Robot friction parameter identification method and system based on nominal constraint

Abstract

The invention belongs to the related technical field of robot parameter identification, and discloses a robot friction parameter identification method and system based on nominal constraint, and the method comprises the steps: building a nonlinear kinetic equation, carrying out the linearization of the nonlinear kinetic equation into a kinetic regression matrix, and determining an initial value of a minimum inertial parameter set of a robot; a first excitation mode is adopted to drive the robot to perform high-dynamic motion, joint driving torque error two norms are adopted as a target function for iterative optimization, and a determined robot minimum inertial parameter set is obtained to serve as a constraint; performing low-speed reciprocating motion by adopting a second excitation mode, constructing a kinetic equation based on a coulomb-viscous friction model, and estimating friction parameters of each joint by utilizing a constrained least square method. According to the method, the robot kinetic equation and the coulomb-viscous friction model are utilized, the known kinetic parameters serve as constraint information to identify the robot friction parameters, the least square method friction parameter identification method with constraints is formed, and the friction parameter identification performance is remarkably improved.

Description

Technical Field

[0001] This invention belongs to the technical field of robot parameter identification, and more specifically, relates to a method and system for identifying robot friction parameters based on nominal constraints. Background Technology

[0002] In robot motion control, accurate identification of joint friction parameters is crucial for improving trajectory tracking accuracy. Friction often leads to problems such as low-speed crawling and steady-state errors, especially in high-precision applications, where its impact is particularly significant. Current technologies mainly rely on physical models and data-driven methods to identify friction parameters.

[0003] In terms of physical models, the Coulomb-viscous friction model is widely used because it can effectively describe the frictional characteristics of robot joints. This model can effectively combine the effects of Coulomb friction and viscous friction, and accurately reflect the frictional characteristics in the low-speed region. However, existing friction identification methods still have some limitations, especially when facing complex loads and dynamic environments. The identification results are often affected by the coupling effect of frictional force and inertial force, leading to parameter estimation bias. Among data-driven methods, the traditional least squares (LS) method is often used for parameter estimation, but it suffers from sensitivity to initial values ​​and insufficient solution accuracy in friction identification. Although methods such as weighted least squares (WLS) and genetic algorithms (GA) can improve model accuracy, these methods usually require a large amount of experimental data for training, resulting in high computational costs and poor adaptability to high loads and complex dynamic environments. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a robot friction parameter identification method and system based on nominal constraints, which solves the problems of large parameter estimation deviation, large computational load and poor adaptability of the existing robot friction parameter identification methods.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for identifying robot friction parameters based on nominal constraints is provided, comprising: S1. Based on the recursive Newton-Euler method, establish the nonlinear dynamic equation of the robot, and use the parameter linearization method to transform the nonlinear dynamic equation into a linear function of the robot's inertial parameters. Construct a dynamic regression matrix containing the minimum set of inertial parameters, and determine the initial value of the minimum set of inertial parameters of the robot according to the robot model. S2, the robot is driven to perform high-dynamic motion using the first excitation mode. The joint angle and angular velocity are collected by the joint encoder, and the actual joint driving torque is obtained by the driving current. Starting from the initial value of the robot's minimum inertial parameter set, iterative optimization is performed with the L2 norm of the joint driving torque error as the objective function to obtain the determined robot minimum inertial parameter set. S3 uses the second excitation mode to sample low-speed reciprocating motion data. Under the constraint of the determined minimum inertial parameter set of the robot, the dynamic equation containing friction is constructed based on the Coulomb-viscous friction model, and the friction parameters of each joint are estimated by the constrained least squares method.

[0006] According to the robot friction parameter identification method based on nominal constraints provided by the present invention, S3 further includes: A nominal load with known inertial parameters is rigidly connected to the end effector of the robot. Then, under the constraints of the determined minimum set of robot inertial parameters and the known load inertial parameters, the friction parameters of each joint are estimated using the constrained least squares method.

[0007] According to the robot friction parameter identification method based on nominal constraints provided by the present invention, the first excitation mode is multi-joint coordinated motion of each joint under high speed and high acceleration; the second excitation mode is periodic reversing motion of each joint in the low speed range.

[0008] According to the robot friction parameter identification method based on nominal constraints provided by the present invention, the nonlinear dynamic equation is as follows: ; in, , , These represent the robot's joint position, joint angular velocity, and joint angular acceleration, respectively. M The inertial tensor matrix, C For the matrices of centrifugal force and Coriolis force, G The gravity term matrix, F Here is the friction matrix. This represents the joint drive torque matrix of the robot. The dynamic regression matrix containing the minimum set of inertial parameters is shown below: ; in, The matrix is ​​a regression matrix of the robot's dynamic parameters. This represents the minimum set of inertial parameters for the robot.

[0009] According to the robot friction parameter identification method based on nominal constraints provided by the present invention, S2 specifically includes: The angular positions and angular velocities of each joint of the robot are obtained during operation in the first excitation mode, and the measured driving torque of the robot's joint motors is obtained through the joint driving current. Using the robot's minimum inertial parameter set as the initial value for the optimization algorithm, the parameter identification value obtained in each iteration is denoted as... Substitute the data to calculate the theoretical driving torque for each step. The optimization is performed using the L2 norm of the torque error vector as the objective function, which is as follows: ; By minimizing the objective function This yields a definite set of minimum inertial parameters for the robot.

[0010] According to the robot friction parameter identification method based on nominal constraints provided by the present invention, the construction of dynamic equations containing friction based on the Coulomb-viscous friction model in S3 specifically includes: The dynamic model considering friction under load is constructed as follows: ; in, To obtain the joint driving torque acquired by operating the second excitation mode under load, To determine the minimum set of inertial parameters for the robot, The regression matrix changes due to the load. For load inertia parameters, To balance the joint torques of friction during operation under load, This is a noise signal; The robot joint friction model is represented by the Coulomb-viscous friction model as follows: ; in, Here is the friction force matrix for the robot joints. For switching functions, These are the Coulomb friction parameters of each joint. These are the viscous friction parameters of each joint, and the friction observation matrix. , , n Represents the number of joints, friction parameter matrix , ; Therefore, the actual joint driving torque for: ; in, For dynamic parameters, the corresponding observation matrix W It is a full-rank matrix.

[0011] According to the robot friction parameter identification method based on nominal constraints provided by the present invention, in S3, the friction parameters of each joint are estimated using the constrained least squares method as follows: The known minimum set of robot inertial parameters and load inertia parameters Recorded as Let C be the constraint matrix. d Given a vector of known values, for Given the elements, the constraints can be expressed as: ; The constrained least squares objective function is: ; in, This represents the sum of squared errors.

[0012] According to the robot friction parameter identification method based on nominal constraints provided by the present invention, the constrained least squares solution is specifically as follows: make: , B = C , ; The constrained least squares solution is: ; Furthermore from The value of the friction parameter is obtained from the expression.

[0013] According to another aspect of the present invention, a robot friction parameter identification system based on nominal constraints is provided. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the robot friction parameter identification method based on nominal constraints as described above.

[0014] In summary, compared with the prior art, the robot friction parameter identification method and system based on nominal constraints provided by this invention offer the following advantages: 1. By utilizing the robot's dynamic equations and the Coulomb-viscous friction model, known dynamic parameters are used as constraint information to identify the robot's friction parameters, forming a friction parameter identification method based on constrained least squares. By introducing the constraint condition of the robot's minimum inertial parameter set, it is beneficial to ensure the stability and robustness of the parameter estimation process, thereby overcoming the limitation of traditional methods where the identification results are often affected by the coupling effect of friction and inertial forces, leading to parameter estimation deviations. Furthermore, it avoids solving for the robot's inertial parameters, which is beneficial to improving the identification accuracy and computational efficiency, and significantly enhances the performance of friction parameter identification. 2. This method combines the robot dynamics equations and the Coulomb-viscous friction model, and takes into account the influence of load changes, which can effectively improve the identification accuracy and real-time performance under complex working conditions; 3. To identify the robot's inertial parameters, the first excitation mode is adopted, which drives the joints of the robotic arm to move at high speed and acceleration. The high dynamic motion makes the dynamic effect dominant. By averaging, the friction effect is suppressed, and the dynamic parameters are accurately estimated. To identify the friction parameters, a second excitation mode (low-speed reciprocating motion excitation) is designed, which makes the joint motion trajectory periodically low-speed forward and reverse rotation. The aim is to make the joint frequently change direction in the low-speed range to highlight the influence of Coulomb friction and viscous friction, and improve the identification accuracy. 4. This method does not require adding additional sensors to the robot; it only needs to collect information on the robot's joint motor current and joint angle to detect contact force, reducing dependence on the experimental environment. By setting physical constraints, unreasonable parameter solutions can be eliminated, ensuring that the parameter identification results conform to actual physical laws and improving identification accuracy. At the same time, this method is highly adaptable and can flexibly adjust the constraints according to different application scenarios, ensuring the efficiency and accuracy of friction parameter identification in various engineering applications. Attached Figure Description

[0015] Figure 1 The flowchart shows the robot friction parameter identification method based on nominal constraints provided by the present invention.

[0016] Figure 2 This is a schematic diagram of a seven-degree-of-freedom robotic arm model with load used in this invention.

[0017] Figure 3 This is a schematic diagram of the joint position trajectories of the first excitation mode used in this invention.

[0018] Figure 4 This is a schematic diagram of the joint position trajectories of the second excitation mode used in this invention.

[0019] Figure 5 This is a schematic diagram of the Coulomb-viscous friction model used in this invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0021] Please see Figure 1 This embodiment provides a method for identifying robot friction parameters based on nominal constraints. The method includes: S1 Dynamics Modeling and Linearization: The nonlinear dynamic equations of the robot are established based on the recursive Newton-Euler method, and the nonlinear dynamic equations are transformed into linear functions of the robot's inertial parameters using the parameter linearization method. A dynamic regression matrix containing the minimum set of inertial parameters is constructed, and the initial values ​​of the minimum set of inertial parameters of the robot are determined according to the robot model. S2 robot inertial parameter identification: The robot is driven to perform high-dynamic motion using the first excitation mode. Joint angles and angular velocities are collected through joint encoders, and the actual joint driving torque is obtained through driving current. Starting from the initial values ​​of the robot's minimum inertial parameter set, iterative optimization is performed with the L2 norm of the joint driving torque error as the objective function to obtain a determined minimum inertial parameter set of the robot. S3 Friction Parameter Identification: Low-speed reciprocating motion sampling data is collected using the second excitation mode. Under the constraint of the determined minimum inertial parameter set of the robot, the dynamic equation containing friction is constructed based on the Coulomb-viscous friction model, and the friction parameters of each joint are estimated using the constrained least squares method.

[0022] In some embodiments, S3 further includes: A nominal load with known inertial parameters is rigidly connected to the end effector of the robot. Then, under the constraints of the determined minimum set of robot inertial parameters and the known load inertial parameters, the friction parameters of each joint are estimated using the constrained least squares method.

[0023] The nominal load's mass, center of mass position, and moment of inertia were obtained through 3D modeling and parameter measurement, and were used as additional dynamic parameters of the end link in the regression matrix construction. The friction model adopted a piecewise Coulomb-viscous friction combined model, where the Coulomb friction parameters and viscous friction parameters were obtained by fitting low-speed motion data.

[0024] Optionally, the first excitation mode is multi-joint coordinated motion of each joint at high speed and high acceleration, to significantly enhance inertial force and Coriolis effect and suppress the influence of friction. The second excitation mode is periodic directional motion of each joint in the low-speed range, to enhance the effects of Coulomb friction and viscous friction.

[0025] S1 specifically includes: constructing the dynamic equations of the robotic arm based on the recursive Newton-Euler method, and calculating any link by outward recursion. i angular velocity and angular acceleration and linear acceleration The inertial forces of each link are calculated using the Newton-Euler formula. Inertial torque Acting on the connecting rod i The combined force at the center of mass Resultant torque at the center of mass ; recursively calculate each link inwards i -1 acts on the connecting rod i The force on and the torque And joint driving force and joint driving torque vector Since the joints and links of a serial articulated robot have the same numbering and quantity, the subscript... i It can represent the first i The first link can also represent the second link. i Each joint is distinguished according to its specific use. (Top left) i Indicates the link i The corresponding coordinate system.

[0026] For an independent, serially articulated robot, the nonlinear dynamic equations are as follows: ; in, , , These represent the robot's joint position, joint angular velocity, and joint angular acceleration, respectively. M The inertial tensor matrix, C For the matrices of centrifugal force and Coriolis force, G The gravity term matrix, F Here is the friction matrix. This represents the joint drive torque matrix of the robot. The recursive Newton-Euler method is used to calculate the angular velocity, angular acceleration, linear acceleration, inertial force, inertial torque, and net force and torque at the center of mass of each link in the robot. Taking a 7-DOF robotic arm as an example: Outward recursion ( i :0->6) obtained: ; Among them, the connecting rod i In the connecting rod i coordinate system { i angular velocity angular acceleration linear acceleration Inertial force Inertial torque ;joint i angular velocity angular acceleration ; From the connecting rod i +1 coordinate system { i +1} to the link i coordinate system { i The rotation transformation matrix of} It is a connecting rod i +1 rotation axis direction, It is a coordinate system { i The origin of +1} is relative to the coordinate system { i The position of the origin is offset. It is a connecting rod i The centroid of +1 lies in the coordinate system { i The linear acceleration in +1} It is a coordinate system { i The centroid of +1} relative to the coordinate system { i +1} offset of the origin position, It is a connecting rod. i +1 Regarding the coordinate system of the connecting rod's center of mass { i The inertial tensor at the origin (+1) It is a connecting rod i +1 mass.

[0027] The driving torque of each joint is obtained by recursively working inward.

[0028] Backward iteration (i: 7->1): ; in, It is a connecting rod i Force, It is a connecting rod. i The centroid relative to the coordinate system { i The position of the origin is offset. It is a joint i The joint driving torque.

[0029] The aforementioned nonlinear equations are quite complex in analysis and control design because, in actual engineering, the inertial parameters of a system (such as the mass, center of mass coordinates, and moment of inertia of a complex structure) are often difficult to obtain accurately through direct measurement. In order to clearly separate the "known kinematic information" from the "unknown inertial parameters", it is necessary to transform them into a more manageable form through linearization.

[0030] During the inward recursive process of the Newton-Euler method, the connecting rod is obtained. i Torque at joints By the parallel axis theorem, we can obtain: ; in, It acts on the connecting rod i Torque acting at the center of mass (including inertial torque). It is a connecting rod i In coordinate system { i The inertial tensor about the origin in} Indicates the link i The center of mass is in the connecting rod i Corresponding coordinate system { i The position vector in}.

[0031] available: ; in, Represents the coordinate system { i The origin of +1} is in the coordinate system { i The position vector in} It is a connecting rod i Unknown inertial parameter vector, in the subscript xyz Represents the components of the corresponding coordinate axes; matrix operators: , .

[0032] link i +1 acts on the connecting rod i The force and torque can be written as: ; ; in Indicates from coordinate system { i} to coordinate system { j The rotation matrix of} , Reflecting the subsequent rods j Pole i Influence of kinetic properties. (Subscript) i , j , kThese all represent the joint or link number; let the link i Relative to coordinate system { i The force spinor of} is , pole j Pole i The dynamic influence is ,link i centroid relative to coordinate system { i The force spinor of} is , To make the force spinor from the coordinate system { i}arrive{ j The transformation matrix of} when j = i When +1, there is ,thereby: ; in, ; Joint torque ,so: ; in, Indicates the link i The direction of the axis of rotation, superscript T Indicates transpose. , is a function relating only to the joint motion state, and is independent of inertial parameters. Irrelevant. Therefore, the joint moment vector is linearized as follows: ; It can be written as: ; in, This is the driving torque under ideal conditions. It is about , , The nonlinear matrix, and The set of fundamental parameters representing the dynamics, for each individual link. i In other words, 10 parameters can be used. To characterize its dynamic features, but not every parameter affects the joint torque values ​​of the robot, so the basic parameter set... It can be further simplified to a minimal set of parameters. , The dynamic regression matrix containing the minimum set of inertial parameters is shown below: ; in, The matrix is ​​a regression matrix of the robot's dynamic parameters. This represents the minimum set of inertial parameters for the robot. Both the regression matrix and the minimum parameter set were solved using the open-source Python toolkit symPybotics. Minimum parameter set The geometric and inertial parameters in the expression are obtained through a 3D model. The minimum parameter set is obtained through geometric modeling and symbolic computation tools (such as SymPybotics). The minimum inertial parameter set is determined by the robot's inertial parameters, and its initial values ​​can be determined based on the 3D model.

[0033] In some specific embodiments, the initial values ​​of the obtained minimum inertial parameter set are as follows:

[0034] like Figure 2 As shown in the diagram, this embodiment uses a seven-DOF robotic arm model with load. By setting the material properties, the mass, center of mass position, and inertia tensor of each link of the robotic arm can be obtained in SolidWorks through the mass property in the evaluation column.

[0035] In some embodiments, S2 specifically includes optimizing the collected data using a genetic algorithm based on a dynamic model to accurately estimate the inertial parameters of the robotic arm, specifically: Acquire the robot in the first stimulus mode (high dynamic motion stimulus, such as...) Figure 3 As shown, the angular position and angular velocity of each joint during operation are obtained, and the measured driving torque of the robot's joint motors is obtained through the joint driving current. Using the robot's minimum inertial parameter set As the initial value for the optimization algorithm, the parameter identification value obtained in each iteration is denoted as . Substitute the data to calculate the theoretical driving torque for each step. The optimization is performed using the L2 norm of the torque error vector as the objective function, which is as follows: ; By minimizing the objective function The determined minimum set of robot inertial parameters is obtained. .

[0036] In some embodiments, S3 uses known dynamic inertial parameters as constraint information to perform least-squares parameter estimation on friction parameters to achieve high-precision identification of friction parameters. Specifically: A load with known inertial parameters is rigidly connected to the end effector of the robotic arm, and a second excitation mode (periodic reversing motion in the low-speed range, such as...) is employed. Figure 4 As shown, the loaded robotic arm is excited, and motion and torque data are collected; the dynamic equations involving friction are constructed based on the Coulomb-viscous friction model in S3, specifically including: The dynamic model considering friction under load is constructed as follows: ; in, To obtain the joint driving torque acquired by operating the second excitation mode under load, To determine the minimum set of inertial parameters for the robot, To balance the joint torques of friction during operation under load, This is a noise signal; When the end effector of the robotic arm is rigidly connected to a load, the load inertia parameters will be... (quality Inertial parameters Location of the center of mass (This is considered as an end link) n Additional parameters, It is a regression matrix that changes due to the load.

[0037] Adopting such Figure 5 The Coulomb-viscous friction model shown can well characterize the frictional characteristics of a robot at low speeds or with varying speeds. The robot joint friction model is represented by the Coulomb-viscous friction model as follows: ; in, Robot joints i Friction at the point, It is a joint i The relative rotational speed at that point It is a joint i Coulomb friction parameters at the location, It is a joint i Viscous friction parameters at the location, switching function: ; Transformed into: ; in, Here is the friction force matrix for the robot joints. For switching functions, These are the Coulomb friction parameters of each joint. These are the viscous friction parameters of each joint, and the friction observation matrix. , , n Represents the number of joints, friction parameter matrix , ; Therefore, the actual joint driving torque for: ; in, For dynamic parameters, the corresponding observation matrix W It is a full-rank matrix.

[0038] Furthermore, in S3, the friction parameters of each joint are estimated using the constrained least squares method as follows: The known minimum set of robot inertial parameters and load inertia parameters Recorded as Let C be the constraint matrix, and then... and constitute, d Given a vector of known values, for Given the elements, the constraints can be expressed as: ; The constrained least squares objective function is: ; in, This represents the sum of squared errors between the predicted and actual values.

[0039] The solution using the constrained least squares method is as follows: Introducing the Lagrange multiplier vector Construct the Lagrange function: ; Therefore, we can obtain information about and The system of linear equations: ; In order to solve We can use the method of finding the inverse of a block matrix, let: , B = C , ; The constrained least squares solution is: ; Furthermore from Friction parameters are obtained from the expression. The value of .

[0040] In other embodiments, a robot friction parameter identification system based on nominal constraints is also provided. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the robot friction parameter identification method based on nominal constraints described above.

[0041] To verify the accuracy of the Coulomb-viscous friction model parameters obtained from simulation data, a verification module was built in the Simulink environment, using the same trajectory excitation mode as the parameter identification stage, to ensure that the verification conditions are consistent with the identification conditions.

[0042] Based on the Coulomb-viscous friction model, the identified friction parameters are input. In addition to the velocity signal, the model outputs the predicted frictional resistance. Then, the identified dynamic parameters and angle, velocity, and angular velocity signals are input, and the model outputs the joint torques predicted by the model to drive the model's motion. The joint torque value was then compared with joint torque data acquired through simulation. Verification showed that the friction parameter identification method provided in this embodiment of the invention has good identification accuracy.

[0043] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for identifying robot friction parameters based on nominal constraints, characterized in that, include: S1. Based on the recursive Newton-Euler method, establish the nonlinear dynamic equation of the robot, and use the parameter linearization method to transform the nonlinear dynamic equation into a linear function of the robot's inertial parameters. Construct a dynamic regression matrix containing the minimum set of inertial parameters, and determine the initial value of the minimum set of inertial parameters of the robot according to the robot model. S2, the robot is driven to perform high-dynamic motion using the first excitation mode. The joint angle and angular velocity are collected by the joint encoder, and the actual joint driving torque is obtained by the driving current. Starting from the initial value of the robot's minimum inertial parameter set, iterative optimization is performed with the L2 norm of the joint driving torque error as the objective function to obtain the determined robot minimum inertial parameter set. S3 uses the second excitation mode to sample low-speed reciprocating motion data. Under the constraint of the determined minimum inertial parameter set of the robot, the dynamic equation containing friction is constructed based on the Coulomb-viscous friction model, and the friction parameters of each joint are estimated by the constrained least squares method.

2. The robot friction parameter identification method based on nominal constraints as described in claim 1, characterized in that, S3 also includes: A nominal load with known inertial parameters is rigidly connected to the end effector of the robot. Then, under the constraints of the determined minimum set of robot inertial parameters and the known load inertial parameters, the friction parameters of each joint are estimated using the constrained least squares method.

3. The robot friction parameter identification method based on nominal constraints as described in claim 1, characterized in that, The first excitation mode is multi-joint coordinated movement of each joint at high speed and high acceleration; the second excitation mode is periodic reversing movement of each joint in the low speed range.

4. The robot friction parameter identification method based on nominal constraints as described in claim 2, characterized in that, The nonlinear dynamic equations are shown below: ； in, , , These represent the robot's joint position, joint angular velocity, and joint angular acceleration, respectively. M The inertial tensor matrix, C For the matrices of centrifugal force and Coriolis force, G The gravity term matrix, F Here is the friction matrix. This represents the joint drive torque matrix of the robot. The dynamic regression matrix containing the minimum set of inertial parameters is shown below: ； in, The matrix is ​​a regression matrix of the robot's dynamic parameters. This represents the minimum set of inertial parameters for the robot.

5. The robot friction parameter identification method based on nominal constraints as described in claim 4, characterized in that, S2 specifically includes: The angular positions and angular velocities of each joint of the robot are obtained during operation in the first excitation mode, and the measured driving torque of the robot's joint motors is obtained through the joint driving current. Using the robot's minimum inertial parameter set as the initial value for the optimization algorithm, the parameter identification value obtained in each iteration is denoted as... Substitute the data to calculate the theoretical driving torque for each step. The optimization is performed using the L2 norm of the torque error vector as the objective function, which is as follows: ； By minimizing the objective function This yields a definite set of minimum inertial parameters for the robot.

6. The robot friction parameter identification method based on nominal constraints as described in claim 4, characterized in that, The dynamic equations involving friction in S3, based on the Coulomb-viscous friction model, specifically include: The dynamic model considering friction under load is constructed as follows: ； in, To obtain the joint driving torque acquired by operating the second excitation mode under load, To determine the minimum set of inertial parameters for the robot, The regression matrix changes due to the load. For load inertia parameters, To balance the joint torques caused by friction during operation under load, This is a noise signal; The robot joint friction model is represented by the Coulomb-viscous friction model as follows: ； in, Here is the friction force matrix for the robot joints. For switching functions, These are the Coulomb friction parameters of each joint. These are the viscous friction parameters of each joint, and the friction observation matrix. , , n Represents the number of joints, friction parameter matrix , ; Therefore, the actual joint driving torque for: ； in, For dynamic parameters, the corresponding observation matrix W It is a full-rank matrix.

7. The robot friction parameter identification method based on nominal constraints as described in claim 6, characterized in that, In S3, the friction parameters of each joint are estimated using the constrained least squares method as follows: The known minimum set of robot inertial parameters and load inertia parameters Recorded as Let C be the constraint matrix. d Given a vector of known values, for Given the elements, the constraints can be expressed as: ； The constrained least squares objective function is: ； in, This represents the sum of squared errors.

8. The robot friction parameter identification method based on nominal constraints as described in claim 7, characterized in that, The solution using the constrained least squares method is as follows: make: , B = C , ； The constrained least squares solution is: ； Furthermore from The value of the friction parameter is obtained from the expression.

9. A robot friction parameter identification system based on nominal constraints, characterized in that, The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the robot friction parameter identification method based on nominal constraints as described in any one of claims 1-8.

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