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CN-116625381-B - Multiple-accessibility coverage method for evaluating star group orbital transfer maneuver

CN116625381BCN 116625381 BCN116625381 BCN 116625381BCN-116625381-B

Abstract

The invention discloses a multiple reachability coverage assessment method for satellite constellation orbital transfer maneuver, which is suitable for rapid assessment of a satellite constellation multiple-star reachability area and belongs to the field of aerospace. The method comprises the steps of carrying out equal volume dispersion on a target area in two dimensions of a distance and a zenith angle under a geocentric fixedly connected spherical coordinate system, taking an reachable azimuth interval of a central line of a discrete unit as an evaluation index, calculating an intersection point of the central line and an reachable domain envelope, carrying out detailed judgment to obtain a single-star reachable azimuth interval, adopting a node sequencing and one-time sequential reading method to obtain a multi-star reachable azimuth interval corresponding to the central line of the target, simultaneously intercepting the multi-star reachable azimuth interval by combining the target azimuth area, and integrating the multi-star reachable intervals of all the central lines of the target to obtain a multi-star reachable area of a constellation to the target area, thereby realizing multi-star orbit maneuver multiple reachable coverage evaluation of the constellation. The time complexity of the invention is compressed to O (n 2 +n).

Inventors

  • WEN CHANGXUAN
  • Sun Yangyuqian
  • QIAO DONG
  • ZHANG RUI
  • WANG LINBO

Assignees

  • 北京理工大学
  • 北京电子工程总体研究所

Dates

Publication Date
20260512
Application Date
20230526

Claims (7)

  1. 1. A multiple accessibility coverage method for evaluating a star group orbital maneuver is characterized by comprising the following steps, Step one, using part of three-dimensional sphere layer for the target area S under the geocentric fixedly connected coordinate system S I or the geocentric inertial coordinate system S J Representation, part of the three-dimensional sphere layer Performing equal volume dispersion in the dimensions of distance r and zenith angle theta, and azimuth angle The dimension is analyzed to obtain I multiplied by J equal volume rings R ij , and the reachable condition of the center line C ij of the equal volume rings is taken as the reachable condition of the equal volume rings R ij ; Step two, aiming at the equal volume ring central line C ij obtained by equal volume dispersion in the step two and the single star reachable three-dimensional envelope converted into the inertial coordinate system S J , the single star reachable three-dimensional envelope is split into a plurality of triangular patches, and the in-plane intersection point of the central line C ij and the triangular patches is calculated in the spherical coordinate system to obtain a corresponding single star reachable azimuth angle matrix And a target azimuth matrix Φ TAR(ij) ; Step three, for the reachable azimuth sequence of the reachable domain of the mth satellite, which is obtained in the step two and is represented by the starting node and the ending node, to C ij Multi-star reachable matrix of constellation to central line C ij is obtained through node ordering and one-time sequential reading According to the target azimuth interval pair in phi TAR(ij) Intercepting to obtain a multi-star reachable matrix of a given target area Step four, a multi-star reachable matrix of the target area is given according to the central line C ij obtained in the step three And calculating N star reachable azimuth angles Γ RDNX(ijp) (N) of the single discrete unit R ij , and integrating the multi-star reachable intervals of all the target central lines to obtain a multi-star reachable area of the constellation to the target area, namely realizing multi-star orbit maneuver multiple reachability coverage evaluation.
  2. 2. The method for evaluating multiple reachability of a star-group orbital transfer maneuver of claim 1, further comprising the step of realizing visual characterization of multiple star reachable areas according to the multiple reachability of the star-group orbital transfer maneuver evaluated in the step four, improving the precision and efficiency of evaluating the multiple star reachable areas in multi-star collaboration and further improving the precision and efficiency of executing multi-star collaborative tasks.
  3. 3. A method of assessing multiple reachability of a constellation orbital maneuver as in claim 2 wherein said multi-star collaborative task includes observation, guidance and interception.
  4. 4. The method for evaluating multiple reachability of a constellation orbit maneuver as in claim 1, 2 or 3, wherein step one is accomplished by, Firstly, defining an adopted coordinate system, and considering an earth inertia coordinate system, an earth fixed coordinate system and a satellite orbit coordinate system: the gravity inertial coordinate system S J , the origin of which is positioned at the gravity center E of the earth, and the reference plane is defined as the average equatorial plane of the earth, wherein the X axis points to the point of the flat spring, the Z axis points to the north pole perpendicular to the equatorial plane, and the Y axis is determined by the right hand rule that Y=Z×X; The earth center is fixedly connected with a coordinate system S I , the origin is positioned at the gravitational center E, the reference plane is defined as the average equatorial plane of the earth, the X I axis points to the north pole along the intersection line of the Greenwich meridian plane and the equatorial plane of the earth, the Z I axis is perpendicular to the equatorial plane, and the Y I axis is determined by the right rule, Y I ＝Z I ×X I ; The satellite orbit coordinate system S 0 takes a satellite centroid o as a coordinate origin, takes a current position vector direction r Sat of the spacecraft as an x 0 axis, and the z 0 axis is perpendicular to the pointing normal line direction of the orbit plane, and y 0 is determined by the right-hand rule, namely y 0 ＝z 0 ×x 0 ; For single-star reachable domain calculation, the reachable domain envelope is expressed under an orbit coordinate system S 0 , for multi-star reachable domain calculation, the reachable domain envelope needs to be uniformly expressed under an inertial coordinate system S J , and for specific satellites with six orbits expressed as [ a, e, i, omega, f ], the reachable domain envelope needs to be uniformly expressed under the inertial coordinate system S J through a conversion matrix as shown in a formula (1): Where u=ω+f, M is a rotation matrix about the corresponding axis; Only the uniform rotation factor of the earth is considered in the conversion of the earth center inertial system and the earth center fixedly connected system, the influence of time difference, nutation and polar movement is ignored, the coordinate system only rotates around the Z axis, and the corresponding conversion matrix is as follows: When GAST is the Greenner flat star, the rotation angle of the earth from the flat spring point at the satellite position moment to the Greenner meridian is calculated; setting a distance interval [ r L ,r U ] and a zenith angle interval [ theta L ,θ U ] according to the S and task requirements to define a three-dimensional sphere layer under a geocentric fixedly connected coordinate system S I or a geocentric inertial coordinate system S J according to different target characteristics, wherein the target area S is given by longitude, latitude and distance or is given by a three-dimensional grid envelope Expressed as: then part of the three-dimensional sphere layer Is of the volume of (2) The method comprises the following steps: For three-dimensional ball layers Discrete in the distance r and zenith angle θ dimensions and in azimuth The dimensions are resolved, and the obtained I×J equal-volume discrete rings R ij are expressed as: where r i and θ j are the nodes that perform the discretization: r 0 ＝r L ,r I ＝r U ,θ 0 ＝θ L ,θ J ＝θ U The discrete loop volume V ij given the three-dimensional information is: determining nodes r i and theta j by adopting an equal volume discrete method, wherein the volume of part of the three-dimensional sphere layer is given by the formula (3), and the volume V ij of each discrete ring is Combining formula (4) and formula (5), nodes r i and θ j are represented as: The centerline of the discrete unit R ij is defined as C ij , denoted as: Wherein C ij is a circle determined by nodes r i and θ j , and the reachable condition of the center line is an azimuth interval corresponding to the satellite reachable domain in the constellation A representation; When the parameters I and J of the discrete units are sufficiently large, the divided discrete ring volume V ij is small, and the approximate performance increase using the centerline reachable case Φ RD(ij) for the reachable case R RD(ij) of a single discrete unit is expressed as: The equal volume dispersion of the three-dimensional space region target is realized by the distance and zenith angle two-dimensional dispersion calculated quantity I multiplied by J, the space region target is represented by the resolved azimuth angle center ring reachable interval, and the method is suitable for any target region given by longitude and latitude or grid envelope.
  5. 5. The method for evaluating multiple reachability of a constellation orbit maneuver as described in claim 4, wherein step two is implemented by, The single star reachable envelope is denoted r (x, y, z) 0 in the orbit coordinate system S 0 , where the three-axis positions are given by a grid matrix of mxn, which is converted to r (x, y, z) J in the inertial coordinate system S J , or r (x, y, z) I in the fixed coordinate system S I ; Calculating azimuth intervals corresponding to satellite reachable domains, namely obtaining intersection points of a center circle C ij and all grid planes forming an envelope, wherein the envelope is expressed under spherical coordinates for simplifying calculation, and the grid matrix of m multiplied by n is also adopted for expression, and the problem is equivalent to obtaining intersection points of a straight line of r= (r i-1 +r i )/2 and theta= (theta j-1 +θ j )/2 and all grid planes forming the envelope; The adjacent 2X 2 matrixes in the m X n grid matrixes are equivalent to a non-planar grid surface unit, and k= (n-1) (m-1) are altogether calculated, the extreme values of the distance and zenith angle are respectively calculated, whether C ij is located in the r and theta ranges of the grid surface is judged, and the screened grid surface is expressed as a set K; Judging that the grid surface set K is not repeated, forming 1 triangular surface patch when the number of points is 3, and forming two triangular surface patches when the number of points is 4; Calculating azimuth angles of all intersection points P meeting the requirements in the set K, wherein the number of the intersection points is necessarily even 2K m because the envelope is a closed curved surface, and arranging the intersection points of the reachable domain of the mth satellite to C ij according to the azimuth angle sequence from small to large to obtain a sequence as follows: Wherein +1 represents the start point of the reachable section, -1 represents the end point of the reachable section, and the total number of the sections is K m The azimuth angle value range is [0,2 pi ] when all grid points are converted into the spherical coordinate system When the azimuth angle value range is changed to [ -pi, pi ], if the azimuth angle value range is still used, the two conditions are that 1) the Z axis is intersected with the envelope, 2) the envelope is intersected with a plane formed by the X axis positive direction and the Z axis positive direction, and the Z axis is not intersected with the envelope Determining as case 1, otherwise determining as case 2; For the case 1, when the intersection point exists between the C ij and the envelope under the spherical coordinate system, further judging whether the intersection point corresponds to an reachable area or an unreachable area, taking the midpoint of two azimuth angle nodes under the Cartesian coordinate system The positive direction of Z axis is used as the intersection point of ray and reachable domain envelope, the mode is the same as that under the spherical coordinates, if the intersection point is odd number, the correspondent azimuth angle interval is reachable area, otherwise, it is unreachable area, the change is correspondent to the positive and negative of two nodes, namely If the intersection point does not exist between the C ij and the envelope under the spherical coordinate system, whether the C ij is positioned in the envelope is further judged, under the same Cartesian inertial coordinate system, a point on the C ij is taken as a ray along the Z-axis forward direction to calculate the intersection point with the reachable domain envelope, if the intersection point is an odd number, the C ij is positioned in the envelope, and the reachable azimuth angle interval is [0,2 pi ]; For cases 1 and 2, the azimuth angle of the intersection point can be located in the interval of [ -pi, 0] and converted into the interval of [0,2 pi ] for calculation, the node of the azimuth angle located in the interval of [ -pi, 0] is equivalently converted into the interval of [0,2 pi ], the azimuth angles are arranged in order from small to large again, if the first row of second rows is-1, the last row of second rows is +1, and a starting node is added And a termination node By splitting the single-star reachable three-dimensional envelope into a plurality of triangular patches, calculating the in-plane intersection point of a central line C ij and the triangular patches under a spherical coordinate system, and obtaining the azimuth sequence of the single-star reachable domain and a target central line C ij under any condition according to a formula (5) The target azimuth sequence Φ TAR(ij) is obtained in the same way.
  6. 6. The method for evaluating multiple reachability of a constellation orbital maneuver of claim 5 wherein step three is implemented, The reachable azimuth angles of all M satellites obtained in the step two are processed Combining to obtain the following components: at this time, the matrix The number of nodes in (a) is: Then, matrix is formed The method comprises the following steps of: defining the number of reachable stars as N and setting its initial value of N 0 =0, then sequentially reading the matrix When the S-th element is +1 (s.e. {1, 2.. The number of points of the second row is equal to S }), the corresponding first row angle represents the starting point of a new reachable interval, so that the number of reachable stars is increased by N s ＝N s-1 +1, conversely, when the S-th element is-1 (s.e. {1, 2.. The number of points of the second row is equal to S }), the corresponding first row angle represents the ending point of an existing reachable interval, so that the number of reachable stars is reduced by N s ＝N s-1 -1, and when all the elements are read, the corresponding N s is represented in the third row of the matrix to obtain a brand new matrix The method comprises the following steps: Wherein N s is an interval The number of reachable stars; Then, it is necessary to reach the matrix for multiple satellites according to the target azimuth interval Φ TAR(ij) Transform and represent 2p azimuth nodes in phi TAR(ij) as And is connected with The nodes of the matrix are arranged together according to the ascending order of azimuth angles to obtain a new matrix The method comprises the following steps: Wherein the method comprises the steps of Third row of the column The number of reachable stars N in the third row of the previous column Adding all 0 columns to the first column of the list, so that Time of day When multiple points have a plurality of points When the zenith angles are the same, it is necessary to ensure At the end of the sequence, The sorting machine is positioned at the forefront of the sorting machine; Positioning And In a parallel pair of Intercepting to obtain p corresponding target multi-star reachable matrixes Expressed as: multi-star reachable matrix of constellation for given target area of central line C ij is obtained through node ordering and one-time sequential reading
  7. 7. The method for evaluating multiple reachability of a constellation orbit maneuver as described in claim 6, wherein said step four is implemented by, The maximum number of reachable stars is defined as N max ＝max(N ps ), the initial multi-star reachable angle is defined as Γ RDNX(ijp) (N) =0, where N e { 1..sub.n max }, then traversing In the third row, N s =n corresponds to the azimuth node, and the reachable azimuth angle of N star is: at the target interval corresponding to the central line C ij of each discrete unit After the N star reach angle, reach angle Γ CovNX(ijp) (N) and target angle The ratio of the target area in the whole discrete unit is approximated as the accessibility of the target area in the whole discrete unit, then the multi-star accessibility volume V RDNX(ij) (N) of all targets of the center line C ij satisfies: When the reachable interval of a single discrete unit is given, the reachable volume of the single discrete unit can be directly obtained, the sum of the reachable volumes of all the discrete units is the reachable volume of the whole space target area, and for I multiplied by J equal-volume discrete circular rings, the reachable volume is expressed as: where V RDNX (N) is the N star achievable volume of the entire spatial target region.

Description

Multiple-accessibility coverage method for evaluating star group orbital transfer maneuver Technical Field The invention relates to a multiple reachable coverage method for evaluating orbital maneuver of a constellation, which is suitable for rapid evaluation of a satellite constellation multiple reachable area and belongs to the field of aerospace. Background The satellite orbit maneuver reachable domain can represent the space range which can possibly reach in a future period of time, and has important significance for maintaining the on-orbit safety of the spacecraft and improving the space situation awareness capability. The reachability domain calculations for a single satellite have been more comprehensive, including both pulsed and continuous thrust reachability domains. The reachable domains are expressed by three-dimensional grids, so that the reachable judgment of the point target is simpler and more convenient, and is equivalent to judging whether the point is positioned in the polyhedron. And carrying out discrete point taking on the surface of the three-dimensional space target and then carrying out point accessibility judgment. The research on the calculation of the multi-satellite reachable domain is less, and the existing method is to carry out statistical analysis on the reachable characteristics of each satellite to the target. For M satellites whose respective reach envelopes are described by n faces, the multi-star reachability of the target area represented by M discrete points requires making mn calculation decisions, and the required calculation amount is unacceptable. Meanwhile, only surface discrete point taking can not quantitatively calculate the volume of the multi-star reachable target area, but the number of m needed by the discrete point taking of the whole target area is extremely large, so that the calculated amount is further increased. Thus, the quantization computation and geometric visualization of the multi-star reachable domain is typically aided by boolean algorithms of existing three-dimensional mesh models. The spatial Boolean operation of the three-dimensional grid model is performed in prior art [1] (see spatial Boolean operation of three-dimensional grid model [ J ] (university of science and technology, nature science edition), bi Lin, wang Liguan, chen Jianhong, feng Xinglong, 2008,294 (5): 82-85). The method comprises the steps of obtaining intersecting lines between two intersecting triangle patches through an intersecting test, obtaining a polygon by the intersecting triangle and the intersecting lines, performing triangulating on the polygon again, and judging the choice of other grids according to the recombined model. However, if the intersection test is simply performed, performing a boolean operation on two three-dimensional regions described by n mesh triangular patches requires n (n-1)/2 intersection determinations, which would be unacceptably time consuming. The detection of rapid intersections is therefore typically performed using specific techniques. The prior art [2] (see the three-dimensional grid model voxelization method based on octree [ J ] (engineering theory report, wu Xiaojun, liu Weijun, wangnatural, 2005 (4): 1-7) recursively divides a space cube into 8 small space cubes, and can quickly position intersected triangles only by intersecting detection of triangular patches positioned in the same subspace, thereby improving the overall operation efficiency of a Boolean operation algorithm. On the other hand, in the prior art [3] (see OBBTree:A Hierarchical Structure for Rapid Interference Detection[C]"Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques",Gottschalk S,Lin M C,Manocha D,1996) for an OBB bounding box algorithm, pre-processing, screening and removing part of triangular patches which cannot be intersected in advance, reducing the number of the patch pairs which need to be intersected, and improving the running efficiency of Boolean operation. However, these algorithms are based on the extraction of the final model mesh from the intersecting loops, so that various special and complex situations need to be considered, and the robustness of the algorithm needs to be improved. Meanwhile, the algorithm can only operate on the models in sequence, N-fold reachable domain calculation is needed to be performed on M satellites, m|/(N-1) | (M-N) | times of Boolean calculation is still unacceptable. Therefore, the invention provides a multi-star reachable domain calculation method based on line coverage. Disclosure of Invention The invention mainly aims to provide a multiple reachable coverage method for evaluating a star group orbital transfer maneuver, which comprises the steps of carrying out equal volume dispersion on a target area in two dimensions of a distance and a zenith angle under a geocentric fixedly connected spherical coordinate system, taking a reachable azimuth interval of a discrete unit