A robot positioning error hierarchical calibration compensation method and system

Abstract

The application discloses a kind of robot positioning error grading calibration compensation method and system, comprising: acquisition calibration sample data, including robot end pose and joint angle;Joint is modeled as linear torsional spring, and the deformation of linear torsional spring is solved according to the relationship between robot joint pose and joint movement and mechanics, compensates calibration sample data;Robot is modeled based on Robert line representation method, establishes geometric parameter error identification model, solves geometric parameter error identification model, compensates geometric parameter error;Incomplete residual data set is obtained, and incomplete residual data set is enhanced based on information diffusion method based on sample, and residual error is predicted based on sample enhanced residual data set using machine learning algorithm based on decision tree, compensates residual error, and corrects robot end pose.The method of the application, the calibration compensation of each stage can gradually improve the positioning accuracy of robot, greatly improve the absolute positioning accuracy of robot.

Description

Technical Field

[0001] This invention belongs to the field of robot accuracy calibration technology, and more specifically, relates to a robot positioning error graded calibration and compensation method and system. Background Technology

[0002] Currently, the application of serial robots in industry continues to grow, but the low absolute pose accuracy of serial robots remains a major obstacle limiting their expansion in precision manufacturing, assembly, and measurement. Errors affecting absolute pose accuracy can be categorized into geometric errors and non-geometric errors. Geometric errors refer to the errors between the actual and nominal kinematic models caused by imperfect geometric shapes of robot structural elements, such as manufacturing tolerances, assembly errors, and positional deviations between links. Non-geometric errors refer to errors caused by joint flexibility, gear transmission errors, component wear, and temperature drift. Currently, sequential calibration of geometric and non-geometric errors is an economical and effective method for compensating for robot absolute pose accuracy, ensuring that both types of errors can be identified as completely as possible and gradually improving the robot's absolute pose accuracy.

[0003] Existing technologies for robot modeling compensate for geometric errors through parameter identification, but they do not consider non-geometric errors and hierarchical calibration. Because industrial serial robots increase load and flexibility, they exhibit significant elasticity. This increased elasticity inevitably leads to joint vibration during start-up, stopping, and movement, resulting in a substantial decrease in the robot's absolute positioning accuracy. Therefore, work without separately calibrating stiffness is incomplete. To address this issue, existing technologies first calibrate the robot's geometric errors, then calibrate the residual errors based on a spatial similarity residual error model, and finally compensate for the robot's absolute positioning accuracy. While this approach considers hierarchical calibration compensation, it does not further subdivide the residual errors into joint flexibility errors, instead broadly including joint flexibility errors within the residual errors, resulting in low accuracy.

[0004] Due to the approximation of the error calibration model, the calculation error of the iterative algorithm, and the incompleteness of the error sources and error parameters, geometric calibration compensation and joint flexibility calibration compensation alone cannot eliminate the error to the greatest extent. This invention combines geometric calibration compensation, joint flexibility calibration compensation, and residual error for calibration compensation, thereby further improving the absolute pose accuracy of the robot. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a robot positioning error classification calibration compensation method and system, which improves the absolute pose accuracy of the robot by classifying and calibrating the robot positioning error into three levels.

[0006] To achieve the above objectives, according to one aspect of the present invention, a robot positioning error classification and calibration compensation method is provided, comprising: Collect calibration sample data, including robot end-effector pose and joint angles; The joints are modeled as linear torsion springs. The deformation of the linear torsion springs is solved based on the robot's joint pose and the relationship between joint motion and mechanics. The joint angles of the calibration sample data are then compensated. The robot is modeled using the Robert line representation method to obtain the robot's forward kinematics model. Based on the robot's forward kinematics model, the relationship between geometric parameter error and pose error is determined, a geometric parameter error identification model is established, the geometric parameter error identification model is solved, and geometric parameter errors are compensated. An incomplete residual dataset is obtained, and sample augmentation is performed on the incomplete residual dataset based on the information diffusion method. Based on the sample augmentation, a decision tree-based machine learning algorithm is used to predict the residuals, compensate for the residual errors, and correct the robot end-effector pose.

[0007] Furthermore, the step of modeling the joint as a linear torsion spring includes:

[0008] in, and These are matrices representing the differences in joint angle deformation and torque acting on the joint before and after joint rotation, respectively. It is a diagonal matrix composed of the elastic coefficients of each joint.

[0009] Furthermore, the step of calculating the deformation of the linear torsion spring based on the robot's joint pose and the relationship between joint motion and mechanics, and compensating for the joint angles in the calibration sample data, includes: Measure the actual joint angles corresponding to any two different theoretical joint angles, and take the difference between the actual joint angle difference and the theoretical joint angle difference to obtain the joint angle deformation difference for any two different poses. Based on the relationship between joint motion and mechanics, the joint torque in any pose is determined, and the joint torque difference corresponding to the joint angle deformation difference matrix between any two different poses is obtained. The elastic coefficient matrix of the joint can be obtained by considering the difference in joint angle deformation between any two different poses and the corresponding difference in joint torque.

[0010] Furthermore, the step of calculating the deformation of the linear torsion spring based on the robot's joint pose and the relationship between joint motion and mechanics, and compensating for the joint angles in the calibration sample data, further includes: The joint torque of the joint angle to be compensated is obtained based on the robot end pose and joint angle of the calibration sample data. The difference between the torque of the joint angle to be compensated and the 0-degree joint angle is the joint torque of the joint angle to be compensated. The joint angle deformation difference of the joint angle to be compensated is obtained based on the torque difference between the joint angle to be compensated and the 0-degree joint angle, the elastic coefficient matrix of the joint, and the linear torsion spring. The sum of the joint angle and the joint angle deformation difference in the calibration sample data is the compensated joint angle.

[0011] Furthermore, the robot is modeled based on the Robert line representation to obtain the robot's forward kinematics model, including: Using Robert's line notation, additional parameters are added to the robot's end effector link to obtain the transformation between two adjacent links:

[0012] Q i It is a motion matrix that separates joint variables from link parameters. For a rotary joint, Qi = Rot(z, θ) i ) represents a rotation θ around the i-th joint axis z. i For a moving joint, Qi = Trans(0,0, d i ) represents movement d along the i-th joint axis z. i V i It is a shape matrix specified by fixed link parameters, depending on the i-th joint variable. V i This represents the rotation angle of the i-th coordinate system around its own x, y, and z axes, respectively. Then move a distance along the x, y, and z axes of its own coordinate system, respectively. , where T is the matrix transpose.

[0013] The robot's forward kinematics model is obtained based on the transformation of two adjacent links:

[0014] Where i = 0, ..., n+1 are the indices of the base coordinate system {B} and the tool coordinate system {t1}, respectively.

[0015] Furthermore, the step of determining the relationship between geometric parameter errors and pose errors based on the robot's forward kinematics model and establishing a geometric parameter error identification model includes: The linear correlation between the cumulative pose error of the base coordinate system and the errors of various geometric parameters of the link is determined based on the robot's forward kinematics model. Based on the linear correlation between the cumulative pose error and the errors of various geometric parameters of the link, a geometric parameter error identification model is established:

[0016] Where J is the distance from ∆q to Jacobian transformation matrix, It represents the measured pose error, and T is the matrix transpose.

[0017] Furthermore, the solution of the geometric parameter error identification model and the compensation of geometric parameter errors include: The pose error is obtained from the actual measured pose and the nominal pose in the base coordinate system. Based on the pose error, the least squares solution method is used to solve the geometric parameter error identification model to obtain the kinematic parameter error; Geometric parameter errors are compensated based on kinematic parameter errors and nominal kinematic parameters.

[0018] Furthermore, the step of obtaining the incomplete residual dataset and performing sample augmentation on the incomplete residual dataset based on the information diffusion method includes: Incomplete residual datasets were obtained using a random sampling method:

[0019] in, This represents the k-th sample pair. This represents the sequence of joint angles, where 1 to n are the indices of the joints. This represents the positional error of the tool coordinate system {t1} in the x, y, z directions; k is the number of samples, k = 1, ..., s; s is the maximum sample size; Based on the diffusion function ℓ, the information diffusion method is used to augment the incomplete residual dataset, resulting in an augmented dataset:

[0020] Among them, diag ∨ (•) indicates that a diagonal matrix is ​​vectorized into a 1×n row vector. Represents the Kronecker product. Represents the Hadamard product, I n×1 Let μ be an n×1 unit column vector. Γ Let Γ be the membership function of the fuzzy set Γ of X, and let Σθ and ΣD be the diagonal matrices of the diffusion coefficients with respect to θ and D, respectively. , Let θ be the right and left biases. , The right and left biases of D are defined as follows: In this invention, the ratio of the number of left and right samples to the total number of samples characterizes asymmetric diffusion, i.e., left and right bias. It is the square root; Based on the augmented dataset, a decision tree-based machine learning algorithm is used to train the residual estimation model to predict the residuals; The robot end-effector pose is corrected based on the residual sample data.

[0021] Furthermore, the loss function of the decision tree-based machine learning algorithm is:

[0022] in, Let represent the (t-1)th cumulative model. Let h(θ) represent the t-th cumulative model. i ) represents the new decision tree, θ is the set of joint angle data, θ i For the joint angle data of the i-th different sample pair.

[0023] A robot positioning error classification and calibration compensation system includes: The first main module is used to collect calibration sample data, including robot end-effector pose and joint angles; The second main module is used to model the joints as linear torsion springs, solve the deformation of the linear torsion springs based on the robot's joint pose and the relationship between joint motion and mechanics, and compensate for the joint angles in the calibration sample data. The third main module is used to model the robot based on the Robert line representation method, obtain the robot's forward kinematics model, determine the relationship between geometric parameter errors and pose errors based on the robot's forward kinematics model, establish a geometric parameter error identification model, solve the geometric parameter error identification model, and compensate for geometric parameter errors. The fourth main module is used to acquire incomplete residual datasets, perform sample augmentation on the incomplete residual datasets based on the information diffusion method, and use a decision tree-based machine learning algorithm to predict residuals, compensate for residual errors, and correct the robot end pose of the sample data based on the sample augmented incomplete residual datasets.

[0024] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: 1. The robot positioning error hierarchical calibration and compensation method of the present invention accurately divides the robot's absolute positioning error into joint flexibility error, geometric parameter error, and residual non-geometric error (i.e., residual). By sequentially calibrating and compensating the joint flexibility error, geometric parameter error, and residual, each level of calibration and compensation can gradually improve the robot's positioning accuracy. In particular, the residual non-geometric error calibration after joint flexibility error calibration and geometric error calibration can reduce the error by nearly half, greatly improving the robot's absolute positioning accuracy.

[0025] 2. The robot positioning error classification and calibration compensation method of the present invention, based on information diffusion technology, proposes a new model-free residual calibration method, which solves the problems of uneven distribution of randomly collected data samples, which makes it difficult to cover the real distribution space, resulting in the mapping relationship not being able to effectively explain the real sample space, thus leading to problems such as getting trapped in local optima and overfitting. Attached Figure Description

[0026] Figure 1 This is a flowchart of the robot positioning error classification and calibration compensation method according to an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the theoretical poses and actual joint angle deformations of the present invention. Figure 3 This is a schematic diagram of the multi-parallel-axis robot structure and joint loading according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the calibration of a multi-parallel-axis robot according to an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the effect of joint flexibility error calibration in an embodiment of the present invention. Detailed Implementation

[0027] 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.

[0028] In the description of this invention, unless otherwise explicitly specified and limited, the terms "connected," "linked," and "fixed" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0029] Those skilled in the art will understand that, unless otherwise stated, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the word “comprising” as used in the specification of this application means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or combinations thereof.

[0030] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as in the embodiments of this application.

[0031] The robot positioning error classification and calibration compensation method provided by this invention is used for robot absolute accuracy positioning and can be applied to robot automated production, processing, grinding, handling and other technical fields.

[0032] like Figure 1 The diagram shown is a flowchart of the robot positioning error classification calibration and compensation method provided in an embodiment of the present invention. The robot positioning error classification calibration and compensation method of the present invention specifically includes steps S100 to S400.

[0033] Step S100: Collect calibration sample data, including robot end-effector pose and joint angles; A certain number of robot end-effector positions and random end-effector postures within a small range are randomly generated in the workspace, along with their corresponding joint angles. The obtained joint angles differ from the actual joint angles due to the flexible deformation of the joints and links caused by the weight of the links and external loads. The flexible deformation of the joints and links caused by the weight of the links and external loads is usually called joint flexibility error. It is coupled with kinematic parameters, thus affecting the accuracy of geometric calibration. Therefore, joint flexibility calibration compensation is required. Specifically, joint flexibility calibration compensation is for the error of joint angle deformation.

[0034] Step S200: Model the joint as a linear torsion spring, solve the deformation of the linear torsion spring based on the robot joint pose and the relationship between joint motion and mechanics, and compensate for the joint angle of the calibration sample data; Specifically, this invention proposes an equivalent joint stiffness method to solve for the compensation value of the joint angle. The joint torque and deformation of a robot joint are different at different angles, but the joint stiffness remains unchanged within a certain range.

[0035] In an embodiment of the present invention, the joint is modeled as a linear torsion spring, including:

[0036] in, and These are matrices representing the differences in joint angle deformation and torque acting on the joint before and after joint rotation, respectively. It is a diagonal matrix composed of the elastic coefficients of each joint.

[0037] Since the deformation is quite small, the joint stiffness within this range can be considered a constant value. Therefore, the joint is modeled as a linear torsional spring. For the diagonal matrix of the elastic coefficients of each joint, the elastic coefficient of the joint, as the reciprocal of the joint stiffness, is also a constant value. By solving the diagonal matrix of the elastic coefficients of each joint, it can be used for joint flexibility calibration compensation.

[0038] Specifically, the deformation of the linear torsion spring is calculated based on the robot's joint pose and the relationship between joint motion and mechanics, and the joint angles of the calibration sample data are compensated, including: Step S201: Measure the actual joint angles corresponding to any two different theoretical joint angles, and take the difference between the actual joint angle difference and the theoretical joint angle difference to obtain the joint angle deformation difference for any two different poses. Specifically, the difference in joint angle deformation can be obtained by subtracting the theoretical joint angle difference from the actual joint angle difference between the two configurations, such as... Figure 2 As shown, Φ1 and Φ2 represent the deformation of the joint at positions 1 and 2 due to its own weight, the weight of the subsequent connecting rod, and the external load, respectively. 理论 Φ represents the theoretical angle of rotation of the connecting rod relative to this joint axis. 实际 This indicates the actual angle of rotation of the connecting rod relative to the axis of this joint. Φ3 represents the angle value shared by the theoretical angle of rotation of the connecting rod and the actual angle of rotation of the connecting rod.

[0039] The difference in joint angle deformation between the two configurations can be obtained by subtracting the theoretical angle of rotation from the actual angle of rotation of the connecting rod.

[0040] It can be seen that the joint angle deformation ΔΦ of the same joint under different postures can be obtained by subtracting the theoretical joint angle change from the actual joint angle change.

[0041] In an optional embodiment of the present invention, the theoretical change in joint angle is the difference between two selected angle values, and the actual change in joint angle can be obtained by angle measurement. For example, the actual change in joint angle is obtained by measuring the angle between the joint axes using a laser tracker.

[0042] Step S202: Determine the joint torque in any pose based on the relationship between joint motion and mechanics, and obtain the joint torque difference corresponding to the joint angle deformation difference matrix of any two different poses; Specifically, for each joint, the resultant torque generated by the weight of the subsequent link and the external load at this joint axis will change with the robot's pose. The joint torque at this point can be calculated using the method described above.

[0043] Let the position of the center of mass of the k-th link in the {k} joint coordinate system be . Then the position of the centroid of the k-th link in coordinate {i} It can be represented as

[0044] In the formula, It is the rotation transformation matrix of the {k} coordinate system relative to the {i} coordinate system.

[0045] Next, we transform the gravitational acceleration to the {i} coordinate system. The gravitational acceleration in the base coordinate system is known to be...

[0046] By multiplying by the rotation transformation matrix of the base coordinate system relative to the {i} coordinate system, the representation of gravitational acceleration in the {i} coordinate system is obtained.

[0047] Then the weight of the k-th link in the {i} coordinate system for

[0048] In the formula, m k Let K be the mass of the connecting rod.

[0049] Since the robot's joints are revolute joints, they can only rotate along the Z-axis. Therefore, it is necessary to multiply the spatial torque by a unit vector along the Z-axis. At this point, we obtain the torque generated by link k at the axis of joint i.

[0050] The resultant torque at the axis of joint i is

[0051] In the formula, Let {i} be the position of the centroid of the end load in coordinate {i}. Let be the gravity of the end load in the {i} coordinate system.

[0052] After determining the moments of the joint at two different configurations, the difference in moments between the two configurations can be calculated. .

[0053] Step S203: Obtain the joint elastic coefficient matrix based on the joint angle deformation difference between any two different poses and their corresponding joint torque difference.

[0054] Specifically, the step of calculating the deformation of the linear torsion spring based on the robot joint pose and the relationship between joint motion and mechanics, and compensating for the joint angles in the calibration sample data, further includes: Step S204: Obtain the joint torque of the joint angle to be compensated based on the robot end pose and joint angle of the calibration sample data. The difference between the torque of the joint angle to be compensated and the 0-degree joint angle is the joint torque of the joint angle to be compensated. Step S205: Obtain the joint angle deformation difference of the joint angle to be compensated based on the torque difference between the joint angle to be compensated and the 0-degree joint angle, the elastic coefficient matrix of the joint, and the linear torsion spring; the sum of the joint angle and the joint angle deformation difference of the calibration sample data is the compensated joint angle.

[0055] When a joint is at 0 degrees, the joint deformation is zero, and the joint torque it experiences is also zero. Therefore, to compensate for the joint angle error at any angle, we need to calculate the joint's elastic coefficient beforehand, and then calculate the joint torque at any angle. Subtracting the zero torque at 0 degrees from this torque gives us the torque difference. Substituting the torque difference and the joint's elastic coefficient into the formula for a linear torsion spring gives us the joint deformation at that angle (i.e., the joint angle error). The sum of the joint angle in the calibrated sample data and the joint angle deformation difference is the compensated joint angle.

[0056] In another embodiment of the present invention, by establishing a model of the joint angle deformation difference, torque difference and joint equivalent stiffness acting on the joint before and after joint rotation, the joint equivalent stiffness is solved, and joint flexibility error compensation is performed by the method of the above embodiment.

[0057] For each joint, the resultant torque generated by the weight of the subsequent link and the external load at this joint axis varies with the robot's pose. The joint torque at this point can be calculated using the method described above. After solving for the torques at two different poses, the torque difference between the two poses can be determined. If the difference in the joint angle deformation between the two poses is known, the equivalent stiffness of the joint can be calculated.

[0058] Because the joint torque and deformation of a robot joint vary at different angles, but within a certain range, the joint stiffness k remains constant. Furthermore, at 0 degrees, the joint deformation and torque are both zero. Therefore, to compensate for the joint angle error at any angle, we need to calculate the joint stiffness k beforehand, then calculate the joint torque at any angle. Subtracting the zero torque at 0 degrees from this torque gives us the torque difference. Substituting this torque difference and stiffness k into the established model of the joint angle deformation difference, torque difference, and equivalent joint stiffness before and after joint rotation yields the joint deformation at that angle (i.e., the joint angle error).

[0059] Step S300: Model the robot based on the Robert line representation method to obtain the robot's forward kinematics model. Based on the robot's forward kinematics model, determine the relationship between geometric parameter error and pose error, establish a geometric parameter error identification model, solve the geometric parameter error identification model, and compensate for the geometric parameter error. Specifically, step S300 includes steps S301 to S302.

[0060] Step S301: Using Robert's line notation, add an additional parameter γ to the robot's end effector link. n and This yields the transformation of two adjacent links:

[0061] Where Qi is the motion matrix that separates joint variables from link parameters. For a rotary joint, Qi = Rot(z, θ) i ) represents a rotation θ around the i-th joint axis z. i For a moving joint, Qi = Trans(0,0, d i ) represents movement d along the i-th joint axis z. i V i It is a shape matrix specified by fixed link parameters, depending on the i-th joint variable. V i This represents the rotation angle of the i-th coordinate system around its own x, y, and z axes, respectively. Then move a distance along the x, y, and z axes of its own coordinate system, respectively. .

[0062] The robot positioning error classification and calibration compensation method of this invention is particularly suitable for multi-parallel-axis robots, such as multi-parallel-axis robots with 6 rotary joints. Figure 3 As shown, joints 2, 3, and 4 are parallel to each other, while joints 4 and 5 are perpendicular to each other. Traditional kinematic modeling methods, such as the DH model, are prone to singularity and numerical instability. The embodiment of this invention uses the Robert line representation, which adds two parameters at the end link. This allows the variational joint parameters to be separated from other fixed link parameters, ensuring the continuity and integrity of the parameters.

[0063] Step S302: Obtain the robot's forward kinematics model based on the transformation of two adjacent links:

[0064] Where i = 0, ..., n+1 are the indices of the base coordinate system {B} and the tool coordinate system {t1}, respectively.

[0065] In addition, the additional parameter γ of the last linkn and (where n is a variable representing the nth joint or link) This allows for further unification of the end-effector installation error {t1} with the robot's geometric error for i = 1,…, n−1,γ i = 0, l i ,z = 0. Thus, the robot's forward kinematics model is derived from the base coordinate system {B} to the tool coordinate system {t1}.

[0066] In the current coordinate system, the directional error δ of the i-th link is... i =[ δ i,x δ i,y δ i,z ] T and position error d i = [d i, x d i,y d i,z ] T Its angular kinematic parameter error ∆σ i =[∆α i ∆β i ∆γ i ] T and position kinematic parameters ∆L i =[∆l i,x ∆l i,y ∆l i,z ] T They exhibit a linear correlation, which can be expressed as:

[0067] Where k i Here is the error rotation matrix.

[0068] Therefore, the cumulative pose error in the base coordinate system {B} The error ∆q of each geometric parameter of the connecting rod is linearly correlated.

[0069] Furthermore, the step of determining the relationship between geometric parameter errors and pose errors based on the robot's forward kinematics model and establishing a geometric parameter error identification model includes: Step S303: Determine the linear correlation between the cumulative pose error of the base coordinate system and the errors of each geometric parameter of the link based on the robot's forward kinematics model; Step S304: Based on the linear correlation between the cumulative pose error and the errors of each geometric parameter of the link, establish a geometric parameter error identification model:

[0070] Where J is the distance from ∆q to Jacobian transformation matrix, It represents the measured pose error, and T is the matrix transpose.

[0071] Furthermore, the solution of the geometric parameter error identification model and the compensation of geometric parameter errors include: Step S305: Obtain the pose error based on the actual measured pose and nominal pose in the base coordinate system; Step S306: Based on the pose error, the least squares solution method is used to solve the geometric parameter error identification model to obtain the kinematic parameter error; Step S307: Compensate for geometric parameter errors based on kinematic parameter errors and nominal kinematic parameters.

[0072] Specifically, the geometric calibration process can be described as follows: under positive kinematics conditions, by measuring the actual pose of {t1} and subtracting its nominal pose, the pose error is obtained. Then, the kinematic parameter errors are calculated using the geometric parameter error identification model, and the nominal kinematic parameters are compensated accordingly. Robot calibration, for example... Figure 4 As shown.

[0073] Specifically, the actual pose can be measured by a laser tracker. The nominal pose and nominal kinematic parameters are input values ​​and are known quantities. The nominal pose is calculated through the kinematic model and joint angle theory, and the nominal kinematic parameters are the kinematic parameters of the corresponding robot model, which are obtained from the data of the corresponding robot model.

[0074] After the geometric parameter error and joint flexibility error calibration are completed, the remaining residual errors are mainly caused by lubrication, temperature changes and transmission errors, which can be further eliminated by the model-free method.

[0075] Step S400: Obtain the incomplete residual dataset, perform sample augmentation on the incomplete residual dataset based on the information diffusion method, and use a decision tree-based machine learning algorithm to predict the residuals based on the sample-augmented incomplete residual dataset, compensate for residual errors, and correct the robot end pose of the sample data.

[0076] Specifically, step S400 includes steps S401 to S403.

[0077] Step S401: Obtain the incomplete residual dataset using a random sampling method.

[0078] in, This represents the k-th sample pair. This represents the sequence of joint angles, where 1 to n are the indices of the joints. This represents the positional error of the tool coordinate system {t1} in the x, y, z directions; k is the number of samples, k = 1, ..., s; s is the maximum sample size; Step S402: Based on the diffusion function ℓ, the information diffusion method is used to augment the incomplete residual dataset to obtain the augmented dataset:

[0079] Among them, diag ∨ (•) indicates that a diagonal matrix is ​​vectorized into a 1×n row vector. Represents the Kronecker product. Represents the Hadamard product, I n×1 Let μ be an n×1 unit column vector. Γ Let Γ be the membership function of the fuzzy set Γ of X, and let Σθ and ΣD be the diagonal matrices of the diffusion coefficients with respect to θ and D, respectively. , Let θ be the right and left biases. , The right and left biases of D are defined as follows: In this invention, the ratio of the number of left and right samples to the total number of samples characterizes asymmetric diffusion, i.e., left and right bias. It is the square root; Specifically, the original dataset undergoes information diffusion processing to make it closer to the real sample space, thereby making the diffusion estimation more closely resemble the true relationships. Furthermore, this invention employs the diffusion function ℓ to achieve sample augmentation, which can improve the accuracy of residual estimation.

[0080] Step S403: Based on the augmented dataset, a decision tree-based machine learning algorithm is used to train the residual estimation model and predict the residuals; Step S404: Calibrate the robot end-effector pose based on the residual compensation sample data.

[0081] Specifically, the sum of the residual and the robot end-effector pose of the sample data is the result after robot end-effector pose compensation.

[0082] The new augmented dataset DS(X) can be represented as

[0083] Where μ Γ (θ) = μ Γ (D), abbreviated as μ Γ The subscripts (1,…,g) are used to distinguish between different membership values.

[0084] Specifically, randomly collected data samples are unevenly distributed and cannot accurately cover the true distribution space. This results in the mapping relationship F failing to effectively explain the true sample space, leading to problems such as getting trapped in local optima and overfitting, particularly affecting the accurate estimation of residuals. The method of this invention, based on information diffusion technology, proposes a novel model-free residual calibration method to solve the above problems. Information diffusion processing is applied to the original dataset to make it closer to the true sample space, thereby making the diffusion estimation closer to the true relationship.

[0085] Specifically, the loss function of the decision tree-based machine learning algorithm is:

[0086] in, Let represent the (t-1)th cumulative model. Let h(θ) represent the t-th cumulative model. i ) represents the new decision tree, θ is the set of joint angle data, θ i For the joint angle data of the i-th different sample pair.

[0087] To verify the feasibility of this invention, an experiment was conducted using the UR10 robot as the subject.

[0088] First, the stiffness coefficients of each joint of the robot were calculated using the stiffness calibration method. Eighty robot end-effector positions and a small range of random end-effector poses were generated randomly in the workspace, and joint flexibility calibration compensation was performed on all corresponding joint angles. Next, 20 sets of data were randomly selected for geometric parameter calibration, and the remaining 60 sets of data were then compensated for geometric parameters. From the compensated 60 sets of data, 42 sets were randomly selected to calculate residual errors, perform data diffusion, and train the estimation model. Finally, the remaining 18 sets of data were used to identify and compensate for residual non-geometric errors (i.e., residual errors). The calibration and compensation results are as follows: Figure 5 As shown.

[0089] The implementation of the various embodiments of the present invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention can be encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a robot positioning error grading calibration and compensation system, which is used to execute a robot positioning error grading calibration and compensation method from the above method embodiments. The system includes: The first main module is used to collect calibration sample data, including robot end-effector pose and joint angles; The second main module is used to model the joints as linear torsion springs, solve the deformation of the linear torsion springs based on the robot's joint pose and the relationship between joint motion and mechanics, and compensate for the joint angles in the calibration sample data. The third main module is used to model the robot based on the Robert line representation method, obtain the robot's forward kinematics model, determine the relationship between geometric parameter errors and pose errors based on the robot's forward kinematics model, establish a geometric parameter error identification model, solve the geometric parameter error identification model, and compensate for geometric parameter errors. The fourth main module is used to acquire incomplete residual datasets, perform sample augmentation on the incomplete residual datasets based on the information diffusion method, and use a decision tree-based machine learning algorithm to predict residuals based on the sample augmented incomplete residual datasets to compensate for the robot end pose of the calibration sample data.

[0090] It should be noted that the apparatus in the system embodiments provided by the present invention can be used not only to implement the methods in the above method embodiments, but also to implement the methods in other method embodiments provided by the present invention. The only difference is that corresponding functional modules are set. Its principle is basically the same as that of the above system embodiments provided by the present invention. As long as those skilled in the art can improve the apparatus in the above system embodiments by referring to the specific technical solutions in other method embodiments and combining technical features to obtain corresponding technical means and technical solutions composed of these technical means, on the basis of the above system embodiments, and on the premise of ensuring the practicality of the technical solutions, they can obtain corresponding system-like embodiments for implementing the methods in other method-like embodiments.

[0091] The methods in the embodiments of the present invention are implemented using electronic devices; therefore, it is necessary to describe the relevant electronic devices. For this purpose, embodiments of the present invention provide an electronic device comprising: at least one processor, a communication interface, at least one memory, and a communication bus, wherein the at least one processor, the communication interface, and the at least one memory communicate with each other via the communication bus. The at least one processor can invoke logical instructions in the at least one memory to execute all or part of the steps of the methods provided in the foregoing method embodiments.

[0092] Furthermore, when the logical instructions in at least one of the aforementioned memories can be implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various method embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0093] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0094] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0095] 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 hierarchical calibration and compensation of robot positioning errors, characterized in that, include: Collect calibration sample data, including robot end-effector pose and joint angles; The robot is modeled using the Robert line representation to obtain the robot's forward kinematics model; The joints are modeled as linear torsion springs. The deformation of the linear torsion springs is solved based on the robot's forward kinematics model and the relationship between joint motion and mechanics. The joint angles in the calibration sample data are then corrected. Based on the robot's forward kinematics model, the relationship between geometric parameter error and pose error is determined, a geometric parameter error identification model is established, the geometric parameter error identification model is solved, and geometric parameter error is compensated. An incomplete residual dataset is obtained, and sample augmentation is performed on the incomplete residual dataset based on the information diffusion method. Based on the sample augmentation residual dataset, a decision tree-based machine learning algorithm is used to predict the residuals, compensate for residual errors, and correct the robot end pose. The process of determining the relationship between geometric parameter errors and pose errors based on the robot's forward kinematics model, and establishing a geometric parameter error identification model, includes: The linear correlation between the cumulative pose error of the base coordinate system and the errors of various geometric parameters of the link is determined based on the robot's forward kinematics model. Based on the linear correlation between the cumulative pose error and the errors of various geometric parameters of the link, a geometric parameter error identification model is established: ； Where J is the distance from ∆q to Jacobian transformation matrix, It is the measured pose error, and T is the matrix transpose; The solution to the geometric parameter error identification model, which compensates for geometric parameter errors, includes: The pose error is obtained from the actual measured pose and the nominal pose in the base coordinate system. Based on the pose error, the least squares solution method is used to solve the geometric parameter error identification model to obtain the kinematic parameter error; The compensated geometric parameters are obtained based on the kinematic parameter error and the nominal kinematic parameters; The process of obtaining the incomplete residual dataset and performing sample augmentation on the incomplete residual dataset based on the information diffusion method includes: Incomplete residual datasets were obtained using a random sampling method: ； in, This represents the k-th sample pair. This represents the sequence of joint angles, where 1 to n are the indices of the joints. This represents the positional error of the tool coordinate system {t1} in the x, y, z directions; k is the number of samples, k = 1, ..., s, and S is the maximum sample value; Based on the diffusion function ℓ, the information diffusion method is used to augment the incomplete residual dataset, resulting in an augmented dataset: ; Among them, diag ∨ (•) indicates that a diagonal matrix is ​​vectorized into a 1×n row vector. Represents the Kronecker product. I represents the Hadamard product. n×1 Let μ be an n×1 unit column vector. Γ Let Γ be the membership function of the fuzzy set Γ of X, and let Σθ and ΣD be the diagonal matrices of the diffusion coefficients with respect to θ and D, respectively. , Let θ be the right and left biases. , , where are the right and left offsets of D. It is the square root; Based on the augmented dataset, a decision tree-based machine learning algorithm is used to train the residual estimation model to predict the residuals; The robot end-effector pose in the residual compensation calibration sample data is determined.

2. The robot positioning error classification and calibration compensation method according to claim 1, characterized in that, The robot modeling based on the Robert line representation, resulting in the robot's forward kinematics model, includes: Using Robert's line notation, additional parameters are added to the robot's end effector link to obtain the transformation between two adjacent links: ； Where Qi is the motion matrix that separates joint variables from link parameters, and Vi is the shape matrix specified by fixed link parameters. For a rotary joint, , , This indicates rotation around the x, y, z axes of the i-th joint. , , , This represents the distance moved along the x, y, and z axes of its own coordinate system, respectively. T is the matrix transpose. The robot's forward kinematics model is obtained based on the transformation of two adjacent links: 。 3. The robot positioning error classification and calibration compensation method according to claim 1, characterized in that, The method of modeling the joint as a linear torsion spring includes: ； in, and These are matrices representing the differences in joint angle deformation and torque acting on the joint before and after joint rotation, respectively. It is a diagonal matrix composed of the elastic coefficients of each joint.

4. The robot positioning error classification and calibration compensation method according to claim 3, characterized in that, Based on the robot's forward kinematics model and the relationship between joint motion and mechanics, the deformation of the linear torsion spring is calculated, and the joint angles in the calibration sample data are corrected, including: Measure the actual joint angles corresponding to any two different theoretical joint angles, and take the difference between the actual joint angle difference and the theoretical joint angle difference to obtain the joint angle deformation difference for any two different poses. Based on the positive kinematics model and the relationship between joint motion and mechanics, the joint torque in any pose is determined, and the joint torque difference corresponding to the joint angle deformation difference matrix between any two different poses is obtained. The elastic coefficient matrix of the joint can be obtained by considering the difference in joint angle deformation between any two different poses and the corresponding difference in joint torque.

5. The robot positioning error classification and calibration compensation method according to claim 4, characterized in that, Based on the robot's forward kinematics model and the relationship between joint motion and mechanics, the deformation of the linear torsion spring is calculated, and the joint angles in the calibration sample data are corrected. This also includes: The joint torque of the joint angle to be compensated is obtained from the robot joint angle and positive kinematics in the calibration sample data. The difference between the torque of the joint angle to be compensated and the 0-degree joint angle is the joint torque of the joint angle to be compensated. The joint angle deformation difference of the joint angle to be compensated is obtained based on the torque difference between the joint angle to be compensated and the 0-degree joint angle, the elastic coefficient matrix of the joint, and the linear torsion spring. The sum of the joint angle and the joint angle deformation difference in the calibration sample data is the compensated joint angle.

6. The robot positioning error classification and calibration compensation method according to claim 1, characterized in that, The loss function of the decision tree-based machine learning algorithm is: ； in, Let represent the (t-1)th cumulative model. Let h(θ) represent the t-th cumulative model. i ) represents the new decision tree, θ is the set of joint angle data, θ i For the joint angle data of the i-th different sample pair.

7. A robot positioning error hierarchical calibration and compensation system, used to implement the method as described in any one of claims 1-6, characterized in that, include: The first main module is used to collect calibration sample data, including the robot's end-effector pose and joint angles; The second main module is used to model the robot based on the Robert line representation method to obtain the robot's forward kinematics model. Based on the robot's forward kinematics model and the relationship between joint motion and mechanics, the deformation of the linear torsion spring is solved, and the joint angles in the calibration sample data are corrected. The third main module determines the relationship between geometric parameter error and pose error based on the robot's forward kinematics model, establishes a geometric parameter error identification model, solves the geometric parameter error identification model, and compensates for geometric parameter error. The fourth main module is used to acquire incomplete residual datasets, perform sample augmentation on the incomplete residual datasets based on the information diffusion method, and use a decision tree-based machine learning algorithm to predict residuals, compensate for residual errors, and correct the robot end-effector pose based on the sample augmented residual datasets.

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