CN110047110B - Flexible satellite-borne antenna on-orbit vibration measurement method based on sequence image - Google Patents

Flexible satellite-borne antenna on-orbit vibration measurement method based on sequence image Download PDF

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CN110047110B
CN110047110B CN201910180967.5A CN201910180967A CN110047110B CN 110047110 B CN110047110 B CN 110047110B CN 201910180967 A CN201910180967 A CN 201910180967A CN 110047110 B CN110047110 B CN 110047110B
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image
target mark
antenna
point
flexible satellite
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葛东明
张庆君
朱宇
史纪鑫
肖刚
邹元杰
邓润然
朱卫红
李晓云
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Beijing Institute of Spacecraft System Engineering
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
    • G—PHYSICS
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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Abstract

A flexible satellite-borne antenna on-orbit vibration measurement method based on sequence images is characterized in that target mark points are pasted on the flexible satellite-borne antenna, and image acquisition is carried out according to time sequence to obtain sequence images of the flexible satellite-borne antenna; extracting target mark points from the sequence image of the flexible satellite-borne antenna to obtain the outline of each target mark point; respectively fitting the outlines of all the target mark points into sub-pixel precision ellipses, and determining the central pixel coordinates of all the sub-pixel precision ellipses; establishing a camera projection model; calibrating external parameters of a camera projection model according to the central pixel coordinates of each sub-pixel precision ellipse to finish on-orbit calibration; and according to the camera projection model after external parameters are calibrated, performing on-orbit vibration measurement on the target mark point pasted by the flexible satellite-borne antenna. The measurement result provides input for antenna surface type fine adjustment, vibration suppression, dynamic model on-orbit correction and load-to-ground imaging compensation, and provides measurement and image information for satellite on-orbit fault diagnosis and on-orbit health monitoring.

Description

Flexible satellite-borne antenna on-orbit vibration measurement method based on sequence image
Technical Field
The invention relates to a flexible satellite-borne antenna on-orbit vibration measurement method based on sequence images, and belongs to the technical field of spacecraft dynamics.
Background
With the increasing application of satellites in the aspects of earth exploration, radio astronomy, deep space communication, energy transmission and the like, the flexible satellite-borne antenna is expected to be a main direction for the development of future deployable antennas. In the future, the satellite-borne antenna will develop towards the direction of light weight, economy, multifunction, agility and quickness. Therefore, the space-borne antenna structure has the dynamic characteristics of large span, light weight, low rigidity, weak damping and the like, belongs to a typical large flexible space structure, and brings a series of dynamic and control problems for the spacecraft. In the future, more and more large deployable antennas are applied to spacecrafts, the caliber is larger and larger, the index is stricter, and the vibration of the large flexible antenna is inevitably caused by mechanical motion caused by attitude and orbit control, thermal vibration and the like of a satellite, so that the electrical property is reduced, and the task completion quality is influenced. Therefore, the on-orbit vibration measurement and state monitoring of the satellite-borne SAR antenna are carried out, the unfolding flatness of the SAR antenna is obtained in real time, and the on-orbit vibration state and amplitude are important bases for the on-orbit fine adjustment of the antenna surface type, the vibration measurement and suppression, the on-orbit correction of a dynamic model and the ground imaging compensation.
The traditional contact type measuring method needs to install a sensor on a measured structure, such as an acceleration sensor, piezoelectric ceramics and the like, and has several disadvantages: 1) due to the complex structure of the antenna device, the position and space of the sensor arrangement are limited; 2) the sensor is used as an additional mass, and can change the mass distribution and the structural rigidity of the antenna, so that the dynamic characteristics of the antenna are changed, and the structural reliability is reduced; 3) contact measurements may affect the antenna operating state and interfere with its mission function. In view of the above limitations, the non-contact measurement mode is a necessary trend of on-track measurement of large flexible structures in the future. The current non-contact measurement method mainly adopts camera vision measurement or laser radar measurement, and the given method has several limitations: 1) due to the large span of the antenna, a binocular or multi-eye measurement method is mostly adopted for realizing long-distance measurement, but the depth resolution ratio is reduced along with the increase of the distance in a square relation, so that the index requirement (millimeter level) of the measurement precision can not be met; 2) based on monocular measurement, the relative position relation of the mark points needs to be utilized, but after the antenna is unfolded in orbit, the stress release and the thermal deformation can change the calibration result before emission, and the final measurement precision is influenced; 3) the laser three-dimensional imaging has higher ranging precision (sub-centimeter level), but has lower transverse resolution, needs a scanning mechanism and has three-dimensional image motion distortion, and is suitable for medium and long distance detection and quasi-static targets.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method for measuring the on-orbit vibration of the flexible satellite-borne antenna based on the sequence images is provided for solving the problem of on-orbit vibration measurement of the large satellite-borne flexible antenna. According to the method, millimeter-scale vibration measurement of the flexible satellite-borne antenna can be realized only by arranging mark points of the directional reflecting material on the antenna structure and adopting on-orbit calibration, so that input is provided for antenna surface type fine adjustment, vibration suppression, dynamic model on-orbit correction and load on-earth imaging compensation, and meanwhile, measurement and image information is provided for satellite on-orbit fault diagnosis and on-orbit health monitoring.
The technical scheme of the invention is as follows: the flexible satellite-borne antenna in-orbit vibration measurement method based on the sequence image comprises the following steps:
(1) pasting a target mark point on the flexible satellite-borne antenna, wherein the target mark point is circular, and acquiring images of the flexible satellite-borne antenna according to a time sequence to obtain a sequence image of the flexible satellite-borne antenna;
(2) extracting target mark points from the sequence image of the flexible satellite-borne antenna to obtain the outline of each target mark point;
(3) respectively fitting the outlines of all the target mark points into sub-pixel precision ellipses, and determining the central pixel coordinates of all the sub-pixel precision ellipses;
(4) establishing a camera projection model to represent the projection relation between an object point and an image point, wherein the object point is a target mark point pasted on the flexible spaceborne antenna, and the image point is the central pixel coordinate of a sub-pixel precision ellipse corresponding to the object point; the camera projection model comprises internal parameters and external parameters;
(5) calibrating external parameters of a camera projection model according to the central pixel coordinates of each sub-pixel precision ellipse to finish on-orbit calibration;
(6) and (5) calibrating the camera projection model after external reference according to the step (5), and performing on-orbit vibration measurement on the target mark point pasted by the flexible satellite-borne antenna.
The method comprises the following steps of (1) pasting a target mark point on the flexible satellite-borne antenna, wherein the target mark point is circular, and carrying out image acquisition on the flexible satellite-borne antenna according to a time sequence to obtain a sequence image of the flexible satellite-borne antenna, and the method specifically comprises the following steps:
(1.1) according to the vibration mode of the flexible satellite-borne antenna, pasting a target mark point at the obvious deformation position;
(1.2) selecting mark points with directional light reflecting performance, wherein the shape is selected to be a circle with the same size;
and (1.3) acquiring images of the flexible satellite-borne antenna by adopting a visible light optical camera according to a certain frame rate, wherein the frame rate is selected to be one order of magnitude higher than the frequency value of the vibration mode of the flexible satellite-borne antenna.
Extracting target mark points from the sequence image of the flexible satellite-borne antenna to obtain the outline of each target mark point, wherein the specific steps are as follows:
(2.1) carrying out image binarization processing on a sequence image of the flexible satellite-borne antenna, namely an obtained original image, so as to obtain a binarized image;
(2.2) extracting a connected domain of each target mark point in the binary image;
(2.3) carrying out edge detection on the connected domain of each target mark point to obtain the outline of each target mark point;
and (3) respectively fitting the outlines of all target mark points into a sub-pixel precision ellipse, which is as follows:
(3.1) establishing an equation of the image contour of each target mark point, wherein the image of each target mark point is a plane ellipse as follows:
ax2+bxy+cy2+dx+ey+f＝0 (1)
(3.2) fitting the outline of each target mark point by using an elliptic least square fitting algorithm to obtain the coefficient of the equation of the image of each target mark point;
(3.3) determining the center coordinates (x) of each target mark point in the image coordinate system according to the coefficient of the ellipse equation of the image of each target mark point0,y0)；
Figure BDA0001991323250000041
In order to suppress the influence of image noise, the contour of each target marker point is fitted twice. After the first fitting, counting the distance between the pixel points forming the outline and the elliptical equation, removing the pixel points with larger distance, and performing second fitting on the pixel points forming the outline by using an elliptical least square fitting algorithm to obtain the coefficient of the elliptical equation of the image of each target mark point for inhibiting the influence of image noise; determining the center coordinates (x) of each target mark point in the image coordinate system according to the coefficient of the ellipse equation of the image of each target mark point for inhibiting the influence of image noise0,y0)；
Fitting a sub-pixel precision ellipse to the ellipse equation of the image of each target landmark point for which the equation coefficients are determined in step (3.2).
Establishing a camera projection model to represent the projection relation between an object point and an image point, wherein the object point is a target mark point pasted on the flexible spaceborne antenna, and the image point is the central pixel coordinate of a sub-pixel precision ellipse corresponding to the object point; the camera projection model comprises internal parameters and external parameters, and specifically comprises the following steps:
(4.1) selecting 4 coplanar mark points from the target mark points pasted on the flexible satellite-borne antenna;
(4.2) establishing a camera projection model according to the selected 4 coplanar mark points, wherein the model comprises the following steps:
Figure BDA0001991323250000042
wherein s is an arbitrary scalar factor, u and v are coordinates of the image point of the selected marker point in the image coordinate system, X and Y are coordinates of the X axis and the Y axis of the selected marker point in the antenna coordinate system, and r is a linear coordinate of the selected marker point in the antenna coordinate system1，r2，r3A column vector of a coordinate transformation matrix R for the antenna coordinate system to the camera coordinate system (R is denoted as [ R ]1r2r3]) T is the translation vector from the antenna coordinate system to the camera coordinate system, A is the internal reference of the camera, and R and t are external references. Let M be [ X, Y ]]TCoordinates representing a marking point, m ═ u, v]TRepresenting coordinates of image points of the index points, and
Figure BDA0001991323250000043
Figure BDA0001991323250000044
thus, formula (3) is described as formula (4)
Figure BDA0001991323250000045
Calibrating external parameters of a camera projection model according to the central pixel coordinates of each sub-pixel precision ellipse to finish on-orbit calibration, which comprises the following steps:
the known camera internal parameter A and external parameter are calculated by the following formula
r1＝λA-1h1,r2＝λA-1h2,r3＝r1×r2,t＝λA-1h3 (5)
Wherein λ 1/| | a-1h1||＝1/||A-1h2||。
Step (6) according to the camera projection model after external parameters are calibrated in the step (5), the on-orbit vibration measurement is carried out on the target mark point pasted by the flexible satellite-borne antenna, and the preferable scheme is as follows:
the measured mark point is P, and the vibration quantity of the measured mark point on the x axis of the camera coordinate system is deltaxFocal length of camera is f, and coordinate of principal point under image coordinate system is u0、v0The coordinates of the image point in the image coordinate system are u and v, and the coordinate of the known P point in the Z-axis of the camera coordinate system is ZpAccording to the measuring principle of monocular cameras, deltaxCan be calculated from the following formula
Figure BDA0001991323250000051
Accordingly, the vibration quantity δ of the marker point on the y-axis of the camera coordinate systemyIs composed of
Figure BDA0001991323250000052
Compared with the prior art, the invention has the advantages that:
(1) the vibration measuring method has the advantages of no damage to the measured structure, no interference to the task function and the dynamic characteristic of the measured structure;
(2) the vibration measurement method has the in-orbit calibration function after the antenna is in orbit, and realizes the in-orbit correction of the position relation of the measured mark point;
(3) the vibration measurement method of the invention fully utilizes the high resolution in the camera imaging plane, realizes the out-of-plane vibration measurement of the antenna structure, and the measurement precision can reach millimeter level;
(4) the vibration measurement method has the advantages of small calculation amount of algorithm, operability and realizability, and is easy to meet the on-orbit real-time measurement requirement;
(5) according to the vibration measurement method, only one camera is needed to meet the measurement requirement, the problems of high-precision installation, calibration and the like of a binocular camera are solved, and the system reliability is high.
Drawings
FIG. 1 is a block flow diagram of the method of the present invention;
FIG. 2 is a schematic diagram of a monocular vision measurement configuration of a phased array antenna;
fig. 3 is a schematic diagram of image processing, in which (a) is a schematic diagram of original image acquisition, (b) is a schematic diagram of binarization segmentation, (c) is a schematic diagram of connected domain extraction, and (d) is a schematic diagram of edge detection;
figure 4 ellipse fitting
FIG. 5 is a schematic diagram of a camera projection imaging;
FIG. 6 is a schematic view of monocular camera measurement calculations;
FIG. 7 is a schematic view of a flexible sheet vibration measurement test;
FIG. 8 is a comparison of monocular and binocular vision measurements; wherein (a) is a vibration quantity diagram of the mark point in the x direction and the y direction of the camera coordinate system; (b) the difference between the monocular measurement and the binocular measurement of the vibration quantity of the mark point in the x direction and the y direction of the camera coordinate system is shown schematically.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
The invention relates to an on-orbit vibration measurement method of a flexible satellite-borne antenna based on a sequence image, which comprises the following steps of (1) pasting a target mark point on the flexible satellite-borne antenna, and carrying out image acquisition on the flexible satellite-borne antenna according to a time sequence to obtain a sequence image of the flexible satellite-borne antenna; (2) extracting target mark points from the sequence image of the flexible satellite-borne antenna to obtain the outline of each target mark point; (3) respectively fitting the outlines of all the target mark points into sub-pixel precision ellipses, and determining the central pixel coordinates of all the sub-pixel precision ellipses;
(4) establishing a camera projection model (5), calibrating external parameters of the camera projection model according to the central pixel coordinates of each sub-pixel precision ellipse, and completing on-orbit calibration; (6) and (5) calibrating the camera projection model after external reference according to the step (5), and performing on-orbit vibration measurement on the target mark point pasted by the flexible satellite-borne antenna. The measurement result provides input for antenna surface type fine adjustment, vibration suppression, dynamic model on-orbit correction and load-to-ground imaging compensation, and provides measurement and image information for satellite on-orbit fault diagnosis and on-orbit health monitoring.
According to the method, millimeter-scale vibration measurement of the flexible satellite-borne antenna can be realized only by arranging mark points of the directional reflecting material on the antenna structure and adopting on-orbit calibration, so that input is provided for antenna surface type fine adjustment, vibration suppression, dynamic model on-orbit correction and load on-earth imaging compensation, and meanwhile, measurement and image information is provided for satellite on-orbit fault diagnosis and on-orbit health monitoring.
As shown in fig. 1, a method for measuring in-orbit vibration of a flexible satellite-borne antenna based on a sequence image includes the following steps:
(1) pasting a target mark point on the flexible satellite-borne antenna, wherein the target mark point is circular, and acquiring images of the flexible satellite-borne antenna according to a time sequence to obtain a sequence image of the flexible satellite-borne antenna;
(2) extracting target mark points from the sequence image of the flexible satellite-borne antenna to obtain the outline of each target mark point;
(3) respectively fitting the outlines of all the target mark points into sub-pixel precision ellipses, and determining the central pixel coordinates of all the sub-pixel precision ellipses;
(4) establishing a camera projection model to represent the projection relation between an object point and an image point, wherein the object point is a target mark point pasted on the flexible spaceborne antenna, and the image point is the central pixel coordinate of a sub-pixel precision ellipse corresponding to the object point; the camera projection model includes internal and external parameters, as shown in FIG. 5;
(5) calibrating external parameters of a camera projection model according to the central pixel coordinates of each sub-pixel precision ellipse to finish on-orbit calibration;
(6) calibrating the camera projection model after external reference according to the step (5), and performing on-orbit vibration measurement on a target mark point pasted by the flexible satellite-borne antenna;
step 1: as shown in fig. 2, a target mark point is pasted on the flexible satellite-borne antenna, the target mark point is circular, image acquisition is performed on the flexible satellite-borne antenna according to a time sequence to obtain a sequence image of the flexible satellite-borne antenna, and a coordinate system is defined as follows
Camera coordinate system OcxcyczcDefining: camera coordinate system OcxcyczcIs a rectangular coordinate system defined on the optical center of the left camera, and the origin of the coordinate system is Oc，OczcThe axis coincides with the camera optical axis and points to the scene, and the direction pointing to the scene is defined as the positive direction. Wherein, OcxcThe axis is parallel to the horizontal axis of the image plane; o iscycThe axis is parallel to the vertical axis of the image plane. Optical center OcThe distance f to the image plane is called the focal length of the camera.
The image pixel coordinate system uv defines: the digital image is stored in the computer in the form of a two-dimensional array, and in an image pixel coordinate system uv, the coordinate of each pixel is (u, v), (u, v) represents the column number and the row number of the pixel in the two-dimensional array, and the unit of the coordinate system is the pixel.
Antenna coordinate system OzxzyzzzDefining: antenna coordinate system OzxzyzzzHas an origin of OzCoinciding with the origin of the camera coordinate system, OzzzThe axis pointing in the direction of extension of the antenna, OzyzThe axis pointing in the normal direction of the antenna, the direction to ground being positive, OzxzDetermined by the right hand rule. Camera coordinate system OcxcyczcFrom the antenna coordinate system OzxzyzzzAround OzyzThe shaft rotation angle theta is obtained.
The method comprises the following specific steps:
(1.1) analyzing the vibration mode of the flexible satellite-borne antenna, and selecting a target mark point to be pasted at a position with obvious deformation;
(1.2) selecting mark points with directional light reflecting performance, wherein the shape is selected to be a circle with the same size;
and (1.3) acquiring images of the flexible satellite-borne antenna by adopting a visible light optical camera according to a certain frame rate, wherein the frame rate is selected to be one order of magnitude higher than the frequency value of the vibration mode of the flexible satellite-borne antenna.
Step 2: extracting target mark points from the sequence image of the flexible satellite-borne antenna to obtain the outline of each target mark point, as shown in (a), (b), (c) and (d) of fig. 3, specifically as follows:
(2.1) carrying out image binarization processing on a sequence image of the flexible satellite-borne antenna, namely an obtained original image, so as to obtain a binarized image;
(2.2) extracting a connected domain of each target mark point in the binary image;
(2.3) carrying out edge detection on the connected domain of each target mark point to obtain the outline of each target mark point;
and step 3: the outlines of the target mark points are respectively fitted into a sub-pixel precision ellipse, as shown in fig. 4, specifically as follows:
(3.1) establishing an equation of the image contour of each target mark point, wherein the image of each target mark point is a plane ellipse as follows:
ax2+bxy+cy2+dx+ey+f＝0 (1)
(3.2) fitting the outline of each target mark point by using an elliptic least square fitting algorithm to obtain the coefficient of the equation of the image of each target mark point;
(3.3) determining the center coordinates (x) of each target mark point in the image coordinate system according to the coefficient of the ellipse equation of the image of each target mark point0,y0)；
Figure BDA0001991323250000091
In order to suppress the influence of image noise, the contour of each target marker point is fitted twice. After the first fitting, counting the distance between the pixel points forming the outline and the elliptical equation, removing the pixel points with larger distance, and performing second fitting on the pixel points forming the outline by using an elliptical least square fitting algorithm to obtain the coefficient of the elliptical equation of the image of each target mark point for inhibiting the influence of image noise; determining the center coordinates (x) of each target mark point in the image coordinate system according to the coefficient of the ellipse equation of the image of each target mark point for inhibiting the influence of image noise0,y0). Fitting a sub-pixel precision ellipse to the ellipse equation of the image of each target landmark point for which the equation coefficients are determined in step (3.2).
And 4, step 4: establishing a camera projection model to represent the projection relation between an object point and an image point, wherein the object point is a target mark point pasted on the flexible spaceborne antenna, and the image point is the central pixel coordinate of a sub-pixel precision ellipse corresponding to the object point; the camera projection model comprises internal parameters and external parameters, and specifically comprises the following steps:
(4.1) selecting 4 coplanar mark points from the target mark points pasted on the flexible satellite-borne antenna;
(4.2) establishing a camera projection model according to the selected 4 coplanar mark points, wherein the model comprises the following steps:
Figure BDA0001991323250000092
where s is an arbitrary scalar factor and u and v are selected criteriaThe coordinates of the image point of the mark point in the image coordinate system, X and Y are the X-axis and Y-axis coordinates of the selected mark point in the antenna coordinate system, r1，r2，r3A column vector of a coordinate transformation matrix R for the antenna coordinate system to the camera coordinate system (R is denoted as [ R ]1r2r3]) T is the translation vector from the antenna coordinate system to the camera coordinate system, A is the internal reference of the camera, and R and t are external references. Let M be [ X, Y ]]TCoordinates representing a marking point, m ═ u, v]TRepresenting coordinates of image points of the index points, and
Figure BDA0001991323250000093
Figure BDA0001991323250000094
thus, formula (3) is described as formula (4)
Figure BDA0001991323250000095
And 5: calibrating external parameters of a camera projection model according to the central pixel coordinates of each sub-pixel precision ellipse to finish on-orbit calibration, which comprises the following steps:
the known camera internal parameter A and external parameter are calculated by the following formula
r1＝λA-1h1,r2＝λA-1h2,r3＝r1×r2,t＝λA-1h3 (5)
Wherein λ 1/| | a-1h1||＝1/||A-1h2||。
Step 6: calibrating the camera projection model after external reference according to the step (5), and performing on-orbit vibration measurement on a target mark point pasted by the flexible satellite-borne antenna, wherein the on-orbit vibration measurement specifically comprises the following steps:
let O be the camera optical center of the camera projection model and OA be the optical axis of the camera projection model, assuming that the vibration direction of the marker point is parallel to the phase plane of the camera projection model, at t0At time A, the position of the target mark point on the optical axis is shown, and the height before the displacement due to vibration isH, B represents the image position formed by the target mark point before the displacement generated by vibration, the height is H', after the vibration time t of the target mark point, the mark point is upwards displaced in the plane by w, the displacement is w, the height of the image of the target mark point formed by the camera after the displacement is H, and the displacement delta H of the mark point obtained by the similarity relation is:
Figure BDA0001991323250000101
where a denotes the distance of an image point from the camera's optical center, i.e. the camera's focal length, and b denotes the distance of an object point from the camera's optical center.
At this time, the displacement amount of the target mark point and the pixel change magnitude thereof have a nearly linear relationship, so the spatial in-plane displacement amount w can be represented by the pixel displacement magnitude Δ h of the target mark point image, and therefore, the in-plane vibration information of the target mark point is obtained by extracting the characteristics of the central pixel point of the vibration image, and the on-track vibration measurement is realized.
As shown in FIG. 6, the measured mark point is P, and the vibration quantity of the measured mark point on the x-axis of the camera coordinate system is deltaxFocal length of camera is f, and coordinate of principal point under image coordinate system is u0、v0The coordinates of the image point in the image coordinate system are u and v, and the coordinate of the known P point in the Z-axis of the camera coordinate system is ZpAccording to the measuring principle of monocular cameras, deltaxCan be calculated from the following formula
Figure BDA0001991323250000102
Accordingly, the vibration quantity δ of the marker point on the y-axis of the camera coordinate systemyIs composed of
Figure BDA0001991323250000103
Test verification: the flexible thin plate is used as an antenna vibration simulation piece, and a vibration test experiment is used for verifying the effectiveness of the method. The reflective markers are attached to the ends of the board as shown in figure 7. Giving a tiny initial deformation to the thin plate, adopting a binocular camera to acquire images of the thin plate for 150 frames at a frame rate of 33fps, and acquiring the centroid of the identification mark point by utilizing an image processing algorithm. Taking a certain mark point as an example, the method of the invention is adopted to obtain the vibration displacement of the X axis and the Y axis of the mark point, and the maximum error is 0.8mm compared with the result of the binocular measurement method, for example, as shown in fig. 8(a) and (b).
The vibration measuring method has the advantages of no damage to the measured structure, no interference to the task function and the dynamic characteristic of the measured structure; the invention has the on-track calibration function after the antenna is in track, and realizes the position relation of the measured mark points to be corrected in track;
the vibration measurement method of the invention fully utilizes the high resolution in the camera imaging plane, realizes the off-plane vibration measurement of the antenna structure, and the measurement precision can reach millimeter level; moreover, the algorithm has small calculation amount, operability and realizability, and is easy to meet the on-orbit real-time measurement requirement; the invention can meet the measurement requirement only by one camera, avoids the problems of high-precision installation, calibration and the like of a binocular camera and has high system reliability.

Claims (5)

1. A flexible satellite-borne antenna in-orbit vibration measurement method based on sequence images is characterized by comprising the following steps:
(1) pasting a target mark point on the flexible satellite-borne antenna, wherein the target mark point is circular, and acquiring images of the flexible satellite-borne antenna according to a time sequence to obtain a sequence image of the flexible satellite-borne antenna;
(2) extracting target mark points from the sequence image of the flexible satellite-borne antenna to obtain the outline of each target mark point;
(3) respectively fitting the outlines of all the target mark points into sub-pixel precision ellipses, and determining the central pixel coordinates of all the sub-pixel precision ellipses;
(4) establishing a camera projection model to represent the projection relation between an object point and an image point, wherein the object point is a target mark point pasted on the flexible spaceborne antenna, and the image point is the central pixel coordinate of a sub-pixel precision ellipse corresponding to the object point; the camera projection model comprises internal parameters and external parameters, and specifically comprises the following steps:
(4.1) selecting 4 coplanar mark points from the target mark points pasted on the flexible satellite-borne antenna;
(4.2) establishing a camera projection model according to the selected 4 coplanar mark points, wherein the model comprises the following steps:
Figure FDA0002924113420000011
wherein s is an arbitrary scalar factor, u and v are coordinates of the image point of the selected marker point in the image coordinate system, X and Y are coordinates of the X axis and the Y axis of the selected marker point in the antenna coordinate system, and r is a linear coordinate of the selected marker point in the antenna coordinate system1，r2，r3A column vector of a coordinate transformation matrix R from the antenna coordinate system to the camera coordinate system, R being denoted as [ R1 r2 r3]T is a translation vector from an antenna coordinate system to a camera coordinate system, A is an internal reference of the camera, and R and t are external references; let M be [ X, Y ]]TCoordinates representing a marking point, m ═ u, v]TRepresenting coordinates of image points of the index points, and
Figure FDA0002924113420000012
Figure FDA0002924113420000013
thus, formula (1) is described as formula (2)
Figure FDA0002924113420000014
(5) Calibrating external parameters of a camera projection model according to the central pixel coordinates of each sub-pixel precision ellipse to finish on-orbit calibration;
(6) and (5) calibrating the camera projection model after external reference according to the step (5), and performing on-orbit vibration measurement on the target mark point pasted by the flexible satellite-borne antenna.
2. The on-orbit vibration measurement method of the flexible satellite-borne antenna based on the sequence image as claimed in claim 1, characterized in that: the method comprises the following steps of (1) pasting a target mark point on the flexible satellite-borne antenna, wherein the target mark point is circular, and carrying out image acquisition on the flexible satellite-borne antenna according to a time sequence to obtain a sequence image of the flexible satellite-borne antenna, and the method specifically comprises the following steps:
(1.1) according to the vibration mode of the flexible satellite-borne antenna, pasting a target mark point at the obvious deformation position;
(1.2) selecting mark points with directional light reflecting performance, wherein the shape is selected to be a circle with the same size;
and (1.3) acquiring images of the flexible satellite-borne antenna by adopting a visible light optical camera according to a certain frame rate, wherein the frame rate is selected to be one order of magnitude higher than the frequency value of the vibration mode of the flexible satellite-borne antenna to be measured, and obtaining a sequence image of the flexible satellite-borne antenna.
3. The on-orbit vibration measurement method of the flexible satellite-borne antenna based on the sequence image as claimed in claim 1, characterized in that: extracting target mark points from the sequence image of the flexible satellite-borne antenna to obtain the outline of each target mark point, wherein the specific steps are as follows:
(2.1) carrying out image binarization processing on a sequence image of the flexible satellite-borne antenna, namely an obtained original image, so as to obtain a binarized image;
(2.2) extracting a connected domain of each target mark point in the binary image;
and (2.3) carrying out edge detection on the connected domain of each target mark point to obtain the outline of each target mark point.
4. The on-orbit vibration measurement method of the flexible satellite-borne antenna based on the sequence image as claimed in claim 1, characterized in that: and (3) respectively fitting the outlines of all target mark points into a sub-pixel precision ellipse, which is as follows:
(3.1) establishing an ellipse equation of the image of each target mark point, wherein the image of each target mark point is a plane ellipse;
(3.2) fitting the outline of each target mark point by using an elliptic least square fitting algorithm to obtain the coefficient of an elliptic equation of the image of each target mark point;
(3.3) determining the center coordinates (x) of each target mark point in the image coordinate system according to the coefficient of the ellipse equation of the image of each target mark point0,y0)。
5. The on-orbit vibration measurement method of the flexible satellite-borne antenna based on the sequence image as claimed in claim 4, characterized in that: (3.3) determining the center coordinates (x) of each target mark point in the image coordinate system according to the coefficient of the ellipse equation of the image of each target mark point0,y0)；
Figure FDA0002924113420000031
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