CN102809367A - Space rotating angle measuring method based on double-shaft obliquity sensor - Google Patents

Abstract

The invention discloses a space rotating angle measuring method based on a double-shaft obliquity sensor. The method is to establish a physical model between a sensor and a rotating shaft through a measuring module formed by a double-shaft sensor according to three unknown space angles formed based on an installation mode of the sensor and a spatial relation among the rotating shafts, so as to obtain a calculation method of the three unknown installing angles, so that the rotating angle around the space rotating shafts is detected. According to the traditional technology of detecting an angle through an obliquity sensor, the rotating shafts of a detected object must be levelly arranged, and the sensor and the measuring module also must be kept in level state, all the operations are hard to implement in engineering; compared with traditional technology, the method disclosed by the invention has the advantages that the space rotating angle measuring method can be achieved only if the module is arranged not close and vertical to the level, thereby the space rotating angle measuring method is beneficial for the application in engineering.

Description

A kind of space rotation angle measurement method based on double-shaft tilt angle sensor

Technical field

The invention belongs to the measurement of geometric length technical field, relate to a kind of space rotation angle measurement method, especially a kind of space rotation angle measurement method based on double-shaft tilt angle sensor.

Background technology

In the prior art,, several different methods is arranged, like mechanical pointer angular instrument, the laser measurement anglec of rotation, electronic compass, obliquity sensor and gyroscope about measurement of angle.

The mechanical pointer angel measuring instrument can only be fit to the situation of space rotating shaft parallel in surface level.Because mechanical type angel measuring instrument, the swing of its pointer are the minimal friction that relies on gravity and needle pivot, if turning axle tilts, then needle pivot friction force increases, and causes the beat of pointer inaccurate.Electronic compass is to be benchmark with faint magnetic direction, detects the angle of current direction and magnetic direction, obtains current position angle.Obviously, can not to detect with the magnetic direction be the anglec of rotation of turning axle to electronic compass.And generally speaking, magnetic direction almost is exactly a horizontal direction, so electronic compass can not detect the inclination angle of a direction.Gyroscope is a rate sensor, can detect current speed of rotation, and the through-rate integration can obtain the current anglec of rotation, and is omnibearing angular detection.But gyrostatic subject matter is exactly its migration error, even under isogonal situation, gyro still has the output signal, and this obviously can't accurately take measurement of an angle.

Obliquity sensor can detect any one non-perpendicular to the static angle between surface level and the surface level, and measurement result is stable, reliable.The miniature obliquity sensor that particularly adopts MEMS technology to make now, its accuracy of measurement is higher.But existing obliquity sensor and module thereof have two shortcomings: 1) can only the measure static angle, promptly can only measure the angle between frontal plane and surface level, and energy measurement turning axle and surface level do not have the space rotation angle under the angle situation; 2) require sensor with and shell must surface level install, otherwise measure inaccurate.

Summary of the invention

The objective of the invention is to overcome the shortcoming of above-mentioned prior art; A kind of space rotation angle measurement method based on double-shaft tilt angle sensor is provided; It is through spatial relation between sensor and the turning axle; Set up mathematical model, and obtain analytic solution, thereby calculate around the angle of turning axle rotation.So this method can the measurement space anglec of rotation, and this turning axle not necessarily is parallel to surface level,

The objective of the invention is to solve through following technical scheme:

This space rotation angle measurement method based on double-shaft tilt angle sensor may further comprise the steps:

1) make two axles of double-shaft tilt angle sensor vertical each other, its output voltage is to be the sine value of the angle of reference with the surface level; With the turning axle is the Y axle, establishes to be rotated counterclockwise direction for just, and the anglec of rotation is θ, and it is projected as the y axle surface level, and two axle intersection points are o, establish the angle β of turning axle and surface level, i.e. β=∠ Yoy, β ∈ [0, pi/2]; The z axle is set the x direction of principal axis perpendicular to surface level, constitutes right-handed Cartesian coordinate system xyzo; Make X axle and x axle overlap, the vertical X of Z axle, Y axle constitute cartesian coordinate system XYZo equally; If two axles of double-shaft tilt angle sensor are u and v, its intersection point fixes on the o point, because ou and ov are orthogonal, the normal vector of establishing the uov plane that o orders is ow; And ou, ov and ow are unit length vector, and the unit length of ou is made as oP=|ou|, and oP is projected as oQ on the yoz plane; Angle between definition oQ and the turning axle Y is γ, γ ∈ [pi/2, pi/2]; If the angle between oP and the x/X axle is α, α ∈ [0,2 π];

2) serve as to rotate on the yoz plane with the ow axle of uvwo coordinate system with reference to zero-bit, promptly ow, oZ, oz, oQ, oY and oy all in one plane, so, ∠ Zoz=β and ∠ woZ=γ; If the ow axle not on the yoz plane, just through rotation oY axle, rotates to the yoz plane with the ow axle, and as zero-bit;

3) establish ow; Ou; The vector of unit length of ov and oY is respectively

and

its vector at the xyzo coordinate system and is expressed as:

${\left[\begin{array}{c}{\stackrel{\‾}{n}}_{\mathrm{ow}}\\ {\stackrel{\‾}{n}}_{\mathrm{oY}}\\ {\stackrel{\‾}{n}}_{\mathrm{ou}}\end{array}\right]}_{\mathrm{xyzo}}={\left[\begin{array}{ccc}0& -\cos (\mathrm{\β}+\mathrm{\γ})& \sin (\mathrm{\β}+\mathrm{\γ})\\ 0& \cos \mathrm{\β}& \sin \mathrm{\β}\\ \cos \mathrm{\α}& \sin \mathrm{\α}\·\cos (\mathrm{\β}+\mathrm{\γ})& \sin \mathrm{\α}\·\sin (\mathrm{\β}+\mathrm{\γ})\end{array}\right]}^T$

These 4 vectors are equivalent to the xyzo coordinate system in the expression of XYZo coordinate system and have been rotated counterclockwise angle beta around the x/X axle, and its rotation matrix is:

$R_x=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\β}& -\sin \mathrm{\β}\\ 0& \sin \mathrm{\β}& \cos \mathrm{\β}\end{array}\right]$

Then, these 4 vectors being expressed as under the XYZo coordinate system:

${\left[\begin{array}{c}{\stackrel{\‾}{n}}_{\mathrm{oz}}\\ {\stackrel{\‾}{n}}_{\mathrm{oY}}\\ {\stackrel{\‾}{n}}_{\mathrm{ou}}\end{array}\right]}_{\mathrm{XYZo}}=R_x\·{\left[\begin{array}{c}{\stackrel{\‾}{n}}_{\mathrm{oz}}\\ {\stackrel{\‾}{n}}_{\mathrm{oY}}\\ {\stackrel{\‾}{n}}_{\mathrm{ou}}\end{array}\right]}_{\mathrm{xyzo}}=\left[\begin{array}{ccc}0& \sin \mathrm{\β}& \cos \mathrm{\β}\\ 0& 1& 0\\ 0& \cos \mathrm{\γ}& \sin \mathrm{\γ}\end{array}\right]$

Vector

is rotated counterclockwise angle θ around the oY axle under the XYZo coordinate system, its rotation matrix is:

$R_Y=\left[\begin{array}{ccc}\cos \mathrm{\θ}& 0& \sin \mathrm{\θ}\\ 0& 1& 0\\ -\sin \mathrm{\θ}& 0& \cos \mathrm{\θ}\end{array}\right]$

Hutchison

Rotate subsequent vector

which is expressed as follows:

${\stackrel{\‾}{n}}_{\mathrm{\θ}}=R_Y\·{\stackrel{\‾}{n}}_{\mathrm{XYZo}}=\left[\begin{array}{ccc}\cos \mathrm{\θ}& 0& \sin \mathrm{\θ}\\ 0& 1& 0\\ -\sin \mathrm{\θ}& 0& \cos \mathrm{\θ}\end{array}\right]\·\left[\begin{array}{c}0\\ \cos \mathrm{\γ}\\ \sin \mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}\sin \mathrm{\γ}\·\sin \mathrm{\θ}\\ \cos \mathrm{\γ}\\ \sin \mathrm{\γ}\·\cos \mathrm{\θ}\end{array}\right]$

If vector

With horizontal plane angle be θ _u, vector With

The angle that constitutes is θ _Un, θ then _Un+ θ _u=pi/2, and θ _UnCosine be:

${\cos \mathrm{\θ}}_{\mathrm{un}}={\sin \mathrm{\θ}}_u={\stackrel{\‾}{n}}_{\mathrm{\θ}}\·{\stackrel{\‾}{n}}_{\mathrm{oz}}=\sin \mathrm{\β}\·\cos \mathrm{\γ}+\cos \mathrm{\β}\·\sin \mathrm{\γ}\·\cos \mathrm{\θ}$

The magnitude of voltage of double-shaft tilt angle sensor output is sin θ just _u, making it is the x axle output voltage values of double-shaft tilt angle sensor, that is:

x=sinα·cosγ·sinβ-cosα·cosβ·sinθ+sinα·sinγ·cosβ·cosθ

Equally, also have for vector

:

y=cosα·cosγ·sinβ+sinα·cosβ·sinθ+cosα·sinγ·cosβ·cosθ

4 variable: α, β, γ and θ are arranged here; When sensor is exported 3 groups of data [x ₁, y ₁], [x ₂, y ₂], [x ₃, y ₃], just can obtain this 4 variablees; Like this, double-shaft tilt angle sensor can calculate its space anglec of rotation through the output of detecting sensor 4 positions in the space in the anglec of rotation in space.

Than prior art, the present invention has following beneficial effect:

The present invention sets up its mathematical model, and obtains its analytic solution through spatial relation between sensor and the turning axle, thereby calculates around the angle of turning axle rotation.So the present invention can the measurement space anglec of rotation, and this turning axle is not necessarily parallel and surface level, as long as out of plumb and surface level.Simultaneously, owing in the space analysis process, consider the mounting process of sensor or its module, not requiring it must level install, and this will reduce the service condition of sensor.

Through application of the present invention, turning axle and horizontal plane angle less than 75 ° situation under, can realize ± 15 ° measurement range, accuracy of measurement reaches in 0.2 °; Turning axle and horizontal plane angle less than 15 ° situation under, can realize ± 70 ° measurement range, accuracy of measurement reaches in 0.1 °.

Description of drawings

Fig. 1 is the installation model synoptic diagram of double-shaft tilt angle sensor of the present invention.

Embodiment

Below in conjunction with accompanying drawing the present invention is done and to describe in further detail:

Referring to Fig. 1, the space rotation angle measurement method that the present invention is based on double-shaft tilt angle sensor is specially:

Two axles of double-shaft tilt angle sensor are orthogonal, and its output voltage is to be the sine value of the angle of reference with the surface level.With the turning axle is the Y axle, establishes to be rotated counterclockwise direction for just, and the anglec of rotation is θ, and it is projected as the y axle surface level, and two axle intersection points are o, establish the angle β of turning axle and surface level, i.e. β=∠ Yoy, and β ∈ [0, pi/2], as shown in Figure 1.The z axle is set the x direction of principal axis perpendicular to surface level, constitutes right-handed Cartesian coordinate system xyzo.Make X axle and x axle overlap, the vertical X of Z axle, Y axle constitute cartesian coordinate system XYZo equally.If two axles of obliquity sensor are u and v, its intersection point fixes on the o point, because ou and ov are orthogonal, the normal vector of establishing the uov plane that o orders is ow; And ou, ov and ow are unit length vector, and the unit length of ou is made as oP=|ou|, and oP is projected as oQ on the yoz plane; Angle between definition oQ and the turning axle Y is γ, γ ∈ [pi/2, pi/2]; If the angle between oP and the x/X axle is α, α ∈ [0,2 π].

With the ow axle of uvwo coordinate system serves as to rotate with reference to zero-bit on the yoz plane, promptly ow, oZ, oz, oQ, oY and oy all in one plane, so, ∠ Zoz=β and ∠ woZ=γ.If the ow axle not on the yoz plane, just through rotation oY axle, rotates to the yoz plane with the ow axle, and as zero-bit.

If ow; Ou; The vector of unit length of ov and oY is respectively

and

its vector at the xyzo coordinate system and is expressed as:

${\left[\begin{array}{c}{\stackrel{\‾}{n}}_{\mathrm{ow}}\\ {\stackrel{\‾}{n}}_{\mathrm{oY}}\\ {\stackrel{\‾}{n}}_{\mathrm{ou}}\end{array}\right]}_{\mathrm{xyzo}}={\left[\begin{array}{ccc}0& -\cos (\mathrm{\β}+\mathrm{\γ})& \sin (\mathrm{\β}+\mathrm{\γ})\\ 0& \cos \mathrm{\β}& \sin \mathrm{\β}\\ \cos \mathrm{\α}& \sin \mathrm{\α}\·\cos (\mathrm{\β}+\mathrm{\γ})& \sin \mathrm{\α}\·\sin (\mathrm{\β}+\mathrm{\γ})\end{array}\right]}^T$

These 4 vectors are equivalent to the xyzo coordinate system in the expression of XYZo coordinate system and have been rotated counterclockwise angle beta around the x/X axle, and its rotation matrix is:

$R_x=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\β}& -\sin \mathrm{\β}\\ 0& \sin \mathrm{\β}& \cos \mathrm{\β}\end{array}\right]$

So, these 4 vectors being expressed as under the XYZo coordinate system:

${\left[\begin{array}{c}{\stackrel{\‾}{n}}_{\mathrm{oz}}\\ {\stackrel{\‾}{n}}_{\mathrm{oY}}\\ {\stackrel{\‾}{n}}_{\mathrm{ou}}\end{array}\right]}_{\mathrm{XYZo}}=R_x\·{\left[\begin{array}{c}{\stackrel{\‾}{n}}_{\mathrm{oz}}\\ {\stackrel{\‾}{n}}_{\mathrm{oY}}\\ {\stackrel{\‾}{n}}_{\mathrm{ou}}\end{array}\right]}_{\mathrm{xyzo}}=\left[\begin{array}{ccc}0& \sin \mathrm{\β}& \cos \mathrm{\β}\\ 0& 1& 0\\ 0& \cos \mathrm{\γ}& \sin \mathrm{\γ}\end{array}\right]$

Vector

is rotated counterclockwise angle θ around the oY axle under the XYZo coordinate system, its rotation matrix is:

$R_Y=\left[\begin{array}{ccc}\cos \mathrm{\θ}& 0& \sin \mathrm{\θ}\\ 0& 1& 0\\ -\sin \mathrm{\θ}& 0& \cos \mathrm{\θ}\end{array}\right]$

Hutchison

Rotate subsequent vector

which is expressed as follows:

${\stackrel{\‾}{n}}_{\mathrm{\θ}}=R_Y\·{\stackrel{\‾}{n}}_{\mathrm{XYZo}}=\left[\begin{array}{ccc}\cos \mathrm{\θ}& 0& \sin \mathrm{\θ}\\ 0& 1& 0\\ -\sin \mathrm{\θ}& 0& \cos \mathrm{\θ}\end{array}\right]\·\left[\begin{array}{c}0\\ \cos \mathrm{\γ}\\ \sin \mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}\sin \mathrm{\γ}\·\sin \mathrm{\θ}\\ \cos \mathrm{\γ}\\ \sin \mathrm{\γ}\·\cos \mathrm{\θ}\end{array}\right]$

If vector

With horizontal plane angle be θ _u, vector With

The angle that constitutes is θ _Un, then can know θ by figure _Un+ θ _u=pi/2, and θ _UnCosine be:

${\cos \mathrm{\θ}}_{\mathrm{un}}={\sin \mathrm{\θ}}_u={\stackrel{\‾}{n}}_{\mathrm{\θ}}\·{\stackrel{\‾}{n}}_{\mathrm{oz}}=\sin \mathrm{\β}\·\cos \mathrm{\γ}+\cos \mathrm{\β}\·\sin \mathrm{\γ}\·\cos \mathrm{\θ}$

The magnitude of voltage of obliquity sensor output is sin θ just _u, making it is the x axle output voltage values of sensor, that is:

x=sinα·cosγ·sinβ-cosα·cosβ·sinθ+sinα·sinγ·cosβ·cosθ

Equally; For vector

similar result is arranged also, that is:

y=cosα·cosγ·sinβ+sinα·cosβ·sinθ+cosα·sinγ·cosβ·cosθ

4 variable: α, β, γ and θ are arranged here.When sensor is exported 3 groups of data [x ₁, y ₁], [x ₂, y ₂], [x ₃, y ₃], just can obtain this 4 variablees.

Like this, double-shaft tilt angle sensor can just can calculate its space anglec of rotation through the output of detecting sensor 4 positions in the space in the anglec of rotation in space.

The present invention has carried out experimental applications in the detection of the rudder face anglec of rotation, the turning axle of this rudder face becomes 70 ° angle with level, and rotation angle range is ± 45 °, requires accuracy of measurement less than 0.2 °.The present invention can also use on tank turret.When tank is positioned on the plane that is not level, need fort be raised or when rotating to an angle, this method can provide predetermined angular accurately.

Claims (1)

1. the space rotation angle measurement method based on double-shaft tilt angle sensor is characterized in that, may further comprise the steps:

1) make two axles of double-shaft tilt angle sensor vertical each other, its output voltage is to be the sine value of the angle of reference with the surface level; With the turning axle is the Y axle, establishes to be rotated counterclockwise direction for just, and the anglec of rotation is θ, and it is projected as the y axle surface level, and two axle intersection points are o, establish the angle β of turning axle and surface level, i.e. β=∠ Yoy, β ∈ [0, pi/2]; The z axle is set the x direction of principal axis perpendicular to surface level, constitutes right-handed Cartesian coordinate system xyzo; Make X axle and x axle overlap, the vertical X of Z axle, Y axle constitute cartesian coordinate system XYZo equally; If two axles of double-shaft tilt angle sensor are u and v, its intersection point fixes on the o point, because ou and ov are orthogonal, the normal vector of establishing the uov plane that o orders is ow; And ou, ov and ow are unit length vector, and the unit length of ou is made as oP=|ou|, and oP is projected as oQ on the yoz plane; Angle between definition oQ and the turning axle Y is γ, γ ∈ [pi/2, pi/2]; If the angle between oP and the x/X axle is α, α ∈ [0,2 π];

2) serve as to rotate on the yoz plane with the ow axle of uvwo coordinate system with reference to zero-bit, promptly ow, oZ, oz, oQ, oY and oy all in one plane, so, ∠ Zoz=β and ∠ woZ=γ; If the ow axle not on the yoz plane, just through rotation oY axle, rotates to the yoz plane with the ow axle, and as zero-bit;

3) Let ow, ou, ov and oY unit vectors are

and

in xyzo vector coordinates expressed as:

${\left[\begin{array}{c}{\stackrel{\‾}{n}}_{\mathrm{ow}}\\ {\stackrel{\‾}{n}}_{\mathrm{oY}}\\ {\stackrel{\‾}{n}}_{\mathrm{ou}}\end{array}\right]}_{\mathrm{xyzo}}={\left[\begin{array}{ccc}0& -\cos (\mathrm{\β}+\mathrm{\γ})& \sin (\mathrm{\β}+\mathrm{\γ})\\ 0& \cos \mathrm{\β}& \sin \mathrm{\β}\\ \cos \mathrm{\α}& \sin \mathrm{\α}\·\cos (\mathrm{\β}+\mathrm{\γ})& \sin \mathrm{\α}\·\sin (\mathrm{\β}+\mathrm{\γ})\end{array}\right]}^T$

These 4 vectors are equivalent to the xyzo coordinate system in the expression of XYZo coordinate system and have been rotated counterclockwise angle beta around the x/X axle, and its rotation matrix is:

$R_x=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\β}& -\sin \mathrm{\β}\\ 0& \sin \mathrm{\β}& \cos \mathrm{\β}\end{array}\right]$

Then, these 4 vectors being expressed as under the XYZo coordinate system:

${\left[\begin{array}{c}{\stackrel{\‾}{n}}_{\mathrm{oz}}\\ {\stackrel{\‾}{n}}_{\mathrm{oY}}\\ {\stackrel{\‾}{n}}_{\mathrm{ou}}\end{array}\right]}_{\mathrm{XYZo}}=R_x\·{\left[\begin{array}{c}{\stackrel{\‾}{n}}_{\mathrm{oz}}\\ {\stackrel{\‾}{n}}_{\mathrm{oY}}\\ {\stackrel{\‾}{n}}_{\mathrm{ou}}\end{array}\right]}_{\mathrm{xyzo}}=\left[\begin{array}{ccc}0& \sin \mathrm{\β}& \cos \mathrm{\β}\\ 0& 1& 0\\ 0& \cos \mathrm{\γ}& \sin \mathrm{\γ}\end{array}\right]$

Vector

is rotated counterclockwise angle θ around the oY axle under the XYZo coordinate system, its rotation matrix is:

$R_Y=\left[\begin{array}{ccc}\cos \mathrm{\θ}& 0& \sin \mathrm{\θ}\\ 0& 1& 0\\ -\sin \mathrm{\θ}& 0& \cos \mathrm{\θ}\end{array}\right]$

Hutchison

Rotate subsequent vector

which is expressed as follows:

${\stackrel{\‾}{n}}_{\mathrm{\θ}}=R_Y\·{\stackrel{\‾}{n}}_{\mathrm{XYZo}}=\left[\begin{array}{ccc}\cos \mathrm{\θ}& 0& \sin \mathrm{\θ}\\ 0& 1& 0\\ -\sin \mathrm{\θ}& 0& \cos \mathrm{\θ}\end{array}\right]\·\left[\begin{array}{c}0\\ \cos \mathrm{\γ}\\ \sin \mathrm{\λ}\end{array}\right]=\left[\begin{array}{c}\sin \mathrm{\γ}\·\sin \mathrm{\θ}\\ \cos \mathrm{\γ}\\ \sin \mathrm{\γ}\·\cos \mathrm{\θ}\end{array}\right]$

If vector

With horizontal plane angle be θ _u, vector

With

The angle that constitutes is θ _Un, θ then _Un+ θ _u=pi/2, and θ _UnCosine be:

${\cos \mathrm{\θ}}_{\mathrm{un}}={\sin \mathrm{\θ}}_u={\stackrel{\‾}{n}}_{\mathrm{\θ}}\·{\stackrel{\‾}{n}}_{\mathrm{oz}}=\sin \mathrm{\β}\·\cos \mathrm{\γ}+\cos \mathrm{\β}\·\sin \mathrm{\γ}\·\cos \mathrm{\θ}$

The magnitude of voltage of double-shaft tilt angle sensor output is sin θ just _u, making it is the x axle output voltage values of double-shaft tilt angle sensor, that is:

x=sinα·cosγ·sinβ-cosα·cosβ·sinθ+sinα·sinγ·cosβ·cosθ

Equally, also have for vector

:

y=cosα·cosγ·sinβ+sinα·cosβ·sinθ+cosα·sinγ·cosβ·cosθ

4 variable: α, β, γ and θ are arranged here; When sensor is exported 3 groups of data [x ₁, y ₁], [x ₂, y ₂], [x ₃, y ₃], just can obtain this 4 variablees; Like this, double-shaft tilt angle sensor can calculate its space anglec of rotation through the output of detecting sensor 4 positions in the space in the anglec of rotation in space.

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