A fuel-optimal active drift three-dimensional imaging orbit control method

Abstract

The present invention discloses a fuel-optimal active drift three-dimensional imaging orbit control method, including: obtaining a drift calculation formula based on the satellite orbit sub-satellite point trajectory coincidence principle and the relationship between the satellite orbit operation period and the semi-major axis; obtaining initial active drift based on the satellite semi-major axis and orbit period principle and the drift calculation formula; obtaining precise active drift control with maximum control pulse interval based on initial active drift control, high-precision absolute orbit prediction method and Newton iteration method; constructing an orbit transfer control fuel consumption model, and realizing fuel optimal control based on precise active drift control and orbit transfer control fuel consumption models. The present invention meets the different task requirements of global complex terrain elevation measurement and three-dimensional imaging, and takes into account the goals of optimal fuel consumption and transfer time.

Description

Technical Field

[0001] The invention belongs to the field of aerospace technology, and in particular relates to a fuel optimal active drift three-dimensional imaging orbit control method. Background Art

[0002] Most of the designs at home and abroad are made under the perturbation of the Earth J2 or J4. For the strict recurrence orbit under the high-order gravity field, the commonly used method is to apply virtual pulses so that the actual trajectory of the satellite is within the "pipeline radius" of the reference trajectory. In order to reduce the control frequency and fuel consumption, it is necessary to design a strict natural recurrence orbit without applying virtual pulses under the high-order gravity field.

[0003] Through the investigation of the current orbit change control strategy, the existing literature mainly focuses on the fuel saving for orbit transfer strategy. However, for the three-dimensional imaging SAR application technology, the satellite drift time consumption should also be further considered. How to achieve low orbit fuel consumption and optimal transfer time under certain constraints should become the focus of current research. Summary of the invention

[0004] The purpose of the present invention is to provide a fuel optimal active drift three-dimensional imaging trajectory control method to solve the problems existing in the above-mentioned prior art.

[0005] To achieve the above object, the present invention provides a fuel optimal active drift three-dimensional imaging trajectory control method, comprising:

[0006] The drift calculation formula is obtained based on the satellite orbit sub-satellite point trajectory coincidence principle and the relationship between the satellite orbit period and the semi-major axis;

[0007] The initial active drift is obtained based on the principle of the satellite semi-major axis and orbital period and the drift calculation formula;

[0008] Based on the initial active drift control, the high-precision absolute orbit prediction method and the Newton iteration method, accurate active drift control with maximum control pulse interval is obtained;

[0009] A fuel consumption model for orbital transfer control is constructed, and optimal fuel control is achieved based on precise active drift control and the fuel consumption model for orbital transfer control.

[0010] Optionally, the process of obtaining the drift calculation formula includes:

[0011] Based on the rotation characteristics of the earth and the precession principle of the satellite on the orbital node line, a double-satellite design with overlapping sub-satellite point trajectories is carried out. The double-satellite design is analyzed based on the principle of overlapping sub-satellite orbital points, and the influence relationship between the longitude difference of the ascending node of the satellite orbit plane with overlapping trajectories and the satellite orbit phase difference is obtained. Based on the relationship between the satellite orbital operation period and the semi-major axis and the influence relationship between the longitude difference and the phase difference, the calculation formula of the drift amount is obtained.

[0012] Optionally, the drift amount is determined by a change in the satellite orbit period and an expected number of revisit orbit periods.

[0013] Optionally, the process of acquiring the initial active drift control includes: based on the principle of satellite semi-major axis and orbital period, obtaining the orbital period change formed by the semi-major axis difference, and combining the drift amount and the orbital period change to obtain the initial active drift control.

[0014] Optionally, the high-precision absolute orbit prediction method includes: constructing a high-precision absolute orbit prediction model based on the influence of disturbance noise characteristics, kinematics and dynamics equations, and performing recursive calculation based on the high-precision absolute orbit prediction model.

[0015] Optionally, during the recursive calculation process, recursive calculation is performed based on the high-precision determined value of the absolute orbit, and an iterative solution is performed, wherein the high-precision determined value is a preset value, including: obtaining the six elements of the orbit, performing multiple coordinate transformations on the six elements of the orbit, obtaining corrections to the gravity field coefficients of solid tides and ocean tides, calculating the non-spherical gravitational acceleration of the earth, and obtaining the Cartesian coordinate acceleration components in the inertial system based on the non-spherical gravitational acceleration, the gravitational acceleration of the center of the earth, and the acceleration caused by the atmosphere and solar pressure, and after recursion and coordinate transformation, obtaining the recursive six elements of the orbit; and performing an iterative solution until the preset performance requirements are met.

[0016] Optionally, the process of obtaining the precise active drift control includes: based on the high-precision absolute orbit prediction model and the initial active drift control, using the Newton iteration method, taking the maximum time interval between two in-plane pulse ignitions as the optimization target, optimizing and solving the pulses along the track, and obtaining the control speed pulse with the maximum interval between two in-plane three-dimensional imaging drift orbit control pulses as the precise active drift control.

[0017] Optionally, the process of constructing the orbit transfer control fuel consumption model: based on the Gaussian perturbation equation described by the E / I vector, the control pulses within the orbit control plane and the control pulses outside the orbit control plane are explained separately.

[0018] Optionally, during the process of optimal fuel control, a three-pulse control method is used within the orbital control plane, and a single-pulse control method is used outside the orbital control plane to obtain the pulse ignition speed increment and ignition latitude angle to achieve optimal fuel control.

[0019] The technical effects of the present invention are:

[0020] The method based on the present invention meets the different task requirements of global complex terrain elevation measurement and three-dimensional imaging. The optimal transfer time is achieved by calculating the control speed pulse with the largest interval between two in-plane three-dimensional imaging drift orbit control pulses. The optimal fuel control is achieved by controlling the ignition pulse latitude angle and pulse interval, and the switching track change plan is completed. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0022] Figure 1 The research idea of ​​the fuel optimal active drift three-dimensional imaging orbit control in the embodiment of the present invention;

[0023] Figure 2 Schematic diagram of the overlap space of the sub-satellite point trajectories of adjacent orbital planes in an embodiment of the present invention;

[0024] Figure 3 A high-precision orbital dynamics recursive calculation flow chart in an embodiment of the present invention;

[0025] Figure 4 Schematic diagram of pulse iterative solution for in-plane three-dimensional imaging drift trajectory control in an embodiment of the present invention. DETAILED DESCRIPTION

[0026] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0027] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0028] Embodiment 1

[0029] like Figure 1 As shown, this embodiment provides a fuel optimal active drift three-dimensional imaging trajectory control method, including:

[0030] (1) Modeling of baseline drift in active drift 3D imaging

[0031] a. Active drift modeling

[0032] In order to understand the process of active drift control to form the longitude baseline, an active drift model based on the satellite orbit period deviation is established. First, the principle of the star point trajectory of the adjacent orbital binary constellation is considered. For a binary constellation with the same orbital height and inclination, based on the rotation characteristics of the earth and the precession principle of the satellite on the orbital node line, by reasonably designing the longitude difference of the ascending node between the orbital planes and the phase angle difference between satellites in different orbital planes, the binary satellites can be operated along the same ground track. The specific principle is as follows: Figure 2 shown.

[0033] Assume λ i and λ j are the right ascension values ​​of the ascending node of satellite i and j respectively, and the right ascension difference between the two satellite orbital planes is

[0034] Δλ=|λ i -λ j |

[0035] Δω is the phase of satellite j lagging behind satellite i, ω e is the Earth's angular velocity, and its direction of movement is from west to east around the Earth's axis.

[0036] according to Figure 2 As shown in the figure, according to the principle of satellite orbit subsatellite point trajectory overlap, if the time taken by satellite j to move from its current position to its ascending node position along the orbital plane is the same as the time taken by the longitude difference Δλ of the earth's rotation under the J2 perturbation, then satellite j and satellite i have the same subsatellite point trajectory. Based on this, it can be deduced that the right ascension difference of the ascending node of the adjacent satellite orbital planes and the satellite orbit phase difference that overlap the subsatellite point trajectory should satisfy the following conditions

[0037]

[0038] Where Δλ is the longitude difference between the ascending nodes of adjacent orbital planes; ω e is the angular velocity of the Earth's rotation; is the average rate of precession of the satellite orbital nodal line (i.e., the rate of change of the right ascension J2 term of the ascending node); Δω is the phase difference between satellites in adjacent orbital planes; ω s is the angular velocity of the satellite in orbit.

[0039] From the design of double satellites with subsatellite point trajectory overlap, it can be known that by changing the phase difference of the satellite in the orbital plane, a longitude difference can be formed in the longitude direction of the earth. Based on this principle, combined with the relationship between the satellite orbit operation period and the semi-major axis, assuming that the period number of the active drift regression orbit is N, the number of regression circles is M, and the period difference formed by orbit control is ΔT, the drift amount within the original revisit period can be expressed as

[0040]

[0041] Where k represents the number of original revisit orbit cycles.

[0042] b. Initial design strategy for active drift control instructions

[0043] The drift calculation formula shows that the expected drift is mainly determined by the change in the satellite orbit period and the expected number of revisit orbit periods. Based on this, in order to determine the main drift control strategy for tomography, the initial design strategy for active drift control instructions will be derived based on the principle of satellite semi-major axis and orbit period.

[0044] The results of satellite orbit research show that under the main perturbation conditions of low-orbit space, the calculation expression of satellite orbit angular velocity is

[0045]

[0046] In the formula, is the rate of change of the satellite's mean anomaly angle due to J2 perturbation, and n is the satellite's orbital angular velocity, which is mainly determined by the semi-major axis of the satellite's orbit and can be calculated as

[0047]

[0048] Where a represents the semi-major axis and μ represents the standard gravity parameter.

[0049] Since the changes in the mean anomaly angle and the ascending node right ascension are relatively small, the change in the satellite orbit period can be approximated as the periodic change caused by the semi-major axis difference. Assuming the ideal orbit semi-major axis is a nom , the change of the orbital semi-major axis is Δa. According to the above formula, the change of the orbital period caused by the semi-major axis difference is

[0050]

[0051]

[0052] Combining the calculation formula of orbital period variation caused by drift and semi-major axis difference, the initial design expression of active drift control command can be obtained as follows:

[0053]

[0054] Where T0 represents the initial orbital period.

[0055] (2) Precise planning of active drift control instructions based on Newton iteration

[0056] The initial control instructions generated based on the three-dimensional imaging baseline active drift model are only applicable to active drift control under the J2 gravity field. However, the on-orbit motion of low-orbit satellites is not only affected by the gravity of the center of the earth, but also by the perturbations of the earth's non-spherical gravity, solid tides, ocean tides, atmosphere and solar pressure. If only based on the initial control instructions, the satellite active drift control will diverge quickly and the control will be frequent.

[0057] In order to solve the above problems, based on the high-precision absolute orbit prediction method and the idea of ​​Newton iteration, a precise planning method for active drift control instructions based on Newton iteration is proposed to achieve precise active drift control instructions with the maximum control pulse interval.

[0058] a. High-precision absolute orbit prediction

[0059] Based on the high-precision determined value of the absolute orbit, the absolute orbit state in the future is accurately predicted. The high-precision orbit dynamics recursive calculation process is as follows: Figure 3 shown.

[0060] According to the above processing flow, the high-precision orbit recursive calculation first converts the six elements of the orbit into Cartesian components in the inertial coordinate system, and converts the position components in the inertial system into position components in the earth-fixed coordinate system through the coordinate conversion matrix, and then obtains the spherical coordinate position components in the earth-fixed system through the Cartesian-spherical coordinate component conversion; obtains the correction of the gravity field coefficients of solid tide and ocean tide through the spherical coordinate position components in the earth-fixed system, and then calculates the non-spherical gravitational acceleration of the earth under the gravity field EGM2008 model; obtains the Cartesian component of the non-spherical gravitational acceleration in the inertial system through the spherical-Cartesian component conversion and the earth-fixed-inertial coordinate transformation; obtains the Cartesian coordinate acceleration component in the inertial system by adding the gravitational acceleration of the earth's center, the acceleration caused by the non-spherical gravitational acceleration of the earth, the atmosphere, the solar pressure and other perturbations; in the inertial coordinate system, obtains the recursive position and velocity components through the rkf7(8) recursion, and finally obtains the recursive six elements of the orbit through the Cartesian-orbit coordinate conversion.

[0061] b. Precise control instruction planning based on Newton iteration

[0062] Considering that the actual atmospheric density is difficult to accurately model, and the influence of dynamic changes in perturbations such as solar pressure on the orbital state, the orbital drift generated by the active drift model can only be used as an initial guess for the three-dimensional imaging drift orbit control. Accurate three-dimensional imaging drift orbit control pulse Δv TIt is necessary to use the established high-precision orbit prediction model, based on the Newton iteration method, and take the maximum time interval between two in-plane pulse ignitions as the optimization goal to calculate the pulse Δv along the track. T Perform optimization solution.

[0063] Schematic diagram of pulse iterative solution for 3D imaging drift orbit control in the absolute orbit plane Figure 4 In order to reduce the number of times the orbit control engine is started, the time interval between two in-plane drift controls needs to be maximized. The pulse iterative solution process is as follows:

[0064] Based on the established high-precision orbit prediction model, the orbit space error is calculated. Once the orbit space error exceeds the three-dimensional imaging drift orbit control requirement, the drift control pulse along the track in the plane is calculated. This value is used as the initial guess. Based on the Newton iteration method, the control speed pulse that can maximize the interval between two in-plane three-dimensional imaging drift orbit control pulses is found.

[0065] (3) Fuel-optimal 3D imaging drift trajectory control

[0066] According to the decoupling characteristics of satellite orbit transfer control in-plane and out-of-plane orbit, the control pulses in-plane and out-of-plane orbit control are explained respectively based on the Gaussian perturbation equation described by E / I vector, so as to establish the orbit transfer control fuel consumption model and support the optimal fuel control instruction planning.

[0067] a. Optimal three-pulse control of in-plane fuel

[0068] From the orbit transfer mechanism described by the E / I vector, it can be seen that the orbit transfer control ignition direction with the minimum control amount must choose the direction of the orbit transfer vector change, thereby determining the orbit transfer control ignition latitude angle k is 0, 1, 2...n, where n is determined by the number of ignition pulses; for

[0069]

[0070] According to the above minimum fuel consumption expression, the control correction amount in the orbit transfer plane can be reduced from 4 to 3, and the orbit transfer E vector amplitude change δe can be expressed as

[0071]

[0072] Based on the above formula, based on n pulse ignition control along the track, the correction amount of the control parameter in the formation configuration plane can be expressed as:

[0073]

[0074]

[0075]

[0076] Where, t i Indicates the time corresponding to the ignition pulse action, Indicates the change in value corresponding to the action of the ignition pulse.

[0077] The time interval between the first ignition pulse and the second ignition pulse is recorded as Δt1, the time interval between the second ignition pulse and the third ignition pulse is recorded as Δt2, and the time interval between the third ignition pulse and the next three-pulse ignition control start pulse is t. It can be expressed as

[0078]

[0079]

[0080]

[0081] Δe represents the deviation between the standard orbit transfer E vector amplitude and the actual orbit transfer E vector amplitude.

[0082] The deviation along the track is processed to obtain

[0083]

[0084] The constant deviation change Δλ along the track during the three-pulse maintenance control ignition process s for

[0085]

[0086] The constant deviation change Δλ along the track from the end of the first three-pulse maintenance control to the second three-pulse maintenance control t for

[0087]

[0088] Assume that the expected semi-major axis change after the three-pulse orbit transfer control ignition is Δa m , the constant offset change along the track is Δλ sm , the change in the E vector amplitude is Δe m , then we can get

[0089]

[0090]

[0091]

[0092] Let Δt1 = Δt2 = T / 2 (T is the orbital period of the formation's primary star), and and is positive, is negative. Then it can be expressed as

[0093]

[0094]

[0095]

[0096] Solving the above equation, we get

[0097]

[0098]

[0099]

[0100] b. Optimal single pulse control of out-of-plane fuel

[0101] In view of the out-of-plane orbit transfer control requirements, the single pulse control method is selected. Based on this, the minimum single pulse ignition speed increment and ignition latitude angle for out-of-plane orbit transfer control can be solved as follows:

[0102] δv nN =naδi

[0103] u MN =arctan(δi y / δi x )+k2π

[0104] Where δi is the change of the control vector I outside the orbit transfer plane, δi x is the change in the x-axis, δi y is the change in the y-axis.

[0105] The above is only a preferred specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A fuel optimal active drift three-dimensional imaging trajectory control method, characterized in that: The following steps are involved: The drift calculation formula is obtained based on the satellite orbit sub-satellite point trajectory coincidence principle and the relationship between the satellite orbit period and the semi-major axis; The initial active drift is obtained based on the principle of the satellite semi-major axis and orbital period and the drift calculation formula; Based on the initial active drift control, the high-precision absolute orbit prediction method and the Newton iteration method, accurate active drift control with maximum control pulse interval is obtained; The high-precision absolute orbit prediction method comprises: constructing a high-precision absolute orbit prediction model based on the influence of disturbance noise characteristics, kinematics and dynamics equations, and performing recursive calculation based on the high-precision absolute orbit prediction model; In the process of recursive calculation, recursive calculation is performed based on the high-precision determined value of the absolute orbit, and iterative solution is performed, wherein the high-precision determined value is a preset value, including: obtaining six orbital elements, performing multiple coordinate transformations on the six orbital elements, obtaining corrections to the gravity field coefficients of solid tides and ocean tides, calculating the non-spherical gravitational acceleration of the earth, obtaining the Cartesian coordinate acceleration components in the inertial system based on the non-spherical gravitational acceleration, the gravitational acceleration of the center of the earth, and the acceleration caused by the atmosphere and solar pressure, and obtaining the recursive six orbital elements after recursion and coordinate transformation; performing iterative solution until the preset performance requirements are met; A fuel consumption model for orbital transfer control is constructed, and optimal fuel control is achieved based on precise active drift control and the fuel consumption model for orbital transfer control.

2. The fuel optimal active drift three-dimensional imaging trajectory control method according to claim 1 is characterized in that: The process of obtaining the drift calculation formula includes: Based on the rotation characteristics of the earth and the precession principle of the satellite on the orbital node line, a double-satellite design with overlapping sub-satellite point trajectories is carried out. The double-satellite design is analyzed based on the principle of overlapping sub-satellite orbital points, and the influence relationship between the longitude difference of the ascending node of the satellite orbit plane with overlapping trajectories and the satellite orbit phase difference is obtained. Based on the relationship between the satellite orbital operation period and the semi-major axis and the influence relationship between the longitude difference and the phase difference, the calculation formula of the drift amount is obtained.

3. The fuel optimal active drift three-dimensional imaging trajectory control method according to claim 2 is characterized in that: The amount of drift is determined by the change in the satellite orbital period and the expected number of revisit orbital periods.

4. The fuel optimal active drift three-dimensional imaging trajectory control method according to claim 1, characterized in that: The acquisition process of the initial active drift control includes: based on the principle of satellite semi-major axis and orbital period, obtaining the orbital period variation formed by the semi-major axis difference, and combining the drift amount with the orbital period variation to obtain the initial active drift control.

5. The fuel optimal active drift three-dimensional imaging trajectory control method according to claim 1, characterized in that: The process of obtaining the precise active drift control includes: based on the high-precision absolute orbit prediction model and the initial active drift control, using the Newton iteration method, taking the maximum time interval between two in-plane pulse ignitions as the optimization goal, optimizing and solving the pulses along the track, and obtaining the control speed pulse with the maximum interval between two in-plane three-dimensional imaging drift orbit control pulses as the precise active drift control.

6. The fuel optimal active drift three-dimensional imaging trajectory control method according to claim 1, characterized in that: The construction process of the orbit transfer control fuel consumption model: Based on the Gaussian perturbation equation described by the E / I vector, the control pulses within the orbit control plane and the control pulses outside the orbit control plane are explained respectively.

7. The fuel optimal active drift three-dimensional imaging trajectory control method according to claim 6, characterized in that: During the process of optimal fuel control, a three-pulse control method is used within the orbital control plane, and a single-pulse control method is used outside the orbital control plane to obtain the pulse ignition speed increment and ignition latitude angle to achieve optimal fuel control.

Images