CN111967125A - Mars detection ground antenna pointing correction method based on error quaternion - Google Patents
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Abstract
The invention relates to a Mars detection ground antenna pointing correction method based on an error quaternion, which comprises the following specific steps: s1, defining spatial three-dimensional rotation quaternion and establishing a mechanical coordinate system of the detector; s2, based on ground accurate measurement data, adopting a strategy of gradual error correction to correct the final ground antenna X-axis driving angle alpha and Y-axis driving angle beta; and S3, obtaining error angles d alpha under different X-axis driving angles alpha and error angles d beta under different Y-axis driving angles beta based on-orbit calibration data, and obtaining the relation between the error angles and the driving angles through linear fitting for correction. The method and the device correct the ground accurate measurement result and the in-orbit calibration result, the ground accurate measurement result is corrected based on the rotation quaternion, the in-orbit calibration result is corrected based on one-time linear error fitting, and errors under different driving angles can be effectively guaranteed.
Description
Technical Field
The invention relates to a driving control technology of a Mars detection mechanism, in particular to a Mars detection ground antenna pointing correction method based on an error quaternion.
Background
China will launch Mars detectors in 2020, and the conventional three-step flow of 'winding', 'falling' and 'patrolling' is realized at one time. As the detector flies to mars, the ground distance increases, and compared with a near-earth satellite, the communication delay is directly increased, and the large-loop control in real time cannot be implemented by the satellite and the ground.
On the other hand, due to different requirements of measurement and control data transmission, the system is configured with high-gain high-speed data transmission on the ground antenna protector. Due to the limitation of antenna beam, the pointing accuracy of the ground antenna is required to be high, and the on-orbit calibration and correction capability is provided.
The traditional error correction scheme of the on-orbit directional antenna is constant error correction, namely, a constant error of a driving angle is obtained by calibrating a two-dimensional driving angle of the directional antenna through the ground, and the detector performs constant correction before transmitting, the method is mainly applied to two-dimensional small-angle (the rotating angle is less than 10 degrees) rotation of the directional antenna, and for two-dimensional large-angle (the rotating angle reaches 70 degrees) rotation of the directional antenna, the constant correction strategy error is increased (more than 0.1 degree), the requirement of the antenna pointing accuracy is exceeded, and a ground communication link cannot be established.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method is based on the quaternion of three-dimensional rotation, based on the scheme of ground calibration and in-orbit calibration combination, the primary error quaternion is obtained through ground accurate measurement and calibration, the accurate error quaternion is further obtained through the repeated spiral scanning scheme, and high-precision data transmission pointing of the ground antenna is provided for Mars detection.
The technical scheme of the invention is as follows:
a mars detection ground antenna pointing correction method based on error quaternion adopts error quaternion to express installation and deformation errors among multi-level coordinate systems through the definition of a cascade coordinate system, takes ground calibration as an initial value, and corrects a final error quaternion by using an on-orbit calibration result, and comprises the following specific steps:
s1, defining spatial three-dimensional rotation quaternion as
Where phi is the spatial rotational euler angle,
rotating the euler shaft for space;
establishing a mechanical coordinate system O of the detectorhXhYhZhAnd OdXdYdZdRotational quaternion of
Wherein q iszhA rotation quaternion, q, from the mechanical coordinate system to the unfolding axis coordinate systemxzFor the rotation quaternion, q, of the unfolding axis coordinate system to the X drive axis coordinate systemyxIs a rotation quaternion, q, from an X drive axis coordinate system to a Y drive axis coordinate systemdyIs the rotation quaternion from the Y drive axis coordinate system to the electric axis coordinate system.
S2, accurately measuring data on the basis of the ground and simultaneously installing error quaternion dq on the basis of the base and the unfolding shaftzhQuaternion dq of connecting rod deformation errorxzQuaternion dq of mounting error of drive shaftyxAnd electric axis deformation error quaternion dqdyCorrecting the final ground antenna X-axis driving angle alpha and Y-axis driving angle beta by adopting a strategy of gradually correcting errors;
and S3, obtaining error angles d alpha under different X-axis driving angles alpha and error angles d beta under different Y-axis driving angles beta based on-orbit calibration data, and obtaining the relation between the error angles and the driving angles through linear fitting for correction.
Further, in step S1, each rotation quaternion is calculated,
wherein, lambda,
A rotary Euler angle and a rotary Euler axis from a mechanical coordinate system to an unfolding axis coordinate system; a
Rotating Euler angles and rotating Euler shafts from a Y-drive coordinate system to an electric axis coordinate system; alpha is the driving angle of the X axis of the ground antenna,
A rotary Euler axis for unfolding an axis coordinate system to an X-drive coordinate system; beta is the driving angle of the Y axis,
A rotating euler axis from an X-drive coordinate system to a Y-drive coordinate system.
Further, in the step S2, the method for calculating the driving angle α of the ground antenna on the X axis and the driving angle β on the Y axis is,
C(qdh)＝C(qdy)C(qyx)C(qxz)C(qzh) (6)
wherein the content of the first and second substances,
a unit vector of the detector under a mechanical coordinate system pointing to the earth;
and a unit vector C (-) pointing to the earth of the detector under the electric axis coordinate system is an attitude quaternion-to-attitude matrix algorithm.
Further, combining formulas (5) and (6), we can find:
order to
The X-axis drive angle and the Y-axis drive angle are
Further, in step S2, after errors of each stage are introduced, the rotation quaternion from the mechanical coordinate system to the electrical axis coordinate system is introduced
Wherein, q'dhThe rotation quaternion of the mechanical coordinate system of the detector to the electric axis coordinate system of the earth antenna after correction.
Further, combining formulas (5) (6) yields:
order to
Obtaining the corrected X-axis drive angle and Y-axis drive angle
Wherein, alpha 'is the X-axis driving angle after introducing the multi-stage rotation error, and beta' is the Y-axis driving angle after introducing the multi-stage rotation error.
Further, in step S3, according to the sequence of d α (n), d β (n), n being 1,2,3, … …, which is the tested deviations at different angles of the track,
dα＝dα0+kα (14)
dβ＝dβ0+kβ (15)
wherein alpha is0、β0For linearity error, k is the linear slope.
Further, a corrected driving angle based on ground accurate measurement and on-orbit calibration is finally obtained
α″＝α′+dα (16)
β″＝β′+dβ (17)
Wherein, α "is the finally corrected X-axis driving angle, β" is the finally corrected Y-axis driving angle, and α ', β' are the corrected X-axis and Y-axis driving angles.
Further, a mechanical coordinate system O of the detector is definedhXhYhZhIn which O ishFor the centre of the arrow-link plane of the detector, OhXhAxial direction to the top plate, OhZhDirected in the opposite direction to the mounting surface of the ground antenna, OhYhThe axis meets the right hand rule;
unfolding axis coordinate system OzXzYzZzIn which O iszXzTo unfold a jointAnd with OhXhParallel, after deployment in place OzZzAnd OhZhThe axes are parallel.
Further, X drive axis coordinate system OxXxYxZxIn which O isxXxThe shaft is a rotating shaft and is connected with the OzXzParallel, OxZxAnd OzZzThe axes are parallel;
y-drive axis coordinate system OyXyYyZyIn which O isyYyThe shaft is a rotating shaft and is connected with the OxYxParallel, OyZyAnd OxZxThe axes are parallel;
earth antenna axis coordinate system OdXdYdZdThree axes thereof and OyXyYyZyParallel.
Compared with the prior art, the invention has the beneficial effects that:
(1) the driving angle instruction of the counterparty antenna is corrected by adopting a rotating quaternion method, and an error model of each link can be included by establishing a multi-joint driving coordinate system and a rotating quaternion between the coordinate systems;
(2) according to the method, the conversion from a mechanical coordinate system of the detector to an electric axis coordinate system is described by adopting the rotating quaternion, so that the relation between the driving angle and the target vector angle can be more intuitively established, and the driving angle is solved based on vector constraint;
(3) the method corrects the ground accurate measurement result and the in-orbit calibration result, the ground accurate measurement result is corrected based on the rotation quaternion, the in-orbit calibration result is corrected based on the linear error fitting, and errors under different driving angles can be effectively guaranteed;
(4) the method has engineering realizability, and can better realize error correction under large-angle driving compared with the traditional simple constant correction strategy.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The invention is further illustrated by the following examples.
A Mars detection ground antenna pointing correction method based on error quaternion adopts error quaternion to express installation and deformation errors among multi-level coordinate systems through the definition of a cascade coordinate system, and corrects a final error quaternion by utilizing an on-orbit calibration result based on ground calibration as an initial value, as shown in figure 1, and comprises the following specific steps:
defining the mechanical coordinate system O of the detectorhXhYhZhIn which O ishFor the centre of the arrow-link plane of the detector, OhXhAxial direction to the top plate, OhZhDirected in the opposite direction to the mounting surface of the ground antenna, OhYhThe axis meets the right hand rule;
unfolding axis coordinate system OzXzYzZzIn which O iszXzFor extending the axis of rotation of the joint and with OhXhParallel, after deployment in place OzZzAnd OhZhThe axes are parallel.
X-drive axis coordinate system OxXxYxZxIn which O isxXxThe shaft is a rotating shaft and is connected with the OzXzParallel, OxZxAnd OzZzThe axes are parallel;
y-drive axis coordinate system OyXyYyZyIn which O isyYyThe shaft is a rotating shaft and is connected with the OxYxParallel, OyZyAnd OxZxThe axes are parallel;
earth antenna axis coordinate system OdXdYdZdThree axes thereof and OyXyYyZyParallel.
S1, defining spatial three-dimensional rotation quaternion as
Where phi is the spatial rotationThe angle of the euler curve is such that,
rotating the euler shaft for space;
establishing a mechanical coordinate system O of the detectorhXhYhZhAnd OdXdYdZdRotational quaternion of
Wherein q iszhA rotation quaternion, q, from the mechanical coordinate system to the unfolding axis coordinate systemxzFor the rotation quaternion, q, of the unfolding axis coordinate system to the X drive axis coordinate systemyxIs a rotation quaternion, q, from an X drive axis coordinate system to a Y drive axis coordinate systemdyIs the rotation quaternion from the Y drive axis coordinate system to the electric axis coordinate system.
S2, accurately measuring data on the basis of the ground and simultaneously installing error quaternion dq on the basis of the base and the unfolding shaftzhQuaternion dq of connecting rod deformation errorxzQuaternion dq of mounting error of drive shaftyxAnd electric axis deformation error quaternion dqdyCorrecting the final ground antenna X-axis driving angle alpha and Y-axis driving angle beta by adopting a strategy of gradually correcting errors;
and S3, obtaining error angles d alpha under different X-axis driving angles alpha and error angles d beta under different Y-axis driving angles beta based on-orbit calibration data, and obtaining the relation between the error angles and the driving angles through linear fitting for correction.
In step S1, the rotation quaternion of each stage is calculated,
wherein, lambda,
A rotary Euler angle and a rotary Euler axis from a mechanical coordinate system to an unfolding axis coordinate system; a
Rotating Euler angles and rotating Euler shafts from a Y-drive coordinate system to an electric axis coordinate system; alpha is the driving angle of the X axis of the ground antenna,
A rotary Euler axis for unfolding an axis coordinate system to an X-drive coordinate system; beta is the driving angle of the Y axis,
A rotating euler axis from an X-drive coordinate system to a Y-drive coordinate system.
In the step S2, the method for calculating the driving angle α of the ground antenna on the X axis and the driving angle β on the Y axis is,
C(qdh)＝C(qdy)C(qyx)C(qxz)C(qzh) (6)
wherein the content of the first and second substances,
a unit vector of the detector under a mechanical coordinate system pointing to the earth;
algorithm for converting unit vector C (DEG) pointing to earth of detector into attitude quaternion into attitude matrix under electric axis coordinate system。
Combining formulas (5) and (6), yields:
order to
The X-axis drive angle and the Y-axis drive angle are
In step S2, after errors at each stage are introduced, the rotation quaternion from the mechanical coordinate system to the electrical axis coordinate system is introduced
Wherein, q'dhThe rotation quaternion of the mechanical coordinate system of the detector to the electric axis coordinate system of the earth antenna after correction.
The combination of formulas (5) and (6) gives:
order to
Obtaining the corrected X-axis drive angle and Y-axis drive angle
Wherein, alpha 'is the X-axis driving angle after introducing the multi-stage rotation error, and beta' is the Y-axis driving angle after introducing the multi-stage rotation error.
In step S3, according to the sequence of d α (n), d β (n), n being 1,2,3, … …, which is the tested deviation under different angles of the track,
dα＝dα0+kα (14)
dβ＝dβ0+kβ (15)
wherein alpha is0、β0For linearity error, k is the linear slope.
Finally obtaining a corrected driving angle based on ground accurate measurement and on-orbit calibration
α″＝α′+dα (16)
β″＝β′+dβ (17)
Wherein, α "is the finally corrected X-axis driving angle, β" is the finally corrected Y-axis driving angle, and α ', β' are the corrected X-axis and Y-axis driving angles.
Example 1
Default q for Mars Detectordh＝[1,0,0,0]T；qzd＝[1,0,0,0]T；qxz＝[1,0,0,0]T；qyx＝[1,0,0,0]T；qdy＝[1,0,0,0]T；
And (3) ground accurate measurement and correction: q. q.sdh、qzdThe deviation around the Z axis is 0.1 degrees, when the X axis driving angle is 0 degrees and the Y axis driving angle is 0 degrees, the error angle is 0.1 degrees, and when the X axis driving angle is 50 degrees and the Y axis driving angle is 50 degrees, the error angle is about 0.16 degrees; a constant value correction scheme is adopted, only 0.1 degree is corrected, the error of small-angle driving is about 0, and when large-angle driving is that the maximum error reaches 0.06 degree; when the quaternion rotation scheme is adopted for correction, after 0.1 degree of correction, the large angle error is less than 0.001 degree.
After in-orbit calibration, when the X-axis and Y-axis driving angles are corrected by adopting a constant error, the maximum error is about 0.01 degrees during large-angle driving, and after first-order linear fitting, the maximum error is less than 0.001 degrees, so that the maximum error can be improved by one order of magnitude.
The driving angle instruction of the counterparty antenna is corrected by adopting a rotating quaternion method, and an error model of each link can be included by establishing a multi-joint driving coordinate system and a rotating quaternion between the coordinate systems;
according to the method, the conversion from a mechanical coordinate system of the detector to an electric axis coordinate system is described by adopting the rotating quaternion, so that the relation between the driving angle and the target vector angle can be more intuitively established, and the driving angle is solved based on vector constraint;
the method corrects the ground accurate measurement result and the in-orbit calibration result, the ground accurate measurement result is corrected based on the rotation quaternion, the in-orbit calibration result is corrected based on the linear error fitting, and errors under different driving angles can be effectively guaranteed;
the method has engineering realizability, and can better realize error correction under large-angle driving compared with the traditional simple constant correction strategy.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.
Claims (10)
1. A mars detection ground antenna pointing correction method based on error quaternion is characterized in that through definition of a cascade coordinate system, an error quaternion is adopted to represent installation and deformation errors among multi-level coordinate systems, ground calibration is used as an initial value, and an on-orbit calibration result is utilized to correct a final error quaternion, and the method specifically comprises the following steps:
s1, defining spatial three-dimensional rotation quaternion as
Where phi is the spatial rotational euler angle,
rotating the euler shaft for space;
establishing a mechanical coordinate system O of the detectorhXhYhZhAnd OdXdYdZdRotational quaternion of
Wherein q iszhA rotation quaternion, q, from the mechanical coordinate system to the unfolding axis coordinate systemxzFor the rotation quaternion, q, of the unfolding axis coordinate system to the X drive axis coordinate systemyxIs a rotation quaternion, q, from an X drive axis coordinate system to a Y drive axis coordinate systemdyIs the rotation quaternion from the Y drive axis coordinate system to the electric axis coordinate system.
S2, accurately measuring data on the basis of the ground and simultaneously installing error quaternion dq on the basis of the base and the unfolding shaftzhQuaternion dq of connecting rod deformation errorxzQuaternion dq of mounting error of drive shaftyxAnd electric axis deformation error quaternion dqdyCorrecting the final ground antenna X-axis driving angle alpha and Y-axis driving angle beta by adopting a strategy of gradually correcting errors;
and S3, obtaining error angles d alpha under different X-axis driving angles alpha and error angles d beta under different Y-axis driving angles beta based on-orbit calibration data, and obtaining the relation between the error angles and the driving angles through linear fitting for correction.
2. The method for correcting the orientation of the Mars sounding ground antenna based on the error quaternion as claimed in claim 1, wherein: in step S1, the rotation quaternion of each stage is calculated,
wherein, lambda,
A rotary Euler angle and a rotary Euler axis from a mechanical coordinate system to an unfolding axis coordinate system; a
Rotating Euler angles and rotating Euler shafts from a Y-drive coordinate system to an electric axis coordinate system; alpha is the driving angle of the X axis of the ground antenna,
A rotary Euler axis for unfolding an axis coordinate system to an X-drive coordinate system; beta is the driving angle of the Y axis,
A rotating euler axis from an X-drive coordinate system to a Y-drive coordinate system.
3. The method for correcting the orientation of the Mars sounding ground antenna based on the error quaternion as claimed in claim 1, wherein: in the step S2, the method for calculating the driving angle α of the ground antenna on the X axis and the driving angle β on the Y axis is,
C(qdh)＝C(qdy)C(qyx)C(qxz)C(qzh) (6)
wherein the content of the first and second substances,
a unit vector of the detector under a mechanical coordinate system pointing to the earth;
and a unit vector C (-) pointing to the earth of the detector under the electric axis coordinate system is an attitude quaternion-to-attitude matrix algorithm.
4. The method for correcting the orientation of the Mars sounding ground antenna based on the error quaternion as claimed in claim 3, wherein:
combining formulas (5) and (6), yields:
order to
The X-axis drive angle and the Y-axis drive angle are
5. The method for correcting the orientation of the Mars sounding ground antenna based on the error quaternion as claimed in claim 3, wherein: in step S2, after errors at each stage are introduced, the rotation quaternion from the mechanical coordinate system to the electrical axis coordinate system is introduced
Wherein, q'dhThe rotation quaternion of the mechanical coordinate system of the detector to the electric axis coordinate system of the earth antenna after correction.
6. The method for correcting the orientation of the Mars sounding ground antenna based on the error quaternion as claimed in claim 5, wherein: the combination of formulas (5) and (6) gives:
order to
Obtaining the corrected X-axis drive angle and Y-axis drive angle
Wherein, alpha 'is the X-axis driving angle after introducing the multi-stage rotation error, and beta' is the Y-axis driving angle after introducing the multi-stage rotation error.
7. The method for correcting the multi-dimensional pointing error of the Mars detection earth antenna based on Euler rotation as claimed in claim 1, wherein: in step S3, according to the sequence of d α (n), d β (n), n being 1,2,3, … …, which is the tested deviation under different angles of the track,
dα＝dα0+kα (14)
dβ＝dβ0+kβ (15)
wherein alpha is0、β0For linearity error, k is the linear slope.
8. The method of claim 7, wherein the multi-dimensional pointing error of the Mars detection ground antenna is corrected based on Euler rotation, and the method comprises the following steps:
finally obtaining a corrected driving angle based on ground accurate measurement and on-orbit calibration
α″＝α′+dα (16)
β″＝β′+dβ (17)
Wherein, α "is the finally corrected X-axis driving angle, β" is the finally corrected Y-axis driving angle, and α ', β' are the corrected X-axis and Y-axis driving angles.
9. The method for correcting the multi-dimensional pointing error of the Mars detection earth antenna based on Euler rotation as claimed in claim 1, wherein: defining the mechanical coordinate system O of the detectorhXhYhZhIn which O ishFor the centre of the arrow-link plane of the detector, OhXhAxial direction to the top plate, OhZhDirected in the opposite direction to the mounting surface of the ground antenna, OhYhThe axis meets the right hand rule;
unfolding axis coordinate system OzXzYzZzIn which O iszXzFor extending the axis of rotation of the joint and with OhXhParallel, after deployment in place OzZzAnd OhZhThe axes are parallel.
10. The method of claim 9, wherein the multi-dimensional pointing error correction method for the Mars detection ground antenna based on Euler rotation comprises:
x-drive axis coordinate system OxXxYxZxIn which O isxXxThe shaft is a rotating shaft and is connected with the OzXzParallel, OxZxAnd OzZzThe axes are parallel;
y-drive axis coordinate system OyXyYyZyIn which O isyYyThe shaft is a rotating shaft and is connected with the OxYxParallel, OyZyAnd OxZxThe axes are parallel;
earth antenna axis coordinate system OdXdYdZdThree axes thereof and OyXyYyZyParallel.
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