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CN-122009528-A - Design and control method for formation relative movement configuration of earth-moon translational point orbit spacecraft

CN122009528ACN 122009528 ACN122009528 ACN 122009528ACN-122009528-A

Abstract

The invention discloses a design and control method for formation relative motion configuration of a spacecraft with earth-moon translational point orbit, and belongs to the technical field of spacecraft orbit dynamics and control. The method comprises the steps of firstly constructing a double-layer dynamics model consisting of a circular limiting three-dimensional problem model and a high-precision ephemeris model, defining orbit amplitude differences and phase differences as configuration parameters, setting three types of natural relative motion configurations according to different orbit amplitude differences and phase differences, rapidly generating a periodic orbit under the circular limiting three-dimensional problem model, carrying out multi-circle correction by utilizing the high-precision ephemeris model and two-stage multiple targeting, establishing a layered constraint model aiming at a controlled task of fixed position, plane and space surrounding, and solving control pulses by adopting a two-stage optimization strategy. The invention realizes the efficient design and stable control of formation configuration under complex dynamic environment, and is suitable for various translational point orbit tasks.

Inventors

  • WEN GUOGUANG
  • HU HUANQIN
  • Guo Zisen
  • JIANG BOCHUAN
  • MENG YUNHE

Assignees

  • 北京交通大学

Dates

Publication Date
20260512
Application Date
20260227

Claims (10)

  1. 1. The design and control method for the formation relative movement configuration of the earth-moon translational point orbit spacecraft is characterized by comprising the following steps: S1, aiming at formation of earth-moon translational point orbit spacecraft, defining orbit amplitude difference and phase difference as parameters for describing formation relative motion configuration, and constructing a double-level dynamics model, wherein the double-level dynamics model comprises a circular limiting three-body problem model and a high-precision ephemeris model, and aiming at different translational points and orbit families, generating a series of periodic orbits with different amplitudes as reference orbits of formation design; S2, setting three types of natural relative motion configurations according to different track amplitude differences and phase difference combinations based on the reference track; S3, completing rapid generation of a multi-circle periodic orbit and a natural relative motion configuration under a circular limiting three-body problem model; S4, carrying out multi-circle orbit correction on the result of the circular restriction three-body problem model under a high-precision ephemeris model; s5, establishing a constrained optimization model of the controlled configuration according to the preset formation task requirement, and solving the speed increment required by maintaining the configuration.
  2. 2. The method for designing and controlling the relative movement configuration of the formation of the earth-moon translational point orbit spacecraft according to claim 1, wherein in step S1, the method comprises the steps of Representing the state vector of the spacecraft, in the earth-moon rotation coordinate system, the constructed normalized motion equation of the circular restriction three-body problem is expressed as follows: ; Wherein, the Representing potential functions Respectively about Partial derivative of (F), potential function The definition is as follows: ; Wherein, the For the gravitational constant of the earth and the month, Representing the distance of the spacecraft and the two main celestial bodies, respectively: , 。
  3. 3. The method for designing and controlling the formation relative motion configuration of the earth-moon translational point orbit spacecraft according to claim 1, wherein the high-precision ephemeris model is built in the step S1, wherein the motion equation of the spacecraft is built under a lunar inertial coordinate system, the motion equation comprises a circular limiting three-body gravitational term and an additional perturbation term, the additional perturbation term specifically comprises solar gravitational perturbation, solar pressure perturbation and global non-spherical gravitational perturbation, and the perturbation generated by the solar gravitational perturbation is expressed as: ; Wherein, the Representing the gravitational constant of the sun, Representing a position vector from the moon to the sun, Is the position vector of the spacecraft under the lunar J2000 inertial coordinate system; the calculation process of the solar pressure perturbation term is as follows: (1) Calculating solar light pressure according to the relative position relation among the spacecraft, the sun and the moon: ; Wherein the method comprises the steps of For the speed of light in vacuum, For total solar irradiance: ; Wherein the method comprises the steps of For the solar brightness power, the power of the solar energy, Distance from spacecraft to sun; (2) Judging whether the spacecraft is in a moon shadow area, if so, meeting the solar corrosion condition And judging that the spacecraft is in a shadow area, wherein the light pressure perturbation is zero, otherwise, calculating the light pressure perturbation: ; Wherein, the As the distance from the center of the sun to the spacecraft, As the distance from the sun center to the tangent point of the moon, Is the included angle between the solar center-spacecraft connecting line and the solar center-lunar center connecting line, Is the included angle between the connecting line of the sun center and the moon center and the connecting line of the sun center and the moon tangent point, Is the cross-sectional area of the spacecraft, In order to obtain the radiation pressure coefficient, Wherein the value of (2) is between 0 and 2, 0 represents no reflection, 1 represents a black body, 2 represents complete reflection; For the global non-spherical gravitational perturbation term, the perturbation acceleration of the global non-spherical gravitational field on the spacecraft is calculated by adopting the spherical harmonic expansion of the global gravitational field position function, wherein the spherical harmonic expansion is expressed as: Wherein, the Is the constant of the gravitational force, For the radial distance of the spacecraft centroid to the earth center, Is the equatorial radius of the earth reference ellipsoid, For the order of the expansion of the spherical harmonics, Is that The order band harmonic coefficients are used to determine, Is a first-class legendre polynomial, Is the geocentric latitude of the spacecraft in the geodetic coordinate system, For the number of times the spherical harmonic is deployed, Is that Step(s) The second first class of associative legendre polynomials, Is the geocentric longitude of the spacecraft in the geodetic fixed coordinate system, Is that Step(s) The sub-cosine term Tian Xie is a coefficient, Is that Step(s) A subsinusoidal term Tian Xie coefficient; Order the Intercepting the gravity perturbation to J2 term to represent the influence of the global non-spherical gravity perturbation; further, the perturbation acceleration of the non-spherical gravitation of the earth to the spacecraft is solved by the following steps: a. Calculating the radial distance of the earth gravitational field position function pair Latitude of the earth's center Longitude of earth center Partial derivative of (2) 、 、 ; B. the partial derivative in the spherical coordinate system is expressed by the coordinate components in the rectangular coordinate system: ; ; ; Wherein, the ; C. and multiplying the partial derivative by the gradient component to synthesize the partial derivative, thereby obtaining the gravitational acceleration of the spacecraft under the solid-solid coordinate system: ; d. And further calculating differential acceleration: ; Wherein, the For a rotation matrix from the lunar inertial coordinate system to the geodetic coordinate system, Is a position vector of the spacecraft under the lunar J2000 inertial coordinate system, Is a position vector pointing from the lunar centroid to the earth centroid.
  4. 4. The method for designing and controlling the formation relative motion configuration of the earth-moon translational point orbit spacecraft according to claim 1, wherein the three types of natural relative motion configurations in step S2 are respectively: (1) The working conditions with the same amplitude and different phases are that the master spacecraft and the slave spacecraft operate on the same translational point period orbit, and the amplitude is different With a non-zero initial phase difference between the two spacecraft, ; (2) Working conditions with different amplitude values in the same phase are that a main spacecraft and a slave spacecraft run on two adjacent translational point period orbits in a family, the two spacecrafts have the same initial phase angle, Meanwhile, the two spacecrafts have non-zero orbit amplitude difference, ; (3) Different amplitude and phase conditions are that a master spacecraft and a slave spacecraft operate on two adjacent translational point period orbits in a family, and the two spacecrafts have non-zero initial phase difference, In turn, has a non-zero track magnitude difference, 。
  5. 5. The method for designing and controlling the formation relative motion configuration of the earth-moon translational point orbit spacecraft according to claim 1, wherein the step S3 is specifically: S31, under a circular limiting three-body problem dynamics model, loading reference orbit data and interpolating to obtain initial states of a reference orbit and a target orbit, wherein the reference orbit is a main spacecraft flight orbit, the target orbit is a slave spacecraft flight orbit, and numerical integration is adopted to generate corresponding initial multi-circle periodic orbits respectively; s32, correcting and splicing the initial multi-circle periodic track into a continuous track by a two-stage multi-targeting method; s33, calculating the relative states of the master spacecraft and the slave spacecraft in the earth-moon rotation coordinate system and the earth-sun rotation coordinate system, wherein the relative states are obtained by subtracting the states of the master spacecraft and the slave spacecraft in the same period, and outputting the maximum/minimum relative distance and the maximum relative coordinate component, so as to generate a three-dimensional configuration diagram to describe the natural relative motion configuration and geometric characteristics, and the maximum/minimum relative distance is the norm of the relative states.
  6. 6. The method for designing and controlling the relative motion configuration of the formation of the earth-moon translational point orbit spacecraft according to claim 5, wherein the two-stage multiple targeting method in step S32 specifically comprises: s321, discretizing the whole track on a time axis according to a preset track period and calculated turns, and setting a series of targeting points Each targeting point includes a position vector Velocity vector Corresponding time of flight ; S322, first stage speed correction, namely fixing the positions of all the target points And time of flight For each target point except the last target point Solving for initial velocity correction at that point using a single targeting differential corrector So that the end position of the shot from the point is matched with the next shooting point Is the position of (2) Overlap, thereby eliminating the spatial position discontinuity of the orbit at the target point, the initial velocity correction The calculation formula of (2) is as follows: ; Wherein, the For a sensitivity sub-matrix of speed versus position in the state transition matrix, Is the end position error; S323, the second-stage time-space joint correction is carried out by combining For the position of each target point And time of Solving bias guide and constructing adjustment quantity of all target points And time adjustment amount Is summed with the velocity discontinuities of the track at each target point The target is minimized, the adjustment quantity of the target shooting point is calculated by a least square method, namely = , Wherein, the The method comprises the following steps: ; and updating the positions and time of each targeting point by using the solved correction amount, and returning to the execution step S322 until the position and speed discontinuities at all the targeting points are converged within a preset tolerance range.
  7. 7. The method for designing and controlling the formation relative motion configuration of the earth-moon translational point orbit spacecraft according to claim 6, wherein the step S4 is specifically implemented by correcting the segmentation state by adopting a two-stage multiple targeting method under a high-precision dynamics model containing perturbation aiming at a multi-circle periodic orbit generated under an S3 circular restriction three-body problem model, converting the segmentation state into an earth-moon rotation coordinate system and an earth-sun rotation coordinate system, drawing absolute configuration diagrams of two spacecraft, finally calculating the three-dimensional relative position between an orbit pair by interpolating a synchronous orbit time axis, extracting the maximum relative coordinate component as a relative motion configuration performance index, and drawing the relative configuration diagrams of the two spacecraft.
  8. 8. The method for designing and controlling the formation relative motion configuration of the earth-moon translational point orbit spacecraft according to claim 7, wherein in the process of adopting a two-stage multiple targeting method under a high-precision dynamics model, when the time of a periodic orbit is segmented according to the orbit period and the calculated number of turns to obtain a segmentation initial value, aiming at a near-linear corona orbit NRHO, a sensitive area segmentation point positioned near a near-moon point is removed, and the sensitive area segmentation point is specifically a time node which has strong nonlinear characteristics in a dynamics environment and leads to numerical iteration divergence of a differential correction process; the remaining segmentation point states are then converted to a lunar inertial coordinate system as initial guesses for two-stage multi-targeting.
  9. 9. The method for designing and controlling the formation relative motion configuration of the earth-moon translational point orbit spacecraft according to claim 8, wherein the forming task in step S5 comprises: (1) A fixed position formation step, wherein the slave spacecraft is kept at a specified fixed relative position relative to the master spacecraft in a selected coordinate system, and the relative position deviation is smaller than a preset distance threshold; (2) Plane forced surrounding formation, namely, a slave spacecraft moves around a main spacecraft along a closed polygonal path or a quasi-closed path in a specific plane of a selected coordinate system, wherein the vertex of the polygon is a control point, and the slave spacecraft realizes the surrounding of the main spacecraft by exciting maneuvering pulse at the control point; (3) Space three-dimensional surrounding formation, namely, a slave spacecraft moves around a main spacecraft in three-dimensional space, and the proportional constraint of the maximum relative distance and the minimum relative distance is met.
  10. 10. The method for designing and controlling the relative movement configuration of the formation of the earth-moon translational point orbit spacecraft according to claim 9, wherein the solving process of the formation controlled configuration at the fixed position is as follows: Loading reference track data and interpolating to obtain an initial state of a reference track, adding a specific initial bias on the basis of the reference track to construct an initial state of a target track, respectively adopting numerical integration to generate a corresponding initial multi-circle periodic track, and then obtaining a speed increment matched with the configuration bias by a one-stage multiple targeting method to obtain a fixed position configuration diagram; The solution process of the plane forced surrounding formation controlled configuration and the space three-dimensional surrounding formation controlled configuration is as follows: Loading reference track data and interpolating to obtain an initial state of a reference track, obtaining an optimized bias through a two-stage optimization algorithm, adding the optimized bias on the basis of the reference track to obtain a standard surrounding track, and then obtaining a speed increment matched with a configuration through a one-stage multiple targeting method to obtain a corresponding configuration diagram; the two-stage optimization algorithm specifically comprises the following steps for a plane forced surrounding formation and a space three-dimensional surrounding formation controlled configuration: (1) Determining design variables according to the formation plane types: If the formation is limited to a fixed coordinate plane, the fixed coordinate plane comprises an xy plane, an xz plane and a yz plane, and the design variable is that Angular position parameter , For the number of configuration points, the angular position parameters control the azimuth distribution of polygon vertexes on the plane circumference; If the formation is a space plane, the design variables are as follows On the basis of the angular position parameters, 2 plane orientation parameters are additionally introduced The method comprises the steps of determining a normal direction of a space formation plane; (2) Generating a target relative position of the slave spacecraft with respect to the master spacecraft based on the design variables: For a fixed coordinate plane, the relative position of the target is formed by the maximum relative distance With the angular position parameter determination, if the xy plane is adopted, the target relative position is specifically expressed as: ; if the coordinate axis is an xz/yz plane, setting the corresponding coordinate axis component to be 0; for spatial planes, the pass plane orientation parameter Constructing two orthogonal basis vectors in a plane And generating a target relative position by combining the angular position parameters, namely: ; (3) The objective function is designed with the objective of minimizing the cumulative velocity delta norm required to maintain formation from the spacecraft: ; Wherein the method comprises the steps of In order to design a set of variables, A speed increment for the kth maneuver; the constraint conditions include: , presetting a maneuverability threshold for the spacecraft, wherein the relative position deviation is smaller than the maximum relative distance of formation ; (4) Solving through two-stage optimization: The method comprises the steps of performing agent global optimization in a first stage, performing global sampling in a design variable value range, and executing each sample point, namely, generating target relative positions at each maneuvering time according to design variables, b, performing orbit propagation and position targeting under a high-precision ephemeris model, and solving the speed increment required by each maneuver; and in the second stage, performing sequence quadratic programming local refinement, namely taking the candidate design variable solution output in the first stage as an initial value, performing local constraint optimization by adopting a sequence quadratic programming algorithm, starting a feasibility priority mechanism to enable the constraint violation to be suppressed preferentially in the iteration process, further reducing the accumulated speed increment, and finally continuously correcting the diagonal position parameter in the same design variable space and the plane orientation parameter under the space plane condition until the convergence criterion is met, outputting a final design variable solution, and further obtaining the target relative position of each maneuvering moment through the final design variable solution as an optimization bias.

Description

Design and control method for formation relative movement configuration of earth-moon translational point orbit spacecraft Technical Field The invention relates to the technical field of spacecraft orbit dynamics and control, in particular to a design and control method of relative movement configuration of a geosynchronous orbit spacecraft formation. Background The earth-moon translational point orbit is a special area with balanced gravitation in an earth-moon system, has the advantages of low fuel consumption, strong long-term residence capacity and the like, and is a core orbit selection for tasks such as deep space exploration, relay communication, moon polar region observation and the like. When the spacecraft formation flies in the translational point orbit, the functions of three-dimensional observation, data relay enhancement and the like can be realized through multi-star cooperation, and the task efficiency is obviously improved. Therefore, the design and control of the relative motion configuration of the translational point orbit spacecraft formation are a research hot spot and engineering difficulty in the current aerospace dynamics field. Currently, research on translational point orbit spacecraft formation mainly expands around natural and controlled configurations, but the following key problems exist: the existing relative motion and control design is mostly dependent on simplifying periodic orbits and linearization structures in the model, but in the high-precision ephemeris model, multi-body gravitation and environmental perturbation introduce non-autonomous effects, a strict periodic orbit structure is destroyed, the coupling of relative geometric constraint and control time sequence is enhanced, the relative motion and control time sequence is extremely sensitive to initial values and disturbance, and the solving difficulty and the calculating cost of the multi-circle formation configuration are obviously increased. The natural relative motion configuration law is insufficiently characterized in that the natural configuration depends on the amplitude difference and the phase difference induction of the initial state of the spacecraft, the existing work mostly carries out scattered analysis on a single orbit family or specific working conditions, and the orbit families with different translational points and different bias working conditions lack unified configuration patterns and evolution laws, so that engineering model selection and safety margin assessment still mainly depend on scattered calculation examples and experience judgment, and systematic guidance is lacked. The problem of numerical stability of a strong nonlinear region is that in the strong nonlinear region, particularly in the near-month section of a near-straight corona track NRHO, the traditional numerical construction method is easy to cause the problem of iteration non-convergence or numerical divergence, and when the near-month end height of the track is low or the state transition sensitivity is increased, the convergence domain of splicing point selection and differential correction is obviously contracted, so that the reliability of batch generation of multi-circle reference tracks and corresponding configurations is reduced, and the coverage range of a configuration database is limited. The global contradiction with optimality of controlled configuration solving is that aiming at controlled configurations such as fixed positions, plane forced surrounding and the like, pulse time and pulse amplitude are required to be determined simultaneously and multiple constraints such as relative distance, relative speed and task period are met, the calculation cost of global optimization is huge under a high-precision model, while the efficiency can be improved by simply relying on a proxy model, but the precision in an optimal solution neighborhood is often insufficient, so that the solving process is complex and sensitive to algorithm parameters and initial guess height, and global exploration and local optimization are difficult to be considered. Therefore, a spacecraft formation relative motion configuration design and control method capable of opening up a simplified model and a high-precision model, systematically revealing natural configuration rules, having high numerical stability and achieving global and local optimization is needed. Disclosure of Invention In order to solve the problems in the background technology, the invention provides a design and control method for formation relative motion configuration of earth-moon translational point orbit spacecraft, which comprises the following steps: S1, aiming at formation of earth-moon translational point orbit spacecraft, defining orbit amplitude difference and phase difference as parameters for describing formation relative motion configuration, and constructing a double-level dynamics model, wherein the double-level dynamics model comprises a circular limiting