CN115373264A - Optimal control method and device for adjusting fuel by using high-precision spacecraft intersatellite point trajectory - Google Patents
Optimal control method and device for adjusting fuel by using high-precision spacecraft intersatellite point trajectory Download PDFInfo
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Abstract
A fuel optimal control method and equipment for adjusting a high-precision spacecraft intersatellite point trajectory belong to the technical field of spacecraft orbit control. The method aims to solve the problems of low control precision and high fuel consumption of the conventional method for adjusting the track of the satellite points. According to the scene starting time, the ground target longitude and latitude and the target orbit information, the time at which the off-satellite point observation is realized within one day is calculated, the total time of the mission is selected, and the expected state of the mission spacecraft during observation is obtained. And then calculating to obtain transfer orbit information according to the initial orbit information and the target orbit information, setting the first maneuvering time as a variable according to Hoeman transfer characteristics and constraint conditions, performing high-precision orbit recursion search to obtain a proper maneuvering time, substituting an orbit control instruction into a high-precision orbit dynamics model to perform orbit recursion, simulating an observation error, performing phase modulation processing on the maneuvering time to obtain a corrected orbit control instruction, and realizing high-precision observation on the ground target.
Description
Technical Field
The invention belongs to the technical field of spacecraft orbit control, and particularly relates to a high-precision spacecraft intersatellite point trajectory adjustment fuel optimal control method, device and medium.
Background
For the earth observation satellite of the near-earth orbit, due to the requirement of tasks, the earth observation satellite often needs to enter the adjustment of the lower point track of the planet through orbital maneuver, so that the spacecraft can quickly run to the upper space of a ground target for observation, and meanwhile, the earth observation satellite is required to be adjusted to an ultra-low orbit (the orbit height is 120km-300 km) and reduce the fuel consumption as much as possible. For the problem of the adjustment of the satellite point trajectory, the conventional method is to perform analysis and solution under a two-body condition at present, but the algorithm has the defects that the influence of perturbation factors such as earth non-spherical gravity, atmospheric resistance and the like cannot be overcome, so that the control precision is not high, the high-precision satellite point trajectory adjustment cannot be realized, and meanwhile, the solved fuel consumption is high, so that the application of the high-precision satellite point trajectory adjustment is very limited.
Disclosure of Invention
The invention aims to solve the problems of low control precision and high fuel consumption of the conventional method for adjusting the track of the satellite points.
The optimal control method for adjusting the fuel by the high-precision spacecraft intersatellite point trajectory comprises the following steps:
s1, calculating to obtain a moment having a chance of realizing the observation of the off-satellite point according to the scene starting time, the longitude and latitude of the point B and the initial orbit information of the satellite A, taking the moment as the total task time, and simultaneously obtaining an expected state of the satellite A during observation;
the star A is a task spacecraft, and the point B represents observation of a ground target B;
s2, obtaining relevant constraint conditions of the track maneuvering according to the Hoeman transfer characteristics, setting the first maneuvering time as a variable, substituting the initial track information and the expected state of the satellite A into a high-precision track dynamics model to perform track recursion search to obtain a proper maneuvering time, and meanwhile, combining the initial track and the target track information to obtain maneuvering pulses required by corresponding maneuvering points, thereby obtaining a track control instruction;
s3, substituting the track control instruction into the high-precision track dynamics model to carry out track recursion, simulating an observation error, carrying out phase modulation correction on maneuvering moments according to the error, and finally obtaining an optimal control strategy for adjusting the fuel according to the track of the subsatellite point observed by the ground target;
under the earth inertial coordinate system, the high-precision orbit dynamics model is as follows:
wherein (x, y, z) is the position of the mission spacecraft in the earth inertial coordinate system, v x 、v y 、v z Respectively performing superscript expression on first derivative operators of the task spacecraft at the corresponding positions of three axes of an earth inertia coordinate system, namely the speeds of the three axes; a is x 、a y 、a z Respectively representing the accelerations of the mission spacecraft in the directions of an x axis, a y axis and a z axis under an earth inertial coordinate system; r represents the distance from the centroid of the mission spacecraft to the geocentric; μ represents an earth gravity constant; f. of x 、f y 、f z Respectively representing the components of the acceleration generated by the non-conservative force on the mission spacecraft in the directions of an x axis, a y axis and a z axis under the inertial coordinate system of the earth.
Further, the interference items contained in the non-conservative force suffered by the mission spacecraft at least comprise disturbance of the earth's non-spherical gravity and disturbance of atmospheric resistance, f x 、f y 、f z The expression is specifically as follows:
wherein f is cx 、f cy 、f cz Respectively representing the acceleration generated by the control force to which the mission spacecraft is subjected on the earth inertia seatThe components in the x, y and z directions under the standard system; f. of ex 、f ey 、f ez Respectively representing the components of the acceleration generated by the perturbation of the earth non-spherical gravity to the mission spacecraft in the directions of x, y and z axes in an earth inertia coordinate system; f. of Ax 、f Ay 、f Az Respectively representing the components of the acceleration generated by the atmospheric resistance on the mission spacecraft in the directions of x, y and z axes under the inertial coordinate system of the earth;
further, the task spacecraft is subjected to the component f of acceleration generated by the perturbation of the earth's non-spherical gravity in the directions of x, y and z axes in the earth's inertial coordinate system ex 、f ey 、f ez The following:
wherein Re is the earth radius and has harmonic coefficient J 2 、J 3 、J 4 Are all constants.
Further, the component f of the acceleration generated by the atmospheric resistance on the mission spacecraft in the directions of the x, y and z axes of the earth inertial coordinate system Ax 、f Ay 、f Az The following:
wherein, F Ax 、F Ay 、F Az Respectively representing the atmospheric drag F experienced by the mission spacecraft A And the components in the directions of the x axis, the y axis and the z axis under the earth inertial coordinate system, wherein M is the mass of the mission spacecraft.
Further, the atmospheric drag F experienced by the mission spacecraft A The following were used:
wherein: ρ is the atmospheric density; v R Velocity of atmosphere relative to spacecraftDegree; c D Is a coefficient of resistance; a. The P The area of the incident flow surface; v is the unit vector of the incoming flow direction.
Further, the specific process of step S2 is as follows:
firstly, two moments at which the observation of the off-satellite point is realized within one day are calculated and obtained according to the scene starting time, the longitude and latitude of the ground target and the target track information by utilizing the characteristics of the in-plane maneuver;
setting initial orbit number oev of mission spacecraft 0 ＝[a 0 ,e 0 ,i 0 ,ω 0 ,Ω 0 ,f 0 ]Wherein a is 0 As an initial semi-major axis, e 0 To initial eccentricity, i 0 At initial orbital inclination angle, ω 0 Is the initial perigee argument, Ω 0 Is the initial ascension point right ascension, f 0 Is the initial true proximal angle; h f Is the target orbital height, re is the earth radius;
number of tracks of target track oev based on in-plane maneuver f1 ＝[Re+H f ,e 0 ,i 0 ,ω 0 ,Ω 0 ,f 0 ]Substituting the position vector into a high-precision orbit dynamics model to recur for one orbit period to obtain a position vector corresponding to any moment in a target orbit period
A set of (a); then combining the scene starting time and the latitude and longitude (Lon) of the target t ,Lat t ) And calculating the position vector of the ground target in one day under an ECI coordinate system by considering the nutation and the time difference of the earth rotation
A set of vectors, the set of vectors being a cone; by traversing each sequence
With respect to each sequence
Calculating the included angle by dot-and-multiply to obtain one dayTwo moments t at which there is an opportunity to realize the observation of the point under the satellite f1 And t f2 According to t f1 And t f2 One of the specific numerical values is selected as the total task time, and the total task time t is taken for convenience of description without loss of generality f ＝t f1 (ii) a At the same time, get t f Corresponding on the target track of time
Respectively representing an expected position vector and an expected speed vector of the mission spacecraft in an earth inertial coordinate system;
then searching to obtain a proper Hoeman transfer moment; the problem of adjusting the trajectory of the sub-satellite points is described as follows: from the departure point of time t 0 At the beginning, a suitable maneuver point time t is sought 1 One Hohmann transfer is carried out, and after half a transfer orbit period, the Hohmann transfer reaches a maneuvering point 2, and the time at the moment is recorded as t 2 Maneuvering to a target circular orbit, after a period of time, at t f At the moment, the subsatellite point of the spacecraft reaches the position near the target position; for the problem, the position speed of the starting point task spacecraft is known, the transfer orbit period can be calculated in advance, and the expected position speed of the end point task spacecraft is known;
from this problem description, the search algorithm is determined as follows:
(a) Latency sequence of set sequences
Δ t is the time step, using
Represents the ith latency in the sequence, i =1,2, ·, n,
start and end times, respectively; thus according to the constraint t w1 ＝t 1 -t 0 Obtaining corresponding sequences
According to the constraint condition t tf ＝t 2 -t 1 Obtaining corresponding sequences
Wherein t is tf Is the transfer time; finally according to the constraint condition t w2 ＝t f -t 2 Obtaining corresponding sequences
Thereby obtaining a result of determining a specific waiting time
The resulting specific solution;
(b) For the ith time series, recursion from the starting point orbit
Time-derived position vector of maneuver point 1
Backward push from the end point track
Time-derived position vector of maneuver point 2
(c) Obtained by dot-product calculation
And
an included angle is set as an error margin epsilon if
The particular solution is not a suitable solution;
updating the sequence, i = i +1, and updating the ith time sequence
And
substituting into (b) and (c) to calculate; when the temperature is higher than the set temperature
The system finds the appropriate Hoeman transfer time and records the time
Exiting the loop;
therefore, a proper Hoeman transfer moment is obtained, and the size of the maneuvering pulse is calculated;
therefore, the fuel optimal control command is adjusted based on the satellite point track of the Hoeman transfer.
Further, the transfer time is as follows:
wherein, a tf Representing the transfer orbit semi-major axis, n representing the number of additional turns of the transfer orbit, n =1 representing the spacecraft running 1.5 turns on the transfer orbit.
Further, in the phase modulation correction process of the maneuvering time according to the error, the deviation between the latitude and longitude of the subsatellite point and the latitude and longitude of the target is considered as that the task spacecraft is affected by perturbation, and the spacecraft passes right above the target when approaching in a phase modulation mode, and the phase modulation correction method specifically comprises the following steps:
distance d between spacecrafts subsatellite point and target at same latitude s-t To describe the initial control error in d s-t The symbol of (2) represents the positional relationship of the two: d s-t When > 0, the target is to the right of the subsatellite point, d s-t < 0, the target is on the left side of the sub-satellite point;
the target moves with the earth's rotation, and the velocity of the target in inertial space is expressed as:
v target ＝2π*R e *cos(Lat t )/86400 (12)
wherein R is e Representing the radius of the earth, lat t Represents the latitude of the target;
time delta t still needed for the target to reach the projection right below the orbit t Expressed as:
Δt t ＝d s-t /v target (13)
Δt t to represent the target lag negatively, Δ t is also required t I arrives directly below the track, a positive value indicates that the target has been at Δ t t Before | reach right below the track;
the spacecraft passes right above the target when approaching by a phase modulation mode.
A computer storage medium having stored therein at least one instruction that is loaded and executed by a processor to implement the high-precision spacecraft undersatellite point trajectory adjusted fuel optimal control method.
The device comprises a processor and a memory, wherein at least one instruction is stored in the memory, and the at least one instruction is loaded and executed by the processor to realize the optimal control method for adjusting the fuel by the high-precision spacecraft satellite point trajectory.
Has the beneficial effects that:
according to the method, a high-precision orbit dynamics model for orbit prediction is established, then an optimal control algorithm for adjusting fuel based on the track of the sub-satellite points of Hoeman transfer is established based on the model, and meanwhile, the high-precision orbit dynamics model considering the influence of perturbation factors such as atmospheric resistance, J2, J3 and J4 is used, so that the method is suitable for accurate adjustment of the track of the sub-satellite points. The method is simple and easy to implement, can accurately and reliably calculate the required maneuvering control pulse and maneuvering time, and can accurately and reliably obtain the required maneuvering control instruction to perform accurate adjustment on the track of the satellite points; in addition, the fuel consumption can be saved to the greatest extent, and the service life of the spacecraft is prolonged.
Drawings
FIG. 1 is a schematic diagram of an optimal control algorithm for adjusting fuel by a high-precision spacecraft intersatellite point trajectory according to an embodiment.
Fig. 2 is a schematic diagram of various common coordinate systems in track control provided by the embodiment.
Fig. 3 is a schematic view of calculating an observation time of a sub-satellite point of the coplanar orbit maneuver provided by the embodiment.
Fig. 4 is a schematic diagram of a classical huffman transfer adjusted by a track of a point under a satellite according to an embodiment.
FIG. 5 shows the X-axis prediction error of the orbit dynamics orbit prediction with high precision provided by the embodiment.
FIG. 6 shows the high-precision orbit dynamics orbit prediction Y-axis prediction error provided by the embodiment.
FIG. 7 shows the Z-axis prediction error of the orbit dynamics orbit prediction with high precision provided by the embodiment.
Fig. 8 is a schematic diagram of an error analysis of an intersatellite point provided by the embodiment, where fig. 8 (a) is a schematic diagram of an error analysis of an intersatellite point at a time when a spacecraft approaches, and fig. 8 (b) is a schematic diagram of an error analysis of an intersatellite point at a time when an orbit projects over a vertex.
Fig. 9 is a schematic diagram of phase modulation correction provided by the embodiment.
Fig. 10 is a schematic diagram of a track of the sub-satellite points according to the embodiment.
Fig. 11 is a partial enlargement of the schematic diagram of the substellar point trajectory provided by the embodiment.
Fig. 12 is a schematic diagram of the distance between the spacecraft and the target according to the embodiment.
Detailed Description
The first embodiment is as follows: the present embodiment is described in connection with figure 1,
the embodiment is an optimal control method for adjusting fuel by using a high-precision spacecraft intersatellite point trajectory. In the embodiment, the A star is used as a task spacecraft to observe the ground target B.
Firstly, by utilizing the characteristics of in-plane maneuver, the moment which is possibly used for realizing off-satellite observation is calculated according to the scene starting time, the longitude and latitude of the point B and the initial orbit information of the satellite A, and the moment is used as the total task time, and meanwhile, the expected state of the satellite A during observation is obtained.
Then, relevant constraint conditions of the track maneuvering are obtained according to the characteristics of Hoeman transfer, the first maneuvering time is set as a variable, the initial track information and the expected state of the A star are substituted into a high-precision track dynamics model to conduct track recursion search to obtain a proper maneuvering time, and meanwhile maneuvering pulses required by corresponding maneuvering points are obtained by combining the initial track and target track information, and therefore a track control instruction is obtained. Substituting the control instruction into a high-precision orbit dynamics model to carry out orbit recursion, simulating an observation error, carrying out phase modulation correction on maneuvering time according to the error, and finally obtaining an optimal control strategy for adjusting the fuel according to the track of the subsatellite point observed by the ground target.
The following is a detailed description:
1. high-precision orbit forecasting:
in the study of spacecraft attitude and orbit dynamics, common coordinate systems include an Earth-Centered Inertial coordinate system (ECI coordinate system for short), an Earth-Centered Earth-Fixed coordinate system (ECEF coordinate system for short), and a spacecraft orbit coordinate system (LVLH coordinate system for short), as shown in fig. 2. In FIG. 2, X J 、Y J 、Z J Is a coordinate axis schematic of an ECI coordinate system which can also be called as a J2000.0 coordinate system; x E 、Y E 、Z E Is indicated by coordinate axes of an ECEF coordinate system; x L 、Y L 、Z L It is indicated by the coordinate axes of the LVLH coordinate system.
Under the earth inertial coordinate system, the high-precision orbit dynamics model can be expressed as:
wherein (x, y, z) is the position of the mission spacecraft in the earth inertial coordinate system, v x 、v y 、v z Respectively is the mission spacecraft in the earth inertial coordinate system IIIThe first derivative of the corresponding position of each axis, namely the speed in the direction of three axes, is marked by a mark to represent a first derivative operator; a is x 、a y 、a z Respectively representing the accelerations of the mission spacecraft in the directions of the x axis, the y axis and the z axis under an earth inertia coordinate system; r represents the distance from the centroid of the mission spacecraft to the geocentric; μ represents an earth gravity constant; f. of x 、f y 、f z Respectively representing the components of the acceleration generated by the non-conservative force on the mission spacecraft in the directions of x, y and z axes under the earth inertial coordinate system;
the interference items contained in the non-conservative force of the mission spacecraft at least comprise disturbance of the earth's non-spherical gravity and disturbance of atmospheric resistance, f x 、f y 、f z The expression is specifically as follows:
wherein f is cx 、f cy 、f cz Respectively representing the components of the acceleration generated by the control force applied to the mission spacecraft in the directions of the x axis, the y axis and the z axis under the earth inertial coordinate system; f. of ex 、f ey 、f ez Respectively representing the components of the acceleration generated by the perturbation of the earth non-spherical gravity to the mission spacecraft in the directions of x, y and z axes in an earth inertia coordinate system; f. of Ax 、f Ay 、f Az Respectively representing the components of the acceleration generated by the atmospheric resistance of the mission spacecraft in the directions of the x axis, the y axis and the z axis of the earth inertial coordinate system.
The earth is generally assumed to be a uniform sphere, at the moment, the gravity of the earth to the spacecraft is only inversely proportional to the square of the earth center distance and is irrelevant to the longitude and latitude of the spacecraft, under the assumed condition, the spacecraft runs in an earth center gravity field, and the motion characteristic can be completely described by the Kepler's law. In fact, the mass of the earth is unevenly distributed, it is an irregular oblate spheroid whose equatorial radius is not equal to its polar axis, and the equator is slightly elliptical, resulting in the tangential and normal directions of the spacecraft orbit being simultaneously acted on by gravity, these factors being called the earth's non-spherical gravitational perturbation. Therefore, the equipotential surface of the earth gravity does not coincide with the isocenter surface, and a series of spherical harmonic functions, which are called perturbation functions, need to be added to the gravitational potential function.
For a near-earth orbit spacecraft, earth perturbation mainly occurs in a flat state of the earth, in an earth gravitational potential function, the influence of field harmonic terms is generally ignored, only a gravitational potential function with harmonic terms is considered, and 4-order harmonic terms (J2, J3 and J4) are considered in the scheme, so f ex 、f ey 、f ez The specific expression is as follows:
wherein Re is the earth radius, generally Re =6378.1km and a harmonic term coefficient J 2 、J 3 、J 4 Are all constants, typically take J 2 ＝1.0826×10 -3 ,J 3 ＝-2.5356×10 -6 ,J 4 ＝-1.6234×10 -6 。
At medium and low orbital altitudes, the atmospheric density is lower than that of the earth surface, but when the spacecraft flies in the atmosphere at a higher speed for a long time, the accumulation of atmospheric resistance finally reflects the influence on the orbital perturbation of the spacecraft, thereby causing the divergence of the orbital motion of the spacecraft. The invention establishes a resistance model by using the atmospheric molecular friction spacecraft surface to obtain the resistance model generated by the atmosphere:
wherein: ρ is the atmospheric density;
V R is the velocity of the atmosphere relative to the spacecraft;
C D the resistance coefficient is generally 2.2-2.6;
A P the area of the incident flow surface;
v is the unit vector of the incoming flow direction.
Therefore, the component f of the acceleration generated by the atmospheric resistance of the mission spacecraft in the directions of the x, y and z axes of the earth inertial coordinate system Ax 、f Ay 、f Az Can be expressed as:
wherein, F Ax 、F Ay 、F Az Respectively representing the atmospheric drag F experienced by the mission spacecraft A And the components in the directions of the x axis, the y axis and the z axis under the earth inertial coordinate system, wherein M is the mass of the mission spacecraft.
In the present invention, the "WGS84-EGM96" earth gravitational field model is used, and the "US Standard1976" model is used for atmospheric resistance.
Based on the model and the orbit dynamics equation, the embodiment of the invention takes the orbit information shown in table 1 as an example of the initial orbit parameter of the spacecraft.
TABLE 1 spacecraft initial orbit information
| Initial time UTC | 2010-01-01 04：00：00 |
| Rx/km | 773.923949 |
| Ry/km | -3514.073825 |
| Rz/km | 5506.746152 |
| v x /km×s -1 | -0.578737 |
| v y /km×s -1 | 6.580464 |
| v z /km×s -1 | 4.11792 |
Based on the initial parameters of the orbit shown in table 1, the orbit prediction for one day can be performed using the above-mentioned high-precision orbit dynamics model, and the three-axis prediction errors obtained by comparing the predicted values with the values obtained by the same parameters of the satellite simulation Software (STK) are shown in fig. 5 to 7, respectively. As can be seen from fig. 5 to 7, within one day, the position error between the orbit information obtained by recursion and the orbit information obtained by simulation of satellite simulation Software (STK) is less than 1.5km, which meets the accuracy requirement.
The invention develops the C language program of the high-precision orbit dynamics model, and obviously shortens the calculation time of orbit recursion in the searching process.
2. Adjusting a fuel optimal control algorithm based on the Hoeman transfer subsatellite point track:
the Hoeman transfer refers to the transfer between two circular tracks, and the Hoeman transfer track is tangent to the inner circle and the outer circle. The Hotman transfer is the most fuel-saving maneuvering mode between two circular orbits, so that the Hotman transfer is widely applied to engineering. Therefore, in order to reduce fuel consumption to the maximum extent and improve the service life of the spacecraft, an optimal control algorithm for adjusting fuel by using the track of the satellite points is designed based on a Hoeman transfer maneuver mode.
The optimal control problem description of adjusting the fuel based on the Hoeman transfer satellite point track is as follows: when a scene begins, the longitude and latitude of a ground target, six initial orbits of a task spacecraft and the height of the target orbit are given, wherein the initial orbit and the target orbit are circular orbits, and two maneuvering instructions including maneuvering time and maneuvering pulse transferred by Hoeman are solved, so that at a certain time after transition to the target orbit, the track of the subsatellite point of the task spacecraft passes through the ground target, and the high-precision observation of the ground target is realized.
First, as shown in fig. 3, two moments at which the intersatellite point observation is realized within one day are calculated and obtained according to the scene starting time, the ground target longitude and latitude and the target orbit information by using the characteristics of the in-plane maneuver. Setting initial orbit number oev of mission spacecraft 0 ＝[a 0 ,e 0 ,i 0 ,ω 0 ,Ω 0 ,f 0 ]Wherein a is 0 As an initial semi-major axis, e 0 To initial eccentricity, i 0 At initial orbital inclination, ω 0 Is the initial argument of the perigee, omega 0 Is the initial ascension point right ascension, f 0 Is the initial true proximal angle; target track height H f Since the earth radius Re is in-plane maneuvering, the number of orbits of the target orbit oev can be approximated f1 ＝[Re+H f ,e 0 ,i 0 ,ω 0 ,Ω 0 ,f 0 ]Substituting the position vector into a high-precision orbit dynamics model to recur for one orbit period to obtain a position vector corresponding to any moment in a target orbit period
Then combining scene start time, target latitude and longitude (Lon) t ,Lat t ) And calculating the position vector of the ground target in the ECI coordinate system in one day (86400 s) by considering the nutation and the time difference of the earth rotation
The set of vectors is a cone. By traversing each sequence
With respect to each sequence
Calculating the included angle by dot-and-multiply to obtain two points which can realize the observation of the point under the satellite in one dayA time t f1 And t f2 Can be according to t f1 And t f2 One of the specific numerical values is selected as the total task time, and the total task time t is taken for convenience of description without loss of generality f ＝t f1 . At the same time, t can be obtained f Corresponding on the target track of time of day
Respectively a desired position vector and a desired velocity vector of the mission spacecraft in an earth inertial coordinate system.
Next a search is made for a suitable huffman transfer instant. As shown in fig. 4, the problem of adjusting the trajectory of the sub-satellite points can be described as: from the departure point time t 0 At the beginning, a suitable maneuver point time t is sought 1 One Hohmann transfer is carried out, and after half a transfer orbit period, the Hohmann transfer reaches a maneuvering point 2, and the time at the moment is recorded as t 2 Maneuvering to a target circular orbit, after a period of time, at t f And at the moment, the subsatellite point of the spacecraft reaches the vicinity of the target position. For the problem, the position speed of the starting point task spacecraft is known, the transfer orbit period can be calculated in advance, and the expected position speed of the end point task spacecraft is known.
From the problem description, a waiting time t is defined w1 Defining a transfer time t as the time of the departure point to the maneuver point 1 tf Defining an approach time t for the time of arrival of maneuver point 1 at maneuver point 2 w2 For the time of the maneuver point 2 reaching the end point, the above parameters should satisfy the following constraints:
t w1 ＝t 1 -t 0 (6)
t tf ＝t 2 -t 1 (7)
t w2 ＝t f -t 2 (8)
from the constraints (6) to (8), it can be readily seen that the problem of adjusting orbital maneuver for the intersatellite point is due to t 0 ,t f As long as the waiting time t is determined, it is known w1 Due to rotation ofTime t of shift tf Can be calculated in advance, then the maneuvering point 1 and the maneuvering point 2 are all determined.
The transfer time was calculated as follows:
wherein, a tf Representing the semi-major axis of the transfer orbit and n representing the number of additional turns of the transfer orbit, e.g. n =1 illustrates that the spacecraft has performed 1.5 turns on the transfer orbit.
The position radial of the maneuvering point 1 and the maneuvering point 2 is easy to know by the Hulman transfer characteristic to form a 180-degree phase, and the following search algorithm can be obtained through the analysis:
(a) Latency sequence of set sequences
Δ t is the time step, using
Represents the ith latency in the sequence, i =1,2, ·, n,
start and end times, respectively; so that the corresponding sequence is obtained according to the constraint (6)
While obtaining corresponding sequences according to constraints (7)
Finally, the corresponding sequence can be obtained according to the constraint condition (8)
This makes it possible to determine a specific waiting time
The particular solution obtained.
(b) For the ith time series, recursion from the starting point orbit
Time-derived position vector of maneuver point 1
Backward push from terminal track (speed reversal)
Time-derived position vector of maneuver point 2
(c) Obtained by dot-product calculation
And
the included angle is set with error margin epsilon, generally 0 < epsilon < 3 deg., if
Indicating that this particular solution is not a suitable solution.
(d) Updating the sequence, i = i +1, and updating the updated ith time sequence
And
the calculation was performed by substituting into (b) and (c). When in use
The system finds the appropriate Hoeman transfer time and records the time
The loop is exited.
Therefore, the proper Hoeman transfer time is obtained, and the maneuvering pulse size is calculated through a vitality formula:
wherein, Δ v 1 And Δ v 2 The first maneuvering pulse direction is along the speed direction, and the second maneuvering pulse direction is opposite to the speed direction.
Therefore, the fuel optimal control command is adjusted based on the satellite point track of the Hoeman transfer.
3. Phase correction method
For the above-mentioned infrastar point adjusting maneuver strategy, the way of calculating the maneuver control pulse is based on the two-body model, which results in the orbit maneuver according to the maneuver control pulse, and finally, a large control error exists. The invention provides a method for completing error correction based on adjustment of initial waiting time.
As shown in fig. 8, fig. 8 (a) shows that when the mission spacecraft approaches, the latitude and longitude of the satellite point deviates from the latitude and longitude of the target to a certain extent, and fig. 8 (b) shows that after the diagram a runs for a certain time, the target runs under the orbit of the spacecraft along with the rotation of the earth. For the case shown in fig. 8 (a) and 8 (b), it can be understood that the mission spacecraft is affected by perturbation and comes to a maneuvering point too early, i.e. the phase of the spacecraft is advanced. In order to make the spacecraft approach just right above the target, phase modulation must be performed.
The invention relates to a distance d between a spacecraft infrasatellite point and a target at the same latitude s-t To describe the initial control error in d s-t The symbol of (2) represents the positional relationship of the two: d is a radical of s-t When > 0, the target is to the right of the subsatellite point, d s-t < 0, target to the left of the subsatellite point.
The velocity of the target in inertial space, with the movement of the target on earth rotation, can be expressed as:
v target ＝2π*R e *cos(Lat t )/86400 (12)
wherein R is e Representing the radius of the earth, lat t Representing the latitude of the target.
Time deltat still needed for the target to reach the projection right below the orbit t Can be expressed as:
Δt t ＝d s-t /v target (13)
Δt t to represent the target lag negatively, Δ t is also required t I arrives directly below the track, a positive value indicates that the target has been at Δ t t Before | reach right below the track.
Analyzing FIGS. 8 (a) and 8 (b) for example, the target falls to the left of the locus of the points under the star, illustrating Δ t t Is less than 0. Therefore, by Δ t t Negative for example, indicating a target at | Δ t t And if the spacecraft arrives right below the orbit after the moment I, the spacecraft is slightly higher than the expected speed, and the spacecraft arrives at the expected position slowly, so that the observation precision is improved. This is achieved by adjusting the operating time of the spacecraft on each orbit, Δ t, as shown in fig. 9 t When the phase is negative, the spacecraft should be delayed in phase, so that the spacecraft is required to be operated on the initial high orbit for a period of time delta t 1 Setting an initial track period T 1 Target track period T 2 Then Δ t 1 Can be expressed as:
therefore, the optimal control instruction of the fuel is adjusted based on the Hohman transfer satellite point trajectory through phase modulation correction, and high observation precision is achieved.
The initial orbit information for the mission spacecraft a is shown in table 2:
TABLE 2 initial orbit information for mission spacecraft A
Ground target B latitude and longitude (Lon) t ,Lat t ) = (13 ° 26'N,144 ° 43' E), target track height H f =200km, the transfer orbit took 1.5 revolutions.
And searching and solving to obtain the following control instructions:
TABLE 3 underfloor adjustment maneuvering control Instructions
| Maneuver time/sec | Pulse size/m × s -1 | Direction of motion (under ECI) | |
| First maneuver | 5972 | 41.2 | [0.585,-0.230,0.777] |
| Second maneuver | 14065 | 39.4 | [-0.589,0.222,-0.777] |
The track of the intersatellite point is shown in fig. 10, fig. 11 is a schematic diagram of the track of the intersatellite point, which is partially enlarged, and it can be known from the diagram that the difference between the latitude and longitude of the intersatellite point of the spacecraft and the target is about 0.03 degrees, the nearest distance between the intersatellite point of the mission spacecraft and the target B is about 7km, and higher observation precision is achieved.
Fig. 12 shows a schematic diagram of the distance between the mission spacecraft a and the target B, and it can be known from the diagram that after two orbital maneuvers, the mission spacecraft a finally reaches the target overhead in 32395 seconds, and the orbital height is 200km, which proves the accuracy of the maneuvering control strategy.
The second embodiment is as follows:
the embodiment is a computer storage medium, wherein at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to realize the optimal control method for adjusting the fuel by the high-precision spacecraft intersatellite point trajectory.
It should be understood that any method described herein, including any methods described herein, may accordingly be provided as a computer program product, software, or computerized method, which may include a non-transitory machine-readable medium having stored thereon instructions, which may be used to program a computer system, or other electronic device. Storage media may include, but is not limited to, magnetic storage media, optical storage media; a magneto-optical storage medium comprising: read-only memory ROM, random access memory RAM, erasable programmable memory (e.g., EPROM and EEPROM), and flash memory layers; or other type of media suitable for storing electronic instructions.
The third concrete implementation mode:
the embodiment is a high-precision spacecraft intersatellite point trajectory adjustment fuel optimal control device, which comprises a processor and a memory, and it is understood that the device comprises any device comprising the processor and the memory, which is described in the invention, and the device can also comprise other units and modules which perform display, interaction, processing, control and other functions through signals or instructions;
at least one instruction is stored in the memory and loaded and executed by the processor to realize the high-precision spacecraft below-satellite point trajectory fuel optimal control method.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (10)
1. The optimal control method for adjusting the fuel by the high-precision spacecraft intersatellite point trajectory is characterized by comprising the following steps of:
s1, calculating to obtain a moment having a chance of realizing the observation of the off-satellite point according to the scene starting time, the longitude and latitude of the point B and the initial orbit information of the satellite A, taking the moment as the total task time, and simultaneously obtaining an expected state of the satellite A during observation;
the star A is a task spacecraft, and the point B represents observation of a ground target B;
s2, obtaining relevant constraint conditions of the track maneuvering according to the Hoeman transfer characteristics, setting the first maneuvering time as a variable, substituting the initial track information and the expected state of the satellite A into a high-precision track dynamics model to perform track recursion search to obtain a proper maneuvering time, and meanwhile, combining the initial track and the target track information to obtain maneuvering pulses required by corresponding maneuvering points, thereby obtaining a track control instruction;
s3, substituting the track control instruction into a high-precision track dynamics model to perform track recursion, simulating an observation error, performing phase modulation correction on maneuvering moments according to the error, and finally obtaining an optimal control strategy for adjusting fuel to the track of the sub-satellite point observed by the ground target;
under the earth inertial coordinate system, the high-precision orbit dynamics model is as follows:
wherein (x, y, z) is the position of the mission spacecraft in the earth inertial coordinate system, v x 、v y 、v z Respectively inertial inertia of the mission spacecraft on earthThe first derivative of the corresponding position of three axes of the linear coordinate system, namely the speed in the direction of the three axes, is marked with a mark and represents a first derivative operator; a is a x 、a y 、a z Respectively representing the accelerations of the mission spacecraft in the directions of the x axis, the y axis and the z axis under an earth inertia coordinate system; r represents the distance from the centroid of the mission spacecraft to the geocentric; μ represents an earth gravity constant; f. of x 、f y 、f z Respectively representing the components of the acceleration generated by the non-conservative force to which the mission spacecraft is subjected in the directions of the x axis, the y axis and the z axis under the inertial coordinate system of the earth.
2. The method for optimally controlling the high-precision spacecraft intersatellite point trajectory adjusting fuel according to claim 1, wherein interference items contained in the non-conservative force applied to the mission spacecraft at least comprise earth non-spherical gravity perturbation interference and atmospheric resistance perturbation interference, f x 、f y 、f z The expression is specifically as follows:
wherein f is cx 、f cy 、f cz Respectively representing the components of the acceleration generated by the control force applied to the mission spacecraft in the directions of the x axis, the y axis and the z axis under the earth inertial coordinate system; f. of ex 、f ey 、f ez Respectively representing the components of the acceleration generated by the perturbation of the earth non-spherical gravity to the mission spacecraft in the directions of x, y and z axes in an earth inertia coordinate system; f. of Ax 、f Ay 、f Az Respectively representing the components of the acceleration generated by the atmospheric resistance on the mission spacecraft in the directions of x, y and z axes under the inertial coordinate system of the earth;
3. the method for optimally controlling the high-precision spacecraft intersatellite point trajectory adjusting fuel according to claim 2, wherein the acceleration generated by the perturbation of the earth's non-spherical gravity on the mission spacecraft is in the directions of x, y and z axes under the earth's inertial coordinate systemComponent f ex 、f ey 、f ez The following:
wherein Re is the radius of the earth and has harmonic coefficient J 2 、J 3 、J 4 Are all constants.
4. The method for optimally controlling the fuel for adjusting the track of the substellar point of the high-precision spacecraft according to claim 3, wherein the component f of the acceleration generated by the atmospheric resistance of the mission spacecraft in the directions of the x axis, the y axis and the z axis of the acceleration under the inertial coordinate system of the earth is the component f Ax 、f Ay 、f Az The following were used:
wherein, F Ax 、F Ay 、F Az Respectively representing the atmospheric resistance F experienced by the mission spacecraft A And the components in the directions of the x axis, the y axis and the z axis under the earth inertia coordinate system, wherein M is the mass of the mission spacecraft.
5. The method of claim 4, wherein the mission spacecraft is subjected to atmospheric drag F A The following were used:
wherein: ρ is the atmospheric density; v R Is the velocity of the atmosphere relative to the spacecraft; c D Is a coefficient of resistance; a. The P The area of the incident flow surface; v is the unit vector of the incoming flow direction.
6. The method for controlling fuel optimization for high-precision spacecraft intersatellite point trajectory adjustment according to one of claims 1 to 5, wherein the specific process of the step S2 is as follows:
firstly, two moments at which the observation of the off-satellite point is realized within one day are calculated and obtained according to the scene starting time, the longitude and latitude of the ground target and the target track information by utilizing the characteristics of the in-plane maneuver;
setting initial orbit number oev of mission spacecraft 0 ＝[a 0 ,e 0 ,i 0 ,ω 0 ,Ω 0 ,f 0 ]Wherein a is 0 As an initial semi-major axis, e 0 To initial eccentricity, i 0 At initial orbital inclination, ω 0 Is the initial argument of the perigee, omega 0 Is the initial ascent point right ascension, f 0 Is the initial true proximal angle; h f Is the target orbital height, re is the earth radius;
number of tracks of target track oev based on in-plane maneuver f1 ＝[Re+H f ,e 0 ,i 0 ,ω 0 ,Ω 0 ,f 0 ]Substituting the position vector into a high-precision orbit dynamics model to recur for one orbit period to obtain a position vector corresponding to any moment in a target orbit period
A set of (a); then combining the scene starting time and the latitude and longitude (Lon) of the target t ,Lat t ) And calculating the position vector of the ground target in one day under an ECI coordinate system by considering the nutation and the time difference of the earth rotation
A set of vectors, the set of vectors being a cone; by traversing each sequence
With respect to each sequence
Calculating the included angle by dot-and-multiply to obtain two moments which have the opportunity of realizing the observation of the point under the satellite in one dayt f1 And t f2 According to t f1 And t f2 One of the specific numerical values is selected as the total task time, and the total task time t is taken for convenience of description without loss of generality f ＝t f1 (ii) a At the same time, get t f Corresponding on the target track of time
Respectively representing an expected position vector and an expected speed vector of the mission spacecraft in an earth inertial coordinate system;
then searching to obtain a proper Hoeman transfer moment; the problem of adjusting the trajectory of the sub-satellite points is described as follows: from the departure point of time t 0 At the beginning, a suitable maneuver point time t is sought 1 One Hohmann transfer is carried out, and after half a transfer orbit period, the Hohmann transfer reaches a maneuvering point 2, and the time at the moment is recorded as t 2 Maneuvering to a target circular orbit, after a period of time, at t f At the moment, the subsatellite point of the spacecraft reaches the position near the target position; for the problem, the position speed of the starting point task spacecraft is known, the transfer orbit period can be calculated in advance, and the expected position speed of the end point task spacecraft is known;
from this problem description, the search algorithm is determined as follows:
(a) Latency sequence of set sequences
Δ t is the time step, using
Represents the ith latency in the sequence, i =1,2, ·, n,
start and end times, respectively; thus according to the constraint t w1 ＝t 1 -t 0 Obtaining corresponding sequences
According to the constraint condition t tf ＝t 2 -t 1 Obtaining corresponding sequences
Wherein t is tf Is the transfer time; finally according to constraint condition t w2 ＝t f -t 2 Obtaining corresponding sequences
Thereby obtaining a result of determining a specific waiting time
The resulting specific solution;
(b) For the ith time series, recursion from the starting point orbit
Time-derived position vector of maneuver point 1
Backward push from the end point track
Time-derived position vector of maneuver point 2
(c) Obtained by dot-product calculation
And
an included angle is set as an error margin epsilon if
The particular solution is not a suitable solution;
updating the sequence, i = i +1, and updating the ith time sequence
And
substituting into (b) and (c) to calculate; when in use
The system finds the appropriate Hoeman transfer time and records the time
Exiting the loop;
therefore, a proper Hoeman transfer moment is obtained, and the size of the maneuvering pulse is calculated;
therefore, the fuel optimal control command is adjusted based on the satellite point track of the Hoeman transfer.
7. The method for optimally controlling the high-precision spacecraft infrasatellite point trajectory adjusting fuel according to claim 6, wherein the transfer time is as follows:
wherein, a tf Representing the transfer orbit semi-major axis, n representing the number of additional turns of the transfer orbit, n =1 representing the spacecraft running 1.5 turns on the transfer orbit.
8. The optimal control method for the high-precision spacecraft intersatellite point trajectory adjustment fuel according to claim 6, wherein in the process of phase modulation correction on maneuvering time according to the error, the deviation between the latitude and longitude of the intersatellite point and the target latitude and longitude is considered as the task spacecraft due to perturbation influence, and the spacecraft passes right above the target when approaching in a phase modulation mode, and the method specifically comprises the following steps:
distance d between spacecrafts subsatellite point and target at same latitude s-t To describe the initial control error in d s-t The symbol of (2) represents the positional relationship of the two: d s-t When > 0, the target is to the right of the subsatellite point, d s-t < 0, the target is on the left side of the subsatellite point;
the target moves with the earth's rotation, and the velocity of the target in inertial space is expressed as:
v target ＝2π*R e *cos(Lat t )/86400 (12)
wherein R is e Representing the radius of the earth, lat t Represents the latitude of the target;
time deltat still needed for the target to reach the projection right below the orbit t Expressed as:
Δt t ＝d s-t /v target (13)
Δt t to represent the target lag negatively, Δ t is also required t I arrives directly below the track, a positive value indicates that the target has been at Δ t t Before | reach right below the track;
the spacecraft passes right above the target when approaching by a phase modulation mode.
9. A computer storage medium having stored therein at least one instruction, the at least one instruction being loaded and executed by a processor to implement a high-precision spacecraft undersatellite point trajectory adjustment fuel optimum control method according to one of claims 1 to 8.
10. A high-precision spacecraft undersatellite point trajectory adjustment fuel optimal control device, which is characterized by comprising a processor and a memory, wherein at least one instruction is stored in the memory, and is loaded and executed by the processor to realize the high-precision spacecraft undersatellite point trajectory adjustment fuel optimal control method according to one of claims 1 to 8.
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