CN109141385B - Positioning method of total station instrument without leveling - Google Patents
Positioning method of total station instrument without leveling Download PDFInfo
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- CN109141385B CN109141385B CN201810665704.9A CN201810665704A CN109141385B CN 109141385 B CN109141385 B CN 109141385B CN 201810665704 A CN201810665704 A CN 201810665704A CN 109141385 B CN109141385 B CN 109141385B
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- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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- G01C15/002—Active optical surveying means
Abstract
The invention discloses a positioning method of a total station instrument without leveling, which comprises the following steps: establishing three coordinate systems by taking the optical center of the total station as the origin of the coordinate systems; the three coordinate systems are respectively a total station coordinate system, a total station outer frame coordinate system and a total station inner frame coordinate system; measuring the slant distance, the horizontal angle and the vertical angle of the N datum points by using a total station according to the three coordinate systems; converting to obtain the coordinates of each reference point in a total station coordinate system according to the slant distance, the horizontal angle and the vertical angle of each reference point; selecting a global coordinate system, and measuring the coordinate of each reference point in the global coordinate system; and solving a conversion matrix of the global coordinate system and the total station coordinate system according to the coordinates of each datum point in the global coordinate system and the coordinates of each total station coordinate system so as to position the coordinates of the point to be measured in any total station coordinate system in the global coordinate system. The invention provides a basis for statics dynamics research and various engineering measurements of a multi-body mechanical system.
Description
Technical Field
The invention relates to a total station positioning method, in particular to a positioning method of a total station without leveling, belonging to the technical field of engineering measurement.
Background
The total station is widely used in the field of engineering survey, but the total station is mostly used for surveying under the leveling condition at present, and the total station is often required to be precisely leveled during surveying, so that the time cost is high, and the labor is consumed. The existing measurement method for the total station under the condition of no leveling exists, but because the establishment of the coordinate system of the total station is not completely expressed, the solution of the coordinate conversion matrix is mostly only a least square method, so that the error of a calculation result is large, and a method for converting the coordinate system of the total station and any given global coordinate system is lacked. For the static and dynamic study of the positioning of the mass center and the like of each individual in mechanical engineering of a multi-body mechanical system, the conversion relation between a total station coordinate system and a global coordinate system of each individual needs to be obtained.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a total station leveling-free positioning method, which realizes that the coordinates of a point to be measured in a total station coordinate system are converted into the coordinates in a global coordinate system under the condition that the total station is leveling-free, and provides a basis for statics dynamics research and various engineering measurements of a multi-body mechanical system.
The purpose of the invention can be achieved by adopting the following technical scheme:
a total station leveling-free positioning method, the method comprising:
establishing three coordinate systems by taking the optical center of the total station as the origin of the coordinate systems; the three coordinate systems are respectively a total station coordinate system, a total station outer frame coordinate system and a total station inner frame coordinate system;
measuring the slant distance, the horizontal angle and the vertical angle of the N datum points by using a total station according to the three coordinate systems; wherein N is more than or equal to 3;
converting to obtain the coordinates of each reference point in a total station coordinate system according to the slant distance, the horizontal angle and the vertical angle of each reference point;
selecting a global coordinate system, and measuring the coordinate of each reference point in the global coordinate system;
and solving a conversion matrix of the global coordinate system and the total station coordinate system according to the coordinates of each datum point in the global coordinate system and the coordinates of each total station coordinate system so as to position the coordinates of the point to be measured in any total station coordinate system in the global coordinate system.
Further, the establishing of three coordinate systems with the optical center of the total station as the origin of coordinates specifically includes:
taking an optical center of a total station as an origin of a total station coordinate system, wherein three coordinate axes of the total station coordinate system are respectively an X axis, a Y axis and a Z axis, setting a horizontal angle zero setting direction as the Y axis, setting a vertical angle zero setting direction as the Z axis, determining the X axis by using a right-hand rule, and establishing the total station coordinate system;
taking the optical center of the total station as the origin of the total station outer frame coordinate system, and taking three coordinate axes of the total station outer frame coordinate system as X1Axis, Y1Axis and Z1Axis, setting the direction perpendicular to the main viewing plane of the outer frame as Y1Axis, setting Z axis direction of total station coordinate system as Z1Axis, setting the direction of the instrument center mark as X1The axis is used for establishing an outer frame coordinate system of the total station;
taking the optical center of the total station as the origin of the total station inner frame coordinate system, wherein three coordinate axes of the total station inner frame coordinate system are respectively X2Axis, Y2Axis and Z2Axis setting the center direction of the objective lens of the inner frame as Y2Axis, setting the direction perpendicular to the principal viewing plane of the inner frame as Z2Axis, X of the total station outer frame coordinate system1The axial direction is set as X2And an axis, establishing a total station inner frame coordinate system.
Further, the coordinates of each reference point in the total station coordinate system are obtained through conversion according to the slant distance, the horizontal angle and the vertical angle of each reference point, and the conversion formula is as follows:
X＝-S·sinβ·sinα
Y＝S·sinβ·cosα
Z＝S·cosβ
wherein S is an oblique distance, α is a horizontal angle, β is a vertical angle, X, Y and Z are respectively an X-axis coordinate, a Y-axis coordinate and a Z-axis coordinate of any datum point in a total station coordinate system.
Further, solving a transformation matrix between the global coordinate system and the total station coordinate system according to the coordinates of each reference point in the global coordinate system and the coordinates of each reference point in the total station coordinate system, specifically:
substituting the coordinates of each datum point in the global coordinate system and the coordinates of each datum point in the total station coordinate system into a coordinate conversion formula, and solving a conversion matrix of the global coordinate system and the total station coordinate system by adopting a Gaussian-Newton iteration method;
when the number of the reference points is three, directly adopting a conversion matrix of the solved global coordinate system and the total station coordinate system; and when the number of the reference points is four or more, selecting three reference points with smaller error of the transformation matrix of the global coordinate system and the total station coordinate system, and solving the transformation matrix of the global coordinate system and the total station coordinate system again.
Further, the coordinate transformation formula is as follows:
wherein, XC、YCAnd ZCRespectively X of any reference point in the global coordinate systemCAxial coordinate, YCAxial coordinate and ZCAxis coordinates; x, Y and Z are respectively X-axis coordinates, Y-axis coordinates and Z-axis coordinates of any datum point in a total station coordinate system; t is a translation matrix converted from a total station coordinate system to a global coordinate system, and R is a rotation matrix converted from the total station coordinate system to the global coordinate system.
Further, the rotation matrix is an orthogonal matrix, which satisfies the following equation:
further, solving a transformation matrix of the global coordinate system and the total station coordinate system by using a gaussian-newton iteration method specifically includes:
programming in the MATLAB, inputting the coordinates of each reference point in the global coordinate system and the coordinates of each reference point in the total station coordinate system, running an MATLAB program, and solving a conversion matrix of the global coordinate system and the total station coordinate system by adopting a Gauss-Newton iteration method.
Further, the method further comprises:
substituting the coordinates of the M known verification points in a total station coordinate system into a coordinate conversion formula, solving to obtain the theoretical coordinates of each verification point in a global coordinate system, comparing the theoretical coordinates of each verification point with the known coordinates of each verification point in the global coordinate system, verifying accuracy and analyzing errors; wherein M is more than or equal to 1.
Furthermore, at least three reference points in the N reference points are not on the same straight line.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, on the basis of the traditional total station non-leveling measurement, three coordinate systems, namely a total station coordinate system, a total station outer frame coordinate system and a total station inner frame coordinate system, are established, and the slant distance, the horizontal angle and the vertical angle can be accurately and clearly shown, so that the coordinates of any point to be measured in the total station coordinate system can be rapidly solved by using the three parameters of the slant distance, the horizontal angle and the vertical angle, the total station is used for positioning each point to be measured in the overall coordinate system, the time can be saved, the precision is improved, and the problems of complex operation and poor measurement result precision of the traditional manual tape measuring point coordinates in a large-scale multi-body mechanical system are solved.
2. According to the coordinate of the plurality of datum points under the global coordinate system and the coordinate of the total station coordinate system, the conversion matrix (the translation matrix and the rotation matrix) of the global coordinate system and the total station coordinate system is solved, the total station is calibrated, the conversion relation between any global coordinate system and the total station coordinate system is obtained, namely the coordinate of any point to be measured under the total station coordinate system is converted into the coordinate of the global coordinate system, and the analysis of various mass center motions in the multi-body dynamic system is facilitated.
3. On the basis of a traditional method for solving a coordinate transformation matrix by only measuring three points, the method provides that four or more reference points are measured, three reference points with smaller solving errors are selected, a Gaussian-Newton iteration method is adopted to solve and obtain the transformation matrix (a translation matrix and a rotation matrix) of a global coordinate system and a total station coordinate system, convergence is faster, a calculation result is more accurate than a result obtained by a traditional method for solving a nonlinear equation by a least square method, redundant reference points can also be used as verification points to be substituted into a coordinate transformation formula, the theoretical coordinate of each verification point under the global coordinate system is obtained by solving, and the theoretical coordinate of each verification point under the global coordinate system is compared with the known coordinate of each verification point under the global coordinate system, the accuracy is verified, and errors are analyzed.
Drawings
Fig. 1 is a flowchart of a total station leveling-free positioning method according to embodiment 1 of the present invention.
Fig. 2 is a schematic structural diagram of a total station according to embodiment 1 of the present invention.
Fig. 3 is an enlarged view of the three coordinate systems established on the total station at a in fig. 2.
Fig. 4 is a schematic diagram of converting the measured three parameters of the slant range, the horizontal angle and the vertical angle into coordinates in a corresponding total station coordinate system by using a spherical coordinate system according to embodiment 1 of the present invention.
Fig. 5 is a schematic diagram of the transformation of coordinates of a reference point in a total station coordinate system to coordinates in a global coordinate system according to embodiment 1 of the present invention.
The system comprises a total station outer frame 1, a total station inner frame 2, a base 3, a tripod 4, a horizontal angle α, a vertical angle β, a total station optical center Q, an objective lens center W and an instrument center A.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Example 1:
as shown in fig. 1, the present embodiment provides a total station leveling-free positioning method, including the following steps:
s101, establishing three coordinate systems by taking the optical center of the total station as the origin of the coordinate systems.
In this step, three coordinate systems need to be established on the basis of the total station instrument free from leveling, and the established three coordinate systems are respectively a total station instrument coordinate system, a total station instrument outer frame coordinate system and a total station instrument inner frame coordinate system.
As shown in fig. 2 and 3, the total station of the present embodiment includes a total station outer frame 1, a total station inner frame 2, and a base 3, the total station inner frame 2 having an objective lens and an eyepiece, being disposed in the total station outer frame 1 and being rotatable in a vertical direction around the total station outer frame 1, the total station outer frame 1 being disposed on the base 3 and being rotatable in a horizontal direction around a central axis of the base 3, and the base 3 being detachably fixed on a tripod 4 for supporting a stable operation of the total station.
The establishment process of the total station coordinate system comprises the following steps: the optical center Q of the total station is used as the origin of a total station coordinate system, three coordinate axes of the total station coordinate system are respectively an X axis, a Y axis and a Z axis, the horizontal angle zero setting direction is set as the Y axis, namely the horizontal angle zero setting direction is coincident with the Y axis direction, the vertical angle zero setting direction is set as the Z axis, namely the vertical angle zero setting direction is coincident with the Z axis direction, the X axis is determined by utilizing the right-hand rule, the total station coordinate system is established, and the total station coordinate system can be regarded as a spherical coordinate system.
The process of establishing the total station outer frame coordinate system comprises the following steps: taking an optical center Q of the total station as an origin of an outer frame coordinate system of the total station, wherein three coordinate axes of the outer frame coordinate system of the total station are respectively X1Axis, Y1Axis and Z1Axis, setting the direction perpendicular to the main viewing plane of the outer frame as Y1Axis, setting Z axis direction of total station coordinate system as Z1Axis, i.e. Z1The axial direction is coincident with the Z-axis direction, and the direction of the instrument center mark A is set as X1Axes, i.e. X1And the axis direction is the direction of a connecting line QA of the optical center Q and the instrument center mark A, and an outer frame coordinate system of the total station is established and fixed on the outer frame of the total station.
The process of establishing the total station inner frame coordinate system comprises the following steps: taking an optical center Q of the total station as an origin of an inner frame coordinate system of the total station, wherein three coordinate axes of the inner frame coordinate system of the total station are respectively X2Axis, Y2Axis and Z2Shaft for centering the objective lens in the inner frameW direction is set as Y2Axes, i.e. Y2The axial direction is the direction of the connecting line QW between the optical center Q and the objective lens center W, and the direction perpendicular to the main viewing plane of the inner frame is set as Z2Axis, X of the total station outer frame coordinate system1The axial direction is set as X2Axes, i.e. X2Axial direction and X1And (4) overlapping the axis directions, and establishing a coordinate system of an inner frame of the total station, wherein the coordinate system is fixed on the inner frame of the total station.
And S102, measuring the slope distance S, the horizontal angle HAR (α) and the vertical angle ZA (β) of the datum point P by using the total station according to the three coordinate systems.
In the step, a total station coordinate system, a total station outer frame coordinate system and a total station inner frame coordinate system are utilized, so that the included angle between coordinate axes can be directly used for representing the horizontal angle and the vertical angle when the total station measures a point, and the horizontal angle is from the Y axis to the Y axis2Included angle of the axes, vertical angle being Z-axis to Z2And when the horizontal angle and the vertical angle are zero, the total station coordinate system, the total station outer frame coordinate system and the total station inner frame coordinate system are superposed.
Six experimental points P were determined using a total station in this example, as shown in table 1 below; wherein P1, P2, P3 and P4 are reference points, and P5 and P6 are verification points.
TABLE 1 Total station data (unit: m)
And S103, converting the coordinates of each reference point P in the total station coordinate system according to the slope distance S, the horizontal angle α and the vertical angle β of each reference point P, as shown in FIG. 4.
In the step, the total station is used for measuring the slant distance, the horizontal angle and the vertical angle of the four datum points in the non-leveling state of the total station.
According to the slope distance S, the horizontal angle α and the vertical angle β of each reference point P, the coordinates of each reference point P in the total station coordinate system are obtained through conversion, and the conversion formula is as follows:
X＝-S·sinβ·sinα
Y＝S·sinβ·cosα
Z＝S·cosβ
x, Y and Z are respectively an X-axis coordinate, a Y-axis coordinate and a Z-axis coordinate of any datum point in a total station coordinate system; in the present embodiment, according to the above formula, in addition to the coordinates of the four reference points in the total station coordinate system, the coordinates of the two verification points in the total station coordinate system are obtained, as shown in table 2 below.
TABLE 2 coordinates of the experimental points in the Total station coordinate System (unit: m)
S104, selecting a global coordinate system, and measuring the coordinate of each reference point P in the global coordinate system.
In this step, the coordinates (X) of each reference point P in the global coordinate system are manually measuredC，YC，ZC)。
In addition to the coordinates of the four reference points in the global coordinate system, the present embodiment also measures the coordinates of the two verification points in the global coordinate system, as shown in table 3 below.
TABLE 3 coordinates of the experimental points in the Global coordinate System (unit: m)
S105, solving a conversion matrix of the global coordinate system and the total station coordinate system according to the coordinates of each reference point P in the global coordinate system and the coordinates of each total station coordinate system, so as to position the coordinates of the point to be measured in any total station coordinate system in the global coordinate system, as shown in FIG. 5.
The transformation matrix of the global coordinate system and the coordinate system of the total station comprises a translation matrix T and a rotation matrix R, the rotation matrix R is an orthogonal matrix defined by the transformation matrix of the coordinate system, so that six equations can be determined, and the six equations are needed to solve twelve unknowns in the translation matrix T and the rotation matrix R, and the process is a calibration process of the total station. Solving the translation matrix T and the rotation matrix R requires the use of at least three reference points (the coordinates in the global coordinate system and the coordinates in the total station coordinate system have been found as described above), because the reference points with larger errors of the calculation result can be omitted in the actual calculation process, the more the number of the reference points is selected, the more accurate the embodiment omits the point P3 with larger errors of solving the translation matrix T and the rotation matrix R, selecting three reference points P1, P2 and P4, establishing nine equations, adding six equations determined by the rotation matrix R, subtracting three repeated constraints caused by the fixed distance between the points, adding nine equations, subtracting three equations and totally twelve equations, and just solving twelve unknowns in the translation matrix T and the rotation matrix R, so that the translation matrix T and the rotation matrix R can be solved through the equations; the coordinate conversion formula is as follows:
wherein, XC、YCAnd ZCRespectively X of any reference point in the global coordinate systemCAxial coordinate, YCAxial coordinate and ZCAxis coordinates; x, Y and Z are respectively the X-axis coordinate, the Y-axis coordinate and the Z-axis coordinate of any reference point in the total station coordinate system.
Since the rotation matrix R is an orthogonal matrix, it satisfies the following six equations:
solving a conversion matrix of the global coordinate system and the total station coordinate system by adopting a Gaussian-Newton iteration method according to the coordinate conversion formula, which specifically comprises the following steps:
programming in MATLAB, inputting coordinates of three reference points P1, P2 and P4 in a global coordinate system and coordinates in a total station coordinate system, running an MATLAB program, solving a conversion matrix of the global coordinate system and the total station coordinate system by adopting a Gaussian-Newton iteration method, and solving a translation matrix T and a rotation matrix R which are obtained as shown in the following table 4.
TABLE 4 transformation parameters of Global coordinate System and Total station coordinate System
And S106, substituting the coordinates of the two verification points P5 and P6 in the coordinate system of the total station into the coordinate conversion formula in the step S105, solving to obtain the coordinates of the two verification points in the global coordinate system as (-0.0710,0,9922,0.8569), (1.6911,0.9906,0.6610), and comparing the actually measured coordinates of the two verification points in the global coordinate system (see the table 3 above), so that the positioning precision of the total station to the midpoint of the global coordinate system under the leveling-free condition can be 3cm, and the positioning method of the embodiment has reliable precision and feasibility.
It will be appreciated by those skilled in the art that the above reference points may be three or more, and the verification point may be one or more.
In summary, on the basis of the traditional total station non-leveling measurement, the three coordinate systems of the total station coordinate system, the total station outer frame coordinate system and the total station inner frame coordinate system are established, and the slant distance, the horizontal angle and the vertical angle can be accurately and clearly shown, so that the coordinates of any point to be measured in the total station coordinate system can be conveniently and quickly solved by using the three parameters of the slant distance, the horizontal angle and the vertical angle, the total station can position each point to be measured in the global coordinate system, the time can be saved, the precision can be improved, and the problems that the traditional manual tape measuring point coordinates are complex to operate and the measuring result precision is poor for a large-scale multi-body mechanical system are solved.
The above description is only for the preferred embodiments of the present invention, but the protection scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution and the inventive concept of the present invention within the scope of the present invention.
Claims (8)
1. The positioning method of the total station without leveling is characterized in that: the method comprises the following steps:
establishing three coordinate systems by taking the optical center of the total station as the origin of the coordinate systems; the three coordinate systems are respectively a total station coordinate system, a total station outer frame coordinate system and a total station inner frame coordinate system;
measuring the slant distance, the horizontal angle and the vertical angle of the N datum points by using a total station according to the three coordinate systems; wherein N is more than or equal to 3;
converting to obtain the coordinates of each reference point in a total station coordinate system according to the slant distance, the horizontal angle and the vertical angle of each reference point;
selecting a global coordinate system, and measuring the coordinate of each reference point in the global coordinate system;
solving a conversion matrix of the global coordinate system and the total station coordinate system according to the coordinates of each datum point in the global coordinate system and the coordinates of each total station coordinate system so as to position the coordinates of the point to be measured in any total station coordinate system in the global coordinate system;
the method for establishing three coordinate systems by using the optical center of the total station as the origin of coordinates specifically comprises the following steps:
taking an optical center of a total station as an origin of a total station coordinate system, wherein three coordinate axes of the total station coordinate system are respectively an X axis, a Y axis and a Z axis, setting a horizontal angle zero setting direction as the Y axis, setting a vertical angle zero setting direction as the Z axis, determining the X axis by using a right-hand rule, and establishing the total station coordinate system;
taking the optical center of the total station as the origin of the total station outer frame coordinate system, and taking three coordinate axes of the total station outer frame coordinate system as X1Axis, Y1Axis and Z1Axis, setting the direction perpendicular to the main viewing plane of the outer frame as Y1Axis, setting Z axis direction of total station coordinate system as Z1Axis, setting the direction of the instrument center mark as X1The axis is used for establishing an outer frame coordinate system of the total station;
taking the optical center of the total station as the origin of the total station inner frame coordinate system, wherein three coordinate axes of the total station inner frame coordinate system are respectively X2Axis, Y2Axis and Z2Axis setting the center direction of the objective lens of the inner frame as Y2Axis, setting the direction perpendicular to the principal viewing plane of the inner frame as Z2Axis, X of the total station outer frame coordinate system1The axial direction is set as X2The axis is used for establishing a coordinate system of an inner frame of the total station;
the horizontal angle and the vertical angle are represented by an included angle between coordinate axes, and the horizontal angle is from Y axis to Y axis2Included angle of the axes, vertical angle being Z-axis to Z2The angle of the axes.
2. The total station leveling-free positioning method according to claim 1, characterized in that: and converting the coordinates of each reference point in a total station coordinate system according to the slant distance, the horizontal angle and the vertical angle of each reference point, wherein the conversion formula is as follows:
X＝-S·sinβ·sinα
Y＝S·sinβ·cosα
Z＝S·cosβ
wherein S is an oblique distance, α is a horizontal angle, β is a vertical angle, X, Y and Z are respectively an X-axis coordinate, a Y-axis coordinate and a Z-axis coordinate of any datum point in a total station coordinate system.
3. The total station leveling-free positioning method according to claim 1, characterized in that: the method comprises the following steps of solving a conversion matrix of a global coordinate system and a total station coordinate system according to the coordinates of each datum point in the global coordinate system and the coordinates of each datum point in the total station coordinate system, and specifically comprises the following steps:
substituting the coordinates of each datum point in the global coordinate system and the coordinates of each datum point in the total station coordinate system into a coordinate conversion formula, and solving a conversion matrix of the global coordinate system and the total station coordinate system by adopting a Gaussian-Newton iteration method;
when the number of the reference points is three, directly adopting a conversion matrix of the solved global coordinate system and the total station coordinate system; and when the number of the reference points is four or more, selecting three reference points with smaller error of the transformation matrix of the global coordinate system and the total station coordinate system, and solving the transformation matrix of the global coordinate system and the total station coordinate system again.
4. The total station leveling-free positioning method according to claim 3, characterized in that: the coordinate conversion formula is as follows:
wherein, XC、YCAnd ZCRespectively X of any reference point in the global coordinate systemCAxial coordinate, YCAxial coordinate and ZCAxis coordinates; x, Y and Z are respectively X-axis coordinates, Y-axis coordinates and Z-axis coordinates of any datum point in a total station coordinate system; t is a translation matrix converted from a total station coordinate system to a global coordinate system, and R is a rotation matrix converted from the total station coordinate system to the global coordinate system.
5. The total station leveling-free positioning method according to claim 4, characterized in that: the rotation matrix is an orthogonal matrix that satisfies the following equation:
6. the total station leveling-free positioning method according to claim 3, characterized in that: the method for solving the transformation matrix of the global coordinate system and the total station coordinate system by adopting the Gaussian-Newton iteration method specifically comprises the following steps:
programming in the MATLAB, inputting the coordinates of each reference point in the global coordinate system and the coordinates of each reference point in the total station coordinate system, running an MATLAB program, and solving a conversion matrix of the global coordinate system and the total station coordinate system by adopting a Gauss-Newton iteration method.
7. The total station leveling-free positioning method according to any one of claims 1-6, wherein: the method further comprises the following steps:
substituting the coordinates of the M known verification points in a total station coordinate system into a coordinate conversion formula, solving to obtain the theoretical coordinates of each verification point in a global coordinate system, comparing the theoretical coordinates of each verification point with the known coordinates of each verification point in the global coordinate system, verifying accuracy and analyzing errors; wherein M is more than or equal to 1.
8. The total station leveling-free positioning method according to any one of claims 1-6, wherein: at least three reference points in the N reference points are not on the same straight line.
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