CN104554828A - Pulse modulation-based 180-degree rotating angle transfer orbit mis-convergence solving method - Google Patents

Abstract

The invention relates to a pulse modulation-based 180-degree rotating angle transfer orbit mis-convergence solving method and belongs to the field of the aerospace technology. The method comprises, under the condition around a 180-degree rotation angle, introducing a deep space maneuver point to divide the entire transfer orbit where planet 1-planet 2 transfers into two sections of orbits including a planet 1-deep space maneuver point transfer orbit and a deep space maneuver point-planet 2 transfer orbit; then, due to the fact that the rotating angles of the two sections of orbits divided according to the deep space maneuver point are both smaller than 180 degrees, solving the transfer problems of the two orbits respectively through the Gauss algorithm; optimizing the time ti and the position Ri of the deep space maneuver point to obtain a minimum pulse sum. Compared with the Gauss algorithm, the pulse modulation-based 180-degree rotating angle transfer orbit mis-convergence solving method can help find low-inclination and low-pulse transfer orbits when the rotating angle is nearby 180 degrees, thereby obtaining more real and more comprehensive planet-planet transfer opportunities.

Description

Based on the solution that 180 ° of corner transfer orbits of pulse regulation and control are not restrained

Technical field

The present invention relates to a kind of interplanetary transfer orbit method of designing, particularly a kind of solution do not restrained based on 180 ° of corner transfer orbits of pulse regulation and control, belongs to field of aerospace technology.

Background technology

Interplanetary transfer orbit design is the key link that planetary exploration mission is implemented.Designed by transfer orbit, we can obtain earth transmission date t ₁, planet intersection date t ₂, earth escape pulse Δ v _escapewith intersection velocity increment Δ v _rendevousdeng the key message of transfer orbit.The method that interplanetary transfer orbit design is commonly used is conic section splicing.Theoretical according to earth-satellite orbit, interplanetary transfer orbit can be divided into three sections: earth escape orbit, around the track that cruises of sun flight, target planet catch track.Wherein earth escape orbit and target planet are caught track and are hyperbola, and the track around sun flight is oval, implement splicing that is oval and hyperbolic orbit and namely can complete Track desigh task.But under the large scale of interplanetary transfer, earth escape orbit and target planet catch track and detector compared with the very long flight track of the sun, negligible.Therefore, initiating task analysis adopts elliptical orbit to connect the earth and target celestial body usually.The key problem of interplanetary transfer orbit design how to solve this elliptical orbit.

For solving of this elliptical orbit problem, Gauss is [see K.F.Gauss, Theory of motion ofthe heavenly bodies moving about the Sun in conic sections, a translation oftheoria motus by C.H.Davis, Dover Publications, Inc., New York, 1963], Battin [see R.H.Battin, Lambert ' s problem revisited, AIAA Journal, 1977,15:707-713] etc. propose various analytic solution and alternative manner ^[1-2], be called Gauss algorithm.This algorithm may be summarized to be:

[v ₁,v ₂]＝f(R ₁,R ₂,t ₁,t ₂)； (1)

That is, known position R when setting out ₁with time t ₁, arrive position R ₂with time t ₂, by Gauss algorithm, speed v when setting out can be tried to achieve ₁with speed v when arriving ₂.For the transfer orbit calculating of planets of the solar system-planet, R ₁and R ₂the i.e. position vector of planet, with time t ₁and t ₂the corresponding relation of existence anduniquess, is obtained by JPL ephemeris DE405.Therefore, for planet-planet transfer, formula (1) can be abbreviated as,

[v ₁,v ₂]＝f(t ₁,t ₂)； (2)

Earth escape pulse Δ v _escapepulse Δ v is caught with target planet _rendevouscan by corresponding formula by v ₁and v ₂convert, conversion formula is,

${\mathrm{\Δv}}_{\mathrm{escape}}=\sqrt{{|v_1-V_E|}^2-\frac{{2U}_E}{H_E}}-\sqrt{\frac{{2U}_E}{H_E}};---\left(\text{3}\right)$

${\mathrm{\Δv}}_{\mathrm{rendevous}}=\sqrt{{|v_2-V_T|}^2-\frac{{2U}_T}{H_T}}-\sqrt{\frac{{2U}_T}{H_T}};---\left(\text{4}\right)$

Wherein V _eand V _tbe respectively the target planet velocity vector in the ball speed vector intersection moment in moment of escaping, U _eand U _tbe respectively the gravity constant of the earth and target planet, H _eand H _tbe respectively earth parking orbit and target planet parking orbit height.Usually, by Δ v _escape+ Δ v _rendevousjudge the quality of transfer orbit.

But, when adopting Gauss algorithm calculating formula (1), as corner (R ₁and R ₂angle) can lose efficacy when spending close to 180 °.The earth as shown in Figure 1-Mars transfer, its corner is about 180 °, tries to achieve transfer orbit inclination angle close to 90 ° by Gauss method, and this causes earth escape pulse and Mars intersection pulse sum, i.e. Δ v _escape+ Δ v _rendevous, sharply increase, reach 35km/s.The impact that this phenomenon is brought is as follows: interplanetary transfer orbit design does not consider that corner is the transfer meeting near 180 °; When interplanetary transfer can be searched for, show the Δ v within the scope of certain hour according to contour map _escape+ Δ v _rendevous, will non-continuous event be there is near corner 180 °, as shown in Figure 2 in the regularity of distribution.

The design of planetary detection transfer orbit is the key link that the mankind explore origin of life, the understanding solar system, space-ward immigrant.Although Gauss algorithm can solve transfer orbit, when corner is about 180 °, algorithm convergence failure, the transfer orbit inclination angle of acquisition is very big, causes escaping with to catch pulse sum higher.But, when corner is near 180 °, there is the transfer meeting that transfer orbit inclination angle is less, pulse sum is less in essence.

Summary of the invention

The object of the invention is the problem lost efficacy when solving transfer orbit near corner 180 ° to solve Gauss algorithm, a kind of solution do not restrained based on 180 ° of corner transfer orbits of pulse regulation and control is proposed, the method successfully can avoid 180 ° of corners, makes the calculating transfer orbit that Gauss algorithm can remain valid.

Thought of the present invention be near 180 ° of corners in situation by introducing deep space maneuver point, the whole transfer orbit that planet 1-planet 2 shifts is divided into the transfer of planet 1-deep space maneuver point, deep space maneuver point-planet 2 shifts two sections of tracks.Like this, be all less than 180 ° with two sections of transfer orbit corners that deep space maneuver point divides, Gauss algorithm can solve the type branch problem by actv..Then, by deep space maneuver point time t _iwith position R _ioptimizing, minimum to reach pulse sum.

For achieving the above object, the present invention is achieved through the following technical solutions:

Based on the solution that 180 ° of corner transfer orbits of pulse regulation and control are not restrained, comprise the following steps:

Step one, escape according to planet 1 date t ₁with the target planet t time of advent ₂obtain transfer orbit initial position R ₁with terminal position R ₂;

Step 2, calculating R ₁and R ₂angle theta, if 170 °≤θ≤190 °, then forwards step 3 to; Otherwise, terminate;

Step 3, find optimum deep space maneuver point position R by following Optimized model _iwith time t _i:

min.Δv _escape+Δv _i+Δv _rendevous

t ₁≤t _i≤t ₂

St.R _ibetween planet 1 and target planetary orbit

Wherein, ${\mathrm{\Δv}}_i=|v_i^{-}-v_i^{+}|;$

Step 4, the Optimized model of employing differential evolution global optimization approach to step 3 are optimized and solve, and obtain the position R of optimum deep space maneuver point _iwith time t _i.

The principle of the inventive method is explained as follows:

When corner is 180 °, find a deep space maneuver point, whole transfer orbit is shifted two sections of tracks formed by the transfer of planet 1-deep space maneuver point, deep space maneuver point-planet 2.Like this, the corner of every section of track is not all near 180 °, and Gauss algorithm is effective.Meanwhile, the transfer orbit speed that the method obtains will be discontinuous at deep space maneuver point place, introduce the 3rd motor-driven---the motor-driven Δ v of deep space _imake up.

Known by formula (1 ~ 2), the key solving these two sections of transfer orbits respectively finds the position R of deep space maneuver point _iwith execution time t _i, solving of two sections of transfer orbits can be written as,

$[v_1,v_i^{-}]=f(R_i,t_1,t_i)---\left(\text{5}\right)$

$[v_i^{+},v_2]=f(R_i,t_i,t_2)---\left(6\right)$

Then transfer orbit velocity pulse sum is by Δ v _escape+ Δ v _rendevousbecome ${\mathrm{\Δv}}_{\mathrm{escape}}+$ $|v_i^{-}-v_i^{+}|+{\mathrm{\Δv}}_{\mathrm{rendevous}}.$ Deep space is motor-driven ${\mathrm{\Δv}}_i=|v_i^{-}-v_i^{+}|.$

Here global optimization approach is adopted---differential evolution [see www1.icsi.berkeley.edu/ ~ storn/code.html], by maneuver point time t _iwith position R _ioptimizing, minimum to reach pulse sum.Optimized model is as follows:

min.Δv _escape+Δv _i+Δv _rendevous

t ₁≤t _i≤t ₂(7)

St.R _ibetween the earth and target planetary orbit

Beneficial effect

Contrast Gauss algorithm, the inventive method can find out the low inclination angle when corner is near 180 °, low pulse transfer orbit, thus obtains truer and comprehensive planet-planet transfer meeting.

Accompanying drawing explanation

Earth when Fig. 1 is near corner 180 °-Mars transfer orbit schematic diagram;

Fig. 2 is the earth-Mars Search for launch window: Δ v _escape+ Δ v _rendevouscontour line km/s schematic diagram;

Fig. 3 is the earth-Mars transfer orbit schematic diagram obtained via the embodiment of the present invention;

Fig. 4 is the earth-contour line schematic diagram of Mars transfer after three burst process near the embodiment of the present invention 180 ° of corners.

Detailed description of the invention

Below in conjunction with drawings and Examples, the present invention is described in detail, also describe technical matters and the beneficial effect of technical solution of the present invention solution simultaneously, it is pointed out that described embodiment is only intended to be convenient to the understanding of the present invention, and any restriction effect is not play to it.

Embodiment

The present embodiment is emitted as example with the earth-Mars, introduces the implementation process of the inventive method in detail.

1) by earth escape date t ₁with the Mars t time of advent ₂inquiry JPL405 ephemeris obtains transfer orbit initial position R ₁with terminal position R ₂;

2) R is calculated ₁and R ₂angle theta, if 170 °≤θ≤190 °, then goes to step 3; Otherwise, terminate;

3) optimized variable---deep space maneuver point position R in Optimized model (7) is set _iwith time t _ispan;

In the present embodiment, optimized variable t _iand R _iconstraint condition be t ₁≤ t _i≤ t ₂, R _ithree components R _ix, R _iy, R _izspan be [-1.5AU 1.5AU], [-1.5AU 1.5AU], [-0.2AU 0.2AU].Wherein AU is astronomic unit, 1AU=1.4959 × 10 ⁸km;

4) adopt differential evolution global optimization approach to be optimized above-mentioned Optimized model and obtain optimum t _iand R _i, because differential evolution global optimization approach is after arranging Optimal Parameters, optimizing can be carried out to Optimized model, this step only introduce key parameter setting and described in being described as follows:

(1) expect the minimum value (when reaching this value in optimizing process, optimize and stop) reaching: 0km/s, wish that pulse sum is the smaller the better;

(2) the variable number of Optimized model: 4 is three-dimensional position vector R respectively _iwith scalar t _i;

(3) upper and lower bound of optimized variable:

Higher limit [1.5AU 1.5AU 0.2AU t ₂], lower limit [-1.5AU-1.5AU-0.2AU t ₁];

(4) population number (2-5 of variable number doubly): 20;

(5) iterations: 300;

(6) crossing-over rate (between [0,1]): 0.8; The present embodiment selects 0.8, also can select other value, but can have an impact to optimized algorithm convergence rate.

As shown in Figure 3, compared to Figure 1, transfer orbit inclination angle reduces the transfer orbit that the present embodiment method is tried to achieve, and pulse sum is reduced to 2.1km/s.The transfer orbit adopting the present embodiment method to calculate near corner 180 ° obtains the earth-Mars launching opportunity contour map as shown in Figure 4, and compared with Fig. 2, contour map becomes continuous.By the Interplanetary transfer orbit design method that the present embodiment provides, the transfer orbit inclination angle near corner 180 ° is less, pulse sum is less, can as the candidate scheme of interplanetary exploration task.

In sum, the solution do not restrained based on 180 ° of corner transfer orbits of pulse regulation and control provided by the invention can well solve the problem that Gauss algorithm lost efficacy when solving transfer orbit near corner 180 °.

Above-described specific descriptions; the object of inventing, technical scheme and beneficial effect are further described; be understood that; the foregoing is only specific embodiments of the invention; the protection domain be not intended to limit the present invention; within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (3)

1., based on the solution that 180 ° of corner transfer orbits of pulse regulation and control are not restrained, it is characterized in that, comprise the steps:

Step one, to escape date t according to planet 1 ₁with the target planet t time of advent ₂obtain transfer orbit initial position R ₁with terminal position R ₂;

Step 2, calculates R ₁and R ₂angle theta, if 170 °≤θ≤190 °, then forwards step 3 to; Otherwise, terminate;

Step 3, finds optimum deep space maneuver point position R by following Optimized model _iwith time t _i:

min.Δv _escape+Δv _i+Δv _rendevous

t ₁≤t _i≤t ₂

St.R _ibetween planet 1 and target planetary orbit

Wherein, $\mathrm{\Δ}{v}_i=|v_i^{-}-v_i^{+}|;$

Step 4, adopts the Optimized model of differential evolution global optimization approach to step 3 to be optimized and solves, obtain the position R of optimum deep space maneuver point _iwith time t _i.

2. a kind of solution do not restrained based on 180 ° of corner transfer orbits of pulse regulation and control according to claim 1, is characterized in that: described step 1 can according to t ₁and t ₂transfer orbit initial position R is obtained by inquiry JPL405 ephemeris ₁with terminal position R ₂.

3., based on the solution that the 180 ° of corner earth-Mars transfer orbits of pulse regulation and control are not restrained, it is characterized in that: comprise the following steps:

Step one, by the earth escape date t ₁with the Mars t time of advent ₂inquiry JPL405 ephemeris obtains transfer orbit initial position R ₁with terminal position R ₂;

Step 2, calculating R ₁and R ₂angle theta, if 170 °≤θ≤190 °, then goes to step 3; Otherwise, terminate;

Step 3, set optimized variable in following Optimized model---deep space maneuver point position R _iwith time t _ispan;

min.Δv _escape+Δv _i+Δv _rendevous

Wherein, $\mathrm{\Δ}{v}_i=|v_i^{-}-v_i^{+}|;$

T _iand R _iconstraint condition be respectively t ₁≤ t _i≤ t ₂, R _ithree components R _ix, R _iy, R _izspan be [-1.5AU 1.5AU], [-1.5AU 1.5AU], [-0.2AU 0.2AU], wherein AU is astronomic unit, 1AU=1.4959 × 10 ⁸km;

Step 4, employing differential evolution global optimization approach are optimized above-mentioned Optimized model and obtain optimum t _iand R _i, the setting of the key parameter of described differential evolution global optimization approach and described in being described as follows:

(1) minimum value that expectation reaches is 0km/s;

(2) the variable number of Optimized model is 4, is three-dimensional position vector R respectively _iwith scalar t _i;

(3) upper and lower bound of optimized variable:

Higher limit [1.5AU, 1.5AU, 0.2AU, t ₂],

Lower limit [-1.5AU ,-1.5AU ,-0.2AU, t ₁];

(4) population number is 20;

(5) iterations is 300;

(6) crossing-over rate is 0.8.