CN110193829B - Robot precision control method for coupling kinematics and rigidity parameter identification - Google Patents
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Abstract
The invention discloses a robot precision control method for coupling kinematics and rigidity parameter identification, and belongs to the technical field of precision compensation of industrial robots. The method corrects errors of a robot kinematics model by identifying kinematic parameters of the industrial robot, realizes rigidity modeling of the robot by a rigidity identification method, provides a second-order compensation scheme for compensating geometric errors of the robot and flexible errors under a load state by combining six-dimensional force sensor online dynamic sensing operation loads, and realizes accurate positioning of the robot under a working condition state. According to the method, the accurate calculation of the geometric error and the flexibility error of the robot is adopted, so that the high-precision control of the absolute positioning error of the robot in the machining state can be realized, and the technical requirements of the robot in the high-precision machining fields such as hole making, milling and the like are met.
Description
Technical Field
The invention belongs to the technical field of robot precision compensation, and particularly relates to a robot precision control method for coupling kinematics and rigidity parameter identification, which can effectively improve the absolute positioning precision of a robot in a working state.
Background
The industrial robot is used as a typical flexible high-precision operation carrier, has the characteristics of high operation flexibility, high automation degree, low space requirement and low operation cost, can realize processing tasks such as hole making, milling, polishing and the like by matching with a multifunctional end effector, and is core processing equipment in high-end manufacturing industry, particularly aerospace high-added-value manufacturing and assembling fields. However, the serial chain structure of the industrial robot causes low rigidity and absolute positioning accuracy of the robot body, and the weak rigidity property also causes low tolerance capability of the robot in operation load, thereby affecting the positioning accuracy and operation quality of the tail end in a machining state. Therefore, it is necessary to calculate and compensate the absolute positioning error of the robot in the working state.
The robot precision compensation technology is the most common means for improving the positioning precision of the robot, the robot precision compensation technology of the robot in an idle state has already been studied at home and abroad to a certain extent, most researchers develop research from the calibration of a kinematic model because kinematic parameter errors are the main error source of the positioning errors of the robot, and the robot model is calibrated by modifying parameters of a robot controller to realize body error compensation. Least squares are used in the "ZAK G, BENHABIB B, FENTON R, equivalent.application of the weighted least squares parameter estimation method to the robot calibration. Journal of Mechanical Design,1994,116(3): 890-. However, the kinematics calibration method as a method for processing the preposed off-line positioning error has the following defects:
(1) the robot is used as a rigid body, the influence of flexibility on the positioning error of the robot is ignored, the positioning accuracy of the robot in the operation state is not only dependent on the structural parameter error of the robot body, but also can generate a tail end flexibility error under the action of a load borne by the operation process, and the capability of further improving the accuracy of the robot is lacked;
(2) the processing test result shows that the improvement of the absolute positioning precision of the robot by using the calibration method can not meet the operation requirement in the high-precision operation field.
The robot positioning accuracy in the cutting state is studied in the documents "Slavkovic N R, Milutinovic D S, Glaveonjic M M.A method for off-line compensation of cutting force-induced errors in mechanical path modification. the International Journal of Advanced manufacturing technology,2014,70(9-12): 2083-2096", and a positioning error geometric prediction method is proposed on the basis of a robot stiffness model, but in practical application, the method has the following disadvantages:
(1) the establishment of the robot stiffness model is based on the robot kinematics model, and the accuracy of the kinematics model is not discussed or researched;
(2) the offline compensation needs to establish a cutting force action model, the approximation degree of the mathematical model and the actual load borne by the robot in the cutting process is difficult to guarantee, the actual compensation effect upper limit is reduced, and the actual application effect does not achieve the expected effect.
Disclosure of Invention
In view of the defects of the prior art, the invention aims to provide a robot precision control method for coupling kinematics and stiffness parameter identification, so as to solve the problems that the existing robot calibration method has insufficient adaptability to actual processing tasks and the precision of an offline positioning error prediction method is difficult to guarantee.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention discloses a robot precision control method for coupling kinematics and rigidity parameter identification, which comprises the following steps:
step 1: dividing the whole working space into a series of uniform cubic grids according to a given step length in a given robot effective working space, selecting eight vertexes of each cubic grid as sampling point positions, planning a series of reachable postures at each target position, designing a tail end load to simulate processing stress, measuring the pose change of the tail end of the robot before and after loading at different poses by using a laser tracker, and obtaining the load information borne by different poses by a six-dimensional force sensor;
step 2: the method comprises the following steps of establishing a robot kinematic parameter error model by solving the partial derivatives of various kinematic parameters of a robot, and determining the internal association between the micro change dq of the input end of the robot and the micro change dP of the terminal pose:
wherein dx, dy, dz, deltax, deltay and deltaz are positioning and attitude errors of the tail end of the robot respectivelyProjection in the tool coordinate System, Ja、Jα、Jd、JθThe robot kinematics model correction method comprises the following steps that a robot obtains a jacobian matrix of derivation of joint connecting rod length, joint torsion angle, joint offset distance and joint corner, wherein delta a, delta α, delta d and delta theta are errors of the derivation of the joint connecting rod length, the joint torsion angle, the joint offset distance and the joint corner respectively;
and step 3: selecting not less than 8 sampling positions with evenly distributed operation ranges, selecting not less than 3 reachable postures at each position, and realizing the rigidity identification of the robot joint in the whole operation space; establishing a Jacobian matrix on the basis of the corrected robot kinematics model; combining a pose conversion matrix before and after the tail end is loaded, force sensor information and a robot correction kinematics model, and utilizing a robot static stiffness model F (KD) and J (J)-TKθJ-1D, identifying the joint stiffness of the robot;
and 4, step 4: and realizing accurate modeling of the rigidity of the robot on the basis of the corrected kinematic model, and sensing the stress of the tail end of the robot in the operation pose in real time in actual processing operation, thereby realizing online prediction of the operation positioning error of the robot, and realizing accurate positioning control of the robot in the condition state by reversely compensating the operation positioning error of the tail end of the robot.
Furthermore, in the step 1, the effective operation space at the tail end of the robot is divided into three-dimensional grids, and the sampling points meet the technical requirements of kinematic parameter identification and rigidity parameter identification at the same time.
Furthermore, in the step 1, the rotation axial direction of the robot around the tail end is selected according to the operation type, the actual operation posture of the robot is simulated, and the diversity and the reliability of sampling posture selection are considered.
Further, in the step 2, the deviation of each kinematic parameter of the robot is calculated, and the conversion relation between the kinematic error source at the front end of the robot and the pose error at the tail end of the robot is established.
Further, the kinematic parameters in step 2 include joint connecting rod length, joint torsion angle, joint offset distance, and joint rotation angle.
Further, in the step 1, the laser tracker is used for measuring the positions of a group of target balls arranged on a robot flange plate to fit the positions to obtain the change of the tail end pose of the robot, and a six-dimensional force sensor arranged on the robot flange plate is used for sensing the tail end load.
Further, in the step 3, a conversion relation of the pose of the flange before and after loading the load is obtained through least square fitting based on singular value decomposition.
Furthermore, in the step 3, a jacobian matrix is established by using the robot kinematics parameters for identification and correction through a differential transformation method, so that the joint stiffness identification accuracy is improved.
Furthermore, in the step 4, high-precision positioning control of the robot in the working state is realized through an off-line parameter identification and an on-line compliance error prediction two-order compensation method.
The invention has the beneficial effects that:
1. the method can determine the step length for dividing the grid space for the industrial robots of given models, simultaneously realize the target sampling of kinematics and joint rigidity, and reduce the workload in the early stage;
2. according to the invention, the robot rigidity modeling is completed on the basis of the robot structure model corrected by the kinematic parameters, the established rigidity model is closer to the actual rigidity characteristic of the robot, and the accuracy of the robot rigidity model is effectively improved;
3. the method can greatly improve the accuracy of rigidity modeling of the industrial robot, improve the prediction capability of the tail end deformation of the robot in the cutting operation, effectively improve the operation precision of the robot, and meet the technical requirements of the robot in the high-precision machining field of aerospace and the like.
Drawings
Fig. 1 is a schematic diagram of robot working grid space division and sampling point pose.
Fig. 2 is a schematic diagram of a robot link coordinate system and a kinematic parameter model.
Fig. 3 is a schematic diagram of the effect of robot positioning compensation on 25 test points.
Detailed Description
In order to facilitate understanding of those skilled in the art, the present invention will be further described with reference to the following examples and drawings, which are not intended to limit the present invention.
Step 1: the laser tracker is placed in a suitable position to facilitate measurement. And measuring and constructing a coordinate system consisting of a robot Base coordinate system Base, a Flange plate coordinate system Flange, a Tool coordinate system Tool, a six-dimensional Force sensor coordinate system Force and the like by using a laser tracker.
Step 2: within the robot effective working space, the working space is divided into a series of cubic grids according to given grid step length, and the fixed points of the grids are taken as the target positions of the sampling points of kinematics and joint stiffness identification (see Tag 1-Tag 8 in FIG. 1, wherein X isi、Yi、ZiThree direction axes of a Tool coordinate system Tool in a posture corresponding to the tail end position respectively), and a series of sampling postures of the robot at each position are planned by selecting proper angle rotation around a certain coordinate axis (such as the operation axis direction, namely the X direction of the coordinates of the target point), the laser tracker finishes target posture sampling, the tail end load size and the connection mode are designed, the working condition environment is simulated, and the tail end stress size and the tail end stress direction of the robot in different postures are finished through a six-dimensional force sensor.
And step 3: build a kinematic model of the robot, see FIG. 2 (where x)0、y0、z0Form a robot base coordinate system, x1、y1、z1To x5、y5、z5Coordinate system of links constituting the front five joints of the robot, xf、yf、zfA flange plate coordinate system of the robot is formed and is consistent with a connecting rod coordinate system of a sixth joint), micro-change of geometric parameters of the robot is taken as an error source and introduced into a kinematic model, and a conversion relation between a kinematic error source dq at the front end of the robot and a pose error dP at the tail end of the robot is established through matrix differential transformation:
wherein dx, dy, dz, δ x, δ y, δ z are projections of positioning and attitude errors of the robot end in the tool coordinate system, Ja、Jα、Jd、JθThe robot kinematics model correction method comprises the following steps that a robot obtains a jacobian matrix of derivation of joint connecting rod length, joint torsion angle, joint offset distance and joint corner, wherein delta a, delta α, delta d and delta theta are errors of the derivation of the joint connecting rod length, the joint torsion angle, the joint offset distance and the joint corner respectively;
calculating a Jacobian matrix and a single step error change vector matrix of the robot:
Δqi＝-{[J(qi)]T·J(qi)+μi·I}·[J(qi)]T·ΔP(qi)
i represents the number of iterations, I represents the identity matrix; Δ q ofiRepresenting the change in parameter error at the i-th iteration, qiRepresents the parameter error, Δ P (q), of the ith iterationi) Representing the error vector, mu, between the current qi parameter error state and the actual positioniRepresenting the damping factor at the i-th iteration, obtained by the following rule:
by q at the completion of each iterationi+1＝qi+ΔqiAnd updating the geometric parameters of the robot, and finally realizing the kinematic parameter identification of the robot and the accurate establishment of a kinematic model of the robot.
And 4, step 4: selecting not less than 8 sampling points which are uniformly distributed in the full operation space in the grid space, selecting not less than 3 reachable postures at each position, and identifying the rigidity of the joint of the robot by measuring pose information and force sensing information before and after a load:
the position information of the target balls arranged on the robot flange plate before and after the load is obtained through measurement, the pose change of the robot flange plate before and after the load is fitted through singular value decomposition, and the measured stress information is converted into the same coordinate system at the same time.
Identifying the rigidity of the robot joint by using the robot static rigidity model, wherein the calculation formula is expressed as follows:
F＝KD＝J-TKθJ-1D
wherein, F and D are generalized load matrix and end deformation matrix received by the end flange of the robot, and KθRespectively a robot tail end rigidity matrix and a robot joint rigidity matrix, J is a robot Jacobian matrix, the Jacobian matrix is established through a differential transformation method, and corrected kinematic parameters identified by the kinematic parameters are used in the process of establishing the Jacobian matrix; the modification is that:
D＝JKxJTF＝AKx
wherein the content of the first and second substances,
to
Is the inverse of the stiffness of 6 joints of the robot, and a is a matrix related to the force matrix and the jacobian matrix, expressed as:
wherein, FiLine i of the external force F.
Joint stiffness can be passed through Kx＝(ATA)-1ATD, calculating to obtain, and realizing accurate identification of the joint stiffness of the robot.
And 5: completing kinematic parameters of the robot as described aboveAnd the robot rigidity model can be accurately established by identifying the joint rigidity parameters, the stress on the tail end of the robot is sensed in real time under the corresponding operation pose of the robot in the actual processing operation, and the terminal stress is sensed in real time by D (JK)xJTAnd F, realizing the on-line prediction of the operation positioning error of the robot, and realizing the accurate control of the operation positioning of the robot under the condition state through the reverse compensation of the positioning error.
The following example of KUKA-KR500 industrial robot is used to illustrate the specific implementation method of the present invention:
firstly, a robot is used for establishing a coordinate system, and in a space of 800mm multiplied by 800mm, a robot working space is divided into 64 spatial three-dimensional grids according to a grid step length of 200 mm;
secondly, planning and determining the robot pose coordinate information of 8 target positions of all grids in the off-line programming software, and respectively rotating the initial pose by +/-10 degrees around the X axis of a tool coordinate system to obtain three different poses so as to simulate the robot processing task within a certain range;
thirdly, sampling the pose of the target in an idle state, and recording the position of the target ball on the flange plate by a laser tracker; the tail end is fixedly connected with a 50KG load simulation robot, the tail end stress of the robot in the operation process is simulated, the target pose sampling is completed again in the load state, and the position information of a target ball on a flange plate in the load state of the robot is recorded through a laser tracker;
and finally, processing the collected load information and pose information, and calculating by using an identification algorithm to obtain kinematic parameters and joint stiffness of the robot, wherein the kinematic parameters and the joint stiffness are shown in tables 1 and 2, so that joint stiffness identification of the full working space of the robot and accurate modeling of the robot stiffness are realized.
TABLE 1 robot link parameter error identification result
TABLE 2 robot Joint identification results
On the basis of rigidity modeling, a six-dimensional force sensor is combined in the machining process to carry out online actual measurement on a compression load, online prediction and compensation of a positioning error of a robot in a machining state can be realized, 25 robot operation poses are randomly selected, positioning compensation of the robot in a load state of the poses is realized, the result is shown in figure 3, the error after compensation is improved to be within 0.4mm from 1.8-3 mm, and the precision is improved to be more than 70%.
While the invention has been described in terms of its preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.
Claims (8)
1. A robot precision control method for coupling kinematics and rigidity parameter identification is characterized by comprising the following steps:
step 1: dividing the whole working space into a series of uniform cubic grids according to a given step length in a given robot effective working space, selecting eight vertexes of each cubic grid as sampling point positions, planning a series of reachable postures at each target position, designing a tail end load to simulate processing stress, measuring the pose change of the tail end of the robot before and after loading at different poses by using a laser tracker, and obtaining the load information borne by different poses by a six-dimensional force sensor;
step 2: the method comprises the following steps of establishing a robot kinematic parameter error model by solving the partial derivatives of various kinematic parameters of a robot, and determining the internal association between the micro change dq of the input end of the robot and the micro change dP of the terminal pose:
wherein dx, dy, dz, deltax, deltay and deltaz are the projection of the positioning and attitude errors of the tail end of the robot on a tool coordinate system respectivelyShadow, Ja、Jα、Jd、JθThe robot kinematics model correction method comprises the following steps that a robot obtains a jacobian matrix of derivation of joint connecting rod length, joint torsion angle, joint offset distance and joint corner, wherein delta a, delta α, delta d and delta theta are errors of the derivation of the joint connecting rod length, the joint torsion angle, the joint offset distance and the joint corner respectively;
and step 3: selecting not less than 8 sampling positions with evenly distributed operation ranges, selecting not less than 3 reachable postures at each position, and realizing the rigidity identification of the robot joint in the whole operation space; establishing a Jacobian matrix on the basis of the corrected robot kinematics model; combining a pose conversion matrix before and after the tail end is loaded, six-dimensional force sensor information and a robot correction kinematics model, and utilizing a robot static stiffness model F (KD) and J (J)-TKθJ-1D, identifying the joint stiffness of the robot; wherein, F and D are generalized load matrix and end deformation matrix received by the end flange of the robot, and KθRespectively a robot tail end rigidity matrix and a robot joint rigidity matrix, and J is a robot Jacobian matrix;
and 4, step 4: the robot rigidity accurate modeling is realized on the basis of the corrected kinematic model, the stress of the tail end of the robot under the operation pose is sensed in real time in the actual processing operation, so that the on-line prediction of the operation positioning error of the robot is realized, and the accurate positioning control under the robot condition state is realized by the reverse compensation of the operation positioning error of the tail end of the robot;
and 2, the kinematic parameters in the step 2 comprise joint connecting rod length, joint torsion angle, joint offset distance and joint rotation angle.
2. The robot precision control method for coupling kinematics and stiffness parameter identification according to claim 1, wherein in the step 1, an effective working space at the tail end of the robot is divided into three-dimensional grids, and sampling points simultaneously meet technical requirements of kinematics parameter identification and stiffness parameter identification.
3. The robot precision control method for coupling kinematics and stiffness parameter identification according to claim 1, wherein in the step 1, the robot is selected according to the operation type, and the robot rotates around the end axial direction to simulate the actual operation posture of the robot.
4. The robot precision control method for coupling kinematics and stiffness parameter identification according to claim 1, wherein in the step 2, the partial derivatives of the kinematics parameters of the robot are calculated, and the conversion relation between the kinematic error source at the front end of the robot and the pose error at the tail end of the robot is established.
5. The method for controlling the robot precision through coupled kinematics and stiffness parameter identification according to claim 1, wherein in the step 1, a laser tracker is used for measuring the positions of a group of target balls mounted on a robot flange plate to fit the positions to obtain the change of the terminal pose of the robot, and a six-dimensional force sensor mounted on the robot flange plate is used for sensing the terminal load.
6. The robot precision control method based on coupled kinematics and stiffness parameter identification according to claim 5, wherein the conversion relationship of the pose of the flange before and after loading is obtained through least square fitting based on singular value decomposition in the step 3.
7. The method for controlling robot precision through coupled kinematics and stiffness parameter identification according to claim 1, wherein in the step 3, a jacobian matrix is established by using a differential transformation method and robot kinematics parameters for identification and correction, so as to improve the accuracy of joint stiffness identification.
8. The method for controlling the precision of the robot by coupling the kinematics and the stiffness parameter identification according to claim 1, wherein the step 4 is implemented by using an off-line parameter identification and an on-line compliance error prediction two-step compensation method to control the high-precision positioning of the robot in the working state.
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| CN108406768A (en) * | 2018-03-09 | 2018-08-17 | 汇川技术（东莞）有限公司 | A kind of robot calibration method and system based on dead weight and load deformation compensation |
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