provided by this invention will be described in detail below. Contents not described in detail in the embodiments of this invention are prior art known to those skilled in the art. Where specific conditions are not specified in the embodiments of this invention, they shall be performed according to conventional conditions in the art or conditions recommended by the manufacturer. Reagents or instruments used in the embodiments of this invention whose manufacturers are not specified are all conventional products that can be purchased commercially.

[0034] like Figure 1 As shown, this invention provides a method for identifying the configuration-related stiffness of a six-axis industrial robot, including:

[0035] Step S1: Use a dual inertia model to describe the dynamic characteristics of the identified flexible joint of the six-axis industrial robot and establish a lightweight flexible joint dynamic model.

[0036] Step S2: Select the main flexible joint as the target joint for identification in the flexible joint dynamic model in step S1, and establish the configuration-stiffness analytical function between the robot configuration and the stiffness of the target joint.

[0037] Step S3: Establish a set of robot configurations that decouples the dynamics between joints through robot configuration optimization. Under this set of configurations, decouple the target subsystem containing only the target joint from the flexible joint dynamics model in step S1.

[0038] Step S4: Under the robot configuration in the configuration set in step S3, apply multi-frequency sinusoidal signal excitation to the target joint, and use the motor servo driver of the target joint to collect the speed and torque data of the motor during the excitation process.

[0039] Step S5: Based on the speed and torque data of the motor collected in step S4, the target subsystem obtained in step S3 is parameter identified using a cascaded identification strategy to obtain the estimated value of the frequency response function and the initial value of the model parameters, and finally the refined identification parameters.

[0040] Step S6: Extract joint stiffness values ​​under different configurations from the refined identification parameters in step S5, fit the unknown coefficients of the configuration-stiffness analytical function established in step S2, and complete the analytical calculation of the stiffness related to the target joint configuration.

[0041] Preferably, in the above method, the six-axis industrial robot includes seven rigid links connected sequentially from the base end to the end end. The seven rigid links, from the base end to the end end, are, in order, base 11, rotating seat 12, upper arm 13, motor base 14, forearm 15, wrist 16, and end flange 17. Each pair of rigid links is connected by a rotating joint, and the six rotating joints are arranged in series, from the base end to the end end, as follows: first joint 18, second joint 19, third joint 20, fourth joint 21, fifth joint 22, and sixth joint 23. Among them, the first joint, second joint, and third joint are used to adjust the position of the end of the six-axis industrial robot. The proximal joints are positioned in a three-dimensional workspace; the fourth, fifth, and sixth joints form a spherical wrist structure for adjusting the working posture of the six-axis industrial robot end effector; each rotary joint is equipped with a servo drive unit, and each servo drive unit includes: a servo driver, a servo motor, a motor-end encoder, and a reducer; wherein, the servo motor drives the corresponding joint to rotate through the reducer; the motor-end encoder is used to collect the angular displacement signal of the servo motor in real time and feed it back to the servo driver, so that the servo driver can calculate the torque command in combination with the position command sent by the user and output the current to drive the servo motor.

[0042] Preferably, in step S1 of the above method, the dynamic characteristics of the identified six-axis industrial robot flexible joint are described based on a dual-inertia model, and a lightweight dynamic model of the flexible joint robot is established, including:

[0043] A spring-damped dual-inertia model is established to describe the dynamic characteristics of each flexible joint of the identified six-axis industrial robot. The dual-inertia model is as follows:

[0044] (1);

[0045] In equation (1), The load inertia at joint i of the six-axis industrial robot; , These are the joint rotation angle at joint i of the six-axis industrial robot and the motor rotation angle calculated to the load side after reduction ratio; , These are the joint angular velocity and joint angular acceleration at joint i of the six-axis industrial robot, respectively. , These are the motor angular velocity and motor angular acceleration at joint i of the six-axis industrial robot, calculated to the load side after reduction ratio; , These are the stiffness and damping values ​​at joint i of the six-axis industrial robot, respectively. , These are the motor rotor inertia and motor torque at joint i of the six-axis industrial robot, calculated to the load side after reduction ratio;

[0046] Based on the established dual-inertia model, the multi-degree-of-freedom dynamic model of the six-axis industrial robot is derived as follows:

[0047] (2);

[0048] In equation (2), , , These are the inertia matrix, Coriolis and centripetal matrix of the six joints of the six-axis industrial robot, and gravity, respectively. , These refer to the robot configuration and motor rotation angles of the six joints of the six-axis industrial robot, respectively. , These are the robot configuration velocity and robot configuration acceleration of the six-axis industrial robot, respectively. , These are the motor angular velocities and motor angular accelerations of the six joints of the six-axis industrial robot, respectively. , These are the configuration-related stiffness diagonal matrix and damping diagonal matrix of the six joints of the six-axis industrial robot, respectively. , These are the diagonal matrix of motor rotor inertia and motor torque for the six joints of the six-axis industrial robot, respectively.

[0049] When the robot is in a quasi-static state, the motor torque of the six-axis industrial robot With motor speed The relationship between them can be described by a linear time-invariant system. In the Laplace domain, this relationship is written as:

[0050] (3);

[0051] In equation (3), Let be the frequency response function matrix of the linear time-invariant system; For the Laplace transform operator;

[0052] Based on equation (2), the equation is linearized under quasi-static conditions, and the expression for the frequency response function matrix of the linear time-invariant system is derived as follows:

[0053] (4);

[0054] In equation (4), The identity matrix; the diagonal matrix of the rotor inertia of the motors at the six joints of a six-axis industrial robot. Configuration-related damping diagonal matrix of the six joints of a six-axis industrial robot Configuration-related stiffness diagonal matrix of the six joints of a six-axis industrial robot Inertia matrix of the six joints of a six-axis industrial robot All are parameter matrices to be identified;

[0055] The obtained multi-degree-of-freedom dynamic model and the expression of the frequency response function matrix of the linear time-invariant system are used as the basis for establishing a lightweight flexible joint dynamic model.

[0056] Preferably, in step S2 of the above method, the main flexible joints are selected as the target joints for identification in the following manner, and a configuration-stiffness analytical function between the robot configuration and the stiffness of the target joints is established, including:

[0057] The first, second, and third joints of the six-axis industrial robot are selected as the main flexible joints and used as the target joints for identification.

[0058] Based on a function that can establish the equivalent joint stiffness caused by the elasticity of the links at the joint as the robot configuration, a configuration-stiffness analytical function in linear form is established between the robot configuration and the stiffness of the first joint. for:

[0059] (5);

[0060] In equation (5), This refers to the robot configuration of the six-axis industrial robot. , All are dimensionless coefficients to be identified; This is the distance from the end of the forearm link of a six-axis industrial robot to the axis of rotation of the first joint;

[0061] The configuration-stiffness analytical function in the form of the linear function The first joint stiffness of the six-axis industrial robot is calculated by establishing a mapping relationship between the square of the distance from the end of the link to the first joint axis and the stiffness of the first joint.

[0062] Based on the function that can establish the equivalent joint stiffness caused by the elasticity of the link at the joint as the robot configuration, configuration-stiffness analytical functions in the form of a square hyperbolic tangent function are established between the robot configuration and the stiffness of the second and third joints. , for:

[0063] (6);

[0064] (7);

[0065] In equations (6) and (7), This refers to the robot configuration of the six-axis industrial robot. , , , , , All are dimensionless coefficients to be identified; It is the square hyperbolic tangent function; for; These are the second and third elements of the robot's gravity.

[0066] Configuration-stiffness analytical function in the form of the square hyperbolic tangent function , The mapping relationship between the static gravitational torque of the joints and the stiffness of the second and third joints is established to calculate the stiffness of the second and third joints of the six-axis industrial robot.

[0067] Preferably, in step S3 of the above method, the coupling terms between target joints and non-target joints in the robot inertia matrix are minimized through robot configuration optimization in the following manner, thereby establishing a set of robot configurations that decouple the dynamics between joints:

[0068] Step S31, to minimize the inertia matrix The sum of the absolute values ​​of the off-diagonal elements in the first row is used to eliminate the dynamic coupling between the first joint and other joints. The first optimization objective is as follows:

[0069] (8);

[0070] in, This indicates taking the minimum value; This represents the inertia coupling term between the i-th joint and the first joint;

[0071] To adjust the reflected load inertia of the first joint To the preset reference inertia value By adjusting the reference inertia value in each optimization To ensure that the identification results cover different load conditions, the following second optimization objective is established:

[0072] (9);

[0073] Step S32: Use a multi-objective genetic algorithm to iteratively solve the first optimization objective and the second optimization objective simultaneously to obtain the Pareto optimal solution set;

[0074] Step S33: Select robot configurations that satisfy preset decoupling conditions from the obtained optimal solution set to form a set of robot configurations that decouple the dynamics between joints. The preset decoupling condition is: the reflected load inertia of the first joint. The magnitude is at least two orders of magnitude greater than the sum of the corresponding off-diagonal elements;

[0075] The following methods are used to decouple a low-dimensional subsystem containing only the target joint from the high-dimensional dynamic system within the robot configuration set:

[0076] On the selected set of robot configurations that decouple the joint dynamics

[0077] On the selected set of optimized configurations, the frequency response function matrix is ​​defined according to equation (4). satisfy , , Let represent the frequency response function from the torque of the motor at the i-th joint to the speed of the motor at the first joint; thus, the single-input, single-output target subsystem containing only the first joint can be decoupled from equation (3):

[0078] (10);

[0079] in, The motor speed of the first joint; The frequency response function of the motor torque to the motor speed at the first joint; The motor torque for the first joint;

[0080] For the second and third joints, through the above configuration optimization process, equation (3) is decoupled into a dual-input dual-output target subsystem containing only the second and third joints:

[0081] (11);

[0082] in, The motor speed of the second joint; The frequency response function of the motor torque to motor speed at the second joint; The frequency response function from the torque of the third joint motor to the speed of the second joint motor; The motor torque for the second joint; The motor speed of the third joint; The frequency response function from the torque of the second joint motor to the speed of the third joint motor; The frequency response function of the motor torque to motor speed at the third joint; The motor torque for the third joint;

[0083] The two target subsystems defined by equations (10) and (11) are the target subsystems to be identified.

[0084] Preferably, in step S4 of the above method, under the robot configuration in the configuration set of step S3, a multi-frequency sinusoidal signal excitation is applied to the target joint, and the speed and torque data of the motor during the excitation process are collected using the motor servo driver of the target joint, including:

[0085] Step S41: For the target subsystem defined by equation (10) or equation (11) obtained in step S3, generate independent random phase multi-sine trajectories as excitation trajectories;

[0086] The incentive trajectory for:

[0087] (12);

[0088] In equation (12), For multiple sinusoidal trajectory amplitudes; It is the set of frequency points that are logarithmically distributed along the frequency axis; For the number of frequency points, Frequency point number; () represents the sine function; for time; It is a random phase; The number of joints within the target subsystem;

[0089] Step S42: After obtaining the excitation trajectory, drive the six-axis industrial robot and maintain it at each identified configuration in the configuration set obtained in step S3, and perform the following data acquisition actions: In the closed-loop position control state, send the multi-sine trajectory defined by equation (12) as a reference signal to the servo drive unit of each joint of the target subsystem; synchronously read the motor torque of each target joint from the servo driver at a preset sampling frequency. With motor speed Using a pre-identified friction model, calculate the Coulomb-viscosity friction torque at the current motor speed. Subtracting the Coulomb-viscous friction torque from the total torque signal yields the net motor torque used for flexibility identification. .

[0090] Preferably, in step S5 of the above method, based on the motor speed and torque data collected in step S4, the physical parameters of the target subsystem obtained in step S3 are identified using a cascaded identification strategy to obtain initial parameter values, and the initial parameter values ​​are refined using a nonlinear programming algorithm to obtain refined identification parameters, including:

[0091] Step S51: Based on the motor torque and speed signals collected during the excitation cycle in step S4, calculate the frequency response function from motor torque to motor speed using the local rational method.

[0092] Step S52: Use vector fitting to fit the frequency response function with a rational function, and extract the initial values ​​of the model parameters based on the zeros and poles of the fitted rational function.

[0093] Step S53: Starting from the initial values ​​of the obtained model parameters, the logarithmic error between the measurement function and the model function is minimized by a nonlinear programming algorithm to obtain refined identification parameters.

[0094] Preferably, in step S6 of the above method, the unknown coefficients of the configuration-stiffness analytical function established in step S2 are fitted using the stiffness obtained in step S5 under different configurations, thereby completing the analytical calculation of the stiffness related to the target joint configuration, including:

[0095] The discrete stiffness values ​​obtained under different configurations are used as sample points. The unknown coefficients in the configuration-stiffness analytical function of step S2 are fitted using a linear regression algorithm. Based on the fitted unknown coefficients, a configuration-stiffness mapping model covering the entire workspace of the six-axis industrial robot is constructed. The six-axis industrial robot is then compensated and controlled according to the configuration-stiffness mapping model.

[0096] This invention also provides a processing apparatus, comprising:

[0097] At least one memory for storing one or more programs;

[0098] At least one processor is capable of executing one or more programs stored in the memory, such that when the processor executes one or more programs, the processor can implement the methods described above.

[0099] The present invention further provides a readable storage medium storing a computer program that, when executed by a processor, can implement the above-described method.

[0100] To more clearly demonstrate the technical solution and its effects provided by the present invention, the following detailed description of the solution provided by the embodiments of the present invention is provided with reference to specific examples.

[0101] like Figure 1 As shown, this invention provides a method for identifying the configuration-related stiffness of a six-axis industrial robot. Based on a simplified flexible joint model, it describes the nonlinear mapping relationship between robot configuration and stiffness through analytical functions. Combining a decoupling identification strategy and a cascaded identification process, it achieves robust identification of model parameters using only feedback data from the motor end. The method includes:

[0102] Step S1: Describe the dynamic characteristics of the flexible joint of the six-axis industrial robot based on the dual inertia model, and establish a lightweight flexible joint robot dynamic model.

[0103] Step S2: Select joints with significant flexibility as identification targets and establish an analytical function relationship between robot configuration and target joint stiffness;

[0104] Step S3: Determine a set of robot configurations that minimize the dynamic coupling effect between the target joint and non-target joints through robot configuration optimization. Under this set of configurations, decouple a low-dimensional system containing only the target joint from the high-dimensional dynamic system.

[0105] Step S4: Under the robot configuration determined in step S3, apply multi-frequency sinusoidal signal excitation to the target joint, and use the motor servo driver to collect motor speed and torque data during the excitation process;

[0106] Step S5: Use the cascaded identification strategy to identify the model parameters corresponding to different configurations. First, calculate the frequency response function of motor torque to speed using the local rational method. Then, use the vector fitting method to extract a set of initial values ​​of model parameters from the frequency response function. Finally, use the nonlinear programming algorithm to complete the refined identification of parameters.

[0107] Step S6: Using the stiffness parameters identified in step S5 under different configurations, fit the unknown coefficients of the configuration-stiffness analytical function established in step S2 to achieve analytical calculation of the stiffness related to the target joint configuration.

[0108] like Figure 3 As shown, preferably, in the above method, the six-axis industrial robot being identified comprises seven rigid links, which, from the base end to the end end, are: base 11, rotary seat 12, upper arm 13, motor base 14, forearm 15, wrist 16, and end flange 17; each pair of links is connected by a rotary joint, and the six rotary joints are arranged in series, from the base end to the end end, as follows: first joint, second joint, third joint, fourth joint, fifth joint, and sixth joint; wherein,

[0109] The first, second, and third joints are proximal master joints, mainly used to adjust the position of the robot's end effector in the three-dimensional workspace; the fourth, fifth, and sixth joints form a spherical wrist structure, mainly used to adjust the robot's end effector's working posture; each of the aforementioned rotating joints is equipped with a servo drive unit, which includes a servo driver, a servo motor, a motor-end encoder, and a reducer; the servo motor drives the corresponding joint to rotate through the reducer; the motor-end encoder is used to collect the angular displacement signal at the motor end in real time and feed it back to the servo driver, so that the servo driver can calculate the torque command in combination with the position command sent by the user and output the drive current.

[0110] Preferably, in step S1 of the above method, the flexible joint dynamic model of the six-axis industrial robot is established in the following manner, including:

[0111] A spring-damped dual-inertia model is established to describe each joint of the six-axis industrial robot. The dual-inertia system model includes the motor rotor inertia, joint side inertia, joint stiffness, and joint damping parameters. Based on the established dual-inertia system model, the multi-degree-of-freedom dynamic equations and frequency response functions of the six-axis industrial robot are derived.

[0112] Preferably, in step S2 of the above method, the proximal joint of the six-axis industrial robot is considered as the main flexible joint; a configuration-related target joint stiffness function is established, wherein the configuration-related factors considered include:

[0113] Firstly, considering the nonlinear stiffness characteristics of the reducer in the servo drive unit, its torsional stiffness changes nonlinearly with the torque applied at the joint, and the torsional stiffness tends to be constant when the torque is large; based on this, the quadratic hyperbolic tangent function is used to establish the mapping relationship between the static gravitational torque of the joint and the joint stiffness. This function is used to calculate the stiffness of the second and third joints of the six-axis industrial robot.

[0114] Secondly, considering the equivalent joint stiffness generated by the flexibility of the link under different configurations, especially for the upper arm link and lower arm link of the six-axis industrial robot, the torsional stiffness of the link flexibility equivalent to the joint side is linearly related to the square of the distance from the link end to the joint axis. Based on this, a linear function is used to establish the mapping relationship between the square of the distance from the link end to the joint axis and the joint stiffness. This function is used to calculate the first joint stiffness of the six-axis industrial robot.

[0115] Preferably, in step S3 of the above method, in order to decouple the high-dimensional dynamic system into a target subsystem containing only the target joints, the coupling terms between the target joints and non-target joints in the robot inertia matrix are minimized through robot configuration optimization, thereby establishing a set of robot configurations that decouple the dynamics between joints.

[0116] Preferably, in step S4 of the above method, under the decoupled configuration, a multi-frequency sinusoidal speed reference signal with random phase is sent to the servo driver of the target joint, and the motor speed and motor torque signals during the excitation cycle are acquired in real time by the servo driver.

[0117] like Figure 2 As shown, preferably, in step S5 of the above method, a cascade strategy is used to identify parameters of the established flexible joint dynamic model, including:

[0118] Step S51: Based on the motor torque and speed signals collected during the excitation cycle, calculate the frequency response function from motor torque to motor speed using the local rational method;

[0119] Step S52: Use the vector fitting method to fit the calculated frequency response function to a rational function, and extract the initial values ​​of the model parameters based on the zeros and poles of the fitted rational function;

[0120] Step S53: Starting from the obtained initial value, minimize the logarithmic error between the measurement function and the model function using a nonlinear programming algorithm to complete the refined parameter identification.

[0121] Preferably, in step S6 of the above method, the discrete stiffness values ​​identified under different configurations are used as sample points, and the unknown coefficients in the analytical function described in step S2 are fitted using a linear regression algorithm to construct a configuration-stiffness mapping model covering the entire workspace of the robot.

[0122] To more clearly demonstrate the technical solution and its effects provided by the present invention, the following detailed description of the motor and joint angle conversion correction and kinematic calibration method for the rope robot provided by the present invention is given with reference to specific embodiments.

[0123] Example 1

[0124] This embodiment provides a method for identifying the configuration-related stiffness of a six-axis industrial robot, applicable to: Figure 3 The six-axis industrial robot shown here can only acquire signals limited to the motor rotation angle and angular velocity measured by the motor encoder, and the motor torque value recorded by the servo driver. This embodiment is based on... Figure 1 The steps shown are as follows:

[0125] Step S1: Use a dual inertia model to describe the dynamic characteristics of the identified flexible joint of the six-axis industrial robot and establish a dynamic model of the flexible joint.

[0126] like Figure 4 As shown, a dual-inertia system model is established to describe the dynamic characteristics of each flexible joint as follows:

[0127] (1);

[0128] In equation (1), Let i be the load inertia at joint i of the six-axis industrial robot; , These are the joint rotation angle at joint i of the six-axis industrial robot and the motor rotation angle (calculated to the load side after reduction ratio); , These are the stiffness and damping values ​​at joint i of a six-axis industrial robot, respectively. , These are the motor rotor inertia and motor torque at joint i of the six-axis industrial robot (referred to the load side after reduction ratio);

[0129] Considering the dynamic coupling effect between the joints of the serial multi-degree-of-freedom robotic arm and the effect of gravity, the multi-degree-of-freedom dynamic model of the six-axis industrial robot is established based on equation (1):

[0130] (2);

[0131] In equation (2), , , These represent the inertia matrix, Coriolis force, centripetal matrix, and gravity of the six joints of a six-axis industrial robot. , These refer to the robot configuration and motor rotation angles of the six joints of the six-axis industrial robot. , These are the configuration-related stiffness diagonal matrix and damping diagonal matrix of the six joints of the six-axis industrial robot, respectively. , These are the diagonal matrix of motor rotor inertia and motor torque for the six joints of the six-axis industrial robot, respectively.

[0132] When the robot is in a quasi-static state, the motor torque and motor speed of the six-axis industrial robot are... The relationship can be described by a linear time-invariant system, which, in the Laplace domain, is written as:

[0133] (3);

[0134] In equation (3), Let be the frequency response function matrix of the linear time-invariant system. For the Laplace transform operator;

[0135] Based on equation (2), the equation is linearized under quasi-static conditions, and the complete expression of the system frequency response function matrix is ​​derived as follows:

[0136] (4);

[0137] In equation (4), It is the identity matrix. , , , All are parameter matrices to be identified;

[0138] The obtained multi-degree-of-freedom dynamic model and the expression of the frequency response function matrix of the linear time-invariant system are used as the dynamic model of the established flexible joint.

[0139] Step S2: Select the main flexible joints as the target joints for identification, and establish the configuration-stiffness analytical function between the robot configuration and the stiffness of the target joints.

[0140] Considering that the flexibility of the first, second, and third joints in the six-axis industrial robot has a significant impact on the robot's motion performance, these three joints are set as target joints to be identified, and the stiffness of the target joints is modeled as a joint stiffness function related to the robot's configuration. The configuration-related factors considered are summarized as follows:

[0141] Firstly, considering the nonlinear stiffness of the reducer in the servo drive unit, the torsional stiffness of the reducer at joint i is... Modeled as transmission torque The nonlinear function, specifically, uses the square hyperbolic tangent function to simulate the zero rate of stiffness change when the transmission torque is zero, and the characteristic that the stiffness tends to saturate when the transmission torque is large, and establishes the configuration-stiffness function as follows:

[0142] (13);

[0143] In equation (13), , These are the minimum and maximum values ​​of the torsional stiffness variation range of the reducer at joint i, respectively. The coefficients are dimensionless. Due to limitations in the available signals, it is difficult to obtain the real-time changing torque of the reducer in this embodiment. Therefore, the gravitational torque at joint i is used instead. In the substitution (13) ,conduct Approximate estimate:

[0144] (14);

[0145] Depend on Figure 3 As can be seen from the robot's kinematic structure shown, Since it is a configuration-independent constant, therefore It is a constant. , These are variables related to the robot's configuration.

[0146] Secondly, the equivalent joint stiffness generated by the elasticity of the link under different configurations is considered. In particular, the influence of the elasticity of the upper arm link and the lower arm link of the six-axis industrial robot on the stiffness of the first joint, the second joint, and the third joint is considered. Specifically, the elasticity of the upper arm link along the rotation direction of the second joint is converted to the stiffness of the second joint, the elasticity of the lower arm link along the rotation direction of the third joint is converted to the stiffness of the third joint, and the total elasticity of the upper arm link and the lower arm link along the rotation direction of the first joint is converted to the stiffness of the first joint.

[0147] First, consider the equivalent joint stiffness at the first joint 51 caused by the elasticity of the connecting rod, such as... Figure 5 As shown, the upper arm link 52 and the lower arm link 53 are simplified as flexible beams with uniform density, and the remaining links are simplified as point masses; a constant force is applied at the end of the lower arm link in the tangential direction of the rotational motion of the first joint. And produce a small linear displacement. , along force Linear stiffness in direction It is related to the Young's modulus, section moment, and length of the beam, due to the force Approximately perpendicular to the connecting rod between the upper arm and forearm. It is approximately a constant; therefore, the force With deformation The following relationship exists:

[0148] (15);

[0149] The distance from the end of the forearm link to the axis of rotation of the first joint can be calculated using the robot's forward kinematics. Thus, the linear displacement Transformed into equivalent deformation at the first joint , tangential force Converted to equivalent torque at the first joint Substituting into equation (15), we get:

[0150] (16);

[0151] Similarly, considering the equivalent joint stiffness at the second and third joints caused by the elasticity of the connecting rod, the following can be derived:

[0152] (17);

[0153] (18);

[0154] In equation (17), This is the distance from the end of the boom link to the pivot point of the second joint. This is the distance from the end of the forearm link to the pivot point of the third joint;

[0155] Combining equations (17) and (18), it can be seen that the equivalent joint stiffness caused by the elasticity of the link at joint i is... Establish as robot configuration Functions:

[0156] (19);

[0157] Depend on Figure 3 As can be seen from the robot's kinematic structure shown, , All of these are configuration-independent constants, therefore , All are constants. These are variables related to the robot's configuration.

[0158] Equations (14) and (19) give the two main factors affecting the joint stiffness of a six-axis industrial robot due to the robot's configuration. Based on the above derivation and practical experience, the following function is designed to predict the actual stiffness of the three target joints:

[0159] (5);

[0160] (6);

[0161] (7);

[0162] In equations (5), (6), and (7), For robot configuration; , All are dimensionless coefficients to be identified; for; , , , , , All are dimensionless coefficients to be identified; It is the square hyperbolic tangent function; The second element of the robot's gravity; This is the third element of the robot's gravity.

[0163] Step S3: Minimize the coupling terms between target joints and non-target joints in the robot inertia matrix through robot configuration optimization, and establish a set of robot configurations that decouples the dynamics between joints. Under this set of configurations, decouple the target subsystem containing only the target joints from the high-dimensional dynamic model.

[0164] Considering the strong coupling characteristics of the robot's dynamic equations under normal poses, the system's frequency response function is simultaneously affected by the model parameters of both the target joints and non-target joints, making it difficult to achieve optimal identification results. To avoid the perturbation of identification results by non-target joint parameters, the robot configuration is optimized to minimize the coupling terms between target and non-target joints in the inertia matrix, thereby decoupling the high-dimensional dynamic system into a target subsystem containing only the target joints. Specifically, when the target joints are the first, second, and third joints, further decoupling can be performed within the target joint set, resulting in a single-input single-output subsystem containing only the first joint and a dual-input dual-output subsystem containing only the second and third joints. Taking the decoupling of the first joint as an example, the optimization process includes:

[0165] First, establish the optimization objective, one of which is to minimize the inertia matrix. The sum of the absolute values ​​of the off-diagonal elements in the first row is used to eliminate the dynamic coupling between the first joint and other joints. The first optimization objective is established as follows:

[0166] (8);

[0167] Secondly, it adjusts the reflected load inertia of the first joint. To the preset reference inertia value By adjusting in each optimization The value of is used to ensure that the identification results cover different load conditions. The second optimization objective is established as follows:

[0168] (9);

[0169] Secondly, a multi-objective genetic algorithm (preferably NSGA-II) is used to iteratively solve the two optimization objectives to obtain a Pareto optimal solution set. Finally, configurations that satisfy preset decoupling conditions are selected from the solution set to form an optimized configuration set. In this embodiment, the preset decoupling condition is preferably: the reflection load inertia of the first joint. The magnitude is at least two orders of magnitude greater than the sum of the corresponding off-diagonal elements.

[0170] On the selected set of optimized configurations, the frequency response function matrix is ​​defined according to equation (4). satisfy , Therefore, the single-input single-output target subsystem containing only the first joint can be decoupled from equation (3) as follows:

[0171] (10);

[0172] Similarly, for the second and third joints, through the above configuration optimization process, equation (3) is decoupled into a target subsystem containing only the second and third joints, with two inputs and two outputs, as follows:

[0173] (11);

[0174] Equations (10) and (11) define the two target subsystems to be identified in this embodiment.

[0175] Step S4: For the target subsystem defined by equation (10) or equation (11), generate independent random phase multi-sine trajectories as excitation trajectories:

[0176] (12);

[0177] In equation (12), For the amplitude of multiple sine trajectories, It is the set of frequency points that are logarithmically distributed along the frequency axis. For the number of frequency points, For random phase, The number of joints within the target subsystem.

[0178] After obtaining the excitation trajectory, the six-axis industrial robot is driven and held at each identified configuration obtained in step S3, and the following data acquisition actions are performed: under closed-loop position control, the multi-sine trajectory defined by equation (12) is sent to the servo drive unit of each joint of the target subsystem as a reference signal; from the servo drive, the motor torque of each target joint is synchronously read at a preset sampling frequency (preferably 250Hz and above). With motor speed Using a pre-identified friction model, calculate the Coulomb-viscous friction torque at the current velocity. Subtracting the Coulomb-viscous friction torque from the motor torque yields the net motor torque used for flexibility identification. .

[0179] Step S5: Based on the speed and torque data of the motor collected in step S4, the physical parameters of the target subsystem obtained in step S3 are identified using a cascaded identification strategy to obtain initial parameter values. Then, the initial parameter values ​​are refined using a nonlinear programming algorithm to obtain refined identification parameters.

[0180] This step employs a cascading strategy to analyze the actual physical parameters contained in the target subsystem. , , , The identification process includes the following steps:

[0181] Step S51: Input from the target subsystem collected in step S4 and output The signal is converted to the frequency domain by Fast Fourier Transform to obtain the corresponding frequency domain signal. , ;

[0182] To suppress the interference of measurement noise and friction identification error, the local rational method is used to evaluate the frequency response function of the target subsystem defined by equation (10) or equation (11). Perform estimation; define the window length on the frequency axis. At each discrete frequency point Local window Within, rational function pairs where both numerator and denominator are polynomials are used. To make a prediction, the rational function is defined in the following form:

[0183] (20);

[0184] In equation (20), , For the selected polynomial order, , For a polynomial matrix, the elements in the i-th row and j-th column are uniformly defined as:

[0185] (twenty one);

[0186] For ease of representation, let's denote the coefficients of all unknown polynomials. The unknown parameter vector formed is To obtain an accurate prediction of the frequency response function of the target subsystem Construct the following optimization problem for... Optimize:

[0187] (twenty two);

[0188] Equation (22) defines an unconstrained linear least squares problem. Preferably, the order of the current polynomial is obtained by the least squares method. , The determined optimal parameter set To evaluate the prediction quality of the frequency response function under the current parameter set, the prediction residual is defined as:

[0189] (twenty three);

[0190] Based on the defined prediction residuals, a minimum description length criterion is constructed to automatically select the polynomial order in equation (22). , For optimal selection, the criteria are defined as follows:

[0191] (twenty four);

[0192] Preferably, the order of the denominator is fixed. And search in the candidate set {1, 2, 3} for the molecular order that minimizes the criterion value defined by equation (24). Based on optimal The corresponding optimal parameter set The frequency response function of the target subsystem is calculated using equation (20). An optimal prediction .

[0193] Step S52: Based on the optimal prediction obtained in step S51 Constructing a vector fitting problem in the frequency domain:

[0194] (25);

[0195] In equation (22), This represents the complex conjugate operation. For the residual function, Let the transfer function of the system to be identified be defined by equation (10) or equation (11), where Let be the poles of the function to be found. Represents the set of complex numbers. , , , Several items are left to be requested. Represents the set of real numbers;

[0196] Preferably, the following vector fitting algorithm is used to solve the problem defined in equation (25):

[0197] according to The positions of the resonant peak and anti-resonant peak in the amplitude-frequency response curve are determined by first manually selecting a set of initial poles. Construct a constrained linear least squares problem:

[0198] (26);

[0199] In equation (26), This refers to the number of frequency domain discrete points obtained through the Fast Fourier Transform in step S51. This represents extracting the real part of the input variable.

[0200] Secondly, preferably, a convex optimization solver is used to solve the constrained linear least squares problem defined in equation (26) to obtain the residue term. , , , ;

[0201] Finally, use The convergence of the algorithm is judged, among which The set convergence threshold is used; if the algorithm fails to converge, the residual function will be... The zero point is taken as the initial pole. Then, resolve the constrained linear least squares problem defined by equation (26) until the algorithm converges, and obtain the result. extreme point and the corresponding residue terms , .

[0202] In the Laplace domain, as defined by comparison (25) and the definition of equation (4) We can derive the equations relating the actual physical parameters to the pole and residue parameters:

[0203] (27);

[0204] (28);

[0205] In equation (28), for The denominator polynomial is defined as:

[0206] (29);

[0207] By making the polynomial coefficients on both sides of equation (28) equal, and combining this with equation (27), a set of solutions for actual physical parameters can be obtained. , , , .

[0208] Step S53: Based on the physical parameter solution obtained in step S52, using it as the initial value, minimize it through a nonlinear programming algorithm. and The logarithmic error between them is used to construct the optimization problem as follows:

[0209] (30);

[0210] In equation (28), These are preset residual weights corresponding to different frequencies;

[0211] The objective function is iteratively optimized using a nonlinear programming algorithm. The iteration stops when the objective function converges to a preset accuracy, and the final refined identification parameter results are output. , , , .

[0212] Step S6: Collect the discrete stiffness values ​​of each target joint identified in step S5 at all optimized configurations determined in step S3. , , ;

[0213] For the first joint, the distance from the end of the forearm link to the axis of rotation of the first joint is calculated based on each identified configuration. For the second and third joints, calculate the corresponding static gravitational moments based on each identified configuration. , ;

[0214] Using the configuration-stiffness analytical functions defined by equations (5), (6), and (7), coefficients are fitted using the data described above; for the first joint, the unknown linear coefficients are solved directly using the linear least squares regression algorithm. , For the second and third joints, dimensionless coefficients are set. , The search interval is selected in each iteration, choosing a specific set of intervals. , The dimensionless coefficients are obtained using the linear least squares regression algorithm. , , , Using grid search to find , The one with the smallest fitting residual , value.

[0215] Finally, the dimensionless coefficients obtained in step S6 are... , , , , , and dimensionless coefficient , The data is stored in the storage unit of the robot controller; during the actual operation of the robot, the controller adjusts the data based on the real-time joint configuration. Substituting the configuration-stiffness analytical functions defined in equations (5), (6), and (7), the equivalent stiffness values ​​of each joint are calculated. And feedforward compensation is performed on the joint position command using the following formula:

[0216] (31);

[0217] In equation (31), For the desired joint-side trajectory command, The trajectory commands that need to be executed on the motor side; by... Sending data to each joint servo drive unit allows for the acquisition of ratios. Superior vibration suppression and accuracy enhancement.

[0218] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0219] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. The information disclosed in the background section is intended only to enhance the understanding of the overall background technology of the present invention and should not be construed as an admission or implication in any way that such information constitutes prior art known to those skilled in the art.

Claims

1. A method for identifying the configuration-related stiffness of a six-axis industrial robot, characterized in that, include: Step S1: Use a dual inertia model to describe the dynamic characteristics of the identified flexible joint of the six-axis industrial robot and establish a lightweight flexible joint dynamic model. Step S2: Select the main flexible joint as the target joint for identification in the flexible joint dynamic model in step S1, and establish the configuration-stiffness analytical function between the robot configuration and the stiffness of the target joint. Step S3: Establish a set of robot configurations that decouples the dynamics between joints through robot configuration optimization. Under this set of configurations, decouple the target subsystem containing only the target joint from the flexible joint dynamics model in step S1. Step S4: Under the robot configuration in the configuration set in step S3, apply multi-frequency sinusoidal signal excitation to the target joint, and use the motor servo driver of the target joint to collect the speed and torque data of the motor during the excitation process. Step S5: Based on the speed and torque data of the motor collected in step S4, the target subsystem obtained in step S3 is parameter identified using a cascaded identification strategy to obtain the estimated value of the frequency response function and the initial value of the model parameters, and finally the refined identification parameters are obtained. Step S6: Extract joint stiffness values ​​under different configurations from the refined identification parameters in step S5, fit the unknown coefficients of the configuration-stiffness analytical function established in step S2, and complete the analytical calculation of the stiffness related to the target joint configuration.

2. The method for identifying the configuration-related stiffness of a six-axis industrial robot according to claim 1, characterized in that, In the method, the six-axis industrial robot includes seven rigid links connected sequentially from the base end to the end end. The seven rigid links, from the base end to the end end, are, in order, the base (11), the rotating seat (12), the upper arm (13), the motor base (14), the forearm (15), the wrist (16), and the end flange (17). Each pair of rigid links is connected by a rotating joint. The six rotating joints are arranged in series, from the base end to the end end, as the first joint (18), the second joint (19), the third joint (20), the fourth joint (21), the fifth joint (22), and the sixth joint (23). Among them, the first joint, the second joint, and the third joint are used for adjusting the six-axis industrial robot. The six-axis industrial robot end effector has proximal joints in its three-dimensional workspace; the fourth, fifth, and sixth joints form a spherical wrist structure for adjusting the working posture of the end effector; each rotary joint is equipped with a servo drive unit, which includes a servo driver, a servo motor, a motor-end encoder, and a reducer; the servo motor drives the corresponding joint to rotate through the reducer; the motor-end encoder is used to collect the angular displacement signal of the servo motor in real time and feed it back to the servo driver, so that the servo driver can calculate the torque command in combination with the position command sent by the user and output the current to drive the servo motor.

3. The method for identifying the configuration-related stiffness of a six-axis industrial robot according to claim 2, characterized in that, In step S1, the dynamic characteristics of the identified six-axis industrial robot flexible joint are described based on a dual-inertia model, and a lightweight flexible joint dynamic model is established, including: A spring-damped dual-inertia model is established to describe the dynamic characteristics of each flexible joint of the identified six-axis industrial robot. The dual-inertia model is as follows: （1）； In equation (1), The load inertia at joint i of the six-axis industrial robot; , These are the joint rotation angle at joint i of the six-axis industrial robot and the motor rotation angle calculated to the load side after reduction ratio; , These are the joint angular velocity and joint angular acceleration at joint i of the six-axis industrial robot, respectively. , These are the motor angular velocity and motor angular acceleration at joint i of the six-axis industrial robot, calculated to the load side after reduction ratio; , These are the stiffness and damping values ​​at joint i of the six-axis industrial robot, respectively. , These are the motor rotor inertia and motor torque at joint i of the six-axis industrial robot, calculated to the load side after reduction ratio; Based on the established dual-inertia model, the multi-degree-of-freedom dynamic model of the six-axis industrial robot is derived as follows: （2）； In equation (2), , , These are the inertia matrix, Coriolis and centripetal matrix of the six joints of the six-axis industrial robot, and gravity, respectively. , These refer to the robot configuration and motor rotation angles of the six joints of the six-axis industrial robot, respectively. , These are the robot configuration velocity and robot configuration acceleration of the six-axis industrial robot, respectively. , These are the motor angular velocities and motor angular accelerations of the six joints of the six-axis industrial robot, respectively. , These are the configuration-related stiffness diagonal matrix and damping diagonal matrix of the six joints of the six-axis industrial robot, respectively. , These are the diagonal matrix of motor rotor inertia and motor torque for the six joints of the six-axis industrial robot, respectively. When the robot is in a quasi-static state, the motor torque of the six-axis industrial robot With motor speed The relationship between them can be described by a linear time-invariant system. In the Laplace domain, this relationship is written as: （3）； In equation (3), Let be the frequency response function matrix of the linear time-invariant system; For the Laplace transform operator; Based on equation (2), the equation is linearized under quasi-static conditions, and the expression for the frequency response function matrix of the linear time-invariant system is derived as follows: （4）； In equation (4), The identity matrix; the diagonal matrix of the rotor inertia of the motors at the six joints of a six-axis industrial robot. Configuration-related damping diagonal matrix of the six joints of a six-axis industrial robot Configuration-related stiffness diagonal matrix of the six joints of a six-axis industrial robot Inertia matrix of the six joints of a six-axis industrial robot All are parameter matrices to be identified; The obtained multi-degree-of-freedom dynamic model and the complete expression of the frequency response function matrix of the linear time-invariant system serve as a lightweight flexible joint dynamic model for the flexible joint robot.

4. The method for identifying the configuration-related stiffness of a six-axis industrial robot according to claim 3, characterized in that, In step S2, the main flexible joints are selected as the target joints for identification in the following manner, and a configuration-stiffness analytical function between the robot configuration and the stiffness of the target joints is established, including: The first, second, and third joints of the six-axis industrial robot are selected as the main flexible joints and used as the target joints for identification. Based on a function that can establish the equivalent joint stiffness caused by the elasticity of the links at the joint as the robot configuration, a configuration-stiffness analytical function in linear form is established between the robot configuration and the stiffness of the first joint. for: （5）； In equation (5), This refers to the robot configuration of the six-axis industrial robot. , All are dimensionless coefficients to be identified; This is the distance from the end of the forearm link of a six-axis industrial robot to the first joint axis. The configuration-stiffness analytical function in the form of the linear function The first joint stiffness of the six-axis industrial robot is calculated by establishing a mapping relationship between the square of the distance from the end of the link to the first joint axis and the stiffness of the first joint. Based on the function that can establish the equivalent joint stiffness caused by the elasticity of the link at the joint as the robot configuration, configuration-stiffness analytical functions in the form of a square hyperbolic tangent function are established between the robot configuration and the stiffness of the second and third joints. , for: （6）； （7）； In equations (6) and (7), This refers to the robot configuration of the six-axis industrial robot. , , , , , All are dimensionless coefficients to be identified; It is the square hyperbolic tangent function; , These are the second and third elements of gravity for a six-axis industrial robot, respectively. Configuration-stiffness analytical function in the form of the square hyperbolic tangent function , The mapping relationship between the static gravitational torque of the joints and the stiffness of the second and third joints is established to calculate the stiffness of the second and third joints of the six-axis industrial robot.

5. The method for identifying the configuration-related stiffness of a six-axis industrial robot according to claim 4, characterized in that, In step S3, robot configuration optimization is performed in the following manner to minimize the coupling terms between target joints and non-target joints in the robot inertia matrix, thereby establishing a set of robot configurations that decouple the dynamics between joints: Step S31, to minimize the inertia matrix The sum of the absolute values ​​of the off-diagonal elements in the first row is used to eliminate the dynamic coupling between the first joint and other joints. The first optimization objective is as follows: （8）； in, This indicates taking the minimum value; This represents the inertia coupling term between the i-th joint and the first joint; To adjust the reflected load inertia of the first joint To the preset reference inertia value By adjusting the reference inertia value in each optimization To ensure that the identification results cover different load conditions, the following second optimization objective is established: （9）； Step S32: Use a multi-objective genetic algorithm to iteratively solve the first and second optimization objectives simultaneously to obtain the Pareto optimal solution set; Step S33: Select robot configurations that satisfy preset decoupling conditions from the obtained optimal solution set to form a set of robot configurations that decouple the joint dynamics. The preset decoupling condition is: the reflected load inertia of the first joint. The magnitude is at least two orders of magnitude greater than the sum of the corresponding off-diagonal elements; The following methods are used to decouple a low-dimensional subsystem containing only the target joint from the high-dimensional dynamic system within the robot configuration set: On the selected set of robot configurations that decouple the joint dynamics On the selected set of optimized configurations, the frequency response function matrix is ​​defined according to equation (4). satisfy , , Let represent the frequency response function from the torque of the motor at the i-th joint to the speed of the motor at the first joint; thus, the single-input, single-output target subsystem containing only the first joint can be decoupled from equation (3). for: （10）； in, The motor speed of the first joint; The frequency response function of the motor torque to the motor speed at the first joint; The motor torque for the first joint; For the second and third joints, through the configuration optimization process, equation (3) is decoupled into a target subsystem consisting only of the second and third joints, with two inputs and two outputs: （11）； in, The motor speed of the second joint; The frequency response function of the motor torque to motor speed at the second joint; The frequency response function from the torque of the third joint motor to the speed of the second joint motor; The motor torque for the second joint; The motor speed of the third joint; The frequency response function from the torque of the second joint motor to the speed of the third joint motor; The frequency response function of the motor torque to motor speed at the third joint; The motor torque for the third joint; The two target subsystems defined by equations (10) and (11) are the target subsystems to be identified.

6. The method for identifying the configuration-related stiffness of a six-axis industrial robot according to claim 5, characterized in that, In step S4, under the robot configuration in the configuration set of step S3, a multi-frequency sinusoidal signal excitation is applied to the target joint in the following manner, and the speed and torque data of the motor during the excitation process are collected using the motor servo driver of the target joint, including: Step S41: For the target subsystem defined by equation (10) or equation (11) obtained in step S3, generate independent random phase multi-sine trajectories as excitation trajectories; Step S42: After obtaining the excitation trajectory, drive the six-axis industrial robot and maintain it at each identified configuration in the configuration set obtained in step S3, and perform the following data acquisition actions: In closed-loop position control state, send the defined multi-sine trajectory as a reference signal to the servo drive unit of each joint of the target subsystem; synchronously read the motor torque and motor speed of each target joint from the servo driver at a preset sampling frequency; calculate the Coulomb-viscosity friction torque at the current motor speed using the pre-identified friction model; subtract the Coulomb-viscosity friction torque from the total torque signal to obtain the net motor torque used for flexibility identification.

7. The method for identifying the configuration-related stiffness of a six-axis industrial robot according to claim 5, characterized in that, In step S5, based on the motor speed and torque data collected in step S4, the physical parameters of the target subsystem obtained in step S3 are identified using a cascaded identification strategy to obtain initial parameter values. Then, a nonlinear programming algorithm is used to refine the initial parameter values ​​to obtain refined identification parameters, including: Step S51: Based on the motor torque and speed signals collected during the excitation cycle in step S4, calculate the frequency response function from motor torque to motor speed using the local rational method. Step S52: Use vector fitting to fit the frequency response function with a rational function, and extract the initial values ​​of the model parameters based on the zeros and poles of the fitted rational function. Step S53: Starting from the initial values ​​of the obtained model parameters, the logarithmic error between the measurement function and the model function is minimized by a nonlinear programming algorithm to obtain refined identification parameters.

8. The method for identifying the configuration-related stiffness of a six-axis industrial robot according to claim 4 or 7, characterized in that, In step S6, the unknown coefficients of the configuration-stiffness analytical function established in step S2 are fitted using the stiffness obtained in step S5 under different configurations, thereby completing the analytical calculation of the stiffness related to the target joint configuration, including: The discrete stiffness values ​​obtained under different configurations are used as sample points. The unknown coefficients in the configuration-stiffness analytical function of step S2 are fitted using a linear regression algorithm. Based on the fitted unknown coefficients, a configuration-stiffness mapping model covering the entire workspace of the six-axis industrial robot is constructed. The six-axis industrial robot is then compensated and controlled according to the configuration-stiffness mapping model.

9. A processing device, characterized in that, include: At least one memory for storing one or more programs; At least one processor is capable of executing one or more programs stored in the memory, such that when the one or more programs are executed by the processor, the processor can perform the method according to any one of claims 1-8.

10. A readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it can implement the method described in any one of claims 1-8.

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