CN115373423A - Formation capture method for commercial satellite - Google Patents
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Abstract
The invention discloses a formation capturing method for commercial satellites, relates to the technical field of satellite formation, and solves the problems that a shooting motion mechanism of a satellite is urgently needed and the formation capturing method can be realized only by consuming lower fuel, and the method comprises the following steps: w is realized by changing i or a according to the selection of the orbital inclination angle i of the formation satellite s A change in (b); when choosing to realize W by changing i s When the inclination angle of the formation satellite is changed, the inclination angle change quantity of the formation satellite is calculated
According to
Calculating the size of the speed increment; when selecting to realize W by changing a s When the change of the satellite orbit is carried out, the change quantity of the semi-major axis of the formation satellite orbit is calculated
According to
The speed increment size is calculated. The invention can greatly reduce the fuel requirement for formation capture, and is suitable for commercial satellites with fuel cost limitation; the method adopts an impulse control mode in the capturing process, and is easy to realize in engineering; the method has less control batches and can be implemented only at the front edge and the rear edge of the drift time period.
Description
Technical Field
The invention relates to the technical field of satellite formation, in particular to a formation capturing method for commercial satellites.
Background
With the rapid development of commercial satellites, the formation of satellites is gradually scheduled, and the formation of satellites can form stable and accurate baselines among a plurality of satellites, so that the method has high application value in the aspects of optical stereo imaging, synthetic aperture radar imaging, accurate target positioning and the like. However, for commercial satellites, on one hand, in order to save the carrying and launching cost, a multi-satellite orbit entering mode is generally adopted, and therefore the formation capture needs to be realized by depending on the control capability of the commercial satellites; on the other hand, from the viewpoint of manufacturing cost, commercial satellites have limited fuel carrying capacity and weak orbit control capability.
The concept of satellite formation is put forward, and formation acquisition is a problem to be solved firstly.
In the aspect of solving the formation capture problem, many scholars at home and abroad convert the formation capture problem into an optimal control problem on the basis of a relative motion dynamics equation, namely a known state equation and an initial value, and the set performance index is optimal through designing a classical or advanced control law, so that the transfer of state parameters is realized, and the performance index is often optimal for fuel (optimal for required time under special conditions). Taking a circular formation with a radius of 10km as an example, the above method requires a speed increment of several hundreds to several kilometers per second, which obviously cannot bear such a huge fuel demand for commercial satellites. In addition, a method is also provided, which is characterized in that formation parameters are converted into six orbital parameters of a satellite, the orbital parameters of the formation satellite are adjusted through a classical N impulse control method, and formation capture is realized, the method has high engineering application value, and according to related research, the circular formation speed increment requirement with the radius of 10km by adopting the method is about 10m/s.
In fact, the above methods are all in the framework of a classical motion equation, neglecting the space perturbation force of the satellite, and realizing the direct capture of formation.
Therefore, in the field of satellite formation, a method for realizing formation acquisition by using the shooting mechanism of the satellite and consuming low fuel is needed.
Disclosure of Invention
In order to solve the above problems, the present invention provides a formation acquisition method for commercial satellites.
The technical scheme adopted by the invention for solving the technical problem is as follows:
a formation acquisition method for commercial satellites, comprising:
w is realized by changing i or a according to the size selection of the orbital inclination angle i of the formation satellite s When i ∈ [ (90-. Beta.) °, (90 + γ) ° is changed]When W is realized by changing i s Otherwise, W is realized by changing a s With both beta and gamma being positive numbers, a denotes the semi-major axis of the formation satellite orbit, W s Representing the base length between the formation satellite orbit surface and the reference satellite orbit surface;
when selecting to realize W by changing i s When the inclination angle of the formation satellite is changed, the inclination angle change amount of the formation satellite is calculated
According to
Calculating the size of the speed increment; when selecting to realize W by changing a s When the satellite orbit semi-major axis changes, the change quantity of the formation satellite orbit semi-major axis is calculated
According to
The speed increment size is calculated.
The beneficial effects of the invention are:
the invention provides a formation capturing method for commercial satellites, which changes the precession speed of a satellite orbit plane in an inertial space by changing an inclination angle or a semimajor axis according to the principle of the pickup motion between the satellite orbit planes, so that the formation satellites form stable difference on a rising intersection red warp, and further realize the formation capturing of the satellites. The method can greatly reduce the fuel requirement for formation capture, thus being suitable for commercial satellites with fuel cost limitation; the method adopts an impulse control mode in the capturing process, and is easy to realize in engineering; the method has less control batches and can be implemented only at the front edge and the rear edge of the drift time period.
Drawings
Fig. 1 is a flowchart of a formation acquisition method for commercial satellites according to the present invention.
Fig. 2 is a partial parameter diagram of a formation acquisition method for commercial satellites according to the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
Example one
The embodiment provides a formation capturing method for commercial satellites, which is used for solving the problems that the space power of the satellites is neglected and the fuel consumption is high in the existing formation capturing problem.
Firstly, according to the existing formation kinematics theory, it can be known that the formation of the satellites needs to make fine adjustment on eccentricity so that the formation satellites can realize elliptical motion in the orbital plane around the reference satellite, and on the other hand, the formation of the satellites needs to form difference with the reference satellite in the rising intersection or the orbital inclination so as to form simple pendulum motion out of the orbital plane of the formation satellites. For the adjustment of the eccentricity, according to the Gaussian perturbation equation, a larger space baseline can be realized only by applying smaller impulse; however, for adjusting the ascension point right ascension and the orbit inclination, a larger impulse is needed to obtain the same spatial baseline, and in general application, the ascension point right ascension is adjusted mostly, and the orbit inclination is rarely adjusted, because if the orbit inclination is adjusted, the spatial baseline of the formation satellite in a low latitude area is the smallest, and the formation satellite is not suitable for observation in a low latitude. The embodiment and other embodiments described below creatively utilize the pickup motion of the right ascension of the satellite orbit, so as to realize the formation capture with less fuel consumption.
The formation acquisition method for the commercial satellite of the embodiment comprises the following steps:
w is realized by changing i or a according to the size selection of the orbital inclination angle i of the formation satellite s When i ∈ [ (90-beta) °, (90 + gamma) ° changes]When W is realized by changing i s Otherwise, W is realized by changing a s Where β and γ are both positive numbers, a represents the semi-major axis of orbit of the formation satellite, W s Representing the base length between the formation satellite orbit surface and the reference satellite orbit surface;
when choosing to realize W by changing i s When the inclination angle of the formation satellite is changed, the inclination angle change quantity of the formation satellite is calculated
According to
Calculating the size of the speed increment; when selecting to realize W by changing a s When the change of the satellite orbit is carried out, the change quantity of the semi-major axis of the formation satellite orbit is calculated
According to
The speed increment size is calculated.
Example two
The embodiment provides a method for acquiring formation of commercial satellites, as shown in fig. 1, including:
w is realized by changing i or a according to the size selection of the orbital inclination angle i of the formation satellite s When i ∈ [ (90-. Beta.) °, (90 + γ) ° is changed]When W is realized by changing i s Otherwise, W is realized by changing a s With both beta and gamma being positive, a representing the semi-major axis of orbit of the formation satellite, W s Representing the base length between the formation satellite orbit surface and the reference satellite orbit surface;
when choosing to realize W by changing orbital inclination angle i of formation satellite s According to the formation requirement W s Calculating the ascension difference delta omega of the rising intersection point of the formation satellite orbit plane and the reference satellite orbit plane by using a formula (1),
calculating the inclination angle change of the formation satellite according to the delta omega by using the formula (15)
According to
The formula (4.2) calculates the speed increment of the formation satellite,
wherein μ is the Earth constant, J 2 Is a second order coefficient of earth's ellipticity perturbation, R e Is the average radius of the earth, e is the eccentricity, n is the orbital angular velocity of the formation satellite, u is the latitude argument, Δ ν a The track direction velocity increment of the formation satellite orbit is obtained.
W is realized by changing orbital semimajor axis a of formation satellite s Can realize discrete W s When selecting to realize W by changing a s In accordance with equation (13) or equation (14), calculating the discrete W s The number of discrete units D of (a),
w according to formula (9), D and the formation requirement s Calculating semi-major axis variation of formation satellite orbit
Wherein, the first and the second end of the pipe are connected with each other,
n represents the number of complete circles of the formation satellite in circular motion around the earth, N is a positive integer, and the value of N passes through D and W required by formation s Determining that N equals W of the formation requirement s Dividing the value of D to carry out rounding up; t represents W by changing a s Time of change, i.e., time cost.
According to
The velocity increment Δ v is calculated using equation (4.1) a
Wherein, Δ v a The track of the formation satellite is increased towards the speed.
In the implementation ofW s Before and after the time t required for changing (starting time and ending time), providing a speed increment once respectively, namely providing impulse (namely pulse) according to the speed increment, realizing the change of the red warp at the rising point of the formation satellite, namely realizing W s Is changed.
EXAMPLE III
A method for a formation acquisition of commercial satellites, comprising the steps of:
step one, converting the length of a base line between the track surfaces into the ascension crossing point declination.
According to the existing formation kinematics theory, the formation satellite can realize elliptical motion in the formation satellite orbit plane around the reference satellite to perform fine adjustment on the eccentricity. As shown in FIG. 2, FIG. 2 shows that when not formed, the orbital inclination of the reference satellite is equal to the orbital inclination i of the formed satellite, the orbital inclination is simply called the inclination, the orbital semimajor axis of the reference satellite is equal to the orbital semimajor axis a of the formed satellite, and the base length between the orbital plane of the formed satellite and the orbital plane of the reference satellite is W s . The ascension difference delta omega of the rising intersection point of the formation satellite orbit surface and the reference satellite orbit surface can be obtained according to the cosine formula of the spherical right-angled triangle:
step two, selecting control parameters according to the orbital inclination angle of the formation satellites
According to the influence of the earth oblateness on the right ascension of the satellite orbit in the spacecraft orbit theory and the elevation right ascension difference obtained in the step one, the precession angular velocity of the right ascension of the satellite orbit is obtained
Comprises the following steps:
in the above formula, f (a, i) represents a function of variables a and i, R e Is the mean radius of the earth, μ is the earth constant, and μ =398600.4418km 3 /s，J 2 And (3) calculating the partial derivative of the formula (2) for a second-order coefficient of earth oblateness perturbation, i is the orbit inclination angle of formation, and e is the eccentricity ratio:
according to the Gaussian shot motion equation, under the condition that the dot locus under the formation satellite is a circular orbit (the eccentricity e is approximately equal to 0), a and i satisfy the following formula:
wherein n is the orbital angular velocity of the formation satellite, u is the latitude argument, and Δ v a For formation of satellite orbital trajectory velocity increments, Δ v a The semi-major axis a, delta v of the orbit of the formation satellite can be changed i For formation of normal velocity increments of satellite orbits, Δ v i The inclination angle i for changing the formation satellite can be also shown in the formulas (4.1) and (4.2), and the inclination angle i needs to be changed at the position with the latitude argument of 0 ° or 180 °, namely the position of the elevation intersection point of the formation satellite.
According to the formula (3), when the formula (3) meets the condition of the formula (5), the same result is obtained by changing the semi-major axis a of the orbit of the formation satellite or changing the inclination angle i of the orbit of the formation satellite
Substituting equations (4.1) and (4.2) into equation (5) can yield:
the formula (6) shows that when the inclination angle i e [81.87 DEG, 98.13 DEG ] of the formation satellite]When the speed increment for changing the inclination angle i of the formation satellite is minimum, the inclination angle is changed to realize W s When the inclination angle i of the formation satellite is not in the interval, the speed increment of changing the semi-major axis a of the orbit of the formation satellite is minimum, and then the change a is selected to realize W s Is changed.
Therefore, control parameters including the orbit semi-major axis and the orbit inclination angle can be selected according to the inclination angle of the orbit of the formation satellite, namely, a or i is selected to be changed according to the inclination angle of the orbit of the formation satellite.
For the case of changing the semi-major axis, the following details are made:
since changing the semi-major axis will cause the formation satellite and the reference satellite to gradually pull apart the phase in the flight direction, obviously, the basic condition of satellite formation is deviated (the semi-major axis of the formation satellite and the reference satellite should be kept consistent), therefore, it must be thought to make the formation satellite return to the vicinity of the reference satellite again, consider that the satellite makes circular motion around the earth, therefore, it can be ensured that the formation satellite returns to the vicinity of the reference satellite through fastening the circle, the fastening means that the satellite makes circular motion around the earth at least one complete circular motion, the fastening N times means that the satellite makes N times of circular motion around the earth, i.e. N circles, N is a positive integer, and N means the number of complete circles of the formation satellite makes circular motion around the earth.
The orbital angular velocity formula of the formation satellite is as follows:
when the semi-major axis of the formation satellite orbit is applied with the change quantity of the semi-major axis of the formation satellite orbit
After the variable quantity, the formation satellite completes N times of circle deduction (N times of deduction)Circle, namely, N circles around the earth) is required to satisfy the following time t:
t represents an implementation change W s By changing a s Time of change of (c).
The formula (8) is linearized to obtain:
wherein the content of the first and second substances,
after N times of circle buckling of the formation satellites are completed, the semilong axis needs to be recovered, so that the ascending intersection point right ascension angular velocity of the formation satellites is consistent with the ascending intersection point right ascension angular velocity of the reference satellite, and a stable ascending intersection point right ascension difference delta omega is formed.
Considering the situation that the orbit of the satellite points under the formation satellite is a circular orbit, and carrying out linearization processing on the formula (10) can obtain:
substituting equation (9) into equation (11):
since N is an integer, the formula (12) shows that the formation capture can only be changed to discrete inter-orbital-surface base length W by changing the semi-major axis of the formation satellite orbit s And discrete unit D is:
considering general base length W between formation track surfaces s Is far smaller than the semi-major axis a of the track, the above formula can be simplified as follows:
meanwhile, the equation (9) gives the time cost and the fuel cost of the inter-track-plane adjustment.
For the case of changing the inclination angle, the following is detailed: :
unlike changing the semi-major axis a, changing the inclination i is simpler and does not cause the satellite to drift in the direction of flight. Changing the inclination i only needs to apply the impulse twice, and the inclination change amount of the formation satellite is utilized
So that the formation satellite and the reference satellite form a rising intersection declination delta omega.
t represents an implementation change W s In particular here by changing i to realize W s Time of change of (c).
Step three, realizing the change of the red meridians of the rising points of the formation satellites by using two-time pulse control
According to the second step, the control quantity of the semimajor axis or the inclination angle and the time cost t can be obtained, the change of the red warp at the rising intersection point of the formation satellite can be completed only by applying the speed increment once respectively at the starting time and the ending time of the time period t according to the formulas (4.1) and (4.2), and the change of the red warp at the rising intersection point of the formation satellite is realized according to the speed increment, namely the change of the red warp at the rising intersection point of the formation satellite is realized, namely the W is realized s Is changed.
Step four, adjusting other formation parameters to realize formation capture
Finally, the parameter (mainly eccentricity) in the satellite orbit plane of the formation satellite is adjusted, and formation capture can be completed. From the expressions (4.1) and (4.2), the fuel consumption for adjusting the track in-plane parameters is relatively small, and for example, a 2km in-plane base line length can be obtained with a velocity increase of 1 m/s.
The calculation and simulation of two application cases are carried out by utilizing the formation capturing method for the commercial satellite, and the specific process and the implementation result are as follows:
the application case one: the formation capture of the solar synchronous satellite with the height of 535km is completed within 90 days, the formation configuration is circular formation, and the formation radius is 10km;
firstly, according to the first step, the ascent point declination is solved, and according to the round formation theory, the length W of the base line between the track surfaces required by formation can be known s Is composed of
Δ Ω =1.26 × 10 converted from the formula (1) -3 rad。
According to the second step, because the nominal inclination angle of the solar synchronous orbit at the height of 535km is 97.54 degrees, the speed increment for changing the inclination angle is small, and therefore, the change of the inclination angle is selected to realize the base line between the orbit surfaces;
the difference in inclination angle required to form the ascent point declination difference in 90 days was calculated by the formula (15)
And (4) solving the size of the speed increment of two times before and after the 90-day time period to be 0.82m/s by using a formula (4.2) according to the step three.
And adjusting the parameters in the track surface according to the fourth step, wherein the major axis of the ellipse in the track surface is 10km according to a circular formation theory (namely a circular formation relative motion equation obtained based on a C-W equation), so that the speed increment of adjusting the eccentricity ratio twice is 2.5m/s.
From the above analysis, the total velocity delta requirement was 6.64m/s.
Application case two: completing 500km height 35-degree low-inclination satellite formation capture in 90 days, wherein the capture configuration is a Pendulum Pendulum formation, and the length of a base line is near 50 km;
according to the steps I, II and III, the formation capture under the inclination angle is realized by changing the semi-major axis, but the semi-major axis is only suitable for the length of the discrete track surface base line. Since the discrete element can calculate D as 66km according to the expression (14), the length of the base line between the track surfaces can only be an integral multiple of 66 km. Meanwhile, according to the formula (9), the time cost is
Since the base length required by formation is about 50km, if the number of times of loop fastening is N =1, the control quantity of the semi-major axis is increased
And (4) solving the size of the speed increment of two times before and after the 90-day time period by using a formula (4.1) according to the step three.
And the Pendulum Pendulum formation does not need to adjust the eccentricity parameter, so the fourth step does not need to be calculated.
From the above analysis, the total velocity increment requirement was 3.7m/s.
Through the two case analyses, the method for acquiring the formation has the advantage that the requirement of speed increment is far lower than that of the existing method, and the method is suitable for commercial satellites.
Claims (7)
1. A method for formation acquisition of commercial satellites, comprising:
w is realized by changing i or a according to the selection of the orbital inclination angle i of the formation satellite s When i ∈ [ (90-beta) °, (90 + gamma) ° changes]When W is realized by changing i s Otherwise, W is realized by changing a s With both beta and gamma being positive numbers, a denotes the semi-major axis of the formation satellite orbit, W s Representing the base length between the formation satellite orbit surface and the reference satellite orbit surface;
when choosing to realize W by changing i s When the inclination angle of the formation satellite is changed, the inclination angle change quantity of the formation satellite is calculated
According to
Calculating the size of the speed increment; when selecting to realize W by changing a s When the satellite orbit semi-major axis changes, the change quantity of the formation satellite orbit semi-major axis is calculated
According to
The speed increment size is calculated.
2. The method of claim 1, wherein W is selected to be implemented by changing i s According to the formation requirement W s Calculating the ascent point declination difference delta omega between the formation satellite orbit plane and the reference satellite orbit plane by using a formula (1),
calculating the inclination angle change of the formation satellite according to the delta omega by using the formula (15)
According to
Calculate velocity delta Δ v using equation (4.2) i ，
Wherein μ is the Earth constant, J 2 Is a second order coefficient of earth's ellipticity perturbation, R e Is the average radius of the earth, e is the eccentricity, n is the orbital angular velocity of the formation satellite, u is the latitude argument, Δ ν i For formation of normal speed increment of satellite orbit, t is to change W s Time of (d).
3. A method of convoy acquisition for commercial satellites according to claim 2, it is characterized in that the preparation method is characterized in that,
realizing W by changing a s Can realize discrete W s When selecting W by changing a s In accordance with formula (13) or formula (14), calculating the discrete W s The number of discrete units D of (a),
w according to formula (9), D and the formation requirement s Calculating out
Wherein the content of the first and second substances,
n represents the number of complete circles of the formation satellite in circular motion around the earth, N is a positive integer, and the value of N passes through D and W required by formation s Determining;
according to
The velocity increment Δ v is calculated using equation (4.1) a
Wherein, Δ v a The track of the formation satellite is increased towards the speed.
4. The method of claim 3, wherein N is equal to W required for formation s Divide by the value of D to round up.
5. The method for formation capture of commercial satellites according to claim 1 further comprising the step of adjusting eccentricity.
6. The formation acquisition method for commercial satellites according to claim 1, wherein β = γ =8.13 °.
7. The method of claim 1, wherein determining β and γ comprises:
obtaining the ascension angle speed of the right ascension channel of the satellite orbit at the elevation intersection point according to the cosine formula of the spherical right triangle
Wherein f (a, i) represents a function of variables a and i, R e Denotes the mean radius of the earth, μ denotes the earth constant, J 2 The second-order coefficient of the earth oblateness perturbation is shown, and e represents the eccentricity;
the formula (2) is subjected to partial derivation to obtain:
according to the Gaussian shot motion equation, under the condition that the orbit of the subsatellite points of the formation satellites is a circular orbit, a and i satisfy the following formula:
wherein n is the orbital angular velocity of the formation satellite, u is the latitude argument, and delta v a For formation of satellite orbital trajectory velocity increments, Δ v a For varying the semi-major axis a, av of the orbits of the formation satellites i For formation of satellite orbital normal velocity increments, Δ v i The method is used for changing the inclination angle i of the formation satellites, and according to a formula (4.2), the inclination angle i needs to be changed at a position with a latitude argument of 0 degrees or 180 degrees;
when the formula (3) satisfies the condition of the formula (5), changing a or changing i can result in the same
Substituting expressions (4.1) and (4.2) into expression (5) can obtain:
β and γ are determined according to equation (6).
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| CN117270557A (en) * | 2023-09-14 | 2023-12-22 | 中国西安卫星测控中心 | Optimal satellite formation control method for inclination angle and semi-long axis combined bias |
| CN117478207A (en) * | 2023-12-25 | 2024-01-30 | 广东世炬网络科技有限公司 | Satellite-to-ground link communication method, device, equipment and storage medium |
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