CN110749257B - Measurement datum point non-coplanar error compensation method of pull-wire type measurement system - Google Patents

Measurement datum point non-coplanar error compensation method of pull-wire type measurement system Download PDF

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CN110749257B
CN110749257B CN201910715658.3A CN201910715658A CN110749257B CN 110749257 B CN110749257 B CN 110749257B CN 201910715658 A CN201910715658 A CN 201910715658A CN 110749257 B CN110749257 B CN 110749257B
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points
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CN110749257A (en
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鲍晟
王聪聪
马书根
袁建军
贾文川
高辕
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University of Shanghai for Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
    • G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
    • G01B21/045—Correction of measurements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B5/00—Measuring arrangements characterised by the use of mechanical techniques

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Abstract

The invention discloses a method for compensating the non-coplanar error of a measurement datum point of a guyed measurement system, which comprises the following steps: selecting three measuring reference points to establish a reference plane and a reference coordinate system, collecting the line length between every two measuring reference points and the line length from the measuring reference points to the measured point of the end effector, and estimating the spatial coordinate of the measured point of the end effector; calculating possible solutions of the spatial positions of the other measuring reference points under the reference coordinate system according to the geometric relation; calculating and pre-estimating the virtual line length from the measured point of the end effector to the rest of the measurement datum points, comparing the actual measured line length with the virtual line length, and determining the spatial positions of the rest of the measurement datum points; and correcting the rest of the measurement datum points into the reference plane to obtain a substitute measurement datum point, compensating the original line length according to the geometric relation, and optimizing the spatial position of the measured point of the end effector based on the position of all the measurement datum points and the information of the line length in the reference plane. The method can omit the step of manually adjusting the coplanarity of all the measurement datum points, and effectively improve the working efficiency.

Description

Measurement datum point non-coplanar error compensation method of pull-wire type measurement system
Technical Field
The invention relates to the field of measurement error compensation, in particular to a method for compensating non-coplanar errors of measurement reference points of a pull-wire type measurement system.
Background
With the increasing trend of modern robot automation production, the requirement on the positioning precision of the robot is higher and higher. Measuring mechanisms for positioning accuracy of industrial robots are generally classified into two types, i.e., mechanical and optical. Compared with an optical measuring mechanism, the mechanical measuring mechanism based on the stay wire encoder (stay wire measuring system for short) is simple in structure, convenient to operate and low in environmental requirement, and is more suitable for field application requirements of industrial robots and the like.
The trilateration principle, originally used in GPS positioning systems, uses the distances from three GPS satellites to the point to be measured to determine the precise location of the point. The guyed measuring system usually works on the principle of trilateration, i.e. the spatial position of a fixed point on the end effector is determined from the geometric relationship using three measuring reference points and their respective wire lengths to the measuring adapters. In order to apply the trilateration principle, when the number of the measurement reference points of the pull-wire measurement system is more than three, all the measurement reference points are generally required to be in the same reference plane, and the reference points are generally required to be manually adjusted to be coplanar before measurement starts, so that the use difficulty of the measurement system is increased, and the efficiency is reduced.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method for compensating the non-coplanar errors of the measurement reference points of the pull-wire type measurement system.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for compensating the non-coplanar error of the measurement datum points of a pull-wire type measurement system comprises the following steps:
s1: selecting three measuring reference points to establish a reference plane and a reference coordinate system, collecting the line length between every two measuring reference points and the line length from the measuring reference points to the measured point of the end effector, and estimating the space coordinate of the measured point of the end effector;
s2: calculating possible solutions of the space positions of the other measuring reference points under the reference coordinate system according to the coordinates of the three measuring reference points in the S1 and the line lengths from the three measuring reference points to the other measuring reference points;
s3: calculating and pre-estimating the virtual line length from the measured point of the end effector to the rest of the measurement datum points, comparing the actual measured line length with the virtual line length, and determining the spatial positions of the rest of the measurement datum points;
s4: and correcting the rest of the measurement reference points into the reference plane to obtain the substitute measurement reference points, compensating the original line length according to the triangle congruent law and the space vector method, and optimally solving the space position of the measured point of the end effector based on the position and the length information of all the measurement reference points in the reference plane.
Compared with the prior art, the invention has the following advantages:
the method can omit the step of manually adjusting the coplanarity of all the measurement datum points, and effectively improve the working efficiency.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of a pull-wire type measurement system according to the present invention.
FIG. 3 is a diagram of an error compensation model according to the present invention.
Fig. 4 is a geometric relationship diagram of the line length and the linear distance of the present invention.
Fig. 5 is a geometric relationship diagram of the distance between the straight line and the line length according to the invention.
Fig. 6 is a schematic diagram of error compensation in accordance with the present invention.
Detailed Description
The following further describes a specific embodiment of the present invention with reference to the drawings.
As shown in figure 1, the method for compensating the error of the non-coplanarity of the measuring reference points of the pull-wire type measuring system adopts the pull-wire type measuring system with four measuring reference points, as shown in figure 2, and the system comprises an industrial robot, a measuring adapter, a pull-wire encoder, a data acquisition card and an industrial personal computer. The measuring adapter is arranged at the tail end of the industrial robot, and the stay wire encoder is connected with the measuring adapter through a test cable; the extension lines of the four test cables intersect at one point in the space; the stay wire encoder is connected with the data acquisition card through a wire, and then the data acquisition card is arranged in the industrial personal computer case; the method specifically comprises the following steps:
s1: selecting three measuring reference points to establish a reference plane and a reference coordinate system, collecting the line length between every two measuring reference points and the line length from the measuring reference points to the measured point of the end effector, and estimating the space coordinate of the measured point of the end effector.
As shown in FIG. 3, three non-collinear measuring reference points are selected from the measuring reference points, which are marked as points A, B, C, a reference plane and a reference coordinate system are established, and the line length l between the measuring reference points is recordedAB,lAC,lBCBased on the geometrical relationship, as shown in FIG. 4, the distance L between the measurement reference points is obtained by using the line length between the measurement reference pointsAB,LAC,LBCThe method comprises the following specific steps:
line length lABFrom arc segment
Figure GDA0003095958080000021
And straight line segment LBKIs composed of, i.e.
Figure GDA0003095958080000022
From the geometry of fig. 5:
Figure GDA0003095958080000023
r is the pulley radius; in the case of the delta ABK, the peak value,
Figure GDA0003095958080000024
at Δ OAIn BA, ω -2 pi- β - θ,
Figure GDA0003095958080000025
at Δ OAIn the case of KA, the first step is,
Figure GDA0003095958080000026
in the case of the delta BKA,
Figure GDA0003095958080000027
by substituting the parameters, L can be obtainedAB(ii) a Repeating the above steps to obtain LAC,LBC；
Calculating the coordinate A (x) of the reference pointA,yA,0)、B(xB,yB,0)、C(xC,yC0); line length l of measurement record A, B, C leading to measurement adapterA,lB,lCAnd recording the space coordinate of the measured point of the end effector as P (x, y, z), and estimating the space coordinate of the measured point of the end effector by solving the following equation:
Figure GDA0003095958080000031
in the formula (f)A,fB,fCThe function relationship satisfied by the length of the stay wire and the space coordinate of the measured point of the end effector is shown.
S2: and calculating possible solutions of the spatial positions of the other measuring reference points under the reference coordinate system according to the geometric relation.
The other measuring reference points are recorded as D, E, F … in turn, taking point D as an example, by respectively measuring the length l of the line from the point D to the measuring reference point A, B, CDA,lDB,lDCThen, the distance L is obtained according to the line lengthDA,LDB,LDCSolving the following system of equations:
Figure GDA0003095958080000032
calculating possible solution (x) of space position of D point under reference coordinate systemD,yD,±zD) (ii) a And repeating the steps to sequentially solve the possible spatial position solutions of the other measurement datum points.
S3: and calculating and predicting the virtual line length from the measured point of the end effector to the rest of the measurement datum points, comparing the actual line length with the virtual line length, and determining the spatial positions of the rest of the measurement datum points.
Respectively calculating a virtual line length l 'from the point D to the measured point of the end effector according to two possible position coordinates of the point D'Di,i＝1,2；
Fig. 6 shows a possible solution of the D measurement reference point, which has the following virtual line length:
Figure GDA0003095958080000033
introducing vectors based on the geometric relationships of FIG. 6
Figure GDA0003095958080000034
Reconstructing vector for normal vector of plane formed by P, D and O
Figure GDA0003095958080000035
Can be obtained by the following formula
Figure GDA0003095958080000036
Figure GDA0003095958080000037
Solving the coordinates of the center of a circle of a pulley
Figure GDA0003095958080000038
Establishing a vector
Figure GDA0003095958080000041
Substituting the following formula:
Figure GDA0003095958080000042
finding coordinates
Figure GDA0003095958080000043
At Δ PG' ODIn (1),
Figure GDA0003095958080000044
Figure GDA0003095958080000045
corresponding central angle δ:
Figure GDA0003095958080000046
solving for
Figure GDA0003095958080000047
Calculate the virtual line length
Figure GDA0003095958080000048
Repeating the steps to solve the virtual line l'D2(ii) a Comparing the line length l of the measuring reference point D to the measuring adapterDThe length of the virtual line is taken to be min (| l)D-l'DiI) the position coordinates of the D point which is established, namely the space position of the measuring reference point D can be determined; and repeating the steps to sequentially determine the space position coordinates of the rest measuring reference points E and F ….
S4: and correcting the rest of the measurement datum points into the reference plane to obtain a substitute measurement datum point, compensating the original line length according to the geometric relation, and optimally calculating the spatial position of the measured point of the end effector based on the position of all the measurement datum points and the information of the line length in the reference plane.
As shown in fig. 6, translating the measurement reference point D into the reference plane in the direction parallel to the test cable results in an alternative measurement reference point D' (x)D',yD'0), the extension line of the test cable intersects the reference plane and is marked as N (x)N,yN,0). In the space coordinate system, C, P, D form a plane, so that points D', N are in the plane;
introduction of
Figure GDA0003095958080000049
Is the normal vector of the planar CPD, based on
Figure GDA00030959580800000410
Figure GDA00030959580800000411
Solve out
Figure GDA00030959580800000412
According to arc segment
Figure GDA00030959580800000413
The straight-line distance between D and G points, which can be obtained from the radius r of the pulley and the corresponding central angle, is combined with LPGAnd an
Figure GDA0003095958080000051
Solving the coordinates of the G point; according to
Figure GDA0003095958080000052
And
Figure GDA0003095958080000053
Figure GDA0003095958080000054
determining N (x)N,yN,zN)；
According to arc segment
Figure GDA0003095958080000055
And arc segment
Figure GDA0003095958080000056
Corresponding central angles are the same and
Figure GDA00030959580800000510
the length of G' N can be obtained; obtaining L according to the aboveGG'＝LPN-LPG-LG'NAnd LD'N＝LG'N(ii) a According to
Figure GDA0003095958080000057
And LD'NThe coordinates of the D' point can be solved; l 'thus'DHas a length of a straight line segment LPG'Length of arc
Figure GDA0003095958080000058
L's of'D＝LPG'+LG'D'＝lD+LGG'(ii) a Recording the correction point as D', calculating the compensation value l of the line length according to the geometric relationshipD supplementAnd satisfies the following relationship:
l'D＝lD+ld supplement
Repeating the steps, and sequentially determining the corrected point positions E ', F' … of the other measuring reference points and the compensated line length lE supplement，lF supplement…, respectively; establishing an overdetermined equation set based on the position and line length information of all measurement datum points in the datum plane:
Figure GDA0003095958080000059
and (5) optimizing and solving the space coordinates of the measured point P of the end effector.

Claims (5)

1. A method for compensating the non-coplanar error of the measurement datum points of a pull-wire type measurement system is characterized by comprising the following steps:
s1: selecting three measuring reference points to establish a reference plane and a reference coordinate system, collecting the line length between every two measuring reference points and the line length from the measuring reference points to the measured point of the end effector, and estimating the space coordinate of the measured point of the end effector;
s2: calculating possible solutions of the space positions of the other measuring reference points under the reference coordinate system according to the coordinates of the three measuring reference points in the S1 and the line lengths from the three measuring reference points to the other measuring reference points;
s3: calculating and pre-estimating the virtual line length from the measured point of the end effector to the rest of the measurement datum points, comparing the actual measured line length with the virtual line length, and determining the spatial positions of the rest of the measurement datum points;
s4: and correcting the rest of the measurement reference points into the reference plane to obtain the substitute measurement reference points, compensating the original line length according to the triangle congruent law and the space vector method, and optimally solving the space position of the measured point of the end effector based on the position and the length information of all the measurement reference points in the reference plane.
2. The method for compensating the out-of-plane errors of the measured reference points of the guyed measurement system according to claim 1, wherein the step S1 comprises the following steps: selecting three non-collinear measuring reference points from the measuring reference points, recording the three non-collinear measuring reference points as points A, B, C, establishing a reference plane and a reference coordinate system, and measuring and recording the line length l between the reference pointsAB,lAC,lBCThe distance L between the measurement reference points is obtained by using the line length between the measurement reference points according to the geometric relationAB,LAC,LBCCalculating the reference point coordinate A (x)A,yA,0)、B(xB,yB,0)、C(xC,yC0); line length l of measurement record A, B, C leading to measurement adapterA,lB,lCAnd recording the space coordinate of the measured point of the end effector as P (x, y, z), and estimating the space coordinate of the measured point of the end effector by solving the following equation:
Figure FDA0003072496700000011
in the formula (f)A,fB,fCThe function relationship satisfied by the length of the stay wire and the space coordinate of the measured point of the end effector is shown.
3. The method for compensating the out-of-plane errors of the measured reference points of the guyed measurement system according to claim 1, wherein the step S2 comprises the following steps: the other measuring reference points are recorded as D, E, F … in turn, taking point D as an example, by respectively measuring the length l of the line from the point D to the measuring reference point A, B, CDA,lDB,lDCThen, the distance L is obtained according to the line lengthDA,LDB,LDCSolving the following system of equations:
Figure FDA0003072496700000012
calculating possible solution (x) of space position of D point under reference coordinate systemD,yD,±zD) (ii) a And repeating the steps to sequentially solve the possible spatial position solutions of the other measurement datum points.
4. The method for compensating the out-of-plane errors of the measured reference points of the guyed measurement system according to claim 1, wherein the step S3 comprises the following steps: respectively calculating the virtual line length from the measuring datum point D point to the measured point of the end effector according to two possible position coordinates of the measuring datum point D point, and recording the virtual line length as l'DiI is 1, 2; comparing the line length l of the measuring reference point D to the measuring adapterDThe length of the virtual line is taken to be min (| l)D-l'DiI) the true spatial position coordinates of the D points; repeating the above steps to determine the rest measurement references in sequenceThe spatial location coordinates of the points.
5. The method for compensating the out-of-plane errors of the measured reference points of the guyed measurement system according to claim 1, wherein the step S4 comprises the following steps: correcting the rest measuring reference points to the reference plane to obtain the substitute measuring reference point, compensating the original wire length according to the geometric relationship, taking the measuring reference point D as an example, recording the correction point as D', and calculating the wire length compensation value l according to the geometric relationshipD supplementCompensated line length l'DWith the length l of the line from the measuring reference point D to the measuring adapterDThe following relationship is satisfied:
l'D＝lD+ld supplement
Repeating the steps, and sequentially determining the corrected point positions E ', F' … of the other measuring reference points and the compensated line length lE supplement，lF supplement…, respectively; based on the spatial coordinates of all the measurement reference points A, B, C in the reference plane and the length l of the line to the measurement adapterA、lB、lCAnd the remaining measurement reference points D … and their compensated line lengths l 'to the measurement adapter'D…, formula f, according to the distance between two points in spaceA、fB、fC、fD… an overdetermined system of equations is established:
Figure FDA0003072496700000021
and (5) optimizing and solving the space coordinates of the measured point P of the end effector.
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