CN112643712A - Zero position measurement calibration method for large mechanical arm base - Google Patents

Zero position measurement calibration method for large mechanical arm base Download PDF

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CN112643712A
CN112643712A CN202011042704.7A CN202011042704A CN112643712A CN 112643712 A CN112643712 A CN 112643712A CN 202011042704 A CN202011042704 A CN 202011042704A CN 112643712 A CN112643712 A CN 112643712A
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base
coordinate
plane
observation points
coordinate system
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CN112643712B (en
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范越
王志宏
周晖
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Yangzhou Institute Of Marine Electronic Instruments No723 Institute Of China Shipbuilding Industry Corp
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Yangzhou Institute Of Marine Electronic Instruments No723 Institute Of China Shipbuilding Industry Corp
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    • 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
    • B25J19/0095—Means or methods for testing manipulators
    • 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
    • B25J9/1692—Calibration of manipulator

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Abstract

The invention discloses a zero position measurement calibration method for a large mechanical arm base, which comprises the following steps: marking a plurality of observation points on the rocker arm base, wherein the observation points are positioned on the same circumference; erecting a north seeker and a total station between the rocker arm base and a receiving target; observing the coordinates of a signal receiving target point and any 3 observation points marked on the rocker arm base through a total station, and establishing a coordinate system by taking the signal receiving target point as an origin; obtaining a plane equation of the base by coplanar constraint of the 3 observation points, and obtaining a circle center coordinate of the base and a plane normal vector; determining a plane longitudinal and transverse swing angle according to the normal vector; and establishing a new coordinate system according to the measured pitch angle and roll angle, and determining the position of the rocker arm and the coordinate point of the airplane in the new coordinate system through coordinate transformation. The method has the advantages of simple and convenient actual operation process and high efficiency, eliminates the influence of the inclination angle of the base of the large mechanical arm on the system model after use, and obviously improves the positioning precision of the system.

Description

Zero position measurement calibration method for large mechanical arm base
Technical Field
The invention belongs to a rocker arm type motion simulation supporting technology, and particularly relates to a zero position measurement calibration method for a base of a large mechanical arm.
Background
The rocker arm type motion simulation supporting equipment is characterized in that an antenna and a power amplifier are arranged on a tail end platform, so that the motion tracks of the antenna and the power amplifier can simulate the equivalent motion track of an airplane, and in the motion process of simulating the flight track of the airplane, a horn antenna carried by the rocker arm type motion simulation supporting equipment is required to be always over against a signal receiving target, and the rocker arm type motion simulation supporting equipment is essentially a large mechanical arm. Because the length of the rocker arm type motion simulation supporting equipment arm reaches 10 meters and the weight is about 3 tons, the base is difficult to level by a conventional method, the leveling is not performed, errors are brought to the simulation precision of the control motion track, and the equipment cannot normally work due to the fact that the base is large in inclination angle, so that further measurement and calibration are needed.
Disclosure of Invention
The invention aims to provide a zero position measurement calibration method for a base of a large mechanical arm.
The technical solution for realizing the purpose of the invention is as follows: a zero position measurement calibration method for a large mechanical arm base comprises the following steps:
marking a plurality of observation points on the rocker arm base, wherein the observation points are positioned on the same circumference;
erecting a north seeker and a total station between the rocker arm base and a receiving target;
observing the coordinates of a signal receiving target point and any 3 observation points marked on the rocker arm base through a total station, and establishing a coordinate system by taking the signal receiving target point as an origin;
obtaining a plane equation of the base by coplanar constraint of the 3 observation points, and obtaining a circle center coordinate of the base and a plane normal vector;
determining a plane longitudinal and transverse swing angle according to the normal vector;
and establishing a new coordinate system according to the measured pitch angle and roll angle, and determining the position of the rocker arm and the coordinate point of the airplane in the new coordinate system through coordinate transformation.
Preferably, the number of the observation points is not less than 3.
Preferably, the plane equation of the base obtained by the coplanar constraint of the 3 observation points is specifically:
A1x+B1y+C1z+D1＝0
in the formula:
A1＝y1·z2-y1·z3-z1·y2+z1·y3+y2·z3-y3·z2
B1＝-x1·z2+x1·z3+z1·x2-z1·x3-x2·z3+x3·z2
C1＝x1·y2-x1·y3-y1·x2+y1·x3+x2·y3-x3·y2
D1＝-x1·y2·z3+x1·y3·z2+x2·y1·z3-x3·y1·z2-x2·y3·z1+x3·y2·z1
x1＝x10-xo0,y1＝y10-yo0,z1＝z10-zo0；x2＝x20-xo0,y2＝y20-yo0,z2＝z20- zo0；x3＝x30-xo0,y3＝y30-yo0,z3＝z30-zo0(ii) a Wherein (xo)0,yo0,zo0) To receive the target point coordinates, (xi)0,yi0,zi0) I is the coordinate of 3 observation points, 1,2, 3.
Preferably, the specific process of obtaining the coordinates of the center of the circle of the base and the normal vector of the plane is as follows:
assuming that the radius of the space circle is R, the distance from the 3 observation points to the center of the space circle can be obtained by the following equation:
Figure BDA0002707116600000021
from the above formula, one can obtain:
2(x2-x1)x+2(y2-y1)y+2(z2-z1)z+x1 2+y1 2+z1 2-x2 2-y2 2-z2 2＝0
2(x3-x1)x+2(y3-y1)y+2(z3-z1)z+x1 2+y1 2+z1 2-x3 2-y3 2-z3 2＝0
is recorded as:
A2x+B2y+C2z+D2＝0
A3x+B3y+C3z+D3＝0
the system of linear algebraic equations for obtaining the spatial coordinates about the center of the circle is:
Figure BDA0002707116600000022
the coordinate of the circle center P is obtained by solving:
Figure BDA0002707116600000023
obtaining the base plane normal vector by the base plane equation
Figure BDA0002707116600000024
Preferably, the specific method for determining the plane pitch and roll angle according to the normal vector is as follows:
the normal vector of the base plane is changed into a vector after rotating by a pitch angle alpha and a roll angle beta
Figure BDA0002707116600000031
Expression is as followsThe following:
Figure BDA0002707116600000032
in the formula Rα、RβIn order to be a matrix of rotations,
Figure BDA0002707116600000033
Figure BDA0002707116600000034
the following can be obtained:
Figure RE-GDA0002910286520000035
in the formula:
Figure BDA0002707116600000036
the following can be obtained:
Figure BDA0002707116600000037
Figure BDA0002707116600000038
preferably, P is coordinated as P ' ═ x in the new coordinate system OX ' Y ' Z0' y0' z0']TThe expression is as follows:
Figure RE-GDA0002910286520000039
the coordinate of the airplane in the original coordinate system oxyz is F ═ Fx Fy Fz]TObtaining the coordinate F ' of the aircraft F in the new coordinate system OX ' Y ' Z ═ Fx' Fy' Fz']TThe method specifically comprises the following steps:
Figure RE-GDA0002910286520000041
compared with the prior art, the invention has the following remarkable advantages: the method has the advantages of simple and convenient actual operation process and high efficiency, eliminates the influence of the inclination angle of the base of the large mechanical arm on the system model after use, and obviously improves the positioning precision of the system.
The present invention is described in further detail below with reference to the attached drawings.
Drawings
Fig. 1 is a schematic view of a rocker arm structure.
FIG. 2 is a top plan view of the calibration space.
FIG. 3 is a schematic diagram of the position and attitude of the rocker arm base.
Detailed Description
A zero position measurement calibration method for a base of a large mechanical arm is characterized in that a north finder and a total station integrated measuring instrument is used for carrying out coordinate measurement on a mark point on the base of the mechanical arm, the circle center coordinate of the base and the longitudinal and transverse rolling angles of the base are obtained through space coordinate calculation, and finally a coordinate system is corrected to improve the positioning accuracy of the system.
A plurality of points which are convenient to observe are marked on the periphery of the rocker arm base, and the points are ensured to be on the same circumference. After the installation of the rocker arm base is completed, the coordinates of a signal receiving target point and 3 observation points on the same circumference on the rocker arm base are respectively measured by a measuring instrument integrating a north seeker and a total station, and a coordinate system is established by taking the signal receiving target point as an origin. The coplanar constraint of the 3 observation points can obtain a plane equation of the 3 observation points, namely a plane equation of the base, and the distance from the 3 observation points to the center of the space is equal to obtain the coordinate of the center of the base. And a plane normal vector can be obtained simultaneously according to a plane equation of the base, and the plane longitudinal and transverse swing angles can be obtained through the normal vector. And finally, establishing a new coordinate system according to the measured inclination angle, and calculating the position of the rocker arm and a coordinate point of the airplane in the new coordinate system through coordinate transformation so as to eliminate the influence of the inclination of the base on the system, wherein the method comprises the following specific steps:
step 1: marking a plurality of observation points on the rocker arm base, wherein the observation points are positioned on the same circumference; the number of the observation points is not less than 3;
step 2: erecting a north seeker and a total station between the rocker arm base and a receiving target;
specifically, as shown in fig. 2, a north finder + a total station is erected at any convenient observation position selected between the swing arm base and the reception target point. After the erection is finished, initializing the north finder, wherein the point O is the origin of a coordinate system of an observation space point of the total station, the positive west direction is an X0 axis, the positive south direction is a Y0 axis, and the vertical upward direction is a Z0 axis.
And step 3: observing the coordinates of a signal receiving target point and any 3 observing points marked on the rocker arm base through a total station, and establishing a coordinate system by taking the signal receiving target point as an origin;
and 4, step 4: obtaining a plane equation of the base by coplanar constraint of the 3 observation points, and obtaining a circle center coordinate of the base and a plane normal vector;
in a further embodiment, the plane equation of the base obtained by the coplanar constraint of the 3 observation points is specifically as follows:
A1x+B1y+C1z+D1＝0
in the formula:
A1＝y1·z2-y1·z3-z1·y2+z1·y3+y2·z3-y3·z2
B1＝-x1·z2+x1·z3+z1·x2-z1·x3-x2·z3+x3·z2
C1＝x1·y2-x1·y3-y1·x2+y1·x3+x2·y3-x3·y2
D1＝-x1·y2·z3+x1·y3·z2+x2·y1·z3-x3·y1·z2-x2·y3·z1+x3·y2·z1
x1＝x10-xo0,y1＝y10-yo0,z1＝z10-zo0；x2＝x20-xo0,y2＝y20-yo0,z2＝z20- zo0；x3＝x30-xo0,y3＝y30-yo0,z3＝z30-zo0(ii) a Wherein (xo)0,yo0,zo0) To receive the target point coordinates, (xi)0,yi0,zi0) I is the coordinate of 3 observation points, 1,2, 3.
The specific process of obtaining the circle center coordinate of the base and the plane normal vector comprises the following steps:
assuming that the radius of the space circle is R, the distance from the 3 observation points to the center of the space circle can be obtained by the following equation:
Figure BDA0002707116600000051
from the above formula, one can obtain:
2(x2-x1)x+2(y2-y1)y+2(z2-z1)z+x1 2+y1 2+z1 2-x2 2-y2 2-z2 2＝0
2(x3-x1)x+2(y3-y1)y+2(z3-z1)z+x1 2+y1 2+z1 2-x3 2-y3 2-z3 2＝0
is recorded as:
A2x+B2y+C2z+D2＝0
A3x+B3y+C3z+D3＝0
the system of linear algebraic equations for obtaining the spatial coordinates about the center of the circle is:
Figure BDA0002707116600000061
the coordinate of the circle center P is obtained by solving:
Figure BDA0002707116600000062
obtaining the base plane normal vector by the base plane equation
Figure BDA0002707116600000063
And 5: determining a plane longitudinal and transverse swing angle according to the normal vector;
in a further embodiment, the base plane normal vector is changed into a pitch angle α (around the Oy axis direction) and a roll angle β (around the Ox axis direction) after being rotated
Figure BDA0002707116600000064
The expression is as follows:
Figure BDA0002707116600000065
in the formula Rα、RβIn order to be a matrix of rotations,
Figure BDA0002707116600000066
Figure BDA0002707116600000067
the following can be obtained:
Figure RE-GDA0002910286520000068
in the formula:
Figure RE-GDA0002910286520000071
the following can be obtained:
Figure RE-GDA0002910286520000072
Figure RE-GDA0002910286520000073
step 6: and establishing a new coordinate system according to the measured pitch angle and roll angle, and determining the position of the rocker arm and the coordinate point of the airplane in the new coordinate system through coordinate transformation.
The rocker position P has a coordinate [ x ] in the original coordinate system oxyz0 y0 z0]TAnd the coordinate system is OX ' Y ' Z ' after the oxyz coordinate passes through the pitch angle alpha and the roll angle beta is rotated, wherein the OX ' Y ' plane is parallel to the plane of the rocker arm base, and the coordinate of P in the coordinate system OX ' Y ' Z ' is P ' ═ x0' y0' z0']TThe expression is as follows:
Figure RE-GDA0002910286520000074
let the coordinate of the plane F in the original coordinate system oxyz be F ═ Fx Fy Fz]TObtaining the coordinate F ' of the airplane F in the coordinate system OX ' Y ' Z ═ Fx' Fy' Fz']TThe method specifically comprises the following steps:
Figure RE-GDA0002910286520000075
at this time, the center point of the rocker arm base and the coordinates of the airplane are converted into an OX ' Y ' Z ' coordinate system, the inclination angle of the rocker arm base is zero in the coordinate system, and zero correction is finished.
Examples
Step 1: marking a plurality of observation points on the rocker arm base, wherein the observation points are positioned on the same circumference;
step 2: erecting a north seeker and a total station between the rocker arm base and a receiving target;
and step 3: and observing the coordinates of each point. And observing and receiving a D point at the position of the target and A, B, C3 observation point coordinates on the base circle of the rocker arm through the lens of the total station, and recording the coordinates.
And 4, step 4: obtaining a plane equation of the base by coplanar constraint of the 3 observation points, and obtaining a circle center coordinate of the base and a plane normal vector;
the coordinate of the D point is (xo) measured by an instrument0,yo0,zo0) The coordinate of point A is (x 1)0,y10,z10) And the coordinate of point B is (x 2)0,y20,z20) And the coordinate of the point C is (x 3)0,y30,z30). In a coordinate system with D as an origin, let the coordinates of point A be (x1, y1, z1), the coordinates of point B be (x2, y2, z2), and the coordinates of point C be (x3, y3, z3), wherein
x＝xo0,y＝yo0,z＝zo0；
x1＝x10-xo0,y1＝y10-yo0,z1＝z10-zo0；
x2＝x20-xo0,y2＝y20-yo0,z2＝z20-zo0；
x3＝x30-xo0,y3＝y30-yo0,z3＝z30-zo0；。
The coplanar constraint from the 3 observation points yields the 3 observation point plane equation as follows:
Figure BDA0002707116600000081
namely: a. the1x+B1y+C1z+D1＝0(2)
Wherein:
A1＝y1·z2-y1·z3-z1·y2+z1·y3+y2·z3-y3·z2
B1＝-x1·z2+x1·z3+z1·x2-z1·x3-x2·z3+x3·z2
C1＝x1·y2-x1·y3-y1·x2+y1·x3+x2·y3-x3·y2
D1＝-x1·y2·z3+x1·y3·z2+x2·y1·z3-x3·y1·z2-x2·y3·z1+x3·y2·z1
assuming that the radius of the space circle is R, the distance from the 3 observation points to the center of the space circle can be obtained by the following equation:
Figure BDA0002707116600000091
from the above formula, one can obtain:
2(x2-x1)x+2(y2-y1)y+2(z2-z1)z+x1 2+y1 2+z1 2-x2 2-y2 2-z2 2＝0 (4)
2(x3-x1)x+2(y3-y1)y+2(z3-z1)z+x1 2+y1 2+z1 2-x3 2-y3 2-z3 2＝0 (5)
is recorded as:
A2x+B2y+C2z+D2＝0 (6)
A3x+B3y+C3z+D3＝0 (7)
linear algebraic equation system of space coordinate about center of circle is obtained through (2), (6) and (7)
Figure BDA0002707116600000092
The coordinate of the circle center P is obtained by solving:
Figure BDA0002707116600000093
the normal vector of the plane of the base is obtained by the equation of the plane of the base
Figure BDA0002707116600000094
And 5: the vector is changed into a vector after rotating by a pitch angle alpha (around the Oy axis direction) and a roll angle beta (around the Ox axis direction)
Figure BDA0002707116600000095
The expression is as follows:
Figure BDA0002707116600000096
the following can be obtained:
Figure RE-GDA0002910286520000097
in the formula:
Figure RE-GDA0002910286520000098
the following can be obtained:
Figure RE-GDA0002910286520000101
Figure RE-GDA0002910286520000102
step 6: and establishing a new coordinate system according to the measured pitch angle and roll angle, and determining the position of the rocker arm and the coordinate point of the airplane in the new coordinate system through coordinate transformation.
The rocker position P has a coordinate [ x ] in the original coordinate system oxyz0 y0 z0]TAnd the coordinate system is OX ' Y ' Z ' after the oxyz coordinate passes through the pitch angle alpha and the roll angle beta is rotated, wherein the OX ' Y ' plane is parallel to the plane of the rocker arm base, and the coordinate of P in the coordinate system OX ' Y ' Z ' is P ' ═ x0' y0' z0']TThe expression is as follows:
Figure RE-GDA0002910286520000103
let the coordinate of the plane F in the original coordinate system oxyz be F ═ Fx Fy Fz]TObtaining the coordinate F ' of the airplane F in the coordinate system OX ' Y ' Z ═ Fx' Fy' Fz']TThe method specifically comprises the following steps:
Figure RE-GDA0002910286520000104

Claims (6)

1. a zero position measurement calibration method for a large mechanical arm base is characterized by comprising
Marking a plurality of observation points on the rocker arm base, wherein the observation points are positioned on the same circumference;
erecting a north seeker and a total station between the rocker arm base and a receiving target;
observing the coordinates of a signal receiving target point and any 3 observation points marked on the rocker arm base through a total station, and establishing a coordinate system by taking the signal receiving target point as an origin;
obtaining a plane equation of the base by coplanar constraint of the 3 observation points, and obtaining a circle center coordinate of the base and a plane normal vector;
determining a plane longitudinal and transverse swing angle according to the normal vector;
and establishing a new coordinate system according to the measured pitch angle and roll angle, and determining the position of the rocker arm and the coordinate point of the airplane in the new coordinate system through coordinate transformation.
2. The method for calibrating the zero position measurement of the base of the large mechanical arm according to claim 1, wherein the number of the observation points is not less than 3.
3. The method for calibrating the zero position measurement of the base of the large mechanical arm according to claim 1, wherein a plane equation of the base obtained by coplanar constraint of 3 observation points is as follows:
A1x+B1y+C1z+D1＝0
in the formula:
A1＝y1·z2-y1·z3-z1·y2+z1·y3+y2·z3-y3·z2
B1＝-x1·z2+x1·z3+z1·x2-z1·x3-x2·z3+x3·z2
C1＝x1·y2-x1·y3-y1·x2+y1·x3+x2·y3-x3·y2
D1＝-x1·y2·z3+x1·y3·z2+x2·y1·z3-x3·y1·z2-x2·y3·z1+x3·y2·z1
x1＝x10-xo0,y1＝y10-yo0,z1＝z10-zo0；x2＝x20-xo0,y2＝y20-yo0,z2＝z20-zo0；x3＝x30-xo0,y3＝y30-yo0,z3＝z30-zo0(ii) a Wherein (xo)0,yo0,zo0) To receive the target point coordinates, (xi)0,yi0,zi0) I is the coordinate of 3 observation points, 1,2, 3.
4. The method for measuring and calibrating the zero position of the base of the large mechanical arm according to claim 3, wherein the specific process for obtaining the center coordinates of the base and the normal vector of the plane is as follows:
assuming that the radius of the space circle is R, the distance from the 3 observation points to the center of the space circle can be obtained by the following equation:
Figure FDA0002707116590000021
from the above formula, one can obtain:
2(x2-x1)x+2(y2-y1)y+2(z2-z1)z+x1 2+y1 2+z1 2-x2 2-y2 2-z2 2＝0
2(x3-x1)x+2(y3-y1)y+2(z3-z1)z+x1 2+y1 2+z1 2-x3 2-y3 2-z3 2＝0
is recorded as:
A2x+B2y+C2z+D2＝0
A3x+B3y+C3z+D3＝0
the system of linear algebraic equations for obtaining the spatial coordinates about the center of the circle is:
Figure FDA0002707116590000022
the coordinate of the circle center P is obtained by solving:
Figure FDA0002707116590000023
obtaining the base plane normal vector by the base plane equation
Figure FDA0002707116590000024
5. The method for measuring and calibrating the zero position of the base of the large mechanical arm according to claim 4, wherein the specific method for determining the plane pitch angle and the plane roll angle according to the normal vector comprises the following steps:
the normal vector of the base plane is changed into a vector after rotating by a pitch angle alpha and a roll angle beta
Figure RE-FDA0002910286510000025
The expression is as follows:
Figure RE-FDA0002910286510000026
in the formula Rα、RβIn order to be a matrix of rotations,
Figure RE-FDA0002910286510000027
Figure RE-FDA0002910286510000028
the following can be obtained:
Figure RE-FDA0002910286510000031
in the formula:
Figure RE-FDA0002910286510000032
the following can be obtained:
Figure RE-FDA0002910286510000033
Figure RE-FDA0002910286510000034
6. the method for calibrating zero position measurement of base of large robot arm according to claim 5, wherein P is represented by P ' ═ x in the new coordinate system OX ' Y ' Z0' y0' z0']TThe expression is as follows:
Figure RE-FDA0002910286510000035
the coordinate of the airplane in the original coordinate system oxyz is F ═ Fx Fy Fz]TObtaining the coordinate F ' of the aircraft F in the new coordinate system OX ' Y ' Z ═ Fx' Fy' Fz']TThe method specifically comprises the following steps:
Figure RE-FDA0002910286510000036
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CN113865432A (en) * 2021-09-17 2021-12-31 中国人民解放军陆军工程大学 Self-propelled artillery barrel orientation detection method
CN115372911A (en) * 2022-08-30 2022-11-22 中国船舶集团有限公司第七二三研究所 Virtual scene and real test platform space position mapping conversion method

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