A method for realizing reference measurement and conversion based on a single theodolite

Abstract

The application discloses a method for realizing reference measurement and conversion based on a single theodolite, and is applied to the technical field of photoelectric testing. The method comprises the following steps: acquiring normal vectors of a plane mirror, reference vectors and to-be-measured vectors at first and second observation points respectively; obtaining two groups of coefficient arrays through conversion of the first reference vector and the first to-be-measured vector in a first coordinate system; similarly, obtaining another two groups of coefficient arrays through conversion of the second reference vector and the second to-be-measured vector in a second coordinate system; obtaining a conversion relationship of the to-be-measured vector in a reference coordinate system based on the four groups of coefficient arrays, and then determining a conversion relationship between a to-be-measured coordinate system and the reference coordinate system; and precise space vector measurement and coordinate system conversion are realized by using the single theodolite.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of photoelectric testing, in particular to a method for realizing reference measurement and conversion based on a single theodolite. BACKGROUND

[0002] In the process of instrument equipment installation or use, it is often necessary to calibrate the relative attitude between devices, usually using theodolite autocollimation of each device as a reference cube mirror or plane mirror, and then converting the measured normal vectors of each mirror to the same coordinate system through the reference to obtain the relative attitude between devices.

[0003] The commonly used reference measurement and conversion method is the theodolite station measurement method, which at least needs two theodolites. While measuring autocollimation, the normal vectors of each mirror measured by the two theodolites are converted to the measurement coordinate system of one of the theodolites through mutual sighting. In order to make the cursors of the two theodolites completely coincide in the mutual sighting process, the theodolite for mutual sighting needs to be calibrated, and the calibration process is complex. At the same time, the leveling error of the two theodolites will also reduce the conversion accuracy of the measurement coordinate system. If a high-precision theodolite is selected in the actual measurement process, the measurement cost will also increase substantially.

[0004] In order to overcome these defects, the present application provides a method for realizing reference measurement and conversion based on a single theodolite. SUMMARY

[0005] The purpose of the present application is to provide a method for realizing reference measurement and conversion based on a single theodolite, which aims to solve the above problems.

[0006] To achieve the above purpose, the present application provides the following technical scheme:

[0007] The present application provides a method for realizing reference measurement and conversion based on a single theodolite, comprising:

[0008] Measurement stage:

[0009] Place two plane mirrors near the reference surface and the measured surface, and the two plane mirrors are not parallel; select two points as the first observation point and the second observation point, and the two observation points must satisfy that the first plane mirror and the second plane mirror can be observed simultaneously using the theodolite;

[0010] Using the theodolite, measure at the first observation point and the second observation point:

[0011] At the first observation point, establish a first theodolite coordinate system, and obtain the first normal vector and the second normal vector of the first plane mirror and the second plane mirror at the first observation point; obtain the first reference vector and the first measured vector of the first reference surface and the first measured surface at the first observation point;

[0012] At the second observation point, a second theodolite coordinate system is established, and a third normal vector and a fourth normal vector of the first plane mirror and the second plane mirror at the second observation point are obtained; a second reference vector and a second to-be-measured vector of a second reference plane and a second to-be-measured plane at the second observation point are obtained;

[0013] The first reference plane and the second reference plane are non-parallel;

[0014] The number of to-be-measured vectors can be increased or decreased according to actual needs, and the number of to-be-measured vectors obtained at any observation point can be increased or decreased during measurement;

[0015] The arrangement and conversion stage:

[0016] A first coordinate system is established with the origin of the first theodolite coordinate system at the first observation point as a first origin and with the first normal vector and the second normal vector as axes; a second coordinate system is established with the origin of the second theodolite coordinate system at the second observation point as a second origin and with the third normal vector and the fourth normal vector as axes;

[0017] A reference coordinate system is established with a point on the intersection line of the first reference plane and the second reference plane as a reference origin and with the first reference vector and the second reference vector as axes; a to-be-measured coordinate system is established with a point on the intersection line of the first to-be-measured plane and the second to-be-measured plane as a to-be-measured origin and with the first to-be-measured vector and the second to-be-measured vector as axes;

[0018] The conversion relationship between the first theodolite coordinate system and the first coordinate system and the conversion relationship between the second theodolite coordinate system and the second coordinate system are determined; the conversion relationship between the first coordinate system and the second coordinate system is determined;

[0019] First and second coefficient arrays are obtained based on the conversion of the first reference vector of the first reference plane and the first to-be-measured vector in the first coordinate system; third and fourth coefficient arrays are obtained based on the conversion of the second reference vector of the second reference plane and the second to-be-measured vector in the second coordinate system;

[0020] The conversion relationship between the first to-be-measured vector and the second to-be-measured vector in the reference coordinate system is obtained based on the first, second, third and fourth coefficient arrays; and the conversion relationship between the to-be-measured coordinate system and the reference coordinate system can be further obtained.

[0021] Preferably, for convenience of calculation, the vectors and normal vectors can be represented as unit vectors;

[0022] Preferably, the first coordinate system, the second coordinate system, the reference coordinate system and the method for establishing the to-be-measured coordinate system are not unique, and for the convenience of calculation, the right-hand rule is preferably used to determine the direction of another axis;

[0023] Preferably, for the convenience of measurement and conversion, the first and second plane mirrors remain in place during measurement, and the poses thereof do not change, and the second coordinate system can be regarded as being obtained by translation of the first coordinate system. In the case of only considering the direction of a vector, the first coordinate system and the second coordinate system can be processed and regarded as the same coordinate system.

[0024] The application provides a method for realizing reference measurement and conversion based on a single theodolite, and has the following beneficial effects:

[0025] (1) Cost saving. The traditional reference measurement and conversion method requires at least two theodolites, while the application only needs one theodolite and two plane mirrors, thereby greatly reducing the investment in equipment and saving the measurement cost.

[0026] (2) Simplified measurement steps and shortened measurement time. The traditional measurement method requires mutual sighting of theodolites, and this process requires complex calibration and is easily affected by operation errors, thereby reducing the measurement accuracy. The application does not require mutual sighting, but only needs measurement and calculation of a single theodolite, so as to express the to-be-measured vector in the reference coordinate system, thereby greatly simplifying the measurement steps and shortening the measurement time. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 FIG. 1 is a flowchart of a method for realizing reference measurement and conversion based on a single theodolite according to Embodiment 1 of the application;

[0028] Figure 2 FIG. 2 is a schematic diagram of reference measurement according to Embodiment 1 of the application;

[0029] Figure 3 FIG. 3 is a schematic diagram of theodolite coordinates according to Embodiment 1 of the application; DETAILED DESCRIPTION

[0030] It should be understood that the specific embodiments described herein are merely intended to explain the application, and are not intended to limit the application.

[0031] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the application.

[0032] Embodiment 1

[0033] Referring to Figure 1 , a flowchart of a method for realizing reference measurement and conversion based on a single theodolite according to Embodiment 1 of the present application; wherein one or more to-be-measured vectors can be selected according to requirements, and measurement is performed at a first observation point or a second observation point according to the placement position, and two to-be-measured vectors are selected in this embodiment.

[0034] Referring to Figure 2 , a reference measurement diagram according to Embodiment 1 of the present application, and the specific operation steps in the measurement stage are as follows:

[0035] A theodolite and two plane mirrors are taken for measurement, and then the to-be-measured vectors are expressed in the coordinate system of the reference cube mirror according to the theodolite readings. The specific measurement method is as follows:

[0036] The first plane mirror and the second plane mirror are taken and placed near the reference cube mirror and the to-be-measured vectors, and the normal vectors of the first plane mirror and the second plane mirror are ensured to intersect.

[0037] A point is selected as the first observation point of the theodolite, and at this point, the first plane mirror, the second plane mirror, the first reference surface, and the first to-be-measured vector must be simultaneously observed.

[0038] A point is selected as the second observation point of the theodolite, and at this point, the first plane mirror, the second plane mirror, the second reference surface, and the second to-be-measured vector must be simultaneously observed.

[0039] The measurement stage includes the following steps:

[0040] S1: A first theodolite coordinate system is established at the first observation point, the first normal vector and the second normal vector of the first plane mirror and the second plane mirror at the first observation point are obtained, and the first reference vector and the first to-be-measured vector of the first reference surface and the first to-be-measured surface at the first observation point are obtained.

[0041] In this embodiment, the first normal vector of the first plane mirror at the first observation point is the second normal vector of the second plane mirror at the first observation point is the first reference vector of the first reference cube mirror is the first to-be-measured vector is

[0042] The theodolite is placed at the first observation point, and the first plane mirror and the second plane mirror are measured respectively, and the theodolite readings are recorded as αread 11 βread 11 , αread 21 βread 21 ; then the first reference surface and the first to-be-measured vector are measured using the theodolite, and the theodolite readings are recorded as αread j1 βreadj1 α read d1 β read d1 .

[0043] The first normal vector, the second normal vector, the first reference vector and the first to-be-measured vector can be respectively represented as:

[0044]

[0045] S2: A second theodolite coordinate system is established at a second observation point, and a third normal vector and a fourth normal vector of the first plane mirror and the second plane mirror at the second observation point are obtained; a second reference vector and a second to-be-measured vector of the second reference surface and the second to-be-measured surface at the second observation point are obtained.

[0046] In the embodiment, let the third normal vector of the first plane mirror at the second observation point be The fourth normal vector of the second plane mirror at the second observation point is The second reference vector is The second to-be-measured vector is

[0047]

[0048] The theodolite is placed at the second observation point, and the first plane mirror and the second plane mirror are measured respectively, and the theodolite readings are recorded as α read 12 β read 12 , α read 22 β read 22 ; then the theodolite is used to measure the second reference surface and the second to-be-measured vector respectively, and the theodolite readings are recorded as α read j2 β read j2 , α read d2 β read d2 .

[0049] The third normal vector, the fourth normal vector, the second reference vector and the second to-be-measured vector can be respectively represented as:

[0050]

[0051] The arrangement and calculation stage steps are as follows:

[0052] S3: The origin of the first theodolite coordinate system at the first observation point is taken as a first origin, and a first coordinate system is established with the first normal vector and the second normal vector as axes respectively; the origin of the second theodolite coordinate system at the second observation point is taken as a second origin, and a second coordinate system is established with the third normal vector and the fourth normal vector as axes respectively; the conversion relationship of the first theodolite coordinate system and the second theodolite coordinate system with the first coordinate system and the second coordinate system respectively, and the conversion relationship of the first coordinate system and the second coordinate system are obtained.

[0053] S4: establishing a reference coordinate system with a preset point on the intersection line of the first reference surface and the second reference surface as a reference origin, and with the first reference vector and the second reference vector as axes; and establishing a to-be-measured coordinate system with a preset point on the intersection line of the first to-be-measured surface and the second to-be-measured surface as a to-be-measured origin, and with the first to-be-measured vector and the second to-be-measured vector as axes.

[0054] Please refer to Figure 3 , which is a theodolite coordinate diagram of Embodiment 1 of the present application. Let α = 360° - α 读 , β = β 读 .

[0055] Therefore, taking the first observation point as the coordinate origin O1, and assuming that the normal vectors of each surface are unit vectors, the first normal vector of the first plane mirror can be expressed as:

[0056]

[0057] The second normal vector of the second plane mirror can be expressed as:

[0058]

[0059] The first reference vector can be expressed as:

[0060]

[0061] The first to-be-measured vector can be expressed as:

[0062]

[0063] Similarly, taking the second observation point as the coordinate origin O2, a second theodolite coordinate system is established, and assuming that the normal vectors of each surface are unit vectors, the third normal vector of the first plane mirror in the second coordinate system can be expressed as:

[0064]

[0065] The fourth normal vector of the second plane mirror can be expressed as:

[0066]

[0067] The second reference vector can be expressed as:

[0068]

[0069] The second to-be-measured vector It can be represented as:

[0070]

[0071] Then, taking the origin of the first theodolite coordinate system at the first observation point as the origin O1, and the first normal vector of the first plane mirror as the origin, respectively... The second normal vector of the second plane mirror Establish a first coordinate system C1 with respect to the axis. Take the origin O2 of the theodolite coordinate system at the second observation point as the origin, and the third normal vector of the first plane mirror... The fourth normal vector of the second plane mirror Establish a second coordinate system C2 for the axis.

[0072] In the first coordinate system C1, the first reference vector and the first vector to be tested They can be represented as:

[0073]

[0074] In the second coordinate system C2, the second reference vector Second test vector They can be represented as:

[0075]

[0076] S5: Based on the transformation of the first reference vector of the first reference plane and the first vector to be measured in the first coordinate system, a first coefficient group and a second coefficient group are obtained; based on the transformation of the second reference vector of the second reference plane and the second vector to be measured in the second coordinate system, a third coefficient group and a fourth coefficient group are obtained.

[0077] In this embodiment, in the first coordinate system C1, the first reference vector of the first reference cubic mirror is... and the first vector to be tested They are represented as follows:

[0078]

[0079]

[0080] This leads to the first set of coefficients [λ] j11 , λ j12 , λ j13 ] and the second coefficient group [λ d11 , λ d12 , λ d13 The first and second coefficient groups can be represented as follows:

[0081]

[0082] In the second coordinate system C2, the second reference vector of the second reference plane and the second to-be-measured vector are respectively represented as:

[0083]

[0084] Further, a third array [λ j21 , λ j22 , λ j23 ] and a fourth array [λ d21 , λ d22 , λ d23 ] are obtained. The third array and the fourth array can be respectively represented as:

[0085]

[0086] Therefore, a first array [λ j11 , λ j12 , λ j13 ], a second array [λ d11 , λ d12 , λ d13 ], a third array [λ j21 , λ j22 , λ j23 ], and a fourth array [λ d21 , λ d22 , λ d23 ] are obtained respectively.

[0087] S6: Based on the first array, the second array, the third array, and the fourth array, a conversion relationship of the first to-be-measured vector and the second to-be-measured vector in the reference coordinate system is obtained; and further, a conversion relationship of the to-be-measured coordinate system and the reference coordinate system is obtained.

[0088] In the embodiment, if no coordinate system is defined and only the vectors themselves are concerned, the first normal vector and the fourth normal vector the second normal vector and the fifth normal vector are completely the same; that is, the normal vector of the first plane mirror is the normal vector of the second plane mirror is

[0089] the first reference vector the second reference vector the first to-be-measured vector And the second to-be-measured vector Respectively represented as:

[0090]

[0091] The first to-be-measured vector And the second to-be-measured vector Respectively represented as:

[0092]

[0093] Further obtained:

[0094]

[0095] Available

[0096]

[0097] A to-be-measured coordinate system is established with a preset angle of the to-be-measured cube mirror as an origin O3 and with [a1, a2, a3] and [b1, b2, b3] as axes. The above can obtain [a1, a2, a3] and [b1, b2, b3], that is, the to-be-measured coordinate system is converted into the reference coordinate system of the reference cube mirror.

[0098] In summary, the embodiment 1 of the present application realizes the reference measurement and conversion method without mutual sighting by adopting a single theodolite combined with a plane mirror and a reference cube mirror. The normal vectors of the plane mirror and the reference cube mirror can be accurately obtained through theodolite readings, and the expression of the to-be-measured vector in the reference cube mirror coordinate system is derived using these normal vectors, thereby simplifying the traditional two-theodolite stationing measurement method. The present application not only reduces the measurement cost and time, but also avoids the cumbersome process caused by mutual sighting of two theodolites, and improves the measurement accuracy.

[0099] It should be noted that in this document, the terms "comprising", "containing", or any other similar term are intended to encompass non-exclusive inclusion, so that a process, device, article or method including a series of elements includes not only those elements, but also other elements not explicitly listed, or other elements inherent to such a process, device, article or method. Without more limitations, the element defined by the statement "including a" does not exclude the presence of another identical element in the process, device, article or method including the element.

[0100] The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation using the content of the specification and drawings, or direct or indirect application in other related technical fields, is also included in the patent protection scope of the present application.

[0101] While embodiments of the present application have been shown and described, it is to be understood that the embodiments described are merely divergences of the principles and specific embodiments disclosed herein and that numerous modifications, changes, substitutions, and alterations can be made by one skilled in the art without departing from the spirit and scope of the application. The scope of the application is limited only by the claims and the full scope of equivalents to each claim.

[0102] Of course, the present application also has other various embodiments, and based on the embodiments, other embodiments obtained by those skilled in the art without any creative work fall within the scope of protection of the present application.

Claims

1. A method for realizing reference measurement and conversion based on a single theodolite, characterized in that, The application relates to a method for measuring a plurality of surfaces, comprising the following steps: establishing a first theodolite coordinate system at a first observation point, and obtaining a first normal vector and a second normal vector of a first plane mirror and a second plane mirror at the first observation point; obtaining a first reference vector and a first measurement vector of a first reference surface and a first measurement surface at the first observation point; establishing a second theodolite coordinate system at a second observation point, and obtaining a third normal vector and a fourth normal vector of the first plane mirror and the second plane mirror at the second observation point; obtaining a second reference vector and a second measurement vector of a second reference surface and a second measurement surface at the second observation point; establishing a first coordinate system with the first theodolite coordinate system origin of the first observation point as a first origin and with the first normal vector and the second normal vector as axes; establishing a second coordinate system with the second theodolite coordinate system origin of the second observation point as a second origin and with the third normal vector and the fourth normal vector as axes; obtaining the conversion relationship between the first theodolite coordinate system and the first coordinate system, the conversion relationship between the second theodolite coordinate system and the second coordinate system, and the conversion relationship between the first coordinate system and the second coordinate system; establishing a reference coordinate system with a preset point on the intersection line of the first reference surface and the second reference surface as a reference origin and with the first reference vector and the second reference vector as axes; establishing a measurement coordinate system with a preset point on the intersection line of the first measurement surface and the second measurement surface as a measurement origin and with the first measurement vector and the second measurement vector as axes; obtaining a first coefficient array and a second coefficient array based on the conversion of the first reference vector of the first reference surface and the first measurement vector in the first coordinate system; obtaining a third coefficient array and a fourth coefficient array based on the conversion of the second reference vector of the second reference surface and the second measurement vector in the second coordinate system; obtaining the conversion relationship between the first measurement vector and the second measurement vector in the reference coordinate system based on the first coefficient array, the second coefficient array, the third coefficient array and the fourth coefficient array, and further obtaining the conversion relationship between the measurement coordinate system and the reference coordinate system.

2. The method for realizing reference measurement and conversion based on a single theodolite according to claim 1, characterized in that, The first plane mirror and the second plane mirror are not parallel.

3. The method for realizing reference measurement and conversion based on a single theodolite according to claim 1, characterized in that, The first reference surface and the second reference surface are not parallel.

4. The method for realizing reference measurement and conversion based on a single theodolite according to claim 1, characterized in that, The number of measurement vectors is determined according to actual requirements.

5. The method for realizing reference measurement and conversion based on a single theodolite according to claim 1, characterized in that, At least one theodolite is needed when measuring at the first observation point and the second observation point; when there is only one theodolite, the theodolite is placed at the first observation point and the second observation point in sequence for measurement; if there are several theodolites, the theodolites are placed at the first observation point and the second observation point for measurement.

6. The method for realizing reference measurement and conversion based on a single theodolite according to claim 1, characterized in that, The establishment methods of the first coordinate system, the second coordinate system, the reference coordinate system and the measurement coordinate system are not unique.

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