CN111619825B - Cross-cut formation method and device based on star-sail rope system - Google Patents
Cross-cut formation method and device based on star-sail rope system Download PDFInfo
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Abstract
The application discloses based on star-sail rope systemThe system cross-section formation method and device comprises a star-sail rope system and a solar sail, wherein the star and the solar sail are connected through a metal conductive rope, and the method comprises the following steps: determining orbit parameters of a main star and a solar sail, and calculating motion parameters of the system according to the orbit parameters and a preset motion model of a star-sail-rope system mass center; calculating the attitude parameters of the star-sail-rope system according to the motion parameters and a preset rotation model of the star-sail-rope system around the mass center; at earth oblateness J2Determining the control acceleration of the solar sail according to the attitude and orbit parameters obtained by calculation and preset ideal attitude and orbit parameters under the conditions of perturbation and keeping the stable relative baseline between the solar sail and the main satellite; and controlling the relative motion of the solar sail and the main star according to the track parameters, the motion parameters and the control acceleration to realize cross-section formation. The stability relatively poor technical problem of transversal formation among the prior art has been solved in this application.
Description
Technical Field
The application relates to the technical field of satellite formation, in particular to a transverse formation method and device based on a star-sail rope system.
Background
The formation of the satellite refers to a system with complete functions and distributed cooperative work of a plurality of satellites, and compared with the traditional single satellite, the formation of the satellite has the advantages of large aperture, long measurement baseline, capability of realizing functions which cannot be realized by the single satellite and the like, and is widely applied. During the formation of the satellite, the relative baseline between the satellites is not fixed and changes along with the movement of the satellites, the formation of the satellite formation affects the parameters of the baseline of the satellites, for example, the parameters of the baseline include the length, the direction, the change condition and the like of the baseline, and the parameters of the baseline of the satellites not only affect the image quality of the satellites, but also affect the accuracy of the spatial satellite interferometry. Therefore, how to realize the configuration of the formation of the satellites has an important influence on the images of the satellites.
Currently, it is common to implement a cross formation of satellites based on a solar sail, and the specific process is as follows: the method comprises the steps of determining a sun synchronous orbit according to the selected height of the sun synchronous orbit and a descending intersection point, transmitting a sun sail to the sun synchronous orbit as a combination body of a main satellite, ejecting the sun sail through an ejection device in the sun synchronous orbit, enabling the sun sail to enter a non-open-type suspension orbit which moves at the same frequency as the main satellite under the action of solar radiation pressure, determining the distance between the sun sail and a synchronous orbit satellite where the main satellite is located, and then controlling the movement of the sun sail according to the distance to enable the sun sail and the main satellite to keep stable relative baselines so as to achieve cross formation. In other words, in the prior art, in order to maintain a stable relative baseline between the solar sail and the main star, the movement of the solar sail is controlled by taking the synchronous orbit of the main star as a reference, but the main star may receive atmospheric resistance or other forces during the operation of the solar synchronous orbit, so that the actual operation synchronous orbit of the main star changes. Therefore, the prior art controls the movement of the solar sail by taking the synchronous track where the main star is positioned as a reference, and the stability of the cross-section formation is poor.
Disclosure of Invention
The technical problem that this application was solved is: in the scheme provided by the embodiment of the application, the relative motion between the main star and the solar sail is controlled through the attitude parameters and the motion parameters of the star-sail rope system, so that the problem of poor stability of the transverse formation caused by controlling the motion of the solar sail by taking the synchronous track where the main star is located as the reference is avoided.
In a first aspect, the present embodiments provide a cross-section formation method based on a star-sail-rope-system, the star-sail-rope-system including a main star and a solar sail, wherein the main star and the solar sail are connected by a metal conductive rope, the method including:
determining orbit parameters of the main star and the solar sail, and calculating motion parameters of the mass center of the star-sail-rope system according to the orbit parameters and a preset motion model of the mass center of the star-sail-rope system;
calculating the attitude parameters of the star-sail-rope system according to the motion parameters and a preset rotation model of the star-sail-rope system around the mass center;
at earth oblateness J2Determining the control acceleration of the solar sail according to the attitude and orbit parameters and preset ideal attitude and orbit parameters under the conditions of perturbation and keeping the solar sail and the main satellite to keep stable relative baseline;
and controlling the relative motion of the solar sail and the main star according to the track parameters, the motion parameters and the control acceleration to realize cross-section formation.
In the scheme provided by the embodiment of the application, a solar sail and a main satellite are connected through a metal conductive rope to form a star-sail rope system, orbit parameters of the main satellite and the solar sail are determined in the star-sail rope system, a motion parameter of a mass center of the star-sail rope system is determined according to the orbit parameters, an attitude parameter of the star-sail rope system is determined according to a motion parameter of the star-sail rope system around the mass center, and the earth oblateness J is2And under the condition of perturbation and keeping the stable relative baseline of the solar sail and the main star, controlling the relative motion of the solar sail and the main star according to the track parameters, the motion parameters and the control acceleration, and further realizing transverse formation. Therefore, in the scheme provided by the embodiment of the application, the relative motion between the main star and the solar sail is controlled through the attitude parameters and the motion parameters of the star-sail rope system, so that the problem of poor stability of transverse formation caused by controlling the motion of the solar sail by taking the synchronous track where the main star is located as a reference is avoided.
Optionally, determining orbit parameters of the main star and the solar sail comprises:
determining the height of the track at morning and evening and the local time of the descending intersection point according to the input task information, and determining the height of the track at morning and evening and the local time of the descending intersection point according to the height of the track at morning and evening and the J2Calculating the morning of the main starA stunning track parameter;
and calculating the acceleration of solar radiation required by the orbit of the solar sail, which moves with the same frequency as the main satellite under the action of the solar radiation pressure, and the included angle between the acceleration and the normal direction of the sail surface of the solar sail according to the preset rope length.
Optionally, calculating a motion parameter of the center of mass of the star-sail-rope system according to the track parameter and a preset motion model of the center of mass of the star-sail-rope system, including:
under an earth center inertial coordinate system, calculating the acceleration of the center of mass according to the track parameters and the motion model;
and calculating the position and the speed of the centroid under the geocentric inertial coordinate system at any moment according to the acceleration.
Optionally, calculating the acceleration of the center of mass from the orbit parameter and the motion model comprises: the acceleration is calculated according to the following formula:
wherein r isbRepresenting the position vector, r, of said centroid in an inertial frame of the earth's centerb＝[xb yb zb]T；
Representing an acceleration of the center of mass; μ represents a normalized earth gravity constant; reRepresents the radius of the earth; j. the design is a square2Representing the earth oblateness perturbation coefficient; mu.sdRepresenting the weight of the solar sail in the proportion of the whole rope system; t isciRepresenting the control acceleration, T, in the inertial frame of the Earth's centerci＝[TX Ty Tz]T；asiRepresenting the acceleration of solar radiation.
Optionally, calculating an attitude parameter of the star-sail-rope system according to the motion parameter and a preset rotation model of the star-sail-rope system around the center of mass, including: under the body coordinate system, the external moment under the body coordinate system is calculated according to the following formula:
wherein, MbRepresenting external moment under a body coordinate system; { J }bRepresenting a rotational inertia matrix; { J }b＝diag(Jx，Jy，Jz),Jx＝0，
m1Represents the mass of the main star, m2Representing the mass of the solar sail, /)1Representing the line length between the principal star and the center of mass,/2Representing the line length between the solar sail and the center of mass,/2＝l-l1And l represents the line length between the main star and the solar sail; { omega }bRepresenting the rotational angular velocity of the body coordinate system relative to the earth's center inertial coordinate system.
Calculating the attitude parameter according to the external moment by the following formula:
{M}b＝Ry(-η2)·Rz(η1)·{M}i
wherein, Mi＝[Mxi Myi Mzi]T；RyA rotation matrix representing the y-axis; rzRepresenting a z-axis rotation matrix; eta1Representing the relative position vector ar at xi-yiProjection on plane and xiAngle between axes, 0 ≤ η1≤2π；η2Denotes Δ r and xi-yiThe angle between the planes, -pi/2 ≤ eta2≤π/2。
Optionally, controlling the relative movement of the solar sail and the main star according to the orbit parameter, the motion parameter and the control acceleration comprises:
respectively calculating the positions and the speeds of the solar sail and the main star under the geocentric inertial coordinate system according to the motion parameters and the attitude parameters;
determining a conversion matrix corresponding to the conversion of the position and the speed from the geocentric inertial coordinate system to a main satellite orbit coordinate system;
determining relative motion parameters between the solar sail and the main satellite according to the conversion matrix, the track parameters and the control acceleration;
and controlling the relative motion of the solar sail and the main star according to the relative motion parameters.
Optionally, respectively calculating the position and the speed of the solar sail and the main star under the geocentric inertial coordinate system according to the motion parameter and the attitude parameter, including:
calculating the position and the velocity by the following formulas:
wherein r iscRepresenting the position vector of the main star in the geocentric inertial coordinate system; r isdRepresenting a position vector of the solar sail in the geocentric inertial coordinate system;
representing the velocity vector of the main star in the earth's center inertial coordinate system,
representing the velocity vector of the solar sail in the geocentric inertial frame,
optionally, determining a transformation matrix corresponding to the transformation of the position and the velocity from the geocentric inertial coordinate system to the main satellite orbit coordinate system includes:
determining the transformation matrix according to the following formula:
wherein L is0iRepresenting the transformation matrix.
Optionally, determining a relative motion parameter between the solar sail and the main satellite according to the transformation matrix, the orbit parameter, and the control acceleration includes:
determining the position and speed of relative movement between the solar sail and the primary star according to the following formula:
Δro＝Loi·Δri
Δri＝rd-rc
wherein, Δ roRepresenting the position of relative motion under the orbit coordinate system of the main satellite; Δ riRepresenting the position of relative motion under an earth-centered inertial coordinate system;
represents a principalThe speed of relative motion under the star orbit coordinate system;
representing the velocity of relative motion in the earth's center inertial frame.
In a second aspect, embodiments of the present application provide a cross-section formation device based on a star-sail-rope-system, the star-sail-rope-system including a main star and a solar sail, wherein the main star and the solar sail are connected by a metal conductive rope, the device including:
the first determining unit is used for determining the orbit parameters of the main star and the solar sail, and calculating the motion parameters of the mass center of the star-sail-rope system according to the orbit parameters and a preset motion model of the mass center of the star-sail-rope system;
the computing unit is used for computing the attitude parameters of the star-sail-rope system according to the motion parameters and a preset rotation model of the star-sail-rope system around the mass center;
a second determination unit for determining the ellipticity J of the earth2Determining the control acceleration of the solar sail according to the attitude and orbit parameters and preset ideal attitude and orbit parameters under the conditions of perturbation and keeping the solar sail and the main satellite to keep stable relative baseline;
and the control unit is used for controlling the relative motion of the solar sail and the main satellite according to the track parameters, the motion parameters and the control acceleration so as to realize transverse formation.
Optionally, the first determining unit is specifically configured to:
determining the height of the track at morning and evening and the local time of the descending intersection point according to the input task information, and determining the height of the track at morning and evening and the local time of the descending intersection point according to the height of the track at morning and evening and the J2Calculating the morning and evening orbit parameters of the main star;
and calculating the acceleration of solar radiation required by the orbit of the solar sail, which moves with the same frequency as the main satellite under the action of the solar radiation pressure, and the included angle between the acceleration and the normal direction of the sail surface of the solar sail according to the preset rope length.
Optionally, the first determining unit is specifically configured to:
under an earth center inertial coordinate system, calculating the acceleration of the center of mass according to the track parameters and the motion model;
and calculating the position and the speed of the centroid under the geocentric inertial coordinate system at any moment according to the acceleration.
Optionally, the first determining unit is specifically configured to: the acceleration is calculated according to the following formula:
wherein r isbRepresenting the position vector, r, of said centroid in an inertial frame of the earth's centerb＝[xb yb zb]T；
Representing an acceleration of the center of mass; μ represents a normalized earth gravity constant; reRepresents the radius of the earth; j. the design is a square2Representing the earth oblateness perturbation coefficient; mu.sdRepresenting the weight of the solar sail in the proportion of the whole rope system; t isciRepresenting the control acceleration, T, in the inertial frame of the Earth's centerci＝[TX Ty Tz]T；asiRepresenting the acceleration of solar radiation.
Optionally, the first determining unit is specifically configured to: under the body coordinate system, the external moment under the body coordinate system is calculated according to the following formula:
wherein, MbRepresenting external moment under a body coordinate system; { J }bRepresenting a rotational inertia matrix; { J }b＝diag(Jx，Jy，Jz),Jx＝0，
m1Represents the mass of the main star, m2Representing the mass of the solar sail, /)1Representing the line length between the principal star and the center of mass,/2Representing the line length between the solar sail and the center of mass,/2＝l-l1And l represents the line length between the main star and the solar sail; { omega }bRepresenting the rotational angular velocity of the body coordinate system relative to the earth's center inertial coordinate system.
Calculating the attitude parameter according to the external moment by the following formula:
{M}b＝Ry(-η2)·Rz(η1)·{M}i
wherein, Mi＝[Mxi Myi Mzi]T；RyA rotation matrix representing the y-axis; rzRepresenting a z-axis rotation matrix; eta1Representing the relative position vector ar at xi-yiProjection on plane and xiAngle between axes, 0 ≤ η1≤2π；η2Denotes Δ r and xi-yiThe angle between the planes, -pi/2 ≤ eta2≤π/2。
Optionally, the control unit is specifically configured to:
respectively calculating the positions and the speeds of the solar sail and the main star under the geocentric inertial coordinate system according to the motion parameters and the attitude parameters;
determining a conversion matrix corresponding to the conversion of the position and the speed from the geocentric inertial coordinate system to a main satellite orbit coordinate system;
determining relative motion parameters between the solar sail and the main satellite according to the conversion matrix, the track parameters and the control acceleration;
and controlling the relative motion of the solar sail and the main star according to the relative motion parameters.
Optionally, the control unit is specifically configured to: calculating the position and the velocity by the following formulas:
wherein r iscRepresenting the position vector of the main star in the geocentric inertial coordinate system; r isdRepresenting a position vector of the solar sail in the geocentric inertial coordinate system;
representing the velocity vector of the main star in the earth's center inertial coordinate system,
representing the velocity vector of the solar sail in the geocentric inertial frame,
optionally, the control unit is specifically configured to: determining the transformation matrix according to the following formula:
wherein L is0iRepresenting the transformation matrix
Optionally, the control unit is specifically configured to: determining the position and speed of relative movement between the solar sail and the primary star according to the following formula:
Δro＝Loi·Δri
Δri＝rd-rc
wherein, Δ roRepresenting the position of relative motion under the orbit coordinate system of the main satellite; Δ riRepresenting the position of relative motion under an earth-centered inertial coordinate system;
representing the speed of relative motion under the orbit coordinate system of the main satellite;
representing the velocity of relative motion in the earth's center inertial frame.
In a third aspect, the present application provides a computer device, comprising:
a memory for storing instructions for execution by at least one processor;
a processor for executing instructions stored in a memory to perform the method of the first aspect.
In a fourth aspect, the present application provides a computer readable storage medium having stored thereon computer instructions which, when run on a computer, cause the computer to perform the method of the first aspect.
Drawings
Fig. 1 is a schematic structural diagram of a star-sail-tether system according to an embodiment of the present disclosure;
fig. 2 is a schematic flow chart of a cross-section formation method based on a star-sail-rope system according to an embodiment of the present application;
FIG. 3 is a schematic illustration of a relative baseline of the main star and the solar sail according to an embodiment of the present disclosure;
FIG. 4 is a schematic diagram of relative motion of a star-sail-tether system in a primary star orbital coordinate system transverse to formation provided by an embodiment of the present application;
fig. 5 is a schematic structural diagram of a cross-section formation device based on a star-sail-rope system according to an embodiment of the present application;
fig. 6 is a schematic structural diagram of a computer device according to an embodiment of the present application.
Detailed Description
In order to better understand the technical solutions, the technical solutions of the present application are described in detail below with reference to the drawings and specific embodiments, and it should be understood that the specific features in the embodiments and examples of the present application are detailed descriptions of the technical solutions of the present application, and are not limitations of the technical solutions of the present application, and the technical features in the embodiments and examples of the present application may be combined with each other without conflict.
For ease of understanding, the various coordinate systems referred to in the embodiments of the present application are defined below:
geocentric inertial coordinate system: the origin of coordinates is the geocentric; the x axis is a yellow-white intersection line; the z-axis is the normal of the white road surface and is consistent with the rotation angular velocity direction; the y-axis being determined by the right-hand rule
Body coordinate system: the origin of coordinates is the mass center of the star-sail rope system; the x axis is along the rope direction and points to the solar sail from the main star; the y axis is in the longitudinal symmetrical plane of the star-sail rope system and is vertical to the x axis; the z-axis is determined by the right hand rule.
Main satellite orbit coordinate system: the origin of coordinates is a main star; the x-axis points from the earth's center to the primary star; the z-axis is the main star velocity direction; the y-axis is determined by the right hand rule.
Referring to fig. 1, the present application provides a star-sail-rope-tied system, which includes a main star 1 and a solar sail 2, wherein the main star 1 and the solar sail 2 are connected by a metal conductive rope.
The cross-section formation method based on the star-sail-rope system provided by the embodiment of the present application is further described in detail with reference to the drawings in the specification, and the method is based on the star-sail-rope system shown in fig. 1, and the specific implementation manner of the method may include the following steps (the flow of the method is shown in fig. 2):
step 201, determining orbit parameters of the main star and the solar sail, and calculating motion parameters of a mass center of the star-sail-rope system according to the orbit parameters and a preset motion model of the mass center of the star-sail-rope system.
Specifically, in the solution provided in the embodiment of the present application, there are various methods for determining the orbit parameters of the main star and the solar sail, and a preferred method is described as an example below.
In one possible implementation, determining the orbit parameters of the main star and the solar sail comprises: determining the height of the track at morning and evening and the local time of the descending intersection point according to the input task information, and determining the height of the track at morning and evening and the local time of the descending intersection point according to the height of the track at morning and evening and the J2Calculating the morning and evening orbit parameters of the main star; and calculating the acceleration of solar radiation required by the orbit of the solar sail, which moves with the same frequency as the main satellite under the action of the solar radiation pressure, and the included angle between the acceleration and the normal direction of the sail surface of the solar sail according to the preset rope length.
In the solution provided in the embodiment of the present application, the computer device may obtain task information input by a user, where the task information includes a task type or a task scene, and parameters such as a morning and evening track height and a descending point position corresponding to the task scene or the task type are also stored in advance in a database of the computer device. Therefore, after acquiring the task information, the computer device determines the corresponding morning and evening track height and the corresponding descending point from the database according to the task information.
The computer device then perturbs the coefficient J according to the track height at morning and evening, the local time at the descent intersection, and the global oblation2Calculating morning and evening orbit parameters for the main star, wherein the morning and evening orbit parameters include, but are not limited to: sun synchronous railSemimajor axis, sun synchronous orbit inclination, latitude argument, ascent point right ascension. Specifically, the morning and evening orbit parameters are calculated by the following formula:
calculating the morning and evening orbit parameters under the geocentric inertial frame by:
a＝Re+H，e＝0
Ω＝15·TDN+Wraant
wherein a represents a semi-major axis of the sun-synchronous orbit; reRepresents the radius of the earth; e represents eccentricity; i represents a track inclination angle; u represents the latitude argument; ω represents the angular velocity of the object,
GM represents an earth gravity constant; Ω represents the right ascension of the ascending crossing point; t isDNWhen the point of intersection is shown; wraanRepresents the oblateness J of the earth2Resulting in an average rate of change of the ascension channel omega at the point of ascent,
J2is the perturbation coefficient of the earth oblateness.
Further, the computer device calculates the acceleration k of solar radiation required by the orbit of the solar sail, which moves with the main satellite at the same frequency, under the action of the solar radiation pressure according to the following formula:
further, the computer device calculates an angle α between the acceleration and a normal direction of a sail surface of the solar sail according to the following formula:
further, the acceleration vector a of the solar radiation under the geocentric inertial coordinate system is calculated according to the acceleration k of the solar radiation by the following formulasi：
asi＝Rz(-Ω)Rx(-i)Rz(-u)[k sin(α) 0 k cos(α)]T
Wherein R isz(·)、Rx(. cndot.) represents a rotation matrix around the z-axis and x-axis, respectively, in the specific form:
further, a motion model of the center of mass of the star-sail-rope system is also stored in the database of the computer device, and after the computer device calculates the orbit parameters of the main star and the solar sail, the computer device calculates the motion parameters of the center of mass of the star-sail-rope system according to the motion model of the center of mass of the star-sail-rope system, wherein the motion parameters of the center of mass include but are not limited to: acceleration of the center of mass, position of the center of mass, and velocity. There are various ways for the computer device to calculate the motion parameters of the center of mass of the star-sail-rope system according to the motion model of the center of mass of the star-sail-rope system, and a preferred way is described below as an example.
In one possible implementation manner, calculating the motion parameter of the center of mass of the star-sail-rope system according to the track parameter and a preset motion model of the center of mass of the star-sail-rope system includes: under an earth center inertial coordinate system, calculating the acceleration of the center of mass according to the track parameters and the motion model; and calculating the position and the speed of the centroid under the geocentric inertial coordinate system at any moment according to the acceleration.
In one possible implementation, calculating the acceleration of the center of mass from the orbit parameter and the motion model includes: the acceleration is calculated according to the following formula:
wherein r isbRepresenting the position vector, r, of said centroid in an inertial frame of the earth's centerb＝[xb yb zb]T；
Representing an acceleration of the center of mass; μ represents a normalized earth gravity constant; reRepresents the radius of the earth; j. the design is a square2Representing the earth oblateness perturbation coefficient; mu.sdRepresenting the weight of the solar sail in the proportion of the whole rope system; t isciRepresenting the control acceleration, T, in the inertial frame of the Earth's centerci＝[TX Ty Tz]T；asiRepresenting the acceleration of solar radiation.
Further, under the geocentric inertial coordinate system, after the acceleration of the centroid of the star-sail rope system is calculated, the speed and the position of the centroid at any moment are calculated according to the following formula:
wherein t represents an arbitrary time;
representing the velocity of the centroid at any time.
Step 202, calculating attitude parameters of the star-sail-rope system according to the motion parameters and a preset rotation model of the star-sail-rope system around the center of mass.
Specifically, in the solution provided in the embodiment of the present application, there are various ways for the computer device to calculate the attitude parameter of the star-sail-tether system according to the motion parameter and a preset rotation model of the star-sail-tether system around the center of mass, and a preferred way is described as an example below.
In one possible implementation manner, calculating the attitude parameter of the star-sail-tether system according to the motion parameter and a preset rotation model of the star-sail-tether system around the center of mass includes:
under the body coordinate system, the external moment under the body coordinate system is calculated according to the following formula:
wherein, MbRepresenting external moment under a body coordinate system; { J }bRepresenting a rotational inertia matrix; { J }b＝diag(Jx，Jy，Jz),Jx＝0，
m1Represents the mass of the main star, m2Representing the mass of the solar sail, /)1Representing the line length between the principal star and the center of mass,/2Representing the line length between the solar sail and the center of mass,/2＝l-l1And l represents the line length between the main star and the solar sail; { omega }bRepresenting the rotational angular velocity of the body coordinate system relative to the earth's center inertial coordinate system.
Calculating the attitude parameter according to the external moment by the following formula:
{M}b＝Ry(-η2)·Rz(η1)·{M}i
wherein, Mi＝[Mxi Myi Mzi]T；RyA rotation matrix representing the y-axis; rzIndicating rotation of the z-axisRotating the matrix; eta1Representing the relative position vector ar at xi-yiProjection on plane and xiAngle between axes, 0 ≤ η1≤2π；η2Denotes Δ r and xi-yiThe angle between the planes, -pi/2 ≤ eta2≤π/2。
Specifically, in the scheme provided in the embodiment of the application, RyThe expression is as follows:
η1and η2Are two attitude angles defined in advance. { M }i＝[Mxi Myi Mzi]TThe specific expressions of the parameters are as follows:
(-l2 sinη1 cosη2yb+l2 cosη1 cosη2yb)+m2(az+Tz)l2 cosη1 cosη2
then, according to { M } calculated aboveiAfter each parameter in (1), determining an external moment { M } according to the external moment calculation equationb＝[Mxb Myb Mzb]TThe expression of each parameter in (1) is specifically as follows:
Mxb＝0
(-l2 sinη1yb+l2 cosη1yb)-m2(ay+Ty)l2 sinη1+m2(az+Tz)l2 cosη1
wherein r iscRepresenting the position vector of the main star in the geocentric inertial coordinate system; r isdThe position vector of the sub-sail in the geocentric inertial coordinate system is represented.
Then according to { omega }bAnd { η1，η2，η1，η2The relationship between:
it can be deduced that:
and calculating a rotation acceleration equation of two attitude angles according to the attitude parameter equation as follows:
finally, the rotational acceleration according to the two attitude angles
And
the attitude angle eta of the mass center of the star-sail rope system at any moment can be calculated1And η2。
Step 203, at J2And under the condition of perturbation and keeping the solar sail and the main star to be stable relative to the baseline, determining the control acceleration of the solar sail according to the attitude and orbit parameters and preset ideal attitude and orbit parameters.
Specifically, in the solution provided in the embodiment of the present application, an ideal attitude parameter of the centroid of the star-sail-tied system in an ideal state is determined by a proportional-integral-derivative controller (PID), where the ideal state is J and J is a position of the centroid of the star-sail-tied system2Perturbation and keeping the solar sail and the main star in stable relative baseline states; then, calculating the difference value between the attitude parameter and the ideal attitude parameter according to the ideal attitude parameter; then determining the additional control force required to be generated by changing the surface-to-mass ratio of the solar sail and the sail surface attitude according to the difference,so that the solar sail is controlled at J according to the control force2Keeping a stable relative baseline with the main star under perturbation, and finally determining the control acceleration of the solar sail according to the control force.
And 204, controlling the relative motion of the solar sail and the main satellite according to the track parameters, the motion parameters and the control acceleration to realize transverse formation.
In one possible implementation, controlling the relative movement of the solar sail and the main star according to the orbit parameter, the motion parameter and the control acceleration comprises: respectively calculating the positions and the speeds of the solar sail and the main star under the geocentric inertial coordinate system according to the motion parameters and the attitude parameters; determining a conversion matrix corresponding to the conversion of the position and the speed from the geocentric inertial coordinate system to a main satellite orbit coordinate system; determining relative motion parameters between the solar sail and the main satellite according to the conversion matrix, the track parameters and the control acceleration; and controlling the relative motion of the solar sail and the main star according to the relative motion parameters.
In one possible implementation, calculating the position and the speed of the solar sail and the main star in the geocentric inertial coordinate system according to the motion parameter and the attitude parameter respectively includes: calculating the position and the velocity by the following formulas:
wherein r iscRepresenting the position vector of the main star in the geocentric inertial coordinate system; r isdRepresenting a position vector of the solar sail in the geocentric inertial coordinate system;
representing the velocity vector of the main star in the earth's center inertial coordinate system,
representing the velocity vector of the solar sail in the geocentric inertial frame,
in one possible implementation, determining a transformation matrix corresponding to the transformation of the position and the velocity from the geocentric inertial coordinate system to the main satellite orbit coordinate system includes: determining the transformation matrix according to the following formula:
wherein L is0iRepresenting the transformation matrix.
In one possible implementation, determining a relative motion parameter between the solar sail and the main star according to the transformation matrix, the orbit parameter, and the control acceleration includes: determining the position and speed of relative movement between the solar sail and the primary star according to the following formula:
Δro＝Loi·Δri
Δri＝rd-rc
wherein, Δ roRepresenting the position of relative motion under the orbit coordinate system of the main satellite; Δ riRepresenting the position of relative motion under an earth-centered inertial coordinate system;
representing the speed of relative motion under the orbit coordinate system of the main satellite;
representing the velocity of relative motion in the earth's center inertial frame.
To facilitate an understanding of the above-described process of cross-sectional formation, the following description is given by way of example.
For example, to simplify the system, a normalization unit is introduced, where the feature length is the earth radius Re6371004m, unit angular velocity
That is, in the normalized system, the time of one period is 2 pi, and the time which is not normalized in the corresponding actual system is
Based on this, the following main orbit data are all data after normalization.
If the preset rope length between the main star and the solar sail is 1km, the height of the morning and evening orbit of the main star is 1000km, and the T is at the point of intersection descendingDNThe orbit parameter of the sun synchronous orbit can be calculated as follows: 1.156961132 for the semi-major axis a of the track; eccentricity e is 0; the track inclination angle i is 99.484 degrees; latitude argument u is 0.80356t (rad); ascending crossing point of the right ascension
t represents inAnd (4) the time of the normalization.
Then, according to the preset rope length, namely the suspension height of the solar sail in the non-keplerian suspension orbit is the rope length, the solar radiation acceleration k of the sub-sail for maintaining the suspension orbit at the height is 0.00010135 and the pitch angle alpha is 0.01166 degrees. According to the solar radiation acceleration and the numerical values of the ascension point and the ascension channel omega, the latitude amplitude angle u and the orbit inclination angle i at each time, the solar radiation acceleration a in the geocentric inertial coordinate system at any time can be calculatedsi＝Rz(-Ω)Rx(-i)Rz(-u)[k sin(α) 0 k cos(α)]T。
And then, calculating the motion parameters of the mass center of the star-sail-rope system according to a preset motion model of the mass center of the star-sail-rope system. Specifically, if the position and velocity of the primary star are the initial values
The position and speed of the solar sail are initially
The computer equipment is based on the relation between the initial position and speed of the mass center of the star-sail rope system and the initial positions and speeds of the main star and the solar sail
The initial position and the speed of the mass center of the star-sail-rope system are calculated to be
And finally, calculating the motion parameters of the mass center of the star-sail-rope system according to the initial position and the speed of the mass center of the star-sail-rope system and a preset motion model of the mass center of the star-sail-rope system.
Further, calculating the attitude parameters of the star-sail-rope system according to a rotation model of the star-sail-rope system around the center of mass, namely calculating the star-sail-rope system at any momentAttitude angle η of centroid1And η2. The specific process is as follows: tracking the ideal relative motion using a PID controller, thereby at J2A stable, relative baseline perpendicular to the sub-satellite point trajectory was obtained under perturbation. Consider J2The perturbation has different influences on the precession of the sun synchronous orbit and the suspension orbit, the cross-section formation configuration is difficult to maintain, if no control is added, the relative baseline is shown in fig. 3, and the relative baseline is not perpendicular to the track of the sub-satellite points within only 11 cycles. To obtain a stable and vertical relative baseline, the solar sail may generate additional control force by varying the surface-to-mass ratio and sail surface attitude of the solar sail. Because the main star and the sub sails are connected by the ropes, and the distance between the main star and the sub sails is a fixed value, the stable transverse formation configuration can be realized only by controlling the posture. Specifically, the process of controlling the attitude is as follows:
first, the nominal attitude is designed to
And
the specific expression is as follows:
tracking the nominal attitude change rule through PID control, and generating control acceleration T by taking the difference between the actual attitude angle and the ideal attitude angle as a feedback quantityciFinally, the stable state of the formation configuration can be achieved. And calculating the position and the speed of the main star and the sub sail in the geocentric inertial coordinate system according to the position and the attitude angle of the mass center.
Then, a main star orbital coordinate system O (x) is establishedo，yo，zo). Determining according to the position and velocity vector of the main star in the geocentric inertial coordinate systemAnd (3) centering a transformation matrix from the inertial coordinate system to the orbit coordinate system of the main star, and determining relative position parameters of the main star and the solar sail under the orbit coordinate system of the main star according to the transformation matrix.
According to the numerical solution of the kinetic equation and the tracking of ideal postures by PID control, the transverse formation relative motion of the star-sail-rope system in the orbit coordinate system of the main star is shown in FIG. 4. After 500 orbital cycles, there is only a 7m shift in the direction of the main star radius and trajectory, compared to 999m in the hover direction, which can be considered to be still perpendicular to the intersatellite point trajectory relative to the baseline, i.e. under this control, the kite satellite system maintains a stable cross-formation configuration.
Furthermore, as the solar sail and the main star keep interdependence relationship through the metal tether in the transverse formation, the orbit of the main star can be lifted or lowered through the control force action on the metal tether and the sail. And the orbit elements of the orbit of the main star at any moment can be deduced according to the position and the speed of the main star at any moment. If the major axis of the major star orbit is increased, the orbit is lifted, and if the major axis of the major star orbit is decreased, the orbit is lowered.
In the scheme provided by the embodiment of the application, a solar sail and a main satellite are connected through a metal conductive rope to form a star-sail rope system, orbit parameters of the main satellite and the solar sail are determined in the star-sail rope system, a motion parameter of a mass center of the star-sail rope system is determined according to the orbit parameters, an attitude parameter of the star-sail rope system is determined according to the motion parameter of the mass center of the star-sail rope system, and the earth oblateness J is2And under the condition of perturbation and keeping the stable relative baseline of the solar sail and the main star, controlling the relative motion of the solar sail and the main star according to the track parameters, the motion parameters and the control acceleration, and further realizing transverse formation. Therefore, in the scheme provided by the embodiment of the application, the relative motion between the main star and the solar sail is controlled through the attitude parameters and the motion parameters of the star-sail rope system, so that the problem of poor stability of transverse formation caused by controlling the motion of the solar sail by taking the synchronous track where the main star is located as a reference is avoided.
Based on the same inventive concept as the method shown in fig. 2, the embodiment of the present application provides a cross-section formation device based on a star-sail-rope system, which includes a main star and a solar sail, wherein the main star and the solar sail are connected by a metal conductive rope, see fig. 5, and the device includes:
a first determining unit 501, configured to determine orbit parameters of the main satellite and the solar sail, and calculate a motion parameter of a center of mass of the satellite-sail-rope system according to the orbit parameters and a preset motion model of the center of mass of the satellite-sail-rope system;
a calculating unit 502, configured to calculate an attitude parameter of the star-sail-rope system according to the motion parameter and a preset rotation model of the star-sail-rope system around the center of mass;
a second determination unit 503 for determining the earth oblateness J2Determining the control acceleration of the solar sail according to the attitude and orbit parameters and preset ideal attitude and orbit parameters under the conditions of perturbation and keeping the solar sail and the main satellite to keep stable relative baseline;
and the control unit 504 is configured to control the solar sail and the relative motion of the main satellite according to the orbit parameter, the motion parameter and the control acceleration, so as to implement cross-section formation.
Optionally, the first determining unit 501 is specifically configured to:
determining the height of the track at morning and evening and the local time of the descending intersection point according to the input task information, and determining the height of the track at morning and evening and the local time of the descending intersection point according to the height of the track at morning and evening and the J2Calculating the morning and evening orbit parameters of the main star;
and calculating the acceleration of solar radiation required by the orbit of the solar sail, which moves with the same frequency as the main satellite under the action of the solar radiation pressure, and the included angle between the acceleration and the normal direction of the sail surface of the solar sail according to the preset rope length.
Optionally, the first determining unit 501 is specifically configured to:
under an earth center inertial coordinate system, calculating the acceleration of the center of mass according to the track parameters and the motion model;
and calculating the position and the speed of the centroid under the geocentric inertial coordinate system at any moment according to the acceleration.
Optionally, the first determining unit 501 is specifically configured to: the acceleration is calculated according to the following formula:
wherein r isbRepresenting the position vector, r, of said centroid in an inertial frame of the earth's centerb＝[xb yb zb]T；
Representing an acceleration of the center of mass; μ represents a normalized earth gravity constant; reRepresents the radius of the earth; j. the design is a square2Representing the earth oblateness perturbation coefficient; mu.sdRepresenting the weight of the solar sail in the proportion of the whole rope system; t isciRepresenting the control acceleration, T, in the inertial frame of the Earth's centerci＝[TX Ty Tz]T；asiRepresenting the acceleration of solar radiation.
Optionally, the first determining unit 501 is specifically configured to: under the body coordinate system, the external moment under the body coordinate system is calculated according to the following formula:
wherein, MbRepresenting external moment under a body coordinate system; { J }bRepresenting a rotational inertia matrix; { J }b＝diag(Jx，Jy，Jz),
m1Represents the mass of the main star, m2Representing the mass of the solar sail, /)1Representing the line length between the principal star and the center of mass,/2Representing the line length between the solar sail and the center of mass,/2＝l-l1And l represents the line length between the main star and the solar sail; { omega }bRepresenting the rotational angular velocity of the body coordinate system relative to the earth's center inertial coordinate system.
Calculating the attitude parameter according to the external moment by the following formula:
Δr{M}b＝Ry(-η2)·Rz(η1)·{M}i
wherein, Mi＝[Mxi Myi Mzi]T；RyA rotation matrix representing the y-axis; rzRepresenting a z-axis rotation matrix; eta1Representing the relative position vector ar at xi-yiProjection on plane and xiAngle between axes, 0 ≤ η1≤2π；η2Denotes Δ r and xi-yiThe angle between the planes, -pi/2 ≤ eta2≤π/2。
Optionally, the control unit 504 is specifically configured to:
respectively calculating the positions and the speeds of the solar sail and the main star under the geocentric inertial coordinate system according to the motion parameters and the attitude parameters;
determining a conversion matrix corresponding to the conversion of the position and the speed from the geocentric inertial coordinate system to a main satellite orbit coordinate system;
determining relative motion parameters between the solar sail and the main satellite according to the conversion matrix, the track parameters and the control acceleration;
and controlling the relative motion of the solar sail and the main star according to the relative motion parameters.
Optionally, the control unit 504 is specifically configured to: calculating the position and the velocity by the following formulas:
wherein r iscRepresenting the position vector of the main star in the geocentric inertial coordinate system; r isdRepresenting a position vector of the solar sail in the geocentric inertial coordinate system;
representing the velocity vector of the main star in the earth's center inertial coordinate system,
representing the velocity vector of the solar sail in the geocentric inertial frame,
optionally, the control unit 504 is specifically configured to: determining the transformation matrix according to the following formula:
wherein L is0iRepresenting the transformation matrix
Optionally, the control unit 504 is specifically configured to: determining the position and speed of relative movement between the solar sail and the primary star according to the following formula:
Δro＝Loi·Δri
Δri＝rd-rc
wherein, Δ roRepresenting the position of relative motion under the orbit coordinate system of the main satellite; Δ riRepresenting the position of relative motion under an earth-centered inertial coordinate system;
representing the speed of relative motion under the orbit coordinate system of the main satellite;
representing the velocity of relative motion in the earth's center inertial frame.
Referring to fig. 6, the present application provides a computer device comprising:
a memory 601 for storing instructions for execution by at least one processor;
a processor 602 for executing instructions stored in a memory to perform the method described in fig. 2.
A computer-readable storage medium having stored thereon computer instructions which, when executed on a computer, cause the computer to perform the method of fig. 2.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.
Claims (10)
1. A cross-section formation method based on a star-sail tether system, the star-sail tether system comprising a main star and a solar sail, wherein the main star and the solar sail are connected by a metal conductive rope, characterized by comprising:
determining orbit parameters of the main star and the solar sail, and calculating motion parameters of the mass center of the star-sail-rope system according to the orbit parameters and a preset motion model of the mass center of the star-sail-rope system;
calculating the attitude parameters of the star-sail-rope system according to the motion parameters and a preset rotation model of the star-sail-rope system around the mass center;
at earth oblateness J2Determining the control acceleration of the solar sail according to attitude and orbit parameters and preset ideal attitude and orbit parameters under the conditions of perturbation and keeping the solar sail and the main satellite to keep stable relative baseline;
and controlling the relative motion of the solar sail and the main star according to the track parameters, the motion parameters and the control acceleration to realize cross-section formation.
2. The method of claim 1, wherein determining orbital parameters of the primary star and the solar sail comprises:
determining the height of the track at morning and evening and the local time of the descending intersection point according to the input task information, and determining the height of the track at morning and evening and the local time of the descending intersection point according to the height of the track at morning and evening and the J2Calculating the morning and evening orbit parameters of the main star;
and calculating the acceleration of solar radiation required by the orbit of the solar sail, which moves with the same frequency as the main satellite under the action of the solar radiation pressure, and the included angle between the acceleration and the normal direction of the sail surface of the solar sail according to the preset rope length.
3. The method of claim 1, wherein calculating the motion parameter of the center of mass of the star-sail-tether system from the orbit parameter and a preset motion model of the center of mass of the star-sail-tether system comprises:
under an earth center inertial coordinate system, calculating the acceleration of the center of mass according to the track parameters and the motion model;
and calculating the position and the speed of the centroid under the geocentric inertial coordinate system at any moment according to the acceleration.
4. The method of claim 3, wherein calculating the acceleration of the center of mass from the orbit parameters and the motion model comprises:
the acceleration is calculated according to the following formula:
wherein r isbRepresenting the position vector, r, of said centroid in an inertial frame of the earth's centerb＝[xb yb zb]T；
Representing an acceleration of the center of mass; μ represents a normalized earth gravity constant; reRepresents the radius of the earth; j. the design is a square2Representing the earth oblateness perturbation coefficient; mu.sdRepresenting the weight of the solar sail in the proportion of the whole rope system; t isciRepresenting the control acceleration, T, in the inertial frame of the Earth's centerci＝[TX Ty Tz]T；asiRepresenting the acceleration of solar radiation.
5. The method of claim 1, wherein calculating the attitude parameters of the star-sail-tether system based on the motion parameters and a preset model of rotation of the star-sail-tether system about the center of mass comprises:
under the body coordinate system, the external moment under the body coordinate system is calculated according to the following formula:
wherein, MbRepresenting external moment under a body coordinate system; { J }bRepresenting a rotational inertia matrix; { J }b＝diag(Jx，Jy，Jz)，Jx＝0，
m1Represents the mass of the main star, m2Representing the mass of the solar sail, /)1Representing the line length between the principal star and the center of mass,/2Representing the line length between the solar sail and the center of mass,/2＝l-l1And l represents the line length between the main star and the solar sail; { omega }bRepresenting the rotation angular velocity of the body coordinate system relative to the earth center inertia coordinate system;
calculating the attitude parameter according to the external moment by the following formula:
{M}b＝Ry(-η2)·Rz(η1)·{M}i
wherein, Mi＝[Mxi Myi Mzi]T；RyA rotation matrix representing the y-axis; rzRepresenting a z-axis rotation matrix; eta1Representing the relative position vector ar at xi-yiProjection on plane and xiAngle between axes, 0 ≤ η1≤2π；η2Denotes Δ r and xi-yiThe angle between the planes, -pi/2 ≤ eta2≤π/2。
6. The method of any of claims 1 to 5, wherein controlling the relative motion of the solar sail and the primary star based on the orbit parameter, the motion parameter, and the control acceleration comprises:
respectively calculating the positions and the speeds of the solar sail and the main star under the geocentric inertial coordinate system according to the motion parameters and the attitude parameters;
determining a conversion matrix corresponding to the conversion of the position and the speed from the geocentric inertial coordinate system to a main satellite orbit coordinate system;
determining relative motion parameters between the solar sail and the main satellite according to the conversion matrix, the track parameters and the control acceleration;
and controlling the relative motion of the solar sail and the main star according to the relative motion parameters.
7. The method of claim 6, wherein calculating the position and velocity of the solar sail and the starry at the Earth's center inertial frame based on the motion parameters and the attitude parameters, respectively, comprises:
calculating the position and the velocity by the following formulas:
wherein r iscRepresenting the position vector of the main star in the geocentric inertial coordinate system; r isdRepresenting a position vector of the solar sail in the geocentric inertial coordinate system;
representing the velocity vector of the main star in the earth's center inertial coordinate system,
representing the velocity vector of the solar sail in the geocentric inertial frame,
8. the method of claim 6, wherein determining a transformation matrix corresponding to the transformation of the position and the velocity from the geocentric inertial frame to a primary satellite orbital frame comprises:
determining the transformation matrix according to the following formula:
wherein L is0iRepresenting the transformation matrix.
9. The method of claim 6, wherein determining the relative motion parameters between the solar sail and the primary star based on the transformation matrix, the orbit parameters, and the control acceleration comprises:
determining the position and speed of relative movement between the solar sail and the primary star according to the following formula:
Δro＝Loi·Δri
Δri＝rd-rc
wherein, Δ roRepresenting the position of relative motion under the orbit coordinate system of the main satellite; Δ riRepresenting the position of relative motion under an earth-centered inertial coordinate system;
representing the speed of relative motion under the orbit coordinate system of the main satellite;
representing the velocity of relative motion in the earth's center inertial frame.
10. A cross-sectioning formation device based on a star-sail tether system, comprising a main star and a solar sail, wherein the main star and the solar sail are connected by a metal conductive rope, characterized by comprising:
the first determining unit is used for determining the orbit parameters of the main star and the solar sail, and calculating the motion parameters of the mass center of the star-sail-rope system according to the orbit parameters and a preset motion model of the mass center of the star-sail-rope system;
the computing unit is used for computing the attitude parameters of the star-sail-rope system according to the motion parameters and a preset rotation model of the star-sail-rope system around the mass center;
a second determination unit for determining the ellipticity J of the earth2Determining the control acceleration of the solar sail according to attitude and orbit parameters and preset ideal attitude and orbit parameters under the conditions of perturbation and keeping the solar sail and the main satellite to keep stable relative baseline;
and the control unit is used for controlling the relative motion of the solar sail and the main satellite according to the track parameters, the motion parameters and the control acceleration so as to realize transverse formation.
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