Robot connecting rod mass and mass center serial calibration method

Abstract

The invention discloses a robot connecting rod mass and centroid serial calibration method, and relates to the technical field of robot kinetic parameter calibration, the connecting rod mass is decomposed into an XY plane component and a Z-axis component, and a parameter space is simplified by using symmetric mass distribution characteristics; then, through the joint friction force compensation and gravitational torque balance principle, the equivalent mass and the mass center polar coordinates of all the connecting rods in a local coordinate system are sequentially and reversely solved from the tail end connecting rod, and accurate calibration of all the connecting rod parameters can be completed only by utilizing robot body joint torque sensor data and combining a serial recursive algorithm; the method has the advantages that a complex dismounting and measuring process is avoided, the calibration efficiency is remarkably improved, the reliability of parameter identification is guaranteed through theoretical constraint, and the method is suitable for rapid calibration and regular maintenance of an industrial robot production line and has important application value in the aspect of improving the robot motion control precision.

Description

Technical Field

[0001] The present invention relates to the technical field of robot dynamic parameter calibration, and particularly to a serial calibration method for the mass and centroid of robot links. Background Art

[0002] Currently, the field of robot dynamic parameter calibration mainly faces two major technical bottlenecks: on the one hand, traditional overall identification methods such as system identification techniques based on excitation trajectories and least squares have serious parameter coupling problems. Not only do they require complex multi-joint coordinated motion, but they are also prone to generating ill-conditioned equations, resulting in an exponential increase in computational complexity with the degree of freedom. Moreover, they have strict requirements for the motion space and are difficult to implement in restricted environments. On the other hand, direct measurement methods such as disassembly weighing and three-dimensional coordinate measurement have inherent defects such as damaging the integrity of the robot, being unable to obtain assembly-state parameters, and having high equipment costs. Existing calibration theories generally ignore the non-uniform mass distribution characteristics and the precise processing of the Z-axis component, making it difficult to effectively decouple friction compensation and gravity moment calculation, seriously restricting the calibration accuracy and engineering applicability. Therefore, it is particularly important to invent a serial calibration method for the mass and centroid of robot links.

[0003] The prior art has the following defects, specifically manifested as: 1. In the prior art, the overall identification method relies on complex multi-joint coordinated motion, and the parameters of each joint are interrelated and interact with each other, making it extremely easy to generate ill-conditioned equations during parameter calculation, resulting in the continuous amplification of small errors during the calculation process, leading to deviations or even errors in the calculation results. As the degree of freedom of the robot increases, the computational complexity shows an exponential growth, posing extremely high requirements for computing resources and also significantly prolonging the calculation time.

[0004] 2. In the prior art, direct measurement methods have defects such as damaging the integrity of the robot, being unable to obtain assembly-state parameters, and having high equipment costs. Existing calibration theories ignore the non-uniform mass distribution characteristics and the precise processing of the Z-axis component, making it difficult to effectively decouple friction compensation and gravity moment calculation, restricting the calibration accuracy and engineering applicability. At the same time, in actual engineering, the single calibration takes a long time, the existing calibration methods for new structures fail, the identification method based on genetic algorithms has a slow convergence speed and poor repeated accuracy, and the vision-assisted scheme is limited by the installation accuracy of the marking points and cannot meet the requirements of modern precision operations for micron-level accuracy. Summary of the Invention

[0005] The purpose of the present invention is to provide a serial calibration method for the mass and centroid of robot links, which solves the problems existing in the background art.

[0006] To solve the above technical problems, the present invention adopts the following technical solutions: The present invention provides a serial calibration method for the mass and centroid of a robot link, including: Step S1: Establish a robot DH coordinate system and a kinematic model, and define the geometric parameters of the link.

[0007] Step S2: Based on the non-uniform mass decomposition theory, decompose the mass of each link into XY plane components and Z-axis components.

[0008] Step S3: Collect torque data through forward and reverse joint movements, calculate the friction force of each joint, and perform compensation.

[0009] Step S4: Starting from the 6th axis, use the principle of gravity moment balance to construct a parameter identification equation set.

[0010] Step S5: Use the reverse recursive method to sequentially solve the equivalent mass and centroid polar coordinates of the 5th axis to the 2nd axis.

[0011] Step S6: Write the identification results into the robot control system to complete the update of dynamic parameters.

[0012] Preferably, the specific implementation method of the step S1 is: Establish a coordinate system for each joint, where the Z-axis is along the joint rotation axis direction, the X-axis is along the common perpendicular direction of adjacent Z-axes, and the Y-axis is determined by the right-hand rule. After establishing the coordinate system, fill in the link parameter table containing four key parameters of α i-1 , a i-1 , d i , θ i . Among them, α i-1 represents the angle of rotation around the X i-1 axis from Z i-1 to Z i , a i-1 represents the distance along the X i-1 axis from Z i-1 to Z i , d i represents the distance along the Z i axis from X i-1 to X i , θ i represents the angle of rotation around the Z i axis from X i-1 to X i . Through the transformation relationship between adjacent coordinate systems, obtain each transformation matrix, and the continuous multiplication of each transformation matrix gives the position and attitude of the robot end effector relative to the base.

[0013] Preferably, the transformation relationship between adjacent coordinate systems includes:

[0014] is the homogeneous transformation matrix between adjacent coordinate systems, which includes two parts: rotation and translation. The rotation part involves a rotation of θ around the Z-axis i and a rotation of α around the X-axis i-1 , and the translation part includes d along the Z-axis i and a along the X-axis i-1 , where i - 1 represents the reference coordinate system and i represents the target coordinate system. This matrix describes the pure rotation transformation relationship from the (i - 1)-th link coordinate system to the i-th link coordinate system, which is achieved through the composition of two basic rotations: first, rotate by an angle of θ around the Z-axis of the current coordinate system i and then rotate by an angle of α around the X-axis of the new coordinate system i-1 .

[0015] represents the position vector of the origin from the (i - 1)-th link coordinate system to the i-th link coordinate system. Here, the superscript i - 1 represents the reference coordinate system, and the subscript ORGi emphasizes that this is the position description of the origin of the coordinate system. Among them, a i-1 represents the link length along the X i-1 axis, d i represents the link offset along the Z i axis, and α i-1 represents the twist angle between two adjacent joint axes

[0016] represents the inverse rotation transformation from the i-th link coordinate system to the (i - 1)-th link coordinate system. Here, the superscript i represents the source coordinate system, and the subscript i - 1 represents the target coordinate system. It is the inverse matrix of the standard DH forward rotation matrix. According to the orthogonal property of the rotation matrix, its specific form is to interchange the rows and columns of the original matrix while keeping the signs of the rotation angles unchanged. The matrix elements contain both the joint variable θ i and the link fixed parameter α i-1 . Among them, θ i reflects the real-time rotation state of the joint, while α i-1 is determined by the mechanical structure. The construction principle of this matrix is based on the mathematical description of the rotation of a rigid body in three-dimensional space. The first column represents the direction cosine of the original X i axis in the (i - 1) coordinate system, the second column corresponds to the Y i axis, and the third column corresponds to the Z i axis

[0017] It represents the position vector of the origin of the i-th link coordinate system in its own coordinate system, which is a special zero-position calibration parameter. Here, the superscript i represents the reference coordinate system, and the subscript ORGi emphasizes that this is a description of the position of the origin of the coordinate system. Its construction principle stems from the inverse kinematics derivation of the DH parameter method. Its physical meaning can be understood as follows: When looking back at the position of its origin from the i-th link coordinate system, the geometric parameters of the previous link and the influence of the current joint angle need to be considered. Specifically, the X-axis component is -a i-1 cosθ i It reflects the projection of the length of the previous link along the reverse direction of the current X i axis, and the Y-axis component is a i-1 *sinθ i which reflects the modulation of the joint rotation angle θ i on the lateral position, and the Z-axis component is -d i which directly represents the link offset along the negative direction of the Z i axis.

[0018] Preferably, for the step S2, the specific implementation method is: decompose the mass distribution characteristics of each link into an asymmetric component and a symmetric component around its joint axis. The symmetric part makes no contribution to the joint driving torque and is equivalently merged into the previous link. Through mathematical transformation, the asymmetric mass component is further decomposed into XY components parallel to the motion plane and Z components perpendicular to the motion plane. The formula for decomposing the asymmetric mass is: r1 = r2 + Δr, where r1 is the original centroid position vector, r2 is the component in the XY plane, and Δr is the Z-axis component.

[0019] Preferably, for the step S3, the specific implementation method is: each joint performs forward and reverse movements near three different positions. The torque data is collected through the dedicated program obtainTorqueByOppositeMove.m. The friction force is calculated by the difference in torque between the forward and reverse movements. The specific formula is: Friction force = (Forward torque - Reverse torque) / 2. Take the average of the results measured at the three positions to obtain the friction force characteristics of each joint. After obtaining the friction force data, subtract the friction force component from the total measured torque to obtain the torque value purely caused by gravity.

[0020] Preferably, the specific implementation method of step S4 is as follows: Adopt a reverse recursive strategy from the end to the base. Starting from the 6th axis, when the robot remains stationary, the joint torque is completely caused by the gravity of the connecting rod. By changing the joint angle, multiple gravity moment balance equations are established to solve the unknown mass parameters. Uncomment the code segment corresponding to axisObser = 6, and at the same time keep the code segments of other axes in the commented state. In the program, taus represents the torque values at three different positions recorded on the observation axis, thetas represents the corresponding joint angles, and qvec represents the position combination of all joints during measurement. By the principle of gravity moment balance, a system of equations about the mass of the connecting rod and the polar coordinate angle of the center of mass position is established, and solving the system of equations can obtain the equivalent mass mass_t of the 6th connecting rod and the polar coordinate angle theta0 of the center of mass in the XY plane, and fill the obtained parameters into the corresponding fields of the linkDPara structure.

[0021] Preferably, the specific implementation method of step S5 is as follows: Adopt a reverse chain recursive algorithm. After calibrating the parameters of the 6th axis at the end, comment out the code segments of the completed axes and uncomment the code segments of the currently to-be-identified axis. The identification of each axis uses the torque data at three different positions, and a system of equations is established through the gravity moment balance for solution. Substitute the parameters determined in the previous axis as known quantities into the system of equations of the current axis. After each successful identification, fill the results, namely mass_t and theta0, into the corresponding positions of the linkDPara structure. The mass field stores the mass value, and the belta field stores the polar coordinate angle.

[0022] Preferably, the specific implementation method of step S6 is as follows: Organize and convert the mass of each connecting rod, the polar coordinate angle of the center of mass in the XY plane, and the Z-axis coordinate included in the linkDPara structure according to the format required by the control system, and update them into the dynamic model of the robot. Let the robot perform various typical actions, observe the consistency between the actual joint torque and the model prediction value, and perform parameter fine-tuning.

[0023] The beneficial effects of the present invention are as follows: 1. In the present invention, through the non-uniform mass decomposition theory, the problems of the existing calibration theory's insufficient handling of non-uniform mass distribution characteristics and Z-axis components are solved, and the coupling between friction compensation and gravity moment calculation is avoided; combined with the recursive identification method, the complex multi-joint coordinated motion in the traditional overall identification is abandoned, the problem of ill-conditioned equations caused by parameter coupling is eliminated, the calibration accuracy of mass and center of mass parameters is significantly improved, a more accurate dynamic model is constructed, and the calculation complexity is reduced.

[0024] 2. In the present invention, a reverse recursive strategy from the end to the base is adopted to simplify the three-dimensional parameter identification into a two-dimensional plane problem, breaking through the harsh requirements of traditional methods for the motion space; no disassembly measurement is required, avoiding damage to the integrity of the robot, significantly reducing the equipment cost and implementation difficulty, enabling calibration to be completed in a conventional working environment, applicable to various robot scenarios; the modular design and standardized process support regular repeated calibration to meet the long-term maintenance needs of the robot, and the optimized dynamic parameters significantly improve the robot control performance, meeting the high-precision force control application requirements in high-end fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0026] Figure 1 It is a schematic flow chart of the implementation steps of the method of the present invention.

[0027] Figure 2 It is the DH coordinate system of the method of the present invention.

[0028] Figure 3 It is the friction force identification result of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0030] Referring to Figure 1 as shown, the present invention provides a serial calibration method for the mass and centroid of a robot link, including:

[0031] Step S1: Establish the DH coordinate system and kinematic model of the robot, and define the link geometric parameters.

[0032] In a specific embodiment, the specific implementation method of the step S1 is: establish a coordinate system for each joint, where the Z-axis is along the joint rotation axis direction, the X-axis is along the common perpendicular direction of adjacent Z-axes, and the Y-axis is determined by the right-hand rule. After establishing the coordinate system, fill in the values including α i-1 , a i-1 , d i , θ iLink parameter table of four key parameters, where α i-1 represents the angle of rotation from Z i-1 to Z i-1 about the X i axis, a i-1 represents the distance from Z i-1 to Z i-1 along the X i axis, d i represents the distance from X i to X i-1 along the Z i axis, θ i represents the angle of rotation from X i to X i-1 about the Z i axis. By obtaining the transformation matrices between adjacent coordinate systems and multiplying these transformation matrices together, the position and orientation of the robot's end effector relative to the base can be obtained.

[0033] It should be noted that in robot kinematic modeling, the Denavit-Hartenberg (DH) method is the standard method for establishing link coordinate systems and defining geometric parameters. In this way, the relative position and orientation relationships between the links can be clearly described. These parameters completely define the geometric structure of the robot and are the basis for subsequent kinematic and dynamic analyses.

[0034] Table 1 Example of DH parameters for a typical 6-axis robot

[0035]

[0036] In a specific embodiment, the transformation relationship between adjacent coordinate systems includes:

[0037] is the homogeneous transformation matrix between adjacent coordinate systems, which includes both rotation and translation parts. The rotation part involves rotating by an angle θ i about the Z axis and rotating by an angle α i-1 about the X axis. The translation part includes d i along the Z axis and a i-1 along the X axis. i - 1 represents the reference coordinate system, and i represents the target coordinate system. This matrix describes the pure rotation transformation relationship from the (i - 1)-th link coordinate system to the i-th link coordinate system, which is achieved through the composition of two basic rotations: first, rotate by an angle θ i about the Z axis of the current coordinate system, and then rotate by an angle α i-1 about the X axis of the new coordinate system.

[0038] It should be noted that this 3×3 matrix strictly follows the convention of the Denavit-Hartenberg (DH) parameter method. By separating the rotation and translation amounts, it is specifically optimized for the requirements of mass center calibration.

[0039] represents the origin position vector from the (i - 1)-th link coordinate system to the i-th link coordinate system. Here, the superscript i - 1 represents the reference coordinate system, and the subscript ORGi emphasizes that this is the position description of the origin of the coordinate system, where a i-1 represents the link length along the X i-1 axis, and d i represents the link offset along the Z i axis. Among them, α i-1 represents the twist angle between two adjacent joint axes.

[0040] It should be noted that the special form of this 3×1 translation vector stems from the coordinate system setting rules of the DH parameter method: when establishing the i-th coordinate system, it is necessary to first translate along the X i-1 axis by a i-1 , then rotate around the X i-1 axis by an angle of α i-1 , and finally translate along the new Z i axis by d i . The combined result of these three basic transformations forms this position vector. In mass center calibration, the core role of this vector is to work together with the formula to jointly construct the complete coordinate system transformation relationship, specifically for: 1) calculating the absolute position of the origin of each link coordinate system in the base coordinate system, which is the basis for determining the length of the gravity arm; 2) when used in combination with the rotation matrix, the complete homogeneous transformation matrix can be deduced; 3) when establishing the dynamic equation, this vector is required to determine the relative position relationship between each link. Since the document adopts the processing method of separating rotation and translation, this translation vector is specifically responsible for processing position information, with a clear division of labor from the rotation matrix, which not only maintains theoretical rigor but also facilitates practical programming implementation.

[0041] represents the inverse rotation transformation from the i-th link coordinate system to the (i - 1)-th link coordinate system. Here, the superscript i represents the source coordinate system, and the subscript i - 1 represents the target coordinate system. It is the inverse matrix of the standard DH forward rotation matrix. According to the orthogonal characteristics of the rotation matrix, its specific form is to interchange the rows and columns of the original matrix while keeping the sign of the rotation angle unchanged. The matrix elements contain both the joint variable θ i and the link fixed parameter α i-1 . Among them, θ i reflects the real-time rotation state of the joint, while α i-1Determined by the mechanical structure, the construction principle of this matrix is based on the mathematical description of the rigid body rotation in three-dimensional space. The first column represents the direction cosine of the original X-axis in the i-1 coordinate system, the second column corresponds to the Y-axis, and the third column corresponds to the Z-axis. i axis in the i-1 coordinate system, the second column corresponds to the Y i axis, and the third column corresponds to the Z i axis.

[0042] It should be noted that in the mass and centroid calibration, the core role of this inverse rotation matrix is reflected in three aspects: First, it converts the gravity vector measured in the base coordinate system into components in each link coordinate system, which is a prerequisite for calculating the gravity moment; Second, when establishing the dynamic equation, it is needed to handle the force and moment transfer between coordinate systems; Finally, when it is necessary to map the force / moment of the end effector to each joint space, this matrix constitutes a key part of the Jacobian matrix derivation. Compared with the forward rotation matrix, the inverse rotation matrix is more commonly used in application scenarios such as sensor data processing and force control, and its accuracy directly affects the accuracy of parameter calibration and control.

[0043] represents the position vector of the origin of the i-th link coordinate system in its own coordinate system, which is a special zero-position calibration parameter. The superscript i represents the reference coordinate system, and the subscript ORGi emphasizes that this is a description of the origin position of the coordinate system. The construction principle stems from the inverse kinematics derivation of the DH parameter method. Its physical meaning can be understood as: when looking back at the origin position from the i-th link coordinate system, it is necessary to consider the geometric parameters of the previous link and the influence of the current joint angle. Specifically, the X-axis component -a i-1 cosθ i reflects the projection of the length of the previous link along the reverse direction of the current X i axis, the Y-axis component a i-1 *sinθ i reflects the modulation of the lateral position by the joint rotation angle θ i , and the Z-axis component -d i directly represents the link offset along the negative direction of the Z i axis.

[0044] It should be noted that in the mass and centroid calibration, the main uses of this vector include: 1) When establishing the inverse kinematics equation, it is used to calculate the "self-view" position of the origin of the coordinate system in its own coordinate system; 2) In the closed-loop control algorithm, it is used to assist in calculating the differential term of the Jacobian matrix; 3) When it is necessary to trace the sensor data from the end coordinate system to the base coordinate system, it serves as a key parameter for position transformation.

[0045] Step S2: Based on the non-uniform mass decomposition theory, decompose the mass of each link into XY-plane components and Z-axis components.

[0046] In a specific embodiment, the specific implementation method of step S2 is as follows: Decompose the mass distribution characteristics of each link into an asymmetric component and a symmetric component around its joint axis. The symmetric part does not contribute to the joint driving torque and is equivalently merged into the previous link. Through mathematical transformation, the asymmetric mass component is further decomposed into XY components parallel to the motion plane and Z components perpendicular to the motion plane. The formula for decomposing the asymmetric mass is: r1 = r2 + Δr, where r1 is the original centroid position vector, r2 is the component in the XY plane, and Δr is the Z-axis component.

[0047] It should be noted that the physical meaning of this decomposition is that the mass component in the Z-axis direction does not cause a change in the gravitational torque during joint rotation. Therefore, it can be incorporated into the mass parameters of the previous link, and only the mass distribution in the XY plane needs to be considered. This decomposition method simplifies the complexity of parameter identification, transforming the mass distribution problem in three-dimensional space into a two-dimensional plane problem. In actual operation, this means that we only need to identify the equivalent mass and centroid position of each link in the XY plane without considering the influence in the Z-axis direction. This theoretical breakthrough makes the subsequent serial calibration method possible and lays a theoretical foundation for the parameter identification in steps S4 and S5.

[0048] Step S3: Collect torque data by the forward and reverse movement of the joints, calculate the friction force of each joint, and perform compensation.

[0049] In a specific embodiment, the specific implementation method of step S3 is as follows: Each joint performs forward and reverse movement near three different positions. The torque data is collected through the dedicated program obtainTorqueByOppositeMove.m, and the friction force is calculated by the torque difference between the forward and reverse movements. The specific formula is: Friction force = (Forward torque - Reverse torque) / 2. Take the average value of the results measured at the three positions. Refer to Figure 3 , and the friction force characteristics of each joint can be obtained. After obtaining the friction force data, subtract the friction force component from the total measured torque to obtain the torque value purely caused by gravity.

[0050] It should be noted that the accuracy of this step directly affects the accuracy of subsequent parameter identification. Therefore, special attention needs to be paid to the control of the movement speed and the selection of the measurement position to ensure the acquisition of representative friction force data.

[0051] Step S4: Starting from the 6th axis, construct a parameter identification equation set using the principle of gravitational torque balance.

[0052] In a specific embodiment, the specific implementation method of step S4 is as follows: Adopt a reverse recursive strategy from the end to the base. Starting from the 6th axis, when the robot remains stationary, the joint torque is completely caused by the gravity of the connecting rod. By changing the joint angles, establish multiple gravity moment balance equations to solve the unknown mass parameters. Uncomment the code segment corresponding to axisObser = 6, and at the same time keep the code segments of other axes in the commented state. In the program, taus represents the torque values recorded at three different positions on the observation axis, thetas represents the corresponding joint angles, and qvec represents the position combination of all joints during measurement. By the principle of gravity moment balance, establish a system of equations about the mass of the connecting rod and the polar coordinate angle of the center of mass in the XY plane. As shown in the program IdentificationMassVector.m, solving the system of equations can obtain the equivalent mass mass_t of the 6th connecting rod and the polar coordinate angle theta0 of the center of mass in the XY plane, and fill the obtained parameters into the corresponding fields of the linkDPara structure.

[0053] It should be noted that taus represents the torque values recorded at three different positions on the observation axis, and the friction has been deducted; the key to this step lies in the reasonable selection of the measurement position and the correct construction of the system of equations to ensure that the problem is solvable and the solution is unique.

[0054] Step S5: Solve the equivalent mass and the polar coordinates of the center of mass of the 5th axis to the 2nd axis in turn by using the reverse recursive method.

[0055] In a specific embodiment, the specific implementation method of step S5 is as follows: Adopt the reverse chain recursive algorithm. After the parameter calibration of the 6th axis at the end is completed, comment out the code segments of the completed axes and uncomment the code segments of the current axis to be identified. For example, when identifying the 5th axis, four lines of code starting from axisObser = 5 need to be uncommented, and at the same time keep the code segments of other axes in the commented state. The identification of each axis uses the torque data at three different positions, establishes a system of equations through the gravity moment balance to solve, substitutes the parameters determined in the previous axis as known quantities into the system of equations of the current axis. After each successful identification, fill the results, that is, mass_t and theta0, into the corresponding positions of the linkDPara structure. The mass field stores the mass value, and the belta field stores the polar coordinate angle.

[0056] It should be noted that this recursive method from the end to the base makes full use of the characteristics of the robot structure, decomposes the complex multi-parameter identification problem into a series of single-parameter identification problems, greatly simplifies the calibration process, and the whole process needs to be carried out strictly in sequence to ensure that the parameters of each axis are based on the accurate results of the subsequent identified axes.

[0057] Step S6: Write the identification results into the robot control system to complete the update of the dynamic parameters.

[0058] In a specific embodiment, the specific implementation method of step S6 is as follows: The mass of each connecting rod, the polar coordinate angle of the center of mass in the XY plane, and the Z-axis coordinate (z field, with a theoretical value of 0) included in the linkDPara structure are sorted and converted in the format required by the control system, and updated into the dynamic model of the robot. Then, let the robot perform various typical actions, observe the consistency between the actual joint torque and the model prediction value, and perform parameter fine-tuning.

[0059] It should be noted that the completion of this step marks the end of the entire mass center calibration process, and the obtained parameters will be directly used to improve the motion control accuracy and dynamic performance of the robot. Since the working environment and mechanical structure may change over time, it is recommended to repeat the calibration process regularly to ensure the accuracy of the parameters, especially after the robot has undergone major repairs or long-term operation. The entire calibration scheme realizes the high-precision identification of the dynamic parameters of the robot through systematic theoretical derivation and rigorous experimental steps, laying a solid foundation for subsequent advanced control applications.

[0060] The above content is only an example and illustration of the concept of the present invention. Those skilled in the art of this technology can make various modifications, supplements, or use similar methods to replace the described specific embodiments, as long as they do not deviate from the concept of the invention or exceed the scope defined by the present invention, they should all fall within the protection scope of the present invention.

Claims

1. A serial calibration method for the mass and centroid of a robot link, characterized in that, Including: Step S1: Establish the DH coordinate system and kinematic model of the robot, and define the geometric parameters of the connecting rods; Step S2: Based on the non-uniform mass decomposition theory, decompose the mass of each connecting rod into XY plane components and Z-axis components; Step S3: Collect torque data through forward and reverse joint motions, calculate the friction force of each joint, and perform compensation; Step S4: Starting from the 6th axis, construct a parameter identification equation set using the principle of gravity moment balance; Step S5: Use the reverse recursive method to solve the equivalent mass and centroid polar coordinates of the 5th axis to the 2nd axis in sequence; Step S6: Write the identification result into the robot control system to complete the update of dynamic parameters.

2. The serial calibration method for the mass and centroid of a robot link according to claim 1, characterized in that, The specific implementation method of the said Step S1 is: Establish a coordinate system for each joint, where the Z-axis is along the direction of the joint rotation axis, the X-axis is along the common perpendicular direction of adjacent Z-axes, and the Y-axis is determined by the right-hand rule. After establishing the coordinate system, fill in the link parameter table containing the four key parameters of α i-1 , a i-1 , d i , θ i . The α i-1 represents the angle of rotation from Z i-1 to Z i-1 around the X i axis, a i-1 represents the distance from Z i-1 to Z i-1 along the X i axis, d i represents the distance from X i to X i-1 along the Z i axis, and θ i represents the angle of rotation from X i to X i-1 around the Z i axis. The transformation matrices are obtained through the transformation relationships between adjacent coordinate systems, and the product of the transformation matrices gives the position and orientation of the robot end effector relative to the base.

3. A serial calibration method for the mass and centroid of a robot link according to claim 2, characterized in that The transformation relationship between the adjacent coordinate systems includes: It is the homogeneous transformation matrix between adjacent coordinate systems, which includes two parts: rotation and translation. The rotation part involves rotating by θ around the Z-axis i and rotating by α around the X-axis i-1 . The translation part includes d along the Z-axis i and a along the X-axis i-1 . i - 1 represents the reference coordinate system, and i represents the target coordinate system. This matrix describes the pure rotation transformation relationship from the (i - 1)-th link coordinate system to the i-th link coordinate system, which is achieved through the composition of two basic rotations: first, rotate by θ around the Z-axis of the current coordinate system i angle, and then rotate by α around the X-axis of the new coordinate system i-1 angle; denotes the origin position vector from the (i - 1)-th link coordinate system to the i-th link coordinate system, where the superscript i - 1 represents the reference coordinate system, and the subscript ORGi emphasizes that this is the position description of the origin of the coordinate system, where a i-1 denotes the link length along the X i-1 axis, and d i denotes the link offset along the Z i axis, where α i-1 denotes the twist angle between two adjacent joint axes; Represents the inverse rotation transformation from the $i$-th link coordinate system to the $(i - 1)$-th link coordinate system. Here, the superscript $i$ represents the source coordinate system, and the subscript $i - 1$ represents the target coordinate system. It is the inverse matrix of the standard DH forward rotation matrix. According to the orthogonality property of the rotation matrix, its specific form is to interchange the rows and columns of the original matrix while keeping the sign of the rotation angle unchanged. The matrix elements contain the joint variable $\theta$ i and the link fixed parameter $\alpha$ i-1 , where $\theta$ i reflects the real-time rotation state of the joint, while $\alpha$ i-1 is determined by the mechanical structure. The construction principle of this matrix is based on the mathematical description of rigid body rotation in three-dimensional space. The first column represents the direction cosines of the original $X$ i axis in the $(i - 1)$-coordinate system, the second column corresponds to the $Y$ i axis, and the third column corresponds to the $Z$ i axis; Represents the position vector of the origin of the i-th link coordinate system in its own coordinate system, which is a special zero-position calibration parameter. Here, the superscript i represents the reference coordinate system, and the subscript ORGi emphasizes that this is a description of the origin position of the coordinate system. Its construction principle stems from the inverse kinematics derivation of the DH parameter method. Its physical meaning can be understood as follows: When looking back at the origin position from the i-th link coordinate system, the geometric parameters of the previous link and the influence of the current joint angle need to be considered. Specifically, the X-axis component is -a i-1 cosθ i reflects the projection of the length of the previous link along the reverse direction of the current X i axis, and the Y-axis component is a i-1 *sinθ i which reflects the modulation of the joint rotation angle θ i on the lateral position, and the Z-axis component is -d i directly represents the link offset along the negative direction of the Z i axis.

4. A serial calibration method for the mass and centroid of a robot link according to claim 3, characterized in that The specific implementation method of the said Step S2 is: Decompose the mass distribution characteristics of each connecting rod into an asymmetric component and a symmetric component around its joint axis. The symmetric part has no contribution to the joint driving torque and is equivalently merged into the previous connecting rod. Through mathematical transformation, the asymmetric mass component is further decomposed into XY components parallel to the motion plane and Z components perpendicular to the motion plane. The formula for decomposing the asymmetric mass is: r1 = r2 + Δr, where r1 is the original centroid position vector, r2 is the component in the XY plane, and Δr is the Z-axis component.

5. A serial calibration method for the mass and centroid of a robot link according to claim 1, characterized in that, The specific implementation method of the said Step S3 is: Each joint performs forward and reverse motions near three different positions. Collect torque data through the dedicated program obtainTorqueByOppositeMove.m. Calculate the friction force through the torque difference between forward and reverse motions. The specific formula is: Friction force = (Forward torque - Reverse torque) / 2. Take the average of the results measured at the three positions to obtain the friction force characteristics of each joint. After obtaining the friction force data, deduct the friction force component from the total measured torque to obtain the torque value purely caused by gravity.

6. A serial calibration method for the mass and centroid of a robot link according to claim 5, characterized in that, The specific implementation method of the said Step S4 is: Adopt a reverse recursive strategy from the end to the base. Starting from the 6th axis, when the robot remains stationary, the joint torque is completely caused by the gravity of the connecting rods. By changing the joint angles, establish multiple gravity moment balance equations to solve the unknown mass parameters. Uncomment the code segment corresponding to axisObser = 6, and at the same time keep the code segments of other axes in the commented state. In the program, taus represents the torque values at three different positions recorded on the observation axis, thetas represents the corresponding joint angles, and qvec represents the position combination of all joints during measurement. Through the principle of gravity moment balance, establish an equation set about the mass of the connecting rod and the centroid position, and solve the equation set to obtain the equivalent mass mass_t of the 6th connecting rod and the polar coordinate angle theta0 of the centroid in the XY plane, and fill the obtained parameters into the corresponding fields of the linkDPara structure.

7. A serial calibration method for the mass and centroid of a robot link according to claim 6, characterized in that, The specific implementation method of the said Step S5 is: Using the reverse chaining recursive algorithm, after calibrating the parameters of the 6th axis at the end, comment out the code segment of the completed axis, uncomment the code segment of the current axis to be identified. The identification of each axis utilizes the torque data at three different positions, and a system of equations is established and solved through gravity moment balance. The parameters determined for the previous axis are substituted as known quantities into the system of equations for the current axis. After each successful identification, the results, namely mass_t and theta0, are filled into the corresponding positions of the linkDPara structure. The mass field stores the mass value, and the belta field stores the polar coordinate angle.

8. A serial calibration method for the mass and centroid of a robot link according to claim 7, characterized in that, The specific implementation method of step S6 is as follows: Sort and convert the mass, the polar coordinate angle of the center of mass in the XY plane, and the Z-axis coordinate of each link contained in the linkDPara structure according to the format required by the control system, and update them into the dynamic model of the robot. Let the robot perform various typical actions, observe the consistency between the actual joint torque and the model prediction value, and perform parameter fine-tuning.

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