CN114131607B - Kinematic calibration method and system for generalized kinematic errors of industrial robot - Google Patents
Kinematic calibration method and system for generalized kinematic errors of industrial robot Download PDFInfo
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Abstract
The invention relates to a kinematic calibration method and a kinematic calibration system for generalized kinematic errors of an industrial robot. The method comprises the following steps: constructing a joint and a geometric error model of the robot to be identified and determining a generalized kinematic error model according to the two error models; performing parameter identification on the generalized kinematic error model to obtain an identified error model; under the current iteration times, acquiring a nominal joint instruction of the robot to be identified and a compensated joint instruction under the current iteration times; obtaining a joint instruction error matrix under the current iteration times based on the nominal joint instruction, the identified error model and the compensated joint instruction under the current iteration times; judging whether the two norms of the joint instruction error matrix under the current iteration times are smaller than a set tolerance or not; if so, determining the compensated joint instruction under the current iteration number as a final joint instruction; and if not, updating the compensated joint instruction under the next iteration number. The invention can improve the motion of the industrial robot after calibration.
Description
Technical Field
The invention relates to the technical field of robot generalized kinematics error parameter identification and calibration, in particular to a kinematic calibration method and system for generalized kinematics errors of an industrial robot.
Background
With the transformation and upgrading of the manufacturing industry in China, the development and application of an automation equipment platform represented by industrial robots have very important strategic significance for the transformation and upgrading of production modes and the improvement of advanced manufacturing capability of equipment. The modern manufacturing industry, especially the high-precision industry, puts forward strict requirements on the working rhythm, the load capacity and the working precision of the industrial robot, so that the industrial robot faces extreme working conditions such as high speed, heavy load and the like, a high-precision kinematics model representing the characteristics of the system is established, unknown parameters in the model are accurately acquired, and a solid foundation can be laid for the analysis, design and control application of the robot system.
Although robotic kinematic calibration has been extensively studied, most work only considers ideal rigid body motion, including identifying constant joint offsets, while joint-independent error kinematic models may be sufficient to describe geometric errors (e.g., arm length or alignment errors) caused by structural errors in the robotic components, but are not sufficient to characterize complex motion errors, such as periodic gear errors.
Strain wave gears commonly used in industrial robots have complex position-dependent errors. These position-related errors are constituted by manufacturing tolerances, alignment errors and errors in the position of the teeth of the flexspline and the steel spline. The bending of the bearings can also result in a non-parallel connection of the gearboxes, resulting in out-of-plane errors of the end effector, higher in some locations and lower in others. Inaccurate assembly, gear errors and wear together lead to position-related errors and periodic motion errors. Small-amplitude motion errors in strain wave gear transmission are amplified through series connection, so that large-amplitude complex robot errors are caused, but the problems are not considered in the existing error motion model, so that a more accurate model is required to describe the complex motion errors, and the performance after calibration is improved.
Disclosure of Invention
The invention aims to provide a kinematic calibration method and a kinematic calibration system for generalized kinematic errors of an industrial robot, which can improve the kinematic performance of the industrial robot after calibration.
In order to achieve the purpose, the invention provides the following scheme:
a kinematic calibration method for generalized kinematic errors of an industrial robot comprises the following steps:
constructing a joint error model and a geometric error model of the robot to be identified, and determining a generalized kinematic error model according to the joint error model and the geometric error model;
performing parameter identification on the generalized kinematic error model to obtain an identified generalized kinematic error model;
acquiring a nominal joint instruction of the robot to be identified and a compensated joint instruction under the current iteration times;
obtaining a joint instruction error matrix under the current iteration number based on the nominal joint instruction, the identified generalized kinematic error model and the compensated joint instruction under the current iteration number;
judging whether the two norms of the joint instruction error matrix under the current iteration number are smaller than a set tolerance or not;
if so, determining the joint instruction compensated under the current iteration number as the joint instruction finally compensated by the robot to be identified;
if not, determining the compensated joint instruction under the next iteration number according to the compensated joint instruction under the current iteration number and the joint instruction error matrix under the current iteration number, and updating the iteration number to enter the next iteration.
Optionally, the constructing a joint error model and a geometric error model of the robot to be identified specifically includes:
constructing a geometric error model by adopting differential kinematics based on the DH model of the robot to be identified;
and constructing a joint error model by adopting a polynomial fitting method based on the DH model of the robot to be identified.
Optionally, the performing parameter identification on the generalized kinematic error model to obtain an identified generalized kinematic error model specifically includes:
and carrying out parameter identification on the generalized kinematic error model by using an implicit ring method to obtain an identified generalized kinematic error model.
Optionally, the obtaining a joint instruction error matrix in the current iteration number based on the nominal joint instruction, the identified generalized kinematic error model, and the compensated joint instruction in the current iteration number specifically includes:
inputting the compensated joint instruction under the current iteration number into the identified generalized kinematic error model to obtain an actual terminal transformation matrix;
inputting the nominal joint instruction into a nominal DH model preset by the robot to be identified to obtain a nominal positive kinematic transformation matrix;
calculating the difference between the actual terminal transformation matrix and the nominal positive kinematic transformation matrix to obtain a residual error transformation matrix;
and calculating a joint instruction error matrix under the current iteration number according to the residual error transformation matrix and the Jacobian matrix.
Optionally, the determining the compensated joint instruction for the next iteration number according to the compensated joint instruction for the current iteration number and the joint instruction error matrix for the current iteration number specifically includes:
and determining the sum of the compensated joint instruction under the current iteration number and the joint instruction error matrix under the current iteration number as the compensated joint instruction under the next iteration number.
A kinematic calibration method system for generalized kinematic errors of an industrial robot comprises the following steps:
the model building module is used for building a joint error model and a geometric error model of the robot to be identified and determining a generalized kinematic error model according to the joint error model and the geometric error model;
the identification module is used for carrying out parameter identification on the generalized kinematic error model to obtain an identified generalized kinematic error model;
the acquisition module is used for acquiring the nominal joint instruction of the robot to be identified and the compensated joint instruction under the current iteration times;
the joint instruction error matrix determining module is used for obtaining a joint instruction error matrix under the current iteration times based on the nominal joint instruction, the identified generalized kinematic error model and the compensated joint instruction under the current iteration times;
the judging module is used for judging whether the two norms of the joint instruction error matrix under the current iteration times are smaller than a set tolerance or not;
the final compensated joint instruction determining module is used for determining the joint instruction compensated under the current iteration number as the joint instruction finally compensated by the robot to be identified if the final compensated joint instruction is positive;
and if not, determining the compensated joint instruction under the next iteration number according to the compensated joint instruction under the current iteration number and the joint instruction error matrix under the current iteration number, and updating the iteration number to enter the next iteration.
Optionally, the model building module specifically includes:
the geometric error model construction unit is used for constructing a geometric error model by adopting differential kinematics based on the DH model of the robot to be identified;
and the joint error model building unit is used for building a joint error model by adopting a polynomial fitting method based on the DH model of the robot to be identified.
Optionally, the identification module specifically includes:
and the identification unit is used for carrying out parameter identification on the generalized kinematics error model by utilizing an implicit ring method to obtain an identified generalized kinematics error model.
Optionally, the joint instruction error matrix determining module specifically includes:
the actual terminal transformation matrix determining unit is used for inputting the compensated joint instruction under the current iteration times into the identified generalized kinematic error model to obtain an actual terminal transformation matrix;
the nominal positive kinematics transformation matrix determining unit is used for inputting the nominal joint instruction into a nominal DH model preset by the robot to be identified to obtain a nominal positive kinematics transformation matrix;
a residual error transformation matrix determining unit, configured to calculate a difference between the actual end transformation matrix and the nominal positive kinematics transformation matrix to obtain a residual error transformation matrix;
and the joint instruction error matrix determining unit is used for calculating a joint instruction error matrix under the current iteration number according to the residual error transformation matrix and the Jacobian matrix.
Optionally, the update module specifically includes:
and the updating unit is used for determining the sum of the compensated joint instruction under the current iteration times and the joint instruction error matrix under the current iteration times as the compensated joint instruction under the next iteration times.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the method comprises the steps of constructing a joint error model and a geometric error model of a robot to be identified, and determining a generalized kinematic error model according to the joint error model and the geometric error model; performing parameter identification on the generalized kinematic error model to obtain an identified generalized kinematic error model; under the current iteration times, acquiring a nominal joint instruction of the robot to be identified and a compensated joint instruction under the current iteration times; obtaining a joint instruction error matrix under the current iteration number based on the nominal joint instruction, the identified generalized kinematic error model and the compensated joint instruction under the current iteration number; judging whether the two norms of the joint instruction error matrix under the current iteration number are smaller than a set tolerance or not; if so, determining the compensated joint instruction under the current iteration times as the final compensated joint instruction of the robot to be identified; if not, determining the compensated joint instruction under the next iteration number according to the compensated joint instruction under the current iteration number and the joint instruction error matrix under the current iteration number, updating the iteration number to enter the next iteration, integrating a joint error model and a geometric error model by the generalized kinematic error model, and considering various error factors, so that the motion performance of the calibrated industrial robot can be improved when the robot moves according to the finally compensated joint instruction.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is an error source diagram of an industrial robot provided by an embodiment of the invention;
fig. 2 is a flowchart of a kinematic calibration method for a generalized kinematic error of an industrial robot according to an embodiment of the present invention;
fig. 3 is a flowchart of compensating for an articulation command according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The embodiment of the invention provides a kinematic calibration method for a generalized kinematic error of an industrial robot, which comprises the following steps:
and constructing a joint error model and a geometric error model of the robot to be identified, and determining a generalized kinematic error model according to the joint error model and the geometric error model.
And performing parameter identification on the generalized kinematic error model to obtain an identified generalized kinematic error model.
And acquiring the nominal joint instruction of the robot to be identified and the compensated joint instruction under the current iteration times.
And obtaining a joint instruction error matrix under the current iteration number based on the nominal joint instruction, the identified generalized kinematic error model and the compensated joint instruction under the current iteration number.
And judging whether the two norms of the joint instruction error matrix under the current iteration times are smaller than a set tolerance or not.
And if so, determining the joint instruction compensated under the current iteration number as the joint instruction finally compensated by the robot to be identified.
If not, determining the compensated joint instruction under the next iteration number according to the compensated joint instruction under the current iteration number and the joint instruction error matrix under the current iteration number, and updating the iteration number to enter the next iteration.
In practical application, the building of the joint error model and the geometric error model of the robot to be identified specifically includes:
and constructing a geometric error model by adopting differential kinematics based on the DH model of the robot to be identified.
And constructing a joint error model by adopting a polynomial fitting method based on the DH model of the robot to be identified.
In practical application, the generalized kinematic error model is specifically:
wherein Fa represents a generalized kinematic error model, i.e. a robot actual end transformation matrix, i represents the number of joints of the robot, and Delta theta1～i,Δd1～i,Δa1～i,Δα1～iDelta beta is the correction value of each parameter of the DH model corrected by the robot, and according to the rule of the DH model, a coordinate system is established at the joint,
a geometric error matrix (obtained by equations (2) to (21)) representing the coordinate system established from the i-1 st joint to the coordinate system established at the i-th joint,
a joint-related error matrix representing the coordinate system established at the i-1 st joint to the coordinate system established at the i-th joint,
indicates joint-related errors (obtained from equations (22) to (28)) of the ith joint, and Δ q1～iAnd a correction value representing each joint command of the robot.
Under the influence of geometric correlation parameter errors, the actual homogeneous transformation matrix of the robot becomes:
in the formula
Representing a homogeneous transformation matrix from a coordinate system established at the ith-1 joint to the coordinate system established at the ith joint, Rot representing a rotation matrix, Trans representing a translation matrix, Rot representingz(θi+Δθi) Representing a rotation matrix about the Z-axis, Rotx(αi+Δαi) Representing a rotation matrix about the X-axis, Roty(βi+Δβi) Representing a rotation matrix, Trans, about the Y axisz(di+Δdi) Representing a translation matrix, Trans, along the Z-axisx(ai+Δai) Representing a translation matrix along the X-axis.
The first order approximation is performed on the coordinate transformation matrix differential to obtain:
d is a representation of the differential, where
A nominal homogeneous transformation matrix representing the coordinate system established at the i-1 st joint to the coordinate system established at the ith joint,
for a differential transformation matrix, it can be expressed according to differential kinematics as:
δ x, δ y, δ z represent errors in joint pose, dx, dy, dz represent errors in joint position at X, Y, Z, respectively.
The coordinate transformation matrix is fully differentiated to obtain:
c denotes cos and s denotes sin.
Suppose DβiIs betaiCoefficient matrix of (2):
by solving the following steps:
calculate D in the same wayθi、Ddi、Dai、DαiMatrix:
based on the result of the calculation of the coefficient matrix,
can be written as:
thereby obtaining
The error elements in the method are as follows:
δx＝cθiΔαi-sθicαiΔβi (14)
δy＝sθiΔαi+cθicαiΔβi (15)
δz＝Δθi+sαiΔβi (16)
dx＝cθiΔαi-disθiΔαi-(dicθicαi-aisθisαi)Δβi (17)
dy＝sθiΔαi+dicθiΔαi-(disθicαi+aicθisαi)Δβi (18)
dz＝Δdi+aicαiΔβi (19)
from equation (3):
the factors causing the generation of the joint related error are numerous and are difficult to describe by a certain value, and the joint related error changes along with the movement of the robot, so in order to describe the complex joint related error, the Chebyshev function is adopted to represent the joint related error.
The chebyshev function expression is:
C(λ)＝a0+a1c1(λ)+a2c2(λ)+…+ancn(λ) (22)
in which n represents the order of the Chebyshev function, a0,a1,a2,...anThe coefficient of the chebyshev is expressed,
for convenience of data processing, the ith joint instruction q is processediNormalized and recorded as
qi,minRepresents the ith minimum angle of joint motion, qi,maxRepresents the ith maximum angle of articulation:
let us denote the joint related error of the ith joint as Δ qiThe actual joint motion angle is:
wherein:
the actual coordinate transformation matrix is:
further, a joint related error model can be obtained as follows:
Fajrepresenting a robot joint related error model.
In conjunction with the above analysis, when joint related errors are considered, the robot error model (generalized kinematic error model) can be expressed as:
Fa＝Fag(Δθ1～i,Δd1～i,Δa1～i,Δα1～i,Δβ)+Faj(Δq1～i) (29)
further finishing to obtain:
in practical application, the performing parameter identification on the generalized kinematic error model to obtain an identified generalized kinematic error model specifically includes:
and carrying out parameter identification on the generalized kinematic error model by using an implicit ring method to obtain an identified generalized kinematic error model.
In practical applications, the obtaining a joint instruction error matrix in the current iteration number based on the nominal joint instruction, the identified generalized kinematic error model, and the compensated joint instruction in the current iteration number specifically includes:
and inputting the compensated joint instruction under the current iteration times into the identified generalized kinematics error model to obtain an actual terminal transformation matrix.
And inputting the nominal joint instruction into a DH model preset by the robot to be identified to obtain a nominal positive kinematic transformation matrix.
And calculating the difference between the actual terminal transformation matrix and the nominal positive kinematic transformation matrix to obtain a residual error transformation matrix.
And calculating a joint instruction error matrix under the current iteration number according to the residual error transformation matrix and the Jacobian matrix.
In practical application, the determining the compensated joint instruction for the next iteration number according to the compensated joint instruction for the current iteration number and the joint instruction error matrix for the current iteration number specifically includes:
and determining the sum of the compensated joint instruction under the current iteration number and the joint instruction error matrix under the current iteration number as the compensated joint instruction under the next iteration number.
A kinematic calibration method system for generalized kinematic errors of an industrial robot comprises the following steps:
the model building module is used for building a joint error model and a geometric error model of the robot to be identified and determining a generalized kinematic error model according to the joint error model and the geometric error model.
And the identification module is used for carrying out parameter identification on the generalized kinematics error model to obtain an identified generalized kinematics error model.
And the acquisition module is used for acquiring the nominal joint instruction of the robot to be identified and the compensated joint instruction under the current iteration times.
And the joint instruction error matrix determining module is used for obtaining a joint instruction error matrix under the current iteration times based on the nominal joint instruction, the identified generalized kinematic error model and the compensated joint instruction under the current iteration times.
And the judging module is used for judging whether the two norms of the joint instruction error matrix under the current iteration times are smaller than a set tolerance.
And the final compensated joint instruction determining module is used for determining the compensated joint instruction under the current iteration times as the final compensated joint instruction of the robot to be identified if the final compensated joint instruction is positive.
And if not, determining the compensated joint instruction under the next iteration number according to the compensated joint instruction under the current iteration number and the joint instruction error matrix under the current iteration number, and updating the iteration number to enter the next iteration.
As an optional implementation manner, the model building module specifically includes:
and the geometric error model construction unit is used for constructing a geometric error model by adopting differential kinematics based on the DH model of the robot to be identified.
And the joint error model building unit is used for building a joint error model by adopting a polynomial fitting method based on the DH model of the robot to be identified.
As an optional implementation manner, the identification module specifically includes:
and the identification unit is used for carrying out parameter identification on the generalized kinematics error model by utilizing an implicit ring method to obtain an identified generalized kinematics error model.
As an optional implementation manner, the joint instruction error matrix determining module specifically includes:
and the actual terminal transformation matrix determining unit is used for inputting the compensated joint instruction under the current iteration times into the identified generalized kinematic error model to obtain an actual terminal transformation matrix.
And the nominal positive kinematic transformation matrix determining unit is used for inputting the nominal joint instruction into a nominal DH model preset by the robot to be identified to obtain a nominal positive kinematic transformation matrix.
And the residual error transformation matrix determining unit is used for calculating the difference between the actual terminal transformation matrix and the nominal positive kinematic transformation matrix to obtain a residual error transformation matrix.
And the joint instruction error matrix determining unit is used for calculating a joint instruction error matrix under the current iteration number according to the residual error transformation matrix and the Jacobian matrix.
As an optional implementation manner, the update module specifically includes:
and the updating unit is used for determining the sum of the compensated joint instruction under the current iteration times and the joint instruction error matrix under the current iteration times as the compensated joint instruction under the next iteration times.
As shown in fig. 2, the present embodiment provides a more specific kinematic calibration method for characterizing generalized kinematic errors of a robot:
(1) and establishing a generalized kinematic error model.
Analyzing the reasons of error generation of the industrial robot, establishing a generalized kinematics error model containing a geometric error and a joint error of the robot according to error characteristics, and dividing the error of the industrial robot into the geometric error and the joint error, wherein the geometric error is a constant error, and the joint error is a follow-up error. Therefore, the geometric error is described by adopting the differential kinematics model to obtain a geometric error model, the joint error is described by adopting the Chebyshev polynomial to obtain a joint error model, and the two are combined to obtain the generalized kinematics error model.
(2) And identifying parameters of the generalized kinematic error model.
And (6) acquiring data. Acquiring a nominal DH parameter and an actual DH parameter of a robot to be identified; measuring the tool length and the standard deviation of the gauge; the method comprises the steps of randomly selecting measurement points in a working space of the robot, wherein measurement data are tail end position information of the robot and are divided into a test set and a verification set (the test set is used for parameter identification, and the verification set is used for verifying the parameter identification effect).
The identification parameters are coefficients for identifying the Chebyshev polynomial (as shown in figure 1, namely a robot body error, a measuring tool error and a base coordinate conversion error, the body error comprises a geometric correlation error and a joint correlation error, the geometric correlation error comprises a zero offset error, an initial alignment error and a manufacturing and assembling error, and the joint correlation error comprises a screw pitch error, a harmonic drive error, an out-of-plane error and a backlash error); in the actual measurement process, besides the error of the robot body, the error of the measuring tool and the error of the relative position between the measuring tool and the robot all affect the measurement result, and the influence of the factors is eliminated as much as possible, on the basis of the error model, an objective function containing the robot body error, the measuring tool length error and the base standard conversion error is established by using an implicit loop method (equation (31)), and the parameter identification is carried out on the generalized kinematic error model according to the end position information.
(3) Compensation of joint commands.
As shown in fig. 3, the nominal command is used as an initial value of the compensation command, the initial value is substituted into the generalized kinematic error model and the DH model obtained by identification, a nominal positive kinematic transformation matrix and an actual terminal transformation matrix are obtained respectively, the actual terminal transformation matrix and the nominal positive kinematic transformation matrix are subtracted to obtain a residual error conversion matrix, position error elements are extracted to form an error vector, a joint compensation command increment of the error vector is calculated based on the nominal inverse jacobian matrix J, whether the vector is smaller than a given tolerance is judged, if the vector does not meet the requirement of iteration, the final compensation command of each joint angular displacement can be output until the vector is smaller than the given tolerance, and the joint command is updated on the basis of the nominal joint command to realize compensation.
The above steps are described in detail below:
the attitude measurement of the tail end of the robot is difficult, the position measurement of the tail end of the robot is relatively easy, and because the joints of the robot are in a strong coupling relationship, when the position accuracy of the robot is improved, the attitude accuracy of the tail end of the robot is also correspondingly improved, so that only a positioning error model of the tail end of the robot is established in the embodiment.
The position information of the robot in the space can be obtained through the laser measuring instrument, and in the actual measurement, the measured position information is the position information of the target ball on the robot under the measurement coordinate system
Wherein, the first and the second end of the pipe are connected with each other,
a homogeneous transformation matrix representing the transformation of the measured coordinate system with the robot-based coordinate system, Fn (q) predetermined for a nominal DH model of the robot,
indicating the tool length. And (4) performing preliminary calculation on the base standard conversion matrix and the tool length through formulas (33) to (34).
Setting the robot in a certain posture as an initial posture, keeping the position of the robot unchanged, and continuously changing the posture of the robot to obtain the position coordinates of the sphere center (x, y, z) through fitting so as to obtain a tool length and base mark transformation matrix. Let the robot end position coordinate be (x)j,yj,zj) J represents the number of measurement points, the radius is R, n noncoplanar points in the collection space are fitted, and the fitting can be obtained by a formula of a sphere:
after the coordinates (x, y, z) of the center of the sphere are calculated, a certain point (x) is takeni，yi，zi) Calculating the length of the measuring tool as follows:
ptx，pty，ptzexpressing the lengths of the measuring tool in the XYZ three directions, and further calculating a transformation matrix T of the coordinate system by equation (32)0 m。
The calculation of the base coordinate system transformation matrix and the length of the measuring tool is performed before the calibration of the robot, so that part of the error of the robot may be calculated into the base coordinate system transformation matrix and the length of the measuring tool, and therefore, in the subsequent calculation, the correction value is also added to the base coordinate system transformation matrix and the length of the measuring tool
In the formula,. DELTA.mConverting the matrix error matrix for the base label:
in the formula oftx，δty，δtzCorrection of the base index transformation matrix rotation in three directions, X, Y, Z, dtxdtydtzThe correction in three directions to the base index conversion matrix position part XYZ is shown.
The tool length correction value is expressed as:
in the formula,. DELTA.tx，Δty，ΔtzRepresents the correction of the calculated tool lengths in the three directions X, Y, Z,
the tool lengths in the three directions X, Y and Z after correction are shown respectively.
The data obtained by actual measurement is the position data of the target ball at the tail end of the robot under the coordinate system of the measuring instrument:
ξ represents the measurement error of the measuring instrument,
representing the actual position of the robot motion, Fa (q + deltaq) representing the terminal pose matrix of the robot represented by the generalized kinematic error model,
representing the actual tool length. The objective function of parameter identification obtained according to the implicit loop method is as follows:
ξkrepresenting the measurement error matrix, k representing the number of elements in the measurement error matrix,
representing the transposition of a measurement error matrix, identifying parameters of a formula (38) according to an objective function to obtain an identified generalized kinematic error model, and changing a data set on the basis of the calculated parameters to bring the parameters into a robot in order to enable the calculated parameters to be close to the actual conditions of the robotAnd continuously calculating the model, continuously adjusting the parameters, and finally obtaining the optimal estimation of the parameters of the full working space so as to obtain the finally identified generalized kinematic error model.
Compensating for geometric and joint related errors by modifying controller inputs using qnIndicating nominal joint command, by qcRepresenting the compensated joint command, the desired compensation effect is:
Fa(qc)＝Fn(qn) (40)
setting qcHas an initial value of qc 1＝qn，qcThe superscript of (a) indicates the number of iterations, the algorithm begins to have a residual error transformation matrix λ:
wherein, ω is11To omega34Representing the error element, extract the error vector de:
the joint command error matrix dq may be expressed as:
dq＝J(qn)-1de (43)
j denotes a jacobian matrix.
Compensated joint instruction at the r +1 th iteration number
The updating is as follows:
repeating equations (41) -44 until the joint command error satisfies:
||dq||2＜tol (45)
tol represents the set tolerance, the final compensated joint command qnewComprises the following steps:
qnew＝qf (46)
wherein q isfAnd (4) representing the compensated joint instruction at the f-th iteration number when the formula (44) is met at the f-th iteration.
Compared with the prior art, the invention has the beneficial effects that:
(1) according to the method, error reasons are analyzed, according to error characteristics, several errors and joint errors of the robot are respectively characterized by adopting differential kinematics and polynomial fitting modes, and a generalized kinematics error model containing geometric errors and joint errors of the robot is established; according to the error model, considering other errors generated by the robot and the measuring instrument in the experiment, establishing a target function comprising a robot body error, a measuring tool length error and a base standard conversion error by using an implicit loop method to identify parameters; calculating joint compensation instruction increment of the error vector based on the nominal inverse Jacobian matrix, and updating the joint instruction on the basis of the nominal joint instruction so as to realize compensation. By adopting the method, the compensation effect can be greatly improved, and 94% of robot kinematic errors can be reduced.
(2) The kinematic calibration method for the robot system to represent the generalized kinematic errors aims at the operating points in the full working space, is suitable for the global model of the full working space, and solves the problem that the current kinematic identification result is only limited to be effective in a specific state.
(3) Compared with the traditional calibration method, the method considers the model containing the geometric correlation error and the joint correlation error, identifies the robot motion error source, classifies the motion error model, and integrates the errors into a single robot motion error model.
(4) Compared with a traditional polynomial fitting mode or a non-parameter model modeling mode such as a neural network, the method has the advantages that the constant value error and the follow-up error are set, the parameter setting number is greatly reduced, and the identification difficulty is reduced.
(5) The method can realize accurate identification of unknown joint errors in the kinematics model of the robot system, so as to obtain a high-precision kinematics model, and lay a solid foundation for analysis, design and control application of the robot system.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A kinematic calibration method for generalized kinematic errors of an industrial robot is characterized by comprising the following steps:
constructing a joint error model and a geometric error model of the robot to be identified, and determining a generalized kinematic error model according to the joint error model and the geometric error model;
performing parameter identification on the generalized kinematic error model to obtain an identified generalized kinematic error model;
under the current iteration times, acquiring a nominal joint instruction of the robot to be identified and a compensated joint instruction under the current iteration times;
obtaining a joint instruction error matrix under the current iteration number based on the nominal joint instruction, the identified generalized kinematic error model and the compensated joint instruction under the current iteration number;
judging whether the two norms of the joint instruction error matrix under the current iteration number are smaller than a set tolerance or not;
if so, determining the joint instruction compensated under the current iteration number as the joint instruction finally compensated by the robot to be identified;
if not, determining the compensated joint instruction under the next iteration number according to the compensated joint instruction under the current iteration number and the joint instruction error matrix under the current iteration number, and updating the iteration number to enter the next iteration.
2. The kinematic calibration method for the generalized kinematic error of the industrial robot according to claim 1, wherein the constructing a joint error model and a geometric error model of the robot to be identified specifically comprises:
constructing a geometric error model by adopting differential kinematics based on the DH model of the robot to be identified;
and constructing a joint error model by adopting a polynomial fitting method based on the DH model of the robot to be identified.
3. The kinematic calibration method for the generalized kinematic error of the industrial robot according to claim 1, wherein the parameter identification of the generalized kinematic error model to obtain the identified generalized kinematic error model specifically comprises:
and carrying out parameter identification on the generalized kinematic error model by using an implicit ring method to obtain an identified generalized kinematic error model.
4. The kinematic calibration method for the generalized kinematic error of the industrial robot according to claim 1, wherein the obtaining a joint command error matrix for the current iteration number based on the nominal joint command, the identified generalized kinematic error model, and the compensated joint command for the current iteration number specifically comprises:
inputting the compensated joint instruction under the current iteration number into the identified generalized kinematic error model to obtain an actual terminal transformation matrix;
inputting the nominal joint instruction into a nominal DH model preset by the robot to be identified to obtain a nominal positive kinematic transformation matrix;
calculating the difference between the actual terminal transformation matrix and the nominal positive kinematic transformation matrix to obtain a residual error transformation matrix;
and calculating a joint instruction error matrix under the current iteration number according to the residual error transformation matrix and the Jacobian matrix.
5. The method for kinematic calibration of generalized kinematic errors of an industrial robot according to claim 1, wherein the determining the compensated joint command for the next iteration number according to the compensated joint command for the current iteration number and the joint command error matrix for the current iteration number specifically comprises:
and determining the sum of the compensated joint instruction under the current iteration number and the joint instruction error matrix under the current iteration number as the compensated joint instruction under the next iteration number.
6. A kinematic calibration system for generalized kinematic errors of an industrial robot, comprising:
the model construction module is used for constructing a joint error model and a geometric error model of the robot to be identified and determining a generalized kinematic error model according to the joint error model and the geometric error model;
the identification module is used for carrying out parameter identification on the generalized kinematics error model to obtain an identified generalized kinematics error model;
the acquisition module is used for acquiring the nominal joint instruction of the robot to be identified and the compensated joint instruction under the current iteration times;
the joint instruction error matrix determining module is used for obtaining a joint instruction error matrix under the current iteration times based on the nominal joint instruction, the identified generalized kinematic error model and the compensated joint instruction under the current iteration times;
the judging module is used for judging whether the two norms of the joint instruction error matrix under the current iteration times are smaller than a set tolerance or not;
the final compensated joint instruction determining module is used for determining the joint instruction compensated under the current iteration number as the joint instruction finally compensated by the robot to be identified if the final compensated joint instruction is positive;
and if not, determining the compensated joint instruction under the next iteration number according to the compensated joint instruction under the current iteration number and the joint instruction error matrix under the current iteration number, and updating the iteration number to enter the next iteration.
7. The kinematic calibration system for the generalized kinematic error of the industrial robot according to claim 6, wherein the model building module specifically comprises:
the geometric error model building unit is used for building a geometric error model by adopting differential kinematics based on the DH model of the robot to be identified;
and the joint error model building unit is used for building a joint error model by adopting a polynomial fitting method based on the DH model of the robot to be identified.
8. The kinematic calibration system for the generalized kinematic error of the industrial robot according to claim 6, wherein the identification module specifically comprises:
and the identification unit is used for carrying out parameter identification on the generalized kinematics error model by utilizing an implicit ring method to obtain an identified generalized kinematics error model.
9. The kinematic calibration system for the generalized kinematic error of the industrial robot according to claim 6, wherein the joint command error matrix determination module specifically comprises:
the actual terminal transformation matrix determining unit is used for inputting the compensated joint instruction under the current iteration times into the identified generalized kinematic error model to obtain an actual terminal transformation matrix;
the nominal positive kinematics transformation matrix determining unit is used for inputting the nominal joint instruction into a nominal DH model preset by the robot to be identified to obtain a nominal positive kinematics transformation matrix;
a residual error transformation matrix determining unit, configured to calculate a difference between the actual end transformation matrix and the nominal positive kinematics transformation matrix to obtain a residual error transformation matrix;
and the joint instruction error matrix determining unit is used for calculating a joint instruction error matrix under the current iteration number according to the residual error transformation matrix and the Jacobian matrix.
10. The kinematic calibration system for the generalized kinematic error of the industrial robot according to claim 6, wherein the updating module specifically comprises:
and the updating unit is used for determining the sum of the compensated joint instruction under the current iteration times and the joint instruction error matrix under the current iteration times as the compensated joint instruction under the next iteration times.
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