Robot kinematic calibration method based on truncated total least squares regularization

Abstract

The present application relates to a robot kinematics calibration method based on truncated total least squares regularization, and a parallel robot is provided with a data acquisition system, including a moving platform, a base, a branch chain and a linear motor. The method comprises: obtaining the kinematics parameters of the parallel robot, inputting the inverse kinematics parameter error model, obtaining the conversion error between the coordinate systems and the mapping relationship between the kinematics parameter errors, obtaining the measurement data of the data acquisition system and the conversion relationship between the coordinate systems, making the measurement data uniform in the base coordinate system, identifying the parameter error through the truncated total least squares regularization method, optimizing the selection of the truncation factor, obtaining the best regularization parameter, and compensating according to the identified parameter error to update the controller kinematics parameters. The present application designs a complete low-cost and mature calibration scheme for most parallel robots, which can improve the kinematics calibration accuracy of the parallel robot.

Description

TECHNICAL FIELD

[0001] The application relates to a robot kinematics calibration method based on truncated total least squares regularization and belongs to the technical field of robot calibration. BACKGROUND

[0002] In recent years, with the rapid development of parallel robots in the automobile and logistics industries, the parallel robots are mainly applied to fast sorting and carrying (Delta type parallel robots), motion simulation platforms (Stewart parallel robots), mechanical processing (Tricept hybrid mechanism) and other application tasks. In the new 3C (Computer, Communication and Consumer Electronics) industry, the research group has developed a parallel collaborative robot for precise 3C product assembly actions. The above tasks urgently require high precision of the parallel robot motion, and kinematics calibration is an economical and effective method to improve the absolute positioning accuracy of the parallel robot.

[0003] The kinematics calibration process usually includes error parameter modeling and identification process. The traditional forward kinematics error modeling method describes the mapping relationship between geometric parameter errors and end effector pose deviation, and is mainly used in the calibration of serial robots. However, the complete measurement deviation data set involved in the forward kinematics error model usually includes two different units - length unit and angle unit, which are used to represent the position and attitude deviation respectively. The inconsistency of units may affect the accuracy of identification. For parallel robots, it is easier to solve inverse kinematics than forward kinematics, and the units of the executed joints are usually unified and dimensionless. Therefore, some researchers have proposed inverse kinematics error models, which describe the mapping relationship between kinematics parameter errors and executed joint errors.

[0004] Compared with serial robots, parallel robots have more complex geometric structures and strong coupling of geometric errors, so the error mapping model of parallel robots has the possibility of being ill-conditioned. The multicollinearity characteristics of the ill-conditioned error mapping matrix make the identification stability and uniqueness of the geometric error parameters very sensitive to uncontrollable measurement noise or unknown small disturbances. In order to solve the above ill-conditioned problem, many researchers have adopted the calibration pose optimization method, which usually configures a pool of candidate measurement poses, and determines a certain number of calibration poses from the pool based on the maximum or minimum observability index of the iterative method. The time-consuming of the pose optimization method increases exponentially with the increase of the number of poses in the candidate pool, and worse still, for some configurations of parallel robots, the optimal pose selection is still insufficient to meet the good identification conditions. SUMMARY

[0005] The application provides a robot kinematics calibration method based on truncated total least squares regularization, and aims to at least solve one of the technical problems in the prior art.

[0006] The technical scheme of the application is based on a parallel robot, which is provided with a data acquisition system; the parallel robot comprises a moving platform, a base, a branch chain and a linear motor, the moving platform is connected with the base through a passive branch chain, the branch chain comprises an upper spherical joint, a lower spherical joint and a linear joint, the branch chain is connected with the moving platform through the upper spherical joint, the branch chain is connected with the linear joint through the lower spherical joint, and the linear joint is connected with the linear motor; the data acquisition system comprises an upper auxiliary clamp, a lower auxiliary clamp and a plurality of target seats for installing reflective target balls, part of the target seats are installed on the moving platform through the upper auxiliary clamp, and part of the target seats are installed on the linear motor through the lower auxiliary clamp.

[0007] The technical scheme of the application is based on a parallel robot, which is provided with a data acquisition system; the parallel robot comprises a moving platform, a base, a branch chain and a linear motor, the moving platform is connected with the base through a passive branch chain, the branch chain comprises an upper spherical joint, a lower spherical joint and a linear joint, the branch chain is connected with the moving platform through the upper spherical joint, the branch chain is connected with the linear joint through the lower spherical joint, and the linear joint is connected with the linear motor; the data acquisition system comprises an upper auxiliary clamp, a lower auxiliary clamp and a plurality of target seats for installing reflective target balls, part of the target seats are installed on the moving platform through the upper auxiliary clamp, and part of the target seats are installed on the linear motor through the lower auxiliary clamp.

[0008] S100, acquiring kinematics parameters of the parallel robot, inputting to an inverse kinematics parameter error model to obtain conversion errors between a base coordinate system and a moving platform coordinate system and mapping relationships between kinematics parameter errors;

[0009] S200, acquiring measurement data of the data acquisition system and conversion relationships between a laser tracker coordinate system and the base coordinate system and between a tool center coordinate system and the moving platform coordinate system, so that the measurement data is unified in the base coordinate system of the parallel robot after coordinate system conversion;

[0010] S300, identifying parameter errors by a truncated total least squares regularization method, and performing optimal selection of a truncation factor to obtain optimal regularization parameters;

[0011] S400, compensating nominal parameters according to the identified parameter errors to update controller kinematics parameters of the parallel robot.

[0012] Further, in the step S100, the inverse kinematics parameter error model is represented as follows:

[0013]

[0014] In the formula, q represents joint input of the parallel robot, and represents end pose output of the parallel robot, p and R are the position and pose of the end of the parallel robot, respectively, where the superscript m represents that the data is measured, and the subscript j represents the serial number of the position and pose; π represents the kinematics parameters, and the implicit kinematics equation set is represents the parameter error vector, represents the position vector error of the upper spherical joint center, represents the machining error of the length of the branched strut, represents the unit direction error of the shaft movement; δh = h - h n represents the error vector of the center axis of the passive branch; the superscript n represents the theoretical design value of the kinematics parameter, the subscript i represents the serial number of the branch (i = 1, 2, 3), and the subscript j represents the serial number of the position and pose.

[0015] Further, in the step S200, the homogeneous transformation relationship of the base coordinate system, the moving platform coordinate system, the laser tracker coordinate system and the tool center coordinate system is represented as follows:

[0016]

[0017] In the formula,

[0018] The conversion relationship is the homogeneous representation of the moving platform coordinate system in the base coordinate system;

[0019] The conversion relationship is the homogeneous representation of the tool center coordinate system in the moving platform coordinate system;

[0020] The conversion relationship is the homogeneous representation of the tool center coordinate system in the laser tracker coordinate system;

[0021] The conversion relationship is the homogeneous representation of the base coordinate system in the laser tracker coordinate system.

[0022] Further, in the step S200, the determination of the conversion relationship includes the following steps:

[0023] S211, fitting a virtual spherical surface of the tool center point of the parallel robot by random motion to obtain the position vector of ;

[0024] S212, collecting a plurality of measurement points on the base to fit the plane of the base and the z direction vector of ;

[0025] S213. Drive the linear motor to perform single-axis linear joint movement, and obtain the reflective target ball set on the lower auxiliary fixture. The x-direction vector;

[0026] S214, Determined by right-hand rule The y-direction vector.

[0027] Furthermore, in step S200, the transformation relationship The determination includes the following steps:

[0028] S221. Move the three joint axes to the theoretical zero position of the linear motor.

[0029] S222. The origin of the tool center coordinate system is determined by the three reflective target balls set on the upper auxiliary fixture;

[0030] S223, Determine the plane fitted by the center points of the three reflective target balls set on the upper auxiliary fixture. The z-direction vector;

[0031] S224. Determine the origin based on the center point of a certain reflective target ball set on the upper auxiliary fixture. The x-direction vector;

[0032] S225, determined by the right-hand rule The y-direction vector.

[0033] Furthermore, in step S300, the truncated total least squares regularization method includes the following steps:

[0034] S310, Regarding the augmented matrix [A] π Singular value decomposition expansion: |δD]

[0035]

[0036] In the formula, where and Let A and B be orthogonal matrices, and let f be the left and right eigenma matrices of the augmented matrix, respectively. Let scalars h and f be the matrix A and f, respectively. π The number of rows and columns, It is the k-th singular value of the augmented matrix;

[0037] Where, δD=A π ·δπ, where δD and A π It is a known explicit vector matrix that is associated with the end-effector pose data, joint encoder data, and nominal kinematic parameters, and δπ is the parameter error that needs to be estimated.

[0038] S320, selecting a truncation factor λ, wherein λ < n;

[0039] S330, dividing the right feature matrix into four parts according to the truncation factor;

[0040]

[0041] S340, obtaining the estimation of the truncated total least squares with the minimum norm according to the results of steps S310 to S330:

[0042]

[0043] wherein, wherein is the pseudo-inverse of A.

[0044] Further, in the step S300, the optimal regularization parameter is obtained by the following calculation:

[0045]

[0046] wherein, min{G(λ)} represents the minimized objective function; is the pseudo-inverse of A. π

[0047] The technical scheme of the present application further relates to a computer readable storage medium, which stores program instructions, and the program instructions are executed by a processor to implement the above method.

[0048] The technical scheme of the present application further relates to a parallel robot, which comprises a computer device containing the above computer readable storage medium.

[0049] Further, the parallel robot, the middle part of the base is provided with a fixed rod, the passive branch chain comprises an upper driven rod and a lower driven rod, the upper driven rod is hinged with the lower driven rod, the upper driven rod is connected with the middle part of the moving platform, and the lower driven rod is movably connected with the fixed rod.

[0050] The present application has the following advantages.

[0051] ​​The robot kinematics calibration method based on truncated total least squares regularization of the application designs a complete low-cost mature calibration scheme for most parallel robots, and can improve the kinematics calibration accuracy of the parallel robot. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 is a general flowchart of the method according to the application.

[0053] Figure 2a is a model structure diagram of the parallel robot in the application.

[0054] Figure 2b is a structure diagram of the parallel robot in the application.

[0055] Figure 3 is a kinematics parameter vector diagram of a single branch according to the method of the application.

[0056] Figure 4 is a schematic diagram of an upper auxiliary jig for determining the homogeneous transformation relationship between the base coordinate system and the laser tracker coordinate system in the laser measurement system in the embodiment of the application.

[0057] Figure 5 is a schematic diagram of a lower auxiliary jig for determining the homogeneous transformation relationship between the tool center coordinate system and the moving platform coordinate system in the laser measurement system in the embodiment of the application.

[0058] Figure 6 is a regularization parameter selection result based on the GCV method in the embodiment of the application.

[0059] Figure 7a is the attitude angle error of the parallel robot around the X axis based on the T-TLS calibration method according to the application, which contains the results before and after calibration of all poses of the calibration group and the verification group.

[0060] Figure 7b is the attitude angle error of the parallel robot around the Y axis based on the T-TLS calibration method according to the application, which contains the results before and after calibration of all poses of the calibration group and the verification group.

[0061] Figure 7c is the pose angle error of parallel robot around Z axis according to the T-TLS calibration method of the present application, wherein the results of calibration group and verification group before and after calibration are contained.

[0062] Figure 8 is the calibration effect comparison chart of T-TLS calibration method of the present application and traditional Tikhonov regularization and truncated singular value decomposition (TSVD) method on parallel robot.

[0063] Reference signs:

[0064] 100, parallel robot; 110, moving platform; 120, base; 121, bottom plate; 122, fixed rod; 123, three fixed plates; 130, branch chain; 131, upper spherical joint; 132, lower spherical joint; 133, linear joint; 134, support rod; 140, linear motor; 150, passive branch chain; 151, upper driven rod; 152, lower driven rod;

[0065] 200, data acquisition system; 210, upper auxiliary clamp; 220, lower auxiliary clamp; 230, reflective target ball; 240, target seat. DETAILED DESCRIPTION

[0066] The concept, specific structure and generated technical effects of the present application will be described clearly and completely in combination with embodiments and drawings, so as to fully understand the purpose, scheme and effect of the present application.

[0067] It should be noted that, unless otherwise specified, when a certain feature is referred to as being "fixed", "connected" to another feature, it can be directly fixed, connected to the other feature, or indirectly fixed, connected to the other feature. The singular forms "a", "said" and "the" used in this text are also intended to include the plural forms, unless the context clearly indicates otherwise. In addition, unless otherwise defined, all technical and scientific terms used in this text have the same meaning as understood by those skilled in the art. The terms used in the specification of this text are only for the purpose of describing specific embodiments, and are not intended to limit the present application. The term "and / or" used in this text includes any combination of one or more related listed items.

[0068] It should be understood that although the terms up, down, third, etc. may be used in this disclosure to describe various elements, these elements should not be limited to these terms. These terms are only used to distinguish elements of the same type from each other.

[0069] Reference Figure 1The technical scheme of the present application is based on a parallel robot 100, which can be a 3PSS / S parallel robot 100, comprising a moving platform 110, a base 120, three branch chains 130 (PSS) and three linear motors 140. The moving platform 110 is movably arranged on the base 120 through a passive branch chain 150S. The three branch chains 130 are of the same structure, and each PSS branch chain 130 comprises an upper spherical joint 131 (S), a lower spherical joint 132 (S) and a linear joint 133 (P). Each PSS branch chain 130 is connected with the moving platform 110 through the upper spherical joint 131, and is connected with the linear joint 133 through the lower spherical joint 132. The linear motor 140 is arranged on the base 120 and connected with the linear joint 133, so that the linear joint 133 serves as an active joint, and the upper spherical joint 131 (S) and the lower spherical joint 132 (S) serve as passive joints.

[0070] In an application scenario, referring to Figure 1 The passive branch chain 150 comprises an upper driven rod 151 and a lower driven rod 152. The moving platform 110 is a flat circular plate, and the lower middle part of the moving platform 110 is fixedly connected with the end of the upper driven rod 151. The base 120 comprises a bottom plate 121, a fixed rod 122 and three fixed plates 123. The bottom plate 121 is a flat circular plate, and the upper middle part of the bottom plate 121 is fixedly connected with the end of the fixed rod 122. The fixed plate is a right-angled triangular plate, and two right-angle edges of the fixed plate are connected with the bottom plate 121 and the fixed rod 122 respectively. The three fixed plates 123 are uniformly distributed on the outer periphery of the fixed rod 122. The upper end of the lower driven rod 152 is hinged with the upper driven rod 151, and the lower end of the lower driven rod 152 is movably connected with the fixed rod 122 through an intermediate joint.

[0071] In an application scenario, referring to Figure 1 The PSS branch chain 130 comprises a support rod 134, and the two ends of the support rod 134 are connected with the upper spherical joint 131 and the lower spherical joint 132 respectively. The three upper spherical joints 131 are uniformly distributed on the lower side of the moving platform 110. The three linear motors 140 are fixedly arranged on the three bottom plates 121 respectively. The linear motor 140 is connected with the linear joint 133, and the linear joint 133 is connected with the lower spherical joint 132, so as to drive the PSS branch chain 130 to move through the linear motor 140. The parallel robot 100 of the present application embodiment comprises six degrees of freedom for each branch chain 130. The passive branch chain 150 arranged in the middle constrains the moving platform 110, so as to realize the rotation movement of the parallel robot 100 around the XYZ three directions and the accompanying movement of the XYZ three directions generated by the passive branch chain 150.

[0072] In an embodiment, the parallel robot 100 of the present application is provided with a data acquisition system 200, which includes an external measuring instrument, an upper auxiliary fixture 210, a lower auxiliary fixture 220, a reflective target ball 230 (SMR) and a target seat 240. The external measuring instrument is arranged on the side of the parallel robot 100, and the external measuring instrument of the present application includes a laser tracker and a data analysis and measurement software SpatialAnalyzer matched with the laser tracker. The upper auxiliary fixture 210 is fixed to the upper side of the moving platform 110 of the parallel robot 100, and the target seat 240 for fixing the reflective target ball 230 is fixed to the upper auxiliary fixture 210. A plurality of reflective target balls 230 are uniformly distributed on the moving platform 110, and the center point of each reflective target ball 230 is equidistant from the moving platform 110, so as to arrange the plurality of reflective target balls 230 at the end of the parallel robot 100. The number of reflective target balls 230 arranged on the upper auxiliary fixture 210 is equal to the number of branch chains 130, and in some specific embodiments of the present application, the number of upper auxiliary fixtures 210 is three. The lower auxiliary fixture 220 is fixedly connected with the linear motor 140, and two reflective target balls 230 are fixed to the lower auxiliary fixture 220 through the target seat 240. The two reflective target balls 230 are arranged on the side of the lower ball joint 132 connected with the linear motor 140, and the center point of the two reflective target balls 230 is on the same straight line as the lower ball joint 132.

[0073] Referring to Figure 1 In some embodiments, according to the kinematic calibration method of the parallel robot 100 of the present application, the method is applied to the parallel robot 100 provided with a data acquisition system 200. The parallel robot 100 includes a moving platform 110, a base 120, a branch chain 130 and a linear motor 140. The moving platform 110 is connected with the base 120 through a passive branch chain 150. The branch chain 130 includes an upper ball joint 131, a lower ball joint 132 and a linear joint 133. The branch chain 130 is connected with the moving platform 110 through the upper ball joint 131, and the branch chain 130 is connected with the linear joint 133 through the lower ball joint 132. The linear joint 133 is connected with the linear motor 140. The data acquisition system 200 includes an upper auxiliary fixture 210, a lower auxiliary fixture 220 and a plurality of target seats 240 for installing reflective target balls 230. Part of the target seats 240 are installed on the moving platform 110 through the upper auxiliary fixture 210, and part of the target seats 240 are installed on the linear motor 140 through the lower auxiliary fixture 220. The method at least includes the following steps:

[0074] S100, obtain the kinematics parameters of the parallel robot 100, input to the inverse kinematics parameter error model, to obtain the conversion error between the base coordinate system and the moving platform coordinate system, and the mapping relationship between the kinematics parameter errors. The conversion error of the embodiment of the application is the position and attitude error of the parallel robot 100.

[0075] S200, obtain the measurement data of the data acquisition system 200, and the conversion relationship between the laser tracker coordinate system and the base coordinate system and the tool center coordinate system and the moving platform coordinate system, so that the measurement data is unified in the base coordinate system of the parallel robot 100 after coordinate system conversion.

[0076] S300, identify the parameter error by the truncated total least squares regularization method, and perform optimal selection of the truncation factor to obtain the best regularization parameter.

[0077] S400, compensate the nominal parameters according to the identified parameter error, to update the controller kinematics parameters of the parallel robot 100.

[0078] The application is to improve the end absolute positioning accuracy of the parallel robot 100, establish the dimensionless mapping model of inverse kinematics between the robot kinematics parameter error and the execution joint error, and propose a T-TLS regularization method based on inverse kinematics calibration, aiming at the model ill-conditioning problem caused by the strong coupling of the parallel robot 100 parameter error under complex structure.

[0079] Specific implementation of step S100

[0080] In an embodiment, the embodiment method of the application first performs kinematics analysis and parameter error modeling on one of the branch chains 130 of the parallel robot 100, see Figure 2a 、 Figure 2b and Figure 3 The embodiment method of the application establishes two coordinate systems, which are the base coordinate system of the center of the ball joint of the passive branch chain 150 and the moving platform coordinate system located at the geometric center of the three upper ball joints 131, and then establishes the closed loop vector motion equation of the above branch chain 130 (see formula (1) below), and establishes the inverse kinematics parameter error equation of the branch chain 130 based on the first order perturbation method (see formula (2) below).

[0081] p+R·c i =-h+(d i,0 +d i )·w i +l i ·n i (1)

[0082]

[0083] wherein η i = p + R · c i + h - d i,0 · w i . In the formula, p and R are respectively the position and pose of the end of the parallel robot 100, which are measured by a laser tracker in inverse kinematics calibration. i is the direction vector along the center line of the rod, i.e. the connecting line of the center lines of the upper spherical joint 131 and the lower spherical joint 132. represents the position vector error of the center of the upper spherical joint 131, represents the machining error of the rod length of the rod 134 of the branch chain 130, represents the zero point error in the axis movement direction; represents the unit direction error of the axis movement; δh = h - h n represents the error vector of the center axis of the intermediate passive branch chain 150; the superscript n represents the theoretical design value of the kinematics parameter, and the subscript i represents the serial number of the branch chain (i = 1, 2, 3).

[0084] After the kinematics analysis and parameter error modeling of the three branch chains 130 are completed, the inverse kinematics parameter error equations of all the branch chains 130 are integrated, and the error model δD = A π · δπ of the 3PSS / S parallel robot 100 is constructed. π represents the parameter error mapping matrix in the error model of the 3PSS / S robot, represents the parameter error vector, and δD represents the set of the deviations of the joint values from the joint encoder feedback values, wherein the joint values are obtained according to the position and pose measured by an external measuring device (such as a laser tracker) and the inverse kinematics calculation, wherein the superscript m represents that the data are measured, and the subscript j represents the serial number of the position and pose, and in this example, j takes j = 1, 2, …, 30.

[0085] Further, the inverse kinematics parameter error model of the embodiment of the present application can not only be applied to the 3PSS / S parallel robot 100, but also can be generalized to other parallel robots 100. Specifically, the joint input q, the end pose output Φ and the kinematics parameter π of the parallel robot 100 are expressed as an implicit kinematics equation set F(Φ, q, π) = 0, and the total differential transformation thereof is obtained as the following formula (3).

[0086]

[0087] In the inverse kinematics parameter error model, δΦ j ​≈0, meaning that assuming the external measuring instrument's measurement data is completely accurate, the measurement data of the robot's end-effector pose is considered the true value. In this case, the error in the kinematic parameters is the only factor causing joint deviation. It should be noted that the inverse kinematic parameter error model in this embodiment of the invention differs from the traditional forward kinematics error model because the joint input in the forward kinematics error model is fixed, i.e., δq. j ≈0, meaning that the error in kinematic parameters is the only factor causing end-effector pose deviation.

[0088] The unified model of the inverse kinematics parameter error model obtained in this embodiment of the invention is as follows (4), which realizes the application of formula (2) in other parallel robot objects 100, so that solving the error parameters can be regarded as minimizing the joint angle deviation. The optimal estimation problem.

[0089]

[0090] In the formula, q represents the joint input of the parallel robot 100, and Φ represents the end-effector pose output of the parallel robot 100. p and R are the position and orientation of the end effector of the parallel robot 100, respectively. The superscript m indicates that the data is obtained by measurement, and the subscript j indicates the sequence number of the position and orientation. π represents the kinematic parameters, and the implicit kinematic equations are F(Φ,q,π)=0. Represents the parameter error vector. This represents the position vector error of the center of the upper ball joint (131). This indicates the machining error in the length of the support rod 134 (support rod 130). The unit directional error of the axis motion is represented by δh = hh. n This represents the error vector of the central axis of the passive branch 150; the superscript n represents the theoretical design value of the kinematic parameter, and the subscript i represents the branch sequence number (i = 1, 2, 3).

[0091] Detailed Implementation of Step S200

[0092] In one embodiment, see Figure 4 and Figure 5 The method of this embodiment of the invention is provided with a data acquisition system 200 for calibration measurement. The data acquisition system 200 includes an API Radian laser tracker, SpatialAnalyzer data analysis and measurement software that is compatible with the laser tracker, a standard target mount 240 installed at the end of the 3PSS / S parallel robot 100 (i.e., the mobile platform 110), and three reflective target balls 230 (SMR) installed on the target mount 240 in an equilateral triangular geometric distribution.

[0093] Further, the measurement data of the laser tracker is represented in its defined coordinate system, while the kinematic parameter error model is represented in the base coordinate system of the 3PSS / S parallel robot 100, thus the measurement data needs to be transformed from the coordinate system of the laser tracker to the base coordinate system. Wherein, the above transformation involves the laser tracker coordinate system {LT}, the base coordinate system {O}, the moving platform coordinate system {O'}, and the tool center coordinate system {TCP} defined at the geometric center of the fitted reflective target sphere 230, the homogeneous transformation relationship among them can be represented as formula (5)

[0094]

[0095] In the formula, the transformation relationship is the homogeneous representation of the moving platform coordinate system in the base coordinate system; the transformation relationship is the homogeneous representation of the tool center coordinate system in the moving platform coordinate system; the transformation relationship is the homogeneous representation of the tool center coordinate system in the laser tracker coordinate system; and the transformation relationship is the homogeneous representation of the base coordinate system in the laser tracker coordinate system.

[0096] Further, the fixed transformation relationship is determined, i.e. the homogeneous representation of the base coordinate system in the laser tracker coordinate system, which includes the following steps: S211, calculating the position vector of by fitting a virtual spherical surface of the tool center point of the 3PSS / S robot through random motion; S212, fitting the plane of the base 120 and the z-direction vector of by collecting a plurality of measurement points on the base 120; wherein the number of measurement points in the embodiment of the present application is greater than three; S213, driving the linear motor 140 to implement single-axis linear joint 133 motion, and obtaining the projection direction vector of the motion direction vector of the joint axis in the plane of the base 120 through the reflective target sphere 230 (see Figure 4 ) arranged on the lower auxiliary clamp 220, i.e. the x-direction vector of ; S214, determining the y-direction vector of by right-hand rule.

[0097] Further, the fixed transformation relationship is determined, i.e. the homogeneous representation of the tool center coordinate system in the moving platform coordinate system, which includes the following steps: S221, moving all three joint axes to the theoretical zero position of the linear motor 140 S222, determining the position of the tool center point of the 3PSS / S robot in the moving platform coordinate system by the reflective target sphere 230 arranged on the upper auxiliary clamp 210 (see Figure 5) three reflective target balls 230 to determine the origin of the tool coordinate system; S223, determining the z-direction vector of the tool coordinate system by fitting a plane through the three target ball center points disposed on the upper auxiliary fixture 210 ; S224, determining the x-direction vector of the tool coordinate system according to the origin obtained from a certain reflective target ball 230 center point disposed on the upper auxiliary fixture 210 ; S225, determining the y-direction vector of the tool coordinate system by the right-hand rule.

[0098] Specifically, the three linear motors 140 are driven to stop at an arbitrary position, the center points of the three reflective target balls 230 at the end of the parallel robot 100 are measured by using a laser tracker respectively, and the measured target ball center point position coordinates and the motor encoder positions are recorded; the three linear motors 140 are started again to stop at an arbitrary position, and then the above movement, measurement and recording process is repeated, and 30 times of recording are directly completed, and finally the representation relationship between the moving platform coordinate system and the base coordinate system under each motion posture is obtained , and the end posture data is sorted out , and the data acquisition is finally completed.

[0099] The specific implementation of step S300

[0100] In an embodiment, the method of the embodiment of the present application imports the identification group (IG) posture data and joint encoder data collected in step S200 into an error model δD=A π ·δπ, where δD and A π are known and the explicit vector (matrix) related to the end posture data, joint encoder data and nominal kinematic parameters, and δπ is the parameter error to be estimated. The classical error estimation methods, such as the iterative least squares and Kalman filtering method, require that the error mapping matrix A π be well-conditioned, otherwise the end posture data containing measurement noise in δD and A π will seriously interfere with the estimation of δπ. The reciprocal of the condition number of the error mapping matrix (6) is used as the observability index to evaluate whether the current error model is ill-conditioned, and the value of O2 is 10^-6 level, and the estimated value of δπ deviates seriously from the threshold value of the normal parameter error. Therefore, according to the above ill-conditioned analysis, the inverse kinematic parameter error model of the embodiment of the present application supports the use of regularization method to estimate the parameter error.

[0101]

[0102] ​Furthermore, the method in this embodiment of the invention identifies parameter errors through truncated total least squares regularization. Truncation-Truncation Total Least Squares (T-TLS) inherits the overall least squares regularization approach's handling of δD and A on both the left and right sides. π Simultaneously, the accuracy of parameter estimation is affected by measurement noise disturbances, and some smaller singular values ​​σ are removed through a truncation strategy. i And remove A π The corresponding eigenvectors make the augmented matrix [A] π The information content of |δD] entering the identification is reduced in order, thus achieving stability in parameter estimation. The algorithm is described as follows:

[0103] S310, Regarding the augmented matrix [A] π |δD] singular value decomposition expansion, see (7), where and Both are orthogonal matrices, representing the left and right eigenma matrices of the augmented matrix, respectively. It is the k-th singular value of the augmented matrix.

[0104]

[0105] In the formula, where and Let A and B be orthogonal matrices, and let f be the left and right eigenma matrices of the augmented matrix, respectively. Let scalars h and f be the matrix A and f, respectively. π The number of rows and columns, It is the k-th singular value of the augmented matrix. Where δD = A π ·δD, where δD is related to A π It is a known explicit vector matrix that is associated with the end-effector pose data, joint encoder data, and nominal kinematic parameters, and δπ is the parameter error that needs to be estimated.

[0106] S320. Select a cutoff factor λ such that λ < n. The strategy for selecting the cutoff factor is described in step S330. S330. Divide the right eigenma matrix into four parts according to the cutoff factor.

[0107]

[0108] S340. Based on the results of S310 to S330, determine the estimate of the cutoff population least squares of the minimum norm, where... yes The false rebellion.

[0109]

[0110] Further, the method of the embodiment of the present application performs optimal selection of the truncation factor, and uses GCV to select the truncation factor of the regularized T-TLS. In the method, the measurement data is randomly divided into two groups, one of which is used for verification, and the other is used for training the regularized model. The regularization parameter can be determined by minimizing the objective function (10) (see Figure 6 ):

[0111]

[0112] In the formula, min{G(λ)} represents the minimized objective function. is the pseudo-inverse of A π .

[0113] The minimized objective function of the embodiment of the present application considers the prediction performance of the error model on the verification set. By repeating the cross-validation process multiple times in different partitions, the estimation of the model generalization performance can be obtained, and the optimal regularization parameter of the model can be determined.

[0114] The embodiment of the present application selects the regularization parameter using the generalized cross-validation method (GCV). Compared with the traditional L-curve method, because the L-curve method is not necessarily completely accurate in determining the corner of the L-curve for the truncation type regularization (such as T-TLS), the method of the embodiment of the present application has higher accuracy of the calibration results.

[0115] Specific implementation of step S400

[0116] In an embodiment, the method of the embodiment of the present application identifies the parameter error Compensate for the nominal parameters to update the kinematic parameters of the controller.

[0117] Experimental verification of the method according to the present application

[0118] The method of the embodiment of the present application verifies the calibration results by a set of additional verification configurations (Verification Group, VG), see Figure 7a , Figure 7b and Figure 7c The T-TLS calibration method proposed in the present application achieves excellent accuracy, and the angle error of the 3PSS / S parallel robot 100 is controlled within 0.1°. Further, the T-TLS calibration method is compared with other two commonly used Tikhonov regularization and truncated singular value decomposition (TSVD) methods, see Figure 8The method has absolute advantages in precision. The method uses a regularization method to solve the identification ill-posed problem caused by the ill-conditioned error model without relying on the selection of the position. The method replaces the ill-conditioned solution of the original problem with a good approximate solution, ensures the robustness of the identification result, and improves the calibration accuracy of the parallel robot 100. The method initiatively applies a truncated total least squares (T-TLS) regularization method to inverse kinematics calibration of a 3PSS / S parallel robot 100, that is, in the presence of inevitable noise disturbance of the measuring instrument under real conditions, the T-TLS method has higher calibration accuracy in combination with the characteristics of the inverse kinematics error model in which error model disturbance and joint displacement bias data disturbance exist simultaneously.

[0119] It should be appreciated that the method steps in the embodiments of the present application can be realized or implemented by computer hardware, a combination of hardware and software, or through computer instructions stored in a non-transitory computer readable memory. The method can use standard programming techniques. Each program can be implemented in a high-level procedural or object-oriented programming language to communicate with a computer system. However, if necessary, the program can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language. Furthermore, for this purpose, the program can run on a programmed special integrated circuit.

[0120] In addition, the operations of the processes described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes described herein (or variations and / or combinations thereof) can be performed under the control of one or more computer systems configured with executable instructions (e.g., executable instructions, one or more computer programs or one or more applications), hardware or combinations thereof configured to perform the operations described herein. The computer programs include a plurality of instructions executable by one or more processors.

[0121] Further, the method can be implemented in any suitable type of computing platform operably connected thereto. Aspects of the present application can be implemented in machine readable code stored on a non-transitory storage medium or device, whether removable or integrated to the computing platform, such that it can be read by a programmable computer to configure and operate the computer to perform the processes described herein. In addition, the machine readable code, or portions thereof, can be transmitted over a wired or wireless network. The present application can also include the computer itself when programmed in accordance with the methods and techniques described herein.

[0122] A computer program can be applied to input data to perform the functions described herein, thereby transforming the input data to generate output data that is stored to non-volatile memory. The output information can also be applied to one or more output devices such as a display. In a preferred embodiment of the application, the transformed data represents a physical and tangible object, including a particular visual depiction of a physical and tangible object produced on a display.

[0123] The above description is only preferred embodiments of the present application, the present application is not limited to the above-described embodiments, as long as the same means to achieve the technical effects of the present application, any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application, should be included in the scope of protection of the present application. The technical solutions and / or embodiments within the scope of protection of the present application can have various modifications and changes.

Claims

1. A kinematic calibration method for a parallel robot (100), characterized in that, The parallel robot (100) is equipped with a data acquisition system (200); the parallel robot (100) includes a mobile platform (110), a base (120), a branch (130), and a linear motor (140). The mobile platform (110) is connected to the base (120) via a passive branch (150). The branch (130) includes an upper ball joint (131), a lower ball joint (132), and a linear joint (133). The branch (130) is connected to the mobile platform (110) via the upper ball joint (131). 0) The lower ball joint (132) is connected to the linear joint (133), and the linear joint (133) is connected to the linear motor (140); the data acquisition system (200) includes an upper auxiliary clamp (210), a lower auxiliary clamp (220), and multiple target holders (240) for mounting the reflective target ball (230). Some of the target holders (240) are mounted on the mobile platform (110) through the upper auxiliary clamp (210), and some of the target holders (240) are mounted on the linear motor (140) through the lower auxiliary clamp (220); The method includes the following steps: S100. Obtain the kinematic parameters of the parallel robot (100) and input them into the inverse kinematic parameter error model to obtain the transformation error between the base coordinate system and the moving platform coordinate system, as well as the mapping relationship between the kinematic parameter errors; wherein, the inverse kinematic parameter error model is expressed as follows: In the formula, This represents the joint input of the parallel robot (100). This indicates the end-effector pose output of the parallel robot (100). , and These are the position and orientation of the end effector of the parallel robot (100), respectively, where the superscript... The representative data is obtained through measurement, and the subscript is... A sequence number indicating position and attitude; Representing the kinematic parameters, the implicit kinematic equations are as follows: ; Represents the parameter error vector; S200: Obtain the measurement data of the data acquisition system (200), as well as the transformation relationship between the laser tracker coordinate system and the base coordinate system and between the tool center coordinate system and the moving platform coordinate system, so that the measurement data is uniformly represented in the base coordinate system of the parallel robot (100) after coordinate system transformation; S300. Identify parameter errors by using the truncation-based overall least squares regularization method, and make the optimal selection of the truncation factor to obtain the best regularization parameter. S400, The nominal parameters are compensated according to the identified parameter error in order to update the controller kinematic parameters of the parallel robot (100).

2. The method according to claim 1, characterized in that, In step S200, the homogeneous transformation relationship between the base coordinate system, the moving platform coordinate system, the laser tracker coordinate system, and the tool center coordinate system is expressed as follows: In the formula, Transformation Relationship The coordinate system of the moving platform is a homogeneous representation of the coordinate system of the base. Transformation Relationship The coordinate system of the tool center is represented homogeneously in the coordinate system of the moving platform. Transformation Relationship The coordinate system of the tool center is given a homogeneous representation in the coordinate system of the laser tracker. Transformation Relationship This is the homogeneous representation of the base coordinate system in the laser tracker coordinate system.

3. The method according to claim 2, characterized in that, In step S200, the transformation relationship The determination includes the following steps: S211. A virtual sphere is fitted to the tool center point of the parallel robot (100) by random motion to calculate and obtain... The position vector; S212, Collect several measurement points on the base (120) to fit the plane of the base (120) and of Direction vector; S213, drive the linear motor (140) to perform single-axis linear joint (133) movement, and obtain the reflective target ball (230) set on the lower auxiliary clamp (220). of Direction vector; S214, Determined by right-hand rule of Direction vector.

4. The method according to claim 2, characterized in that, In step S200, the transformation relationship The determination includes the following steps: S221. Move the three joint axes to the theoretical zero position of the linear motor (140). ; S222, The origin of the tool center coordinate system is determined by the three reflective target balls (230) set on the upper auxiliary fixture (210); S223, Determine the plane fitted by the center points of the three reflective target balls (230) set on the upper auxiliary clamp (210). of Direction vector; S224. Determine the origin based on the center point of a certain reflective target ball (230) set on the upper auxiliary clamp (210). of Direction vector; S225, determined by the right-hand rule of Direction vector.

5. The method according to claim 2, characterized in that, In step S300, the truncated total least squares regularization method includes the following steps: S310, For augmented matrix Singular value decomposition expansion: In the formula, where and Let be orthogonal matrices and respectively be the left and right eigenma matrices of the augmented matrix, scalar and They are matrices The number of rows and columns, It is the first augmented matrix. One singular value; in, In the formula and It is a known explicit vector matrix that is associated with the end-effector pose data, joint encoder data, and nominal kinematic parameters. It is the parameter error that needs to be estimated; S320. Select a cutoff factor. ,in ; S330. Divide the right characteristic matrix into four parts according to the truncation factor: S340. Based on the results of steps S310 to S330, obtain the estimate of the minimum norm cutoff total least squares: In the formula, where yes The false rebellion.

6. The method according to claim 5, characterized in that, In step S300, the optimal regularization parameter is obtained through the following calculation: In the formula, This represents minimizing the objective function; yes The false rebellion.

7. A computer-readable storage medium having stored thereon program instructions that, when executed by a processor, perform the method as described in any one of claims 1 to 6.

8. A parallel robot (100), characterized in that, include: A computer device comprising the computer-readable storage medium of claim 7.

9. The parallel robot (100) according to claim 8, characterized in that, A fixed rod (122) is provided in the middle of the base (120). The passive branch (150) includes an upper driven rod (151) and a lower driven rod (152). The upper driven rod (151) and the lower driven rod (152) are hinged together. The upper driven rod (151) is connected to the middle of the moving platform (110). The lower driven rod (152) is movably connected to the fixed rod (122).

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