CN114279445A - Attitude calculation method of spinning aircraft - Google Patents

Attitude calculation method of spinning aircraft Download PDF

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CN114279445A
CN114279445A CN202111532545.3A CN202111532545A CN114279445A CN 114279445 A CN114279445 A CN 114279445A CN 202111532545 A CN202111532545 A CN 202111532545A CN 114279445 A CN114279445 A CN 114279445A
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angle
aircraft
attitude
spinning
value
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CN114279445B (en
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童晟翔
史志伟
云涛
李康丽
董益章
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses an attitude calculation method of a spinning aircraft, which comprises the following steps: acquiring a three-axis angular velocity value of a gyroscope of the aircraft, a three-axis geomagnetic field intensity value of the magnetometer and a three-axis acceleration value of an accelerometer; calculating the flapping angle, the pitch angle and the spinning angular speed of the blades of the aircraft according to the triaxial angular speed of the gyroscope; determining the rotation period of the aircraft according to the change of any value of the magnetometer, and calculating the average spin angular velocity according to the rotation period; calculating the inclination angle of the paddle disk according to the acceleration value of the accelerometer in the X-axis direction collected at each moment in the rotation period; calculating the yaw angle of the aircraft according to the obtained flap angle, the obtained pitch angle and the obtained inclination angle of the propeller disc; and performing complementary filtering on the attitude angle calculated by integrating the gyroscope and the calculated attitude angle to obtain the final attitude angle of the aircraft. The method is accurate in calculation result and suitable for attitude calculation of the spinning aircraft.

Description

Attitude calculation method of spinning aircraft
Technical Field
The invention relates to an aircraft attitude calculation method, in particular to an attitude calculation method of a spinning aircraft.
Background
The spinning aircraft is an aircraft which generates lift force by means of the spinning of the whole body and is mainly characterized in that all components of the aircraft rotate at high speed along with the body in the whole flying process, and no component which is relatively stable with the ground is arranged. The aircraft has the advantages of simple structure, low cost and the like, but due to the flight characteristics, the conventional nine-axis attitude calculation method of the accelerometer, the gyroscope and the magnetometer fails, and the main reason is that in a high-speed spinning state, the accelerometer deviates from a rotating shaft by a small distance and generates huge centripetal acceleration so as to interfere the normal work of the accelerometer in attitude calculation, and only the gyroscope and the magnetometer generate a large time accumulated error, so that the conventional nine-axis attitude calculation algorithm fails on a spinning aircraft, and the application of the spinning aircraft is limited.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a method for solving the attitude of a spinning aircraft, which solves the problems that the existing method is not suitable for solving the attitude of the spinning aircraft and the error of the calculation result is large.
The technical scheme is as follows: the invention relates to an attitude calculation method of a spinning aircraft, which comprises the following steps:
(1) acquiring a three-axis angular velocity value of a gyroscope of the aircraft, a three-axis geomagnetic field intensity value of the magnetometer and a three-axis acceleration value of an accelerometer;
(2) calculating the flapping angle, the pitch angle and the spinning angular speed of the blades of the aircraft according to the triaxial angular speed of the gyroscope;
(3) determining the rotation period of the aircraft according to the change of any value of the magnetometer, and calculating the average spin angular velocity according to the rotation period;
(4) calculating the inclination angle of the paddle disk according to the acceleration value of the accelerometer in the X-axis direction collected at each moment in the rotation period;
(5) calculating a yaw angle of the aircraft according to the flap angle and the pitch angle obtained in the step (2) and the inclination angle of the paddle disc obtained in the step (4);
(6) and (5) carrying out complementary filtering on the attitude angle calculated by the gyroscope integration and the attitude angle calculated in the step (5) to obtain the final attitude angle of the aircraft.
Wherein, the calculation formulas of the pitch angle, the spin angular velocity and the flap angle in the step (2) are as follows:
Figure BDA0003411925950000021
Figure BDA0003411925950000022
Figure BDA0003411925950000023
wherein p, q and r are triaxial angular velocity values of the gyroscope, r is greater than p, r is greater than q, beta is a flapping angle,
Figure BDA0003411925950000024
for pitch angle, ΩlIs instantaneous spin angular velocity
The step (3) is specifically as follows:
in a spin period, the state of the aircraft is basically kept unchanged, and the x-axis reading of the current magnetometer is
Figure BDA0003411925950000025
Record the time as TsNext time, the next time
Figure BDA0003411925950000026
Is over
Figure BDA0003411925950000027
When, record the time as Ts+1Then the average spin angular velocity over one rotation period is calculated as follows:
Figure BDA0003411925950000028
the step (4) is specifically as follows:
subdividing the rotation period into T according to the sampling time of the accelerometers 1、Ts 2、…、Ts k、Ts+1And the acceleration value in the x-axis direction sampled at each moment is recorded as
Figure BDA0003411925950000029
It is according to
Figure BDA00034119259500000210
Figure BDA00034119259500000211
Grouping two by two, if k/2 can not be divided completely, taking k/2 equal to or not more than the maximum integer, obtaining:
Figure BDA00034119259500000212
Figure BDA00034119259500000213
the two equations are subtracted to yield:
Figure BDA00034119259500000214
according to the formula, the method can obtain:
Figure BDA00034119259500000215
order:
Figure BDA0003411925950000031
then
Figure BDA0003411925950000032
Is calculated from the above
Figure BDA0003411925950000033
The term in which the absolute value is the largest is recorded as
Figure BDA0003411925950000034
At this time
Figure BDA0003411925950000035
I.e. the angle of inclination of the plane of the paddle disk
Figure BDA0003411925950000036
θpRepresents the theoretical value of the inclination angle of the paddle disk, omega represents the theoretical value of the spin angular velocity,
Figure BDA0003411925950000037
indicates that the time is between TsAnd Ts+1In between, the resulting tilt angle of the paddle disk is measured, g represents the gravitational acceleration and g' represents the gravitational acceleration component.
The step (5) is specifically as follows:
according to the results of steps (2) and (4), T can be obtaineds mAt the moment, the Euler angle of the aircraft, wherein
Figure BDA0003411925950000038
And if so
Figure BDA0003411925950000039
Then
Figure BDA00034119259500000310
Otherwise, then
Figure BDA00034119259500000311
The formula for calculating the yaw angle is as follows:
Figure BDA00034119259500000312
Figure BDA00034119259500000313
are respectively indicated
Figure BDA00034119259500000314
And (4) calculating the roll angle, the pitch angle and the yaw angle of the aircraft according to the sensor data.
The step (6) is specifically as follows:
let T bes<tl<Ts+1，
When (t)l+1-Ts m)(tl-Ts m)<At 0, tl+1The attitude angle at that time is calculated as follows:
Figure BDA00034119259500000315
Figure BDA00034119259500000316
Figure BDA00034119259500000317
wherein i is more than or equal to 1;
when (t)l+1-Ts m)(tl-Ts m)>At 0, output tl+1The three attitude angles of the aircraft at the moment, namely the roll angle, the pitch angle and the yaw angle, are as follows:
Figure BDA0003411925950000041
Figure BDA0003411925950000042
Figure BDA0003411925950000043
wherein the content of the first and second substances,
Figure BDA0003411925950000044
the attitude angle calculated by integrating the gyroscope is shown, and the calculation formula is as follows:
Figure BDA0003411925950000045
Figure BDA0003411925950000046
Figure BDA0003411925950000047
above, tlAnd tl+1Which represents the time instant of two adjacent sample points,
Figure BDA0003411925950000048
θl、ψland
Figure BDA0003411925950000049
θl+1、ψl+1respectively represent tlTime t andl+1a rolling angle, a pitch angle and a yaw angle which are finally output at the moment;
omega obtained by calculation in the step (2)lAnd omega calculated in the step (3)hApproximately equal, it can be considered that satisfying steps (2) - (5) holdsThe attitude of the aircraft relative to the plane of the paddle disk remains stable, with the complementary filter output being closer to
Figure BDA00034119259500000410
On the contrary, the output of the complementary filter is closer to the integral value of the gyroscope
Figure BDA00034119259500000411
Has the advantages that:
the invention relates to a gyroscope and magnetometer fusion attitude calculation method based on the spin angular velocity of an aircraft, which has accurate calculation results and is suitable for attitude calculation of spin aircrafts; the problem that the spinning aircraft cannot accurately acquire attitude data is solved, and the flight control precision of the spinning aircraft during large maneuvering motion can be greatly improved by using the attitude calculation method designed by the invention.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
fig. 2 is a diagram illustrating the definition of important parameters, wherein Ω represents spin angular velocity, β represents flap angle,
Figure BDA00034119259500000412
representing pitch angle, i.e. equivalent to aircraft roll angle, thetapRepresenting the inclination angle of a paddle disk;
FIG. 3 is a schematic view of an aircraft shafting, 1-spin axis, 2-aircraft body shafting y axis, 3-roll angle
Figure BDA00034119259500000413
The system comprises a 4-yaw angle psi, a 5-aircraft body, a 6-aircraft body shafting z-axis, a 7-pitch angle theta and an aircraft body shafting x-axis.
Detailed Description
The present application is further described below with reference to the accompanying drawings.
As shown in FIG. 1, the method for calculating the attitude of the spinning aircraft disclosed by the invention comprises the following steps:
s1: reading the values of the angular velocity of three axes of the gyroscope, and recording as p, q and r; readingTaking the three-axis geomagnetic field intensity value of the magnetometer and recording the value as
Figure BDA0003411925950000051
Reading the acceleration value of the accelerometer in the x-axis direction and recording the value as
Figure BDA0003411925950000052
Wherein, the x, y and z axes of the sensor are superposed with the shafting of the aircraft body;
s2: since the spin-type aircraft has significant spin axes, r in the three-axis angular velocity values will be significantly greater than the other two values, i.e., r > p, r > q. Then, assuming that the attitude of the aircraft relative to the paddle disk is stable, generally speaking, in the hovering state, the flap angle β and the pitch angle can be calculated
Figure BDA0003411925950000053
And spin angular velocity ΩlThe calculation formula is as follows:
Figure BDA0003411925950000054
Figure BDA0003411925950000055
Figure BDA0003411925950000056
s3: in most cases, because the spin speed of the spin aircraft is large, the aircraft state is assumed to remain substantially unchanged in one spin cycle, and therefore, a specific method for estimating the spin angular speed by using the magnetometer is to assume that the current magnetometer reads x-axis as
Figure BDA0003411925950000057
Record the time as TsNext time, the next time
Figure BDA0003411925950000058
Is over
Figure BDA0003411925950000059
When is at time
Figure BDA00034119259500000510
Time (where l and l +1 represent two sensor samples before and after), the time at this time is recorded as Ts+1Then the spin angular velocity at that time can be estimated
Figure BDA00034119259500000511
Here omegahThe spin angular velocity measured for the magnetometer is the average magnitude over one revolution period of the aircraft; Ω in S2lThe spin angular velocity measured for the gyroscope is an instantaneous quantity;
s4: t in S3sTo Ts+1The time between is subdivided into T according to the sampling time of the accelerometers 1、Ts 2、…、Ts k、Ts+1And the acceleration value in the x-axis direction sampled at each moment is recorded as
Figure BDA00034119259500000512
It is according to
Figure BDA00034119259500000513
And grouping two by two, and if k/2 cannot be divided completely, taking k/2 equal to or less than the maximum integer of the k/2. Calculating each pair of time, taking the first pair of time as an example, as shown in FIG. 2, respectively, to obtain
Figure BDA0003411925950000061
Figure BDA0003411925950000062
Since the plane in the figure is not necessarily a vertical plane, g' is less than or equal to g, and the two equations are subtracted:
Figure BDA0003411925950000063
beta is calculated from S2, and thus can be obtained
Figure BDA0003411925950000064
Order:
Figure BDA0003411925950000065
then
Figure BDA0003411925950000066
From this we can calculate
Figure BDA0003411925950000067
Find the one with the largest absolute value, record
Figure BDA0003411925950000068
At this time
Figure BDA0003411925950000069
I.e. the angle of inclination of the plane of the paddle disk
Figure BDA00034119259500000610
θpRepresents the theoretical value of the inclination angle of the paddle disk, omega represents the theoretical value of the spin angular velocity,
Figure BDA00034119259500000611
indicates that the time is between TsAnd Ts+1In between, the resulting tilt angle of the paddle disk is measured, g represents the gravitational acceleration and g' represents the gravitational acceleration component. The definitions of the angle of inclination of the paddle disk, the spin angular speed, etc. are shown in fig. 2.
S5: first, from the calculation results of S2 and S4, T can be obtaineds mAt the moment, the Euler angle of the aircraft, wherein
Figure BDA00034119259500000612
Has already been calculated in S2, i.e.
Figure BDA00034119259500000613
And if so
Figure BDA00034119259500000614
Then
Figure BDA00034119259500000615
Otherwise, then
Figure BDA00034119259500000616
From the magnetometer data, the yaw angle can be further calculated
Figure BDA00034119259500000617
Figure BDA00034119259500000618
Respectively mean Ts mAnd (4) calculating the roll angle, the pitch angle and the yaw angle of the aircraft according to the sensor data. Through the calculation, the parameter which is crucial to the spin type aircraft, namely the inclination direction of the paddle disk, can be obtained simultaneously
Figure BDA00034119259500000619
When the paddle disk inclines in the direction of
Figure BDA00034119259500000620
Otherwise, it is
Figure BDA00034119259500000621
S6: the attitude angle of the aircraft obtained by calculation of S2-S5 is required to be established on the stable hovering state of the aircraft and is sufficiently accurateAnd (8) determining. Because the calculation of the step S2 is required to satisfy the requirement that the attitude of the aircraft relative to the plane of the paddle disk be stable, i.e. beta vs
Figure BDA0003411925950000071
The value of (c) remains unchanged. But in many cases, beta is not equal to
Figure BDA0003411925950000072
Will change in real time, at which time the attitude angle needs to be calculated using gyro integration, i.e.
Figure BDA0003411925950000073
Figure BDA0003411925950000074
Figure BDA0003411925950000075
Wherein the content of the first and second substances,
Figure BDA0003411925950000076
representing attitude angle, t, calculated by integrating with a gyroscopelAnd tl+1Which represents the time instant of two adjacent sample points,
Figure BDA0003411925950000077
θl、ψland
Figure BDA0003411925950000078
θl+1、ψl+1respectively represent tlTime t andl+1and finally outputting a rolling angle, a pitch angle and a yaw angle at the moment.
Wherein l and l +1 represent sensor sampling twice before and after, superscript l represents the aircraft attitude angle output at the last sampling moment, superscript l +1 represents the aircraft attitude angle obtained by integrating at the current sampling moment through a gyroscope. In factΩ calculated in S2lAnd Ω calculated in S3hApproximately equal, it can be considered that the condition of S2-S5 holds, i.e., the attitude of the aircraft relative to the plane of the paddle disk remains stable, and the output of the complementary filter is closer to the plane of the paddle disk
Figure BDA0003411925950000079
On the contrary, the output of the complementary filter is closer to the integral value of the gyroscope
Figure BDA00034119259500000710
The complementary filtering is applied to the two as follows:
let T bes<tl<Ts+1,
When (t)l+1-Ts m)(tl-Ts m)<At 0, tl+1Attitude angle at time is expressed as
Figure BDA00034119259500000711
Figure BDA00034119259500000712
Figure BDA00034119259500000713
Wherein i is more than or equal to 1, which can be selected according to practical situation, and i is 2.
When (t)l+1-Ts m)(tl-Ts m)>At 0, output tl+1The three attitude angles of the aircraft at the moment, namely the roll angle, the pitch angle and the yaw angle, are as follows:
Figure BDA0003411925950000081
Figure BDA0003411925950000082
Figure BDA0003411925950000083
i.e. t is the final outputl+1And three attitude angles of a rolling angle, a pitch angle and a yaw angle of the aircraft at the moment.

Claims (6)

1. An attitude calculation method of a spinning aircraft is characterized by comprising the following steps:
(1) acquiring a three-axis angular velocity value of a gyroscope of the aircraft, a three-axis geomagnetic field intensity value of the magnetometer and a three-axis acceleration value of an accelerometer;
(2) calculating the flapping angle, the pitch angle and the spinning angular speed of the blades of the aircraft according to the triaxial angular speed of the gyroscope;
(3) determining the rotation period of the aircraft according to the change of any value of the magnetometer, and calculating the average spin angular velocity according to the rotation period;
(4) calculating the inclination angle of the paddle disk according to the acceleration value of the accelerometer in the X-axis direction collected at each moment in the rotation period;
(5) calculating a yaw angle of the aircraft according to the flap angle and the pitch angle obtained in the step (2) and the inclination angle of the paddle disc obtained in the step (4);
(6) and (5) carrying out complementary filtering on the attitude angle calculated by the gyroscope integration and the attitude angle calculated in the step (5) to obtain the final attitude angle of the aircraft.
2. The attitude calculation method for a spinning-type aircraft according to claim 1, wherein the calculation formulas of pitch angle, spin angular velocity and flap angle in step (2) are as follows:
Figure FDA0003411925940000011
Figure FDA0003411925940000012
Figure FDA0003411925940000013
wherein p, q and r are triaxial angular velocity values of the gyroscope, r is greater than p, r is greater than q, beta is a flapping angle,
Figure FDA0003411925940000014
for pitch angle, ΩlIs the instantaneous spin angular velocity.
3. The attitude calculation method for a spinning aircraft according to claim 1, wherein the step (3) is specifically as follows:
in a spin period, the state of the aircraft is basically kept unchanged, and the x-axis reading of the current magnetometer is
Figure FDA0003411925940000015
Record the time as TsNext time, the next time
Figure FDA0003411925940000016
Is over
Figure FDA0003411925940000017
When, record the time as Ts+1Then the average spin angular velocity over one rotation period is calculated as follows:
Figure FDA0003411925940000018
4. the attitude calculation method for a spinning aircraft according to claim 3, wherein the step (4) is specifically as follows:
subdividing the rotation period into T according to the sampling time of the accelerometers 1、Ts 2、...、Ts k、Ts+1And the acceleration value in the x-axis direction sampled at each moment is recorded as
Figure FDA0003411925940000021
It is according to
Figure FDA0003411925940000022
Figure FDA0003411925940000023
Grouping two by two, if k/2 can not be divided completely, taking k/2 equal to or not more than the maximum integer, obtaining:
Figure FDA0003411925940000024
Figure FDA0003411925940000025
the two equations are subtracted to yield:
Figure FDA0003411925940000026
according to the formula, the method can obtain:
Figure FDA0003411925940000027
order:
Figure FDA0003411925940000028
then
Figure FDA0003411925940000029
Is calculated from the above
Figure FDA00034119259400000210
The term in which the absolute value is the largest is recorded as
Figure FDA00034119259400000211
At this time
Figure FDA00034119259400000212
I.e. the angle of inclination of the plane of the paddle disk
Figure FDA00034119259400000213
θpRepresents the theoretical value of the inclination angle of the paddle disk, omega represents the theoretical value of the spin angular velocity,
Figure FDA00034119259400000214
indicates that the time is between TsAnd Ts+1In between, the resulting tilt angle of the paddle disk is measured, g represents the gravitational acceleration and g' represents the gravitational acceleration component.
5. The attitude calculation method for a spinning aircraft according to claim 4, wherein the step (5) is specifically as follows:
according to the results of steps (2) and (4), T can be obtaineds mAt the moment, the Euler angle of the aircraft, wherein
Figure FDA00034119259400000215
And if so
Figure FDA00034119259400000216
Then
Figure FDA00034119259400000217
Otherwise, then
Figure FDA00034119259400000218
The formula for calculating the yaw angle is as follows:
Figure FDA0003411925940000031
Figure FDA0003411925940000032
respectively mean Ts mAnd (4) calculating the roll angle, the pitch angle and the yaw angle of the aircraft according to the sensor data.
6. The attitude calculation method for a spinning aircraft according to claim 5, wherein the complementary filtering process in the step (6) is specifically as follows:
let T bes＜tl＜Ts+1，
When (t)l+1-Ts m)(tl-Ts m) T < 0l+1The attitude angle at that time is calculated as follows:
Figure FDA0003411925940000033
Figure FDA0003411925940000034
Figure FDA0003411925940000035
wherein i is more than or equal to 1;
when (t)l+1-Ts m)(tl-Ts m) When > 0, output tl+1Moment aircraft roll angle and pitchThe three attitude angles of elevation and yaw are as follows:
Figure FDA0003411925940000036
Figure FDA0003411925940000037
Figure FDA0003411925940000038
wherein the content of the first and second substances,
Figure FDA0003411925940000039
the attitude angle calculated by integrating the gyroscope is shown, and the calculation formula is as follows:
Figure FDA00034119259400000310
Figure FDA00034119259400000311
Figure FDA00034119259400000312
above, tlAnd tl+1Which represents the time instant of two adjacent sample points,
Figure FDA00034119259400000313
θl、ψland
Figure FDA00034119259400000314
θl+1、ψl+1respectively represent tlTime of dayAnd tl +1A rolling angle, a pitch angle and a yaw angle which are finally output at the moment;
omega obtained by calculation in the step (2)lAnd omega calculated in the step (3)hApproximately equal, the conditions that steps (2) - (5) are satisfied are that the attitude of the aircraft relative to the plane of the paddle disk remains stable, and the output of the complementary filter is closer to that of the aircraft
Figure FDA0003411925940000041
On the contrary, the output of the complementary filter is closer to the integral value of the gyroscope
Figure FDA0003411925940000042
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