CN113500585A - Robot measurement pose evaluation method and evaluation device for kinematics calibration - Google Patents

Robot measurement pose evaluation method and evaluation device for kinematics calibration Download PDF

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CN113500585A
CN113500585A CN202110807852.1A CN202110807852A CN113500585A CN 113500585 A CN113500585 A CN 113500585A CN 202110807852 A CN202110807852 A CN 202110807852A CN 113500585 A CN113500585 A CN 113500585A
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pose
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determining
task space
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CN113500585B (en
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吴军
叶豪
王煜天
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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
    • B25J9/003—Programme-controlled manipulators having parallel kinematics
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/08—Programme-controlled manipulators characterised by modular constructions
    • 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
    • B25J9/1661—Programme controls characterised by programming, planning systems for manipulators characterised by task planning, object-oriented languages
    • 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
    • B25J9/1679—Programme controls characterised by the tasks executed
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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Abstract

The application discloses a robot measurement pose evaluation method and evaluation device for kinematics calibration, for a set of given measurement poses and a task space of which the robot needs to guarantee precision, the method takes the estimated square value expectation of pose residual error root mean square in the task space after the kinematics calibration based on the set of measurement poses as a standard for evaluating the set of measurement poses, and gives corresponding weighted evaluation indexes by considering different noise intensities of measurement components and different weights of pose precision. The method solves the problem that the existing measurement pose evaluation method focuses on geometric error observability and cannot directly reflect the kinematics calibration effect, can accurately and visually link the measurement pose evaluation and the kinematics calibration, and reflects the amplitude of residual errors after the kinematics calibration in the robot task space.

Description

Robot measurement pose evaluation method and evaluation device for kinematics calibration
Technical Field
The application relates to the technical field of robot kinematics calibration, in particular to a robot measurement pose evaluation method and device for kinematics calibration.
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.
For kinematics calibration, in order to ensure the positioning accuracy after calibration in the whole task space and simultaneously consider the problem of measurement cost caused by high number of measurement poses, the measurement poses need to be optimized. The premise of optimizing the measurement pose is that quantitative index evaluation is performed on a group of determined measurement poses.
At present, research aiming at the evaluation method mainly focuses on the analysis of an error identification matrix, namely the analysis aiming at the observability of geometric errors, including a parameter variance minimization index
Figure BDA0003167229300000011
Condition number reciprocal indicator
Figure BDA0003167229300000012
End pose uncertainty minimization index O3＝σLNoise method index
Figure BDA0003167229300000013
And A optimum index
Figure BDA0003167229300000014
In the above prior art, the current evaluation method comprehensively analyzes the error identification equation in each aspect of statistics, but the present evaluation method is limited in that only observability of the geometric error is analyzed, and actually, the estimation deviation of the geometric error does not affect the pose of the end effector consistently, so that the observability of the geometric error and the residual error after kinematic calibration are not strictly consistent. The aim of kinematics calibration is to improve the positioning accuracy of the whole task space, and the observability of geometric errors is indirect reaction, so that an index directly reflecting the positioning accuracy of the whole task space after the kinematics calibration can more intuitively reflect the influence of measurement pose evaluation on the kinematics calibration.
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 method for evaluating a measurement pose of a robot for kinematics calibration, which solves the problem that the existing method for evaluating a measurement pose focuses on the observability of geometric errors and cannot directly reflect the kinematics calibration effect.
Another object of the present application is to provide a robot measurement pose evaluation apparatus for kinematic calibration.
In order to achieve the above object, an embodiment of an aspect of the present application provides a method for evaluating a measurement pose of a robot for kinematics calibration, including:
establishing a geometric error model of the robot;
determining and discretizing a task space of the robot, determining a measurement noise intensity weight and a pose precision weight of the robot, and determining and preprocessing a corresponding error transfer matrix set according to the pose precision weight for each group of poses in the discretized task space of the robot;
determining an error identification equation according to the pose to be evaluated and the geometric error model, determining a root mean square value expected mean value of pose residual errors after kinematic calibration in the task space of the discretized robot according to the measurement noise intensity weight, and evaluating the calibration effect of the robot by utilizing the root mean square value expected mean value of the pose residual errors.
In order to achieve the above object, an embodiment of another aspect of the present application provides a robot measurement pose evaluation apparatus for kinematics calibration, including:
the modeling module is used for establishing a geometric error model of the robot;
the calculation module is used for determining and discretizing the task space of the robot, determining the measurement noise intensity weight and the pose precision weight of the robot, and determining and preprocessing a corresponding error transfer matrix set according to the pose precision weight for each group of poses in the discretized task space of the robot;
and the evaluation module is used for determining an error identification equation according to the pose to be evaluated and the geometric error model, determining a root mean square value expected mean value of pose residual errors after kinematic calibration in the task space of the discretized robot according to the measurement noise intensity weight, and evaluating the calibration effect of the robot by using the root mean square value expected mean value of the pose residual errors.
The robot measurement pose evaluation method and the evaluation device for the kinematics calibration in the embodiment of the application provide a measurement pose evaluation method considering pose residuals in a task space after the kinematics calibration is carried out based on the set of measurement poses. The provided index is different from the conventional evaluation index for representing the observability of the kinematic parameter error, is used for representing the amplitude of the residual error after the kinematic calibration in the robot task space, is used for the field of the kinematic calibration of the robot, and aims to improve the precision of the robot or reduce the number of the measurement poses required by the kinematic calibration based on the optimally selected measurement poses of the method. Therefore, the problem that the existing measurement pose evaluation method focuses on geometric error observability and cannot directly reflect the kinematics calibration effect is solved, so that the measurement pose evaluation and the kinematics calibration are more accurately and intuitively linked, and the amplitude of the residual error after the kinematics calibration in the robot task space is reflected.
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 measurement pose evaluation method for kinematic calibration according to an embodiment of the present application;
FIG. 2 is a typical hybrid robot configuration according to one embodiment of the present application;
FIG. 3 is a diagram illustrating a typical discretization of a task space;
fig. 4 is a schematic structural diagram of a robot measurement pose evaluation device for kinematic calibration 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 measurement pose evaluation method and an evaluation device for kinematic calibration according to an embodiment of the present application with reference to the accompanying drawings.
First, a robot measurement pose evaluation method for kinematics calibration proposed 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 measurement pose evaluation method for kinematic calibration according to an embodiment of the present application.
As shown in fig. 1, the method for evaluating the measurement pose of the robot for kinematics calibration includes the following steps:
and step S1, establishing a geometric error model of the robot.
Optionally, in an embodiment of the present application, the geometric error model of the robot is established as:
Figure BDA0003167229300000031
wherein ,δbEPosition of the end-effector of the robot, omegaEIs the attitude error of the robot end effector,
Figure BDA0003167229300000032
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 terminal actuator and is a function of the displacement vector q of the robot driving shaft.
And step S2, determining and discretizing the task space of the robot, determining the measurement noise intensity weight and the pose precision weight of the robot, and determining and preprocessing a corresponding error transfer matrix set according to the pose precision weight for each group of poses in the discretized task space of the robot.
The method comprises the steps of determining basic information of a robot and preprocessing, firstly, determining and discretizing a task space of the robot, wherein the task space of the robot is a space formed by end poses of the robot for realizing task requirements, and positioning accuracy is generally required to be guaranteed. The task space is a space in which the terminal poses of the robot are continuously distributed, due to the fact that infinite elements are arranged in the space, the infinite elements need to be analyzed in a discretization mode, the discretization refers to the fact that the finite elements in the space serve as the representation of the whole space, and the task space can be uniformly sampled. The discretized task space can be represented as a set of robot drive axis displacement vectors, pi ═ s1，s2，...，smAnd can also be expressed as other mathematical expressions which can uniquely represent the discretization task space.
Secondly, determining the measurement noise intensity weight of the robot, measuring the tail end pose error of the measurement pose of the robot, wherein the measurement precision is influenced by the measurement noise
Figure BDA0003167229300000041
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 BDA0003167229300000042
is normalized to a symmetric positive definite matrix W-1The normalization method can adopt scaling of specific elements to 1 or other ways, and can be used for representing the measurement noise intensity weight of the robot and is determined a priori through a measuring instrument and a measurement scheme.
Thirdly, determining the pose precision weight of the robot: the expression units of the position and the attitude of the robot are different, the requirements of the actual robot on the position and the attitude precision are also different, the attitude precision weight can be expressed as a diagonal matrix C, and particularly, the ratio of the position precision requirement to the attitude precision requirement is r (rad)-1) When C is equal to diag (1, 1, 1, r, r, r).
And finally, data preprocessing is carried out: for each group of poses in the discretization task space pi, determining a corresponding error transfer matrix set which is recorded as piA＝{A1，A2，...，Am}, wherein Ai＝M(si) Preprocessing the matrix
Figure BDA0003167229300000043
The robot for a particular structural parameter, task space and geometric error model only needs to be calculated once.
And step S3, determining an error identification equation according to the pose to be evaluated and the geometric error model, determining the expected mean value of the root mean square value of the pose residual error after kinematic calibration in the task space of the discretized robot according to the measurement noise intensity weight, and evaluating the calibration effect of the robot by utilizing the expected mean value of the root mean square value of the pose residual error.
Optionally, in an embodiment of the present application, S3 further includes:
determining an error identification equation according to the pose to be evaluated and the geometric error model as follows:
δ＝Ma∈
wherein ,
Figure BDA0003167229300000044
Miis an error transfer matrix, and delta is a corresponding pose error measured value;
based on the measured noise intensity weight of the robot, the estimated value of the geometric error is determined according to the weighted least square method
Figure BDA0003167229300000045
Wherein, W is an inverse matrix of a measurement noise variance matrix;
determining an estimated value and an actual value of the geometric error, and normalizing the pose residual error after the kinematics calibration in the task space of the discretized robot
Figure BDA0003167229300000046
wherein ,
Figure BDA0003167229300000047
is the geometric error estimate, e*Is the actual value of the geometric error, C is the matrix corresponding to the pose precision weight, AiIn a pose siA corresponding error transfer matrix;
determining the root mean square of the pose residual error after the kinematic calibration in the task space of the discretized robot according to the estimated value and the pose residual error
Figure BDA0003167229300000051
Wherein m is the total attitude number in the discretization task space;
determining the desired mean of the root mean square values from statistical knowledge
Figure BDA0003167229300000052
Wherein A is a pre-processing matrix.
Specifically, for any measurement pose to be evaluated, first, based on the measurement pose combination Ω to be evaluated and the geometric error model, the error identification equation may be determined to be δ ═ Ma∈, wherein
Figure BDA0003167229300000053
To transfer the matrix M by the errori＝M(qi) Stack determination, δ is the corresponding pose error measurement.
Based on the measured noise intensity weight of the robot, the estimated value of the epsilon can be determined according to a weighted least square method
Figure BDA00031672293000000511
Figure BDA00031672293000000512
The widely used least squares method e-MaTMa-1 MaT δ can be considered as a special case of taking the noise strength equal on each component.
Estimate for ∈
Figure BDA0003167229300000054
And the actual value e*In task space siNormalized pose residual after kinematic calibration can be expressed as
Figure BDA0003167229300000055
Wherein the pose precision weight matrix C of the robot converts pose errors into the same units to realize normalization, and the normalization is directly considered
Figure BDA0003167229300000056
As a specific example of the normalized error, the weight matrix C is used as the identity matrix.
Based on the estimated value, the root mean square of the pose residual error after the kinematic calibration in the discretization task space pi is expressed as
Figure BDA0003167229300000057
Through the analysis of statistical knowledge, the expected mean value of the square value of the statistical knowledge can be determined
Figure BDA0003167229300000058
The eta is used as the pose evaluation number provided by the methodThe larger the value is, the larger the pose residual error after the kinematics calibration is, and the worse the kinematics calibration effect is.
It should be noted that the pose evaluation index
Figure BDA0003167229300000059
Due to the nature of the matrix, η can also be expressed as
Figure BDA00031672293000000510
And the like for the remaining equivalents.
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 flow chart of the robot measurement pose evaluation method for kinematics calibration is applied to the hybrid robot, and the specific method comprises the following steps:
1) for the analysis of the robot configuration, a geometric error model of the robot can be established:
Figure BDA0003167229300000061
wherein δbE、ωERespectively representing the position and attitude errors of the robot end-effector,
Figure BDA0003167229300000062
represents a total of 38 mutually uncorrelated geometric errors, which can be expressed as:
Figure BDA0003167229300000063
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 displacement vector q of a robot driving shaft [ l [ ]1，l2，l3，θC，θA]TA function of where1、l2 and l3Respectively, the length of the three branches, thetaC and θAIs the rotation angle of the C-type and a-type members with respect to the initial attitude.
2) Determining basic information and preprocessing of the robot, mainly comprising:
2-1) determining and discretizing the task space of the robot: taking the 2-dimensional space shown in fig. 3 as an example, where the rectangular range represents the task space of the robot, the set of diamond points uniformly distributed in the rectangular range of fig. 3 can be used as the discretized task space of the robot, where the ellipses represent the diamond points between the rectangular range. For a concrete five-degree-of-freedom hybrid robot, a discrete mode in a 5-dimensional space in fig. 3 is adopted, and a discretized task space can be expressed as a set pi ═ s of displacement vectors of robot driving shafts1，s2，...，sm}。
2-2) determining the measurement noise intensity weight of the robot: 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 BDA0003167229300000064
The variance matrix of (A) is symmetricPositive definite matrix P, will
Figure BDA0003167229300000065
As a normalized variance matrix, where P (1, 1) is the value of row 1, column 1 of matrix P.
2-3) determining the pose precision weight of the robot: the five-degree-of-freedom hybrid robot has different requirements on position and attitude precision, the pose precision weight can be expressed as a diagonal matrix C, and particularly, the ratio of the position and attitude precision requirements is r (rad)-1) When C is equal to diag (1, 1, 1, r, r, r), r may be adjusted according to the robot requirements.
2-4) data preprocessing: for each group of positions n, determining a corresponding set of error transfer matrices nA＝{A1，A2，...，Am}, wherein Ai＝M(si) Preprocessing the matrix
Figure BDA0003167229300000066
3) For any set of measurement poses to be evaluated, expressed as a set of robot drive axis displacement vectors Ω ═ { q }1，q2，...，qn}。
4) Determining evaluation values of the set of measurement poses: based on the measurement pose combination omega to be evaluated and the geometric error model, the error identification equation can be determined as follows: delta-Ma∈, wherein
Figure BDA0003167229300000067
To transfer the matrix M by the errori＝M(qi) Stacking determination is carried out, wherein delta is a corresponding pose error measured value, and the expected mean value of the root mean square value of the pose residual error after kinematic calibration in the discretization task space can be determined through the analysis of statistical knowledge
Figure BDA0003167229300000068
Eta is the evaluation value of the set of poses calculated according to the method.
According to the robot measurement pose evaluation method for kinematics calibration provided by the embodiment of the application, a measurement pose evaluation method considering pose residual errors in a task space after kinematics calibration is performed based on a set of measurement poses is provided, for a set of given measurement poses and a task space of which the robot needs to ensure the precision, the estimated square value of the pose residual error root mean square in the task space after the kinematics calibration is performed based on the set of measurement poses is expected to be used as a standard for evaluating the set of measurement poses, and corresponding weighted evaluation indexes are given by considering different noise intensities and different weights of pose precision of measurement components. The provided index is different from the conventional evaluation index for representing the observability of the kinematic parameter error, is used for representing the amplitude of the residual error after the kinematic calibration in the robot task space, is used for the field of the kinematic calibration of the robot, and aims to improve the precision of the robot or reduce the number of the measurement poses required by the kinematic calibration based on the optimally selected measurement poses of the method. Therefore, the problem that the existing measurement pose evaluation method focuses on geometric error observability and cannot directly reflect the kinematics calibration effect is solved, so that the measurement pose evaluation and the kinematics calibration are more accurately and intuitively linked, and the amplitude of the residual error after the kinematics calibration in the robot task space is reflected.
Next, a robot measurement pose evaluation apparatus for kinematics calibration proposed according to an embodiment of the present application is described with reference to the drawings.
Fig. 4 is a schematic structural diagram of a robot measurement pose evaluation device for kinematic calibration according to an embodiment of the present application.
As shown in fig. 4, the robot measurement pose evaluation apparatus for kinematic calibration includes: a modeling flat module 100, a calculation module 200, and an evaluation module 300.
And the modeling module 100 is used for establishing a geometric error model of the robot.
And the calculating module 200 is used for determining and discretizing the task space of the robot, determining the measurement noise intensity weight and the pose precision weight of the robot, and determining and preprocessing a corresponding error transfer matrix set according to the pose precision weight for each group of poses in the discretized task space of the robot.
The evaluation module 300 is configured to determine an error identification equation according to the pose to be evaluated and the geometric error model, determine a root mean square value expected average value of pose residual errors after kinematic calibration in a task space of the discretized robot according to the measurement noise intensity weight, and evaluate the calibration effect of the robot by using the root mean square value expected average value of the pose residual errors.
Optionally, in an embodiment of the present application, the geometric error model is:
Figure BDA0003167229300000071
wherein ,δbEPosition of the end-effector of the robot, omegaEIs the attitude error of the robot end effector,
Figure BDA0003167229300000072
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 terminal actuator and is a function of the displacement vector q of the robot driving shaft.
Optionally, in an embodiment of the application, for each set of poses in the task space of the discretized robot, determining and preprocessing a respective set of error transfer matrices comprises:
for each set of poses in the task space of the discretized robot, determining a respective set of error transfer matrices as: II typeA＝{A1，A2，...，AmWherein A isi＝M(si) Preprocessing the matrix
Figure BDA0003167229300000081
C is a matrix corresponding to the pose precision weight, siIs the ith driveshaft displacement vector in the discretization task space, and m is the total pose in the discretization task space.
Optionally, in an embodiment of the present application, the evaluation module 300 is specifically configured to determine an error identification equation according to the pose to be evaluated and the geometric error model as follows:
δ＝Ma∈
wherein ,
Figure BDA0003167229300000082
Miis an error transfer matrix, and delta is a corresponding pose error measured value;
based on the measured noise intensity weight of the robot, the estimated value of the geometric error is determined according to the weighted least square method
Figure BDA0003167229300000083
Wherein, W is an inverse matrix of a measurement noise variance matrix;
determining an estimated value and an actual value of the geometric error, and normalizing the pose residual error after the kinematics calibration in the task space of the discretized robot
Figure BDA0003167229300000084
wherein ,
Figure BDA0003167229300000085
is the geometric error estimate, e*Is the actual value of the geometric error, C is the matrix corresponding to the pose precision weight, AiIn a pose siA corresponding error transfer matrix;
determining the root mean square of the pose residual error after the kinematic calibration in the task space of the discretized robot according to the estimated value and the pose residual error
Figure BDA0003167229300000086
Wherein m is the total attitude number in the discretization task space;
determining the desired mean of the root mean square values from statistical knowledge
Figure BDA0003167229300000087
Wherein A is a pre-processing matrix.
Optionally, in an embodiment of the present application, evaluating a calibration effect of the robot by using an expected mean of root-mean-square squares of pose residuals includes:
the larger the expected mean value of the root-mean-square value of the pose residual error is, the worse the calibration effect of the robot is.
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 measurement pose evaluation device for kinematics calibration, a measurement pose evaluation method considering pose residuals in a task space after kinematics calibration based on a set of measurement poses is provided, for a set of given measurement poses and a task space of which the robot needs to guarantee precision, the estimated square value of the root mean square of the pose residuals in the task space after the kinematics calibration based on the set of measurement poses is expected to serve as a standard for evaluating the set of measurement poses, and corresponding weighted evaluation indexes are given by considering different noise intensities of measurement components and different weights of pose precisions. The provided index is different from the conventional evaluation index for representing the observability of the kinematic parameter error, is used for representing the amplitude of the residual error after the kinematic calibration in the robot task space, is used for the field of the kinematic calibration of the robot, and aims to improve the precision of the robot or reduce the number of the measurement poses required by the kinematic calibration based on the optimally selected measurement poses of the method. Therefore, the problem that the existing measurement pose evaluation method focuses on geometric error observability and cannot directly reflect the kinematics calibration effect is solved, so that the measurement pose evaluation and the kinematics calibration are more accurately and intuitively linked, and the amplitude of the residual error after the kinematics calibration in the robot task space is reflected.
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 (10)

1. A robot measurement pose evaluation method for kinematics calibration is characterized by comprising the following steps:
establishing a geometric error model of the robot;
determining and discretizing a task space of the robot, determining a measurement noise intensity weight and a pose precision weight of the robot, and determining and preprocessing a corresponding error transfer matrix set according to the pose precision weight for each group of poses in the discretized task space of the robot;
determining an error identification equation according to the pose to be evaluated and the geometric error model, determining a root mean square value expected mean value of pose residual errors after kinematic calibration in the task space of the discretized robot according to the measurement noise intensity weight, and evaluating the calibration effect of the robot by utilizing the root mean square value expected mean value of the pose residual errors.
2. The method of claim 1, wherein the geometric error model is:
Figure FDA0003167229290000011
wherein ,δbEPosition of the end-effector of the robot, omegaEIs the attitude error of the robot end effector,
Figure FDA0003167229290000012
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 terminal actuator and is a function of the displacement vector q of the robot driving shaft.
3. The method of claim 1, wherein the determining and pre-processing a respective set of error transfer matrices for each set of poses in the discretized task space of the robot comprises:
for each set of poses in the discretized task space of the robot, determining a respective set of error transfer matrices as: II typeA＝{A1,A2,…,AmWherein A isi＝M(si) Preprocessing the matrix
Figure FDA0003167229290000013
C is a matrix, s, corresponding to the pose precision weightiIs the ith driveshaft displacement vector in the discretization task space, and m is the total pose in the discretization task space.
4. The method according to claim 3, wherein the determining an error identification equation according to the pose to be evaluated and the geometric error model, and the determining the expected mean of the root mean square value of the pose residual error after the kinematics calibration in the task space of the discretized robot according to the measurement noise intensity weight comprise:
the error identification equation determined according to the pose to be evaluated and the geometric error model is as follows:
δ＝Ma∈
wherein ,
Figure FDA0003167229290000014
Miis an error transfer matrix, and delta is a corresponding pose error measured value;
determining an estimated value of a geometric error according to a weighted least square method based on the measured noise intensity weight of the robot
Figure FDA0003167229290000015
Wherein, W is an inverse matrix of a measurement noise variance matrix;
determining an estimated value and an actual value of the geometric error, and normalizing pose residual errors after the kinematics calibration in the discretized task space of the robot
Figure FDA0003167229290000016
wherein ,
Figure FDA0003167229290000017
is the geometric error estimate, e*Is the actual value of the geometric error, C is the matrix corresponding to the pose precision weight, AiIn a pose siA corresponding error transfer matrix;
determining the root mean square of the position and posture residual error after the kinematic calibration in the task space of the robot after the discretization according to the estimation value and the position and posture residual error
Figure FDA0003167229290000021
Wherein m is the total attitude number in the discretization task space;
determining the desired mean of the root mean square values from statistical knowledge
Figure FDA0003167229290000022
Wherein A is a pre-processing matrix.
5. The method of claim 1, wherein evaluating the calibration effect of the robot using the expected mean of the root-mean-square squared values of the pose residuals comprises:
the larger the expected mean value of the root-mean-square value of the pose residual error is, the worse the calibration effect of the robot is.
6. A robot measurement pose evaluation device for kinematics calibration is characterized by comprising:
the modeling module is used for establishing a geometric error model of the robot;
the calculation module is used for determining and discretizing the task space of the robot, determining the measurement noise intensity weight and the pose precision weight of the robot, and determining and preprocessing a corresponding error transfer matrix set according to the pose precision weight for each group of poses in the discretized task space of the robot;
and the evaluation module is used for determining an error identification equation according to the pose to be evaluated and the geometric error model, determining a root mean square value expected mean value of pose residual errors after kinematic calibration in the task space of the discretized robot according to the measurement noise intensity weight, and evaluating the calibration effect of the robot by using the root mean square value expected mean value of the pose residual errors.
7. The apparatus of claim 6, wherein the geometric error model is:
Figure FDA0003167229290000023
wherein ,δbEPosition of the end-effector of the robot, omegaEIs the attitude error of the robot end effector,
Figure FDA0003167229290000024
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 terminal actuator and is a function of the displacement vector q of the robot driving shaft.
8. The apparatus of claim 6, wherein the determining and pre-processing a respective set of error transfer matrices for each set of poses in the discretized task space of the robot comprises:
for each set of poses in the discretized task space of the robot, determining a respective set of error transfer matrices as: II typeA＝{A1,A2,…,AmWherein A isi＝M(si) Preprocessing the matrix
Figure FDA0003167229290000025
C is a matrix, s, corresponding to the pose precision weightiIs the ith driveshaft displacement vector in the discretization task space, and m is the total pose in the discretization task space.
9. The apparatus according to claim 8, wherein the evaluation module is specifically configured to determine the error identification equation according to the pose to be evaluated and the geometric error model as:
δ＝Ma∈
wherein ,
Figure FDA0003167229290000031
Miis an error transfer matrix, and delta is a corresponding pose error measured value;
determining an estimated value of a geometric error according to a weighted least square method based on the measured noise intensity weight of the robot
Figure FDA0003167229290000032
Wherein, W is an inverse matrix of a measurement noise variance matrix;
determining an estimated value and an actual value of the geometric error, and normalizing pose residual errors after the kinematics calibration in the discretized task space of the robot
Figure FDA0003167229290000033
wherein ,
Figure FDA0003167229290000034
is the geometric error estimate, e*Is the actual value of the geometric error, C is the matrix corresponding to the pose precision weight, AiIn a pose siA corresponding error transfer matrix;
determining the root mean square of the position and posture residual error after the kinematic calibration in the task space of the robot after the discretization according to the estimation value and the position and posture residual error
Figure FDA0003167229290000035
Wherein m is the total attitude number in the discretization task space;
determining the desired mean of the root mean square values from statistical knowledge
Figure FDA0003167229290000036
Wherein A is a pre-processing matrix.
10. The apparatus of claim 6, wherein evaluating the calibration effect of the robot using the expected mean of the root mean square squared values of the pose residuals comprises:
the larger the expected mean value of the root-mean-square value of the pose residual error is, the worse the calibration effect of the robot is.
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