CN110231019B - Vision-based tethered satellite tether swing angle measurement method - Google Patents

Vision-based tethered satellite tether swing angle measurement method Download PDF

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CN110231019B
CN110231019B CN201910422813.2A CN201910422813A CN110231019B CN 110231019 B CN110231019 B CN 110231019B CN 201910422813 A CN201910422813 A CN 201910422813A CN 110231019 B CN110231019 B CN 110231019B
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coordinate system
tether
marker ball
camera
image
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CN110231019A (en
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康晶杰
文浩
金栋平
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C11/00—Photogrammetry or videogrammetry, e.g. stereogrammetry; Photographic surveying
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C11/00—Photogrammetry or videogrammetry, e.g. stereogrammetry; Photographic surveying
    • G01C11/04—Interpretation of pictures

Abstract

The invention discloses a method for measuring the swing angle of a tether satellite tether based on vision, which comprises the following steps: a marker ball is arranged at the near end of the tether from the main satellite; determining a reference coordinate system and known physical quantities; determining the coordinates of the marker ball pixels through a visual motion capture algorithm; solving the direction vector of the marker ball relative to the camera coordinate system by determining the conversion relation between the pixel coordinate system and the image coordinate system and the relation between the image coordinate system and the camera coordinate system; obtaining a direction vector of the marker ball relative to the main star coordinate system by utilizing a conversion relation between a camera coordinate system and the main star coordinate system; utilizing a tether swing angle to represent a direction vector of the marker ball relative to a main star coordinate system; and reversely solving the swing angle of the tether by using the direction vector which is expressed by the three-dimensional coordinates. Compared with the traditional measuring method by using the tension sensor, the method has the advantages that the requirements on software and hardware are far lower than those of the latter method, and the measurement precision, range and speed are far better than those of the latter method.

Description

Vision-based tethered satellite tether swing angle measurement method
Technical Field
The invention belongs to the technical field of spacecraft measurement and control, and particularly relates to a method for measuring a tether swing angle of a tether satellite based on vision, which can be applied to tether swing angle measurement in a tether satellite system and control of the system.
Background
Tethered satellites are space flight systems formed by two or more satellites connected together by tethers, and are most representative of main satellite-tether-subsatellite systems formed by connecting one satellite (subsatellite) to another satellite (main satellite) with a larger mass through a flexible tether. The system has wide application prospect, such as artificial gravity, rail transfer, space debris cleaning, earth observation and deep space exploration. In the past decades, various researchers have conducted a great deal of theoretical and experimental research on spatial tether systems, and have found that stable release, state retention, and recovery of tethers are essential conditions for the tether systems to perform spatial tasks. However, when the tether moves in space, vibration or oscillation which is not beneficial to the movement of the system occurs due to the influence of coriolis force, and it is important to measure the swing angle of the tether efficiently and accurately in order to effectively realize feedback control of the tether. The currently widely used method for measuring the swing angle of the tether uses a tension sensor, but the sensor still has the common defects of a contact sensor, and compared with a non-contact measuring method, the method has the advantages of high maintenance cost, low measuring speed, small measuring range and low measuring precision.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a method for measuring a tether swing angle of a tethered satellite based on vision, so as to solve the problems of slow measurement speed, small measurement range and low measurement accuracy caused by using a tension sensor in the conventional tether swing angle measurement method.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention relates to a method for measuring a tether satellite tether swing angle based on vision, which comprises the following steps:
step 1: installing a marker ball on a near-end tether of a main satellite in a tethered satellite system to estimate the pivot angle of the tether relative to the main satellite;
step 2: taking the main star as a rigid body, establishing a main star coordinate system and a camera coordinate system, and determining the equivalent focal length of a camera, a camera imaging plane, a marker sphere actual motion plane and the distance between the main star and the marker sphere along the tether direction; establishing a pixel coordinate system and an image coordinate system on a camera imaging plane;
and step 3: obtaining the pixel coordinates of the center position of the marker ball searching area by using a visual tracking algorithm;
and 4, step 4: according to the pixel coordinates, obtaining a direction vector of the marker ball relative to the camera coordinate system represented by the three-dimensional coordinates by utilizing the relation between the camera coordinate system and the image coordinate system and ensuring that the distance between the marker ball and the main star is constant along the tether direction;
and 5: because the camera is fixed on the main satellite and is vertically and downwards placed, the axis of the optical center is basically coincided with the vertical axis of the main satellite, and the direction vector of the marker ball relative to the coordinate system of the main satellite is obtained by utilizing the coordinate conversion relation between the coordinate system of the camera and the coordinate system of the main satellite;
step 6: and (5) combining a geometrical model of the tethered satellite system, representing the direction vector represented by the obtained three-dimensional coordinates in the step 5 by using the swing angle of the tether relative to the main star, and obtaining the swing angle of the tether by inverse solution.
The accuracy of identifying the movement of the marker ball by using the marker ball on the tether can be improved by using a visual tracking algorithm, so that the swing angle of the tether is further calculated, and the measurement of the swing angle of the tether is completed.
Further, the step 3 specifically includes the following steps:
step 31: acquiring an image of the marker ball on the tether by using a camera on the main satellite;
step 32: converting the acquired original color image into an HSV format, and extracting an H component in the HSV image; wherein H represents chroma, saturation S represents the degree of color approaching spectral color, and lightness V represents the brightness degree of color;
step 33: selecting an area where a marker ball in a camera imaging plane is located as a search area, and calculating a color histogram of the area;
step 34: according to the color histogram of the search area, carrying out back projection on the captured image of the current frame to obtain a probability distribution projection image of the current frame;
step 35: tracking window size and initial position (x) in projection images based on probability distribution0,y0) By the zeroth order moment:
Figure GDA0002958116830000021
first moment of x:
Figure GDA0002958116830000022
first moment of y:
Figure GDA0002958116830000023
calculating the centroid within the tracking window:
Figure GDA0002958116830000024
wherein, Io(x, y) is a pixel value of coordinates (x, y); of x and yThe variation range is the size of a search window;
step 36: resetting the size of the search window;
step 37: repeating the steps 35 and 36 until the centroid converges and moving the center position of the search window to the centroid position;
step 38: the center position and the area size of the marker ball search area are obtained, the next frame image is retrieved, and the current center position and the area size are used to go to step 34 to search in the new image frame.
Further, the specific step of obtaining the direction vector of the marker ball relative to the camera coordinate system in the step 4 is:
step 41: obtaining the pixel coordinates (u, v) of the marker ball searching center position in the pixel coordinate system, converting the pixel coordinates (u, v) into the image coordinate system, and obtaining the coordinates (x) of the marker ball searching center position in the image coordinate systemp,yp)，
Figure GDA0002958116830000025
Wherein (u)0,v0) The position of the central point of the pixel coordinate system; dx and dy represent the physical dimensions of each pixel in the horizontal and vertical axes, respectively;
step 42: obtaining by using the relation between the camera coordinate system and the image coordinate system:
Figure GDA0002958116830000031
wherein f is the equivalent focal length of the camera;
Figure GDA0002958116830000032
is the direction vector of the marker ball relative to the camera coordinate system;
step 43: the distance between the marker ball and the main star along the tether direction is certain, namely:
Figure GDA0002958116830000033
wherein l0And (3) obtaining a direction vector of the marker ball relative to a camera coordinate system by combining the main star and the marker ball along the tether distance according to the formula (5), the formula (6) and the formula (7):
Figure GDA0002958116830000034
the invention has the beneficial effects that:
compared with the traditional method of measuring the tether swing angle of the tether satellite system by using a tension sensor and other contact methods, the method provided by the invention can determine the tether swing angle only by adopting a mode of acquiring a marker ball image by a camera; therefore, the method is far higher than the traditional triaxial force sensor in detection efficiency, measurement speed and measurement range, and is lower than a contact type measurement sensor in cost, environmental resistance and software and hardware requirements. These are all very critical improvements for the safe and stable operation of tethered satellites operating in orbit.
Drawings
FIG. 1 is an overall flow diagram of the method of the present invention.
FIG. 2 is a schematic view of the visual imaging relationship of the method of the present invention.
FIG. 3 is a flow chart of a visual tracking algorithm of the method of the present invention.
FIG. 4 is a schematic diagram of a geometric physical model of the method of the present invention.
FIG. 5 is a schematic diagram of the coordinate system transformation relationship of the method of the present invention.
Detailed Description
In order to facilitate understanding of those skilled in the art, the present invention will be further described with reference to the following examples and drawings, which are not intended to limit the present invention.
Referring to fig. 1-5, the method for measuring the swing angle of the tether of the vision-based tethered satellite comprises the following steps:
step 1, as shown in fig. 2, a marker ball 3 is installed at the near end of the tether from the main star 1, so as to estimate the pivot angle of the tether relative to the main star 1.
Step 2, for the convenience of research, please refer to fig. 2 and 4, regarding the main star as a rigid body, establishing a coordinate system xyz of the main star 1 and a camera coordinate system OcXcYcZcImage coordinate system OpXpYpPixel coordinate system O0uv, determining camera focal length
Figure GDA0002958116830000041
The distance l between the main star 1 and the marker ball 3 along the tether0Camera imaging plane C and marker ball actual motion plane a.
Step 3, referring to the flow of the visual tracking algorithm of fig. 3, obtaining the pixel coordinates of the marker ball by using the visual tracking algorithm;
and 3-1, acquiring an image of a marker ball 3 on a tether of the tethered satellite system by using a camera on the main satellite 1.
Step 3-2, converting the acquired original color image into an HSV format, and extracting an H component in the HSV image; where H denotes chromaticity, saturation S denotes the degree to which a color approaches a spectral color, and lightness V denotes the degree to which a color is bright.
And 3-3, selecting the area where the marker ball 3 in the camera imaging plane is located as a search area, and calculating the color histogram of the area.
And 3-4, performing back projection on the captured image of the current frame according to the color histogram of the target area to obtain a probability distribution projection image of the current frame.
Step 3-5, tracking window size and initial position (x) according to color probability distribution diagram0,y0) By passing
Zero order moment:
Figure GDA0002958116830000042
first moment of x:
Figure GDA0002958116830000043
first moment of y:
Figure GDA0002958116830000044
calculating the centroid within the tracking window:
Figure GDA0002958116830000045
wherein, Io(x, y) is a pixel value of coordinates (x, y); the variation range of x and y is the size of the search window;
step 3-6: resetting the size of the search window;
step 3-7: repeating the step 3-5 and the step 3-6 until the centroid is converged, and moving the center position of the search window to the centroid position;
step 3-8: and obtaining the center position and the area size of the marker ball searching area, re-acquiring the next frame of image, and turning to the step 3-4 by using the current center position and the area size to search in a new image frame.
Step 4, solving the direction vector of the marker ball relative to the camera coordinate system;
step 4-1, obtaining the pixel coordinates (u, v) of the center position of the marker ball search area in the pixel coordinate system, referring to fig. 2, converting the pixel coordinates into the image coordinate system, and obtaining the coordinates (x) of the center position of the marker ball search area in the image coordinate systemp,yp)
Figure GDA0002958116830000046
Wherein (u)0,v0) The position of the central point of the pixel coordinate system; dx and dy represent the physical dimensions of each pixel in the horizontal and vertical axes, respectively;
step 4-2, please refer to fig. 2, using the relationship between the camera coordinate system and the image coordinate system to obtain:
Figure GDA0002958116830000051
wherein f is the equivalent focal length of the camera;
Figure GDA0002958116830000052
is the direction vector of the marker ball relative to the camera coordinate system.
Step 4-3, determining the distance between the marker ball and the main star along the tether direction as l0I.e. by
Figure GDA0002958116830000053
Wherein l0The distance between the main star and the marker ball along the tether line; then the joint formula (5), formula (6) and formula (7) obtain the direction vector of the marker ball relative to the camera coordinate system:
Figure GDA0002958116830000054
step 5, because the camera 4 is fixed on the main star 1 and along the Z-axis direction, the optical center ZcThe axis substantially coincides with the Z axis of the main satellite, and referring to fig. 5, the coordinate transformation relationship between the camera coordinate system and the main satellite coordinate system is used to obtain:
Figure GDA0002958116830000055
wherein the content of the first and second substances,
Figure GDA0002958116830000056
the direction vector of the marker ball on the A plane relative to the main star coordinate system;
Figure GDA0002958116830000057
as camera coordinate system OcXcYcZcCoordinate transformation matrix to principal star coordinate system OXYZ, camera coordinate system by rolling gamma and pitchingPitch β and yaw α are obtained in three rotations, namely:
Figure GDA0002958116830000058
wherein the content of the first and second substances,
Figure GDA0002958116830000059
- - -represents a winding ZcA rotation matrix of axis rotation gamma degrees;
Figure GDA00029581168300000510
- - -represents a winding YcA rotation matrix with axes rotated by β degrees;
Figure GDA00029581168300000511
- - -represents a winding XcA rotation matrix of axis rotation alpha degrees;
referring to the relationship between the camera coordinate system and the main satellite coordinate system shown in fig. 4, values of γ, β, and α are 90 °, 0 °, and 180 °, respectively, so as to obtain an equation (11);
Figure GDA0002958116830000061
the direction vector of the marker ball 3 relative to the main star coordinate system is calculated as follows:
Figure GDA0002958116830000062
step 6, please refer to FIG. 4, wherein the swing angle θ and φ of the tether is used to represent qaObtaining:
Figure GDA0002958116830000063
combining the vertical type (12) with the formula (13) to obtain the tether swing angle:
Figure GDA0002958116830000064
while the invention has been described in terms of its preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention.

Claims (3)

1. A method for measuring the swing angle of a tether satellite tether based on vision is characterized by comprising the following steps:
step 1: installing a marker ball on a near-end tether of a main satellite in a tethered satellite system to estimate a tether swing angle;
step 2: taking the main star as a rigid body, establishing a main star coordinate system and a camera coordinate system, and determining the equivalent focal length of a camera, a camera imaging plane, a marker ball actual motion plane and the distance between the marker ball and the main star along the tether direction; establishing a pixel coordinate system and an image coordinate system on a camera imaging plane;
and step 3: obtaining the pixel coordinates of the center position of the marker ball searching area by using a visual tracking algorithm;
and 4, step 4: according to the pixel coordinates, obtaining a direction vector of the marker ball relative to the camera coordinate system represented by the three-dimensional coordinates by utilizing the relation between the camera coordinate system and the image coordinate system and ensuring that the distance between the marker ball and the main star is constant along the tether direction;
and 5: obtaining a direction vector of the marker ball relative to the main star coordinate system by utilizing the coordinate conversion relation between the camera coordinate system and the main star coordinate system;
step 6: and (5) combining a geometric model of the tether satellite system, representing the direction vector represented by the three-dimensional coordinate obtained in the step (5) by using a tether swing angle, and obtaining the tether swing angle through inverse solution.
2. The vision-based tethered satellite tether tilt measurement method of claim 1, wherein said step 3 comprises the steps of:
step 31: acquiring an image of the marker ball on the tether by using a camera on the main satellite;
step 32: converting the acquired original color image into an HSV format, and extracting an H component in the HSV image; wherein H represents chroma, saturation S represents the degree of color approaching spectral color, and lightness V represents the brightness degree of color;
step 33: selecting an area where a marker ball in a camera imaging plane is located as a search area, and calculating a color histogram of the search area;
step 34: according to the color histogram of the search area, carrying out back projection on the captured image of the current frame to obtain a probability distribution projection image of the current frame;
step 35: tracking window size and initial position (x) in projection images based on probability distribution0,y0) By the zeroth order moment:
Figure FDA0002958116820000011
first moment of x:
Figure FDA0002958116820000012
first moment of y:
Figure FDA0002958116820000013
calculating the centroid within the tracking window:
Figure FDA0002958116820000014
wherein, Io(x, y) is a pixel value of coordinates (x, y); the variation range of x and y is the size of the tracking window;
step 36: resetting the size of the tracking window;
step 37: repeating the step 35 and the step 36 until the centroid converges, and moving the central position of the tracking window to the centroid position;
step 38: and obtaining the central position and the area size of the marker ball searching area, re-acquiring the next frame of image, and turning to the step 34 by using the central position and the area size of the current marker ball searching area to search in a new image frame.
3. The vision-based tethered satellite tether swing angle measurement method of claim 1, wherein the specific step of obtaining the direction vector of the marker ball relative to the camera coordinate system in step 4 is:
step 41: obtaining the pixel coordinates (u, v) of the central position of the marker ball searching area in the pixel coordinate system, converting the pixel coordinates into the image coordinate system, and obtaining the coordinates (x) of the central position of the marker ball searching area in the image coordinate systemp,yp)，
Figure FDA0002958116820000021
Wherein (u)0,v0) The position of the central point of the pixel coordinate system; dx and dy represent the physical dimensions of each pixel in the horizontal and vertical axes, respectively;
step 42: obtaining by using the relation between the camera coordinate system and the image coordinate system:
Figure FDA0002958116820000022
wherein f is the equivalent focal length of the camera;
Figure FDA0002958116820000023
is the direction vector of the marker ball relative to the camera coordinate system;
step 43: the distance between the marker ball and the main star along the tether direction is certain, namely:
Figure FDA0002958116820000024
wherein l0And (3) obtaining a direction vector of the marker ball relative to a camera coordinate system by combining the marker ball and the main star along the tether direction, wherein the distance is between the marker ball and the main star, and the direction vector is obtained by the following formula (5), formula (6) and formula (7):
Figure FDA0002958116820000025
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6419191B1 (en) * 1997-09-12 2002-07-16 Robert P. Hoyt Electrodynamic tether control
CN103984812A (en) * 2014-05-09 2014-08-13 西北工业大学 Simulation method applicable to space tethered system of stratospheric satellite system

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6419191B1 (en) * 1997-09-12 2002-07-16 Robert P. Hoyt Electrodynamic tether control
CN103984812A (en) * 2014-05-09 2014-08-13 西北工业大学 Simulation method applicable to space tethered system of stratospheric satellite system

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
绳系系统轨道机动过程中的面内摆角抑制*;薛超;《空间控制技术与应用》;20170430;第43卷(第2期);全文 *

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