CN113119130B - Geometric error identification method for industrial robot - Google Patents
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Abstract
The invention discloses a geometric error identification method for an industrial robot, which comprises the following steps: s1: establishing a robot kinematic geometric error model; s2: acquiring a measurement pose of the robot; s3: establishing a comprehensive level evaluation index of the measurement pose, comprehensively considering a pose observability index, a pose distribution dispersion index and a uniformity index to obtain an optimal measurement pose solution set, and determining the optimal measurement pose from the optimal measurement pose solution set based on an improved sequence floating forward selection algorithm; s4: calculating to obtain theoretical poses corresponding to different joint angle parameters; s5: and identifying the difference between the actual measurement pose and the theoretical pose as a robot terminal positioning error by using a robust estimation method based on a self-adaptive critical value according to an established robot kinematic geometric error model, and iteratively identifying the geometric error to obtain a final geometric parameter error.
Description
Technical Field
The invention relates to the fields of robot kinematics and robot error identification, in particular to a geometric error identification method for an industrial robot.
Background
With the high-speed development of industrial technology, industrial robots are widely applied to many fields of modern manufacturing industry, play an important role in numerous fields of transportation, spraying, welding, assembly and the like, greatly improve the production efficiency and favorably promote the development of economy and society. Industrial robots also play an important role in emerging industries and fields, such as unmanned chemical plants, space exploration, human-computer interaction, and the like, and increasingly become an indispensable important role in the manufacturing industry at present.
In the fields with high complexity or high precision requirement, such as flexible manufacturing, grinding, drilling and the like, the positioning precision requirement of the industrial robot is high. The robot positioning precision is divided into absolute positioning precision and repeated positioning precision, at present, the repeated positioning precision of the robot can reach 0.01mm, the use requirement is basically met, and the absolute positioning precision, namely the error between the actual position and the target position of the robot, influences the robot positioning precision. The error is caused by many reasons, and the positioning accuracy of the end of the robot is reduced due to errors in machining, assembly errors, wear of parts in use, and changes in the working temperature and working load of the robot. Error classification can be classified into geometric errors and non-geometric errors according to the characteristics of error sources. The geometric error refers to an error between an actual value and a nominal value of a kinematic description parameter of the robot, such as a connecting rod length, a connecting rod torsion angle, a joint offset, a joint rotation angle and the like. Through the mechanical mechanism of the robot, errors are transmitted and accumulated among all the connecting rods, and finally the positioning accuracy of the robot is reduced. Non-geometric errors include thermal effects, deformation due to changes in stiffness of the connecting rod, and are difficult to quantify compared to geometric errors. Regarding the precision problem, the geometric error is a main factor causing the reduction of the positioning precision of the tail end of the robot, and the identification aiming at the geometric error is an effective way for improving the positioning precision of the robot.
The identification precision of the geometric errors of the robot is closely related to the selected measurement pose, and the reflection capacities of different measurement poses on the geometric parameter errors are different. Aiming at the evaluation index of the measurement pose, the common observability index does not consider the distribution of the pose; and the comprehensive evaluation indexes of observability and pose distribution are comprehensively considered, and the sensitivity of the indexes is reduced due to the normalization operation. Aiming at the selection of the measurement pose, the widely used selection algorithm has the problem of local convergence, and the convergence effect of the algorithm is influenced by the initial value of the parameter. When geometric errors are identified, the identification precision is also easily influenced by a measuring instrument and rough errors in the measuring process and is reduced.
Disclosure of Invention
In order to solve the defects of the prior art and achieve the purpose of improving the identification precision of the geometric errors of the industrial robot, the invention adopts the following technical scheme:
a geometric error identification method for an industrial robot comprises the following steps:
s1: establishing a robot kinematic geometric error model: Δ X is a positioning error of the tail end of the robot, Δ Q is a geometric parameter error of the robot, and a is a coefficient matrix describing the correlation between the positioning error and the numerical error of the robot;
s2: controlling the robot to move in space, measuring the position coordinates of the end effector of the robot by using a laser tracker, and simultaneously acquiring the angular parameters of the joints of the robot to obtain a large number of measurement poses of the robot;
s3: establishing a comprehensive level evaluation index O of measurement posecComprehensively considering the pose observability index O1Obtaining an optimal measurement pose solution set S by using the pose distribution dispersion index delta and the uniformity index U2Based on improved sequence floating forward selection algorithm, from optimal measurement pose solution set S2In the method, the optimal measurement pose is determined, and the algorithm comprises the following steps:
s31: initializing an empty optimal measurement pose solution set omega, wherein the initialization algorithm parameters comprise: randomly selecting one pose from the pose set phi to be selected as an initial solution, and starting algorithm iteration work;
s32: adding sequences forward, determining a pose from a given pose set phi to be selected, and enabling the observability evaluation index O of the optimal measurement pose solution set omega to be in an observation evaluation mode after adding the pose1Maximum;
s33: deleting the floating condition, judging and deleting unimportant poses in the optimal solution set omega until the observability evaluation index O is deleted after one unimportant pose is deleted1Less than before adding the new pose;
s34: random exchange and deletion, in order to increase the randomness of the whole process to avoid the solution set from falling into a local extreme value, the comprehensive level evaluation index O of the measurement pose is adoptedcAs a judgment criterion, the observability of the weakening coefficient matrix is controlled by the weight, the distribution importance degree of data is increased, k poses are randomly selected from the optimal measurement pose solution set omega in sequence before each iteration is finished, the exchange or deletion with the pose solution set to be selected is randomly executed, and the index O is evaluated according to the comprehensive level of the measurement posescJudging whether to execute exchange or deletion;
s35: loop iteration is carried out, whether the iteration times meet the iteration requirement is judged, the loop is exited, and the optimal measurement pose P is obtainedt；
S4: calculating to obtain theoretical poses P corresponding to different joint angle parameters by using the nominal MD-H value of the robotr；
S5: actual measurement pose PtAnd theoretical pose PrThe difference is a robot tail end positioning error delta X, identification is carried out by a robust estimation method based on a self-adaptive critical value according to an established robot kinematic geometric error model, the influence of measurement disturbance and the error of an instrument in the measurement process is eliminated, the identification precision is improved, geometric error identification is carried out in an iteration mode, and a final geometric parameter error delta Q is obtained.
Further, the step S1 includes the following steps:
s11: according to the robot kinematics MD-H model, through the geometrical parameters in the model: angle of rotation theta of jointiDistance d between jointsiLength of connecting rod aiAngle of torsion of joint alphaiAnd angle of rotation betaiAnd obtaining a homogeneous transformation matrix of adjacent joints of the robot:
wherein S and C represent a sine function sin and a cosine function cos, beta, respectivelyiRepresenting the rotation angle around the y-axis of the corresponding coordinate system, i representing the ith joint;
s12: obtaining the relation between the tail end of the robot and a base coordinate system according to the robot MD-H parameter and the homogeneous transformation matrix between adjacent coordinate systems:
wherein the three components of n, o and a are respectively used for replacing each component of the attitude in the terminal pose of the robot;
s13: due to the processing and assembling errors and the transmission errors of the connecting rod of the robot, andthe robot has geometric parameter errors under the influence of environmental factors, and the geometric parameter errors of the robot connecting rod are respectively marked as: the joint rotation angle error delta theta, the joint torsion angle error delta alpha, the connecting rod length error delta a, the joint distance error delta d and the rotation angle error delta beta are transformed into the matrix T in a homogeneous way under the influence of the geometric parameter errorsi i-1Newly added differential homogeneous perturbation matrix dTi i-1：
S14: considering the geometric parameter error of each joint of the robot, the terminal pose of the robot is expressed as:
wherein N represents the number of joints;
s15: and (3) taking the error between the robot base coordinate system and the measurement coordinate system into consideration to obtain a robot geometric error identification model:
ΔX＝A·ΔQ
wherein, Δ X is the terminal positioning error, a is a coefficient matrix describing the correlation between the parameter error and the positioning error, and Δ Q is the parameter error.
Further, in step S3, the coefficient matrix a of the error identification model is an m × n order matrix, and the coefficient matrix has singular values σ1,σ2...σnAnd obtaining a pose observability evaluation index:
besides the observability indexes of the measurement poses, the spatial distribution condition of the measurement poses needs to be considered, wherein the spatial distribution condition comprises a pose dispersion evaluation index delta and a pose uniformity evaluation index U;
the set of joint angles in the measurement range S is C ═ θ1,θ2,...θn}，θiCorresponding to the end position being p (theta)i) And the obtained distributivity index of the measurement pose is as follows:
i. j belongs to n and respectively represents the ith and jth joint angles, and i is not equal to j;
the evaluation indexes of the discreteness of the measurement pose are as follows:
wherein
Representing the average distance of the measuring point from the central point, d (y, p)k) Denotes y and pkThe euclidean distance between;
introducing a weighting control factor lambda by means of nonlinear normalization of an arctangent function1、λ2、λ3And controlling the weight of each component in the evaluation index to obtain a pose comprehensive evaluation index:
by changing the weight, the observability, the discreteness and the uniformity of the pose are comprehensively considered; if set to O1Weight lambda of the index1If 0, observability is not considered at all, only the distribution of data is considered, and λ may be set1The small weight value avoids optimizing the distribution of the measurement pose under the condition that the observability is greatly interfered;
because the observability index of the coefficient matrix has greater importance on the parameter identification result, O is selected1As a primary index, according to O1Selecting a measurement pose to obtain a set S1To measure the pose and comprehensive level evaluation index OcAs a secondary index, andfor set S1Optimizing, and controlling delta, U and O by weight1From the set S1Comprehensive level evaluation index O according to measurement posecSelecting solution set S for obtaining optimal measurement pose2。
Further, in step S5, because some measured data have large fluctuation due to the influence of factors such as the measuring instrument and the measurement disturbance when measuring the actual pose, the parameter identification is performed on the data with gross error by using the adaptive threshold robust estimation method, and the weight matrix corresponding to the observation value with large error is continuously reduced in the iterative fitting process by modifying the weight matrix of the least square method, so as to suppress the gross error, including the following steps:
s51: constructing a weight matrix P of a robust estimation least square method, wherein the specific form is as follows:
identifying geometric parameter errors by adopting a weight matrix of a weighted least square method;
s52: and calculating a residual error distribution state according to the result of parameter error identification, adjusting a weight matrix based on an IGG3 weight function of a self-adaptive construction critical value, iterating again until the threshold requirement of identification precision or the iteration times is reached, exiting iteration and finishing parameter error identification.
Further, in the step S52, in the iterative calculation process of the weight matrix of the least square method, the weight matrix is determined by an IGG3 weight function, a confidence interval of an assigned confidence level is calculated according to the residual distribution state of each iteration result, and a critical value of the weight function is adaptively constructed according to a limit value of the confidence interval, so that the risk of manually setting the critical value is eliminated;
the weight function of the adaptive critical value structure is as follows:
wherein k is0、k1In order to obtain the harmonic coefficients,
for the purpose of the normalized residual error,
the lower limit value is set as the value of,
the upper formula shows that the weight of the observed value lower than the lower limit of the confidence interval is reserved, the weight of the observed value in the interval is reduced, and the observed value larger than the upper limit is directly discarded.
Further, k is0The value of k is 1.0-1.51The value is 2.5-3.0.
Further, in the step S32, the pose is substituted into the pose evaluation index function fadd(theta) when the function value is larger than the observability evaluation index O1And adding the pose to the optimal measurement pose solution set omega.
Further, in the step S33, the pose is substituted into the pose evaluation index function frmv(theta) when the function value is larger than the observability evaluation index O1And deleting the pose from the optimal measurement pose solution set omega.
Further, in step S34, whether the exchange or the deletion is randomly determined, and the pose to be determined is substituted into the pose evaluation index function frand(theta) when the function value is larger than the observability evaluation index OcIf so, the exchange or deletion is performed.
The invention has the advantages and beneficial effects that:
the invention comprehensively considers the pose observability index and the pose distribution index, increases the randomness of the whole process to avoid the situation that the solution set falls into a local extreme value, weakens the observability of a coefficient matrix through weight control, increases the importance degree of the data distribution, carries out identification by a robust estimation method based on a self-adaptive critical value, eliminates the influence of measurement disturbance and the error of an instrument in the measurement process, solves the problem that the geometric error identification precision of the robot is influenced by the selected measurement pose and the measurement method, and improves the geometric error identification precision.
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FIG. 1 is a schematic flow chart of the method of the present invention.
FIG. 2 is a comparison diagram of robot end positioning errors before and after parameter identification in the present invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the present invention, are given by way of illustration and explanation only, not limitation.
The invention aims to provide a geometric error identification method for an industrial robot, which solves the problem that the geometric error identification precision of the robot is influenced by a selected measurement pose and a measurement method and improves the geometric error identification precision. The process is shown in fig. 1, and comprises the following steps:
s1: establishing a robot kinematic geometric error model;
according to the robot kinematics MD-H model, through the geometric parameters (joint rotation angle theta) in the modeliDistance d between jointsiLength of connecting rod aiAngle of torsion of joint alphaiAnd angle of rotation betai) And obtaining a homogeneous transformation matrix of adjacent joints of the robot:
wherein S and C represent a sine function sin and a cosine function cos, beta, respectivelyiIndicating the rotation angle around the y-axis of the corresponding coordinate system.
Obtaining the relation between the tail end of the robot and a base coordinate system according to the robot MD-H parameter and the homogeneous transformation matrix between adjacent coordinate systems:
wherein the three components of n, o and a are respectively used for replacing each component of the pose in the terminal pose of the robot.
Due to the processing and assembling errors of the robot, the existence of connecting rod transmission errors and the influence of environmental factors, the robot has geometric parameter errors. According to the MD-H model, robot link geometric parameter errors are labeled as Δ θ (joint rotation angle error), Δ α (joint torsion angle error), Δ a (link length error), Δ d (joint distance error), and Δ β (rotation angle error), respectively. Homogeneous transformation of the matrix T under the influence of errors in the geometric parametersi i-1Newly added differential homogeneous perturbation matrix dTi i-1：
Considering the geometric parameter error of each joint of the robot, the terminal pose of the robot is expressed as:
and (3) considering the error between the robot base coordinate system and the measurement coordinate system to obtain a robot geometric error identification model:
ΔX＝A·ΔQ
wherein, Δ X is the terminal positioning error, a is a coefficient matrix describing the correlation between the parameter error and the positioning error, and Δ Q is the parameter error.
S2: measuring the position coordinates of the end effector of the robot by using a laser tracker, and measuring the actual pose of the robot;
the controller is used for controlling the robot to move in space, the laser tracker is used for measuring the position coordinates of the robot end effector, and meanwhile, the robot joint parameters of the corresponding positions are read and recorded, so that a large amount of actual pose data of the robot are obtained.
S3: establishing a comprehensive level evaluation index of the measurement pose, and determining the optimal measurement pose based on an improved sequence floating forward selection algorithm;
the coefficient matrix A of the error identification model is an mxn-order matrix, and the singular value sigma of the coefficient matrix1,σ2...σnAnd obtaining a pose observability evaluation index:
besides the observability index of the measurement pose, the spatial distribution condition of the measurement pose needs to be considered, including the discreteness evaluation index delta and the uniformity evaluation index U of the pose. Let the set of joint angles in the measurement range S be C ═ θ1,θ2,...θn}，θiCorresponding to the end position being p (theta)i) And the obtained distributivity index of the measurement pose is as follows:
the evaluation indexes of the discreteness of the measurement pose are as follows:
wherein
Representing the average distance of the measuring point from the central point, d (y, p)k) Denotes y and pkThe euclidean distance between.
By utilizing the nonlinear normalization of the arctangent function, introducing a weighting control factor lambda, controlling the weight of each component in the evaluation index to obtain a pose comprehensive evaluation index:
because the observability index of the coefficient matrix has greater importance on the parameter identification result, O is selected1Index as primary index according to O1Index selection measurement pose obtaining set S1Evaluation index O with posecAs a secondary indicator, the set S is then paired1And (6) optimizing. From set S by controlling data distribution and observability index importance by weight1The optimal measurement pose S is selected and obtained according to the index2Obtaining a solution set S of the optimal measurement pose problem2。
Further, an improved floating sequence forward selection algorithm is utilized to solve the set S from the optimal measurement pose2The measurement pose is determined, and the algorithm comprises the following specific steps:
1) initializing an empty optimal measurement pose solution set omega, and initializing algorithm parameters including a candidate pose set
The required pose number m, the iteration number e, the pose number P of random exchange deletion, the pose number m of initial solution and other parameters are collected from the pose to be selected
Randomly selecting one posture as an initial solution, and starting iterative work of the algorithm;
2) sequence forward adding, attention pose observability evaluation index O when adding pose1From a given set of candidate poses
Determining a pose, and adding the pose to make the observability evaluation index O of the optimal measurement pose solution set omega1At the maximum, the pose evaluation index function of the adding step is recorded as fadd(θ)；
3) Deleting floating conditions, and paying attention to pose observability evaluation index O when deleting poses1Judging and deleting unimportant poses in the optimal solution set omega until the observability evaluation index O is deleted after one unimportant pose is deleted1The pose evaluation index function which is less than that before adding the new pose and remembers the step of deleting is frmv(θ)；
4) Random exchanges and deletions, for adding integersThe randomness of the process is used for avoiding the solution set from falling into a local extreme value, and an evaluation index O comprehensively considering the observability, the distribution and the discreteness of the pose is adoptedcAs a judgment criterion, the observability of the weakening coefficient matrix is controlled by the weight, the distribution importance degree of data is increased, k poses are randomly selected from the optimal solution set omega in sequence before each iteration is finished, the exchange or deletion with the solution set of poses to be selected is randomly executed, and the comprehensive evaluation index O is usedcJudging whether to execute exchange or deletion, and recording the pose evaluation index function as frand(θ)；
5) Loop iteration is carried out, whether the iteration times meet the iteration requirement is judged, the loop exits, and the actually measured optimal pose P is obtainedt。
S4: and calculating to obtain theoretical poses corresponding to different joint angle parameters by using the nominal MD-H value of the robot.
Substituting the adjacent pose transformation matrix of the robot joint established in the S1 into the nominal robot MD-H parameter to obtain the nominal pose P of the tail end of the robotr
S5: actual measurement pose PtAnd theoretical pose PrThe difference is a robot tail end positioning error delta X, identification is carried out by a robust error estimation method based on a self-adaptive critical value according to an established robot kinematic error model, the influence of measurement disturbance and the error of an instrument in the measurement process is eliminated, the identification precision is improved, and a final geometric parameter error delta Q is obtained;
the robot tip positioning error Δ X can be expressed as:
ΔX＝Pt-Pr
when the actual pose is measured, due to the influence of factors such as a measuring instrument, measurement disturbance and the like, certain measured data have large fluctuation, and therefore parameter identification is carried out on the data with gross errors by using a self-adaptive critical value robust estimation method.
The basic principle of the method for estimating the self-adaptive critical value robust is that the weight matrix of the least square method is modified, the weight matrix corresponding to the observed value with larger error is continuously reduced in the iterative fitting process, and the gross error is restrained. P is a weight matrix of the robust estimation least square method, and the specific form is as follows:
in the least squares iterative calculation process, the weight matrix is determined by the IGG3 weight function. And calculating a confidence interval of the designated confidence level according to the residual distribution state of each iteration result, wherein the critical value of the weight function is adaptively constructed according to the limiting value of the confidence interval, and the risk of manually setting the critical value is eliminated. The weight function constructed by adopting the self-adaptive critical value is as follows:
wherein k is0、k1In order to obtain the harmonic coefficients,
for the purpose of the normalized residual error,
the lower limit value is set as the value of,
is the upper limit value. The above formula shows that the weight of the observed value below the lower limit of the confidence interval is retained, the weight of the observed value in the interval is reduced, and the observed value larger than the upper limit value is directly discarded.
And (3) iteratively identifying the geometric error based on a robust estimation method of a self-adaptive construction critical value. And setting a weight matrix P as an identity matrix at the beginning of iteration, then adopting weighted least square to identify geometric parameter errors, calculating a residual distribution state according to the result of parameter error identification, adjusting the weight matrix based on an IGG3 weight function of a self-adaptive construction critical value, iterating again until reaching the threshold requirement of identification precision or iteration times, exiting iteration and finishing parameter error identification.
The method is utilized to identify the parameters of the calibrated robot, and the nominal D-H parameters of the robot calculate the difference between the tail end position of the corresponding 85 groups of joint angles and the actual measurement point position to obtain the error before parameter error identification, as shown in a light color dot curve of FIG. 2; after the identification is carried out by the method, the difference between the terminal pose of the robot and the actually measured point position is calculated by the D-H parameters after the identification result is corrected, so as to obtain the error after the parameter correction, as shown by a dark square point curve in figure 2.
By contrast, before parameter identification, the comprehensive positioning error of the tail end of the robot is 1.5-3 mm, after the parameter identification is carried out by the method, the positioning error is reduced to 0.5-1.0 mm, the mean value is reduced to 0.7728mm from 2.381mm before identification, the lifting rate is close to 70%, and the effectiveness of the method is effectively verified.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (9)
1. A geometric error identification method for an industrial robot is characterized by comprising the following steps:
s1: establishing a robot kinematic geometric error model: Δ X is a positioning error of the tail end of the robot, Δ Q is a geometric parameter error of the robot, and a is a coefficient matrix describing the correlation between the positioning error and the numerical error of the robot;
s2: controlling the robot to move in space, measuring the position coordinates of the tail end of the robot, and simultaneously acquiring the joint angle parameters of the robot to obtain the measurement pose of the robot;
s3: establishing a comprehensive level evaluation index O of measurement posecAnd comprehensively considering the pose observability evaluation index O1Obtaining a pose distribution dispersion index delta and a uniformity index UTo the optimal measurement pose solution set S2Based on improved sequence floating forward selection algorithm, from optimal measurement pose solution set S2In the method, the optimal measurement pose is determined, and the algorithm comprises the following steps:
s31: initializing an empty optimal measurement pose solution set omega, wherein the initialization algorithm parameters comprise: selecting one pose randomly from the pose set phi to be selected as an initial solution, and starting iterative operation of the algorithm;
s32: adding sequences forward, determining a pose from a given pose set phi to be selected, and enabling the observability evaluation index O of the optimal measurement pose solution set omega to be in an observation evaluation mode after adding the pose1Maximum;
s33: deleting the floating condition, judging and deleting unimportant poses in the optimal solution set omega until the observability evaluation index O is deleted after one unimportant pose is deleted1Less than before adding the new pose;
s34: randomly exchanging and deleting, and evaluating index O by using measurement pose comprehensive levelcAs a judgment criterion, before each iteration is finished, k poses are randomly selected from the optimal measurement pose solution set omega in sequence, the exchange or deletion with the pose solution set to be selected is randomly executed, and the index O is evaluated according to the comprehensive level of the measurement posescJudging whether to execute exchange or deletion;
s35: loop iteration is carried out, whether the iteration times meet the iteration requirement is judged, the loop is exited, and the optimal measurement pose P is obtainedt；
S4: calculating to obtain theoretical poses P corresponding to different joint angle parameters by using the nominal MD-H value of the robotr；
S5: actual measurement pose PtAnd theoretical pose PrAnd the difference is a robot tail end positioning error delta X, identification is carried out according to an established robot kinematic geometric error model and a robust estimation method based on a self-adaptive critical value, and geometric error identification is carried out in an iterative manner to obtain a final geometric parameter error delta Q.
2. An industrial robot oriented geometric error identification method according to claim 1, characterized in that said steps
S1 includes the steps of:
s11: according to the robot kinematics MD-H model, through the geometrical parameters in the model: angle of rotation theta of jointiDistance d between jointsiAngle of torsion of joint alphaiAnd a rotation angle beta around the y-axis of the corresponding coordinate systemiAnd obtaining a homogeneous transformation matrix of adjacent joints of the robot:
wherein S and C represent a sine function sin and a cosine function cos, beta, respectivelyiRepresenting the rotation angle around the y-axis of the corresponding coordinate system, i representing the ith joint;
s12: obtaining the relation between the tail end of the robot and a base coordinate system according to the robot MD-H parameter and the homogeneous transformation matrix between adjacent coordinate systems:
the four components of n, o, a and p respectively represent a normal vector, an orientation vector, an approach vector and a position vector in the terminal pose of the robot, and subscripts x, y and z represent projection components of the vectors on x, y and z axes;
s13: according to the MD-H model, the geometric parameter errors of the robot connecting rod are respectively marked as: the joint rotation angle error delta theta, the joint torsion angle error delta alpha, the connecting rod length error delta a, the joint distance error delta d and the rotation angle error delta beta are transformed in a same order under the influence of the geometric parameter errors
Newly-added differential homogeneous perturbation matrix
Wherein,
a second transformation matrix representing the ith joint of the robot relative to the (i-1) th joint;
s14: considering the geometric parameter error of each joint of the robot, the terminal pose of the robot is expressed as:
wherein, N represents the number of joints,
a transformation matrix representing the base coordinates of the robot to the end coordinate system of the robot,
is composed of
Represents the error of the homogeneous variable matrix;
s15: and (3) taking the error between the robot base coordinate system and the measurement coordinate system into consideration to obtain a robot geometric error identification model:
ΔX＝A·ΔQ
wherein Δ X is the end positioning error, i.e., in S14
A is a coefficient matrix describing the correlation between the parameter error and the positioning error, and delta Q is the parameter error.
3. An industrial robot oriented geometric error recognition method according to claim 1, characterized in that said step S3In the method, the coefficient matrix A of the error identification model is an m × n order matrix, and the singular value sigma of the coefficient matrix1，σ2...σnAnd obtaining a pose observability evaluation index:
measuring the spatial distribution of the pose, including a discreteness evaluation index delta and a uniformity evaluation index U of the pose distribution;
the set of joint angles in the measurement range S is C ═ θ1，θ2，...θn}，θiCorresponding to end position pi(θi) And the obtained discreteness evaluation index of the measurement pose distribution is as follows:
i. j belongs to n and respectively represents the ith and jth joint angles, and i is not equal to j;
the uniformity evaluation indexes of the measurement pose distribution are as follows:
wherein
Representing the average distance of the measuring point from the central point, d (y, p)k) Denotes y and pkEuclidean distance between, pkRepresenting the kth group of measurement poses;
introducing a weighting control factor lambda by means of nonlinear normalization of an arctangent function1、λ2、λ3And obtaining a pose comprehensive evaluation index:
selection of O1As a primary index, according to O1Selecting a measurement pose to obtain a set S1To measure the pose and comprehensive level evaluation index OcAs a secondary indicator, the set S is then paired1Optimizing, and controlling delta, U and O by weight1From the set S1Comprehensive level evaluation index O according to measurement posecSelecting solution set S for obtaining optimal measurement pose2。
4. An industrial robot oriented geometric error identification method according to claim 1, characterized in that said steps
In S5, the method for adaptive threshold robust estimation continuously reduces the weight matrix corresponding to the observed value with a large error in the iterative fitting process by modifying the weight matrix of the least square method, including the following steps:
s51: constructing a weight matrix P of a robust estimation least square method, wherein the specific form is as follows:
identifying geometric parameter errors by adopting a weight matrix of a weighted least square method;
s52: and calculating a residual error distribution state according to the result of parameter error identification, adjusting a weight matrix based on an IGG3 weight function of a self-adaptive construction critical value, iterating again until the threshold requirement of identification precision or the iteration times is reached, exiting iteration and finishing parameter error identification.
5. The method for identifying geometric errors of an industrial robot according to claim 4, wherein in step S52, in the iterative calculation of weight matrix of least square method, the weight matrix is determined by IGG3 weight function, the confidence interval of the assigned confidence level is calculated according to the residual distribution state of each iteration result, the critical value of the weight function is adaptively constructed according to the limit value of the confidence interval;
the weight function of the adaptive critical value structure is as follows:
wherein k is0、k1In order to obtain the harmonic coefficients,
for the purpose of the normalized residual error,
the lower limit value is set as the value of,
and keeping the weight of the observed value which is lower than the lower limit of the confidence interval for the upper limit value, reducing the weight of the observed value which is positioned in the interval, and directly discarding the observed value which is larger than the upper limit value.
6. An industrial robot oriented geometric error identification method according to claim 5, characterized in that said k0The value of k is 1.0-1.51The value is 2.5-3.0.
7. The method for identifying geometric errors of an industrial robot according to claim 1, wherein the step S32 is performed by substituting the pose into a pose evaluation index function of fadd(theta) when the function value is larger than the observability evaluation index O1And adding the pose to the optimal measurement pose solution set omega.
8. The method for identifying geometric errors of an industrial robot according to claim 1, wherein the step S33 is performed by substituting the pose into a pose evaluation index function of frmv(theta) when the function value is larger than the observability evaluation index O1Then, the pose is selected from the mostAnd deleting in the optimal measurement pose solution set omega.
9. The method for identifying geometric errors of an industrial robot according to claim 1, wherein in step S34, whether the exchange or the deletion is randomly determined, the pose to be determined is substituted into a pose evaluation index function frand(theta) when the function value is larger than the observability evaluation index OcIf so, the exchange or deletion is performed.
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104535027A (en) * | 2014-12-18 | 2015-04-22 | 南京航空航天大学 | Robot precision compensation method for variable-parameter error recognition |
| CN104802802A (en) * | 2014-01-23 | 2015-07-29 | 南京聚特机器人技术有限公司 | Error identification method for zero adjustment for swing arm type tracked robot |
| CN107443382A (en) * | 2017-09-12 | 2017-12-08 | 清华大学 | Industrial robot structure parameter error recognizes and compensation method |
| CN107972071A (en) * | 2017-12-05 | 2018-05-01 | 华中科技大学 | A kind of industrial robot link parameters scaling method based on distal point plane restriction |
| CN110370271A (en) * | 2019-04-30 | 2019-10-25 | 杭州亿恒科技有限公司 | The joint transmission ratio error calibration method of industrial serial manipulator |
| CN110662636A (en) * | 2017-05-18 | 2020-01-07 | 川崎重工业株式会社 | Speed reducer angle transmission error identification system and speed reducer angle transmission error identification method |
| CN110709213A (en) * | 2017-06-05 | 2020-01-17 | 川崎重工业株式会社 | Angle transfer error identification system, angle transfer error identification method, and robot system |
-
2021
- 2021-04-28 CN CN202110466047.7A patent/CN113119130B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104802802A (en) * | 2014-01-23 | 2015-07-29 | 南京聚特机器人技术有限公司 | Error identification method for zero adjustment for swing arm type tracked robot |
| CN104535027A (en) * | 2014-12-18 | 2015-04-22 | 南京航空航天大学 | Robot precision compensation method for variable-parameter error recognition |
| CN110662636A (en) * | 2017-05-18 | 2020-01-07 | 川崎重工业株式会社 | Speed reducer angle transmission error identification system and speed reducer angle transmission error identification method |
| CN110709213A (en) * | 2017-06-05 | 2020-01-17 | 川崎重工业株式会社 | Angle transfer error identification system, angle transfer error identification method, and robot system |
| CN107443382A (en) * | 2017-09-12 | 2017-12-08 | 清华大学 | Industrial robot structure parameter error recognizes and compensation method |
| CN107972071A (en) * | 2017-12-05 | 2018-05-01 | 华中科技大学 | A kind of industrial robot link parameters scaling method based on distal point plane restriction |
| CN110370271A (en) * | 2019-04-30 | 2019-10-25 | 杭州亿恒科技有限公司 | The joint transmission ratio error calibration method of industrial serial manipulator |
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