CN104554828B - The solution that 180 ° of corner transfer orbits based on pulse regulation and control are not restrained - Google Patents

Abstract

The present invention relates to the solution that a kind of 180 ° of corner transfer orbits based on pulse regulation and control are not restrained, belong to field of aerospace technology.The inventive method near 180 ° of corners in the case of by introduce 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, it is respectively less than 180 ° next for the two sections of transfer orbits divided with deep space maneuver point due to its corner, solves its branch problem by Gauss algorithm respectively；Then, by deep space maneuver point time t_iWith position R_iOptimizing, minimum to reach pulse sum.Contrast Gauss algorithm, can find out the low inclination angle when corner is near 180 °, low pulse transfer orbit by the inventive method, thus obtain truer and comprehensive planetary planet transfer meeting.

Description

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

Technical field

The present invention relates to a kind of interplanetary transfer orbit method for designing, regulate and control based on pulse particularly to one The solution that do not restrains of 180 ° of corner transfer orbits, belong 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 t₁, planet intersection date t₂, earth escape pulse Δ v_escapeWith Intersection speed increment Δ v_rendevousKey message Deng transfer orbit.Interplanetary transfer orbit design is commonly used Method is conic section splicing.Theoretical according to earth-satellite orbit, interplanetary transfer orbit can be divided into three sections: Earth escape orbit, the cruise track, the capture track of target planet that fly around the sun.Wherein the earth is escaped Ease track and target planet capture track are hyperbola, and the track around sun flight is oval, implements ellipse The splicing of circle and hyperbolic orbit i.e. can complete orbit Design task.But, big in interplanetary transfer Under yardstick, earth escape orbit and target planet capture track and detector are around the very long flight track of the sun Compare, be negligible.Therefore, initiating task analysis generally use elliptic orbit to connect the earth and Target celestial body.The key problem of interplanetary transfer orbit design is how to solve this elliptic orbit.

For solving of this elliptic orbit problem, Gauss [sees K.F.Gauss, Theory of motion of the heavenly bodies moving about the Sun in conic sections,a translation of theoria 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 solutions and alternative manner^[1-2], referred to as Gauss algorithm.This algorithm is permissible It is summarised as:

[v₁,v₂]=f (R₁,R₂,t₁,t₂)； (1)

I.e., it is known that position R when setting out₁With time t₁, arrive position R₂With time t₂, pass through Gauss Algorithm, can try to achieve speed v when setting out₁With speed v when arriving₂.For planets of the solar system-planet Transfer orbit calculate for, R₁And R₂The i.e. position vector of planet, with time t₁And t₂Existence anduniquess Corresponding relation, is obtained by JPL ephemeris DE405.Therefore, for planet-planet transfer, formula (1) Can be abbreviated as,

[v₁,v₂]=f (t₁,t₂)； (2)

Earth escape pulse Δ v_escapePulse Δ v is captured with target planet_rendevousCan be by corresponding Formula is by v₁And v₂Converting, reduction 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_TIt is respectively the target planet speed in the ball speed vector intersection moment in moment of escaping Degree vector, U_EAnd U_TIt is respectively the earth and the gravitational constant of target planet, H_EAnd H_TIt is respectively the earth to stop Pool track and target planet parking orbit height.Generally, by Δ v_escape+Δv_rendevousJudge The quality of transfer orbit.

But, when using Gauss algorithm calculating formula (1), as corner (R₁And R₂Angle) close to 180 ° Can lose efficacy when spending.The earth as shown in Figure 1-Mars transfer, its corner is about 180 °, passes through Gauss Method tries to achieve transfer orbit inclination angle close to 90 °, and this causes earth escape pulse and Mars intersection pulse sum, I.e. Δ v_escape+Δv_rendevous, it is increased dramatically, reaches 35km/s.The impact that this phenomenon is brought As follows: interplanetary transfer orbit design does not consider the transfer meeting that corner is 180 ° neighbouring；At interplanetary turn Δ v when telephone-moving can be searched for, in the range of showing certain time according to contour map_escape+ Δv_rendevousThe regularity of distribution, will appear from non-continuous event, as shown in Figure 2 near corner 180 °.

The design of planetary detection transfer orbit is that the mankind explore origin of life, the understanding solar system, space-ward immigrant Key link.Although Gauss algorithm can solve transfer orbit, but when corner is about 180 °, Algorithmic statement failure, it is thus achieved that transfer orbit inclination angle very big, cause escaping with to capture pulse sum higher. But, when corner is near 180 °, substantially have that transfer orbit inclination angle is less, pulse sum is less Transfer meeting.

Summary of the invention

The invention aims to solve Gauss algorithm lose when solving transfer orbit near corner 180 ° The problem of effect, proposes the solution that a kind of 180 ° of corner transfer orbits based on pulse regulation and control are not restrained, The method can successfully avoid 180 ° of corners, makes the calculating transfer orbit that Gauss algorithm can remain valid.

By introducing deep space maneuver point in the case of idea of the invention is that near 180 ° of corners, by planet 1-planet 2 transfer whole transfer orbit be divided into planet 1-deep space maneuver point transfer, deep space maneuver point- Planet 2 shifts two sections of tracks.So, the two sections of transfer orbit corners divided with deep space maneuver point are respectively less than 180 °, Gauss algorithm can effectively solve the type branch problem.Then, by motor-driven to deep space 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:

The solution that a kind of 180 ° of corner transfer orbits based on pulse regulation and control are not restrained, including following Step:

Step one, escape date t according to planet 1₁With the target planet t time of advent₂At the beginning of acquisition transfer orbit Beginning position R₁With terminal position R₂；

Step 2, calculating R₁And R₂Angle 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

t₁≤t_i≤t₂

st.R_iBetween planet 1 and target planetary orbit

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

The Optimized model of step 3 is optimized and solves by step 4, employing differential evolution global optimization approach, 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 °, finding a deep space maneuver point, whole transfer orbit is by planet 1-deep space machine Two sections of track compositions are shifted in the transfer of dynamic point, deep space maneuver point-planet 2.So, the corner of every section of track The most not near 180 °, Gauss algorithm is effective.Meanwhile, the transfer orbit speed that the method is obtained will At deep space maneuver point discontinuously, the 3rd motor-driven deep space motor-driven Δ v is introduced_iMake up.

By formula (1～2), solve respectively these two sections of transfer orbits it is crucial that find deep space maneuver point Position R_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+Δv_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 differential evolution is used [to 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

t₁≤t_i≤t₂ (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 obtain truer and comprehensive planet-planet transfer meeting.

Accompanying drawing explanation

Fig. 1 is earth time near corner 180 °-Mars transfer orbit schematic diagram；

Fig. 2 is the earth-Mars Search for launch window: Δ v_escape+Δv_rendevousEqual pitch contour 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 that the earth near 180 ° of corners of the embodiment of the present invention-Mars transfer is after three pulses process Equal pitch contour schematic diagram.

Detailed description of the invention

Below in conjunction with drawings and Examples, the present invention is described in detail, also described the present invention simultaneously Technical scheme solves the technical problem that and beneficial effect, it should be pointed out that described embodiment only purport It is being easy to the understanding of the present invention, and it is not being played any restriction effect.

Embodiment

The present embodiment, as a example by the earth-Mars is launched, is discussed in detail the implementation process of the inventive method.

1) by earth escape date t₁With the Mars t time of advent₂Inquiry JPL405 ephemeris obtains transfer rail Road initial position R₁With terminal position R₂；

2) R is calculated₁And R₂Angle 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_iValue model Enclose；

In the present embodiment, optimized variable t_iAnd R_iConstraints be t₁≤t_i≤t₂, 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 astronomical unit, 1AU=1.4959 × 10⁸km；

4) use differential evolution global optimization approach that above-mentioned Optimized model is optimized the optimum t of acquisition_iAnd R_i, Owing to differential evolution global optimization approach is after arranging parameters optimization, Optimized model can be carried out optimizing, This step is only introduced the setting of key parameter and is described as follows described:

(1) minima (when reaching this value during optimization, optimize and stop) that expectation reaches: 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 t₂], lower limit [-1.5AU-1.5AU-0.2AU t₁]；

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

(5) iterations: 300；

(6) crossing-over rate (between [0,1]): 0.8；The present embodiment selects 0.8, it is also possible to select other value, But optimized algorithm convergence rate can be produced impact.

The transfer orbit that the present embodiment method is tried to achieve as it is shown on figure 3, compared to Figure 1, transfer orbit Inclination angle reduces, and pulse sum is reduced to 2.1km/s.The present embodiment method is used to calculate corner 180 ° Near the obtained earth of transfer orbit-Mars launching opportunity contour map as shown in Figure 4, with Fig. 2 Comparing, contour map becomes continuous.The Interplanetary transfer orbit design method be given by the present embodiment, The neighbouring transfer orbit inclination angle of corner 180 ° is less, pulse sum is less, can be as interplanetary The candidate scheme of detection mission.

In sum, 180 ° of corner transfer orbits based on pulse regulation and control that the present invention provides are not restrained Solution can well solve what Gauss algorithm lost efficacy when solving transfer orbit near corner 180 ° Problem.

Above-described specific descriptions, have carried out entering one to purpose, technical scheme and the beneficial effect of invention Step describes in detail, be it should be understood that the specific embodiment that the foregoing is only the present invention, not For limiting protection scope of the present invention, all within the spirit and principles in the present invention, that is done any repaiies Change, equivalent, improvement etc., should be included within the scope of the present invention.

Claims (3)

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

Step one, escapes date t according to planet 1₁With the target planet t time of advent₂At the beginning of acquisition transfer orbit Beginning position R₁With terminal position R₂；

Step 2, calculates R₁And R₂Angle theta, if 170 °≤θ≤190 °, then forwards step 3 to；No Then, 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

t₁≤t_i≤t₂

st.R_iBetween planet 1 and target planetary orbit

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

Step 4, uses differential evolution global optimization approach to be optimized the Optimized model of step 3 and asks Solve, it is thus achieved that the position R of optimum deep space maneuver point_iWith time t_i。

A kind of 180 ° of corner transfer orbits based on pulse regulation and control the most according to claim 1 are not The solution of convergence, it is characterised in that: described step 1 can be according to t₁And t₂By inquiry JPL405 Ephemeris obtains transfer orbit initial position R₁With terminal position R₂。

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

Step one, by the earth escape date t₁With the Mars t time of advent₂Inquiry JPL405 ephemeris obtains Transfer orbit initial position R₁With terminal position R₂；

Step 2, calculating R₁And R₂Angle theta, if 170 °≤θ≤190 °, then goes to step 3；Otherwise, Terminate；

Step 3, set optimized variable deep space maneuver point position R in following Optimized model_iWith time t_i Span；

min.Δv_escape+Δv_i+Δv_rendevous

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

t_iAnd R_iConstraints be respectively t₁≤t_i≤t₂, R_iThree components R_ix, R_iy, R_izTake Value scope is [-1.5AU 1.5AU], [-1.5AU 1.5AU], [-0.2AU 0.2AU], and wherein AU is sky Literary composition unit, 1AU=1.4959 × 10⁸km；

Above-mentioned Optimized model is optimized and obtains by step 4, employing differential evolution global optimization approach Excellent t_iAnd R_i, the setting of the key parameter of described differential evolution global optimization approach and be described as follows described:

(1) minima 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, t₂],

Lower limit [-1.5AU ,-1.5AU ,-0.2AU, t₁]；

(4) population number is 20；

(5) iterations is 300；

(6) crossing-over rate is 0.8.