Rigidity measuring method for servo joint of robot

Abstract

The invention relates to a rigidity measuring method for a servo joint of a robot, which comprises the following steps of: establishing a measuring coordinate system, carrying out coincidence calibration on a base coordinate system of the robot and a world coordinate system, and initializing the pose of the robot; target ball arrangement and non-load reference point acquisition are carried out, a target ball is rigidly bonded to a connecting rod close to a joint shaft to be detected, and target ball coordinate points in a non-load state are acquired and fitted to obtain a related reference; graded tail end load application and six-dimensional force synchronous acquisition are carried out, loading is carried out step by step according to incremental loads, and six-dimensional force data are recorded; robot joint torque is calculated, a kinematic model is called to obtain a force Jacobian matrix, and joint torque increment is calculated; then target ball displacement is collected under the load, and joint deformation is calculated; fitting the joint basic stiffness k through linear regression, evaluating a fitting effect by using a decision coefficient, and outputting the joint basic stiffness. The method can accurately measure the rigidity of the servo joint of the robot, and provides a reliable basis for evaluating the performance of the robot.

Description

Technical Field

[0001] This invention belongs to the field of server heat dissipation technology, and in particular relates to a method for measuring the stiffness of a robot servo joint. Background Technology

[0002] In the field of industrial robotics, the stiffness of servo joints is a core indicator that determines the robot's motion accuracy, dynamic response performance, and operational reliability. It directly affects the robot's end-effector positioning error and trajectory tracking accuracy under load, as well as its force control performance when interacting with the external environment. Therefore, accurate measurement of servo joint stiffness is of significant engineering importance.

[0003] Currently, methods for measuring robot joint stiffness mainly include static loading and dynamic excitation methods. Static loading methods apply a known load to the joint and measure its deformation to calculate stiffness. However, traditional methods often suffer from inconsistent coordinate systems, leading to a lack of spatial consistency in the measurement data and introducing additional errors. Dynamic excitation methods apply dynamic signals to the joint and analyze the response characteristics to solve for stiffness, but they are easily affected by system damping and inertial parameters, and struggle to reflect stiffness characteristics under static and low-dynamic conditions.

[0004] Furthermore, existing measurement techniques often employ single or continuous load application methods, lacking a systematic design for graded loading, making it difficult to obtain stiffness variation patterns under different load levels. In deformation measurement, the distance between the measurement point and the joint's rotation axis often leads to significant interference from the flexible deformation of the connecting rod, reducing the accuracy of stiffness calculations. Simultaneously, some methods fail to establish a precise mapping relationship between torque and deformation, or the fitting algorithms used lack effective evaluation mechanisms for fitting performance, making it difficult to guarantee the reliability of the measurement results.

[0005] Therefore, in view of the problems existing in the existing technology, such as inconsistent coordinate system references, unsystematic load application, insufficient deformation measurement accuracy, and lack of reliability of fitting methods, there is an urgent need for a robot servo joint stiffness measurement method that can achieve unified coordinate references, graded and accurate loading, high-precision deformation measurement, and scientific fitting analysis. Summary of the Invention

[0006] The purpose of this invention is to provide a method for measuring the stiffness of robot servo joints, in order to solve the technical problems existing in the prior art, such as inconsistent coordinate system references, unsystematic load application, insufficient deformation measurement accuracy, and lack of reliability of fitting methods.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A method for measuring the stiffness of a robot servo joint includes the following steps:

[0009] S1: Establish the measurement coordinate system and initialize the robot pose;

[0010] S2: Perform target ball placement and no-load reference point acquisition;

[0011] S3: Perform graded end-load application and synchronous acquisition of six-dimensional force;

[0012] S4: Calculate the joint torque τ of the robot, i.e., torque mapping;

[0013] S5: Under load, collect target ball displacement and calculate joint deformation δθ;

[0014] S6: Perform linear regression to fit the basic joint stiffness k.

[0015] Preferably, the specific process of establishing the measurement coordinate system and initializing the robot pose in step S1 is as follows:

[0016] S11: Align and calibrate the robot's base coordinate system {B} with the world coordinate system {W} to provide a unified spatial reference for subsequent target ball position acquisition and torque mapping;

[0017] S12: Adjust each joint angle to the preset measurement pose through the robot controller, including Pose1: θ1=0°, θ2=0°, θ3=0°….

[0018] Preferably, the specific process of aligning and calibrating the robot's base coordinate system {B} with the world coordinate system {W} in step S11 is as follows:

[0019] S111: Make the origin of the robot's base coordinate system {B} coincide with the origin of the world coordinate system {W}: By measuring the deviation between the two, denoted as the translation vector WtB, the subsequent compensation is carried out in the control system. The ultimate goal is to make WtB = (0,0,0)T.

[0020] S112: Align the X, Y, and Z axes of the robot's base coordinate system {B} with those of the world coordinate system {W}: calibrate the directions of the X, Y, and Z axes respectively to ensure that the axis vectors of the two coordinate systems are parallel and in the same direction, i.e., the rotation matrix is ​​the identity matrix W. RB =I;

[0021] S113: Control the robot to move to more than 3 different poses, covering the workspace range, and record the theoretical coordinates BP of the end effector under {B} and the measured coordinates WP under {W} respectively. If {B} and {W} coincide, then WP = BP is satisfied. The error should be ≤0.1mm and the angle error should be ≤0.05°.

[0022] If errors exist, they can be corrected in the following ways:

[0023] Origin error: Remeasure the deviation between {B} and {W} origin, and adjust the translation parameters in the control system;

[0024] Axial direction error: The deviation between the measured trajectory and the theoretical trajectory is fitted using the least squares method, the rotation angle correction value is calculated, the small rotations around the X / Y / Z axes are used to update the rotation matrix in the control system.

[0025] Preferably, the specific process of target ball placement and no-load reference point acquisition in step S2 is as follows:

[0026] S21: The target ball is rigidly bonded to the connecting rod near the joint axis to be tested, at a distance of ≤50mm from the rotation axis, in order to reduce the flexibility error of the connecting rod;

[0027] S22: Using a Leica AT403 laser tracker, continuously rotate the joint under test ±5° under no-load conditions to collect ≥20 target ball coordinate points;

[0028] S23: Obtain the unloaded rotation center by performing circle fitting using SpatialAnalyzer software. and the initial position of the target ball O1 and P1 serve as the zero-point references for calculating joint deformation.

[0029] Preferably, the specific process of applying graded end loads and synchronously acquiring six-dimensional forces in step S3 is as follows:

[0030] S31: Install the load tray containing 10kg weights onto the robot end effector via the adapter flange;

[0031] S32: Load the load in four progressively increasing increments of 10kg→20kg→30kg→40kg;

[0032] S33: Under each load level, 20 seconds of data are recorded using a six-dimensional force sensor (DECENTγ200, 800Hz), and the average value is taken to obtain the six-dimensional force experienced by the end.

[0033]

[0034] Where F is used in step 4 to calculate the joint torque τ, F i This represents the six-dimensional force value at each moment, where n is the amount of data collected over a period of time. The six-dimensional force under no-load conditions is F. N The six-dimensional force under load is F. L .

[0035] Preferably, the specific process for calculating the robot joint torque τ in step S4 is as follows:

[0036] S41: Based on the robot's current pose, call the kinematic model to calculate the force Jacobian matrix J_F (6×6);

[0037] S42: Calculate the joint torque increment:

[0038] Δτ=J(θ) T (F L -F N );

[0039] Among them, the joint torque increment Δτ is paired with the deformation δθ measured in step S5 for stiffness fitting.

[0040] Preferably, the specific process of acquiring the target ball displacement and calculating the joint deformation δθ under load in step S5 is as follows:

[0041] S51: Repeat the rotation action of step S2 (±5°) to collect the target ball trajectory under each load level;

[0042] S52: Fitting to obtain the load rotation center and the new position of the target ball

[0043] S53: Calculation of joint angle deformation based on the law of cosines:

[0044]

[0045] Or a linear approximation: Δθ≈|P2-P1| / R; where R is the radius of rotation;

[0046] δθ and Δτ from step S4 together form the (Δτ,δθ) dataset.

[0047] Preferably, the specific process of performing linear regression fitting of the joint base stiffness k in step S6 is as follows:

[0048] S61: For the (Δτ, δθ) data of each load level, the linear regression equation of the joint deformation δθ caused by the joint torque increment Δτ of the i-th axis, fitted with a straight line using the least squares method, can be expressed as:

[0049]

[0050] Among them, c i It is the flexibility of the i-th axis joint, q i Let Δτ be the joint stiffness along the i-th axis, ∈ be the random error, and Δτ be the joint stiffness along the i-th axis. i δθ is the joint torque increment along the i-th axis. i It is the actual joint deformation increment value. It is the average value of the joint torque increment. It is the average value of joint deformation;

[0051] S62: After obtaining the stiffness, the coefficient of determination R^2 is used to evaluate the fitting effect of the linear regression method. The value range is [0, 1]. The calculation method of the coefficient of determination R^2 is as follows:

[0052]

[0053] RSS is the sum of squared residuals:

[0054] Where, δθ i It is the actual joint deformation increment value. Here, is the predicted joint deformation increment value of the i-th model, n is the number of samples, and TSS is the total sum of squares: It is the average value of joint deformation;

[0055] in, It is the average value of all torque increments. The closer the coefficient of determination R^2 is to 1, the better the fitting effect of the linear regression method.

[0056] S63: Output the basic stiffness q of the joint i Unit: N·mm / rad.

[0057] The beneficial effects of this invention include:

[0058] The method for measuring the stiffness of robot servo joints provided by this invention firstly ensures that subsequent steps such as target ball position acquisition and torque mapping are performed under a unified spatial reference by aligning the robot's base coordinate system with the world coordinate system. This reduces measurement errors caused by inconsistencies in coordinate systems and provides a reliable spatial reference for the entire measurement process.

[0059] Secondly, placing a target ball near the connecting rod of the joint to be tested, at a distance of ≤50mm from the rotation axis, can effectively reduce the interference of the connecting rod's flexibility on the measurement results. At the same time, by collecting a sufficient number of coordinate points and performing circle fitting using a laser tracker, the rotation center and target ball position under no-load and loaded conditions can be accurately determined, providing high-precision basic data for joint deformation calculation.

[0060] Furthermore, by applying the end load in a graded and incremental manner, and by collecting data for a sufficient period of time using a six-dimensional force sensor and averaging the data, the force characteristics under different load levels can be comprehensively reflected, providing accurate input parameters for joint torque calculation.

[0061] Finally, the joint torque increment is calculated based on the Leyakubi matrix, and the joint angle deformation is obtained by combining the cosine theorem or linear approximation method. Then, the stiffness is fitted by linear regression using the least squares method, and the fitting effect is evaluated by the coefficient of determination. This makes the stiffness calculation process rigorous and the results reliable, and can provide accurate stiffness parameters for robot performance evaluation and optimization. Attached Figure Description

[0062] Figure 1 This is a diagram showing the coordinate changes of the two-joint target of the present invention along the z-axis in the world coordinate system {W}.

[0063] Figure 2 This is a diagram showing the torque increment variation of the two-joint target of the present invention along the z-axis in the world coordinate system {W}.

[0064] Figure 3 This is a graph showing the change in deformation of the two joints of the present invention as a function of the joint torque increment.

[0065] Figure 4 This is a diagram showing the coordinate changes of the three-joint target of the present invention along the z-axis in the world coordinate system {W}.

[0066] Figure 5 This is a diagram showing the torque increment variation of the three-joint target of the present invention in the z-axis direction of the world coordinate system {W}.

[0067] Figure 6 This is a graph showing the variation of the deformation of the three joints of the present invention with the increase of joint torque.

[0068] Figure 7 This is a diagram showing the coordinate changes of the four-joint target of the present invention along the z-axis in the world coordinate system {B}.

[0069] Figure 8 This is a diagram showing the torque increment variation of the four-joint target of the present invention in the z-axis direction of the world coordinate system {B}.

[0070] Figure 9 This is a graph showing the variation of the deformation of the four joints of the present invention with the increase of joint torque.

[0071] Figure 10 This is a diagram showing the coordinate changes of the five-joint target of the present invention along the z-axis in the world coordinate system {B}.

[0072] Figure 11 This is a diagram showing the change in joint torque increments of the five-joint target of the present invention along the z-axis in the world coordinate system {B}.

[0073] Figure 12 This is a graph showing the variation of the deformation of the five joints of the present invention with the increase of joint torque.

[0074] Figure 13 This is a diagram showing the coordinate changes of the six-joint target of the present invention along the z-axis in the world coordinate system {B}.

[0075] Figure 14 This is a diagram showing the change in joint torque increments of the six-joint target of the present invention along the z-axis in the world coordinate system {B}.

[0076] Figure 15 This is a graph showing the variation of the deformation of the six joints of the present invention with the increase of joint torque.

[0077] Figure 16 This is a flowchart illustrating the stiffness measurement method for the robot servo joint of the present invention. Detailed Implementation

[0078] The following is in conjunction with the appendix Figures 1 to 16 The present invention will be further described in detail below:

[0079] Example 1

[0080] See appendix Figure 16 As shown, a method for measuring the stiffness of a robot servo joint includes the following steps:

[0081] S1: Establish the measurement coordinate system and initialize the robot pose;

[0082] S2: Perform target ball placement and no-load reference point acquisition;

[0083] S3: Perform graded end-load application and synchronous acquisition of six-dimensional force;

[0084] S4: Calculate the joint torque τ of the robot, i.e., torque mapping;

[0085] S5: Under load, collect target ball displacement and calculate joint deformation δθ;

[0086] S6: Perform linear regression to fit the basic joint stiffness k.

[0087] The Leica AT403 laser tracker was used in the measurement experiment to measure joint deformation under applied load. The laser tracker is a high-precision measuring device primarily used for three-dimensional coordinate measurement and dynamic tracking in large spaces. It is equipped with high-precision horizontal and vertical angle encoders. During measurement, a laser beam is directed at a target sphere, and the distance between the instrument and the target sphere is calculated by the time or phase change of the laser's return, thus obtaining the target sphere's absolute position in space.

[0088] In this embodiment, the specific process of establishing the measurement coordinate system and initializing the robot pose in step S1 is as follows:

[0089] S11: Align and calibrate the robot's base coordinate system {B} with the world coordinate system {W} to provide a unified spatial reference for subsequent target ball position acquisition and torque mapping;

[0090] S111: Make the origin of the robot's base coordinate system {B} coincide with the origin of the world coordinate system {W}: By measuring the deviation between the two, denoted as the translation vector WtB, the subsequent compensation is carried out in the control system. The ultimate goal is to make WtB = (0,0,0)T.

[0091] S112: Align the X, Y, and Z axes of the robot's base coordinate system {B} with those of the world coordinate system {W}: calibrate the directions of the X, Y, and Z axes respectively to ensure that the axis vectors of the two coordinate systems are parallel and in the same direction, i.e., the rotation matrix is ​​the identity matrix W. RB =I;

[0092] S113: Control the robot to move to more than 3 different poses, covering the workspace range, and record the theoretical coordinates BP of the end effector under {B} and the measured coordinates WP under {W} respectively. If {B} and {W} coincide, then WP = BP is satisfied. The error should be ≤0.1mm and the angle error should be ≤0.05°.

[0093] If errors exist, they can be corrected in the following ways:

[0094] Origin error: Remeasure the deviation between {B} and {W} origin, and adjust the translation parameters in the control system;

[0095] Axial direction error: The deviation between the measured trajectory and the theoretical trajectory is fitted using the least squares method, the rotation angle correction value is calculated, the small rotations around the X / Y / Z axes are used to update the rotation matrix in the control system.

[0096] S12: Adjust each joint angle to the preset measurement pose through the robot controller, including Pose1: θ1=0°, θ2=0°, θ3=0°….

[0097] Example 2

[0098] Based on Example 1, the specific process of target ball arrangement and no-load reference point acquisition in step S2 is as follows:

[0099] S21: The target ball is rigidly bonded to the connecting rod near the joint axis to be tested, at a distance of ≤50mm from the rotation axis, in order to reduce the flexibility error of the connecting rod;

[0100] S22: Using a Leica AT403 laser tracker, continuously rotate the joint under test ±5° under no-load conditions to collect ≥20 target ball coordinate points;

[0101] S23: Obtain the unloaded rotation center by performing circle fitting using SpatialAnalyzer software. and the initial position of the target ball O1 and P1 serve as the zero-point references for calculating joint deformation.

[0102] The specific process of applying graded end loads and synchronously acquiring six-dimensional forces in step S3 is as follows:

[0103] S31: Install the load tray containing 10kg weights onto the robot end effector via the adapter flange;

[0104] S32: Load the load in four progressively increasing increments of 10kg→20kg→30kg→40kg;

[0105] S33: Under each load level, 20 seconds of data are recorded using a six-dimensional force sensor (DECENTγ200, 800Hz), and the average value is taken to obtain the six-dimensional force experienced by the end.

[0106]

[0107] Where F is used in step 4 to calculate the joint torque τ, F i This represents the six-dimensional force value at each moment, where n is the amount of data collected over a period of time. The six-dimensional force under no-load conditions is F. N The six-dimensional force under load is F. L .

[0108] Example 3

[0109] Based on Example 1 or Example 2, when an end load is applied, the increment of the joint torque can be obtained from the data of a six-dimensional force sensor using a force-Jacobi matrix. The measurement scheme for the increment of the joint torque is as follows:

[0110] When there is no load, six-dimensional force sensor data is recorded for a period of time; after applying end-effector load, six-dimensional force sensor data is recorded for more than 20 seconds. In order to gradually apply load to the robot end effector, load weights for applying the load and load trays for fixing the loads (hereinafter referred to as weights and trays) were designed.

[0111] The specific process for calculating the robot joint torque τ in step S4 is as follows:

[0112] S41: Based on the robot's current pose, call the kinematic model to calculate the force Jacobian matrix J_F (6×6);

[0113] S42: Calculate the joint torque increment using the Leyakubi matrix:

[0114] Δτ=J(θ) T (F L -F N );

[0115] Among them, the joint torque increment Δτ is paired with the deformation δθ measured in step S5 for stiffness fitting.

[0116] The specific process of acquiring target ball displacement and calculating joint deformation δθ under load in step S5 is as follows:

[0117] S51: Repeat the rotation action of step S2 (±5°) to collect the target ball trajectory under each load level;

[0118] S52: Fitting to obtain the load rotation center and the new position of the target ball

[0119] S53: Calculation of joint angle deformation based on the law of cosines:

[0120]

[0121] Or a linear approximation: Δθ≈|P2-P1| / R; where R is the radius of rotation; δθ and Δτ in step S4 form the (Δτ,δθ) dataset.

[0122] In this embodiment, the target is positioned near the axis of rotation on the connecting rod to minimize interference from rod deformation on the measurement. Multiple different poses were selected, and end loads were gradually applied. A laser tracker was used to record the absolute position of the target in space. The specific measurement scheme for measuring the joint deformation of the i-th axis is as follows: The i-th axis is rotated under no-load conditions, and the rotation center is fitted. Determine the initial position of the target under no load Apply end load and fit the center of rotation Determine the target position under loaded conditions

[0123] The effects of joint deformation;

[0124] Repeat "Apply end load, fit center of rotation" Determine the target position under loaded conditions The operation of "".

[0125] When |O1O2| is small, the joint deformation of the rotation axis under load can be calculated using the cosine theorem. This calculation method applies to joints 1 and 2 of the robot, which can be considered as having no change in rotation center since they are not affected or are minimally affected by the preceding joints. For other joints, the joint deformation caused by the load can be calculated as follows: After loading, the initial position P1 of the target changes to P1′, and the coordinates of P1′ are:

[0126] The amount of joint deformation is also given by the law of cosines:

[0127]

[0128] The purpose of this operation is to remove the influence of link and joint deformation on the i-th axis before the application of load by using a linearization method, which is applicable to the joint stiffness calculation of 3 to 6 joints of a robot.

[0129] The above measurement methods yielded multiple sets of joint deformations δθ caused by the joint torque increment Δτ. The joint stiffness q was then calculated using a linear regression method. i The mathematical model for linear regression can be expressed as:

[0130]

[0131] Where y is the dependent variable and x is the independent variable. λ0 is the intercept, λ1 is the slope, and ∈ represents the random error.

[0132] The specific process of performing linear regression fitting of the joint's basic stiffness k in step S6 is as follows:

[0133] S61: For the (Δτ, δθ) data of each load level, the linear regression equation of the joint deformation δθ caused by the joint torque increment Δτ of the i-th axis, fitted with a straight line using the least squares method, can be expressed as:

[0134]

[0135] Among them, c i It is the flexibility of the i-th axis joint, q i Let Δτ be the joint stiffness along the i-th axis, ∈ be the random error, and Δτ be the joint stiffness along the i-th axis. i δθ is the joint torque increment along the i-th axis. i It is the actual joint deformation increment value. It is the average value of the joint torque increment. It is the average value of joint deformation;

[0136] S62: After obtaining the stiffness, the coefficient of determination R^2 is used to evaluate the fitting effect of the linear regression method. The value range is [0, 1]. The calculation method of the coefficient of determination R^2 is as follows:

[0137]

[0138] RSS is the sum of squared residuals:

[0139] Where, δθ i It is the actual joint deformation increment value. Here, is the predicted joint deformation increment value of the i-th model, n is the number of samples, and TSS is the total sum of squares: It is the average value of joint deformation;

[0140] in, It is the average value of all torque increments. The closer the coefficient of determination R^2 is to 1, the better the fitting effect of the linear regression method.

[0141] S63: Output the basic stiffness q of the joint i Unit: N·mm / rad.

[0142] Table 1 shows the basic stiffness of the DR270 robot joints obtained by the above methods. The basic stiffness of joint 1 of the robot is measured because it is impossible to effectively apply a load to joint 1, and the rated power of the motor of joint 1 is the largest, and the strength of the planetary gear reducer of joint 1 is the highest. Therefore, joint 1 is considered to be rigid.

[0143] Table 1. Basic Joint Stiffness of DR270 Robot

[0144]

[0145] Elbow basic joint stiffness measurement:

[0146] Joints 1, 2, and 3 are used to determine the robot's position in space. Joints 2 and 3 are used as a measurement combination, and the spherical target (target ball) is placed near the axis of rotation.

[0147] In the workspace, the following three poses were selected as the measurement poses for applying the load. The poses of the end effector coordinate system {F} relative to the world coordinate system {W} and the robot joint angles are shown in Table 2:

[0148] Table 2 Pose of the end coordinate system {F}

[0149]

[0150] Table 3 Joint angles (°) in different poses

[0151]

[0152] When measuring the basic stiffness of the two joints, the body stiffness of the two joints and the supplementary stiffness generated by the cylinder are used as the overall stiffness of the two joints for measurement. See [link / reference] Figures 1-2 2. The coordinates of the joint target in the z-axis direction of the world coordinate system {W} and the change of joint torque increment.

[0153] 2. The deformation of the joint changes with the increment of the joint torque as follows: Figure 3 As shown, the stiffness of the 2-joint foundation was obtained by fitting using the linear regression method. The calculated stiffness of the 2-joint foundation is:

[0154] q2=3648287739.3744N·mm / rad

[0155] Coefficient of determination:

[0156] R2 =0.9679

[0157] The above calculation results show that the basic stiffness fitting effect of the two joints is good, and it can be applied to the construction of simulation models.

[0158] Three-joint foundation stiffness measurement

[0159] The coordinate changes and joint moment increments of the three-joint target along the z-axis in the world coordinate system {W} are as follows: Figure 4 and Figure 5 As shown:

[0160] Rotate the third joint within a small range (-5° to 5°), continuously measure the absolute coordinates of the target ball, and use...

[0161] The center of rotation was determined by circular fitting using SpatialAnalyzer software (hereinafter referred to as SA software). The deformation of the three joints under different loading conditions was calculated, as shown in Table 3.

[0162] Table 3. Variation of three-joint deformation with torque increment.

[0163]

[0164]

[0165] The deformation of the joint changes with the increase of the joint torque as follows: Figure 6 As shown:

[0166] The basic stiffness of the three joints was obtained by fitting using linear regression. The calculated basic stiffness of the three joints is as follows:

[0167] q3 = 2433755902.3736 N·mm / rad

[0168] Coefficient of determination:

[0169] R 2 =0.9680

[0170] The above calculation results show that the basic stiffness fitting effect of the three joints is good, and it can be applied to the construction of simulation models.

[0171] Wrist basic joint stiffness measurement:

[0172] Joints 4, 5, and 6 are used to determine the robot's end effector's posture in space. Joints 4, 5, and 6 are used as a measurement combination, and the target ball is placed near the axis of rotation.

[0173] In the workspace, the following three poses were selected as the measurement poses for applying the load. The end-effector pose and joint angles relative to the world coordinate system {W} are shown in the table:

[0174] Table 4 Flange Coordinate System {F} Position and Pose

[0175]

[0176] Table 5 Joint angles in different positions

[0177]

[0178] The coordinate changes of the joint target in the z-axis direction of the world coordinate system {B} and the changes in joint torque increments are as follows: Figure 7 and Figure 8 As shown:

[0179] 4. The deformation of the joint changes with the increment of the joint torque as follows: Figure 9 As shown:

[0180] The basic stiffness of the four joints was obtained by fitting using linear regression. The calculated basic stiffness of the four joints is as follows:

[0181] q4 = 586158574.7003 N·mm / rad

[0182] Coefficient of determination:

[0183] R 2 =0.9542;

[0184] The above calculation results show that the basic stiffness fitting effect of the four joints is good, and it can be applied to the construction of simulation models.

[0185] Five-joint foundation stiffness measurement:

[0186] In the workspace, the following three poses were selected as the measurement poses for applying the load. The end-effector pose and joint angles relative to the world coordinate system {W} are shown in Tables 6 and 7:

[0187] Table 6 Flange Coordinate System {F} Position and Pose

[0188]

[0189] Table 7 Joint angles (°) in different positions

[0190]

[0191] 5. The coordinate changes of the joint target in the z-axis direction of the world coordinate system {B} and the changes in the joint torque increment are as follows: Figure 10 and Figure 11 As shown:

[0192] 5. The deformation of the joint changes with the increment of the joint torque as follows: Figure 12 As shown:

[0193] The basic joint stiffness of the 5 joints was obtained by fitting using linear regression. The calculated basic stiffness of the 5 joints is as follows:

[0194] q5 = 356830574.4430 N·mm / rad

[0195] Coefficient of determination:

[0196] R 2 =0.9790

[0197] The calculation results show that the basic stiffness of the five joints fits well and can be applied to the construction of simulation models.

[0198] Six-joint foundation stiffness measurement

[0199] In the workspace, the following two poses were selected as the measurement poses for applying the load. The end-effector pose and joint angles relative to the world coordinate system {W} are shown in Tables 8 and 9:

[0200] Table 8 Flange Coordinate System {F} Position and Pose

[0201]

[0202] Table 9 Joint angles in different positions

[0203]

[0204] The coordinate changes and joint moment increments of the 6-joint target in the z-axis direction of the world coordinate system {B} are as follows: Figure 13 and Figure 14 As shown.

[0205] The deformation of joint 6 varies with the increase in joint torque as follows: Figure 15 As shown:

[0206] The basic joint stiffness of the 6 joints was obtained by fitting using linear regression. The calculated basic stiffness of the 6 joints is as follows:

[0207] q6 = 13897162.0482 N·mm / rad

[0208] Coefficient of determination:

[0209] R 2 =0.9566

[0210] The above calculation results show that the basic stiffness fitting effect of the six joints is good, and it can be applied to the construction of simulation models.

[0211] In summary, the robot servo joint stiffness measurement method provided by this invention ensures that subsequent steps such as target ball position acquisition and torque mapping are performed under a unified spatial reference by aligning the robot's base coordinate system with the world coordinate system. This reduces measurement errors caused by coordinate system inconsistencies and provides a reliable spatial reference for the entire measurement process. Placing the target ball near the link of the joint to be measured, at a distance of ≤50mm from the rotation axis, effectively reduces the interference of link flexibility on the measurement results. Simultaneously, by acquiring a sufficient number of coordinate points using a laser tracker and performing circle fitting, the rotation center and target ball position under no-load and loaded conditions can be accurately determined, providing high-precision basic data for joint deformation calculation.

[0212] By applying end-effector loads in a graded, incremental manner, and combining this with data collection from a six-dimensional force sensor for a sufficient duration and averaging the data, the force characteristics under different load levels can be comprehensively reflected, providing accurate input parameters for joint torque calculation. The joint torque increment is calculated based on the force-Jacobi matrix, and the joint angular deformation is obtained using the cosine theorem or linear approximation method. Then, the stiffness is fitted using linear regression with the least squares method, and the coefficient of determination is used to evaluate the fitting effect. This rigorous stiffness calculation process and reliable results provide accurate stiffness parameters for robot performance evaluation and optimization.

Claims

1. A method for measuring the stiffness of a robot servo joint, characterized in that, Includes the following steps: S1: Establish the measurement coordinate system and initialize the robot pose; S2: Perform target ball placement and no-load reference point acquisition; S3: Perform graded end-load application and synchronous acquisition of six-dimensional force; S4: Calculate the joint torque τ of the robot, i.e., torque mapping; S5: Under load, collect target ball displacement and calculate joint deformation δθ; S6: Perform linear regression to fit the basic joint stiffness k.

2. The method for measuring the stiffness of a robot servo joint according to claim 1, characterized in that, The specific process of establishing the measurement coordinate system and initializing the robot pose in step S1 is as follows: S11: Align and calibrate the robot's base coordinate system {B} with the world coordinate system {W} to provide a unified spatial reference for subsequent target ball position acquisition and torque mapping; S12: Adjust each joint angle to the preset measurement pose using the robot controller.

3. The method for measuring the stiffness of a robot servo joint according to claim 1, characterized in that, The specific process of aligning the robot's base coordinate system {B} with the world coordinate system {W} in step S11 is as follows: S111: Make the origin of the robot's base coordinate system {B} coincide with the origin of the world coordinate system {W}: By measuring the deviation between the two, denoted as the translation vector WtB, the subsequent compensation is carried out in the control system. The ultimate goal is to make WtB = (0,0,0)T. S112: Align the X, Y, and Z axes of the robot's base coordinate system {B} with those of the world coordinate system {W}: calibrate the directions of the X, Y, and Z axes respectively to ensure that the axis vectors of the two coordinate systems are parallel and in the same direction, i.e., the rotation matrix is ​​the identity matrix W. RB =I; S113: Control the robot to move to more than 3 different poses, covering the workspace range, and record the theoretical coordinates BP of the end effector under {B} and the measured coordinates WP under {W} respectively. If {B} and {W} coincide, then WP = BP is satisfied. The error should be ≤0.1mm and the angle error should be ≤0.05°. If errors exist, they can be corrected in the following ways: Origin error: Remeasure the deviation between {B} and {W} origin, and adjust the translation parameters in the control system; Axial direction error: The deviation between the measured trajectory and the theoretical trajectory is fitted using the least squares method, the rotation angle correction value is calculated, the small rotations around the X / Y / Z axes are used to update the rotation matrix in the control system.

4. The method for measuring the stiffness of a robot servo joint according to claim 1, characterized in that, The specific process of target ball placement and no-load reference point acquisition in step S2 is as follows: S21: The target ball is rigidly bonded to the connecting rod near the joint axis to be tested, at a distance of ≤50mm from the rotation axis, in order to reduce the flexibility error of the connecting rod; S22: Using a Leica AT403 laser tracker, continuously rotate the joint under test ±5° under no-load conditions to collect ≥20 target ball coordinate points; S23: Obtain the unloaded rotation center by performing circle fitting using SpatialAnalyzer software. and the initial position of the target ball O1 and P1 serve as the zero-point references for calculating joint deformation.

5. The method for measuring the stiffness of a robot servo joint according to claim 1, characterized in that, The specific process of applying graded end loads and synchronously acquiring six-dimensional forces in step S3 is as follows: S31: Install the load tray containing 10kg weights onto the robot end effector via the adapter flange; S32: Load the load in four progressively increasing increments of 10kg→20kg→30kg→40kg; S33: Under each load level, 20 seconds of data are recorded using a six-dimensional force sensor (DECENTγ200, 800Hz), and the average value is taken to obtain the six-dimensional force experienced by the end. Where F is used in step S4 to calculate the joint torque τ, F i This represents the six-dimensional force value at each moment, where n is the amount of data collected over a period of time. The six-dimensional force under no-load conditions is F. N The six-dimensional force under load is F. L .

6. The method for measuring the stiffness of a robot servo joint according to claim 1, characterized in that, The specific process for calculating the robot joint torque τ in step S4 is as follows: S41: Based on the robot's current pose, call the kinematic model to calculate the force Jacobian matrix J_F (6×6); S42: Calculate the joint torque increment: Δτ=J(θ) T (F L -F N ); Among them, the joint torque increment Δτ is paired with the deformation δθ measured in step S5 for stiffness fitting, and the six-dimensional force under no-load condition is F. N The six-dimensional force under load is F. L .

7. The method for measuring the stiffness of a robot servo joint according to claim 1, characterized in that, The specific process of acquiring target ball displacement and calculating joint deformation δθ under load in step S5 is as follows: S51: Repeat the rotation action of step S2 (±5°) to collect the target ball trajectory under each load level; S52: Fitting to obtain the load rotation center and the new position of the target ball S53: Calculation of joint angle deformation based on the law of cosines: Or a linear approximation: Δθ≈|P2-P1| / R; where R is the radius of rotation; δθ and Δτ from step S4 together form the (Δτ,δθ) dataset.

8. The method for measuring the stiffness of a robot servo joint according to claim 1, characterized in that, The specific process of performing linear regression fitting of the joint's basic stiffness k in step S6 is as follows: S61: For the (Δτ, δθ) data of each load level, the linear regression equation of the joint deformation δθ caused by the joint torque increment Δτ of the i-th axis, fitted with a straight line using the least squares method, can be expressed as: Among them, c i It is the flexibility of the i-th axis joint, q i Let τ be the joint stiffness along the i-th axis, ∈ be the random error, and Δτ be the joint stiffness along the i-th axis. i δθ is the joint torque increment along the i-th axis. i It is the actual joint deformation increment value. It is the average value of the joint torque increment. It is the average value of joint deformation; S62: After obtaining the stiffness, the coefficient of determination R^2 is used to evaluate the fitting effect of the linear regression method. The value range is [0, 1]. The calculation method of the coefficient of determination R^2 is as follows: RSS is the sum of squared residuals: Where, δθ i It is the actual joint deformation increment value. Here, is the predicted joint deformation increment value of the i-th model, n is the number of samples, and TSS is the total sum of squares: It is the average value of joint deformation; in, It is the average value of all torque increments. The closer the coefficient of determination R^2 is to 1, the better the fitting effect of the linear regression method. S63: Output the basic stiffness q of the joint i Unit: N·mm / rad.

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