CN108082538B - Multi-body system low-energy track capturing method considering initial and final constraints - Google Patents

Multi-body system low-energy track capturing method considering initial and final constraints Download PDF

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CN108082538B
CN108082538B CN201711366134.5A CN201711366134A CN108082538B CN 108082538 B CN108082538 B CN 108082538B CN 201711366134 A CN201711366134 A CN 201711366134A CN 108082538 B CN108082538 B CN 108082538B
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celestial body
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point
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CN108082538A (en
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乔栋
李翔宇
胡勃钦
杜燕茹
韩宏伟
尚海滨
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a multi-body system low-energy orbit capturing method considering initial and final constraints, particularly relates to a low-energy orbit capturing method considering initial and terminal state constraints, and belongs to the technical field of aerospace. The implementation method of the invention comprises the following steps: based on a multi-system and weak stability boundary theory, the gravity action of the sun is utilized to assist planet capture, the capturing orbit design meeting terminal constraint is realized by screening the inclination angle of a hyperbolic orbit reaching a celestial body and applying orbit correction, the accurate interstellar transfer orbit starting from the earth and the matching of the weak stability boundary orbit are realized by utilizing B plane parameters, and a detector finally enters a task orbit only through two times of braking and one time of orbit correction. The method has the advantages of small required speed increment, wide application range and easy realization.

Description

Multi-body system low-energy track capturing method considering initial and final constraints
Technical Field
The invention relates to a method for capturing orbits by a detector in a multi-body system, in particular to a low-energy orbit capturing method considering initial and terminal state constraints, belongs to the technical field of aerospace, and is suitable for the orbit design of a detector which is captured by a target celestial body from the earth and enters a task orbit in deep space detection.
Background
The detection of extraterrestrial celestial bodies such as planets, satellites and small planets generally requires that a detector reaches the vicinity of a target celestial body through interstellar navigation after being transmitted from the earth, is captured by the target celestial body through orbital maneuver, and moves within the gravitational field range of the target celestial body to carry out detection activities. Therefore, the design of the capture orbit is crucial, whether the detector can be captured by the target celestial body smoothly to enter the task orbit or not is determined, and success or failure of the task is determined. The capture track is expected to consume as little energy as possible to achieve capture, save fuel for the detection track and achieve more detection purposes.
In the prior art [ 1 ] in the design of planet capture at present (see Howard D.Curtis. Orbital mechanics for Engineering Students [ M ]. Butterworth-Heinemann, Boston,2005), an orbit design method adopting near-center point capture is provided, the near-center point of a detector relative to a hyperbolic orbit of a target planet is designed to be the same as a task orbit, and when the detector flies to the hyperbolic near-center point, the orbit capture is realized to enter the task orbit through pulse braking according to task orbit parameters. The capture orbit method requires a short time and is simple to operate, but requires a large speed increment.
In the prior art [ 2 ] (see a two-pulse planet capture orbit method based on weak stable boundary, Jober, Liziyu, Cuiyuan, patent No.: ZL201510599566.5, 2017, 4.5), a planet capture orbit method adopting weak stable boundary is proposed, a detector motion equation is established under a sun-planet centroid rotation system, an optimal phase angle for realizing capture is determined, and task orbit capture is realized through two pulses.
Disclosure of Invention
The invention discloses a multi-body system low-energy orbit capturing method considering initial and final constraints, which aims to solve the technical problem of providing a multi-body system low-energy orbit capturing method considering initial and final constraints.
The purpose of the invention is realized by the following technical scheme:
the invention discloses a multi-body system low-energy capture track method considering start and end constraints, which comprises the following steps:
the method comprises the following steps: and searching an interstellar transfer emission window under the sunset yellow road system according to the selected target celestial body and the task time, and determining the transfer opportunity with the minimum speed increment delta v.
According to the selection of a detection target and the constraint of task time, designing a two-pulse transfer opportunity from the earth to a target celestial body with optimal speed increment, and detectingThe departure time of the detector from the earth is T0Starting state R corresponding to the yellow-line system of the sun0,V0The transit time of the probe from the earth to the target celestial body, and hence the arrival time of the probe at the target celestial body, is T, as determined by the ephemerisf＝T0+ T, the corresponding arrival state R is obtained using ephemeris as wellf,VfAnd solving a Lambert problem of determining the starting state, the ending state and the transfer time to obtain the speed increment delta v required by starting1Delta speed Δ v required for rendezvous2Wherein: Δ v2I.e. hyperbolic overspeed V of the detector relative to the target celestial body∞＝Δv2. According to task constraint pair departure time T0And traversing and searching the transfer time T, and obtaining the transfer opportunity with the minimum speed increment delta v through a contour map or an optimization algorithm.
Step two: establishing a celestial body equator inertia coordinate system, and obtaining hyperbolic overspeed V corresponding to the transfer opportunity with the minimum speed increment delta V according to the step one∞Given a radius r of the proximal pointpCalculating the approximate center point position speed R under different track inclination angles ip,Vp。
Taking the mass center of the target celestial body as an origin, the equatorial plane as an XY plane, the X axis pointing to the spring break point, and the rotation axis as the Z axis to establish an equatorial inertial coordinate system of the celestial body, and enabling R to be the same as the X axisIThe hyperbolic overspeed in the equatorial inertial coordinate system of the celestial body is expressed as
Figure BDA0001512754770000021
Figure BDA0001512754770000022
Expressed as the equatorial inertia system of the celestial body
Figure BDA0001512754770000023
Wherein v is∞Indicating hyperbolic overspeed magnitude, α∞And delta∞Are respectively as
Figure BDA0001512754770000024
The right ascension and declination of
Figure BDA0001512754770000025
Is calculated to obtain
Figure BDA0001512754770000026
Figure BDA0001512754770000027
For a given track inclination angle i, two groups of capture track ascending intersection declination omega and paraxial point argument omega meeting the conditions can be obtained and respectively represent an ascending track and a descending track
Figure BDA0001512754770000031
Figure BDA0001512754770000032
Wherein
Figure BDA0001512754770000033
The semi-major axis a and eccentricity e of the track, expressed as
Figure BDA0001512754770000034
Where μ is the mass coefficient of the target celestial body. The orbit mean approach point angle M of the approach point is 0 degrees, and the approach point position R is obtained according to the conversion relation between the orbit number and the position speedpAnd velocity Vp. The fixed orbit isocenter radius is the minimum safe orbit radius due to the minimum velocity increment required for capture
Figure BDA0001512754770000035
Changing the trapObtaining the track inclination angle i of the track and the position speed R of the near center point under different track inclination angles ip,Vp。
The number of the tracks in the step two comprises a semi-major axis a of the track, an eccentricity e, a track inclination angle i, a rising intersection right ascension omega, a paraxial point amplitude angle omega and a plano-paraxial point angle M.
Step three: the probe is maneuvered at the proximal point to bring the trajectory into a weakly stable boundary trajectory.
Obtaining the velocity R of the position of the isocenter of the hyperbolic orbit according to the step twop,VpApplying maneuver along the speed reverse direction to make the orbit eccentricity of the detector slightly less than 1, entering the weak stable boundary orbit, and recording the state of the near-center point of the detector after applying maneuver as the position RpcAnd velocity Vpc. The motion of the detector in the weak stable boundary orbit is kept stable, but is influenced by multi-body perturbation, the number of the orbits is changed compared with the initial parameters, and particularly the radius r of the near-center point of the orbitpAnd track inclination i, thus for low energy track changes.
And step three, selecting the track eccentricity slightly less than 1 finger eccentricity to meet the requirement that the detector is captured by the central celestial body, obviously influencing the track by solar disturbance, and selecting the eccentricity which is related to the gravitational constant of the central celestial body, wherein the eccentricity is preferably 0.97-0.99.
Step four: establishing a multi-body kinetic equation under the equatorial inertial system of the celestial body, integrating the weak stable boundary orbit obtained in the step three, and recording the radius r of a near center point when the orbit passes through the near center point for multiple timespfAnd track inclination angle ifAnd drawing the corresponding centroidal radius r of the centroidal initial state after different maneuvers are appliedpfAnd track inclination angle ifAnd (5) distribution diagram.
The dynamics of the detector under the inertial system are expressed as
Figure BDA0001512754770000041
Where r denotes the position vector of the detector, rsRepresenting the detector position vector, r, relative to the suns0Representing the position vector, mu, of the sun in the inertial systemsIs the mass coefficient of the sun, riRepresenting the position vector of the detector relative to the ith celestial body other than the sun, ri0Representing the position vector, mu, of the ith celestial body in the inertial systemiIs the mass coefficient of the ith celestial body, aNIs an aspherical gravitational perturbation of the target celestial body, aSRPPerturbation for sunlight pressure.
For different centroidal states R according to equation (8)pc,VpcIntegrating, and recording the corresponding radius r of the near center point when the track passes through the near center pointpfAnd track inclination angle ifRecording the centroidal radius of the first n centroids of the track, since the track may pass the centroidal point several times
Figure BDA0001512754770000042
And track inclination
Figure BDA0001512754770000043
The size of n is related to the track transfer time. Plotting the initial state R of the centripetal point after different applied maneuverspc,VpcCorresponding approximate point radius r after integrationpfAnd track inclination angle ifAnd (5) distribution diagram.
Step five: according to the terminal constraint of the task orbit, the initial inclination angle of the weak boundary orbit closest to the terminal constraint is selected as the inclination angle of the hyperbolic orbit, and accurate interstellar transfer and the hyperbolic orbit are obtained by using a B plane method, so that the initial launching constraint of the orbit is met.
Let the radius of the near center point of the task track be rp0The inclination angle of the track is i0Calculating the deviation between the weak stable boundary orbit state and the task orbit terminal constraint
Figure BDA0001512754770000044
Selecting the weak stable boundary orbit with the minimum deviation as a transfer orbit, and corresponding to the initial inclination angle i*The B plane parameter of the hyperbolic orbit is calculated as the inclination angle of the hyperbolic orbit.
The B plane passes through the center of the target celestial body and is perpendicular to the vector
Figure BDA0001512754770000045
Of the plane of (a). Wherein
Figure BDA0001512754770000051
Unit vector of asymptote of hyperbolic orbit
Figure BDA0001512754770000052
Two unit vectors for describing B-plane parameters are defined as
Figure BDA0001512754770000053
Figure BDA0001512754770000054
Taken generally as the axis of rotation, the Z-axis, of the target celestial body, is a unit reference vector. Theta represents the angle between the B vector and the T axis and is derived from spherical geometry
cosi*＝cosθcosδ∞(10)
Figure BDA0001512754770000055
The components of the B plane parameters, namely the B vectors on the T axis and the R axis are expressed as
BT＝B×T＝||B||cosθ (12)
BR＝B·T＝||B||sinθ (13)
Figure BDA0001512754770000056
And (3) obtaining an accurate interstellar transfer orbit which is from the earth to a target celestial body and meets the hyperbolic dip angle by utilizing the B plane method for correction, and meeting the initial emission constraint of the orbit.
Step six: and D, taking the task track terminal constraint as a target, and performing track correction on the weak stable boundary track selected in the step five to obtain a corrected weak stable boundary track, so that the weak stable boundary track can meet the task track terminal constraint when reaching the near-center point.
Establishing the end state r by differential correctionp0,ip0Sensitivity matrix from speed of a point on weak stability boundary
Figure BDA0001512754770000057
That is, the end state satisfies the following relationship
Figure BDA0001512754770000061
Thus obtaining the relation between the differential correction amount and the end error as
Figure BDA0001512754770000062
The iteration is performed for a plurality of times according to the formula (17) until the speed correction amount delta v satisfying the terminal is obtained as [ delta v ═ delta v [ ]x,Δvy,Δvz]. The probe is typically selected to apply a corrective maneuver to the distal point to meet the terminal proximal point height and tilt constraints.
And the track correction is preferably performed once on the weak stable boundary track selected in the step five.
Step seven: and (5) after the detector reaches a centromere meeting the constraint along the weak stable boundary orbit corrected in the step six, applying brake to realize the orbit entering of the task orbit and finish the low-energy orbit capture.
After the detector reaches the near-center point of the task track along the weak stable boundary track, corresponding maneuver is applied along the speed reverse direction according to the eccentricity constraint of the task track, namely, the detector can enter the task track to finish low-energy track capture.
The invention discloses a multi-body system low-energy orbit capturing method considering initial and final constraints, which is based on multi-system and weak stability boundary theories, utilizes the gravitational effect of the sun to assist planet capturing, screens the inclination angle of a hyperbolic orbit reaching a celestial body and applies orbit correction to realize the design of a capturing orbit meeting terminal constraints, utilizes B plane parameters to realize the accurate matching of an interstellar transfer orbit and a weak stability boundary orbit starting from the earth, and a detector finally enters a task orbit through two times of braking and one time of orbit correction. The method has the advantages of small required speed increment and wide application range, can meet various initial and terminal constraints, and is suitable for capturing the capture orbit from the earth to different celestial bodies.
Has the advantages that:
1. the invention discloses a multi-body system low-energy capture orbit method considering initial and final constraints, wherein an established motion equation of a detector is established under a sun and planet multi-body system, and a capture orbit utilizes the action of disturbance force of the sun, so that the capture speed increment is small compared with a centripetal point only utilizing the action of the gravity of a planet, and further fuel is saved.
2. The multi-body system low-energy orbit capturing method considering the initial and final constraints, disclosed by the invention, is used for capturing a task orbit which meets the constraints of close-to-center point patrinia, orbit inclination angle and eccentricity ratio by screening the inclination angle of a hyperbolic orbit and applying midway maneuver, so that the method disclosed by the invention is wide in application range.
3. The invention discloses a multi-body system low-energy orbit capturing method considering initial and final constraints, which realizes the matching of an interstellar transfer orbit and a weak stable boundary orbit by using B plane parameters and can meet the initial constraints starting from an orbit earth.
Drawings
FIG. 1 is a flow chart of a multi-body system low energy capture trajectory method of the present invention that considers the start and end constraints;
FIG. 2 is a diagram of a weak stable boundary orbit centroidal radius and orbit inclination angle distribution in step four of the multi-body system low energy capture orbit design method considering start and end constraints;
FIG. 3 is a step five B plane parameter diagram of the multi-body system low energy capture orbit design method considering the beginning and end constraints of the invention;
FIG. 4 is a schematic diagram of a transfer and capture trajectory of a multi-body system low energy capture trajectory design method in consideration of start and end constraints according to the present invention.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1:
as shown in fig. 1, taking mars orbit capture as an example, the two-pulse planetary orbit capture method based on the weak stable boundary disclosed in this embodiment includes the following specific steps:
the method comprises the following steps: and searching an interstellar transfer emission window under the sunset yellow road system according to the selected target celestial body and the task time, and determining the transfer opportunity with the minimum speed increment delta v.
According to detection target selection and task time constraint, designing two-pulse transfer opportunity from earth to target celestial body with optimal speed increment, wherein the departure time of a detector from earth is T0Starting state R corresponding to the yellow-line system of the sun0,V0Can be determined from the ephemeris that the transit time of the probe from the earth to the target celestial body is T, and therefore the time of arrival of the probe at the target celestial body is Tf＝T0+ T, the corresponding arrival state R is obtained using ephemeris as wellf,VfAnd solving a Lambert problem of determining the starting state, the ending state and the transfer time to obtain the speed increment delta v required by starting1Delta speed Δ v required for rendezvous2Wherein Δ v2I.e. hyperbolic overspeed V of the detector relative to the target celestial body∞＝Δv2. The departure time T can be adjusted according to task constraints0And traversing and searching the transfer time T, and obtaining the transfer opportunity with the minimum speed increment delta v through a contour map or an optimization algorithm.
The task time of Mars detection is given as 2015-2016, the contour diagram shows that the superior transfer chances are 2015, 12 and 24 days from the earth, 2016, 9 and 26 days from the earth to Mars, and the corresponding hyperbolic overspeed V to Mars∞＝[-2.4735-2.5628-0.6894]km/s。
Step two: establishing a celestial body equator inertia coordinate system, and obtaining hyperbolic overspeed V corresponding to the transfer opportunity with the minimum speed increment delta V according to the step one∞Given a radius r of the proximal pointpCalculating the state R of the near center point under different track inclination angles ip,Vp。
Taking the mass center of the target celestial body as an origin, the equatorial plane as an XY plane, the X axis pointing to the spring break point, and the rotation axis as the Z axis to establish an equatorial inertial coordinate system of the celestial body, and enabling R to be the same as the X axisIThe hyperbolic overspeed in the equatorial inertial coordinate system of the celestial body can be expressed as
Figure BDA0001512754770000081
Figure BDA0001512754770000082
Can be expressed as the equatorial inertia system of the celestial body
Figure BDA0001512754770000083
Wherein v is∞Indicating hyperbolic overspeed magnitude, α∞And delta∞Are respectively as
Figure BDA0001512754770000084
The right ascension and declination of
Figure BDA0001512754770000085
Is calculated to obtain
Figure BDA0001512754770000086
Figure BDA0001512754770000087
For a given track inclination angle i, two groups of capture track ascending intersection declination omega and paraxial point argument omega meeting the conditions can be obtained and respectively represent an ascending track and a descending track
Figure BDA0001512754770000088
Figure BDA0001512754770000089
Wherein:
Figure BDA00015127547700000810
the semi-major axis a and eccentricity e of the track, expressed as
Figure BDA00015127547700000811
Where μ is the mass coefficient of the target celestial body. Obtaining a near-center point position R according to the conversion relation between the number of the tracks and the position speedpAnd velocity Vp. The fixed orbit isocenter radius is the minimum safe orbit radius because of the small velocity increments desired for capture
Figure BDA0001512754770000091
And changing the track inclination angle i of the capture track to obtain the position speed of the near center point under different track inclination angles i. The hyperbolic overspeed under the ecliptic system of the sunset is converted into the hyperbolic overspeed under the Mars equatorial system
Figure BDA0001512754770000092
Corresponding Chijing α∞39.81 ° declination δ∞332.57. Here, the minimum safe radius of the spark is selected
Figure BDA0001512754770000093
Step three: the probe is maneuvered at the proximal point to bring the trajectory into a weakly stable boundary trajectory.
For the hyperbolic orbit centromere position speed R obtained in the step twop,VpApplying maneuver along the speed reverse direction to make the orbit eccentricity of the detector slightly less than 1, entering the weak stable boundary orbit, and recording the state of the near-center point of the detector after applying maneuver as the position RpcAnd velocity Vpc. ProbeAlthough the motion of the detector in the weak stable boundary orbit is kept stable, the detector is influenced by multi-body perturbation, the number of the orbits (semi-major axis a, eccentricity e, orbit inclination angle i, ascension angle omega of ascending intersection point and amplitude angle omega of the near center point) is changed compared with the initial parameters, particularly the height of the near center point and the orbit inclination angle of the orbit, and therefore the detector can be used for low-energy orbit change. The eccentricity e of the detector into the weak stable boundary orbit is 0.982 for mars selection, and the velocity increment required for the first maneuver is Δ ν1＝1.223km/s。
Step four: establishing a multi-body kinetic equation under the equatorial inertial system of the celestial body, integrating the weak stable boundary orbit obtained in the step three, and recording the radius r of a near center point when the orbit passes through the near center point for multiple timespfAnd track inclination angle ifAnd drawing the corresponding centroidal radius r of the centroidal initial state after different maneuvers are appliedpfAnd track inclination angle ifAnd (5) distribution diagram.
The dynamics of the detector under the inertial system can be expressed as
Figure BDA0001512754770000094
Where r denotes the position vector of the detector, rsRepresenting the detector position vector, r, relative to the suns0Representing the position vector, mu, of the sun in the inertial systemsIs the mass coefficient of the sun, riRepresenting the position vector of the detector relative to the ith celestial body other than the sun, ri0Representing the position vector, mu, of the ith celestial body in the inertial systemiIs the mass coefficient of the ith celestial body, aNIs an aspherical gravitational perturbation of the target celestial body, aSRPPerturbation for sunlight pressure.
For different centroidal states R according to equation (8)pc,VpcIntegrating, and recording the corresponding radius r of the near center point when the track passes through the near center pointpfAnd track inclination angle ifSince the track may pass through the isocenter m times, the isocenter radius of the isocenter 5 times before the track is recorded in consideration of the track transfer time
Figure BDA0001512754770000101
And track inclination
Figure BDA0001512754770000102
And drawing corresponding distribution graphs of the radius of the proximal point and the track inclination angle after the initial state integration of different proximal points, as shown in FIG. 4.
Step five: according to the terminal constraint of the task orbit, the initial inclination angle of the weak boundary orbit closest to the terminal constraint is selected as the inclination angle of the hyperbolic orbit, and accurate interstellar transfer and the hyperbolic orbit are obtained by using a B plane method, so that the initial launching constraint of the orbit is met.
Let the radius of the near center point of the task track be rp0The inclination angle of the track is i0Calculating the deviation between the weak stable boundary orbit state and the task orbit terminal constraint
Figure BDA0001512754770000103
Selecting the weak stable boundary orbit with the minimum deviation as a transfer orbit, and corresponding to the initial inclination angle i*The B plane parameter of the hyperbolic orbit is calculated as the inclination angle of the hyperbolic orbit.
The B plane passes through the center of the target celestial body and is perpendicular to the vector
Figure BDA0001512754770000104
As shown in fig. 3. Wherein
Figure BDA0001512754770000105
Unit vector of asymptote of hyperbolic orbit
Figure BDA0001512754770000106
Two unit vectors are used to describe the B-plane parameters, which are defined as:
Figure BDA0001512754770000107
Figure BDA0001512754770000108
taken generally as the axis of rotation, the Z-axis, of the target celestial body, is a unit reference vector. Theta represents the angle between the B vector and the T axis and is derived from spherical geometry
cosi*＝cosθcosδ∞(10)
Figure BDA0001512754770000109
The components of the B plane parameters, namely the B vectors on the T axis and the R axis are expressed as
BT＝B×T＝||B||cosθ (12)
BR＝B·T＝||B||sinθ (13)
Wherein
Figure BDA0001512754770000111
The accurate interstellar transfer orbit from the earth to the target celestial body and meeting the hyperbolic dip angle can be obtained by utilizing the B plane method for correction, and the initial launching constraint of the orbit is met.
The radius of a near center point of a given task orbit is 10000km, the inclination angle of the orbit is 90 degrees, the initial inclination angle corresponding to the nearest weak stable boundary orbit is 61 degrees, the radius of the near center point corresponding to the fourth near center point is 9966km, and the inclination angle of the orbit is 89.24 degrees. The corresponding B plane parameters are respectively BT＝3292.32,BR5049.98, an accurate orbit from earth can be obtained by B-plane correction.
Step six: and D, taking the task track terminal constraint as a target, and performing track correction on the weak stable boundary track selected in the step five to obtain a corrected weak stable boundary track, so that the weak stable boundary track can meet the task track terminal constraint when reaching the near-center point.
Establishing the end state r by differential correctionp0,ip0Sensitivity matrix from speed of a point on weak stability boundary
Figure BDA0001512754770000112
That is, the end state satisfies the following relationship
Figure BDA0001512754770000113
Thus obtaining the relation between the differential correction amount and the end error as
Figure BDA0001512754770000114
The iteration is performed for a plurality of times according to the formula (17) until the speed correction amount delta v satisfying the terminal is obtained as [ delta v ═ delta v [ ]x,Δvy,Δvz]. The probe is typically selected to apply a corrective maneuver to the distal point to meet the terminal proximal point height and tilt constraints.
Selecting a detector to apply one maneuver at a far center point of the weak stable boundary orbit to meet terminal constraint, wherein the maneuver is delta vcorr＝1.5m/s。
Step seven: and (5) after the detector reaches a centromere meeting the constraint along the weak stable boundary orbit corrected in the step six, applying brake to realize the orbit entering of the task orbit and finish the low-energy orbit capture.
After the detector reaches the centripetal point of the task track along the weak stable boundary track, corresponding maneuver is applied along the speed reverse direction according to the eccentricity constraint of the task track, and then the detector can enter the task track, and a complete capture track diagram is shown in fig. 4.
Let the eccentricity of the mission orbit be 0, the increment of the velocity applied by the probe to enter the mission orbit is Deltav20.820km/s, total captured velocity increment Δ v ═ Δ v1+Δv2+Δvcorr2.0443km/s, Δ v required for direct capture using a near-center point as a comparisondWith the method of this patent, the velocity increment can be reduced by 547.5m/s, 2.5918 km/s.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (9)

1. A multi-body system low energy capture trajectory method considering start and end constraints, characterized by: comprises the following steps of (a) carrying out,
the method comprises the following steps: according to the selected target celestial body and the task time, searching an interplanetary transfer emission window under the ecliptic system, and determining a transfer opportunity with the minimum speed increment delta v;
step two: establishing a celestial body equator inertia coordinate system, and obtaining hyperbolic overspeed V corresponding to the transfer opportunity with the minimum speed increment delta V according to the step one∞Given a radius r of the proximal pointpCalculating the approximate center point position speed R under different track inclination angles ip,Vp；
Step three: maneuvering the detector at the proximal point to make the track enter the weak stable boundary track;
obtaining the velocity R of the position of the isocenter of the hyperbolic orbit according to the step twop,VpApplying maneuver along the speed reverse direction to make the orbit eccentricity of the detector slightly less than 1, entering the weak stable boundary orbit, and recording the state of the near-center point of the detector after applying maneuver as the position RpcAnd velocity Vpc(ii) a The motion of the detector in the weak stable boundary orbit is kept stable, but is influenced by multi-body perturbation, the number of the orbits is changed compared with the initial parameters, and particularly the radius r of the near-center point of the orbitpAnd track inclination i, thus track change for low energy;
step four: establishing a multi-body kinetic equation under the equatorial inertial system of the celestial body, integrating the weak stable boundary orbit obtained in the step three, and recording the radius r of a near center point when the orbit passes through the near center point for multiple timespfAnd track inclination angle ifAnd drawing the corresponding centroidal radius r of the centroidal initial state after different maneuvers are appliedpfAnd track inclination angle ifA distribution diagram;
step five: according to the terminal constraint of the task orbit, selecting the initial inclination angle of the weak boundary orbit closest to the terminal constraint as the inclination angle of the hyperbolic orbit, and obtaining accurate interstellar transfer and the hyperbolic orbit by using a B plane method to meet the initial launching constraint of the orbit;
step six: performing track correction on the weak stable boundary track selected in the step five by taking the task track terminal constraint as a target to obtain a corrected weak stable boundary track, and ensuring that the weak stable boundary track meets the task track terminal constraint when reaching the near-center point;
step seven: after the detector reaches a near-center point meeting the constraint along the weak stable boundary orbit corrected in the step six, applying brake to realize the orbit entering of the task orbit and finish the low-energy orbit capture;
after the detector reaches the near-center point of the task track along the weak stable boundary track, corresponding maneuver is applied along the speed reverse direction according to the eccentricity constraint of the task track, namely, the detector can enter the task track to finish low-energy track capture.
2. A multi-body system low energy capture trajectory method considering top and bottom constraints as claimed in claim 1 wherein: the specific implementation method of the step one is that,
according to detection target selection and task time constraint, designing two-pulse transfer opportunity from earth to target celestial body with optimal speed increment, wherein the departure time of a detector from earth is T0Starting state R corresponding to the yellow-line system of the sun0,V0The transit time of the probe from the earth to the target celestial body, and hence the arrival time of the probe at the target celestial body, is T, as determined by the ephemerisf＝T0+ T, the corresponding arrival state R is obtained using ephemeris as wellf,VfDetermining Lambert problem by solving the initial and final states and the transition time to obtain the speed increment delta v required by starting1Delta speed Δ v required for rendezvous2Wherein: Δ v2I.e. hyperbolic overspeed V of the detector relative to the target celestial body∞＝Δv2(ii) a According to task constraint pair departure time T0Traversing and searching with the transfer time T, and obtaining the speed increment through a contour map or an optimization algorithmΔ v minimum chance of metastasis.
3. A multi-body system low energy capture trajectory method considering top and bottom constraints as claimed in claim 2 wherein: the concrete implementation method of the second step is that,
taking the mass center of the target celestial body as an origin, the equatorial plane as an XY plane, the X axis pointing to the spring break point, and the rotation axis as the Z axis to establish an equatorial inertial coordinate system of the celestial body, and enabling R to be the same as the X axisIThe hyperbolic overspeed in the equatorial inertial coordinate system of the celestial body is expressed as
Figure FDA0002457657080000021
Figure FDA0002457657080000022
Expressed as the equatorial inertia system of the celestial body
Figure FDA0002457657080000023
Wherein v is∞Indicating hyperbolic overspeed magnitude, α∞And delta∞Are respectively as
Figure FDA0002457657080000024
The right ascension and declination of
Figure FDA0002457657080000025
Is calculated to obtain
Figure FDA0002457657080000026
Figure FDA0002457657080000027
For a given track inclination angle i, two groups of capture track ascending intersection declination omega and paraxial point argument omega meeting the conditions can be obtained and respectively represent an ascending track and a descending track
Figure FDA0002457657080000031
Figure FDA0002457657080000032
Wherein
Figure FDA0002457657080000033
The semi-major axis a and eccentricity e of the track, expressed as
Figure FDA0002457657080000034
Wherein mu is the mass coefficient of the target celestial body; the orbit mean approach point angle M of the approach point is 0 degrees, and the approach point position R is obtained according to the conversion relation between the orbit number and the position speedpAnd velocity Vp(ii) a The fixed orbit isocenter radius is the minimum safe orbit radius due to the minimum velocity increment required for capture
Figure FDA0002457657080000035
Changing the track inclination angle i of the capture track to obtain the position speed R of the near center point under different track inclination angles ip,Vp。
4. A multi-body system low energy capture trajectory method considering top and bottom constraints as claimed in claim 3 wherein: the concrete implementation method of the step four is that,
the dynamics of the detector under the inertial system are expressed as
Figure FDA0002457657080000036
Where r denotes the position vector of the detector, rsTo representPosition vector of detector relative to the sun, rs0Representing the position vector, mu, of the sun in the inertial systemsIs the mass coefficient of the sun, riRepresenting the position vector of the detector relative to the ith celestial body other than the sun, ri0Representing the position vector, mu, of the ith celestial body in the inertial systemiIs the mass coefficient of the ith celestial body, aNIs an aspherical gravitational perturbation of the target celestial body, aSRPPerturbation for sunlight pressure;
for different centroidal states R according to equation (8)pc,VpcIntegrating, and recording the corresponding radius r of the near center point when the track passes through the near center pointpfAnd track inclination angle ifRecording the centroidal radius of the first n centroids of the track, since the track may pass the centroidal point several times
Figure FDA0002457657080000037
And track inclination
Figure FDA0002457657080000038
The size of n is related to the track transfer time; plotting the initial state R of the centripetal point after different applied maneuverspc,VpcCorresponding approximate point radius r after integrationpfAnd track inclination angle ifAnd (5) distribution diagram.
5. A multi-body system low energy capture trajectory method considering top and bottom constraints as claimed in claim 4 wherein: the concrete implementation method of the step five is that,
let the radius of the near center point of the task track be rp0The inclination angle of the track is i0Calculating the deviation between the weak stable boundary orbit state and the task orbit terminal constraint
Figure FDA0002457657080000041
Selecting the weak stable boundary orbit with the minimum deviation as a transfer orbit, and corresponding to the initial inclination angle i*The inclination angle of the hyperbolic orbit is taken, and the B plane parameter of the hyperbolic orbit is calculated;
the B plane passes through the center of the target celestial bodyPerpendicular to the vector
Figure FDA0002457657080000042
A plane of (a); wherein
Figure FDA0002457657080000043
Is a unit vector of an asymptote of a hyperbolic orbit,
Figure FDA0002457657080000044
two unit vectors for describing B-plane parameters are defined as
Figure FDA0002457657080000045
Figure FDA0002457657080000046
Taking the unit reference vector as the rotation axis Z axis of the target celestial body in general; theta represents the angle between the B vector and the T axis and is derived from spherical geometry
cosi*＝cosθcosδ∞(10)
Figure FDA0002457657080000047
The components of the B plane parameters, namely the B vectors on the T axis and the R axis are expressed as
BT＝B×T＝||B||cosθ (12)
BR＝B·T＝||B||sinθ (13)
Figure FDA0002457657080000048
And (3) obtaining an accurate interstellar transfer orbit which is from the earth to a target celestial body and meets the hyperbolic dip angle by utilizing the B plane method for correction, and meeting the initial emission constraint of the orbit.
6. A multi-body system low energy capture trajectory method considering top and bottom constraints as claimed in claim 5 wherein: the concrete realization method of the sixth step is that,
establishing the end state r by differential correctionp0,ip0Sensitivity matrix from speed of a point on weak stability boundary
Figure FDA0002457657080000051
That is, the end state satisfies the following relationship
Figure FDA0002457657080000052
Thus obtaining the relation between the differential correction amount and the end error as
Figure FDA0002457657080000053
The iteration is performed for a plurality of times according to the formula (17) until the speed correction amount delta v satisfying the terminal is obtained as [ delta v ═ delta v [ ]x,Δvy,Δvz](ii) a The probe is typically selected to apply a corrective maneuver to the distal point to meet the terminal proximal point height and tilt constraints.
7. A multi-body system low energy capture trajectory method considering top and bottom constraints as claimed in claim 1, 2, 3, 4, 5 or 6 wherein: and step three, selecting the track eccentricity slightly less than 1 finger eccentricity to meet the requirement that the detector is captured by the central celestial body, and obviously influencing the track by solar disturbance, wherein the eccentricity selection is related to the gravitational constant of the central celestial body, and the eccentricity selection is between 0.97 and 0.99.
8. A multi-body system low energy capture trajectory method considering top and bottom constraints as claimed in claim 1, 2, 3, 4, 5 or 6 wherein: the number of the tracks comprises a semi-major axis a of the tracks, eccentricity e, track inclination angle i, elevation intersection declination omega, an amplitude angle omega of a near center point and a flat near point angle M.
9. A multi-body system low energy capture trajectory method considering top and bottom constraints as claimed in claim 1, 2, 3, 4, 5 or 6 wherein: and sixthly, performing track correction on the weak stable boundary track selected in the step five, wherein the track correction times are once.
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