Two-step hybrid robot kinematics calibration method and device

Abstract

The invention relates to the technical field of robot calibration, in particular to a two-step hybrid robot kinematics calibration method and device.The method comprises the steps that a first geometric error model used in first-step identification is established, the first geometric error model is used for conducting iteration identification on errors, and a first identification error of a hybrid robot is obtained; and a second geometric error model used in the second-step identification is established, the second geometric error model is used for carrying out single-time error identification, a second identification error of the hybrid robot is obtained, the sum of the first identification error and the second identification error is obtained, a final identification error of the hybrid robot is obtained, and calibration of the kinematics of the hybrid robot is carried out. Therefore, the problem that an existing calibration method is low in precision and efficiency due to the complex structure of the hybrid robot is solved.

Description

Technical Field

[0001] This application relates to the technical field of robot calibration, and particularly to a kinematic calibration method and device for a two-step hybrid robot. Background Art

[0002] In the related art, hybrid robots combine the advantages of serial robots and parallel robots and are widely used in fields such as friction welding, cutting machining, and automatic spraying. Kinematic calibration is an effective method to improve the accuracy of robots, and kinematic calibration includes steps such as error modeling, measurement, parameter identification, and error compensation.

[0003] However, hybrid robots have a closed-loop structure and passive joints. There are passive errors that vary with the robot pose and redundant errors coupled with other errors in their error models, and there are also error constraint relationships in special structures such as over-constrained structures. Therefore, existing calibration methods have problems of low accuracy and efficiency and urgently need to be improved. Summary of the Invention

[0004] This application provides a kinematic calibration method and device for a two-step hybrid robot to solve the problems of low accuracy and efficiency of existing calibration methods due to the complex structure of hybrid robots.

[0005] The first aspect of the embodiments of this application provides a kinematic calibration method for a two-step hybrid robot, including the following steps: establishing a first geometric error model used in the first identification to iteratively identify errors using the first geometric error model to obtain the first identification error of the hybrid robot; establishing a second geometric error model used in the second identification to singly identify errors using the second geometric error model to obtain the second identification error of the hybrid robot; summing the first identification error and the second identification error to obtain the final identification error of the hybrid robot for calibrating the kinematics of the hybrid robot.

[0006] Through the above technical solution, the embodiments of this application can use a simplified serial robot model for rapid first identification to obtain the first identification error; then perform accurate second identification based on the complete hybrid robot model to obtain the second identification error. By summing the two, the overall identification error of the hybrid robot is finally obtained. This method combines the advantages of rapidity and high precision, not only improving the efficiency of kinematic calibration but also enhancing the accuracy and stability of the identification result, providing an effective solution for improving the accuracy of hybrid robots.

[0007] Optionally, in an embodiment of this application, the expression of the first geometric error model is:

[0008] δ E =J I (pI ) δp I

[0009] where p I is the error considered in the first - step identification; J I (p I ) is the first - step identification matrix; δ E is the difference between the calculated value and the measured value of the end - effector position in the same coordinate system.

[0010] Through the above technical solution, the embodiment of the present application can effectively quantify the difference between the calculated value and the measured value of the end - effector position by introducing the relationship between the first identification matrix and the error.

[0011] Optionally, in an embodiment of the present application, the using the first geometric error model to iteratively identify the error to obtain the first identification error of the hybrid robot includes: simplifying the hybrid robot into a serial robot to obtain the forward kinematic solution of the serial robot; obtaining the relationship between the parameter perturbation and the end - effector position according to the forward kinematic solution; obtaining the first identification matrix according to the relationship between the parameter perturbation and the end - effector position, substituting it into a preset iterative formula until the iteration converges, and obtaining the first identification error.

[0012] Through the above technical solution, the embodiment of the present application can simplify the hybrid robot into a serial robot, establish the relationship between the parameter perturbation and the end - effector position through the forward kinematic solution, and then continuously correct the error through the iterative formula until convergence. This improves the speed and efficiency of identification, simplifies the complex error modeling process, and makes the kinematic calibration of the hybrid robot more accurate and economical.

[0013] Optionally, in an embodiment of the present application, the establishing the second geometric error model used in the second - step identification includes: performing geometric error modeling on the parallel part to obtain the error model of the parallel part; after incorporating the serial part into the error model of the parallel part, obtaining the second geometric error model according to the forward kinematic model and in combination with the first geometric error model.

[0014] Through the above technical solution, when the embodiment of the present application establishes the second geometric error model used in the second - step identification, it first performs separate geometric error modeling on the parallel part, which can focus on the complex structural characteristics of the parallel part, accurately analyze its error situation, and obtain a targeted error model of the parallel part. Subsequently, the serial part is incorporated into this model, and in combination with the forward kinematic model and the first geometric error model, the second geometric error model is made more comprehensive and accurate. This step - by - step construction and integration method not only fully considers the respective error characteristics of the parallel part and the serial part of the hybrid robot, but also combines the advantages of different models, and can more accurately reflect the overall error situation of the robot.

[0015] Optionally, in an embodiment of the present application, the expression of the second geometric error model is as follows:

[0016] δ E = J II (p II )δp II

[0017] where p II is the error considered in the second-step identification; J II (p II ) is the second-step identification matrix; δ E is the difference between the calculated value and the measured value of the end position in the same coordinate system.

[0018] Through the above technical solution, the embodiment of the present application can directly analyze and process specific error factors through the second geometric error model, and use the mapping effect of the second-step identification matrix on the error to accurately locate and evaluate its impact on the end position accuracy.

[0019] An embodiment of the second aspect of the present application provides a kinematic calibration device for a two-step hybrid robot, including: a first identification module, configured to establish a first geometric error model used in the first-step identification, so as to iteratively identify errors using the first geometric error model to obtain a first identification error of the hybrid robot; a second identification module, configured to establish a second geometric error model used in the second-step identification, so as to perform single identification of errors using the second geometric error model to obtain a second identification error of the hybrid robot; a calibration module, configured to sum the first identification error and the second identification error to obtain a final identification error of the hybrid robot, so as to perform kinematic calibration of the hybrid robot.

[0020] Through the above technical solution, the embodiment of the present application can use a simplified serial robot model to perform rapid first-step identification to obtain a first identification error; then perform accurate second-step identification based on the complete hybrid robot model to obtain a second identification error. By summing the two, the overall identification error of the hybrid robot is finally obtained. This method combines the advantages of speed and high precision, not only improving the efficiency of kinematic calibration, but also enhancing the accuracy and stability of the identification results, providing an effective solution for improving the accuracy of hybrid robots.

[0021] Optionally, in an embodiment of the present application, the first identification module includes: the expression of the first geometric error model is as follows:

[0022] δ E = J I (p I )δp I

[0023] where p I is the error considered in the first-step identification; J I (p I ) is the first-step identification matrix; δ E is the difference between the calculated value and the measured value of the end position in the same coordinate system.

[0024] Through the above technical solution, the embodiment of the present application can effectively quantify the difference between the calculated value and the measured value of the end position by introducing the relationship between the first identification matrix and the error.

[0025] Optionally, in an embodiment of the present application, the first identification module includes: a simplification unit for simplifying the hybrid robot into a serial robot to obtain the forward kinematic solution of the serial robot; a solution unit for obtaining the relationship between the parameter perturbation and the end position according to the forward kinematic solution; an iteration unit for obtaining the first identification matrix according to the relationship between the parameter perturbation and the end position, substituting it into a preset iteration formula until the iteration converges, and obtaining the first identification error.

[0026] Through the above technical solution, the embodiment of the present application can simplify the hybrid robot into a serial robot, establish the relationship between the parameter perturbation and the end position through the forward kinematic solution, and then continuously correct the error through the iteration formula until convergence. This improves the speed and efficiency of identification, simplifies the complex error modeling process, and makes the kinematic calibration of the hybrid robot more accurate and economical.

[0027] Optionally, in an embodiment of the present application, the second identification module includes: a parallel modeling unit for performing geometric error modeling on the parallel part to obtain an error model of the parallel part; a combined modeling unit for incorporating the serial part into the error model of the parallel part and obtaining the second geometric error model according to the forward kinematic model and in combination with the first geometric error model.

[0028] Through the above technical solution, when establishing the second geometric error model used in the second-step identification in the embodiment of the present application, the parallel part can be separately geometrically error-modeled first, which can focus on the complex structural characteristics of the parallel part, accurately analyze its error situation, and obtain a targeted error model of the parallel part. Subsequently, the serial part is incorporated into this model, and in combination with the forward kinematic model and the first geometric error model, the second geometric error model becomes more comprehensive and accurate. This step-by-step construction and integration method not only fully considers the respective error characteristics of the parallel part and the serial part of the hybrid robot, but also combines the advantages of different models, and can more accurately reflect the overall error situation of the robot.

[0029] Optionally, in an embodiment of the present application, the second identification module includes: The expression of the second geometric error model is:

[0030] δ E = J II (p II )δp II

[0031] where p II is the error considered in the second-step identification; J II (p II ) is the second-step identification matrix; δ E is the difference between the calculated value and the measured value of the end position in the same coordinate system.

[0032] Through the above technical solution, the embodiment of the present application can directly analyze and process specific error factors through the second geometric error model, and use the mapping effect of the second-step identification matrix on the error to accurately locate and evaluate its impact on the end position accuracy.

[0033] An embodiment of the third aspect of the present application provides an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor executes the program to implement the two-step hybrid robot kinematic calibration method as described in the above embodiment.

[0034] An embodiment of the fourth aspect of the present application provides a computer-readable storage medium, and the computer-readable storage medium stores a computer program, and when the program is executed by a processor, the two-step hybrid robot kinematic calibration method as described above is implemented.

[0035] An embodiment of the fifth aspect of the present application provides a computer program product, including a computer program, characterized in that the computer program is executed to implement the two-step hybrid robot kinematic calibration method as described above.

[0036] The embodiments of the present application can

[0037] The additional aspects and advantages of the present application will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The above and / or additional aspects and advantages of the present application will become obvious and easy to understand from the following description of the embodiments in conjunction with the drawings, where:

[0039] Figure 1 is a schematic diagram of a typical hybrid serial-parallel robot configuration according to a specific embodiment of the present application;

[0040] Figure 2A flowchart of a kinematic calibration method for a two-step hybrid robot according to an embodiment of the present application;

[0041] Figure 3 A schematic structural diagram of a kinematic calibration device for a two-step hybrid robot according to an embodiment of the present application;

[0042] Figure 4 A schematic structural diagram of an electronic device according to an embodiment of the present application. Detailed implementation manners

[0043] The embodiments of the present application will be described in detail below. The examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions from beginning to end. The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present application, but should not be construed as a limitation to the present application.

[0044] The kinematic calibration method and device for a two-step hybrid robot according to an embodiment of the present application will be described below with reference to the accompanying drawings. In view of the problem of low accuracy and efficiency of the existing calibration method due to the complex structure of the hybrid robot mentioned in the above background technology, the present application provides a kinematic calibration method for a two-step hybrid robot. In this method, a simplified serial robot model can be used for rapid first-step identification to obtain a first identification error; then, based on the complete hybrid robot model, accurate second-step identification is performed to obtain a second identification error. By summing the two, the overall identification error of the hybrid robot is finally obtained. This method combines the advantages of speed and high accuracy, not only improving the efficiency of kinematic calibration, but also enhancing the accuracy and stability of the identification results, providing an effective solution for improving the accuracy of hybrid robots. Thus, the problem of low accuracy and efficiency of the existing calibration method due to the complex structure of the hybrid robot is solved.

[0045] Taking a typical parallel-series hybrid robot for two-step kinematic calibration as an example, the kinematic calibration method for a two-step hybrid robot proposed by the present application will be elaborated in detail. As Figure 1 shown, Figure 1 is a schematic configuration diagram of a typical parallel-series hybrid robot, including: a base 1; a lower rotating platform 2; an upper rotating platform 3; a first rod 4; a second rod 5; a third rod 6; a fourth rod 7; a fifth rod 8; a triangular connection assembly 9; a sixth rod 10; a seventh rod 11; and an end effector rod 12.

[0046] Specifically, the robot is a typical hybrid robot configuration with five degrees of freedom. The five-degree-of-freedom hybrid robot includes a three-degree-of-freedom parallel mechanism and a two-degree-of-freedom serial mechanism connected in series with the parallel mechanism. The three-degree-of-freedom parallel mechanism includes a first parallelogram link 4, a second link 5, a third link 6, a fourth link 7, a fifth link 8, a sixth link 10, a seventh link 11, a triangular connection assembly 9, and an end effector assembly 12. The two-degree-of-freedom serial mechanism includes a base 1, a lower rotating platform 2, and an upper rotating platform 3. The base 1 is installed on the horizontal ground, and the lower rotating platform 2 is connected to the base 1 through a horizontal rotational pair. The upper rotating platform 3 is connected to the lower rotating platform 2 through a vertical rotational pair. The first link 4, the second link 5, and the third link 6 are all connected to the upper rotating platform 3 through rotating hinges. The triangular connection assembly 9 is respectively hinged to the fifth link 8, the seventh link 11, and the first link 4. The sixth link 10 passes through the hinged joint of the triangular connection assembly 9 and the first link 4, and a certain point on the assembly is hinged to the first link 4 and the triangular connection assembly 9. The end effector link 12 is a special-shaped link, one end of which is hinged to the seventh link 11, the middle bent part is hinged to the sixth link 10, and the other end is usually connected to a spray gun, hereinafter referred to as the end effector. All the above parallel mechanism components are in the same plane, and the drive shafts are located at the hinged joints of the first link 4, the second link 5, and the third link 6 with the upper rotating platform 3, the connection between the upper rotating platform 3 and the lower rotating platform 2, and the connection between the lower rotating platform 2 and the base 1. By driving the first link 4, the second link 5, and the third link 6 respectively with motors, the posture and position of the robot end can be changed.

[0047] Specifically, Figure 2 is a schematic flowchart of a kinematic calibration method for a two-step hybrid robot provided by an embodiment of the present application.

[0048] As Figure 2 shown, the kinematic calibration method for the two-step hybrid robot includes the following steps:

[0049] In step S201, a first geometric error model used in the first-step identification is established to utilize the first geometric error model for iterative identification of errors and obtain the first identification error of the hybrid robot.

[0050] Specifically, the expression of the first geometric error model is:

[0051] δ E =J I (p I )δp I

[0052] where p I is the error considered in the first-step identification; J I (p I ) is the first-step identification matrix; δE The difference between the calculated value and the measured value of the end position in the same coordinate system.

[0053] In the actual execution process, the first geometric error model is used to iteratively identify the error to obtain the first identification error of the hybrid robot, including: simplifying the hybrid robot into a serial robot to obtain the forward kinematic solution of the serial robot; obtaining the relationship between the parameter perturbation and the end position according to the forward kinematic solution; obtaining the first identification matrix according to the relationship between the parameter perturbation and the end position, substituting it into the preset iterative formula until the iteration converges, and obtaining the first identification error.

[0054] Specifically, first simplify the hybrid robot into a serial robot and remove the geometric parameters with redundant constraints. Then, according to the D-H method, the forward kinematic solution of the serial robot is obtained:

[0055]

[0056] where, E n is the calculated position of the end effector in the robot coordinate system; T j is the D-H transformation matrix corresponding to each rotating joint of the robot; p I is the vector composed of the geometric parameters retained in the first step of identification.

[0057] Furthermore, according to the forward solution, the relationship between the parameter perturbation and the end position can be obtained:

[0058] δE = J e δp I

[0059] where, δE is the change in the end position in the robot coordinate system; δp I is the perturbation of the geometric parameter; J e is the Jacobian matrix of the vector function E n (p I ).

[0060] Since the measured value E m of the end position and the calculated value E n are often in different coordinate systems, the following method can be used to consider the coordinate system transformation: Let and perform singular value decomposition on it to obtain Η = UΣV T , then the homogeneous transformation between the laser tracker coordinate system and the robot coordinate system is:

[0061]

[0062] In summary, the first identification matrix of the geometric error model used in the first step of identification can be obtained as:

[0063] JI = [J e (R0E m )^ -I3]

[0064] Furthermore, use the geometric error model identified in the first step to iteratively identify the error. Substitute the first identified matrix, R0, and t0 obtained above into the following iterative method for iteration:

[0065]

[0066] updateJ I ,R0,t0

[0067]

[0068] where (i) the superscript represents the result of the i-th iteration; E n is the calculated value of the end position; E m is the measured value of the end position; the error obtained by iterative convergence is the error identified in the first step.

[0069] Take Figure 1 the parallel-series robot shown as an example to illustrate step S101 in detail.

[0070] To improve the identification accuracy, 40 groups of pose data were collected in the experiment. In the first step of identification, the model simplifies the parallel-series robot into a serial robot composed of a base 1, a lower rotating platform 2, an upper rotating platform 3, a first rod 4, a sixth rod 11, and a seventh rod 12 connected in series.

[0071] The geometric parameters retained in the first step of identification constitute a vector which includes 12 geometric parameters:

[0072] p I = [θ1,θ2,θ3,θ4,θ5,θ9,θ 12 ,h1,h2,l4,l 11 ,l 12 T

[0073] where θ1,θ2,θ3,θ4,θ5 are the rotation angles of the five drive axes; θ9 is the apex angle of the triangular connection component 9; θ 12 is the internal angle of the special-shaped lever 12; h1 is the height of the base 1; h2 is the sum of the heights of the lower rotating platform 2 and the upper rotating platform 3; l4 is the length of the component 4; l 11 is the length of the component 11; l 12 is the length of the lower side rod of the component 12.

[0074] ​According to the simplified forward kinematics of the robot, the calculated pose of the $i$-th end of the robot can be expressed as:

[0075]

[0076] where is the calculated position of the end effector in the robot coordinate system; $T$ j is the D-H transformation matrix corresponding to each rotating joint of the robot; $p$ I is the vector composed of the geometric parameters of the robot.

[0077] Specifically, the overall mechanism has a total of 6 physically and mathematically distinct $i$ matrices, namely $T$ j $(j = 1 \ldots 6)$. Among them, $T_1$ represents the rotating joint connecting the base 1 and the lower rotating platform 2; $T_2$ represents the rotating joint connecting the lower rotating platform 2 and the upper rotating platform 3; $T_3$ represents the rotating joint connecting the upper rotating platform 3 and the component 4; $T_4$ represents the rotating joint connecting the upper rotating platform 3 and the component 5; $T_5$ represents the rotating joint connecting the upper rotating platform 3 and the component 6, and $T_6$ represents the distance from the hinge between the component 12 and the component 10 to the end, that is, the length of the end effector.

[0078] Furthermore, according to the forward kinematics, the following relationship can be obtained between the parameter perturbation and the change in the end position at all poses:

[0079] $\delta E = J$ e $\delta p$ I

[0080] where is the vector function used to calculate the end position corresponding Jacobian matrix; $\delta p$ I is the geometric parameter perturbation; $\delta E$ is the change in the end position.

[0081] Let be the measured position of the end of the end effector in the coordinate system of the laser tracker. Then, before performing error identification, it is also necessary to solve the transformation between the coordinate system of the laser tracker and the coordinate system of the robot according to the following method. Let the matrix Performing singular value decomposition on it gives $\mathbf{H} = \mathbf{U}\mathbf{\Sigma}\mathbf{V}$ T , then the homogeneous transformation between the coordinate system of the laser tracker and the coordinate system of the robot is:

[0082]

[0083] According to the above results, the first identification matrix can be obtained:

[0084] $J$ I $= [J$ e $(R_{0E}$m )^ -I3]

[0085] Among them, the superscript ^ represents the cross product matrix corresponding to the vector.

[0086] Furthermore, based on the first identification matrix obtained above, in order to calculate the parameter error δp according to the difference between the calculated value and the measured value of the end position I , the following iterative method is adopted:

[0087]

[0088] update J I ,R0,t0

[0089]

[0090] Among them, J I is the first identification matrix obtained in 1); is the transformation between the coordinate system of the laser tracker and the robot system obtained in 1); the superscript (i) represents the result of the i-th iteration; The obtained when the iteration converges is the error obtained by the first identification.

[0091] The embodiment of the present application can simplify the hybrid robot into a serial robot to establish the first geometric error model, simplify the complex system structure, reduce the modeling difficulty, and improve the calculation efficiency. The forward kinematic solution is obtained by using the D-H method, making the model have a theoretical basis and accuracy. By deriving the relationship between parameter perturbation and end position, the influence of geometric parameter changes on the end position can be deeply analyzed. Considering the problem that the coordinate systems of the measured value and the calculated value of the end position are inconsistent, singular value decomposition is used for coordinate system transformation to ensure the consistency of data and the reliability of the model. The obtained first identification matrix synthesizes various factors and provides an effective tool for error iterative identification. Using the iterative formula for iterative identification can gradually approach the true error until the first identification error is obtained by convergence, improving the accuracy of error identification.

[0092] In step S202, a second geometric error model used in the second identification is established to perform a single identification error using the second geometric error model to obtain the second identification error of the hybrid robot.

[0093] In the actual execution process, establishing the second geometric error model used in the second identification includes: performing geometric error modeling on the parallel part to obtain the error model of the parallel part; after incorporating the series part into the error model of the parallel part, the second geometric error model is obtained according to the forward kinematic model and in combination with the first geometric error model.

[0094] Specifically, ignoring the serial part of the robot, considering structural errors such as axis alignment deviation, and modeling the geometric errors of the parallel part. The hybrid robot has passive and follower motion joints, so the error terms included in its error model are structural errors and passive errors. The difference between the two lies in whether they change with the robot pose. Let the vector composed of passive error terms be δ passive , and the vector composed of structural error terms be δ parallel . Then, through the vector loop method and perturbation method, it can be known that there is: δE = T1δ passive + T2δ parallel , and there is a linear relationship between passive errors and structural errors: δ passive = Tδ parallel . From this, the error model of the parallel part can be obtained: δE = J st δ parallel .

[0095] Furthermore, incorporating the serial part into the error model of the parallel part, the forward kinematics model is:

[0096]

[0097] Among them, T p is the misalignment caused by the assembly of the serial part and the parallel part; T 35 is the homogeneous transformation matrix corresponding to the whole parallel part; T e is the error caused by the transformation of the hand-eye calibration coordinate system. Taking the perturbation of the above formula can obtain the D-H equation containing geometric errors:

[0098]

[0099] Among them, is the cross product matrix corresponding to the terminal attitude error; is the terminal position error. After ignoring the high-order error terms, the terminal error term can be expressed as: δE = Jδp.

[0100] Performing column pivoting OR decomposition on the J matrix can obtain:

[0101]

[0102] Among them, Q is an orthogonal matrix; E is a permutation matrix; R is an upper triangular matrix; A is an ordinary matrix. Through OR decomposition, the most sensitive error combination δp II and the second-step identification matrix J II that is independent of each column can be calculated and screened, and the second-step identification model can be obtained: δE = J II δp II .

[0103] Among them, p II is the error considered in the second-step identification; JII (p II ) is the second identification matrix; δ E is the difference between the calculated value and the measured value of the end position in the same coordinate system.

[0104] Taking Figure 1 the shown hybrid robot as an example, step S202 will be described in detail.

[0105] The iteration based on the first geometric error model in step S201 can significantly reduce the identified position residuals. Then, structural errors such as the axis deviation of the axis are incorporated into the error model to establish a complete linear geometric error model for the parallel part. The hybrid robot has passive and follower motion joints, and its state is affected by the remaining driving joints. When the component of the geometric error on the passive degree of freedom of the passive joint has the ability to change with the robot pose, this component is defined as the passive error, and the remaining components are used as structural errors. That is, the difference between the passive error and the structural error lies in whether it can change with the robot pose. The vector composed of all passive error terms of the robot is called the passive error vector, and the vector composed of structural error terms is called the structural error vector.

[0106] Due to the characteristics of the passive error, it needs to be converted into a structural error when establishing the error model. Considering that there are multiple closed-loop structures in the parallel part of the robot, the closed-loop vector method and the perturbation method are used to characterize the linear relationship between the passive error vector and the structural error vector, and a complete error model is established. The parallel part of the robot can be split into three vector loops of parallelogram structures, which are composed of the first rod, the third rod, the fourth rod, the sixth rod, the first rod, the second rod, the fifth rod, the triangular connection component, the triangular connection component, the sixth rod, the seventh rod, and the end effector rod respectively. For each vector loop, its ideal position loop and attitude loop are represented by equations respectively. Taking the perturbation of the established equations, the expression of the corresponding error model can be obtained. Through the above method, 3 linearly independent independent equations can be established for each vector loop. The linear relationship between the passive error vector and the structural error vector can be obtained through the 9 equations obtained from the three vector loops. The passive error vector is expressed as:

[0107]

[0108] The structural error vector is:

[0109]

[0110] where the letters correspond to Figure 1 the joint points marked.

[0111] The linear relationship is expressed as:

[0112] T L δpassive = T R δ parallel

[0113] where T R and T L are the mapping matrices between the structural error and the passive error. Therefore, there is a linear transformation relationship between the passive error and the structural error.

[0114] Based on the series part included in the parallel mechanism, a series kinematic chain X-D-I-End can also be established. After establishing the equation for the kinematic chain and taking perturbations, the original geometric error model of the robot can be obtained. Since the parallel part is overconstrained and there are error constraints in the overconstrained structure, only the errors in the plane where the whole is constrained need to be considered for the parallel part, that is, two translational directions and one rotational direction. Therefore, the end pose and position of the robot have 1 and 2 degrees of freedom respectively, and the geometric error model can be expressed as:

[0115]

[0116] where are the end position errors in the y-axis and z-axis directions; is the end pose error; are the mapping matrices between the passive error and the end error and between the structural error and the end error respectively. According to the linear relationship between the passive error and the structural error, the errors of the three degrees of freedom at the end can be characterized by the structural error and the mapping matrix.

[0117] Furthermore, according to the error model of the parallel part, the forward kinematic model is re-analyzed:

[0118]

[0119] where T p is the misalignment caused by the assembly of the series part and the parallel part; T 35 is the homogeneous transformation matrix corresponding to the whole parallel part; T e is the error caused by the transformation of the hand-eye calibration coordinate system. For the end T E taking perturbations, we can get:

[0120]

[0121] where ω is the cross product matrix corresponding to the end pose error; δE is the end position error. For the matrix T i (i = 1, 2, p, 35, e), it is divided into three categories:

[0122] (i) Rotational joint Then there is and respectively represent the spatial pose error and the position error.

[0123] (ii) If the parallel overall structure is characterized by the geometric error model obtained in 3), then where R 35 is the rotation matrix corresponding to the homogeneous transformation of the parallel part, and δθ and δe are the end attitude error and position error obtained in 3).

[0124] (iii) The fixed structure represents the transformation of the pose in the case of joint fixation, then there is

[0125] Through the above process of taking geometric errors by first-order perturbation, the ideal D-H matrix equation T E = T1T2T p T 35 T e can be transformed into a D-H matrix equation containing geometric errors:

[0126] T E +δT E =(T1 + δT1)(T2 + δT2)(T p +δT p )(T 35 +δT 35 )(T e +δT e )

[0127] After ignoring the high-order error terms, the end error term can be expressed as follows according to the above formula:

[0128] δE = J e δ e

[0129] R1 and R2 are the rotation matrices corresponding to the homogeneous transformation matrices of T1 and T2 respectively; δ e =[δr1 T ,δr2 T ,δr p T ,δe T ,δr e T ,ω1 T ,ω2 T ,ω p T T .

[0130] Substituting into the above expression, the final geometric error term and the error mapping matrix at the end can be obtained as:

[0131] δE = Jδp

[0132] where, The vector representing 39 robot geometric errors can be expressed as:

[0133]

[0134] The error mapping matrix J can be expressed as:

[0135]

[0136] For specific institutional constant parameters, the error mapping matrix corresponding to the kth pose of the robot end is denoted as J k , then randomly extract n pose points in the end workspace and stack the constraint matrices under different poses to obtain the total constraint matrix:

[0137] J = [...J k T ...] T

[0138] Performing column pivoting OR decomposition on the J matrix gives:

[0139]

[0140] When J is not column full rank, it means that there are linear relationships among some of the error terms, that is, these error terms will cause residuals in the same direction of the end pose, which means that this part of the structural error can be replaced by the remaining errors in the geometric error model. After calculating and screening to eliminate these redundant errors in the model, the final number of independent error terms is 26, and its vector can be expressed as The second-step identification matrix with each column independent Therefore, the final error model is expressed as:

[0141] δE = J II δp II

[0142] The embodiments of this application can adopt a step-by-step modeling strategy. First, geometric error modeling is carried out separately for the parallel part, fully considering structural errors such as the axis deviation of the shaft and passive errors and structural errors brought by passive and follower joints. The vector loop method and the perturbation method are used to establish the relationship to obtain the error model of the parallel part. This targeted modeling can accurately analyze the error characteristics of the parallel part. Then, the serial part is incorporated into the error model of the parallel part, and the second geometric error model is constructed by combining the forward kinematics model and the first geometric error model, comprehensively and systematically considering the error sources of the whole hybrid robot, making the model more in line with the actual situation. Secondly, in terms of model processing, column pivoting OR decomposition is performed on the obtained error matrix, and the most sensitive error combinations and the second identification matrix that are mutually independent in each column are calculated and screened. This decomposition method can not only effectively reduce the complexity of the model, but also highlight the key error factors, improving the accuracy and efficiency of error identification. By performing a single identification error through this model, the second identification error of the hybrid robot can be obtained, avoiding the complex multiple iteration process and saving computing resources and time costs.

[0143] In step S203, the first identification error and the second identification error are summed to obtain the final identification error of the hybrid robot for kinematic calibration of the hybrid robot.

[0144] Specifically, the least squares method is used to identify the error δp for the second identification model obtained in step S202 II as follows:

[0145]

[0146] The identification error obtained by the two-step kinematic calibration method thus obtained is That is, the finally obtained error is the sum of the first identification error and the second identification error, fully combining the advantages of the two-step identification process. It not only utilizes the high efficiency of the first-step simplified analysis, but also gives play to the accuracy of the second-step refined analysis, enabling the finally obtained identification error to more comprehensively and accurately reflect the actual kinematic errors of the hybrid robot, and thus providing a solid and reliable basis for the high-precision calibration of the kinematics of the hybrid robot.

[0147] Furthermore, error compensation can be performed according to the obtained final identification error, such as realizing kinematic calibration of the hybrid robot. In some embodiments, software compensation can be used to implement the error compensation function in the control software of the robot, taking the final identification error as the compensation amount and adjusting the motion instructions of the robot in real time during the control algorithm. For example, in each control cycle, the joint angle instruction is corrected according to the current error value, enabling the robot to automatically compensate for the error and improve the motion accuracy.

[0148] In the embodiments of the present application, the least squares method can be used in the second-step error identification, which can effectively improve the accuracy of error calculation. Error compensation is performed based on the first identification error and the second identification error to improve the motion accuracy, overall performance, and working quality of the robot.

[0149] According to the two-step kinematic calibration method of the hybrid robot proposed in the embodiments of the present application, a simplified serial robot model can be used for the rapid first-step identification to obtain the first identification error; then, based on the complete hybrid robot model, an accurate second-step identification is performed to obtain the second identification error. By summing the two, the overall identification error of the hybrid robot is finally obtained. This method combines the advantages of speed and high precision, not only improving the efficiency of kinematic calibration but also enhancing the accuracy and stability of the identification results, providing an effective solution for improving the accuracy of hybrid robots.

[0150] Next, a two-step kinematic calibration device for a hybrid robot proposed according to the embodiments of the present application is described with reference to the accompanying drawings.

[0151] Figure 3 It is a block diagram of a two-step kinematic calibration device for a hybrid robot according to an embodiment of the present application.

[0152] As Figure 3 shown, the two-step kinematic calibration device 10 of the hybrid robot includes: a first identification module 100, a second identification module 200, and a calibration module 300.

[0153] Specifically, the first identification module 100 is used to establish a first geometric error model used in the first-step identification, so as to use the first geometric error model to perform iterative identification errors and obtain the first identification error of the hybrid robot.

[0154] The second identification module 200 is used to establish a second geometric error model used in the second-step identification, so as to use the second geometric error model to perform single identification errors and obtain the second identification error of the hybrid robot.

[0155] The calibration module 300 is used to sum the first identification error and the second identification error to obtain the final identification error of the hybrid robot, so as to perform kinematic calibration of the hybrid robot.

[0156] Optionally, in an embodiment of the present application, the first identification module 100 includes: The expression of the first geometric error model is:

[0157] δ E =J I (p I )δp I

[0158] Where p I is the error considered in the first-step identification; JI (p I ) is the first identification matrix; δ E is the difference between the calculated value and the measured value of the end position in the same coordinate system.

[0159] Optionally, in an embodiment of the present application, the first identification module 100 includes: a simplification unit, a solution unit, and an iteration unit.

[0160] Among them, the simplification unit is used to simplify the hybrid robot into a serial robot to obtain the forward kinematic solution of the serial robot.

[0161] The solution unit is used to obtain the relationship between the parameter perturbation and the end position according to the forward kinematic solution.

[0162] The iteration unit is used to obtain the first identification matrix according to the relationship between the parameter perturbation and the end position, substitute it into the preset iteration formula until the iteration converges, and obtain the first identification error.

[0163] Optionally, in an embodiment of the present application, the second identification module 200 includes: a parallel modeling unit and a combined modeling unit.

[0164] Among them, the parallel modeling unit is used to perform geometric error modeling on the parallel part to obtain the error model of the parallel part.

[0165] The combined modeling unit is used to incorporate the series part into the error model of the parallel part, and then obtain the second geometric error model according to the forward kinematic model and in combination with the first geometric error model.

[0166] Optionally, in an embodiment of the present application, the second identification module 200 includes: The expression of the second geometric error model is:

[0167] δ E =J II (p II )δp II

[0168] Among them, p II is the error considered in the second identification; J II (p II ) is the second identification matrix; δ E is the difference between the calculated value and the measured value of the end position in the same coordinate system.

[0169] It should be noted that the foregoing explanation of the embodiments of the kinematic calibration method for the two-step hybrid robot also applies to the kinematic calibration device of the two-step hybrid robot in this embodiment, and will not be elaborated here.

[0170] The kinematic calibration device for a two-step hybrid serial-parallel robot proposed according to the embodiments of the present application can use a simplified serial robot model for rapid first-step identification to obtain the first identification error; then, based on the complete hybrid serial-parallel robot model, perform accurate second-step identification to obtain the second identification error. By summing the two, the overall identification error of the hybrid serial-parallel robot is finally obtained. This method combines the advantages of speed and high precision, not only improving the efficiency of kinematic calibration, but also enhancing the accuracy and stability of the identification results, providing an effective solution for improving the accuracy of hybrid serial-parallel robots.

[0171] Figure 4 The structural schematic diagram of the electronic device provided by the embodiments of the present application. The electronic device may include:

[0172] A memory 401, a processor 402, and a computer program stored on the memory 401 and executable on the processor 402.

[0173] When the processor 402 executes the program, it implements the two-step hybrid serial-parallel robot kinematic calibration method provided in the above embodiments.

[0174] Further, the electronic device further includes:

[0175] A communication interface 403 for communication between the memory 401 and the processor 402.

[0176] The memory 401 is used to store a computer program executable on the processor 402.

[0177] The memory 401 may include a high-speed RAM memory, and may also include non-volatile memory, such as at least one disk memory.

[0178] If the memory 401, the processor 402, and the communication interface 403 are implemented independently, the communication interface 403, the memory 401, and the processor 402 can be interconnected through a bus and communicate with each other. The bus may be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For the sake of representation, Figure 4 only a thick line is shown in the figure, but it does not mean that there is only one bus or one type of bus.

[0179] Optionally, in a specific implementation, if the memory 401, the processor 402, and the communication interface 403 are integrated on a single chip, the memory 401, the processor 402, and the communication interface 403 can communicate with each other through an internal interface.

[0180] The processor 402 may be a central processing unit (CPU for short), or an application specific integrated circuit (ASIC for short), or one or more integrated circuits configured to implement the embodiments of the present application.

[0181] The embodiments of the present application further provide a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the above-mentioned two-step hybrid robot kinematic calibration method is implemented.

[0182] The embodiments of the present application further provide a computer program product, including a computer program, characterized in that the computer program is executed to implement the above-mentioned two-step hybrid robot kinematic calibration method.

[0183] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, without conflict, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples.

[0184] In addition, the terms "first" and "second" are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present application, the meaning of "N" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0185] Any process or method description represented in a flowchart or otherwise described herein can be understood to represent a module, segment, or portion of code including one or more executable instructions for implementing a customized logical function or process. The scope of the preferred embodiments of the present application includes additional implementations where functions may be executed not in the order shown or discussed, including in a substantially simultaneous manner according to the functions involved or in a reverse order, which should be understood by those skilled in the technical field of the embodiments of the present application.

[0186] The logic and / or steps represented in a flowchart or otherwise described herein, for example, can be considered a sequenced list of executable instructions for implementing a logical function, and can be embodied specifically in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, a system including a processor, or other systems that can fetch and execute instructions from the instruction execution system, apparatus, or device. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium include the following: an electrical connection portion having one or more wirings (electronic device), a portable computer diskette (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium can even be paper or other suitable medium on which the program can be printed, as the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpretation, or otherwise processing as appropriate, and then stored in a computer memory.

[0187] It should be understood that various parts of the present application can be implemented by hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0188] Those of ordinary skill in the art can understand that all or part of the steps carried out in implementing the above-described embodiment methods can be completed by instructing relevant hardware through a program. The program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0189] In addition, in each of the embodiments of the present application, the functional units can be integrated in a processing module, or each unit can exist physically alone, or two or more units can be integrated in a module. The above-mentioned integrated module can be implemented in the form of hardware or in the form of a software functional module. When the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0190] The above-mentioned storage medium can be a read-only memory, a magnetic disk, an optical disc, etc. Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present application. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present application.

Claims

1. A two-step hybrid robot kinematic calibration method, characterized in that: The following steps are involved: Establishing a first geometric error model used in the first step of identification, so as to iteratively identify the error using the first geometric error model to obtain a first identification error of the hybrid robot; Establishing a second geometric error model used in the second step of identification, so as to perform a single identification error using the second geometric error model to obtain a second identification error of the hybrid robot; The first identification error and the second identification error are summed to obtain a final identification error of the hybrid robot, so as to calibrate the kinematics of the hybrid robot.

2. The method according to claim 1, characterized in that: The expression of the first geometric error model is: d E =J I (p I )δp I Among them, p I The error considered in the first step of identification; J I (p I ) is the first step identification matrix; δ E It is the difference between the calculated value and the measured value of the end position in the same coordinate system.

3. The method according to claim 1 or 2, characterized in that: The iteratively identifying the error using the first geometric error model to obtain a first identification error of the hybrid robot includes: Simplifying the hybrid robot into a serial robot to obtain a kinematics correct solution of the serial robot; According to the kinematics positive solution, the relationship between the parameter perturbation and the end position is obtained; The first identification matrix is ​​obtained according to the relationship between the parameter perturbation and the end position, and is substituted into a preset iterative formula until the iteration converges to obtain the first identification error.

4. The method according to claim 1, characterized in that The step of establishing a second geometric error model used in the second step of identification includes: Performing geometric error modeling on the parallel part to obtain an error model of the parallel part; After incorporating the series part into the error model of the parallel part, the second geometric error model is obtained according to the forward kinematics model and in combination with the first geometric error model.

5. The method according to claim 1, characterized in that The expression of the second geometric error model is: d E =J II (p II )δp II Among them, p II The error considered for the second step identification; J II (p II ) is the second step identification matrix; δ E It is the difference between the calculated value and the measured value of the end position in the same coordinate system.

6. A two-step hybrid robot kinematic calibration device, characterized in that: include: A first identification module is used to establish a first geometric error model used in the first identification step, so as to iteratively identify the error using the first geometric error model to obtain a first identification error of the hybrid robot; A second identification module is used to establish a second geometric error model used in the second identification step, so as to perform a single identification error using the second geometric error model to obtain a second identification error of the hybrid robot; A calibration module is used to sum the first identification error and the second identification error to obtain a final identification error of the hybrid robot, so as to calibrate the kinematics of the hybrid robot.

7. The device according to claim 6, characterized in that The first identification module includes: the expression of the first geometric error model is: d E =J I (p I )δp I Among them, p I The error considered in the first step of identification; J I (p I ) is the first step identification matrix; δ E It is the difference between the calculated value and the measured value of the end position in the same coordinate system.

8. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the two-step hybrid robot kinematic calibration method as described in any one of claims 1 to 5.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the two-step hybrid robot kinematics calibration method as described in any one of claims 1 to 5.

10. A computer program product, comprising a computer program, characterized in that The computer program is executed to implement the two-step hybrid robot kinematics calibration method according to any one of claims 1 to 5.

Images