CN108458714B - Euler angle solving method without gravity acceleration in attitude detection system - Google Patents

Euler angle solving method without gravity acceleration in attitude detection system Download PDF

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CN108458714B
CN108458714B CN201810027570.8A CN201810027570A CN108458714B CN 108458714 B CN108458714 B CN 108458714B CN 201810027570 A CN201810027570 A CN 201810027570A CN 108458714 B CN108458714 B CN 108458714B
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田新诚
徐小龙
周乐来
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Abstract

The invention discloses a posture detection deviceThe Euler angle solving method without gravity acceleration in the measurement system is realized based on an MARG sensor, wherein the MARG sensor comprises a three-axis gyroscope, a three-axis accelerometer and a three-axis magnetometer, and a navigation coordinate system and a carrier coordinate system of the attitude detection system are firstly determined; calculating a coordinate transformation matrix required for rotating the navigation coordinate system to the carrier coordinate system
Figure DDA0001545452010000011
The elements of the matrix are represented by roll, pitch and yaw angles in euler angles; collecting measurements of a three-axis accelerometer and a three-axis magnetometerba,bm; from measurements of a three-axis accelerometer and a three-axis magnetometerba,bm and coordinate transformation matrix
Figure DDA0001545452010000012
And obtaining an Euler angle calculation formula without the gravity acceleration. The Euler angle of the measured object is solved by using the measured values of the three-axis accelerometer and the three-axis magnetometer, the obtained calculation formula does not contain the gravity acceleration, the influence of the gravity acceleration in the process of solving the attitude angle is completely eliminated, and therefore the accuracy of attitude detection is improved.

Description

Euler angle solving method without gravity acceleration in attitude detection system
Technical Field
The invention relates to the technical field of attitude detection by utilizing a MARG sensor for attitude detection, in particular to a Euler angle solving method without gravity acceleration in an attitude detection system.
Background
With the increasing development of Micro-Electro-Mechanical systems (MEMS), the MARG (Angular Rate, and yield) sensor is increasingly applied in the field of attitude detection. The accurate detection of the object posture is the basis for other intensive researches.
The principle of object attitude detection using the MARG sensor is as follows: firstly, a navigation coordinate system and a carrier coordinate system of the attitude detection system are determined, and a coordinate transformation matrix required for rotating the navigation coordinate system to the carrier coordinate system is calculated, wherein elements in the coordinate transformation matrix are represented by a roll angle, a yaw angle and a pitch angle in Euler angles. Then, the roll angle and the pitch angle of the detected object are calculated through a coordinate transformation matrix according to the triaxial acceleration measured by the triaxial accelerometer, and the yaw angle of the detected object is calculated through the triaxial magnetic field information measured by the triaxial magnetometer according to the coordinate transformation matrix. And finally, obtaining the real-time Euler angle of the detected object, thereby realizing the function of posture detection.
However, in the current posture measurement system based on the MARG sensor, the gravity acceleration is mostly introduced into the calculation formula in the euler angle, that is, the gravity acceleration is introduced into the calculation formula as a known condition. However, since the gravitational acceleration is not a constant value, the value thereof changes with the difference of the altitude and the latitude and longitude of the earth. Also, since the value of the gravitational acceleration is not a finite decimal number, it is necessary to retain a certain number of significant digits when it is brought as a constant value.
The two points can cause the accuracy of the attitude detection to be reduced, so that the search for the Euler angle calculation formula without the gravity acceleration has important significance for improving the accuracy of the attitude detection.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides a Euler angle solving method without gravity acceleration in an attitude detection system.
The invention adopts the following technical scheme:
a Euler angle solving method without gravity acceleration in an attitude detection system is realized based on a MARG sensor, wherein the MARG sensor comprises a three-axis gyroscope, a three-axis accelerometer and a three-axis magnetometer, and comprises the following steps:
determining a navigational coordinate system OX of an attitude detection systemnYnZnAnd a carrier coordinate system OXbYbZb；
Calculating a coordinate transformation matrix required for rotating the navigation coordinate system to the carrier coordinate system
Figure BDA0001545451990000021
The elements of the matrix are represented by roll, pitch and yaw angles in euler angles;
collecting measurements of a three-axis accelerometer and a three-axis magnetometerba,bm；
From measurements of a three-axis accelerometer and a three-axis magnetometerba,bm and coordinate transformation matrix
Figure BDA0001545451990000022
Obtaining an Euler angle calculation formula without gravity acceleration, wherein the Euler angle comprises a roll angle
Figure BDA0001545451990000023
Pitch angle θ and yaw angle ψ.
Further, regarding the determination of the navigation coordinate system and the carrier coordinate system, selecting a northeast coordinate system as the navigation coordinate system, wherein the carrier coordinate system follows a right hand rule, an origin of the carrier coordinate system coincides with a center of mass of the carrier, an X axis is parallel to an axis of the carrier and points to the front of the carrier, a Y axis is perpendicular to the X axis and points to the right of the carrier, and a Z axis is perpendicular to an XY plane and points to the lower of the carrier.
Furthermore, the rotation matrix from the navigation coordinate system to the carrier coordinate system is different due to the difference between the selected navigation coordinate system and the carrier coordinate system, and when the navigation coordinate system is the northeast coordinate system, the navigation coordinate system OX is usednYnZnRotating according to the sequence of Z → Y → X, wherein the direction cosine matrixes of the three rotations are respectively Cz，Cz，CzCan be rotated to the same position as the carrier coordinate system OXbYbZbOverlapping;
wherein
Figure BDA0001545451990000024
Then, a coordinate transformation matrix expressed by euler angles is obtained:
Figure BDA0001545451990000025
wherein the content of the first and second substances,
Figure BDA0001545451990000026
to navigate the coordinate system to the rotation matrix of the carrier coordinate system,
Figure BDA0001545451990000027
theta, psi are respectively the roll angle, pitch angle and yaw angle in euler angles.
Further, the measured values of the three-axis accelerometer and the three-axis magnetometer are collectedba,bm, whereinba＝[bax,bay,baz]，bm＝[bmx,bmy,bmz]，ba is the measured value of the three-axis accelerometer in the carrier coordinate system,bax,bay,bazthe components of the measured value of the triaxial accelerometer on three coordinate axes of a carrier coordinate system are respectively;bm is the measured value of the three-axis magnetometer in the carrier coordinate system,bmx,bmy,bmzthe components of the measured value of the three-axis magnetometer on three coordinate axes of the carrier coordinate system are respectively.
Further, based on the measurements of the three-axis accelerometer and the three-axis magnetometerba,bm and coordinate transformation matrix
Figure BDA0001545451990000028
Deriving roll angle without gravitational acceleration
Figure BDA0001545451990000031
The pitch angle theta and yaw angle psi are calculated by first calculating the roll angle
Figure BDA0001545451990000032
Pitch angle θ:
the gravitational field under the navigation coordinate system isna＝[0,0,g]Wherein g is gravity acceleration, and three-axis acceleration is carried out under a carrier coordinate systemThe speedometer measures values ofba＝[bax,bay,baz]According to the principle of coordinate transformation
Figure BDA0001545451990000033
Is provided with
Figure BDA0001545451990000034
The gravity acceleration g can be eliminated by taking the ratio of the second formula to the third formula in the equation set to obtain the roll angle without the gravity acceleration g
Figure BDA0001545451990000035
Formula for calculating pitch angle theta
Figure BDA0001545451990000036
Figure BDA0001545451990000037
When calculating the yaw angle psi, for simplifying the calculation, it is assumed that only the declination exists in the geomagnetic field and the declination is zero, and the magnetic force field in the navigation coordinate system isnm＝(nmx,0,nmz) The magnetic force field under the carrier coordinate system isbm＝(bmx,bmy,bmz) According to the principle of coordinate transformation
Figure BDA0001545451990000038
Is provided with
Figure BDA0001545451990000039
The formula for calculating the yaw angle can be obtained as follows:
Figure BDA00015454519900000310
compared with the prior art, the invention has the beneficial effects that:
the invention solves the Euler angle of the measured object by using the measured values of the three-axis accelerometer and the three-axis magnetometer, and the obtained Euler angle calculation formula does not contain the gravity acceleration, thereby completely eliminating the influence of the gravity acceleration when the Euler angle is solved and improving the accuracy of attitude detection.
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The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flow chart of a method of the present invention;
fig. 2(a) -fig. 2(b) illustrate a coordinate system selection method provided by the present invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As described in the background, the prior art has shortcomings, and in order to solve the above technical problems, the present application proposes a method for solving euler angles in a micro-electromechanical system based on an accelerometer and a magnetometer.
In a typical embodiment of the present application, as shown in fig. 1, a method for solving euler angles in a micro-electromechanical system based on an accelerometer and a magnetometer is provided, and it is found through research that in an attitude detection algorithm using a MARG attitude detection unit to detect an object attitude, since a gravitational acceleration is taken as a known quantity when an euler angle is calculated, accuracy of attitude detection is reduced.
In view of this, the present invention derives an euler angle calculation formula that completely eliminates the influence of the gravitational acceleration according to the measurement values of the accelerometer and magnetometer of the attitude measurement unit, and improves the accuracy of the attitude detection system. The invention is further described with reference to the accompanying drawings and examples.
The implementation method of the invention comprises the following steps:
the first step is as follows: determining a navigational coordinate system OX of an attitude detection systemnYnZnAnd a carrier coordinate system OXbYbZb(ii) a Fig. 2(a) -2 (b) show a navigation coordinate system and a carrier coordinate system selection method provided by the method, the navigation coordinate system selects a north east earth (NED) coordinate system, the carrier coordinate system follows a right-hand rule, an origin of the carrier coordinate system coincides with a center of mass of the carrier, an X axis is parallel to a carrier axis and points to the front of the carrier, a Y axis is perpendicular to the X axis and points to the right of the carrier, and a Z axis is perpendicular to an XY plane and points to the lower of the carrier.
The second step is that: calculating a coordinate transformation matrix required for rotating the navigation coordinate system to the carrier coordinate system
Figure BDA0001545451990000041
The elements of the matrix are represented by roll, pitch and yaw angles in euler angles. Will navigate the coordinate system OXnYnZnRotating according to the sequence of Z → Y → X, wherein the direction cosine matrixes of the three rotations are respectively Cz，Cz，CzIt can be rotated to the same as the carrier coordinate system OXbYbZbIs superposed therein
Figure BDA0001545451990000042
Then, a coordinate transformation matrix expressed by Euler angles can be obtained
Figure BDA0001545451990000051
Wherein the content of the first and second substances,
Figure BDA0001545451990000052
a coordinate transformation matrix for the navigation coordinate system to the carrier coordinate system,
Figure BDA0001545451990000053
theta, psi are respectively the roll angle, pitch angle and yaw angle in euler angles.
The third step: collecting measurements of a three-axis accelerometer and a three-axis magnetometerba,bAnd m is selected. Whereinba＝[bax,bay,baz]，bm＝[bmx,bmy,bmz]，ba is the measured value of the three-axis accelerometer in the carrier coordinate system,bax,bay,bazthe components of the measured value of the triaxial accelerometer on three coordinate axes of a carrier coordinate system are respectively;bm is the measured value of the three-axis magnetometer in the carrier coordinate system,bmx,bmy,bmzthe components of the measured value of the three-axis magnetometer on three coordinate axes of the carrier coordinate system are respectively.
The fourth step: from measurements of a three-axis accelerometer and a three-axis magnetometerba,bm and coordinate transformation matrix
Figure BDA0001545451990000054
Calculating roll angle without involving gravitational acceleration
Figure BDA0001545451990000055
A pitch angle θ, and a yaw angle ψ. Firstly, the roll angle is calculated
Figure BDA0001545451990000056
Pitch angle θ: the gravitational field under the navigation coordinate system isna＝[0,0,g]Wherein g is the acceleration of gravity, and the measured value of the triaxial accelerometer in the carrier coordinate system isba＝[bax,bay,baz]According to the principle of coordinate transformation
Figure BDA0001545451990000057
Is provided with
Figure BDA0001545451990000058
The gravity acceleration g can be eliminated by taking the ratio of the second formula to the third formula in the equation set to obtain the roll angle without the gravity acceleration g
Figure BDA0001545451990000059
Formula for calculating pitch angle theta
Figure BDA00015454519900000510
Figure BDA00015454519900000511
When calculating the yaw angle psi, for simplifying the calculation, it is assumed that only the declination exists in the geomagnetic field and the declination is zero, and the magnetic force field in the navigation coordinate system isnm＝(nmx,0,nmz) The magnetic force field under the carrier coordinate system isbm＝(bmx,bmy,bmz) According to the principle of coordinate transformation
Figure BDA00015454519900000512
Is provided with
Figure BDA00015454519900000513
The formula for calculating the yaw angle can be obtained as follows:
Figure BDA0001545451990000061
the technical scheme of the invention is not limited to the given coordinate system selection mode, and in the actual attitude detection process, because the coordinate system selection mode is various, but the euler angle calculation formula without the influence of gravity acceleration g is calculated according to the MARG accelerometer and the magnetometer, and the derivation processes of the formula are completely the same, the correction of a specific coordinate system by a person skilled in the art under the thought of the invention still belongs to the technical scheme of the invention.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (3)

1. A Euler angle solving method without gravity acceleration in an attitude detection system is realized based on a MARG sensor, wherein the MARG sensor comprises a three-axis gyroscope, a three-axis accelerometer and a three-axis magnetometer;
according to the measured values of the three-axis accelerometer and the three-axis magnetometer in the MARG sensor, the Euler angle of the measured object is calculated, the calculation method is not influenced by the gravity acceleration, and the influence of the gravity acceleration in the process of solving the Euler angle can be completely eliminated;
the method is characterized by comprising the following steps:
determining a navigational coordinate system OX of an attitude detection systemnYnZnAnd a carrier coordinate system OXbYbZb；
Calculating a coordinate transformation matrix required for rotating the navigation coordinate system to the carrier coordinate system
Figure FDA0002706354140000019
The elements of the matrix are represented by roll, pitch and yaw angles in euler angles;
the rotation matrix from the navigation coordinate system to the carrier coordinate system is different due to the difference between the selected navigation coordinate system and the carrier coordinate system, and when the navigation coordinate system is a northeast coordinate system, the navigation coordinate system OX is usednYnZnRotating according to the sequence of Z → Y → X, wherein the direction cosine matrixes of the three rotations are respectively Cz，Cy，CxCan be rotated to the same position as the carrier coordinate system OXbYbZbIs superposed therein
Figure FDA0002706354140000011
Then, a coordinate transformation matrix expressed by euler angles is obtained:
Figure FDA0002706354140000012
wherein the content of the first and second substances,
Figure FDA0002706354140000013
to navigate the coordinate system to the rotation matrix of the carrier coordinate system,
Figure FDA0002706354140000014
theta and psi are respectively a roll angle, a pitch angle and a yaw angle in Euler angles;
collecting measurements of a three-axis accelerometer and a three-axis magnetometerba,bm；
From measurements of a three-axis accelerometer and a three-axis magnetometerba,bm and coordinate transformation matrix
Figure FDA0002706354140000015
Obtaining an Euler angle calculation formula without gravity acceleration, wherein the Euler angle comprises a roll angle
Figure FDA0002706354140000016
The pitch angle theta and the yaw angle psi are calculated in the following specific process:
firstly, the roll angle is calculated
Figure FDA0002706354140000017
Pitch angle θ: the gravitational field under the navigation coordinate system isna＝[0,0,g]Wherein g is the acceleration of gravity, and the measured value of the triaxial accelerometer in the carrier coordinate system isba＝[bax,bay,baz]According to the principle of coordinate transformation
Figure FDA0002706354140000018
Is provided with
Figure FDA0002706354140000021
The gravity acceleration g can be eliminated by taking the ratio of the second formula to the third formula in the equation set to obtain the roll angle without the gravity acceleration g
Figure FDA0002706354140000022
Formula for calculating pitch angle theta
Figure FDA0002706354140000023
Figure FDA0002706354140000024
When calculating the yaw angle psi, for simplifying the calculation, it is assumed that only the declination exists in the geomagnetic field and the declination is zero, and the magnetic force field in the navigation coordinate system isnm＝(nmx,0,nmz) The magnetic force field under the carrier coordinate system isbm＝(bmx,bmy,bmz) According to the principle of coordinate transformation
Figure FDA0002706354140000025
Is provided with
Figure FDA0002706354140000026
Obtaining a calculation formula of the yaw angle:
Figure FDA0002706354140000027
2. the euler's angle solution method without gravitational acceleration in an attitude sensing system according to claim 1, wherein, regarding the determination of the navigation coordinate system and the carrier coordinate system, the northeast earth coordinate system is selected as the navigation coordinate system, the carrier coordinate system follows the rule of right hand, the origin of the carrier coordinate system coincides with the center of mass of the carrier, the X-axis is parallel to the carrier axis and points to the front of the body, the Y-axis is perpendicular to the X-axis and points to the right of the carrier, and the Z-axis is perpendicular to the XY-plane and points to the lower of the carrier.
3. The method of claim 1, wherein the method comprises collecting measurements from a three-axis accelerometer and a three-axis magnetometerba＝[bax,bay,baz]，bm＝[bmx,bmy,bmz]Wherein, in the step (A),ba is the measured value of the three-axis accelerometer in the carrier coordinate system,bax,bay,bazthe components of the measured value of the triaxial accelerometer on three coordinate axes of a carrier coordinate system are respectively;bm is the measured value of the three-axis magnetometer in the carrier coordinate system,bmx,bmy,bmzthe components of the measured value of the three-axis magnetometer on three coordinate axes of the carrier coordinate system are respectively.
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CN113672862B (en) * 2021-10-22 2021-12-31 中国石油大学胜利学院 Euler angle optimization method under condition of measurement vector component missing
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