CN113334388A - Robot kinematics calibration method and calibration device based on local linear regression - Google Patents

Robot kinematics calibration method and calibration device based on local linear regression Download PDF

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CN113334388A
CN113334388A CN202110773525.9A CN202110773525A CN113334388A CN 113334388 A CN113334388 A CN 113334388A CN 202110773525 A CN202110773525 A CN 202110773525A CN 113334388 A CN113334388 A CN 113334388A
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CN113334388B (en
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吴军
叶豪
于广
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Tsinghua University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
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Abstract

The application discloses a robot kinematics calibration method and a calibration method based on local linear regression, wherein a geometric error model of a robot is determined; further weighting the geometric error model according to the measurement noise variance matrix; and finally, estimating the geometric error at any pose based on a local linear regression method and predicting the corresponding positioning error, thereby realizing the effect of kinematics calibration and reducing the calibration residual error of the traditional method in a large working space.

Description

Robot kinematics calibration method and calibration device based on local linear regression
Technical Field
The application relates to the technical field of robot calibration, in particular to a robot kinematics calibration method and device based on local linear regression.
Background
Due to geometric errors of the robot caused by factors such as manufacturing and assembling, the positioning accuracy of the robot is reduced, and further the industrial application of the robot is limited, so that the robot needs to be subjected to kinematic calibration before being shipped. In a general kinematics calibration method, geometric errors are identified by measuring poses of a plurality of groups of robot end effectors through an established geometric error model and utilizing theoretical and actual pose deviations, and then the robot kinematics model is corrected to improve the robot end positioning pose accuracy.
The previous research divides the kinematics calibration problem into four parts of geometric error modeling, measurement, identification and compensation, wherein the deviation of a geometric error model and an actual structure model is an important factor causing residual errors after the kinematics calibration, and the most important problem is that non-geometric errors such as joint deformation, transmission errors and the like exist in the actual model and errors caused by model linearization and the like exist in the actual model, and the unmodeled errors have the problems of complex modeling, difficult verification and the like.
It is considered that these unmodeled errors usually have a certain locality, i.e. the residual error changes are small locally, although they result in a large distribution of the post-calibration residual error as a whole and thus cause poor kinematic calibration effect. Therefore, the method adopts local linear regression capable of eliminating the local error in the kinematic calibration, and has important significance for improving the positioning accuracy of the robot.
Disclosure of Invention
The present application is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, an object of the present application is to provide a robot kinematics calibration method based on local linear regression, where the local linear regression has a stronger fitting ability in a local error than the conventional linear regression, and the method overcomes the problem of residual error in kinematics calibration caused by difficulty in accurate modeling or unmodeled error to some extent, and further improves the positioning accuracy of the robot.
Another objective of the present application is to provide a robot kinematics calibration apparatus based on local linear regression.
In order to achieve the above object, an embodiment of an aspect of the present application provides a robot kinematics calibration method based on local linear regression, including:
s1, establishing a geometric error model of the robot, and obtaining a positioning error feature vector of a pose error component according to the geometric model;
s2, determining a measurement noise variance matrix of the robot, and weighting the eigenvector according to the measurement noise variance matrix;
and S3, estimating the geometric error at any pose based on a local linear regression method and predicting the corresponding positioning error so as to calibrate the robot.
In order to achieve the above object, another embodiment of the present application provides a robot kinematics calibration apparatus based on local linear regression, including;
the modeling module is used for establishing a geometric error model of the robot and obtaining a positioning error characteristic vector of a pose error component according to the geometric model;
the processing module is used for determining a measurement noise variance matrix of the robot and weighting the eigenvector according to the measurement noise variance matrix;
and the calibration module is used for estimating the geometric error at any pose based on a local linear regression method and predicting the corresponding positioning error so as to calibrate the robot.
According to the robot kinematics calibration method and device based on local linear regression, firstly, a geometric error model of a robot is determined; further weighting the geometric error model according to the measurement noise variance matrix; and finally, estimating the geometric error at any pose based on a local linear regression method and predicting the corresponding positioning error, so that the effect of kinematics calibration is realized, the problem of residual error in kinematics calibration caused by difficult accurate modeling or unmodeled error is solved to a certain extent, the positioning precision of the robot is further improved, and the calibration residual error in a large working space by using the traditional method is reduced.
Additional aspects and advantages of the present application will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the present application.
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The foregoing and/or additional aspects and advantages of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flowchart of a robot kinematics calibration method based on local linear regression according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a typical hybrid robot configuration;
fig. 3 is a schematic structural diagram of a robot kinematics calibration apparatus based on local linear regression according to an embodiment of the present application.
Reference numerals: 1-a first branch; 2-a second branch; 3-third branch; 4-lower fixed platform; a 5-C member; a 6-A member; 7-moving the platform; 8-upper fixed platform.
Detailed Description
Reference will now be made in detail to embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application.
The following describes a robot kinematics calibration method and a calibration device based on local linear regression according to an embodiment of the present application with reference to the accompanying drawings.
First, a robot kinematics calibration method based on local linear regression according to an embodiment of the present application will be described with reference to the accompanying drawings.
Fig. 1 is a flowchart of a robot kinematics calibration method based on local linear regression according to an embodiment of the present application.
As shown in fig. 1, the robot kinematics calibration method based on local linear regression includes the following steps:
and step S1, establishing a geometric error model of the robot, and obtaining a positioning error feature vector of the pose error component according to the geometric model.
Optionally, in an embodiment of the present application, the geometric error model of the robot is established as:
δE＝M(q)∈
wherein the content of the first and second substances,
Figure BDA0003154824620000031
is the position and attitude error of the robot terminal actuator,
Figure BDA0003154824620000032
and M is a corresponding error transfer matrix, represents the influence of the geometric error in the epsilon on the position and attitude error of the robot end actuator and is a function of the displacement vector q of the robot driving shaft.
Therefore, the robot attitude error δEOf arbitrary component δiCan be expressed as:
Figure BDA0003154824620000033
wherein ei(1. ltoreq. i.ltoreq.f) is the unit vector of the corresponding component,
Figure BDA0003154824620000034
as a pose error component deltaiThe positioning error feature vector of (1).
And step S2, determining a measurement noise variance matrix of the robot, and weighting the eigenvector according to the measurement noise variance matrix.
Optionally, in an embodiment of the present application, weighting the eigenvector according to the measurement noise variance matrix specifically includes:
determining the measurement noise weight of the robot: the tail end pose error of the measurement pose of the robot is measured, the measurement precision is influenced by measurement noise, and the measurement noise
Figure BDA0003154824620000035
Assuming that an independent normal distribution with a mean of 0 is satisfied, but the variance of the normal distribution is not uniform due to differences in the intensities of the different components,
Figure BDA0003154824620000036
the variance matrix is normalized to a diagonal positive definite matrix W, and the normalization method can adopt the method of scaling the specific elements of the matrix to 1 or other methods, can be used for representing the measurement noise weight of the robot and is determined a priori through a measuring instrument and a measurement scheme.
For the characteristic vector of positioning error
Figure BDA0003154824620000037
And (3) weighting: transfer the error to equation
Figure BDA0003154824620000038
Equivalent changes are
Figure BDA0003154824620000039
Wherein
Figure BDA00031548246200000310
And
Figure BDA00031548246200000311
representing the weighted pose error component and the corresponding eigenvector, wiIs the value of the ith row and ith column of the normalized measurement noise variance matrix W.
And step S3, estimating the geometric error at any pose based on a local linear regression method and predicting the corresponding positioning error so as to calibrate the robot.
Optionally, in an embodiment of the present application, the step S3 further includes:
obtaining pose errors of a plurality of measurement poses through measurement, and obtaining corresponding weighted positioning error feature vectors;
for any weighted positioning error feature vector of any pose, calculating the distance of any weighted positioning error feature vector in the other measurement poses;
predicting any weighted pose error component of any pose through local linear regression and a geometric error model;
obtaining a predicted value of the positioning error of the robot at the pose according to the predicted weighted pose error components;
and compensating the driving shaft command based on the predicted and determined positioning error through an error compensation method of kinematic calibration.
In particular, for N measurement poses, i.e. pose errors thereof determined by measurement, corresponding weighted positioning error featuresThe vector can be expressed as
Figure BDA0003154824620000041
Wherein 1 ≦ i ≦ f represents different pose error components, 1 ≦ j ≦ N represents different measurement poses
Figure BDA0003154824620000042
Are the measured values of the corresponding pose error components.
Any weighted positioning error feature vector for any pose
Figure BDA0003154824620000043
Calculating the distance between the weighted positioning error feature vector and any weighted positioning error feature vector in the measurement pose
Figure BDA0003154824620000044
Where the distance function may be any function used to characterize the distance between vectors.
Any weighted pose error component δ for any posek,0(1. ltoreq. k. ltoreq.f) can be estimated as
Figure BDA0003154824620000045
Wherein
Figure BDA0003154824620000046
Figure BDA0003154824620000047
W＝diag(d1,1,k,…,df,1,k,…,df,N,k)；
Delta determined from the respective predictionsi,0And the predicted value of the positioning error of the robot at the pose can be obtained
Figure BDA0003154824620000048
And compensating the driving shaft command based on the predicted and determined positioning error through an error compensation method of kinematic calibration.
Fig. 2 shows a typical configuration of a five-degree-of-freedom hybrid robot, which includes a three-degree-of-freedom parallel mechanism and a two-degree-of-freedom series mechanism connected in series with the parallel mechanism. The three-degree-of-freedom parallel mechanism comprises an upper fixed platform 8, a lower fixed platform 4, a parallel linkage platform 7 and three branch assemblies 1, 2 and 3. The first branch component 1 and the second branch component 2 with the same structure in the three branch components are positioned on the same plane, penetrate through the upper fixed platform 8 and are connected with the upper fixed platform 8 through a rotating hinge. The third branch component 3 passes through the lower fixed platform 4 and is connected with the lower fixed platform 4 by a rotating hinge. The front ends of the first branch component 1 and the second branch component 2 are connected with the parallel linkage platform 7 through a rotating hinge, and the front end of the third branch component 3 is fixedly connected with the parallel linkage platform 7. The two-degree-of-freedom attitude tandem mechanism includes a C-shaped member 5 and an a-shaped member 6. The C-shaped component 5 is connected with the parallel linkage platform 7 through a rotating hinge. The first end of the A-shaped component 6 is provided with a matching hole connected with the tool handle, the plane of the hole is used as a terminal moving platform of the robot, and the second end of the A-shaped component is connected with the C-shaped component through a rotating hinge. The C-shaped member 5, the a-shaped member 6 and the three branching assemblies 1, 2, 3 serve as five drive shafts of the robot. The robot kinematics calibration method based on local linear regression is applied to the hybrid robot, and the specific method comprises the following steps:
1) analyzing the configuration of the robot, a first-order geometric error model of the robot can be established:
δE＝M(q)∈
wherein
Figure BDA0003154824620000051
Is the position and attitude error of the robot end effector, f is 5,
Figure BDA0003154824620000052
represents a total of 38 mutually uncorrelated geometric errors, which can be expressed as:
Figure BDA0003154824620000053
m is a radical ofThe error transfer matrix (c) represents the influence of the geometric error in e on the position and orientation error of the robot end effector, and is a robot drive axis displacement vector q ═ l1,l2,l3,θC,θA]TA function of where1、l2And l3Respectively, the length of the three branches, thetaCAnd thetaAIs the rotation angle of the C-type and a-type members with respect to the initial attitude.
2) The eigenvectors are weighted according to the measurement noise variance matrix.
The pose measurement noise can be determined in a priori by a measuring instrument and a measuring scheme in the kinematic calibration of the five-degree-of-freedom hybrid robot
Figure BDA0003154824620000054
The variance matrix of (1) is a diagonal positive definite matrix P, which is to be
Figure BDA0003154824620000055
As a normalized variance matrix, where P (1,1) is the value of row 1, column 1 of matrix P. According to the normalized measurement noise variance matrix W, the positioning error characteristic vector
Figure BDA0003154824620000056
Weighting is performed to weight the feature vector
Figure BDA0003154824620000057
wiIs the value of row i and column i of W, the corresponding weighted pose error component
Figure BDA0003154824620000058
3) And estimating and compensating the positioning error at any pose based on a local linear regression method.
3-1) for N measurement poses, i.e. their pose errors are determined by measurement, the corresponding weighted positioning error eigenvectors can be expressed as
Figure BDA0003154824620000059
WhereinI is more than or equal to 1 and less than or equal to f represents different pose error components, j is more than or equal to 1 and less than or equal to N represents different measurement poses,
Figure BDA00031548246200000510
are the measured values of the respective pose error components;
3-2) any weighted positioning error feature vector for any pose
Figure BDA00031548246200000511
Calculating the distance between the weighted positioning error feature vector and any weighted positioning error feature vector in the measurement pose
Figure BDA00031548246200000512
Wherein the distance function is a cosine distance function, i.e.
Figure BDA0003154824620000061
3-3) any weighted pose error component delta for any posek,0(1. ltoreq. k. ltoreq.f) estimated by local linear regression and geometric error model as
Figure BDA0003154824620000062
Wherein the content of the first and second substances,
Figure BDA0003154824620000063
Figure BDA0003154824620000064
W＝diag(d1,1,k,…,df,1,k,…,df,N,k)；
3-4) delta determined from the respective predictionsi,0And the predicted value of the positioning error of the robot at the pose can be obtained
Figure BDA0003154824620000065
3-5) Jacobian method in the error compensation method by kinematic calibration, i.e. the drive axis variations δ q and δECan be expressed as δ q ═ J δEThen based on the predicted determined locationError deltaEThe compensation amount of the drive shaft command should be-J deltaE。
According to the robot kinematics calibration method based on local linear regression provided by the embodiment of the application, firstly, a geometric error model of the robot is determined; further weighting the geometric error model according to the measurement noise variance matrix; and finally, estimating the geometric error at any pose based on a local linear regression method and predicting the corresponding positioning error to realize the effect of kinematics calibration. The problem of residual error in kinematic calibration caused by difficult accurate modeling or unmodeled errors is solved to a certain extent, the positioning precision of the robot is further improved, and the calibration residual error in a large working space by the traditional method is reduced.
The robot kinematics calibration device based on local linear regression according to the embodiment of the present application is described next with reference to the accompanying drawings.
Fig. 3 is a schematic structural diagram of a robot kinematics calibration apparatus based on local linear regression according to an embodiment of the present application.
As shown in fig. 3, the robot kinematics calibration apparatus based on local linear regression includes: a modeling module 100, a processing module 200, and a calibration module 300.
The modeling module 100 is configured to establish a geometric error model of the robot, and obtain a positioning error feature vector of the pose error component according to the geometric model.
And the processing module 200 is configured to determine a measurement noise variance matrix of the robot, and weight the eigenvector according to the measurement noise variance matrix.
And the calibration module 300 is used for estimating the geometric error at any pose based on a local linear regression method and predicting the corresponding positioning error so as to calibrate the robot.
Optionally, in an embodiment of the present application, the modeling module, in particular for,
the geometric error model of the robot is established as follows:
δE＝M(q)∈
wherein the content of the first and second substances,
Figure BDA0003154824620000066
is the position and attitude error of the robot terminal actuator,
Figure BDA0003154824620000067
representing the total n independent geometric errors, wherein M is a corresponding error transfer matrix, representing the influence of the geometric errors in the epsilon on the position and attitude errors of the robot terminal actuator, and is a function of a displacement vector q of a drive shaft of the robot;
obtaining a positioning error feature vector of a pose error component according to the geometric model
Figure BDA0003154824620000071
Figure BDA0003154824620000072
Wherein e isi(1. ltoreq. i.ltoreq.f) is the unit vector of the corresponding component.
Optionally, in an embodiment of the present application, the calibration module is specifically configured to obtain pose errors of a plurality of measurement poses through measurement, and obtain corresponding weighted positioning error feature vectors; for any weighted positioning error feature vector of any pose, calculating the distance of any weighted positioning error feature vector in the other measurement poses; predicting any weighted pose error component of any pose through local linear regression and a geometric error model; obtaining a predicted value of the positioning error of the robot at the pose according to the predicted weighted pose error components; and compensating the driving shaft command based on the predicted and determined positioning error through an error compensation method of kinematic calibration.
It should be noted that the foregoing explanation of the method embodiment is also applicable to the apparatus of this embodiment, and is not repeated herein.
According to the robot kinematics calibration device based on the local linear regression, firstly, a geometric error model of the robot is determined; further weighting the geometric error model according to the measurement noise variance matrix; and finally, estimating the geometric error at any pose based on a local linear regression method and predicting the corresponding positioning error to realize the effect of kinematics calibration. The problem of residual error in kinematic calibration caused by difficult accurate modeling or unmodeled errors is solved to a certain extent, the positioning precision of the robot is further improved, and the calibration residual error in a large working space by the traditional method is reduced.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.

Claims (6)

1. A robot kinematics calibration method based on local linear regression is characterized by comprising the following steps:
s1, establishing a geometric error model of the robot, and obtaining a positioning error feature vector of a pose error component according to the geometric model;
s2, determining a measurement noise variance matrix of the robot, and weighting the eigenvector according to the measurement noise variance matrix;
and S3, estimating the geometric error at any pose based on a local linear regression method and predicting the corresponding positioning error so as to calibrate the robot.
2. The method according to claim 1, wherein the S1 further comprises:
establishing a geometric error model of the robot as follows:
δE＝M(q)∈
wherein the content of the first and second substances,
Figure FDA0003154824610000011
is the position and attitude error of the robot terminal actuator,
Figure FDA0003154824610000012
representing the total n independent geometric errors, wherein M is a corresponding error transfer matrix, representing the influence of the geometric errors in the epsilon on the position and attitude errors of the robot terminal actuator, and is a function of a displacement vector q of a drive shaft of the robot;
obtaining a positioning error feature vector of a pose error component according to the geometric model
Figure FDA0003154824610000013
Figure FDA0003154824610000014
Wherein e isiIs the unit vector of the corresponding component.
3. The method according to claim 1, wherein the S3 further comprises:
obtaining pose errors of a plurality of measurement poses through measurement, and obtaining corresponding weighted positioning error feature vectors;
for any weighted positioning error feature vector of any pose, calculating the distance of any weighted positioning error feature vector in the other measurement poses;
predicting any weighted pose error component of any pose through local linear regression and a geometric error model;
obtaining a positioning error predicted value of the robot at the pose according to each predicted weighted pose error component;
and compensating the driving shaft command based on the predicted and determined positioning error through an error compensation method of kinematic calibration.
4. A robot kinematics calibration device based on local linear regression is characterized by comprising:
the modeling module is used for establishing a geometric error model of the robot and obtaining a positioning error characteristic vector of a pose error component according to the geometric model;
the processing module is used for determining a measurement noise variance matrix of the robot and weighting the eigenvector according to the measurement noise variance matrix;
and the calibration module is used for estimating the geometric error at any pose based on a local linear regression method and predicting the corresponding positioning error so as to calibrate the robot.
5. The apparatus according to claim 4, characterized in that the modeling module, in particular for,
establishing a geometric error model of the robot as follows:
δE＝M(q)∈
wherein the content of the first and second substances,
Figure FDA0003154824610000021
is the position and attitude error of the robot terminal actuator,
Figure FDA0003154824610000022
representing the total n independent geometric errors, wherein M is a corresponding error transfer matrix, representing the influence of the geometric errors in the epsilon on the position and attitude errors of the robot terminal actuator, and is a function of a displacement vector q of a drive shaft of the robot;
obtaining a positioning error feature vector of a pose error component according to the geometric model
Figure FDA0003154824610000023
Figure FDA0003154824610000024
Wherein e isiIs the unit vector of the corresponding component.
6. The device according to claim 4, characterized in that the calibration module, in particular for,
obtaining pose errors of a plurality of measurement poses through measurement, and obtaining corresponding weighted positioning error feature vectors; for any weighted positioning error feature vector of any pose, calculating the distance of any weighted positioning error feature vector in the other measurement poses; predicting any weighted pose error component of any pose through local linear regression and a geometric error model; obtaining a positioning error predicted value of the robot at the pose according to each predicted weighted pose error component; and compensating the driving shaft command based on the predicted and determined positioning error through an error compensation method of kinematic calibration.
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刘宇哲等: "5轴混联机床运动学标定的测量轨迹评价及误差补偿", 《清华大学学报(自然科学版)》 *

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