CN104266649A - Method for measuring posture angle of base cubic mirror based on gyro theodolite - Google Patents

Abstract

The invention discloses a method for measuring the posture angle matrix of a base cubic mirror, relative to a geodetic coordinate system based on a gyro theodolite. The method comprises the following steps: firstly, measuring any two adjacent side surfaces of the base cubic mirror in an alignment manner by the gyro theodolite and an electronic theodolite respectively to obtain the azimuth angle and zenith distance of the gyro theodolite in the alignment direction and the zenith distance of the electronic theodolite in the alignment direction; secondly, calculating through a vertical relationship between the two surfaces to obtain the azimuth angle of the electronic theodolite in the alignment direction; finally, obtaining the posture angle matrix of the base cubic mirror, relative to the geodetic coordinate system. According to the method, one gyro theodolite is omitted, so that the cost is reduced; meanwhile, the mutual alignment between a general theodolite and the gyro theodolite is avoided, so that the measurement precision and efficiency are improved, and the light path shielding during mutual alignment under the complicated working condition is prevented.

Description

Based on the method for gyro-theodolite measuring basis prism square attitude angle

Technical field

The invention belongs to technical field of industrial measurement, be specifically related to a kind of method fully utilizing gyro-theodolite and electronic theodolite measuring basis prism square coordinate system pose angle relative to the earth, the finger north that the method may be used for inertial equipment in the systems such as spacecraft, aircraft, boats and ships is measured and relative attitude measurement of angle between equipment.

Background technology

In the modern large-scale precision system integration manufacture being representative with spacecraft test and process of the test, need the attitude angle of precision measurement inertial equipment coordinate system relative to the earth.Tested inertial equipment adopts benchmark prism square to carry out the body coordinate system of characterization device usually, points to by the coordinate axis that 3 mutually orthogonal level crossing normals on prism square represent apparatus body coordinate system.Therefore, measuring the attitude angle of inertial equipment coordinate system relative to the earth, is exactly the attitude angle measuring the orthogonal mirror normal of prism square 3 coordinate system relative to the earth.

Usually, the attitude angle of measuring basis prism square (benchmark prism square is arranged on object under test usually) coordinate system relative to the earth often adopts two kinds of methods, one is utilize two of two gyro-theodolites alignment measurements or gyro-theodolite successively alignment measurement benchmark prism square respectively orthogonal sides, measure the vector of minute surface normal under earth coordinates, the vector of prism square three minute surface normals under earth coordinates is obtained finally by multiplication cross, if the Yang Zaihua etc. of this project team is in " Spacecraft Environment Engineering " interim " the precision measure new method of spacelab " delivered of the 26th volume the 5th in 2009.Another kind method utilizes a gyro-theodolite and an electronic theodolite, gyro-theodolite is utilized to measure the vector of a prism square side facet normal under earth coordinates, utilize the normal of any one side adjacent with first minute surface on electronic theodolite alignment measurement prism square, and take aim at mutually with gyro-theodolite, the vector of all minute surface normals of prism square under earth coordinates is obtained by angle transmission, if Ren Chunzhen etc. is described in " Spacecraft Environment Engineering " interim " gyro-theodolite application in large-scale space product accurate measurement " delivered of the 28th volume the 6th in 2011.Adopt first method, it is higher that costs measured by two gyro-theodolites, and refer to that north is longer for search time due to gyro-theodolite, measures efficiency lower when utilizing gyro-theodolite to measure two minute surfaces.Adopt second method owing to utilizing one of them minute surface of electronic theodolite alignment measurement, reduce cost and improve measurement efficiency, but the method needs to take aim at mutually between electronic theodolite and gyro-theodolite, because this reducing precision, and under the field working conditions of some complexity, be blocked owing to taking aim at light path mutually, implement more difficult.

The measuring method proposed in the present invention, only needs a gyro-theodolite and an electronic theodolite, but does not need gyro-theodolite and electronic theodolite to take aim at mutually namely can to measure to obtain the attitude angle of benchmark prism square coordinate system relative to the earth.Not only reduce measurement links, also improve measuring accuracy and measure efficiency, and avoiding the light path in taking aim at mutually and block.Along with spationautics development such as China's moon exploration program, manned engineerings, the demand of measuring basis prism square coordinate system pose angle relative to the earth is also got more and more, therefore this patent is with a wide range of applications, and can promote the development of the large-scale complicated system Integrated manufacture industry such as following space flight and aviation.

Summary of the invention

The object of the present invention is to provide a kind of based on the orthogonality between tested benchmark prism square minute surface normal, the zenith distance of the zenith distance utilizing gyro-theodolite to collimate, position angle and electronic theodolite collimation, calculates the attitude angle of tested benchmark prism square coordinate system relative to the earth.This method avoid taking aim at mutually between electronic theodolite and gyro-theodolite, improve measuring accuracy and measure efficiency, the light path avoided in taking aim at mutually is blocked.

For reaching above object, the technical solution used in the present invention is:

Based on a method for gyro-theodolite measuring basis prism square coordinate system pose angle relative to the earth, the enforcement of the method uses gyro-theodolite, electronic theodolite and benchmark prism square, and gyro-theodolite can be measured and obtain position angle and zenith distance; Electronic theodolite can be measured and obtain zenith distance; Orthogonal benchmark prism square comprises six faces, four adjacent sides and end face opposing upper and lower and bottom surface, gyro-theodolite G during measurement ₁alignment measurement benchmark prism square C _bany one side (being designated as A face), the observed reading at the position angle and zenith distance that obtain gyro-theodolite is respectively α ₁, V ₁, be designated as (α ₁, V ₁), electronic theodolite T ₂alignment measurement benchmark prism square C _bupper any one side (be labeled as B face) adjacent with A face, the observed reading obtaining the zenith distance of electronic theodolite is V ₂, the two adjacent surface angles according to orthogonal benchmark prism square are 90 °, ask for electronic theodolite T by following formula ₂the azimuth angle alpha of direction of collimation ₂:

(1) as electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁right positions time,

α ₂＝α ₁+arccos(-cot(V ₁)cot(V ₂))；

(2) as electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁leftward position time,

α ₂＝α ₁-arccos(-cot(V ₁)cot(V ₂))；

Finally obtain benchmark prism square relative to the earth coordinate system pose angle matrix be:

$\left\{\begin{array}{ccc}a\cos \left(a_x\right)& a\cos \left(a_y\right)& a\cos \left(a_z\right)\\ a\cos \left(b_x\right)& a\cos \left(b_y\right)& a\cos \left(b_z\right)\\ a\cos \left(c_x\right)& a\cos \left(c_y\right)& a\cos \left(c_z\right)\end{array}\right\}$

Wherein:

{a _x,a _y,a _z}＝{sin(V ₁)·cos(α ₁),sin(V ₁)·sin(α ₁),cos(V ₁)}

{b _x,b _y,b _z}＝{sin(V ₂)·cos(α ₂),sin(V ₂)·sin(α ₂),cos(V ₂)}

{c _x,c _y,c _z}＝{a _x,a _y,a _z}×{b _x,b _y,b _z}

Wherein azimuth angle alpha ₁, α ₂with zenith distance V ₁, V ₂earth coordinates all relatively, in the present invention, geodetic coordinates origin can get optional position, coordinate system+Z axis points to zenith direction by initial point for vertical surface level greatly ,+X-axis be the geographic north that points to the earth by initial point to, determine+Y-axis according to right-hand rule.Azimuth angle alpha ₁, α ₂for the projection of direction of collimation in surface level and the angle of earth coordinates+X-axis, zenith distance is the angle of direction of collimation and earth coordinates+Z axis.

Gyro-theodolite G ₁alignment measurement benchmark prism square C _ba face, the A face vector of unit length of normal under earth coordinates of formation is expressed as formula (1):

Suppose electronic theodolite T ₂alignment measurement prism square C _bb surface azimuth be α ₂(can not directly be obtained by electronic theodolite measurement), can obtain the vector of unit length of B face normal under earth coordinates is formula (2):

$\stackrel{\mathrm{\ω}}{b}=\{b_x,b_y,b_z\}=\{\sin \left(V_2\right)\·\cos \left({\mathrm{\α}}_2\right),\sin \left(V_2\right)\·\sin \left({\mathrm{\α}}_2\right),\cos \left(V_2\right)\}---\left(2\right)$

Due to benchmark prism square C _bthe normal of two minute surfaces A, B is orthogonal, a _xb _x+ a _yb _y+ a _zb _z=0, therefore obtain formula (3):

cos(α ₁)cos(α ₂)+sin(α ₁)sin(α ₂)＝-cot(V ₁)cot(V ₂) (3)

Obtain after formula (3) is resolved: as electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁right positions time, α ₂=α ₁+ arccos (-cot (V ₁) cot (V ₂)); As electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁leftward position time α ₂=α ₁-arccos (-cot (V ₁) cot (V ₂)).The α obtained ₂value is brought in formula (2), calculates prism square C _bthe vector of unit length of B face normal under earth coordinates.

Finally by prism square C _ba face normal and the vector of unit length multiplication cross of B face normal obtain prism square C _bthe vector of unit length of minute surface normal under earth coordinates of end face (being labeled as C face), calculates as shown in formula (4):

{c _x,c _y,c _z}＝{a _x,a _y,a _z}×{b _x,b _y,b _z} (4)

The attitude angle matrix of final tested benchmark prism square under earth coordinates is as shown in formula (5):

$\left\{\begin{array}{ccc}a\cos \left(a_x\right)& a\cos \left(a_y\right)& a\cos \left(a_z\right)\\ a\cos \left(b_x\right)& a\cos \left(b_y\right)& a\cos \left(b_z\right)\\ a\cos \left(c_x\right)& a\cos \left(c_y\right)& a\cos \left(c_z\right)\end{array}\right\}---\left(5\right)$

In the method for the invention, measurement mechanism mainly comprises: gyro-theodolite, electronic theodolite, tested benchmark prism square.Gyro-theodolite, for collimating a side of tested benchmark prism square, provides this side facet normal relative to the zenith distance of earth coordinates and position angle.Electronic theodolite, for collimating another side of tested benchmark prism square, provides the zenith distance of this side facet normal relative to earth coordinates.

In this article, term " benchmark prism square " is orthogonal 6 bodies made with optical glass, and as shown in Figure 1, comprise end face, bottom surface and 4 sides, each is all coated with reflectance coating.Two often adjacent mirror surface normals are mutually orthogonal, and 3 mutually orthogonal minute surface normals represent the coordinate axis x of direct orthonormal coordinate system, and y, z point to.

Term " tested benchmark prism square ": the benchmark prism square pasted on equipment under test, the coordinate system of benchmark prism square represents the Installation posture coordinate system of equipment under test.

Term " earth coordinates ": as shown in Figure 2, it is+Z-direction that coordinate origin points to zenith direction with vertical surface level greatly, and pointing to geographical direct north is+X-direction, determines+Y direction by right-hand rule.

Term " zenith distance ": the angle of tested minute surface normal and earth coordinates+Z-direction, marks with V herein.

Term " position angle ": the angle of tested minute surface normal and earth coordinates+X-direction and direct north, marks with α herein.

Term " attitude angle matrix ": the space angle of 3 coordinate axis of 3 coordinate axis relative reference rectangular coordinate systems of tested rectangular coordinate system form 3 × 3 angle matrix, as shown in Figure 3.

The present invention has following beneficial effect:

Measuring method of the present invention, saves a gyro-theodolite, thus reduces cost, it also avoid taking aim at mutually between electronic theodolite and gyro-theodolite simultaneously, and improve measuring accuracy and measure efficiency, light path when taking aim at mutually under overcoming complex working condition is blocked.The method is applied in the testing experiment of the goddess in the moon's No. three lunar orbiters.

Accompanying drawing explanation

Fig. 1 is tested benchmark prism square schematic diagram in the present invention.

Fig. 2 is that in the present invention, earth coordinates point to schematic diagram.

Fig. 3 is the attitude angle matrix schematic diagram of tested coordinate system relative reference coordinate system in the present invention.

Fig. 4 is the method schematic diagram of measuring basis prism square coordinate system pose angle matrix relative to the earth in the present invention.

Wherein, G ₁-gyro-theodolite, T ₂-electronic theodolite, C _b-tested benchmark prism square.

Embodiment

What below introduce is embodiment as content of the present invention, further illustrates content of the present invention below by embodiment.Certainly, describe the content that following detailed description is only example different aspect of the present invention, and should not be construed as the restriction scope of the invention.

Commercial gyro-theodolite includes three can measure the parameter obtained, and is respectively position angle, zenith distance and horizontal angle, and electronic theodolite comprises two parameters can measured and obtain, and is respectively horizontal angle and zenith distance.Orthogonal benchmark prism square comprises six faces, and four adjacent sides and end face opposing upper and lower and bottom surface, for example, see Fig. 1.Collimation plane of the present invention is the side of benchmark prism square and non-top and bottom surface.

As shown in Figure 4, the device that measuring method of the present invention relates to has: gyro-theodolite G ₁, electronic theodolite T ₂, tested orthogonal benchmark prism square C _b.Gyro-theodolite: for collimating a minute surface of tested benchmark prism square, provides this minute surface normal relative to the zenith distance of earth coordinates (see Fig. 2) and position angle.Electronic theodolite: for collimating a minute surface of tested benchmark prism square, provide the zenith distance of this minute surface normal relative to earth coordinates.Tested benchmark prism square: benchmark prism square is orthogonal 6 bodies, and two often adjacent mirror surface normals are mutually orthogonal, the coordinate axis that 3 mutually orthogonal minute surface normals represent coordinate system is pointed to.

Gyro-theodolite G during measurement ₁alignment measurement prism square C _bany one side (being labeled as A face), the observed reading at the position angle and zenith distance that obtain gyro-theodolite is respectively α ₁, V ₁, be designated as (α ₁, V ₁), electronic theodolite T ₂alignment measurement prism square C _bany one side (be labeled as B face) adjacent with A face, the observed reading obtaining the zenith distance of electronic theodolite is V ₂, because two adjacent surface angles of orthogonal benchmark prism square are 90 °, ask for electronic theodolite T according to following formula ₂the azimuth angle alpha of direction of collimation ₂.

(1) as electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁right positions time,

α ₂＝α ₁+arccos(-cot(V ₁)cot(V ₂))；

(2) as electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁leftward position time,

α ₂＝α ₁-arccos(-cot(V ₁)cot(V ₂))；

Finally obtain benchmark prism square relative to the earth coordinate system pose angle matrix be:

$\left\{\begin{array}{ccc}a\cos \left(a_x\right)& a\cos \left(a_y\right)& a\cos \left(a_z\right)\\ a\cos \left(b_x\right)& a\cos \left(b_y\right)& a\cos \left(b_z\right)\\ a\cos \left(c_x\right)& a\cos \left(c_y\right)& a\cos \left(c_z\right)\end{array}\right\}$

Wherein:

{a _x,a _y,a _z}＝{sin(V ₁)·cos(α ₁),sin(V ₁)·sin(α ₁),cos(V ₁)}

{b _x,b _y,b _z}＝{sin(V ₂)·cos(α ₂),sin(V ₂)·sin(α ₂),cos(V ₂)}

{c _x,c _y,c _z}＝{a _x,a _y,a _z}×{b _x,b _y,b _z}

Wherein azimuth angle alpha ₁, α ₂with zenith distance V ₁, V ₂earth coordinates all relatively, in the present invention, geodetic coordinates origin can get optional position, coordinate system+Z axis is that vertical surface level greatly points to zenith direction by initial point ,+X-axis is pointed to the direct north of the earth by initial point, determines+Y-axis according to right-hand rule.Azimuth angle alpha ₁, α ₂for the projection of direction of collimation in surface level and the angle of earth coordinates+X-axis, zenith distance is the angle of direction of collimation and earth coordinates+Z axis, for example, see Fig. 3.

Gyro-theodolite G ₁alignment measurement benchmark prism square C _ba face, the A face vector of unit length of normal under earth coordinates of formation is expressed as formula (1):

Suppose electronic theodolite T ₂alignment measurement prism square C _bb surface azimuth be α ₂(can not directly be obtained by electronic theodolite measurement), in like manner can obtain the vector of unit length of B face normal under earth coordinates is formula (2):

$\stackrel{\mathrm{\ω}}{b}=\{b_x,b_y,b_z\}=\{\sin \left(V_2\right)\·\cos \left({\mathrm{\α}}_2\right),\sin \left(V_2\right)\·\sin \left({\mathrm{\α}}_2\right),\cos \left(V_2\right)\}---\left(2\right)$

Due to benchmark prism square C _bthe normal angle of two minute surfaces A, B is 90 °, a _xb _x+ a _yb _y+ a _zb _z=0, therefore obtain formula (3):

cos(α ₁)cos(α ₂)+sin(α ₁)sin(α ₂)＝-cot(V ₁)cot(V ₂) (3)

Obtain after formula (3) is resolved: as electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁right positions time, α ₂=α ₁+ arccos (-cot (V ₁) cot (V ₂)); As electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁leftward position time α ₂=α ₁-arccos (-cot (V ₁) cot (V ₂)).The α obtained ₂value is brought in formula (2), calculates prism square C _bb face normal and the angle of earth coordinates.

Finally by prism square C _ba face normal and the vector of unit length multiplication cross of B face normal obtain prism square C _bthe vector of unit length of minute surface normal under earth coordinates of end face (being labeled as C face), calculates as shown in formula (4):

{c _x,c _y,c _z}＝{a _x,a _y,a _z}×{b _x,b _y,b _z} (4)

The attitude angle matrix of final tested benchmark prism square under earth coordinates is as shown in formula (5):

$\left\{\begin{array}{ccc}a\cos \left(a_x\right)& a\cos \left(a_y\right)& a\cos \left(a_z\right)\\ a\cos \left(b_x\right)& a\cos \left(b_y\right)& a\cos \left(b_z\right)\\ a\cos \left(c_x\right)& a\cos \left(c_y\right)& a\cos \left(c_z\right)\end{array}\right\}---\left(5\right)$

Although give detailed description and explanation to the specific embodiment of the present invention above; but what should indicate is; we conception according to the present invention can carry out various equivalence change and amendment to above-mentioned embodiment; its function produced do not exceed that instructions and accompanying drawing contain yet spiritual time, all should within protection scope of the present invention.

Claims (3)

1. the method based on gyro-theodolite measuring basis prism square coordinate system pose angle relative to the earth, the enforcement of the method uses gyro-theodolite, electronic theodolite and benchmark prism square, gyro-theodolite can be measured and obtain two parameters, is respectively position angle, zenith distance; Electronic theodolite can measure the parameter zenith distance obtained; Orthogonal benchmark prism square comprises six faces, four adjacent sides and end face opposing upper and lower and bottom surface; Gyro-theodolite G during measurement ₁alignment measurement benchmark prism square C _bany one lateral marks be designated as A face, the observed reading at the position angle and zenith distance that obtain gyro-theodolite is respectively α ₁, V ₁, be designated as (α ₁, V ₁), electronic theodolite T ₂alignment measurement benchmark prism square C _ban any side adjacent with A face be labeled as B face, the observed reading obtaining the zenith distance of electronic theodolite is V ₂, the two adjacent surface angles according to orthogonal benchmark prism square are 90 °, ask for electronic theodolite T by following formula ₂the azimuth angle alpha of direction of collimation ₂:

(1) as electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁right positions time,

α ₂＝α ₁+arccos(-cot(V ₁)cot(V ₂))；

(2) as electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁leftward position time,

α ₂＝α ₁-arccos(-cot(V ₁)cot(V ₂))。

Finally obtain benchmark prism square relative to the earth coordinate system pose angle matrix be:

$\left\{\begin{array}{ccc}a\cos \left(a_x\right)& a\cos \left(a_y\right)& a\cos \left(a_z\right)\\ a\cos \left(b_x\right)& a\cos \left(b_y\right)& a\cos \left(b_z\right)\\ a\cos \left(c_x\right)& a\cos \left(c_y\right)& a\cos \left(c_z\right)\end{array}\right\}$

Wherein:

{a _x,a _y,a _z}＝{sin(V ₁)·cos(α ₁),sin(V ₁)·sin(α ₁),cos(V ₁)}

{b _x,b _y,b _z}＝{sin(V ₂)·cos(α ₂),sin(V ₂)·sin(α ₂),cos(V ₂)}

{c _x,c _y,c _z}＝{a _x,a _y,a _z}×{b _x,b _y,b _z}

2. the method for claim 1, wherein azimuth angle alpha ₁, α ₂with zenith distance V ₁, V ₂earth coordinates all relatively, in the present invention, geodetic coordinates origin can get optional position, coordinate system+Z axis points to zenith direction by initial point for vertical surface level greatly ,+X-axis be the geographic north that points to the earth by initial point to, determine+Y-axis according to right-hand rule.Azimuth angle alpha ₁, α ₂for the projection of direction of collimation in surface level and the angle of earth coordinates+X-axis, zenith distance is the angle of direction of collimation and earth coordinates+Z axis.

3. method as claimed in claim 1 or 2, wherein, gyro-theodolite G ₁alignment measurement benchmark prism square C _ba face, the A face vector of unit length of normal under earth coordinates of formation is expressed as formula (1):

Suppose electronic theodolite T ₂alignment measurement prism square C _bb surface azimuth be α ₂(can not directly be obtained by electronic theodolite measurement), can obtain the vector of unit length of B face normal under earth coordinates is formula (2):

$\stackrel{\mathrm{\ω}}{b}=\{b_x,b_y,b_z\}=\{\sin \left(V_2\right)\·\cos \left({\mathrm{\α}}_2\right),\sin \left(V_2\right)\·\sin \left({\mathrm{\α}}_2\right),\cos \left(V_2\right)\}---\left(2\right)$

Due to benchmark prism square C _bthe normal of two minute surfaces A, B is orthogonal, a _xb _x+ a _yb _y+ a _zb _z=0, therefore obtain formula (3):

cos(α ₁)cos(α ₂)+sin(α ₁)sin(α ₂)＝-cot(V ₁)cot(V ₂) (3)

Obtain after formula (3) is resolved: as electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁right positions time, α ₂=α ₁+ arccos (-cot (V ₁) cot (V ₂)); As electronic theodolite T ₂be arranged in Fig. 4 gyro-theodolite G ₁leftward position time α ₂=α ₁-arccos (-cot (V ₁) cot (V ₂)).The α obtained ₂value is brought in formula (2), calculates prism square C _bthe vector of unit length of B face normal under earth coordinates.

Finally by prism square C _ba face normal and the vector of unit length multiplication cross of B face normal obtain prism square C _bthe vector of unit length of minute surface normal under earth coordinates of end face (being labeled as C face), calculates as shown in formula (4):

{c _x,c _y,c _z}＝{a _x,a _y,a _z}×{b _x,b _y,b _z} (4)

The attitude angle matrix of final tested benchmark prism square under earth coordinates is as shown in formula (5):

$\left\{\begin{array}{ccc}a\cos \left(a_x\right)& a\cos \left(a_y\right)& a\cos \left(a_z\right)\\ a\cos \left(b_x\right)& a\cos \left(b_y\right)& a\cos \left(b_z\right)\\ a\cos \left(c_x\right)& a\cos \left(c_y\right)& a\cos \left(c_z\right)\end{array}\right\}---\left(5\right).$