CN112902828B - Angle calculation method - Google Patents
Angle calculation method Download PDFInfo
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- CN112902828B CN112902828B CN202110067897.XA CN202110067897A CN112902828B CN 112902828 B CN112902828 B CN 112902828B CN 202110067897 A CN202110067897 A CN 202110067897A CN 112902828 B CN112902828 B CN 112902828B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
- G01B7/30—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring angles or tapers; for testing the alignment of axes
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/22—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
- G01B7/004—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring coordinates of points
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
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Abstract
The invention discloses an angle calculation method, which comprises the following steps: establishing three dimension vectors corresponding to the object posture, and determining an initial model state of the object in space; the acceleration, angular velocity and magnetometer data of the collected object are brought into an algorithm to obtain quaternions describing the current gesture of the object; and respectively inserting the defined three-dimensional vectors into 0 to convert the vectors into quaternions, respectively carrying out rotation change calculation on the three quaternions according to the calculated quaternions to obtain three quaternions of the object after spatial rotation, taking the real parts of the three quaternions to obtain three vectors, respectively representing the coordinates of the axis of the object after rotation under a Cartesian coordinate system, and calculating the pitch angle, the roll angle and the yaw angle of the object according to the obtained three-dimensional vectors. The method eliminates the problem of dead lock of the universal joint of the Euler angle, and is a brand new angle calculation mode.
Description
Technical Field
The invention relates to the technical field of angle measurement, in particular to an angle calculation method.
Background
The angle measurement is applied to many aspects of daily life, such as measurement of the joint movement angle of a human body, the prior art is divided into a traditional detection mode and detection by using an MEMS device, the traditional detection mode uses a horizontal instrument and an angle caliper to detect, and the more advanced MEMS device has certain convenience for detecting the angle by fusing acceleration, angular velocity and Euler angle or quaternion generated by a magnetometer of the MEMS.
Because the traditional detection utilizes the characteristics of human error and inconvenience of a horizontal instrument or an angle caliper, the prior art mostly uses Euler angles or quaternions generated after data acquisition and data fusion of MEMS devices to detect, but the Euler angles have the problem of universal joint deadlock, when one rotating shaft is at a certain angle, the angle data of the other shaft is seriously influenced, and the quaternions are not favorable for understanding of people in the application field due to the very abstract expression mode, so the problem to be solved is urgent.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to solve the technical problems of euler angle universal joint deadlock and quaternion display abstraction, and provides a brand-new angle calculation method.
In order to achieve the above task, the present invention adopts the following technical solutions:
the angle calculation method is characterized by comprising the following specific implementation steps:
step S1: the three dimension vectors corresponding to the object posture are established as follows: x (1, 0), y (0, 1, 0), z (0, 1), determining an initial model state of the object in space;
step S2: the acceleration, angular velocity and magnetometer data of the acquired object are brought into a madgwick algorithm to obtain quaternion q (w, x, y, z) describing the current gesture of the object;
step S3: respectively inserting 0 into the vectors of three dimensions defined in the step S1 to be converted into quaternions, marking the quaternions as qx0 (0, 1, 0), qy0 (0, 1, 0), qz0 (0, 1), and then respectively carrying out rotation change calculation on the three quaternions of qx0, qy0 and qz0 according to the quaternions q (w, x, y, z) obtained by calculation in the step S2 to obtain three quaternions of the object after spatial rotation, and taking the real parts of the three quaternions to obtain three vectors, wherein the three vectors respectively represent the coordinates of x, y and z axes of the object after rotation under a Cartesian coordinate system, and are marked as x1 (xx ', xy ', xz '), y1 (yx ', yy ', yz ') and z1 (zx ', zy, zz);
step S4: according to the three-dimensional vector obtained in the step S3, the pitch angle, the roll angle and the yaw angle of the object are obtained through the following calculation:
solving a pitch angle: selecting an x-axis vector x1 (xx ', xy', xz '), dividing xz' by 1 to obtain a sine value of a pitch angle, and then obtaining the pitch angle value by the inverse of the sine value, namely:
sinx＝xz`/1；
pitch＝arcsinx×180/π；
and (5) obtaining a yaw angle: selecting an x-axis vector x1 (xx ', xy', xz '), dividing the xy' coordinate by 1 to obtain a sine value of the yaw angle, and then obtaining the yaw angle value by the inverse of the sine value, namely:
sinz＝xy`/1；
yaw＝arcsinz×180/π；
and (5) calculating a roll angle: selecting a y-axis vector y1 (yx ', yy', yz '), dividing the yz' coordinate by 1 to obtain a sine value of the roll angle, and then obtaining the roll angle value by solving the inverse of the sine value, namely:
siny＝yz`/1；
roll＝arcsiny×180/π。
according to the present invention, the computation process of qx1, qy, qz1 calculated in step S3 is as follows:
first, a conjugated quaternion q-1 of quaternion q (w, x, y, z) is obtained, namely:
mould＝w*w+x*x+y*y+z*z；
q-1＝(w/mould，-x/mould，-y/mould，-z/mould)；
the second step is to calculate three quaternions after rotation, wherein the calculation formula of the cross multiplication of the quaternions is as follows:
q×x＝((wi*xi+wx*xi+wy*xz-wz*xy)；
(wi*xy-wx*xz+wy*xi+wz*xx)；
(wi*xz+wx*xy-wy*xx+wz*xi)；
(wi*xi-wx*xx-wy*xy-wz*xz))；
thus, qx1=qxqx0×q-1 can be finally obtained from qx0 to obtain the transformed object x-axis quaternion qx1 (xw ', xx', xy ', xz');
similarly, qy (yi ', yx', yy ', yz') and qz1 (zi ', zx', xy ', zz') can be obtained;
qx1, qy, the real part of qz1 is the x-axis, y-axis and z-axis coordinates of the object with changed posture in the cartesian coordinate system, and the coordinates are respectively expressed as: x1 (xx ', xy ', xz '), y1 (yx ', yy ', yz '), z1 (zx ', xy ', zz ').
The angle calculation method has the beneficial effects that the problem of dead lock of the universal joint of the Euler angle is solved, and the angle calculation method is a brand new angle calculation mode.
Drawings
FIG. 1 is a schematic flow chart of an angle calculation method of the present invention;
FIG. 2 is an illustration of an angle definition;
FIG. 3 is a pitch waveform;
FIG. 4 is a waveform of Euler angle pitch angle;
FIG. 5 is a waveform diagram of roll angle;
FIG. 6 is a waveform diagram of Euler angle roll angle;
FIG. 7 is a waveform diagram of yaw angle;
fig. 8 is a waveform diagram of euler angle yaw angle;
the present invention will be described in further detail with reference to the accompanying drawings and examples.
Detailed Description
As shown in fig. 1, the present embodiment provides an angle calculating method, including:
setting the sampling frequency of an angular velocity meter, an accelerometer and a magnetometer as 100Hz, calling a madgwick algorithm once every 100Hz, taking the values of the angular velocity, the acceleration and the magnetometer as input and then outputting quaternions q (w, x, y and z), and setting the deltaT of the madgwick algorithm, namely the sampling time interval as 1/100 seconds;
secondly, three vectors x (1, 0), y (0, 1, 0) and z (0, 1) corresponding to the object posture are established, and the initial model state of the object in the space is determined;
thirdly, inputting the acceleration, angular velocity and magnetometer data of the acquired object into a madgwick algorithm to obtain quaternion q (w, x, y, z) describing the current gesture of the object;
fourth, the vectors of three dimensions defined in the first step are respectively inserted into 0 to be changed into quaternions, and are marked as qx0 (0, 1, 0), qy0 (0, 1, 0), qz0 (0, 1), then the quaternions q (w, x, y, z) obtained by calculation according to S2 are respectively calculated on the three quaternions of qx0, qy0 and qz0 to obtain three quaternions of an object after space rotation, the real parts of the three quaternions are taken to obtain three vectors, the three vectors respectively represent the coordinates of x, y and z axes of the object after rotation in a Cartesian coordinate system, and are marked as x1 (xx ', xy ', xz '), y1 (yx '), yx ', yy ', yz 1 (zx, zz '), and the processes of calculating x1, y1, z1 are as follows,
firstly, a conjugated quaternion q-1 of quaternion q (w, x, y, z) is obtained:
mould＝w*w+x*x+y*y+z*z；
q-1＝(w/mould，-x/mould，-y/mould，-z/mould)；
the second step of calculating the cross multiplication calculation formula of the quaternion after rotation is that
q×x＝(wi*xi+wx*xi+wy*xz-wz*xy)；
(wi*xy-wx*xz+wy*xi+wz*xx)；
(wi*xz+wx*xy-wy*xx+wz*xi)；
(wi*xi-wx*xx-wy*xy-wz*xz)；
Thus, qx1=qxqx0×q-1 can be finally obtained from qx0 to obtain the transformed object x-axis quaternion qx1 (xw ', xx', xy ', xz');
similarly, qy (yi ', yx', yy ', yz') and qz1 (zi ', zx', xy ', zz') can be obtained;
the real parts of qx1, qy and qz1 are x-axis, y-axis and z-axis coordinates of the object with changed posture in a Cartesian coordinate system, and the coordinates are respectively x1 (xx ', xy ', xz '), y1 (yx ', yy ', yz ') and z1 (zx ', xy ', zz ');
fifthly, according to the three-dimensional vectors x1, y1 and z1 obtained in the fourth step, the pitch angle, the roll angle and the yaw angle of the object are obtained through the following calculation,
the pitch angle is calculated, an x-axis vector x1 (xx ', xy', xz ') is selected, xz' is divided by 1, the sine value of the pitch angle is calculated, and then the pitch angle value is calculated by inverting the sine value:
sinx＝xz`/1；
pitch＝arcsinx×180/π；
the yaw angle is calculated, an x-axis vector x1 (xx ', xy', xz ') is selected, the xy' coordinates are divided by 1 to calculate a sine value of the yaw angle, and then the sine value is inverted to calculate the yaw angle value:
sinz＝xy`/1；
yaw＝arcsinz×180/π；
the roll angle is calculated, a y-axis vector y1 (yx ', yy', yz ') is selected, the yz' coordinate is divided by 1 to calculate the sine value of the roll angle, and then the sine value is inverted to calculate the roll angle value:
siny＝yz`/1；
roll＝arcsiny×180/π。
as shown in FIG. 2, an angle definition is shown, wherein, when the pitch angle is X1, a point p1 (xx ', xz') is obtained by making a vertical line to an XOZ plane, and an included angle between a connecting line of p1 and an origin O and an X-axis positive half axis is defined as the pitch angle; wherein, the yaw angle is that a point p2 (xx ', xy') is obtained by making a vertical line from X1 to the XOY plane, and an included angle between a connecting line of p2 and an origin O and an X-axis positive half axis is defined as the yaw angle; the roll angle is that a point p3 (yy ', yz ') is obtained by making a perpendicular line from the Y1 plane to the YOZ plane, and an included angle between a connecting line of the yz ' and the origin O and a positive half axis of the Y axis is defined as the roll angle.
As shown in fig. 3 and 4, which are graphs showing the comparison waveforms of the pitch angle and the euler angle, wherein fig. 3 is a waveform in which an object obtained by using the angle calculation method of the present embodiment rotates 360 degrees around the Y axis from 0 degrees, and fig. 4 is a waveform in which an object obtained by using the euler angle rotates 360 degrees around the Y axis from 0 degrees, it can be seen that using the angle calculation method of the present embodiment, the obtained pitch angle variation trend is 0-90, 90-0,0- (-90), and the change of the pitch angle of the euler angle is 0-180, (-180) -0, and the obtained result does not affect the use of the angle calculation method given by the present embodiment as a whole.
As shown in fig. 5 and 6, which are respectively waveforms of roll angle and euler angle, in which fig. 5 is a waveform of an object rotated 360 degrees from 0 degrees around the X-axis by using the angle calculation method of the present embodiment, fig. 6 is a waveform of an object rotated 360 degrees from 0 degrees around the X-axis by using the euler angle, it is apparent from fig. 6 that there is a great change in pitch angle when the roll angle is around 90 degrees, which is in a state of a gimbal deadlock during which the pitch angle is always affected, and the pitch angle is gradually restored when the roll angle is restored from (-90) -0, and fig. 5 is a result obtained by using the angle calculation method of the present embodiment, it can be seen that the pitch angle and yaw angle of the object are not affected during the entire rotation.
Fig. 7 and 8 are waveform diagrams of yaw angle and euler angle yaw angle, respectively, in which fig. 7 is a waveform in which an object obtained by using the angle calculation method of the present embodiment is rotated 360 degrees around the Z axis from 0 degrees, and fig. 8 is a waveform in which an object obtained by using the euler angle is rotated 360 degrees around the Z axis from 0 degrees, it can be seen that using the calculation method of the present embodiment, yaw angle variation trend is 0-90, 90-0,0- (-90), and(-90) -0 undergoes four stages, and the pitch angle of the euler angle is changed to 0-360. In general, the results obtained with the calculation method given in this embodiment do not affect the use.
Claims (2)
1. The angle calculation method is characterized by comprising the following specific implementation steps:
step S1: the three dimension vectors corresponding to the object posture are established as follows: x (1, 0), y (0, 1, 0), z (0, 1), determining an initial model state of the object in space;
step S2: the acceleration, angular velocity and magnetometer data of the acquired object are brought into a madgwick algorithm to obtain quaternion q (w, x, y, z) describing the current gesture of the object;
step S3: respectively inserting vectors of three dimensions defined in the step S1 into 0 to be converted into quaternions, marking the quaternions as qx0 (0, 1, 0), qy0 (0, 1, 0), qz0 (0, 1), and then respectively carrying out rotation change calculation on the three quaternions of qx0, qy0 and qz0 according to the quaternions q (w, x, y, z) obtained by calculation in the step S2 to obtain three quaternions of the object after spatial rotation, taking the real parts of the three quaternions to obtain three vectors, wherein the three vectors respectively represent the coordinates of x, y and z axes of the object after rotation under a Cartesian coordinate system, and are marked as x1 (xx ', xy', xz '), y1 (yx', yy ', yz') and z1 (zx, zy ', zz');
step S4: according to the three-dimensional vector obtained in the step S3, the pitch angle, the roll angle and the yaw angle of the object are obtained through the following calculation:
solving a pitch angle: selecting an x-axis vector x1 (xx ', xy', xz '), dividing xz' by 1 to obtain a sine value of a pitch angle, and then obtaining the pitch angle value by the inverse of the sine value, namely:
sinx＝xz`/1；
pitch＝arcsinx×180/π；
and (5) obtaining a yaw angle: selecting an x-axis vector x1 (xx ', xy', xz '), dividing the xy' coordinate by 1 to obtain a sine value of the yaw angle, and then obtaining the yaw angle value by the inverse of the sine value, namely:
sinz＝xy`/1；
yaw＝arcsinz×180/π；
and (5) calculating a roll angle: selecting a y-axis vector y1 (yx ', yy', yz '), dividing the yz' coordinate by 1 to obtain a sine value of the roll angle, and then obtaining the roll angle value by solving the inverse of the sine value, namely:
siny＝yz`/1；
roll＝arcsiny×180/π。
2. the method of claim 1, wherein the calculating in step S3 is performed by qx1, qy1, and qz1 is performed by:
first, a conjugated quaternion q-1 of quaternion q (w, x, y, z) is obtained, namely:
mould＝w*w+x*x+y*y+z*z；
q-1＝(w/mould,-x/mould,-y/mould,-z/mould)；
the second step is to calculate three quaternions after rotation, wherein the calculation formula of the cross multiplication of the quaternions is as follows:
q×x＝((wi*xi+wx*xi+wy*xz-wz*xy)；
(wi*xy-wx*xz+wy*xi+wz*xx)；
(wi*xz+wx*xy-wy*xx+wz*xi)；
(wi*xi-wx*xx-wy*xy-wz*xz)；
thus, qx1=qxqx0×q-1 can be finally obtained from qx0 to obtain the transformed object x-axis quaternion qx1 (xw ', xx', xy ', xz');
similarly, qy (yi ', yx', yy ', yz') and qz1 (zi ', zx', xy ', zz') can be obtained;
qx1, qy, the real part of qz1 is the x-axis, y-axis and z-axis coordinates of the object with changed posture in the cartesian coordinate system, and the coordinates are respectively expressed as: x1 (xx ', xy ', xz '), y1 (yx ', yy ', yz '), z1 (zx ', xy ', zz ').
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