CN112596382A - Geometric parameter optimization calibration method and system for series servo mechanism - Google Patents

Geometric parameter optimization calibration method and system for series servo mechanism Download PDF

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CN112596382A
CN112596382A CN202011206736.6A CN202011206736A CN112596382A CN 112596382 A CN112596382 A CN 112596382A CN 202011206736 A CN202011206736 A CN 202011206736A CN 112596382 A CN112596382 A CN 112596382A
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calibration
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geometric parameter
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CN112596382B (en
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高景一
王哲
耿金鹏
谭军
张慧
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Beijing Institute of Radio Measurement
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Abstract

The embodiment of the invention discloses a geometric parameter optimization calibration method and a geometric parameter optimization calibration system for a series servo mechanism, wherein the method comprises the following steps: s10, establishing a nominal kinematic model of the series servo mechanism according to the nominal value of the geometric parameter of the series servo mechanism; s20, establishing a geometric parameter error identification model of the serial mechanism according to the selected error measurement method and the nominal kinematic model, and determining error parameters to be identified; s30, determining sampling points of all the shafts in the motion range of all the rotating shafts of the serial mechanism, and further determining a set of position shapes to be measured; s40, selecting an optimized calibration bitmap from the set of bitmaps to be detected by using an observation criterion and a bitmap optimization algorithm; and S50, completing error measurement by using the optimal calibration configuration, and calculating by using a parameter identification method to obtain error parameters.

Description

Geometric parameter optimization calibration method and system for series servo mechanism
Technical Field
The invention relates to the field of kinematics calibration, in particular to a geometric parameter optimization calibration method and system for a series servo mechanism, a storage medium and computer equipment.
Background
The tandem servo mechanism has the advantages of flexible operation and strong mobility, and is widely applied to robots, antenna pointing mechanisms and multi-axis servo turntable systems. Because of inevitable geometric parameter errors caused by the special structural form of the serial mechanism, the absolute positioning accuracy of the serial mechanism is poor, and the serial mechanism is difficult to directly apply to certain application scenes with high requirements on absolute accuracy and needs to be calibrated in kinematics.
Kinematic calibration of a tandem servo is a process of geometric parameter identification and compensation, and the precision of geometric parameter identification determines the precision of calibration. The conventional geometric parameter identification method needs to randomly select a set of serial mechanism configurations in the working space of the tested serial servo mechanism as a calibration configuration set. The selection of the calibration configuration has obvious influence on the identification result of the geometric parameters in different structural forms of the serial mechanism. If the number of the selected calibration configurations is small, the identification result of some geometric parameters may be inaccurate, and the calibration precision of the whole mechanism is affected. If the number of the selected calibration configurations is large, the workload of calibration experiments and data processing is greatly increased, and the accuracy of parameter identification cannot be necessarily improved. Meanwhile, in the parameter identification process, the suppression effect on the measurement noise is also related to the selection of the calibration configuration.
The general geometric parameter calibration method of the series servo mechanism has the following problems:
1. selecting too many calibration configurations will increase the workload of calibration experiments and data processing;
2. the randomly selected calibration configuration may reduce the identification precision;
3. the method for selecting the optimal calibration configuration by using an enumeration method has huge calculation amount.
Disclosure of Invention
In view of this, when calibrating the serial servo mechanism, on the premise of giving the number N of calibration patterns, a group of optimized calibration patterns needs to be actively selected from the set of patterns to be measured in the working space, so that the geometric parameter identification precision in the calibration process is higher.
The first embodiment of the invention provides a geometric parameter optimization calibration method for a series servo mechanism, which comprises the following steps:
s10, establishing a nominal kinematic model of the series servo mechanism according to the nominal value of the geometric parameter of the series servo mechanism;
s20, establishing a geometric parameter error identification model of the serial mechanism according to the selected error measurement method and the nominal kinematic model, and determining error parameters to be identified;
s30, determining sampling points of all the shafts in the motion range of all the rotating shafts of the serial mechanism, and further determining a set of position shapes to be measured;
s40, selecting an optimized calibration configuration from the configuration set to be tested;
and S50, completing error measurement and parameter identification by utilizing the optimized calibration configuration.
In a specific embodiment, the nominal kinematic model established for the tandem mechanism in S10 has the following form:
Figure BDA0002757319130000021
wherein, TnIs the nominal pose of the tail end of the serial mechanism,
Figure BDA0002757319130000022
is a column vector formed by nominal values of M geometric parameters to be identified on a serial mechanism,
Figure BDA0002757319130000023
is the angle control quantity of the rotating shaft with s degrees of freedom of the serial mechanism,
Figure BDA0002757319130000024
is a non-linear functional for describing the kinematics of the tandem mechanism.
In one embodiment, the tandem end pose T is re-represented by a measurable pose vector p, and the geometric parameter error identification model for the tandem is built to have the form:
Figure BDA0002757319130000025
wherein dp represents the differential of the end pose of the serial mechanism, and the calibration model represents dp as the linear combination form of the geometric parameter deviation, so that for a certain pose i, the method includes
Figure BDA0002757319130000026
Wherein, Δ piRepresenting the pose error of the tail end of the serial mechanism;
Figure BDA0002757319130000027
is a geometric parameter error transfer matrix of the series mechanism under the current configuration; Δ φ ═ Δ φ1,Δφ2,…,ΔφM]TIs a column vector formed by errors of various geometric parameters of the series mechanism.
In a specific embodiment, the S30 includes
Within the angle range of the rotating shaft of each freedom degree of the series mechanism, k sampling points are selected according to an evenly distributed method, so that the s freedom degrees can generate k at mostsThe bit patterns to be measured form a bit pattern set { S }.
In a specific embodiment, the S40 includes
S401, randomly selecting N initial calibration bitmaps from the set { S } of bitmaps to be tested to form an initial calibration bitmap set { C }0}；
S402, calculating { C0N initially calibrated error transfer matrices in the
Figure BDA0002757319130000031
The N initial calibration patterns are positioned to form a geometric parameter error transfer matrix
Figure BDA0002757319130000032
Obtaining a parameter identification matrix by arranging according to rows and blocks
Figure BDA0002757319130000033
And calculating an observation matrix
Figure BDA0002757319130000034
Figure BDA0002757319130000035
Inverse matrix of
Figure BDA0002757319130000036
And
Figure BDA0002757319130000037
value of determinant
Figure BDA0002757319130000038
S403, from { C0Selecting a bit pattern, and removing the bit pattern to obtain an observation matrix
Figure BDA0002757319130000039
Value of determinant
Figure BDA00027573191300000310
Maximum;
s404, selecting a new bit pattern from the rest bit patterns in the { S }, so that the { C }0The remaining N-1 bits are added to the bit pattern to obtain a new set of N scaled bit patterns { C }1}. Make the observation matrix
Figure BDA00027573191300000311
Value of determinant
Figure BDA00027573191300000312
Maximum;
s405, repeating the steps S403 and S404 until a new set C with N calibration patternskGet the observation matrix
Figure BDA00027573191300000313
Value of determinant
Figure BDA00027573191300000314
Compared with the last calibration configuration set { Ck-1Determinant of observation matrix of
Figure BDA00027573191300000315
No longer increased, { CkAnd f, selecting an optimized calibration configuration set.
In one embodiment, the observation criteria are selected as:
Figure BDA00027573191300000316
where N is the number of measurement bitmaps contained in the set of bitmaps { C } for calibration, and L is a matrix
Figure BDA00027573191300000317
The value of L is the same as the number M of geometric parameters to be identified,
Figure BDA00027573191300000318
is a matrix M{C,N}A non-zero eigenvalue of.
In a particular embodiment, the observation criterion O1Is equivalent to the matrix M{C,N}Determinant value of | M{C,N}The size of |.
A second embodiment of the present invention provides a geometric parameter optimization calibration system for a tandem servo mechanism, including:
the motion model establishing unit is used for establishing a nominal kinematic model of the series servo mechanism according to the nominal value of the geometric parameter of the series servo mechanism;
the geometric parameter error identification model establishing and to-be-identified error parameter determining unit is used for establishing a geometric parameter error identification model of the serial mechanism according to the selected error measuring method and the nominal kinematic model and determining to-be-identified error parameters;
the device comprises a to-be-detected configuration set determining unit, a to-be-detected configuration set determining unit and a configuration setting unit, wherein the to-be-detected configuration set determining unit is used for determining sampling points of all shafts in the motion range of all rotating shafts of the serial mechanism so as to determine a to-be-detected configuration set;
the optimized calibration configuration selecting unit is used for selecting an optimized calibration configuration from the configuration set to be tested;
and the error measurement and parameter identification unit is used for completing error measurement and parameter identification by utilizing the optimized calibration configuration.
A third embodiment of the invention provides a computer-readable storage medium, on which a computer program is stored, characterized in that the program, when executed by a processor, implements the method according to the first embodiment.
A fourth embodiment of the present invention provides a computing device comprising a processor, wherein the processor executes a program to implement the method according to the first embodiment.
The invention has the following beneficial effects:
according to the geometric parameter optimization calibration method for the series servo mechanism, provided by the invention, a group of optimized calibration topograms are actively selected from the set of topograms to be tested, so that the geometric parameter identification precision is higher in the calibration process.
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The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
FIG. 1 is a schematic diagram illustrating a geometric parameter optimization calibration method for a tandem servo according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of an optimized calibration pattern selection method according to an embodiment of the invention.
Fig. 3 shows a schematic structural diagram of a computer device according to an embodiment of the present invention.
Detailed Description
In order to more clearly illustrate the invention, the invention is further described below with reference to preferred embodiments and the accompanying drawings. Similar parts in the figures are denoted by the same reference numerals. It is to be understood by persons skilled in the art that the following detailed description is illustrative and not restrictive, and is not to be taken as limiting the scope of the invention.
The core idea of the invention is to establish a kinematic model of the serial pointing mechanism, then determine the geometric error parameters and the identification model to be identified on the basis, select a group of optimized calibration configuration in the configuration set to be detected in the working space by using an optimization algorithm, and finally complete error measurement and parameter identification by using the selected configuration.
The geometric parameter optimization calibration method for the series servo mechanism is suitable for various series servo mechanisms, and the modeling, calibration configuration optimization, measurement and parameter identification methods are universal. The measured object can specifically comprise an antenna pointing mechanism, a serial industrial robot, a multi-axis servo turntable and the like; the measurement object can be the tail end position of the servo mechanism and can also be the tail end attitude angle of the servo mechanism; the measuring tool may be a laser tracker, a theodolite, a three-coordinate measuring machine, etc. In summary, the core of the invention is a generic method for calibration modeling and optimization of the tandem servo mechanism, which can be applied to various application scenarios.
Example 1
FIG. 1 is a schematic diagram illustrating a geometric parameter optimization calibration method for a tandem servo mechanism according to an embodiment of the present invention, including:
s10, establishing a nominal kinematic model of the series servo mechanism according to the nominal value of the geometric parameter of the series servo mechanism;
in one example, a nominal kinematic model is built having the form:
Figure BDA0002757319130000051
wherein, TnIs a nominal pose matrix of the tail end of the serial mechanism,
Figure BDA0002757319130000052
is a column vector formed by nominal values of M geometric parameters to be identified on a serial mechanism,
Figure BDA0002757319130000053
is the angle control quantity of the rotating shaft with s degrees of freedom of the serial mechanism,
Figure BDA0002757319130000054
is a non-linear functional for describing the kinematics of the tandem mechanism.
And T is a terminal pose matrix of the serial mechanism, and the mechanism kinematics shows that T has the following form:
Figure BDA0002757319130000055
the tandem mechanism end pose information measured by the measuring tool can be represented by the relevant elements in T. For example, if the measurement information is the end position of the tandem mechanism, the measurable pose vector p is equal to the column vector T of the corresponding displacement in the pose matrix T; if the measurement information is a pointing vector or a spatial attitude angle of the tail end of the tandem mechanism, the measurable pose vector p is equal to one of three basic coordinate vectors n, o and a in the pose matrix T or a vector obtained by sequentially arranging two basic coordinate vectors. That is to say, through simple mathematical transformation, the measured value in the calibration process can be represented by a pose vector p, and further, a geometric parameter error identification model of the series mechanism and a calibration model can be established:
Figure BDA0002757319130000056
wherein dp represents the differential of the pose vector at the tail end of the serial mechanism, the calibration model represents dp as the linear combination form of the geometric parameter deviation, and further, for a certain configuration i, the
Figure BDA0002757319130000057
Wherein, Δ piThe pose error of the tail end of the serial mechanism is shown,
Figure BDA0002757319130000061
is the geometric parameter error transfer matrix of the serial mechanism under the current configuration, and delta phi is [ delta phi ]1,Δφ2,…,ΔφM]TIs a column vector formed by errors of various geometric parameters of the series mechanism.
When the calibration experiment is performed on the servo mechanism, a set of bit patterns to be measured needs to be determined, and then N bit patterns are selected from the set to perform the calibration experiment. The calibration method provided by the invention can firstly set a set of bit patterns to be measured with larger sample size, and the specific design method is as follows:
within the angle range of the rotating shaft of each freedom degree of the series mechanism, k sampling points are selected according to an evenly distributed method, so that the s freedom degrees can generate k at mostsThe bit patterns to be measured form a bit pattern set { S }.
Selecting a subset { C } from the set { S } of the bit patterns to be measured, wherein the subset contains N calibration bit patterns and meets the observation criterion O1The value of (c) is maximum.
Specifically, for each one of the calibration patterns, its error transfer matrix may first be calculated according to equation (4)
Figure BDA0002757319130000062
Then the N bit shape geometric parameter error is transmitted to the matrix
Figure BDA0002757319130000063
Obtaining a parameter identification matrix by row block arrangement:
Figure BDA0002757319130000064
the observation matrix can further be calculated:
Figure BDA0002757319130000065
observation criterion O selected by the invention1The expression is as follows:
Figure BDA0002757319130000066
where N is the number of measurement bitmaps contained in the set of bitmaps { C } for calibration, and L is a matrix
Figure BDA0002757319130000067
The value of L is the same as the number M of geometric parameters to be identified,
Figure BDA0002757319130000068
is a matrix M{N}A non-zero eigenvalue of.
From the formula (5)
Figure BDA0002757319130000069
Equation (6) illustrates criterion O1Is equivalent to the matrix M{C,N}Determinant value of | M{C,N}The size of |.
And (4) replacing the bit patterns in the subsets { C } one by one through iterative computation to finally obtain an optimized calibration bit pattern set. The replacement process is divided into two steps, namely "remove a bit pattern" and "add a bit pattern", respectively. The calculation method and its advantages in this scheme are described below.
Firstly, a measuring method is determined for a to-be-measured series servo mechanism, a calibration model in the form of formula (4) is established, and meanwhile, an error delta p is determinediIs denoted here by d. I.e. after each removal of one bit shape,
Figure BDA0002757319130000071
compared with
Figure BDA0002757319130000072
The d rows are removed; after each time of adding one bit shape,
Figure BDA0002757319130000073
compared with
Figure BDA0002757319130000074
The d rows are added.
For convenience of description and without loss of generality, redundant subscripts are removed herein, with J0Representing the original error transfer matrix, J1Represents the error transfer matrix after adding or removing a bit pattern, and
Figure BDA0002757319130000075
Figure BDA0002757319130000076
the case of "adding one bit shape" is an example:
considering d as 1, the increased bit shape increases the error transfer matrix by 1 row, let j be1', then are
Figure BDA0002757319130000077
Observation matrix
Figure BDA0002757319130000078
The determinant and inverse of the observation matrix can then be calculated as follows:
Figure BDA0002757319130000079
Figure BDA00027573191300000710
from the recursion relationship of the equations (9) and (10), for any d, the added bit shape increases the error transfer matrix by d rows, and the determinant of the corresponding observation matrix is calculated as:
Figure BDA00027573191300000711
wherein j isi(i-1, 2, …, d) is the ith row of the error transfer matrix increment, M0,iIs the observation matrix after the first i rows are added.
Figure BDA00027573191300000712
The calculation is recursive according to equation (10).
Similarly, for the case of "remove one bit shape":
when d is 1, there are
Figure BDA00027573191300000713
Figure BDA00027573191300000714
The determinant and inverse of the observation matrix are calculated as:
Figure BDA00027573191300000715
Figure BDA0002757319130000081
from the recursion relationship of equations (14) and (15), for any d, the removed bit pattern reduces the error transfer matrix by d rows, and the determinant of the corresponding observation matrix is calculated as:
Figure BDA0002757319130000082
by using the above calculation method of "adding a bit pattern" and "removing a bit pattern", the finding of the optimized nominal bit pattern in { S } can be realized, as shown in FIG. 2, with the following specific steps
S401, randomly selecting N initial calibration bitmaps from the set { S } of bitmaps to be tested to form an initial calibration bitmap set { C }0}；
S402, calculating { C0N initially calibrated error transfer matrices in the
Figure BDA0002757319130000083
The N initial calibration patterns are positioned to form a geometric parameter error transfer matrix
Figure BDA0002757319130000084
Obtaining a parameter identification matrix by arranging according to rows and blocks
Figure BDA0002757319130000085
And calculating an observation matrix
Figure BDA0002757319130000086
Figure BDA0002757319130000087
Inverse matrix of
Figure BDA0002757319130000088
And
Figure BDA0002757319130000089
value of determinant
Figure BDA00027573191300000810
S403, from { C0Selecting a bit pattern, and removing the bit pattern to obtain an observation matrix
Figure BDA00027573191300000811
Value of determinant
Figure BDA00027573191300000812
At the maximum, the number of the first,
Figure BDA00027573191300000813
calculating by using a method of removing one bit shape;
s404, selecting a new bit pattern from the rest bit patterns in the { S }, so that the { C }0The remaining N-1 bits are added to the bit pattern to obtain a new set of N scaled bit patterns { C }1}. Make the observation matrix
Figure BDA00027573191300000814
Value of determinant
Figure BDA00027573191300000815
At the maximum, the number of the first,
Figure BDA00027573191300000816
calculating by using a method of adding one bit pattern;
s405, repeating the steps S403 and S404 until a new set C with N calibration patternskGet the observation matrix
Figure BDA00027573191300000817
Value of determinant
Figure BDA00027573191300000818
Compared with the last calibration configuration set { Ck-1Determinant of observation matrix of
Figure BDA00027573191300000819
No longer increased, { CkAnd f, selecting an optimized calibration configuration set.
And finally, completing error measurement by using the optimal calibration configuration, and calculating by using a parameter identification method to obtain an error parameter.
According to the geometric parameter optimization calibration method for the series servo mechanism, provided by the invention, a group of optimized calibration topograms are actively selected from the set of topograms to be tested, so that the geometric parameter identification precision is higher in the calibration process.
Example 3
A computer-readable storage medium, on which a computer program is stored which, when executed by a processor, implements the method of embodiment 1.
In practice, the computer-readable storage medium may take any combination of one or more computer-readable media. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the present embodiment, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated data signal may take many forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.
Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.
Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C + + or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
Example 4
As shown in fig. 3, another embodiment of the present invention provides a schematic structural diagram of a computer device. The computer device 12 shown in FIG. 3 is only an example and should not impose any limitation on the scope of use or functionality of embodiments of the present invention.
As shown in FIG. 3, computer device 12 is in the form of a general purpose computing device. The components of computer device 12 may include, but are not limited to: one or more processors or processing units 16, a system memory 28, and a bus 18 that couples various system components including the system memory 28 and the processing unit 16.
Bus 18 represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. By way of example, such architectures include, but are not limited to, Industry Standard Architecture (ISA) bus, micro-channel architecture (MAC) bus, enhanced ISA bus, Video Electronics Standards Association (VESA) local bus, and Peripheral Component Interconnect (PCI) bus.
Computer device 12 typically includes a variety of computer system readable media. Such media may be any available media that is accessible by computer device 12 and includes both volatile and nonvolatile media, removable and non-removable media.
The system memory 28 may include computer system readable media in the form of volatile memory, such as Random Access Memory (RAM)30 and/or cache memory 32. Computer device 12 may further include other removable/non-removable, volatile/nonvolatile computer system storage media. By way of example only, storage system 34 may be used to read from and write to non-removable, nonvolatile magnetic media (not shown in FIG. 3, and commonly referred to as a "hard drive"). Although not shown in FIG. 3, a magnetic disk drive for reading from and writing to a removable, nonvolatile magnetic disk (e.g., a "floppy disk") and an optical disk drive for reading from or writing to a removable, nonvolatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to bus 18 by one or more data media interfaces. Memory 28 may include at least one program product having a set (e.g., at least one) of program modules that are configured to carry out the functions of embodiments of the invention.
A program/utility 40 having a set (at least one) of program modules 42 may be stored, for example, in memory 28, such program modules 42 including, but not limited to, an operating system, one or more application programs, other program modules, and program data, each of which examples or some combination thereof may comprise an implementation of a network environment. Program modules 42 generally carry out the functions and/or methodologies of the described embodiments of the invention.
Computer device 12 may also communicate with one or more external devices 14 (e.g., keyboard, pointing device, display 24, etc.), with one or more devices that enable a user to interact with computer device 12, and/or with any devices (e.g., network card, modem, etc.) that enable computer device 12 to communicate with one or more other computing devices. Such communication may be through an input/output (I/O) interface 22. Also, computer device 12 may communicate with one or more networks (e.g., a Local Area Network (LAN), a Wide Area Network (WAN), and/or a public network such as the Internet) via network adapter 20. As shown in FIG. 3, the network adapter 20 communicates with the other modules of the computer device 12 via the bus 18. It should be understood that although not shown in FIG. 3, other hardware and/or software modules may be used in conjunction with computer device 12, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, among others.
The processor unit 16 executes various functional applications and data processing by executing programs stored in the system memory 28, for example, to implement the method provided in embodiment 1 of the present invention.
According to the geometric parameter optimization calibration method for the series servo mechanism, provided by the invention, a group of optimized calibration topograms are actively selected from the set of topograms to be tested, so that the geometric parameter identification precision is higher in the calibration process.
It should be understood that the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention, and it will be obvious to those skilled in the art that other variations or modifications may be made on the basis of the above description, and all embodiments may not be exhaustive, and all obvious variations or modifications may be included within the scope of the present invention.

Claims (10)

1. A geometric parameter optimization calibration method for a series servo mechanism is characterized by comprising the following steps:
s10, establishing a nominal kinematic model of the series servo mechanism according to the nominal value of the geometric parameter of the series servo mechanism;
s20, establishing a geometric parameter error identification model of the serial mechanism according to the selected error measurement method and the nominal kinematic model, and determining error parameters to be identified;
s30, determining sampling points of all the shafts in the motion range of all the rotating shafts of the serial mechanism, and further determining a set of position shapes to be measured;
s40, selecting an optimized calibration bitmap from the set of bitmaps to be detected by using an observation criterion and a bitmap optimization algorithm;
and S50, completing error measurement by using the optimal calibration configuration, and calculating by using a parameter identification method to obtain error parameters.
2. The method of claim 1, wherein the nominal kinematic model established for the tandem mechanism in S10 has the form:
Figure FDA0002757319120000011
wherein, TnIs the nominal pose of the tail end of the serial mechanism,
Figure FDA0002757319120000012
is a column vector formed by nominal values of M geometric parameters to be identified on a serial mechanism,
Figure FDA0002757319120000013
is the angle control quantity of the rotating shaft with s degrees of freedom of the serial mechanism,
Figure FDA0002757319120000014
is a non-linear functional for describing the kinematics of the tandem mechanism.
3. A method according to claim 2, characterized in that the tandem mechanism end pose T is re-represented by a measurable pose vector p, and the established tandem mechanism geometric parameter error identification model has the form:
Figure FDA0002757319120000015
wherein dp represents the differential of the end pose of the serial mechanism, and the calibration model represents dp as the linear combination form of the geometric parameter deviation, so that for a certain pose i, the method includes
Figure FDA0002757319120000016
Wherein, Δ piRepresenting the pose error of the tail end of the serial mechanism;
Figure FDA0002757319120000017
is a geometric parameter error transfer matrix of the series mechanism under the current configuration; Δ φ ═ Δ φ1,Δφ2,…,ΔφM]TIs a column vector formed by errors of various geometric parameters of the series mechanism.
4. The method according to claim 3, wherein the S30 includes
Within the angle range of the rotating shaft of each freedom degree of the series mechanism, k sampling points are selected according to an evenly distributed method, so that the s freedom degrees can generate k at mostsThe bit patterns to be measured form a bit pattern set { S }.
5. The method according to claim 4, wherein the S40 includes
S401, randomly selecting N initial calibration bitmaps from the set { S } of bitmaps to be tested to form an initial calibration bitmap set { C }0}；
S402, calculating { C0N initially calibrated error transfer matrices in the
Figure FDA0002757319120000021
The N initial calibration patterns are positioned to form a geometric parameter error transfer matrix
Figure FDA0002757319120000022
Obtaining a parameter identification matrix by arranging according to rows and blocks
Figure FDA0002757319120000023
And calculating an observation matrix
Figure FDA0002757319120000024
Figure FDA0002757319120000025
Inverse matrix of
Figure FDA0002757319120000026
And
Figure FDA0002757319120000027
value of determinant
Figure FDA0002757319120000028
S403, from { C0Selecting a bit pattern, and removing the bit pattern to obtain an observation matrix
Figure FDA0002757319120000029
Value of determinant
Figure FDA00027573191200000210
Maximum;
s404, selecting a new bit pattern from the rest bit patterns in the { S }, so that the { C }0The remaining N-1 bits are added to the bit pattern to obtain a new set of N scaled bit patterns { C }1}. Make the observation matrix
Figure FDA00027573191200000211
Value of determinant
Figure FDA00027573191200000212
Maximum;
s405, repeating the steps S403 and S404 until a new set C with N calibration patternskGet the observation matrix
Figure FDA00027573191200000213
Value of determinant
Figure FDA00027573191200000214
Compared with the last calibration configuration set { Ck-1Determinant of observation matrix of
Figure FDA00027573191200000215
No longer increased, { CkAnd f, selecting an optimized calibration configuration set.
6. A method for optimized calibration of geometrical parameters of a tandem servo according to claim 5, wherein said observation criteria are chosen as:
Figure FDA00027573191200000216
wherein, O1Representing observation criteria, N being the number of measurement bitmaps contained in the set of bitmaps { C } used for calibration, L being a matrix
Figure FDA00027573191200000217
The value of L is the same as the number M of geometric parameters to be identified,
Figure FDA00027573191200000218
is a matrix M{C,N}A non-zero eigenvalue of.
7. Method for the optimized calibration of geometrical parameters of a tandem servo according to claim 6, wherein said observation criterion O1Is equivalent to the matrix M{C,N}Determinant value of | M{C,N}The size of |.
8. A geometric parameter optimization calibration system for a series servo mechanism is characterized by comprising:
the motion model establishing unit is used for establishing a nominal kinematic model of the series servo mechanism according to the nominal value of the geometric parameter of the series servo mechanism;
the geometric parameter error identification model establishing and to-be-identified error parameter determining unit is used for establishing a geometric parameter error identification model of the serial mechanism according to the selected error measuring method and the nominal kinematic model and determining to-be-identified error parameters;
the device comprises a to-be-detected configuration set determining unit, a to-be-detected configuration set determining unit and a configuration setting unit, wherein the to-be-detected configuration set determining unit is used for determining sampling points of all shafts in the motion range of all rotating shafts of the serial mechanism so as to determine a to-be-detected configuration set;
the optimized calibration configuration selecting unit is used for selecting an optimized calibration configuration from the configuration set to be tested;
and the error measurement and parameter identification unit is used for completing error measurement and parameter identification by utilizing the optimized calibration configuration.
9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the method according to any one of claims 1-6.
10. A computing device comprising a processor, wherein the processor implements the method of any one of claims 1-6 when executing a program.
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