CN113247309B - Initial value search method and system for transfer orbits based on collision zone spectrum - Google Patents
Initial value search method and system for transfer orbits based on collision zone spectrum Download PDFInfo
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Abstract
The invention discloses a method and a system for searching initial values of transfer orbits based on a collision zone spectrum, wherein the method comprises the following steps: applying tangential disturbance to points on a target track, integrating the disturbance track, marking the disturbance track capable of impacting the main celestial body, and drawing a collision zone map between the main celestial body and the target track; respectively taking a preset speed increment interval at two sides of each collision zone, randomly taking a plurality of sampling disturbance tracks from the speed increment interval, and integrating to the parking tracks; marking a position direction angle and a speed direction angle when the sampling disturbance track and the parking track are crossed; by linearly interpolating the velocity increments, an initial value of the transfer trajectory tangent to the parking trajectory and the target insertion point is found. The invention systematically pre-estimates the distribution positions of various tangential transfer families and quickly searches tracks of various transfer types, and the system intuitively estimates the number of the various tangential transfer tracks and provides a proper initial value for subsequent accurate solution of the transfer tracks.
Description
Technical Field
The invention relates to the technical field of deep space transfer orbits, in particular to a transfer orbit family initial value searching method and system based on a collision zone spectrum.
Background
For the calculation of the deep space transfer orbit, because the aircraft is far away from the original central celestial body, the aircraft cannot be ignored when being disturbed by the gravitation of other celestial bodies, the movement error of the aircraft under the calculation by adopting the two-body model and the real gravitational field is larger, and the restrictive three-body problem model can better approximate the movement in the actual gravitational field. When the calculation of the transfer orbit is carried out in the three-body problem model, the system is highly sensitive to an initial value due to the complexity of a gravitational field and the nonlinearity of the system; and because of the complexity of the motion calculation process in the system, an initial value close to an accurate solution needs to be given before an accurate transfer orbit is solved.
The method for searching the initial value of the transfer orbit by combining the research results at home and abroad comprises the steps of taking the solution under the two-body model as the initial value, searching through an optimization algorithm, taking the adjacent periodic orbit as the initial value and the like. The initial value obtained by the current method can calculate an accurate transfer orbit, and further can propagate a related family or family of transfer orbits on the basis, but purposeful search and estimation can not be carried out on the distribution of various transfer orbit families in a phase space.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method and a system for searching an initial value of a transfer orbit family based on a collision zone map.
In order to achieve the above object, the present invention provides a method for searching an initial value of a transition orbit family based on a collision band spectrum, the method comprising:
applying tangential disturbance to points on a target track, integrating the disturbance track, marking the disturbance track capable of impacting the main celestial body, and drawing a collision zone map between the main celestial body and the target track;
respectively taking a preset speed increment interval at two sides of each collision zone, randomly taking a plurality of sampling disturbance tracks from the speed increment interval, and integrating to the parking tracks;
marking a position direction angle and a speed direction angle when the sampling disturbance track and the parking track are crossed;
by linearly interpolating the velocity increments, an initial value of the transfer trajectory tangent to the parking trajectory and the target insertion point is found.
As an improvement of the method, the method comprises the steps of applying tangential disturbance to points on a target track, integrating the disturbed track, marking the disturbed track capable of impacting a main celestial body, and drawing a collision zone map between the main celestial body and the target track; the method specifically comprises the following steps:
changing the speed of each point on the target track F within a certain range, and reversely integrating the disturbed track after changing the speed for a period of time, wherein the reverse integration is carried out on the problem of inserting the target track from the main celestial body; for the departure from the target track to insert into the masterThe problem of orbits near the celestial body is forward integrated and then found to be able to strike the main celestial body PiMarking the starting phase and the velocity increment or velocity in a graph to obtain PiAnd the in-phase space collision zone pattern between F and F.
As an improvement of the method, the number of the collision zones in the collision zone map is related to the magnitude of the tangential disturbance and the integral duration, and more collision zones can be obtained when the magnitude of the tangential disturbance and the integral duration are increased.
As an improvement of the above method, the perturbing trajectory randomly takes a plurality of samples from the velocity increment interval and integrates to the parking trajectory; the method specifically comprises the following steps:
randomly taking a plurality of sampling disturbance tracks from a speed increment interval, and adopting reverse integration from a main celestial body to a parking track; forward integration is applied from the target track to the parking track.
As an improvement of the above method, the initial value of the transfer orbit tangent to the parking orbit and the target insertion point is found by linear interpolation of the velocity increment; the method specifically comprises the following steps:
linear interpolation is carried out on the speed increment, and beta is found from the interpolated dataintersect＝βO,αintersect＝αOSo as to find an initial value of the transfer trajectory tangent to the mooring trajectory O and the target insertion point; wherein alpha isintersectAnd betaintersectRespectively is a position direction angle and a speed direction angle when the sampling disturbance track and the parking track O are intersected after interpolation; alpha is alphaOAnd betaORespectively, points on the mooring track O relative to the main celestial body PiThe lower corner mark i is 1, and 2 respectively represents a large main celestial body and a small main celestial body; alpha is alphaintersectAnd betaintersectThe calculation method is as follows:
αintersect＝tan-1(y/x-xP)
βintersect＝tan-1(vy/vx)
wherein x isPRepresents PiX and y are respectively the position coordinates of the interpolated sampling perturbation track and the parking track O when the sampling perturbation track intersects with the parking track O, vx,vyRespectively the velocity in the x-, y-direction when the interpolated sampled perturbation trajectory intersects the parking trajectory O.
As an improvement of the above method, the method further comprises: for the transfer orbit assisted by other celestial body gravitation, the transfer orbit is divided into a transfer orbit before gravitation assistance and a transfer orbit after gravitation assistance, initial value search is respectively carried out, and then the initial values of the transfer orbit are formed by splicing.
A system for initial value search of transition orbitals based on a collision zone spectrum, the system comprising: the system comprises a collision belt map drawing module, a parking track integration module, a direction angle marking module and a transfer track initial value output module; wherein,
the collision zone map drawing module is used for applying tangential disturbance to points on the target track, integrating the disturbance track, marking the disturbance track capable of impacting the main celestial body and drawing a collision zone map between the main celestial body and the target track;
the parking track integration module is used for respectively taking a preset speed increment interval at two sides of each collision zone, randomly taking a plurality of sampling disturbance tracks from the speed increment interval and integrating the sampling disturbance tracks to the parking tracks;
the direction angle marking module is used for marking a position direction angle and a speed direction angle when the sampling disturbance track is intersected with the parking track;
and the initial transfer track value output module is used for finding the initial transfer track value tangent to the parking track and the target insertion point by performing linear interpolation on the speed increment.
Compared with the prior art, the invention has the advantages that:
1. the invention provides a method for generating a tangential collision zone spectrum along a target track for the first time, systematically estimating the distribution of tangential transfer tracks between a periodic track near a celestial body and other periodic tracks in a phase space in a three-body system through the collision zone spectrum, and accordingly providing initial values of various types of tangential transfer track families, wherein supportable transfer tracks comprise direct transfer, gravitation-assisted transfer and the like;
2. the method can systematically and visually evaluate the phase space structure by quickly searching the collision zone atlas between the target track and the large celestial body, thereby systematically predicting the distribution positions of various tangential transfer families and quickly searching tracks of various transfer types;
3. the method can systematically and visually evaluate the number of various types of tangential transfer tracks and provide proper initial values for subsequent accurate solution of the transfer tracks;
4. applying tangential disturbance to points on a target track and integrating the points until the points impact a large main celestial body of the target to draw a collision zone map, wherein the size of the tangential disturbance and the integration duration can be adjusted according to the transfer cost of the target transfer track, and searching for the transfer track in an expected cost range; the step length of taking points of the target track can be larger, and only the distribution position and the number of collision zones in the phase space are disclosed, so that a collision zone map can be quickly obtained;
5. according to the method, sampling points are randomly selected at two sides of each collision zone, the sampling points are integrated to the starting track, initial values close to the accurate solution are quickly searched through linear interpolation, the accurate solution neighborhood is determined to be used as a search interval through the method, and the initial values can be quickly obtained.
Drawings
FIG. 1 is a flow chart of the initial value searching method of the transition orbit family based on the collision zone atlas;
FIG. 2 is a graph of a collision zone between the earth and an SPO near point L4 for a simulation example of the present invention;
FIG. 3 is a state and interpolation result when a randomly sampled trajectory near the upper boundary of the widest collision zone where the insertion point phase angle is 0.2 π intersects with a LEO according to a simulation example of the present invention;
FIG. 4 is a map of the collision zone between the moon and the SPO near point L4 for a simulation example of the present invention;
FIG. 5 is a state and interpolation result when a randomly sampled trajectory near the upper boundary of a lower collider band at an insertion point phase angle of 0.2 π intersects with an LLO according to a simulation example of the present invention;
FIG. 6 is a map of the collision zone between a circular LLO orbit at 100km height and the Earth for a simulation example of the present invention;
FIG. 7 is a state and interpolation result when a randomly sampled trajectory near the upper boundary of the collider band at an insertion point phase angle of 1.125 π intersects with a LEO according to a simulation example of the present invention.
Detailed Description
In order to systematically estimate the position, the quantity and the property of the transfer orbit in the phase space and provide the initial value of the multi-family transfer orbit, the invention searches and draws the collision band spectrum between the target orbit and the main celestial body and provides a method for obtaining the initial value of the multi-family transfer orbit through the collision band spectrum.
The method has the basic principle that tangential small pulses are applied to a target periodic orbit, the disturbed orbit applied with the tangential small pulses is subjected to reverse integration, the disturbed orbit capable of impacting a starting celestial body is marked, a tangential collision zone map of the target orbit is obtained, transfer orbit families are distributed on two sides of each collision zone, random sampling is carried out on two sides of each collision zone, and initial values of the transfer orbits approximately tangent to the starting orbit and a target insertion point are obtained through linear interpolation. The method can rapidly and systematically evaluate the distribution area of the transfer orbital family in the phase space.
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 1, embodiment 1 of the present invention provides a transition orbit family initial value search method based on a collision band map.
In the circular limiting three-body problem, the convergence coordinate system is that one origin is positioned at the mass center of the system, and the x axis is formed by a large main celestial body P1Pointing to a small main celestial body P2The z-axis is parallel to the angular momentum vector of the main celestial motion and the y-axis is determined by the right hand rule. For convenient analysis and calculation, carrying out dimensionless and magnitude normalization on each physical quantity, and defining the corresponding mass unit as the total mass of the main celestial bodies, the length unit as the distance between the two main celestial bodies, and the time unit as the motion of the main celestial bodiesThe period is divided by 2 pi, and the system quality parameter is defined as mu-m2/m1+m2Wherein m is1And m2Respectively represent P1And P2The quality of (c). In the x-y plane convergence coordinate system, the coordinates of the large main celestial body and the small main celestial body are (-mu, 0) and (1-mu, 0), respectively, and the motion equation of the third body
Is composed of
Wherein
To main celestial body Pi(i ═ 1,2) a transition track search between the nearby parking track O and the target periodic track F is carried out by:
step 1) positioning a collision orbit which tangentially reaches a target orbit and can impact a starting main celestial body.
Changing the speed of each point on the target periodic orbit F within a certain range, and reversely integrating the disturbed orbit after changing the speed for a period of time, wherein the reverse integration is carried out on the problem of inserting the target orbit from the main celestial body; the problem of inserting tracks near the main celestial body from the target track is integrated forward. Then, willCan impact the main celestial body PiThe starting phase and the velocity increment size or the velocity size of the disturbed orbit are marked in a graph, and P can be obtainediAnd the in-phase space collision zone pattern between F and F. It should be noted that the number of collision zones in the collision zone map is related to the speed increment size range and the integration time, and more collision zones can be obtained under the condition of larger speed increment range and longer integration time.
And 2) randomly sampling and disturbing the track test near the collision zone.
And respectively taking a small speed increment interval at two sides of each collision zone, and randomly taking a plurality of sampling disturbance tracks in the small speed increment interval to perform reverse/forward integration. For example, can be at
And
3000 sampling points are respectively taken in the sampling points, wherein
Respectively representing the upper and lower bounds of the speed increment corresponding to a certain phase in a collision zone.
And 3) marking the position direction angle and the speed direction angle when the sampling disturbance track intersects with the parking track O.
Sampling the state of the perturbing trajectory intersecting the parking trajectory O can be used with respect to PiIs at a position direction angle alphaintersectAnd a speed direction angle betaintersectAnd characterizing, and calculating the following formula of the two angles:
αintersect＝tan-1(y/x-xP)
βintersect＝tan-1(vy/vx)
wherein xPRepresents PiX-axis position coordinate of (1), x, y, vx,vyThe position coordinates and the speed in the x-direction and the y-direction when the interpolated sampling disturbance track intersects with the parking track O are obtained. In particular, for circular orbits, there is β in the converging coordinate systemO＝αOA relation of + π/2, i.e. with respect to PiIs perpendicular to the velocity vector:
integrating the sampled disturbed orbit until the disturbed orbit intersects the parking orbit O, and recording the position direction angle alpha at the intersection pointintersectAnd a speed direction angle betaintersect。
Step 4) finding the beta value by linear interpolation of the speed incrementintersect＝βO,αintersect＝αOThe approximate satisfaction is that the orbit is a disturbance orbit approximately tangent to the orbit O, and the orbit is the initial value of the transfer orbit which can be subsequently accurately solved and numerically extended.
The transfer orbit assisted by other celestial body gravitation can be divided into two sections of orbit before and after gravitation assistance, and the completed transfer orbit is formed by respectively adopting the method to carry out initial value search and splicing.
Simulation example:
in the limited three-body problem of the Earth-moon type, starting from a circular Low Earth Orbit (LEO), a Short Periodic Orbit (SPO) with an amplitude β of 0.15 is transferred to the vicinity of the lagrange point of L4, and the process of performing initial value search using the method is as follows:
the problem of direct transfer from LEO to SPO is represented in fig. 2 by applying velocity increments to points on the SPO and inverse integrating the collision band pattern between the earth and the SPO obtained over 5 time units (about 21.7 days). The position direction angle and velocity direction angle at which the perturbation trajectory intersects the LEO and the linear interpolation results are shown in fig. 3, sampled at the boundary on the widest collision band where the insertion point phase angle is 0.2 pi.
The problem of transferring from LEO to SPO assisted by Lunar gravity can be divided into two parts, firstly searching the initial value of the transfer section from SPO assisted by Lunar gravity by a method of collision band map search, and then searching the initial value of the transfer section from Earth to near moon Orbit (Low Lunar Orbit, LLO) with fly-by height as Orbit height by a method of collision band map search.
For the first part of the problem, a map of the collision zone between the moon and the SPO obtained by applying a velocity increment to a point on the SPO and inverse integrating 5 time units (about 21.7 days) is shown in fig. 4; the position direction angle and velocity direction angle at the intersection of the perturbation orbit and the LLO and the linear interpolation results are shown in fig. 5, with the lower collision band at an insertion point phase angle of 0.2 pi for boundary sampling. For the second part of the problem, a circular LLO orbit with the height of 100km is taken as an assumed target orbit, the velocity of each point on the assumed target orbit is changed, a collision zone map between the LLO and the earth obtained by inverse integration for 5 time units (about 21.7 days) is shown in fig. 6, a boundary sample is taken on a collision zone at the phase angle of an insertion point of 1.125 pi, and the position direction angle, the velocity direction angle and the linear interpolation result when the disturbed orbit intersects with the LEO are shown in fig. 7.
Example 2
the collision zone map drawing module is used for applying tangential disturbance to points on the target track, integrating the disturbance track, marking the disturbance track capable of impacting the main celestial body and drawing a collision zone map between the main celestial body and the target track;
the parking track integration module is used for respectively taking a preset speed increment interval at two sides of each collision zone, randomly taking a plurality of sampling disturbance tracks from the speed increment interval and integrating the sampling disturbance tracks to the parking tracks;
the direction angle marking module is used for marking a position direction angle and a speed direction angle when the sampling disturbance track is intersected with the parking track;
and the initial transfer track value output module is used for finding the initial transfer track value tangent to the parking track and the target insertion point by performing linear interpolation on the speed increment.
The innovation points of the invention are as follows:
1) applying tangential disturbance to points on a target orbit and integrating the points until the points impact a large main celestial body of the target to draw a collision zone map, wherein the size of the tangential disturbance and the integration duration can be adjusted according to the transfer cost of the target transfer orbit, and searching for the transfer orbit in an expected cost range; the step length of taking points of the target track can be larger, and only the distribution position and the number of the collision zones in the phase space are disclosed, so that the collision zone atlas can be quickly obtained.
2) According to the method, sampling points are randomly selected from two sides of each collision zone, the sampling points are integrated to the starting track, initial values close to an accurate solution are quickly searched through linear interpolation, the accurate solution neighborhood is determined to be used as a search interval through the method, and the initial values can be quickly obtained.
3) Continuous transfer orbit families exist on two sides of each collision zone and are respectively associated with transfer orbit families with different departure directions, transfer time and fuel consumption characteristics, so that system search can be carried out on multiple transfer orbit families in a phase space.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (6)
1. A method for searching initial values of transition orbitals based on a collision zone map, comprising the following steps:
applying tangential disturbance to points on a target track, integrating the disturbance track, marking the disturbance track capable of impacting the main celestial body, and drawing a collision zone map between the main celestial body and the target track;
respectively taking a preset speed increment interval at two sides of each collision zone, randomly taking a plurality of sampling disturbance tracks from the speed increment interval, and integrating to the parking tracks;
marking a position direction angle and a speed direction angle when the sampling disturbance track and the parking track are crossed;
finding a transfer orbit initial value tangent to the parking orbit and the target insertion point by carrying out linear interpolation on the speed increment;
applying tangential disturbance to points on the target track, integrating the disturbance track, marking the disturbance track capable of impacting the main celestial body, and drawing a collision zone map between the main celestial body and the target track; the method specifically comprises the following steps:
changing the speed of each point on the target track F within a certain range, and reversely integrating the disturbed track after changing the speed for a period of time, wherein the reverse integration is carried out on the problem of inserting the target track from the main celestial body; forward integration of the problem of the insertion of the target trajectory into the trajectory near the main celestial body, and then finding the point of impact on the main celestial body PiMarking the starting phase and the speed increment of the disturbed orbit in a graph, or marking the starting phase and the speed increment of the disturbed orbit in the graph to obtain PiAnd the in-phase space collision zone pattern between F and F.
2. The initial value search method for transition orbitals based on a collision band map as claimed in claim 1, wherein the number of collision bands in the collision band map is related to both the magnitude of the tangential disturbance and the integration duration, and more collision bands can be obtained when the magnitude of the tangential disturbance and the integration duration are increased.
3. The initial value search method for the transition orbit family based on the collision zone map as claimed in claim 1, wherein the perturbation orbit is randomly sampled from the velocity increment interval and integrated to the parking orbit; the method specifically comprises the following steps:
randomly taking a plurality of sampling disturbance tracks from a speed increment interval, and adopting reverse integration from a main celestial body to a parking track; forward integration is applied from the target track to the parking track.
4. The method for searching for initial values of a family of transfer trajectories based on a collision band spectrum according to claim 1, wherein the initial values of the transfer trajectories tangent to the parking trajectory and the target insertion point are found by linear interpolation of velocity increments; the method specifically comprises the following steps:
linear interpolation is carried out on the speed increment, and beta is found from the interpolated dataintersect＝βO,αintersect＝αOSo as to find an initial value of the transfer trajectory tangent to the mooring trajectory O and the target insertion point; wherein alpha isintersectAnd betaintersectRespectively is a position direction angle and a speed direction angle when the sampling disturbance track and the parking track O are intersected after interpolation; alpha is alphaOAnd betaORespectively, points on the mooring track O relative to the main celestial body PiThe lower corner mark i is 1, and 2 respectively represents a large main celestial body and a small main celestial body; alpha is alphaintersectAnd betaintersectThe calculation method is as follows:
αintersect＝tan-1(y/x-xP)
βintersect＝tan-1(vy/vx)
wherein x isPRepresents PiX and y are respectively the position coordinates of the interpolated sampling perturbation track and the parking track O when the sampling perturbation track intersects with the parking track O, vx,vyRespectively the velocity in the x-, y-direction when the interpolated sampled perturbation trajectory intersects the parking trajectory O.
5. The initial value search method for transition orbitals based on collision zone spectrum according to claim 1, characterized in that the method further comprises: for the transfer orbit assisted by other celestial body gravitation, the transfer orbit is divided into a transfer orbit before gravitation assistance and a transfer orbit after gravitation assistance, initial value search is respectively carried out, and then the initial values of the transfer orbit are formed by splicing.
6. A system for initial value search of transition orbitals based on a collision zone spectrum, the system comprising: the system comprises a collision belt map drawing module, a parking track integration module, a direction angle marking module and a transfer track initial value output module; wherein,
the collision zone map drawing module is used for applying tangential disturbance to points on the target track, integrating the disturbance track, marking the disturbance track capable of impacting the main celestial body and drawing a collision zone map between the main celestial body and the target track;
the parking track integration module is used for respectively taking a preset speed increment interval at two sides of each collision zone, randomly taking a plurality of sampling disturbance tracks from the speed increment interval and integrating the sampling disturbance tracks to the parking tracks;
the direction angle marking module is used for marking a position direction angle and a speed direction angle when the sampling disturbance track is intersected with the parking track;
the initial transfer track value output module is used for finding the initial transfer track value tangent to the parking track and the target insertion point by performing linear interpolation on the speed increment;
the processing process of the collision zone map drawing module specifically comprises the following steps:
changing the speed of each point on the target track F within a certain range, and reversely integrating the disturbed track after changing the speed for a period of time, wherein the reverse integration is carried out on the problem of inserting the target track from the main celestial body; forward integration of the problem of the insertion of the target trajectory into the trajectory near the main celestial body, and then finding the point of impact on the main celestial body PiMarking the starting phase and the speed increment of the disturbed orbit in a graph, or marking the starting phase and the speed increment of the disturbed orbit in the graph to obtain PiAnd the in-phase space collision zone pattern between F and F.
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