CN113247309B - Method and system for initial value search of transfer orbit family based on collision zone map - Google Patents

Abstract

The invention discloses a method and a system for initial value searching of a transfer orbit family based on a collision zone map. The method comprises: applying tangential disturbance to a point on a target orbit, and integrating the disturbance orbit, so as to detect the disturbance capable of hitting a main celestial body. The orbit is marked, and the collision zone map between the main celestial body and the target orbit is drawn; on both sides of each collision zone, a preset velocity increment interval is taken respectively, and a number of sampling disturbance orbits are randomly selected from the velocity increment interval. And integrate to the parking orbit; mark the position direction angle and velocity direction angle when the sampling disturbance orbit intersects the parking orbit; find the initial value of the transfer orbit tangent to the parking orbit and the target insertion point by linearly interpolating the velocity increment. The present invention systematically estimates the distribution positions of various tangential transfer families and quickly searches for the trajectories of various transfer types. the initial value of .

Description

Method and system for initial value search of transfer orbit family based on collision zone map

technical field

The invention relates to the technical field of deep space transfer orbits, in particular to a method and system for searching initial values of a transfer orbit family based on a collision zone map.

Background technique

For the deep space transfer orbit calculation, since the aircraft is far away from the original central celestial body, the gravitational perturbation of the aircraft by other celestial bodies cannot be ignored. Therefore, the calculation using the two-body model has a large motion error under the real gravitational field. The restricted three-body problem model can better approximate the motion in the actual gravitational field. When calculating the transfer orbit in the three-body problem model, due to the complexity of the gravitational field and the nonlinearity of the system, the system is highly sensitive to the initial value; and due to the complexity of the motion calculation process in the system, it is necessary to solve the precise transfer orbit before solving gives an initial value close to the exact solution.

Combined with the research results at home and abroad, the methods of searching for the initial value of the transfer orbit include taking the solution under the two-body model as the initial value, searching through the optimization algorithm, and taking the adjacent periodic orbit as the initial value, etc. Precise transfer orbits can be calculated from the initial values obtained by the current method, and then a related family or family of transfer orbits can be reproduced on this basis, but the distribution of various transfer orbit families in phase space cannot be targeted. Search and estimate.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the defects of the prior art, and to propose a method and system for searching initial values of transfer orbit family based on a collision zone map.

In order to achieve the above-mentioned purpose, the present invention proposes a method for searching initial values of transfer orbit family based on collision band atlas, and the method includes:

Apply tangential disturbance to the points on the target orbit, and integrate the disturbance orbit, mark the disturbance orbit that can hit the main celestial body, and draw the collision zone map between the main celestial body and the target orbit;

On both sides of each collision zone, a preset velocity increment interval is taken respectively, and a number of sampling disturbance orbits are randomly selected from the velocity increment interval and integrated into the parking orbit;

Mark the position direction angle and velocity direction angle when the sampling disturbance orbit intersects with the parking orbit;

Find the initial value of the transfer orbit that is tangent to the docking orbit and the target insertion point by linearly interpolating the velocity increments.

As an improvement of the above method, the tangential disturbance is applied to the point on the target orbit, and the disturbance orbit is integrated, the disturbance orbit that can hit the main celestial body is marked, and the collision between the main celestial body and the target orbit is drawn. With atlas; specifically include:

Change the velocity of each point on the target orbit F within a certain range, and reversely integrate the disturbed orbit after changing the velocity for a period of time. For the problem of orbits near the celestial body, perform forward integration, and then find the _perturbed orbit that can hit the main celestial body Pi, mark its departure phase and velocity increment or velocity size in the figure, and obtain the phase space between _Pi and F. Collision band map.

As an improvement of the above method, the number of collision zones in the collision zone map is related to the magnitude of the tangential disturbance and the integration duration. When the magnitude of the tangential disturbance and the integration duration are increased, more collision zones can be obtained.

As an improvement of the above method, the random sampling of disturbed orbits is taken from the velocity increment interval, and integrated into the parking orbit; specifically, it includes:

A number of sampling disturbance orbits are randomly selected from the velocity increment interval, and the inverse integration is used for the departure from the main celestial body to the parking orbit; the forward integration is used for the departure from the target orbit to the parking orbit.

As an improvement of the above method, the initial value of the transfer orbit that is tangent to the parking orbit and the target insertion point is found by performing linear interpolation on the velocity increment; specifically, it includes:

Perform linear interpolation on the velocity increment, find the velocity increment of β _intersect = β _O , α _intersect = α _O from the interpolated data, so as to find the initial value of the transfer orbit that is tangent to the parking orbit O and the target insertion point; where , α _intersect and β _intersect are respectively the position direction angle and velocity direction angle when the interpolated sample disturbance orbit intersects with the parking orbit O; α _O and β _O are the position of the point on the parking orbit O relative to the main celestial body _Pi , respectively The direction angle and the speed direction angle, the subscript i=1, 2 respectively represent the major main celestial body and the small main celestial body; the calculation methods of α _intersect and β _intersect are as follows:

α _intersect = tan- ¹ (y/xx _P )

β _intersect =tan- ¹ (v _y /v _x )

Among them, x _P represents the x-axis position coordinate of P _i , x and y are the position coordinates of the interpolated sampling disturbance orbit and the parking orbit O, respectively, v _x , v _y are the interpolated sampling disturbance orbit and the parking orbit, respectively The magnitude of the velocity in the x-, y-direction when O intersects.

As an improvement of the above method, the method further includes: for the transfer orbits assisted by other celestial bodies, firstly divide them into pre-gravitational-assisted transfer orbits and post-gravitational-assisted transfer orbits, perform initial value searches respectively, and then splicing to form transfer orbits the initial value of .

An initial value search system for transfer orbit family based on collision zone atlas, characterized in that the system comprises: a collision zone atlas drawing module, a parking orbit integration module, a direction angle marking module and a transfer orbit initial value output module; wherein,

The collision zone map drawing module is used to apply tangential disturbance to points on the target orbit, integrate the disturbance orbit, mark the disturbance orbit that can hit the main celestial body, and draw the collision between the main celestial body and the target orbit with map;

The parking orbit integration module is used to respectively take a preset speed increment interval on both sides of each collision zone, randomly select a number of sampling disturbance orbits from the speed increment interval, and integrate them into the parking orbit;

The direction angle marking module is used to mark the position direction angle and the speed direction angle when the sampling disturbance track intersects with the parking track;

The initial value output module of the transfer orbit is used for finding the initial value of the transfer orbit that is tangent to the parking orbit and the target insertion point by performing linear interpolation on the speed increment.

Compared with the prior art, the advantages of the present invention are:

1. The present invention proposes for the first time a method of generating a tangential collision zone map along the target orbit, and systematically predicting the tangential transfer orbit between the periodic orbit near the large celestial body and other periodic orbits in the three-body system through the collision zone map. distribution in space, and thus give methods for the initial values of various types of tangential transfer orbital families. The supported transfer orbits include direct transfer, gravity-assisted transfer, etc.;

2. The method of the present invention can systematically and intuitively evaluate the phase space structure by quickly searching the collision zone map between the target orbit and the large celestial body, and then can systematically estimate the distribution positions of various tangential transfer families and quickly. Search for tracks with multiple transfer types;

3. The method of the present invention can systematically and intuitively evaluate the number of tangential transfer orbits of various types, and provide appropriate initial values for subsequent accurate solution of the transfer orbits;

4. The method of the present invention draws a map of the collision zone by applying tangential disturbance to the points on the target orbit and integrating it to the large main celestial body that hits the target, wherein the magnitude and integration time of the tangential disturbance can be adjusted according to the transfer cost of the target transfer orbit. , search for the transfer orbit within the expected cost range; the step size of the target orbit can be larger, and only the distribution position and number of collision zones in the phase space can be revealed, so the collision zone map can be obtained quickly;

5. The method of the present invention randomly selects sampling points on both sides of each collision zone, integrates the sampling points to the departure track, and quickly searches for the initial value close to the exact solution through linear interpolation, and determines the exact solution neighborhood by this method. As a search interval, the initial value can be quickly obtained.

Description of drawings

Fig. 1 is the flow chart of the initial value search method of transfer orbit family based on collision zone map of the present invention;

Fig. 2 is the collision zone map between the simulation example earth of the present invention and the SPO near the L4 point;

Fig. 3 is the state and the interpolation result when the random sampling orbit near the upper boundary of the widest collision band at 0.2π place and the LEO intersection of the simulation example of the present invention is the phase angle of the insertion point;

Fig. 4 is the collision zone map between the moon of the simulation example of the present invention and the SPO near the L4 point;

Fig. 5 is the state and the interpolation result when the random sampling orbit near the upper boundary of the lower collision zone at the 0.2π place of the simulation example insertion point of the present invention intersects with the LLO;

Fig. 6 is the collision zone map between the circular LLO orbit of the simulation example 100km height of the present invention and the earth;

FIG. 7 shows the state and the interpolation result when the randomly sampled orbit near the upper boundary of the collision band intersects with the LEO at the insertion point phase angle of 1.125π in the simulation example of the present invention.

Detailed ways

In order to systematically estimate the position, quantity and properties of the transfer orbits in the phase space, and to give the initial values of the multi-family transfer orbits, the present invention searches and draws the map of the collision zone between the target orbit and the main celestial body, and gives the A method for obtaining initial values of multi-family transfer orbitals from collision band maps.

The basic principle of this method is to apply a small tangential pulse to the target periodic orbit, and reversely integrate the disturbed orbit to which the small tangential pulse is applied, so as to hit the disturbed orbit mark of the departure celestial body to obtain the tangential collision zone of the target orbit. There are transfer orbit families distributed on both sides of each collision zone, randomly sampled on both sides of the collision zone, and through linear interpolation, the initial value of the transfer orbit that is approximately tangent to the departure orbit and the target insertion point is obtained. This method can rapidly and systematically evaluate the distribution region of the transfer orbital family in phase space.

The technical solutions of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

Example 1

As shown in FIG. 1 , Embodiment 1 of the present invention provides a method for searching for initial values of a family of transfer orbits based on a collision band map.

为In the circular restricted three-body problem, the rendezvous coordinate system is an origin located at the center of mass of the system, the x-axis points from the large main celestial body P ₁ to the small main celestial body P ₂ , the z-axis is parallel to the angular momentum vector of the motion of the main celestial body, and the y-axis is determined by the right hand. The rules are determined. For the convenience of analysis and calculation, each physical quantity is dimensionless and magnitude normalized, and the corresponding mass unit is defined as the total mass of the main celestial body, the length unit is the distance between the two main celestial bodies, and the time unit is divided by the motion period of the main celestial body. 2π, the system mass parameter is defined as μ=m ₂ /m ₁ +m ₂ , where m ₁ and m ₂ represent the masses of P ₁ and P ₂ , respectively. In the xy plane meeting coordinate system, the coordinates of the major and minor celestial bodies are (-μ, 0) and (1-μ, 0), respectively. The motion equation of the third body

for

in

The search for the transfer orbit between the parking orbit O and the target periodic orbit F near the main celestial body P _i (i=1, 2) is realized by the following steps:

Step 1) Locate the collision orbit that reaches the target orbit tangentially and can collide with the departure main celestial body.

Change the velocity of each point on the target periodic orbit F within a certain range, and reversely integrate the disturbed orbit after changing the velocity for a period of time. The forward integral of the problem of orbits near the main celestial body. After that, the departure phase and velocity increment or velocity magnitude of the _disturbed orbit that can hit the main celestial body Pi are marked in the figure, and the collision zone map in the phase space between _Pi and F can be obtained. It should be noted that the number of collision zones in the collision zone map is related to the size range of the velocity increment and the integration time, and more collision zones can be obtained with a larger range of velocity increments and a longer integration time.

Step 2) Randomly take sample disturbance orbits near the collision zone for testing.

和

内分别取3000个采样点，其中

分别表示一条碰撞带中某相位对应的速度增量大小上下界。On both sides of each collision band, a small velocity increment interval is respectively taken, and a number of sampling disturbance orbits are randomly selected for reverse/forward integration. For example, in

and

Take 3000 sampling points respectively, among which

respectively represent the upper and lower bounds of the velocity increment corresponding to a certain phase in a collision zone.

Step 3) Mark the position direction angle and the speed direction angle when the sampling disturbance orbit intersects with the parking orbit O.

The state when the sampling disturbance orbit intersects with the parking orbit O can be characterized by the position direction angle α _intersect and the velocity direction angle β _intersect relative to P _i . The calculation formulas of the two angles are as follows:

α _intersect = tan ^-1 (y/xx _P )

β _intersect =tan ^-1 (v _y /v _x )

对采样扰动轨道，将其积分至与停泊轨道O相交，记录交点处的位置方向角α_intersect和速度方向角β_intersect。where x _P represents the x-axis position coordinates of P _i , and x, y, v _x , v _y are the position coordinates and the speed in the x-, y- directions when the interpolated sampling disturbance track intersects with the parking track O. In particular, for circular orbits, there is a relationship of β _O = _{α O} +π/2 in the conjunct coordinate system, that is, the position vector relative to Pi is perpendicular to the velocity vector:

For the sampled disturbed orbit, integrate it to intersect with the parking orbit O, and record the position direction angle α _intersect and the velocity direction angle β intersect at the _intersection .

Step 4) By performing linear interpolation on the velocity increment, find a perturbed orbit that can make β _intersect = β _O , α _intersect = α _O approximately satisfied, that is, approximately tangent to the orbit O, this orbit is the one that can be accurately solved and summed up. The initial value of the transfer orbit for the numerical continuation.

The gravitationally assisted transfer orbits of other celestial bodies can be divided into two orbits before and after gravitational assistance. The above-mentioned methods are used to search for initial values and spliced together to form the completed transfer orbits.

Simulation example:

In the Earth-Moon restricted three-body problem, starting from a circular Low Earth Orbit (LEO) and transferring to a Short Periodic Orbit (Short Periodic Orbit) with an amplitude of β=0.15 near the L4 Lagrangian point. , SPO) as an example, the process of initial value search using this method is as follows:

From the problem of direct transfer from LEO to SPO, the velocity increment is applied to the points on the SPO, and the collision zone map between the Earth and SPO obtained by reverse integration for 5 time units (about 21.7 days) is shown in Figure 2. Sampling at the upper boundary of the widest collision band at the phase angle of the insertion point of 0.2π, the position direction angle, velocity direction angle and linear interpolation results when the perturbation orbit intersects the LEO are shown in Fig. 3.

The problem of transferring from LEO to SPO with lunar gravitational assistance can be divided into two parts. First, the initial value of the transfer segment to SPO after being assisted by lunar gravity is searched by the method of collision zone map search, and then the method of collision zone map search is used. Search for the initial value of the transition segment from the Earth to the Low Lunar Orbit (LLO) with the flyby height as the orbital height.

For the first part of the problem, the velocity increment is applied to the point on the SPO, and the collision zone map between the moon and the SPO obtained by reverse integration for 5 time units (about 21.7 days) is shown in Figure 4; the phase angle at the insertion point is 0.2 The upper boundary of the lower collision zone at π is sampled, the position direction angle, velocity direction angle and linear interpolation results when the perturbation orbit intersects the LLO are shown in Fig. 5. For the second part of the problem, take the circular LLO orbit with a height of 100km as the hypothetical target orbit, change the speed of each point on it, and reversely integrate the collision zone map between the LLO and the earth obtained by 5 time units (about 21.7 days). As shown in Fig. 6, the upper boundary of the collision band is sampled at the phase angle of the insertion point at 1.125π. The position direction angle, velocity direction angle and linear interpolation results when the perturbation orbit intersects the LEO are shown in Fig. 7.

Example 2

Embodiment 2 of the present invention proposes a system for initial value search of transfer orbit family based on collision zone atlas. The system includes: a collision zone atlas drawing module, a parking orbit integration module, a direction angle marking module and a transfer orbit initial value output module; in,

The collision zone map drawing module is used to apply tangential disturbance to points on the target orbit, integrate the disturbance orbit, mark the disturbance orbit that can hit the main celestial body, and draw the collision between the main celestial body and the target orbit with map;

The parking orbit integration module is used to respectively take a preset speed increment interval on both sides of each collision zone, randomly select a number of sampling disturbance orbits from the speed increment interval, and integrate them into the parking orbit;

The direction angle marking module is used to mark the position direction angle and the speed direction angle when the sampling disturbance track intersects with the parking track;

The initial value output module of the transfer orbit is used for finding the initial value of the transfer orbit that is tangent to the parking orbit and the target insertion point by performing linear interpolation on the speed increment.

Innovative points of the present invention:

1) The present invention draws a collision zone map by applying tangential disturbance to points on the target orbit and integrating it to the large main celestial body that hits the target, wherein the size and integration time of the tangential disturbance can be adjusted according to the transfer cost of the target transfer orbit, and the Transfer orbits within the expected cost range; the step size of taking points on the target orbit can be larger, and only the distribution position and number of collision zones in the phase space can be revealed, so the collision zone map can be quickly obtained.

2) The present invention randomly selects sampling points on both sides of each collision zone, integrates the sampling points to the departure track, and quickly searches for the initial value close to the exact solution through linear interpolation, and determines the exact solution neighborhood by this method as the search. interval, and can quickly obtain the initial value.

3) There are continuous transfer orbital families on both sides of each collision band, which are associated with different departure directions, transfer times, and transfer orbital families with different fuel consumption characteristics, so it is possible to systematically search for multiple transfer orbital families in phase space. .

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present invention will not depart from the spirit and scope of the technical solutions of the present invention, and should be included in the present invention. within the scope of the claims.

Claims (6)

1. a method for searching for initial values of a transfer orbit family based on a collision zone map, the method comprising: Apply tangential disturbance to the points on the target orbit, and integrate the disturbance orbit, mark the disturbance orbit that can hit the main celestial body, and draw the collision zone map between the main celestial body and the target orbit; On both sides of each collision zone, a preset velocity increment interval is taken respectively, and a number of sampling disturbance orbits are randomly selected from the velocity increment interval and integrated into the parking orbit; Mark the position direction angle and velocity direction angle when the sampling disturbance orbit intersects with the parking orbit; Find the initial value of the transfer orbit that is tangent to the parking orbit and the target insertion point by linearly interpolating the velocity increments; The tangential disturbance is applied to the point on the target orbit, and the disturbance orbit is integrated, the disturbance orbit that can hit the main celestial body is marked, and the collision zone map between the main celestial body and the target orbit is drawn; specifically, it includes: Change the velocity of each point on the target orbit F within a certain range, and reversely integrate the disturbed orbit after changing the velocity for a period of time. For the problem of orbits near the celestial body, perform forward integration, and then find the _perturbed orbit that can hit the main celestial body Pi, and mark its departure phase and velocity increment in the figure, or mark its departure phase and velocity in the figure, and get Map of the collision bands in phase space between _Pi and F. 2. the initial value search method of transfer orbit family based on collision zone atlas according to claim 1, is characterized in that, the collision zone quantity in described collision zone atlas is related to the size of tangential disturbance and the integral duration, when increasing. The size of the large tangential disturbance and the integration duration can obtain more collision bands. 3. the initial value search method of transfer orbit family based on collision zone atlas according to claim 1, is characterized in that, described randomly takes some sampling disturbance orbits from the speed increment interval, and integrates to the parking orbit; Concrete comprises: A number of sampling disturbance orbits are randomly selected from the velocity increment interval, and the inverse integration is used for the departure from the main celestial body to the parking orbit; the forward integration is used for the departure from the target orbit to the parking orbit. 4. the initial value search method of transfer orbit family based on collision zone map according to claim 1, is characterized in that, described by carrying out linear interpolation to speed increment, finds the transfer orbit tangent to parking orbit and target insertion point Initial value; specifically includes: Perform linear interpolation on the velocity increment, find the velocity increment of β _intersect = β _O , α _intersect = α _O from the interpolated data, so as to find the initial value of the transfer orbit that is tangent to the parking orbit O and the target insertion point; where , α _intersect and β _intersect are respectively the position direction angle and velocity direction angle when the interpolated sample disturbance orbit intersects with the parking orbit O; α _O and β _O are the position of the point on the parking orbit O relative to the main celestial body _Pi , respectively The direction angle and the speed direction angle, the subscript i=1, 2 respectively represent the major main celestial body and the small main celestial body; the calculation methods of α _intersect and β _intersect are as follows: α _intersect = tan ^-1 (y/xx _P ) β _intersect =tan ^-1 (v _y /v _x ) Among them, x _P represents the x-axis position coordinate of P _i , x and y are the position coordinates of the interpolated sampling disturbance orbit and the parking orbit O, respectively, v _x , v _y are the interpolated sampling disturbance orbit and the parking orbit, respectively The magnitude of the velocity in the x-, y-direction when O intersects. 5. The method for initial value search for a family of transfer orbits based on a collision zone map according to claim 1, wherein the method further comprises: for the transfer orbits assisted by other celestial bodies gravitationally, it is first divided into a pre-gravitationally assisted transfer orbit and the gravitationally assisted post-transfer orbit, carry out initial value search respectively, and then splicing to form the initial value of the transfer orbit. 6. A transfer orbit family initial value search system based on a collision zone atlas, characterized in that the system comprises: a collision zone atlas drawing module, a parking orbit integration module, a direction angle marking module and a transfer orbit initial value output module; wherein , The collision zone map drawing module is used to apply tangential disturbance to points on the target orbit, integrate the disturbance orbit, mark the disturbance orbit that can hit the main celestial body, and draw the collision between the main celestial body and the target orbit with map; The parking orbit integration module is used to respectively take a preset speed increment interval on both sides of each collision zone, randomly select a number of sampling disturbance orbits from the speed increment interval, and integrate them into the parking orbit; The direction angle marking module is used to mark the position direction angle and the speed direction angle when the sampling disturbance track intersects with the parking track; The initial value output module of the transfer orbit is used to find the initial value of the transfer orbit that is tangent to the parking orbit and the target insertion point by performing linear interpolation on the speed increment; The processing process of the collision zone atlas drawing module specifically includes: Change the velocity of each point on the target orbit F within a certain range, and reversely integrate the disturbed orbit after changing the velocity for a period of time. For the problem of orbits near the celestial body, carry out forward integration, and then find the _perturbed orbit that can hit the main celestial body Pi, and mark its departure phase and velocity increment in the figure, or mark its departure phase and velocity in the figure, and get Map of the collision bands in phase space between _Pi and F.

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