CN107369167A - A kind of robot self-calibrating method based on biplane constraint error model - Google Patents

A kind of robot self-calibrating method based on biplane constraint error model Download PDF

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CN107369167A
CN107369167A CN201710595019.9A CN201710595019A CN107369167A CN 107369167 A CN107369167 A CN 107369167A CN 201710595019 A CN201710595019 A CN 201710595019A CN 107369167 A CN107369167 A CN 107369167A
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mrow
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王晨学
平雪良
徐超
蒋毅
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Jiangnan University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/20—Analysis of motion
    • G06T7/246—Analysis of motion using feature-based methods, e.g. the tracking of corners or segments
    • G06T7/251—Analysis of motion using feature-based methods, e.g. the tracking of corners or segments involving models
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators

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Abstract

The present invention relates to a kind of robot self-calibrating method based on biplane constraint error model, for obtaining the real link parameters of robot.Initially set up robot kinematics' model that D H methods are combined with MD H methods；Next establishes robot end's site error model；Then robot biplane constraint error model is established, the model is related to the obligatory point on two faces (being parallel to each other or vertical), the single plane fitted according to theoretical position point, while self level is met, also need to ensure the position relationship of pairwise correlation interplanar, reduce the deviation between the plane and the plane that fits of theoretical position point of physical constraint point composition.By two are parallel to each other or vertical constraint plane carry out contact type measurement, the data for most measuring to obtain at last substitute into biplane constraint error model, the real geometry link parameters of robot are picked out, duplicate measurements constraint plane and are recognized after amendment, until reaching required precision.The inventive method has the characteristics of cost is low, precision is higher.

Description

Robot self-calibration method based on biplane constraint error model
Technical Field
The invention relates to a robot self-calibration method, in particular to a robot self-calibration method based on a biplane constraint error model.
Background
1. The positioning accuracy of the robot is an important index for measuring the working performance of the robot, and at present, due to factors such as manufacturing, installation and the like, most robots produced by domestic and foreign manufacturers have low absolute positioning accuracy and cannot meet the requirements of high-precision machining and off-line programming, so that the analysis of various factors causing the positioning error of the robot is carried out, and the improvement of the absolute positioning accuracy of the robot to the greatest extent becomes the core content in the technical research of the robot.
2. In order to reduce the cost and other factors, a plurality of researchers provide a robot kinematic error model based on plane constraint, and the positioning accuracy of the robot is improved to a certain extent. However, the accuracy of the calibration method based on plane constraint does not only depend on the flatness of the constraint plane, and research shows that a plane formed by actual constraint points and a plane fitted by theoretical position points have certain deviation, and the deviation can affect the identification of kinematic parameters, so that the calibration accuracy of the robot can be further improved.
3. Aiming at the technical situation, the invention provides a robot self-calibration method based on a biplane constraint error model.
Disclosure of Invention
Aiming at the defects existing in the prior art: the invention provides a robot self-calibration method based on a biplane constraint error model, which needs to perform contact measurement on two parallel or vertical constraint planes, wherein the error model is related to the constraint points on the two planes, so that the single plane fit by the theoretical position point needs to meet the vertical or parallel relation with the related plane while ensuring the self-flatness, thereby reducing the deviation between the plane formed by the actual constraint points and the plane fit by the theoretical position point and further improving the calibration precision.
The technical scheme of the invention comprises the following steps:
(1) establishing robot kinematics model
Establishing a robot kinematic model combining a D-H method and an MD-H method, and describing the transformation process from a coordinate system i-1 to a coordinate system i as Ai，Ai＝f(αi-1,ai-1,di,θiβ), the matrix of poses of the robot end coordinate system n relative to the base coordinate system0TnComprises the following steps:
0Tn＝A0·A1·...·An
(2) establishing robot tail end position error model
According to the idea of differential transformationiCarrying out full differentiation to obtain a differential perturbation homogeneous matrix dA between adjacent coordinate systems caused by errors of geometrical parameters of the connecting rodi：
AiIs the differential transformation of a joint coordinate system i relative to a coordinate system i-1, the actual alignment between two adjacent connecting rods of the robotSub-coordinate transformationNamely Ai+AiAiThe actual homogeneous transformation matrix T of the robot end coordinate system with respect to the base coordinate systemRComprises the following steps:
and expanding the above formula, omitting a high-order perturbation term, and simplifying to obtain the following formula:
wherein Δ P ═ dPxdPydPz]TIs a robot position error matrix, J is a differential transformation Jacobian matrix of 3 × (4n +1) connecting rod parameters, and delta X is [ delta α delta a delta theta delta d delta β]TIs a (4n +1) × 1 connecting rod parameter error matrix;
(3) establishing robot kinematic error model based on biplane constraint
Is provided withThe nominal position value of the ith contact point on the constraint plane I can be directly calculated through positive kinematics of the robot, JpiThe Jacobian matrix at the position can be obtained by calculating the joint angle value, and the actual position Pi R＝Pi N+JpiΔ X, the deviation vector between two adjacent contact points:
wherein,ΔJpi＝Jpi-Jpi-1；
in the same way as above, the first and second,then a nominal normal vector perpendicular to plane i can be constructed from the two adjacent deviation vectors:
the constraint plane II is perpendicular (parallel) to the constraint plane I,for the nominal position value of the ith contact point, then a nominal normal vector perpendicular to plane ii can be constructed from two adjacent offset vectors:
if plane i is perpendicular to plane ii then:
if plane i is parallel to plane ii then:
(4) the drive robot respectively measures the related constraint planes
Drive robot carries out contact measurement respectively to restraint plane I, II, when measuring head output contact signal, records current each joint angle value immediately to measure next restraint point, gather behind the point of certain quantity, then have:
HΔX+S＝0
wherein,then 3N equations may be generated;
(5) robot link parameter identification
Through the improved least square method, the kinematic parameter errors of the robot are identified as follows:
ΔX＝-(HTH+μI)-1HTS
(6) calibration verification
And (4) substituting the robot kinematic parameter compensation value obtained by identification in the step (5) into robot controller software, re-teaching a plurality of points, comparing whether the theoretical tail end position of the robot is constrained on a plane, and if not, continuing the steps (4), (5) and (6) until the accuracy requirement required by the system is met.
The invention has the beneficial effects that: the robot self-calibration method based on the biplane constraint error model further improves the calibration precision. The robot biplane constraint error model is established by performing contact measurement on two parallel or vertical constraint planes, and is related to constraint points on two surfaces, so that a single plane is fitted according to a theoretical position point, the flatness of the single plane is ensured, and the vertical or parallel relation with the related plane is also required to be met, so that the deviation between the plane formed by the actual constraint points and the plane fitted by the theoretical position point is reduced, and the calibration precision is improved.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention as compared with other methods.
Drawings
The following further describes embodiments of the present invention with reference to the drawings.
FIG. 1 is a calibration field schematic;
FIG. 2 is a schematic view of a bi-planar constraint point;
FIG. 3 is a flow chart of a robot self-calibration method based on a biplane constraint error model.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, and it should be understood that the preferred embodiments described herein are merely for purposes of illustration and explanation and are not intended to limit the present invention.
Referring to the attached drawings 1-3, the robot self-calibration method based on the biplane constraint error model comprises the following steps:
(1) establishing robot kinematics model
Establishing a robot kinematic model combining a D-H method and an MD-H method, and describing the transformation process from a coordinate system i-1 to a coordinate system i as Ai，Ai＝f(αi-1,ai-1,di,θi,βi) Then the pose matrix of the robot end coordinate system n relative to the base coordinate system0TnComprises the following steps:
0Tn＝A0·A1·...·An
(2) establishing robot tail end position error model
According to the idea of differential transformationiCarrying out full differentiation to obtain a differential perturbation homogeneous matrix dA between adjacent coordinate systems caused by errors of geometrical parameters of the connecting rodi：
AiIs the differential transformation of a joint coordinate system i relative to a coordinate system i-1, the actual homogeneous coordinate transformation between two adjacent connecting rods of the robotNamely Ai+AiAiThe actual homogeneous transformation matrix T of the robot end coordinate system with respect to the base coordinate systemRComprises the following steps:
and expanding the above formula, omitting a high-order perturbation term, and simplifying to obtain the following formula:
wherein Δ P ═ dPxdPydPz]TIs a robot position error matrix, J is a differential transformation Jacobian matrix of 3 × (4n +1) connecting rod parameters, and delta X is [ delta α delta a delta theta delta d delta β]TIs a (4n +1) × 1 connecting rod parameter error matrix;
(3) establishing robot kinematic error model based on biplane constraint
Is provided withThe nominal position value of the ith contact point on the constraint plane I can be directly calculated through positive kinematics of the robot, JpiThe Jacobian matrix at the position can be obtained by calculating the joint angle value, and the actual position Pi R＝Pi N+JpiΔ X, then are adjacentDeviation vector between two contact points:
wherein,ΔJpi＝Jpi-Jpi-1；
in the same way as above, the first and second,then a nominal normal vector perpendicular to plane i can be constructed from the two adjacent deviation vectors:
the constraint plane II is perpendicular (parallel) to the constraint plane I,for the nominal position value of the ith contact point, then a nominal normal vector perpendicular to plane ii can be constructed from two adjacent offset vectors:
if plane i is perpendicular to plane ii then:
if plane i is parallel to plane ii then:
(4) the drive robot respectively measures the related constraint planes
Drive robot carries out contact measurement respectively to restraint plane I, II, when measuring head output contact signal, records current each joint angle value immediately to measure next restraint point, gather behind the point of certain quantity, then have:
HΔX+S＝0
wherein,then 3N equations may be generated;
(5) robot link parameter identification
Through the improved least square method, the kinematic parameter errors of the robot are identified as follows:
ΔX＝-(HTH+μI)-1HTS
therefore, all link parameter errors of the robot can be identified.
(6) Calibration verification
And (4) substituting the robot kinematic parameter compensation value obtained by identification in the step (5) into robot controller software, re-teaching a plurality of points, comparing whether the theoretical tail end position of the robot is constrained on a plane, and if not, continuing the steps (4), (5) and (6) until the accuracy requirement required by the system is met.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.

Claims (3)

1. A robot self-calibration method based on a biplane constraint error model is characterized by comprising the following steps: the method comprises the following steps:
(1) establishing robot kinematics model
Establishing a robot kinematic model combining a D-H method and an MD-H method, and describing the transformation process from a coordinate system i-1 to a coordinate system i as Ai，Ai＝f(αi-1,ai-1,di,θiβ), the matrix of poses of the robot end coordinate system n relative to the base coordinate system0TnComprises the following steps:
0Tn＝A0·A1·...·An
(2) establishing robot tail end position error model
According to the idea of differential transformationiCarrying out full differentiation to obtain a differential perturbation homogeneous matrix dA between adjacent coordinate systems caused by errors of geometrical parameters of the connecting rodi：
<mrow> <msub> <mi>dA</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>A</mi> <mi>i</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mi>&amp;Delta;&amp;alpha;</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>A</mi> <mi>i</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mi>&amp;Delta;a</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>A</mi> <mi>i</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </mfrac> <msub> <mi>&amp;Delta;&amp;theta;</mi> <mi>i</mi> </msub> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>A</mi> <mi>i</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> </mrow> </mfrac> <msub> <mi>&amp;Delta;d</mi> <mi>i</mi> </msub> <mo>+</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>A</mi> <mi>i</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>&amp;beta;</mi> </mrow> </mfrac> <mi>&amp;Delta;</mi> <mi>&amp;beta;</mi> <mo>=</mo> <msub> <mi>A</mi> <mi>i</mi> </msub> <msub> <mi>&amp;delta;A</mi> <mi>i</mi> </msub> </mrow>
AiIs the differential transformation of a joint coordinate system i relative to a coordinate system i-1, the actual homogeneous coordinate transformation between two adjacent connecting rods of the robotNamely Ai+AiAiThe actual homogeneous transformation matrix T of the robot end coordinate system with respect to the base coordinate systemRComprises the following steps:
<mrow> <mi>T</mi> <mo>+</mo> <mi>d</mi> <mi>T</mi> <mo>=</mo> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>dA</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>A</mi> <mi>i</mi> </msub> <msub> <mi>&amp;delta;A</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow>
and expanding the above formula, omitting a high-order perturbation term, and simplifying to obtain the following formula:
<mrow> <mi>&amp;Delta;</mi> <mi>P</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>dP</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>dP</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>dP</mi> <mi>z</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>J</mi> <msub> <mi>&amp;alpha;</mi> <mi>x</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>a</mi> <mi>x</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>&amp;theta;</mi> <mi>x</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>d</mi> <mi>x</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>&amp;beta;</mi> <mi>x</mi> </msub> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>J</mi> <msub> <mi>&amp;alpha;</mi> <mi>y</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>a</mi> <mi>y</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>&amp;theta;</mi> <mi>y</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>d</mi> <mi>y</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>&amp;beta;</mi> <mi>y</mi> </msub> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>J</mi> <msub> <mi>&amp;alpha;</mi> <mi>z</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>a</mi> <mi>z</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>&amp;theta;</mi> <mi>z</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>d</mi> <mi>z</mi> </msub> </msub> </mtd> <mtd> <msub> <mi>J</mi> <msub> <mi>&amp;beta;</mi> <mi>z</mi> </msub> </msub> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>&amp;Delta;</mi> <mi>&amp;alpha;</mi> </mtd> </mtr> <mtr> <mtd> <mi>&amp;Delta;</mi> <mi>a</mi> </mtd> </mtr> <mtr> <mtd> <mi>&amp;Delta;</mi> <mi>&amp;theta;</mi> </mtd> </mtr> <mtr> <mtd> <mi>&amp;Delta;</mi> <mi>d</mi> </mtd> </mtr> <mtr> <mtd> <mi>&amp;Delta;</mi> <mi>&amp;beta;</mi> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>J</mi> <mi>&amp;Delta;</mi> <mi>X</mi> </mrow>
wherein Δ P ═ dPxdPydPz]TIs a robot position error matrix, J is a differential transformation Jacobian matrix of 3 × (4n +1) connecting rod parameters, and delta X is [ delta α delta a delta theta delta d delta β]TIs a (4n +1) × 1 connecting rod parameter error matrix;
(3) establishing robot kinematic error model based on biplane constraint
Is provided withThe nominal position value of the ith contact point on the constraint plane I can be directly calculated through positive kinematics of the robot, JpiThe Jacobian matrix at the position can be obtained by calculating the joint angle value, and the actual position Pi R＝Pi N+JpiΔ X, the deviation vector between two adjacent contact points:
<mrow> <msubsup> <mi>&amp;Delta;P</mi> <mi>i</mi> <mi>R</mi> </msubsup> <mo>=</mo> <msubsup> <mi>P</mi> <mi>i</mi> <mi>R</mi> </msubsup> <mo>-</mo> <msubsup> <mi>P</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>R</mi> </msubsup> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;x</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> <mi>N</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;y</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> <mi>N</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;z</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> <mi>N</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>+</mo> <msub> <mi>&amp;Delta;J</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> </msub> <mi>&amp;Delta;</mi> <mi>X</mi> </mrow>
wherein,ΔJpi＝Jpi-Jpi-1；
in the same way as above, the first and second,then a nominal normal vector perpendicular to plane i can be constructed from the two adjacent deviation vectors:
<mrow> <msub> <mi>&amp;Delta;M</mi> <mi>i</mi> </msub> <mo>=</mo> <msubsup> <mi>&amp;Delta;P</mi> <mi>i</mi> <mi>R</mi> </msubsup> <mo>&amp;times;</mo> <msubsup> <mi>&amp;Delta;P</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>R</mi> </msubsup> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>n</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> <mi>x</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>n</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> <mi>y</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>n</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> <mi>z</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>+</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>J</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> <mi>x</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>J</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> <mi>y</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>J</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> <mi>z</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mi>&amp;Delta;</mi> <mi>X</mi> </mrow>
the constraint plane II is perpendicular (parallel) to the constraint plane I,for the nominal position value of the ith contact point, then a nominal normal vector perpendicular to plane ii can be constructed from two adjacent offset vectors:
<mrow> <msub> <mi>&amp;Delta;N</mi> <mi>i</mi> </msub> <mo>=</mo> <msubsup> <mi>&amp;Delta;Q</mi> <mi>i</mi> <mi>R</mi> </msubsup> <mo>&amp;times;</mo> <msubsup> <mi>&amp;Delta;Q</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>R</mi> </msubsup> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>n</mi> <mrow> <mi>q</mi> <mi>i</mi> </mrow> <mi>x</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>n</mi> <mrow> <mi>q</mi> <mi>i</mi> </mrow> <mi>y</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>n</mi> <mrow> <mi>q</mi> <mi>i</mi> </mrow> <mi>z</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>+</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>J</mi> <mrow> <mi>q</mi> <mi>i</mi> </mrow> <mi>x</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>J</mi> <mrow> <mi>q</mi> <mi>i</mi> </mrow> <mi>y</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>J</mi> <mrow> <mi>q</mi> <mi>i</mi> </mrow> <mi>z</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mi>&amp;Delta;</mi> <mi>X</mi> </mrow>
if plane i is perpendicular to plane ii then:
<mrow> <msub> <mi>&amp;Delta;M</mi> <mi>i</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>&amp;Delta;N</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>s</mi> <mi>i</mi> <mi>x</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>s</mi> <mi>i</mi> <mi>y</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>s</mi> <mi>i</mi> <mi>z</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>+</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>h</mi> <mi>i</mi> <mi>x</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>h</mi> <mi>i</mi> <mi>y</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>h</mi> <mi>i</mi> <mi>z</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mi>&amp;Delta;</mi> <mi>X</mi> <mo>=</mo> <mn>0</mn> </mrow>
if plane i is parallel to plane ii then:
<mrow> <msub> <mi>&amp;Delta;M</mi> <mi>i</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>&amp;Delta;N</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>s</mi> <mi>i</mi> <mi>x</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>s</mi> <mi>i</mi> <mi>y</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>s</mi> <mi>i</mi> <mi>z</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>+</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>h</mi> <mi>i</mi> <mi>x</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>h</mi> <mi>i</mi> <mi>y</mi> </msubsup> </mtd> <mtd> <msubsup> <mi>h</mi> <mi>i</mi> <mi>z</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mi>&amp;Delta;</mi> <mi>X</mi> <mo>=</mo> <mn>0</mn> </mrow>
(4) the drive robot respectively measures the related constraint planes
Drive robot carries out contact measurement respectively to restraint plane I, II, when measuring head output contact signal, records current each joint angle value immediately to measure next restraint point, gather behind the point of certain quantity, then have:
HΔX+S＝0
wherein,then 3N equations may be generated;
(5) robot link parameter identification
Through the improved least square method, the kinematic parameter errors of the robot are identified as follows:
ΔX＝-(HTH+μI)-1HTS
(6) calibration verification
And (4) substituting the robot kinematic parameter compensation value obtained by identification in the step (5) into robot controller software, re-teaching a plurality of points, comparing whether the theoretical tail end position of the robot is constrained on a plane, and if not, continuing the steps (4), (5) and (6) until the accuracy requirement required by the system is met.
2. The robot self-calibration method based on the biplane constraint error model according to claim 1, characterized in that: the error model is related to the constraint points on both planes simultaneously.
3. The robot self-calibration method based on the biplane constraint error model according to claims 1 and 2, characterized in that: the calibration precision is ensured by restricting the planeness, verticality and parallelism of the plane.
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