# Adaptive multiple shooting optimisation method for determining optimal spacecraft trajectories

FIELD: physics, navigation.

SUBSTANCE: group of inventions relates to interorbital, including interplanetary, flights of rocket propelled spacecraft. A method of constructing an optimal spacecraft trajectory is based on solving a two-point boundary value problem of the Pontryagin maximum principle and taking into account characteristics of the macro- and microstructure of the cost function. The latter can be the time of flight or fuel consumption during flight. Analytical bases for efficient search of initial domains of values of Lagrange multipliers at each iteration are established. This facilitates the construction of a series of sub-optimal solutions which converge to an optimal solution. A corresponding algorithm yields the optimal solution last or, in case of unattainability thereof (due available resources of the spacecraft) a solution close to optimal. An electronic processor for implementing the method and a spacecraft with said processor are also disclosed.

EFFECT: faster operation, improved convergence, low qualification requirements and wider field of use of the disclosed algorithm and accompanying equipment.

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The technical field TO WHICH the INVENTION RELATES

The present invention relates to determining the optimal movement trajectories of the spacecraft and can be used to solve wide range of problems that involve the optimization of the movement trajectories of spacecraft, such as spacecraft, missiles, space shuttles, etc.

In particular, the present invention allows to determine the optimal trajectory of displacement in this range of age, and the optimal trajectory of movement allows, in General, to meet the requirement of this space mission and, in particular, to minimize travel time, fuel consumption or a combination of them both.

The LEVEL of TECHNOLOGY

As shown, in the literature the definition of best trajectory of the spacecraft for this mission as "two-point boundary value problem", and it consists in determining the trajectory among all possible connecting two different points in space (representing the boundary conditions) and allowing you to maximize or minimize a given cost function (also called cost index). The equations of motion are differential constraints of the task.

There are several optimizations that are useful for solving optimization problems related�data with cosmic movements, which are divided essentially into two main categories:

- classic, indirect methods based on the Pontryagin maximum principle; and

- direct methods that attempt to find the minimum of the cost function many numerical methods and can optionally be grouped into

direct methods used in the calculus, and

search methods.

Genetic algorithms have also been applied to solve problems associated with interplanetary travel.

Below is a brief description of the above known methods.

The Pontryagin maximum principle is the fundamental theorem of variational calculus applied to optimal control theory: it gives some necessary conditions to determine the optimal solution to analyze tasks, and it is based only on the differential properties of certain classes of functions demonstrate at the point of extremum. Under such conditions it is possible to determine the evolution in time of some parameters, the so-called Lagrange multipliers used to estimate the control variables needed to solve the optimization problem. The initial values of the Lagrange multipliers is unknown and can be evaluated numerically to satisfy the boundary conditions. In other words, the optimization problem is completely reduced to defined�of initial values of the Lagrange multipliers. The task becomes even more challenging when the final state is not fully determined, that is, some variables of the state vector is not assigned to boundary conditions. In addition to the conditions given by the Pontryagin maximum principle, one should consider additional constraints defined as "the transversality conditions".

In particular indirect ways by the conditions given by the Pontryagin maximum principle, allow us to determine at run time what is the best way to use control variables for solving optimization problems, but these variables are unknown at the beginning, as shown below.

Let

is a system of differential equations in private derivatives of the first order, where x is the state vector, and u is the so - called vector control, the vector defined during implementation to minimize or maximize a given cost function J. Turning to the wording of the Bolza problem, the cost function may take the form of:

For example, suppose that the cost function J needs to be minimized. This leads to the following condition

Let also H(x, u, λ, t) is the Hamilton function associated with the system, expressed in the form:

previous formulas take the form:

and

where λ is a vector of Lagrange multipliers (which is also specified as a vector of sosotojanie or adjoint variable vector). The Pontryagin maximum principle States that if x(t), λ(t) satisfy the conditions:

and for all

then u* is the desired optimal control that maximizes the Hamilton function H.

In addition to the Pontryagin maximum principle, if the state vector is not fully defined at the boundaries, it is necessary to add additional conditions called "the transversality conditions". The number of these additional constraints is equal to the number of components in the state vector that are not defined at the boundaries. Example�, if the end time is not set, the corresponding condition for the transversality should be:

H_{f}=1,

if we consider the problem of minimal time, or:

H_{f}=0,

if the problem is analysed minimum fuel consumption.

The number and terms of the transversality conditions is changed according to analyze this problem.

Apply the above General formulation for the two-point problem, in the case of interplanetary movements, for example, consider moving Earth-Mars. According to the hypothesis of co-planar movements (all orbits of the major bodies in the Solar system have a small tilt relative to the Ecliptic plane) and considering the inertial system of coordinates xOy, where the origin O coincides with the center of mass of the Sun, the equations of motion can be written as follows:

where {x, y, u, v, m} is the state vector (x, y - components of position vector, a u, v - components of velocity vector; m is the actual mass of the spacecraft), µ is the gravitational parameter of the Sun, T is the thrust levels achievable at a given power plant (continuous manoeuvring) and δ - function on / off, representing the state of the power plant (δ=0 - engine off; δ=1 the motor is operating), {v_{x}v_{y}} is the unit vector decrees�ment direction of thrust.
For data departure time t_{0}and the arrival time t_{f}spacecraft can also define functionality

want to minimize (i.e. we want to minimize travel time); the corresponding Hamilton function must take the form:

or more convenient way:

where {λ_{x},λ_{y},λ_{u},λ_{v}} - vector of Lagrange multipliers (vector sosotojanie). We apply the Pontryagin maximum principle. Control is optimal if and only if:

and

The first condition says that the direction of the thrust vector {v_{x}v_{y}} should be aligned with the vector {λ_{u}, λ_{v}} and the second condition indicates whether it is convenient to include a shunting engine. In respect of derivatives sosotojanie, the Pontryagin maximum principle asserts that:

If all these conditions are fulfilled, the Pontryagin maximum principle is fully satisfied, and the optimal thrust direction is defined analytically using variables sosotojanie λ_{u}, λ_{v}. The main problem affecting this approach is that the initial values {λ_{x}, λ_{y}, λ_{u}, λ_{v}m,} is unknown and cannot be estimated from physical considerations; one can only assume the order of magnitude of each participant on the basis of the corresponding derivative. Of course, there are a limited number of optimal vectors {λ_{x,0}, λ_{y,0}, λ_{u,0}, λ_{v,0}, λ_{m,0}} you need to look for in ℜ^{5}(or in ℜ^{7}if the hypothesis coplanar movement is incorrect), allowing to achieve the desired final conditions. It is clear that this approach, although it gives an analytical expression for the optimal direction and magnitude of thrust, looks very unsatisfactory because of the difficulty of achieving the ultimate conditions.

In contrast, direct methods used in the calculus, based on the approximation of the state vector and function value through the submission sequence. Selecting the proper set of elementary functions for representation of the sequence, on the basis of these hypotheses, it is possible to find the unknown coefficients of the sequence by finding the extremum of the approximate functional value. In other words, the problem of nding the extremum of the functional on the set of functions is reduced to finding the extremum of a function of many parameters. The solution is, in General, an approximate solution if the set of parameters is not bascone�tion set.

In particular, such direct methods are designed to reduce the problem of maximizing (or minimizing) the functionality regarding functions to the problem of maximizing (or minimizing) functions on a set of variables through a representation of the sequence, although the solution is, in General, approximate solution, if the set of parameters is not an infinite set. Consider the 1-dimensional differential problem, expressed in the form

and also

where a_{k}- the coefficients are not time-dependent, and ψ_{k}(t} are known functions. Clearly, we need to apply a truncated form of the previous expression:

It is assumed that this sequence of approximating functions full for functions x(t). By definition, the sequence approxi�arousih functions detailed under the following condition: for all ε> 0 there is an integer j for which:

The importance of this definition is that

if J(x) is strictly continuous and if the sequence of functions is complete. Approximate the functional J_{n}(x_{n}) must take the form:

To solve the optimization problem J_{n}(x_{n}) must be stationary with respect to each of a_{k}i.e.:

Performing the integration, the resulting system of equations can be solved for the stationary points, and these stationary points, which are relative maxima (or minima), you can define search methods. The functional J_{n}(x_{n}) often Express the following:

In addition, search methods based on numerical methods for the estimation of the optimal solution, starting from an approximate evaluation of the cost function. With such an approximation, one can find many variables that maximize (or minimize) a cost function in this area; therefore, these methods are also called "methods". The function can be set analytically or determined experimentally; it may or may not have gaps, and there may be restrictive cheers�tion, limiting case performance measure. In the latter case the problem is called "nonlinear programming". Among the methods of finding the maximum (or minimum) should be mentioned methods, gradient search, univariate search and inconsistent search.

In addition, genetic algorithms are search techniques used to find exact or approximate solutions to optimization and search. They belong to the broad class of evolutionary algorithms that use a theoretical construct, inspired by theory of evolution in biology, for example, heredity, mutation, selection and crossing-over. To solve the optimization problem is chosen more sets consisting of two or more control parameters, called chromosomes; after building the chromosomes are random "coincidences" between chromosomes, and by crossing-over generated new chromosomes (offspring), hopefully, closer to the desired solution. Crossingover occur according to the rules. Then the whole process is repeated until then, until you have obtained significant improvements; thus, the algorithm finds the optimal solution.

All the above optimization methods have intrinsic limitations that restrict their applicability given�Oh task or their effectiveness in finding solutions.

In addition, the applicant drew attention to the fact that "two-point boundary value problem" in relation to the movements of the spacecraft, not just interplanetary, proved more difficult than anticipated (this result will be described below), and this greatly affects the effectiveness of each above-described method.

With regard to indirect methods, although performed on some of the analytical limitations of optimality, it is not possible to pre-set the initial value of the Lagrange multipliers, which allows to meet the boundary conditions. Three-dimensional analysis two-point optimization problem would require six multipliers for the state vector of the spacecraft, plus disatvantage its mass. In addition, if the initial epoch is the optimization parameter, you should also consider the initial time t_{0}for the start of the mission. As for the initial epoch t_{0}may be it is important to emphasize that when considering interplanetary movements, especially in the analysis of movements among inner planets, the choice of the initial epoch t_{0}plays a critical role in planning the mission, because age determines the mutual position of the start and target points. If the mutual arrangement is not selected correctly, a space mission may fail.

As for the direct methods used in the calculus, it is difficult to obtain an analytical expression for the error introduced by the above procedure, and therefore it is difficult to estimate, converges if the approximation of the cost function, which is difficult to understand whether the approximate solution with the real behavior of the optimal solution. In addition, analysis of the N-dimensional tasks, such as interplanetary travel, requires a large number of integrated and coefficients, but all these efforts alone may not be sufficient to ensure satisfactory performance of the functional value due to the interdependence of all the variables in the state vector.

Another limitation affecting such methods, is that the functional value and the components of the state vector must be continuous in the area of integration. Tasks, providing an instantaneous change of the state vector, for example, the transition between coordinate systems during interplanetary travel or waste stage in the analysis of the trajectory of a rocket, can not be confident the solution of these ways.

Gradient methods OS�accepted on the definition of the gradient of the cost function through a series of evaluations of the function relative to these parameters: the better known the gradient function, the higher the probability of finding the minimum (or maximum) in the search pane. Local minima can be obtained quickly if the cost function is smooth with respect to the selected parameters; other tasks, such as estimating the trajectory of the spacecraft, differ strikingly incorrect functional value that shows in the future. Therefore, a gradient search methods may not be reliable in addressing such problems.

The methods of linear search is very simple and easy to implement. Such methods are used, for example, those who have to configure the circuit by adjusting a few parameters. First, one of the options is regulated until further improvement; then configure the other settings, unless there's some additional improvement, etc. After a single adjustment of each parameter, the process repeats by returning to the first parameter and carrying out the above operations. According to the improbable hypothesis that the parameters do not interact with each other, this procedure leads to the desired optimal configuration. The interdependence among the variables strongly influences the scope of this procedure.

Inconsistent search is made at equally spaced points in a simply connected region�and Euclidean space.
Each of the coordinates x_{i}is assigned a set of evenly spaced points, called grid points, and uses only the values x_{i}in these grid points. Then estimate the cost function for all possible combinations of grid points and the grid value of the vector x that provides the best f(x) wins. The search engine should, accordingly, choose grid spacing; with regard to the number of data points, if each coordinate of x_{i}assigned to k-spaced points, the full amount of data is k^{n}where n is the number of components in x. inconsistent Methods do not require assumptions regarding the sharpness of the changes of the state vector and function value, but the large number of assessments makes them completely ineffective.

Let us now consider two-point boundary problem and assume that the total travel time functionality is subject to minimization. The General method used to solve the two-point problem is to minimize

the extended cost function

where (r_{f}-r_{target/sub>
) is the difference between the vector end position of the spacecraft and the position vector of the target, (Vf-Vtarget) is the difference between the vector of the finite speed of the spacecraft and the target speed vector, and Yf- the angle of flight, which should be close to zero, so that the movement trajectory of the spacecraft, in the end, passed along the tangent to the target orbit at the coincidence. The coefficients of δr, δV, δγ are the tolerances, and trefmade in order to make a functional uniform. This functionality value convenient to increase the likelihood of convergence to the optimal solution under given boundary constraints. There is a problem, consisting in the fact that such a function shows two different trends that make finding an optimal solution is very difficult.}

In particular, such a function shows a smooth macroscopic trend and irregular microscopic behavior, as shown in Fig. 1 and Fig. 2, respectively.

In particular, Fig. 1 shows an example of macroscopic trend of the extended cost function

This is proof of the fact that the two-point boundary value problem is often much more difficult than expected, and the convergence to the true optimal solution is a highly unlikely event, at least according to the above-described known optimization algorithms.

OBJECTIVE AND summary of the INVENTION

The applicant conducted a thorough study to determine the feasibility of developing effective, does not require large computational cost of the method, allowing to reliably determine the optimal paths for spacecraft.

The object of the present invention is the provision of a method for determining optimal trajectories of moving spacecraft, which allows to solve the above problems of the known methods and to overcome obstacles that make known algorithms ineffective.

This problem is solved by the present invention which relates to a method of determining optimum tracking of the spacecraft; the software program containing code segments of the software for R�giving up, when it is executed, said method; software product software containing computer-readable medium on which is stored the software program; an electronic processor configured to implement said method; and space aircraft, containing the electronic processor configured to implement said method, as defined in the attached claims.

In particular, the present invention relates to a method for determining the path of movement of the spacecraft, such as spacecraft, rockets, space Shuttle, etc., from primary cosmic body to the target space body with respect to the given Central space body, with a certain trajectory is optimal in relation to the movement of the spacecraft met the requirement of a given space mission; and the method contains the stages on which:

- you provide, according to the Pontryagin maximum principle, physico-mathematical model between model values and physical quantities representing the movement of the spacecraft with respect to the given Central space body, and model the values contain the first ve�Torno-size models and second vector magnitude model the first vector value of the model is the first module, time-varying, and the first orientation in space, which varies in time and sets the first angle of longitude, time-varying, and the first elevation angle, time-varying, and the first vector magnitude model is, moment by moment, corresponding to the optimal thrust direction of the spacecraft relative to the requirements of this space mission, the second vector magnitude model has the second module, time-varying, and a second orientation in space, which varies in time and sets the second angle of longitude, time-varying, and the second elevation angle, time-varying, the second vector magnitude model is, moment by moment, the development in time of the first vector value model;

- establish, in a physico-mathematical model, initial and final boundary conditions, and initial boundary conditions are such that in the initial moment of time moving the position and velocity of the spacecraft close to the position and velocity respectively of primary cosmic body, and the final boundary conditions are such that in a finite time move the position and velocity of a space vehicle�CSOs apparatus close to the position and velocity respectively of the target space of the body;

- establish, in a physico-mathematical model, the first condition so that the second module is connected to the first module by a value related to an angular velocity depending on the given Central space body;

- establish, in a physico-mathematical model, the second condition so that the specific longitude angle, the angle between the first and longitude second angle of longitude, and a specific elevation angle, between the first elevation and the second elevation angle, don't depend on each other;

- consider first the initial time points included in this time range, the first longitude values of the specific longitude angle included in this longitude range, and the first elevation values of the specific elevation angle included in the range of elevation; and

- determine the path of the displacement of the spacecraft on the basis of the physico-mathematical model, of the considered first starting times, of the considered first longitude values, and of the considered first elevation values.

Preferably, the trajectory of the movement of the spacecraft on the basis of the physico-mathematical model, of the considered first starting times, of the considered first longitude values, and consider first the values vozvyshennostei stages, in which:

calculates the values of the cost function associated with the requirement of this space mission, and values of the cost function calculated on the basis of the considered first starting times, of the considered first longitude values, and of the considered first elevation values;

determine the approximate cost function based on the calculated values of the cost function;

calculate the approximate cost function on the basis of the considered first starting times, of the considered first longitude values, and of the considered first elevation values;

identify, among the calculated values approximate the cost function, the extreme value is approximated cost function and, among the considered first starting times, among the considered first longitude values, and among the considered first elevation values, the optimal initial time, the optimal longitude value and the optimal value of elevation, respectively, on the basis of which the calculated extreme value approximated cost function; and

determine the path of the displacement of the spacecraft on the basis of the physico-mathematical model identified optimal started�tion time identified optimal longitude value, and the identified optimal elevation values.

More preferably, the method according to the present invention additionally contains the stages on which:

- if the trajectory is determined based on the physical-mathematical model, of the considered first starting times, of the considered first longitude values, and of the considered first elevation values, does not meet the initial boundary conditions and finite boundary conditions within pre-specified tolerance,

choose the temporal sub-band based on the time range and of the identified optimal starting time,

select a subrange of longitude based on this longitude range and of the identified optimal longitude value,

choose a sub-range of elevation on the basis of this range of elevation and identified the optimal values of elevation,

consider the second initial time points included in the selected time sub-range, the second the longitude values of the specific longitude angle included in the selected sub-band of longitude, and the second elevation values of the specific elevation angle included in the selected sub-range of elevation, and

defining the trajectory of change�in termination of the spacecraft on the basis of physical-mathematical models, consider the second initial moments of time, considering the second value longitude second and consider values of elevation.

In particular, the selection of the temporary sub-band based on the time range and of the identified optimal starting time contains the stages on which:

choose the temporal sub-band, which is included in this time range, has a smaller length than the length of the time range, and centered on the identified optimal starting time.

Additionally, selecting a sub-band of longitude based on this longitude range and of the identified optimal longitude value contains the stages on which:

select a subrange of longitude, which is included in this longitude range, has a smaller length than the length of the given longitude range, and centered on the identified optimal longitude value.

In addition, the choice of sub-band elevation on the basis of this range of elevation and the identified second values of elevation contains the stages on which:

choose a sub-range of elevation, which is included in this range of elevation, has a smaller length than the length of the given range of elevation, and centered on identific�teachers the optimal value of exaltation.

Conveniently, the method according to the present invention also contain:

- if the trajectory is determined based on the physical-mathematical model, of the considered second initial moments of time, considering the second value longitude second and consider the values of elevation, does not meet the initial boundary conditions and finite boundary conditions within pre-specified tolerance, the repetition of the stages at which

choose a new temporary sub-band based on a pre-selected time sub-band and a previously identified optimal starting time,

choose a new subrange of the longitude on the basis of pre-selected sub-band of longitude, and previously identified optimal longitude value,

choose a new sub-range of elevation on the basis of pre-selected sub-band of exaltation and pre-identified optimal values of elevation,

consider new primary times included in the selected new time sub-range, the new longitude values of the specific longitude angle included in the selected new sub-band of longitude, and the new values of the specific elevation angle included in the selected new subband exalted�I, and

determine the path of the displacement of the spacecraft on the basis of the physico-mathematical model, of the considered new initial time moment, the considered new longitude values and considering the new values of elevation;

and the stage at which

- stop the repetition, if the trajectory is determined based on the physical-mathematical model, of the considered new initial time moment, the considered new longitude values and considering the new values of elevation, meets the initial boundary conditions and finite boundary conditions within pre-specified tolerance.

BRIEF description of the DRAWINGS

For a better understanding of the present invention preferred embodiments of intended to serve only as an example, but not limitation, will be described with reference to the accompanying drawings (not to scale) in which:

- Fig. 1 shows a macroscopic trend of the extended cost function subject to minimization for solving two-point boundary value problem;

- Fig. 2 shows microscopic trend of the extended cost function, shown in Fig. 1;

- Fig. 3 shows a logical block diagram of a method for determining optimal trajectories of moving spacecraft according�of the preferred embodiment of the present invention;

- Fig. 4 shows a first grid search, built to determine the optimal trajectories of moving Earth-Mars according to the method shown in Fig. 3;

- Fig. 5 shows the second grid search is built to determine the optimal trajectories of moving Earth-Mars according to the method shown in Fig. 3;

- Fig. 6 shows the second grid search is shown in Fig. 5, together with the third grid search, built to determine the optimal trajectories of moving Earth-Mars according to the method shown in Fig. 3; and

- Fig. 7 shows the optimal trajectory of the moving Earth-Mars determined according to the method shown in Fig. 3.

DETAILED DESCRIPTION of PREFERRED embodiments of the INVENTION

The following review is presented to the specialist in the art could apply and use the invention. Specialists in this field of technology can offer various modifications to the embodiments without departing from the scope of the claimed scope of the present invention. Thus, the present invention does not provide for the limitation of the presented variants of implementation, but must comply with the widest scope consistent with the principles and features disclosed in this document and specified in prila�recovery the claims.

In addition, the present invention is implemented by software that is loaded into the memory of the electronic processor and containing parts of software code for implementing, when the software program is executed by the electronic processor, a method for determining optimal trajectories of moving spacecraft, described below.

The present invention relates to an adaptive method with multiple adjustment, i.e., the algorithm for solving the so-called "two-point boundary value problem", applied to the movement trajectories of spacecraft. This way, taking into account all previous efforts to solve problems concerning the optimization of the spatial trajectory to calculate the thrust direction required to align with the boundary conditions, by minimizing this functional value, according to this power plant.

The applicant drew attention to the fact that above the extended cost function

The algorithm according to the present invention new uses various aspects of the above direct and indirect ways, plus the innovative ability adapt the search of the maximum (or minimum) according to the shape of the cost function. The algorithm according to the present invention may consist of a broad family of algorithms inconsistent factorial search because it contains the evaluation of the functional value based on enumeration of all possible combinations of a given set of parameters, ranging in proper intervals. This set of parameters represented by the initial values of the Lagrange multipliers, selected according to the Pontryagin maximum principle and the transversality conditions. This choice ensures that the necessary optimality conditions are indeed satisfied, otherwise it would be impossible to guarantee that the solution of two-point boundary value problem optimally. This approach actually is new.

In addition, the initial search area initial set of Lagrange multipliers are determined based on innovative analytical considerations put forward by the authors of the invention.

After each iteration, i.e. after iterating through all possible combinations of the initial values of the Lagrange multipliers, only one of them can be selected as the winner; others retain�Xia in the matrices together with the corresponding cost function and the development in time of the state vector. Because the search scope can be restricted by the analytical review, a single iteration leads to a suboptimal solution that is closer to the best achievable. If you need additional iteration, the previously saved data is used to generate the expansion in a series of the state vector whose coefficients depend only on the initial choice of the Lagrange multipliers. Imposing these boundary conditions, one can obtain a new set of initial values, consistent with better boundary conditions and, at the same time satisfying the optimality conditions. There is a fundamental difference between the approach of the present invention and known direct methods used in the calculus. In known direct methods, the coefficients of the state vector of expansion in the series must satisfy the optimality conditions plus the boundary conditions; the coefficients of the expansion in a series in the algorithm according to the present invention needs to satisfy only the boundary conditions, since the optimality conditions approved by the Pontryagin maximum principle, already satisfied. After finding a solution search area changed in size, and the distribution of nodes thickens around so many candidate. The adaptability of the algorithm to changes in the size of the borders on�Asti search accordingly, the ability to self-regulate the distribution of nodes around the set of candidate initial Lagrange multipliers are additional innovative aspects of the algorithm. After a small number of iterations, the optimal solution is obtained.

For a more detailed description of the present invention, Fig. 3 shows a logical block diagram of a method 10 of determining the optimal trajectory and spacecraft according to a preferred embodiment of the present invention.

In particular, as shown in Fig. 3, the method 10 includes:

- the beginning (block 11);

- provision of physical and mathematical models and the establishment of boundary conditions (block 12);

- reducing the number of degrees of freedom (block 13);

- building a grid search for each Lagrange multiplier (block 14);

- multifactorial search (block 15);

- determining an approximate expression of the extended cost function (block 16);

- check whether the found solution is within tolerance (block 17);

- if the found solution is not within tolerances (the case shown in Fig. 3 the first arrow labeled "NO"), the reduction of the search intervals (block 18); and,

- if the found solution is within the tolerances (the case shown in Fig. 3 second St�tree, marked "YES"), the end (block 19).

In the future, the above steps of the method 10 will be described on the example of interplanetary travel Earth-Mars in minimum time with propulsion low thrust (i.e. ionic shunting engine), the optimal trajectory which is determined on the basis of the method 10.

In particular, with regard to the provision of physical and mathematical models and establishing boundary conditions (unit 12), in the coordinate system xyzO, where the x-axis pointing toward the vernal equinox, the y-axis is in the Ecliptic plane, and the z axis is oriented so as to form a right-handed coordinate system, the differential equations of motion take the following form:

where used herein the notation similar to the notation of the above two-dimensional system of equations. As for the boundary conditions, suppose that at time t_{0}space vehicle leaves the sphere of influence of the Earth, and in an unspecified time t_{f}he enters the sphere of influence of Mars (it is assumed that the vectors of position and velocity of the spacecraft close to the vectors of position and velocity of the planets in this system of coordinates):

where r={x; y; z} is the position vector of the space�ski aircraft and V={u; v; w} is the velocity vector of a space flyer

apparatus.

As for the initial epoch t_{0}suppose you need to find the optimal solution in this interval the initial epoch_{f}not defined and analyzed the problem of minimal time, you must add the transversality condition H=1. In addition, you must consider the following condition is the transversality

In addition, with regard to reducing the number of degrees of freedom (block 13), according to the above, the set of Lagrange multipliers can, in principle, be sought in ℜ^{8}but this will require much time before you are satisfied with the solution. The efficiency of the algorithm according to the present invention consists also in the choice of initial search area: the better the choice, the less time is required for convergence of the algorithm.

In particular, will be described in further detailed guidance on reducing the search scope and complexity of the task.

In particular, let λ_{r}, λ_{v}represent vectors

{λ_{x}, λ_{y}, λ_{z}} and {λ_{u}, λ_{v}, λ_{w}} with�responsibly
and

Manipulating the expressions for the derivatives of the Lagrange multipliers, according to the Pontryagin maximum principle, we can prove that:

Substituting

we get:

This expression is indeed important, since it asserts that

In particular, the ratio of approved�assert,
that

Similarly, to move the Earth-Moon similar to the ratio of claims that

When the value of_{r}, ϑ_{r}and ϕ_{V}, ϑ_{V}- longitude and elevation

These four corners are the only variables that need to be defined to ensure that boundary conditions are met, and they are not completely independent from each other, since the transversality conditions also to be found.

Recall the transversality condition is:

It is important to note that the initial mass of the spacecraft is fixed, so δm=0. In addition, the magnitude of change δ, δy, δz are not independent from each other, but proportional to the velocity vector V of the spacecraft. Similarly, the magnitude of change δu, δv, δw is proportional to the gravitational acceleration$math\; display="block">-\frac{\mu}{{r}^{3}}r$. These considerations lead to the following proportions:

so only two of the four angles ϕ_{r}, ϑ_{r}ϕ_{V}, ϑ_{V}truly independent.

It is also possible to estimate the initial value of λ_{m}. As for Hamilton function, we get:

whereas, according to the transversality conditions must be fulfilled the conditions λ_{r}·V=0, λ_{v}·f=0, where f is the vector acceleration of the spacecraft. Therefore:

what gives the analytical value of the Lagrange multiplier associated with the fuel consumption.

These considerations can help narrow the search area from ℜ^{8}to the subspace in ℜ^{3}where only the initial epoch and two angles are truly independent parameters; furthermore, this subspace has a limited radius, because the range of the epoch can be set via the requirements of the mission and the angle ranges between [0;2π] (LON) or

Defining the timeframe of the search, you can perform the discretization of such intervals.

Then, as the grid search for each Lagrange multiplier (block 14), each range is divided by the distribution of nodes; the number of nodes is selected in accordance with the computer performance and the number of parameters to be determined (more than the number of nodes and parameters, the more time it takes to find the local minimum; and the number of possible combinations is equal to N^{1}where N is the number of nodes for each distribution and 1 is the number of parameters to be determined. As for the first iteration, node distribution is equidistant due to the lack of information about the macroscopic trend of the functionality (with respect to this parameter).

Fig. 4 shows a first grid search, built to determine the optimal trajectories of moving Earth-Mars according to the method 10. Fig. 4, each point shows the grid corresponds to a specified combination of the Lagrange multipliers.

The same considerations can, if necessary, to apply to determine the opt�normal starting era: according to this power plant and the mass of the spacecraft may be missing the possibility of the optimal interplanetary mission in the absence of a correct choice of mutual the location of the start and target points.

The algorithm searches for a suboptimal, bystrorastvorimae approximate solution, integrating the simplified system of equations under the hypothesis that the orbits of Earth and Mars are co-planar (two-dimensional motion):

This assumption further reduces the number of degrees of freedom, allowing you to quickly ascertain whether there is a solution.

Further, with regard to multifactorial search (block 15), the cost function is evaluated for all possible combinations of initial values of sosotojanie; the minimum value of the functional and the appropriate combination of the Lagrange multipliers are stored together with the state vector obtained at the end of the passage. This part requires the most amount of time according to the number of nodes in the mesh. Denote by$$$\left\{{\stackrel{\u2322}{\lambda}}_{i\mathrm{,0}}\right\}$$$the vector of multipliers providing minimum value of the cost function among all possible combinations.

Fig. 5 shows the second grid search is built to determine the optimal trajectories of moving Earth-Mars according to the method 10. The white circle shown in Fig. 5 indicates a combination of the angles ϕ_{r
, ϑrapplying for optimality.}

In addition, with regard to the definition of the approximate expression of the extended cost function (block 16), all the simulation performed to determine the critical shape of the cost function, can be used to construct analytical expressions approximating the cost function with respect to the initial set of parameters. The function chosen to approximate representation, change analyzed under this task. Approximate expression of the functional value allows a better assessment of the optimal solution (assuming that new candidates closer to the true optimal set of initial parameters than those obtained by multifactorial search) methods of calculus of variations.

Finally, with regard to the reduction of the search intervals (block 18), the pre-stored data is used to Refine the solution. In particular, each search interval is reduced with the factor β and is centered on the corresponding

Fig. 6 shows two grid search, built to determine the optimal trajectories of moving Earth-Mars with�line with the aforementioned method 10, left grid search is the second grid search, already shown in Fig. 5, and the right grid search grid is the third search, built with the following clarifying solution and centered around possible solutions.

In particular, Fig. 6 two white circle indicate the regulation of the grid search in the neighborhood of the solution obtained according to the aforementioned preferred embodiment of the present invention.

In addition, this method allows to take into account the macroscopic trend of the functional with respect to the given multiplier and to move to effective local minimum. Instead of considering a uniform distribution of nodes in the future will be more convenient to consider the non-linear distribution with a high concentration in the Central region of each interval, where the most likely to find the local minimum of the functional. In the described example for the i-th multiplier of the selected parabolic distribution of points, in fact, a parabolic distribution of grid nodes around the set of approximate values is the simplest method of analysis of the extended cost function in the area where you are most likely to find the optimal set of multipliers.

The whole process is repeated until then, until you are satisfied with the boundary conditions within the given to�start center and until additional improvement solutions.

Fig. 7 shows the final optimal trajectory Earth-Mars determined according to the method 10.

From the foregoing it follows that the most favorable advantages of the present invention are as follows:

1) the short time required for convergence to the optimal solution;

2) if a solution cannot be found (for example, if you incorrectly selected the launch window or if onboard fuel quantity shunting engine is not enough to move), the method according to the present invention allows to converge to the solution closest to the boundary conditions;

3) no need of input from an external operator; and

4) using a reduced set of control parameters to determine the optimal path, each control parameter is truly independent of the other, unlike the known methods.

In particular, the third advantage in the above list represents a significant step forward in comparison with well-known optimization algorithms that require the proper initial set of control parameters for convergence, because the algorithm according to the present invention determines the search scope.

In addition, implemented in software and photos�research Institute of the algorithm according to the present invention needs no fine-tuning at runtime.

All these signs together expand the scope of application of the algorithm in the direction of perturbative control, which involves re-estimation in real time (during a space mission) the optimal action, which is required whenever the actual trajectory of the spacecraft deviates from a certain optimal trajectory due to nondeterministic acceleration.

In addition, the algorithm according to the present invention allows to establish whether the solution of the optimization problem involving the trajectory of the minimum time, and to determine the decision for a limited number of iterations; this approach can even be applied to other types of trajectories, with satisfactory results.

There were no restrictive assumptions regarding state vector or cost function (continuity, differentiability, etc.). The algorithm due to its ability to change shape converges to the optimal solution even in the case of sharp change of the function value in a region of space; taking into account the conditions imposed by the Pontryagin maximum principle, the solution is assumed optimal.

Another important advantage is that the approach of the present invention allows even inexperienced uses�Vatel to solve the optimization problem, since it does not require knowledge of theoretical concepts concerning theory of optimal control. Therefore, this algorithm can use almost every, in particular, also people who have a limited understanding of cosmic dynamics.

Below is some particular embodiments of the present invention.

Option 1. Method of determining the trajectory for the movement of the spacecraft from the initial cosmic body to the target space body with respect to the given Central space body, with a certain trajectory is optimal in relation to the movement of the spacecraft met the requirement of a given space mission, the method contains the stages at which

- you provide, according to the Pontryagin maximum principle, physico-mathematical model between model values and physical quantities representing the movement of the spacecraft with respect to the given Central space body, and model the values contain the first vector value (λ_{v}) model and the second vector value (λ_{r}) model, and the first vector magnitude (λ_{v}model is the first module, time-varying, and the first orientation in space, which changes �about time and sets the first angle (φ_{
V}longitude, time-varying, and the first angle (ϑ_{V}) elevation, time-varying, and the first vector magnitude (λ_{v}) model is, moment by moment, corresponding to the optimal thrust direction of the spacecraft relative to the requirements of this space mission, the second vector magnitude (λ_{r}model has the second module, time-varying, and a second orientation in space, which varies in time and is defined by a second angle (φ_{r}} longitude, time-varying, and the second angle (ϑ_{r}) elevation, time-varying, the second vector magnitude (λ_{r}) model is, moment by moment, the development in time of the first vector value (λ_{v}model,

- establish, in a physico-mathematical model, initial and final boundary conditions, and initial boundary conditions are such that in the initial moment of time (t_{0}) move the position (r) and speed (V) of the spacecraft close to the position (r_{Earth}) and velocity (V_{Earth}), respectively, of primary cosmic body, and the final boundary conditions are such that in a finite time (t_{f}) move the position (r) and speed (V) of the spacecraft close to the position (r_{MA�sa}
) and velocity (V_{Of Mars}), respectively, of the target space of the body,

- establish, in a physico-mathematical model, the first condition so that the second module is connected to the first module by a value related to an angular velocity, depending on the given Central space body,

- establish, in a physico-mathematical model, the second condition so that the specific longitude angle between the first angle (φ_{v}longitude and the second angle (φ_{r}longitude and a specific elevation angle between the first angle (ϑ_{v}) elevation and the second angle (ϑ_{r}) elevation do not depend on each other,

- consider the first initial moments of time (t_{0}included in this time range, the first longitude values of the specific longitude angle included in this longitude range, and the first elevation values of the specific elevation angle included in the range of elevation, and

- determine the path of the displacement of the spacecraft on the basis of the physico-mathematical model, of the considered first starting times (t_{0}), of the considered first longitude values, and of the considered first elevation values.

Option 2. The method of embodiment 1, wherein determining the motion paths of the spacecraft on the basis of physico-mathematics�tion models,
consider the first initial moments of time (t_{0}), of the considered first longitude values, and of the considered first elevation values contains the stages on which:

calculates the values of the cost function

determine the approximate cost function based on the calculated values of the cost function

calculate the approximate cost function on the basis of the considered first starting times (t_{0}), of the considered first longitude values, and of the considered first elevation values,

identify, among the calculated values approximate the cost function, the extreme value of approx�irennoj cost function and,
among the considered first starting times (t_{0}), among the considered first longitude values, and among the considered first elevation values, the optimal initial time (t_{0}), the optimal longitude value and the optimal value of elevation, respectively, on the basis of which the calculated extreme value approximated cost function, and

determine the path of the displacement of the spacecraft on the basis of the physico-mathematical model identified optimal starting time (t_{0}identified optimal longitude value, and the identified optimal elevation values.

Option 3. The method of embodiment 2, wherein the identified optimal longitude value is, in the physical-mathematical model, the value of the specific longitude angle in the identified optimal starting time (t_{0}), and the identified optimal elevation value represents the physical-mathematical model, the value of the specific elevation angle in the identified optimal starting time (t_{0}).

Option 4. The method of embodiment 2 or embodiment 3, wherein the physical-mathematical model based on the Lagrange multipliers.

Option 5. A method according to Liu�WMD from options 2-4,
in which determination of the path of movement of the spacecraft on the basis of the physico-mathematical model, of the considered first starting times (t_{0}), of the considered first longitude values, and of the considered first elevation values further comprises the steps on which:

identify, among the calculated values of the cost function_{0}), among the considered first longitude values, and among the considered first elevation values, suboptimal initial time (t_{0}), sub-optimal longitude value, and a suboptimal value of elevation, respectively, on the basis of which the calculated extreme value of the cost function

Option 6. A method according to any one of options 2-5, further comprising stages on which:

- if the trajectory is determined based on the physical-mathematical model, of the considered first starting times (t_{0}), of the considered first longitude values, and of the considered first elevation values, not consistent with the initial boundary conditions and finite boundary conditions within the pre-given tolerance, choose the temporal sub-band based on the time range and of the identified optimal starting time (t_{0}),

select a subrange of longitude based on this longitude range and of the identified optimal longitude value,

choose a sub-range of elevation on the basis of this range of elevation and identified the optimal values of elevation,

consider the second initial moments of time (t_{0}) included in the selected time sub-range, the second the longitude values of the specific longitude angle included in the selected sub-band of longitude, and the second elevation values of the specific elevation angle included in the selected sub-band elevation,

determine the path of the displacement of the spacecraft on the basis of the physico-mathematical model, of the considered second initial moments of time (t_{0}), consider the second longitude values � considered second values of elevation,

the choice of the interim sub-band based on the time range and of the identified optimal starting time (t_{0}contains a stage, on which:

choose the temporal sub-band, which is included in this time range, has a smaller length than the length of the time range, and centered on the identified optimal starting time (t_{0}),

the choice of sub-band longitude based on this longitude range and of the identified optimal longitude value contains a stage, on which:

select a subrange of longitude, which is included in this longitude range, has a smaller length than the length of the given longitude range, and centered on the identified optimal longitude value,

the choice of sub-band elevation on the basis of this range of elevation and identified the optimal values of the elevation contains a stage, on which:

choose a sub-range of elevation, which is included in this range of elevation, has a smaller length than the length of the given range of elevation, and centered on the identified optimal elevation value.

Option 7. The method of embodiment 6, wherein the first initial moments of time�EIW (t_{
0}) uniformly distributed in a given time range, whereas the majority of the second initial moments of time (t_{0}) concentrated, in the selected time sub-range, around the identified optimal starting time (t_{0}); and of the considered first longitude values uniformly distributed in the given range of longitude, whereas the majority of the second longitude values are concentrated, in the selected band of longitude, around the identified optimal longitude value; and of the considered first elevation values uniformly distributed in the given range of elevation, whereas the majority of the second elevation values are concentrated, in the selected band of elevation, around the identified optimal elevation values.

Option 8. The method of embodiment 7, which consider the second initial moments of time (t_{0}) distributed, in the selected time sub-range, according to the first parabolic distribution, consider the second longitude values are distributed, in the selected band of longitude, according to the second parabolic distribution, and consider the second elevation values are distributed, in the selected band of elevation, according to the third�have a parabolic distribution.

Option 9. A method according to any of the options 6-8, further comprising:

- if the trajectory is determined based on the physical-mathematical model, of the considered second initial moments of time (t_{0}), consider the second value longitude second and consider the values of elevation, does not meet the initial boundary conditions and finite boundary conditions within pre-specified tolerance, the repetition of the stages on which:

choose a new temporary sub-band based on a pre-selected time sub-band and a previously identified optimal starting time (t_{0}),

choose a new subrange of the longitude on the basis of pre-selected sub-band of longitude, and previously identified optimal longitude value,

choose a new sub-range of elevation on the basis of pre-selected sub-band of exaltation and pre-identified optimal values of elevation,

consider new initial moments of time (t_{0}) included in the selected new time sub-range, the new longitude values of the specific longitude angle included in the selected new sub-band of longitude, and the new values of the specific elevation angle included in the selected new p�diapason elevation,
and

determine the path of the displacement of the spacecraft on the basis of the physico-mathematical model, of the considered new initial moments of time (t_{0}), of the considered new longitude values and considering the new values of elevation,

and the stage at which

- stop the repetition, if the trajectory is determined based on the physical-mathematical model, of the considered new initial moments of time (t_{0}), of the considered new longitude values and considering the new values of elevation, meets the initial boundary conditions and finite boundary conditions within pre-specified tolerance.

Variant 10. The method of embodiment 9, in which the majority of the new initial time (t_{0}) concentrated, in the selected new time sub-range, around the previously identified optimal starting time (t_{0}), most of the considered new longitude values are concentrated, in the selected new subrange longitude, around the previously identified optimal longitude value, and most consider the new values of elevation are concentrated, in the selected new sub-range of elevation, around the previously identified optimal value� exaltation.

Variant 11. The method of embodiment 10, in which the considered new second initial moments of time (t_{0}) distributed, in the selected new temporary sub-band, according to the fourth parabolic distribution of the considered new longitude values are distributed, in the selected new sub-band of longitude, according to the fifth parabolic distribution and consider the new values of elevation are distributed, in the selected new sub-range of elevation, according to the sixth parabolic distribution.

Option 12. A method according to any of the options 2-11, in which the approximate function value is determined by interpolating the calculated values of the cost function

Version 13. A method according to any of the above options, where the model values contain a scalar value (λ_{m}) the models associated with the fuel consumption of the spacecraft to move.

Option 14. The method of embodiment 13, in which the requirement of this space mission is the minimum time to move the spacecraft and in which a scalar value (λ_{m}model depends on the derivative of the mass of the space flying apparatus�the time

Option 15. A method according to any of the above options, in which figures from the Central space body is the Sun, the initial space and target space, the body is the cosmic body, the orbital rotating around the Sun, and in which the magnitude of the associated angular velocity is the angular velocity of the orbital rotation around the Sun and depends on the gravitational parameter (µ) of the Sun.

Option 16. A method according to any one of options 1 to 14, in which figures from the Central space body is the Earth, and in which the magnitude of the associated angular velocity is the angular velocity of the orbital rotation around the Earth and depends on the gravitational parameter of the Earth.

Option 17. A method according to any of the above options, in which the requirement of this space mission is a minimum fuel consumption of the spacecraft to move.

Option 18. The software program loaded in the memory of the electronic processor and containing code sections of the software to implement, when run on the electronic processor, the method according to any of the above options.

Option 19. Software product about�software, containing computer-readable medium on which is stored a software program according to embodiment 18.

Version 20. The electronic processor, configured to implement the method according to any one of options 1 through 17.

Option 21. Space vehicle containing an electronic processor configured to implement the method according to any one of options 1 through 17.

It should be understood that the present invention admits of numerous modifications and variations within the scope of the invention defined in the attached claims.

1. Method of determining the trajectory for the movement of the spacecraft from the initial cosmic body to the target space body with respect to the given Central space body, with a certain trajectory is optimal in relation to the movement of the spacecraft met the requirement of a given space mission, the method contains the stages at which

- you provide, according to the Pontryagin maximum principle, the physical-mathematical model, based on Lagrange multipliers and between model values and physical quantities representing the movement of the spacecraft with respect to the given Central space body, and model the values contain �ervay vector magnitude (λ_{
v}) model and the second vector value (λ_{r}) model, and the first vector magnitude (λ_{v}model is the first module, time-varying, and the first orientation in space, which varies in time and sets the first angle (φ_{V}longitude, time-varying, and the first angle (ϑ_{V}) elevation, time-varying, and the first vector magnitude (λ_{v}) model is, moment by moment, corresponding to the optimal thrust direction of the spacecraft relative to the requirements of this space mission, and the second vector magnitude (λ_{r}model has the second module, time-varying, and a second orientation in space, which varies in time and is defined by a second angle (φ_{r}longitude, time-varying, and the second angle (ϑ_{r}) elevation, time-varying, the second vector magnitude (λ_{r}) model is, moment by moment, the development in time of the first vector value (λ_{v}) model, with model values additionally contain a scalar value (λ_{m}) the models associated with the fuel consumption of the spacecraft for travel to and associated with said first module via the derived mass of the spacecraft at time

- establish the physico-mathematical models of the initial and final boundary conditions, and initial boundary conditions are such that in the initial moment of time (t_{0}) move the position (r) and speed (V) of the spacecraft are close respectively to the position (r_{Earth}) and velocity (V_{Earth}) primary cosmic body, and the end boundary conditions are such that in a finite time (t_{f}) move the position (r) and speed (V) of the spacecraft are close respectively to the position (r_{Of Mars}) and velocity (V_{Of Mars}) target space of the body,

- set in a physico-mathematical model of first offer so that the second module is connected to the first module by a value related to an angular velocity, depending on the given Central space body,

- set in a physico-mathematical model the second condition so that the specific longitude angle between the first angle (φ_{v}longitude and the second angle (φ_{r}longitude and a specific elevation angle between the first angle (ϑ_{v}) elevation and the second angle (ϑ_{r}) elevation do not depend on each other,

- consider the first initial moments of time (t_{0}included in this time range, the first longitude values of the specific longitude angle included in this range�he's longitude,
and the first elevation values of the specific elevation angle included in the range of elevation, and

- determine the path of the displacement of the spacecraft on the basis of the physico-mathematical model, of the considered first starting times (t_{0}), of the considered first longitude values, and of the considered first elevation values,

in this case, the trajectory of the movement of the spacecraft on the basis of the physico-mathematical model, of the considered first starting times (t_{0}), of the considered first longitude values, and of the considered first elevation values - contains the stages on which:

- calculates the values of the cost functionassociated with the requirement of this space mission, and values of the given cost functioncalculated on the basis of the considered first starting times, of the considered first longitude values, and of the considered first elevation values,

- determine the approximate cost function based on the calculated values of the cost function

- calculate the approximate cost function on the basis of the considered first starting times (t_{0}), RA�before the first longitude values, and of the considered first elevation values,

- identify among the calculated values approximate the cost function is the extreme value of the approximate function value among the considered first starting times (t_{0}), among the considered first longitude values, and among the considered first elevation values, respectively, the optimal initial time (t_{0}), the optimal longitude value and the optimal value of elevation, on the basis of which the calculated extreme value approximated cost function, and

- determine the path of the displacement of the spacecraft on the basis of the physico-mathematical model identified optimal starting time (t_{0}identified optimal longitude value, and the identified optimal elevation values.

2. A method according to claim 1, wherein the identified optimal longitude value represents the physico-mathematical model the value of the specific longitude angle in the identified optimal starting time (t_{0}), and the identified optimal elevation value represents the physico-mathematical model the value of a particular elevation angle in the identified optimal starting time (t_{0}).

3. A method according to claim 1, wherein about�the definition of a trajectory of movement of the spacecraft on the basis of physical-mathematical models,
consider the first initial moments of time (t_{0}), of the considered first longitude values, and of the considered first elevation values - additionally contains the stages at which identify among the calculated values of the cost functionthe extreme value of the function valueand among the considered first starting times (t_{0}), among the considered first longitude values, and among the considered first elevation values, respectively, suboptimal initial time (t_{0}), sub-optimal longitude value, and a suboptimal value of exaltation, on the basis of which the calculated extreme value of the cost function.

4. A method according to claim 1, further comprising stages, in which case the trajectory is determined based on the physical-mathematical model, of the considered first starting times (t_{0}), of the considered first longitude values, and of the considered first elevation values, not consistent with the initial boundary conditions and finite boundary conditions within the pre-given tolerance

- choose the temporal sub-band based on the time range and identified �optimalnogo the initial moment of time (t_{
0}),

- select a subrange of longitude based on this longitude range and of the identified optimal longitude value,

- select a sub-range of elevation on the basis of this range of elevation and identified the optimal values of elevation,

- consider the second initial moments of time (t_{0}) included in the selected time sub-range, the second the longitude values of the specific longitude angle included in the selected sub-band of longitude, and the second elevation values of the specific elevation angle included in the selected sub-band elevation,

- determine the path of the displacement of the spacecraft on the basis of the physico-mathematical model, of the considered second initial moments of time (t_{0}), consider the second value longitude second and consider the values of elevation, and

- the selection of the temporary sub-band based on the time range and of the identified optimal starting time (t_{0}contains a stage on which choose the temporal sub-band, which is included in this time range, has a smaller length than the length of the time range, and centered on the identified optimal starting time (t_{0}),

- select the subrange to�Goths based on this longitude range and of the identified optimal longitude value contains the stage,
to choose which sub-band of longitude, which is included in this longitude range, has a smaller length than the length of the given longitude range, and centered on the identified optimal longitude value,

- select the sub-band elevation on the basis of this range of elevation and identified the optimal values of elevation contains the stage at which selects the sub-range of elevation, which is included in this range of elevation, has a smaller length than the length of the given range of elevation, and centered on the identified optimal elevation value.

5. A method according to claim 4, wherein the first initial moments of time (t_{0}) uniformly distributed in a given time range, whereas the majority of the second initial moments of time (t_{0}) is concentrated in selected time sub-range around the identified optimal starting time (t_{0}), of the considered first longitude values uniformly distributed in the given range of longitude, whereas the majority of the second longitude values are concentrated in the selected band of longitude around the identified optimal longitude value, of the considered first elevation values uniformly RA�are defined in this range of elevation,
while the majority of the second elevation values are concentrated in the selected band of elevation around the identified optimal elevation values.

6. A method according to claim 5, in which the considered second initial moments of time (t_{0}) are allocated to the selected time sub-range according to the first parabolic distribution, consider the second longitude values are distributed in the selected band of longitude according to the second parabolic distribution, and consider the second elevation values are distributed in the selected band of elevation according to the third parabolic distribution.

7. A method according to claim 4, further comprising if the trajectory is determined based on the physical-mathematical model, of the considered second initial moments of time (t_{0}), consider the second value longitude second and consider values of elevation - does not meet the initial boundary conditions and finite boundary conditions within pre-specified tolerance, the repetition of the stages at which

- choose a new temporary sub-band based on a pre-selected time sub-band and a previously identified optimal starting time (t_{0}),

- choose a new�the longitude range on the basis of pre-selected sub-band of longitude, and previously identified optimal longitude value,

- choose a new sub-range of elevation on the basis of pre-selected sub-band of exaltation and pre-identified optimal values of elevation,

- consider new initial moments of time (t_{0}) included in the selected new time sub-range, the new longitude values of the specific longitude angle included in the selected new sub-band of longitude, and the new values of the specific elevation angle included in the selected new sub-range of elevation, and

- determine the path of the displacement of the spacecraft on the basis of the physico-mathematical model, of the considered new initial moments of time (t_{0}), of the considered new longitude values and considering the new values of elevation, and

stop the repetition when the trajectory is determined based on the physical-mathematical model, of the considered new initial moments of time (t_{0}), of the considered new longitude values and considering the new values of elevation, meets the initial boundary conditions and finite boundary conditions within pre-specified tolerance.

8. A method according to claim 7, in which the majority of the new initial time (t_{0}) is concentrated in selected new temporary p�Diapazon around previously identified optimal starting time (t_{
0}), most of the considered new longitude values are concentrated in selected new subrange of longitude around the previously identified optimal longitude value, and most consider the new values of elevation are concentrated in selected new sub-range of elevation around a previously identified optimal elevation values.

9. A method according to claim 8, in which the considered new second initial moments of time (t_{0}) distributed in selected new temporary sub-band according to the fourth parabolic distribution of the considered new longitude values are distributed in selected new subrange longitude according to the fifth parabolic distribution and consider the new values of elevation are distributed in selected new sub-range of elevation according to the sixth parabolic distribution.

10. A method according to claim 1, wherein the approximate cost function is determined by interpolating the calculated values of the cost function.

11. A method according to claim 1, wherein the requirement of this space mission is the minimum time to move the spacecraft.

12. A method according to claim 1, wherein the data of the Central space body is the Sun, the initial space�skim the body and target space, the body is the cosmic body, orbiting the Sun, and in which the magnitude of the associated angular velocity is the angular velocity of revolution around the Sun and depends on the gravitational parameter (µ) of the Sun.

13. A method according to claim 1, wherein the data of the Central space body is the Earth, and in which the magnitude of the associated angular velocity is the angular velocity of rotation around the Earth and depends on the gravitational parameter of the Earth.

14. A method according to claim 1, wherein the requirement of this space mission is a minimum fuel consumption of the spacecraft to move.

15. The electronic processor, configured to implement the method according to any one of claims. 1-14.

16. Space vehicle containing an electronic processor configured to implement the method according to any one of claims. 1-14.

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FIELD: radio engineering, communication.

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9 dwg

FIELD: transport.

SUBSTANCE: invention relates to space engineering, particularly, to configuration of spacecraft. Vessel is made with three vapour discharge openings. Main of them features centre for vessel central axis to cross it parallel with satellite lengthwise axis directed to satellite centre of gravity. Two extra openings feature centres for another vessel parallel axis to cross, parallel with satellite axis directed in its flight direction. Said vessel is arranged at maximum possible distance of the centre of gravity in direction parallel with said satellite lengthwise axis. Note here that vessel central axis parallel with satellite lengthwise axis is located at minimum departure therefrom. At a time, second central axis of said vessel perpendicular to the former is parallel with satellite axis directed in direction of its flight in orbit. Three vapour discharge openings of said vessel are connected via electric valves with reducer.

EFFECT: decreased weight and power consumption.

3 dwg

FIELD: transport.

SUBSTANCE: invention relates to space engineering. Shuttle tractor comprises airframe, instrumentation module with control system, engine, solar batteries, self-guidance head and garbage remote-control catcher. The latter comprises space finned harpoon, powder-charge engine, rope and casing, container with detachable cover, barrel, two-step pyro cartridge and drum with electric drive.

EFFECT: efficient catch of garbage and garbage path change.

1 cl, 7 dwg

FIELD: aircraft engineering.

SUBSTANCE: proposed system comprises one to seven satellites with communication and surveillance hardware. Said satellites are placed in elliptic orbits with critical inclination and orbit apogee in hemisphere with surveillance area with orbital period depending upon duration of solar days and quantity of system satellites.

EFFECT: decreased quantity of satellites for periodic surveillance of geographical areas at preset local time.

10 dwg

FIELD: aircraft engineering.

SUBSTANCE: invention relates to aerospace engineering and can be used in systems of artificial satellites (SAS). SAS includes at least two artificial panel-design satellites (ASP) integrated into multifunctional network (MN). ASP incorporates required equipment, data exchange and processing hardware, cells control equipment to configure cell power supply in said MN and heat tube to supply heat in MN.

EFFECT: higher reliability and efficiency.

5 cl, 6 dwg

FIELD: transport.

SUBSTANCE: set of intentions relates to space power engineering and may be used for transmission of electric power in the form of laser radiation to Earth surface and for high-accuracy measurements in space, data transfer, etc. Proposed station comprises base module 1, system of mirrors 2, laser radiation summator 3 directed to system 2 and photo converter panel 4 arranged outside of module 1. Every panel 4 consists of two types: photoelectric panels 5 and independent photo emitting panels 6. The latter are connected in chain for self-opening and arranging in closed flat zigzag-like figure. Panels 5 are mounted at the start of chain 5, 6. Note here that the first panel is connected with base module 1. Said module 1 comprises the following systems: control system 8, cooling system 11 and supply system 12. Every panel 5 is connected with supply system 12. Every independent panel 6 is composed of a carcass with Fresnel lenses are carcass end with photo converters (not shown) aligned therewith and located there above. Carcass bottom part base accommodates power accumulators, control unit of panel 6 and fiber lasers with pumping units and laser radiation summator. Aforesaid photo converters of panel 6 are electrically connected via power accumulators with pumping and control units. Summators of independent panels 6 are connected to aforesaid summator via FO 30.

EFFECT: higher efficiency and reliability, longer life and expanded operating performances.

7 cl, 13 dwg

FIELD: transport.

SUBSTANCE: invention relates to earth surface imagery means. Proposed system comprises space imagery segment 1, surface image processing and distributing segment 3 and communication segment 2. Space segment 1 consists of satellites 4, ground segment 3 comprises image processing and distributing devices 5 while communication segment transmits images from segment 1 to segment 3. Every satellite 4 is equipped with, at least, one imaging device focused to the Earth and having spatial resolution of, at least one metre. Devices 5 are connected by communication lines 8 with similar device 5 receiving images of adjacent areas of earth surface. These images when superimposed produce the picture of preset section (or the whole) earth surface. Every image processing and distributing devices 5 comprises image processing module, processed image storage and means to connect it to digital circuit (users).

EFFECT: simplified system and process.

14 cl, 5 dwg

FIELD: physics, atomic power.

SUBSTANCE: invention relates to atomic power engineering and space-rocket engineering. The spacecraft nuclear propulsion system comprises a heater - gas-cooled nuclear reactor, a cooler, a recuperative heat exchanger, a pipe system with a gaseous working medium, coaxial turbine-compressor-electric power generator, electric jet engines, an automatic control system with measurement and control means. The number of loops of the turbine-compressor-electric power generator with equal electric power is a multiple of two with opposite direction of rotation of rotors of the turbine-compressor-electric power generator in each pair, wherein the pipe system connects the output of the heater - gas-cooled nuclear reactor with the input of each turbine, and the output of the turbine with the input of the channel of the heated gaseous working medium of its recuperative heat exchanger, the output of the channel of the heated gaseous working medium of the recuperative heat exchanger with the input of its cooler, the output of the cooler with the input of its compressor, the output of the compressor with the input of the channel of the cold gaseous working medium of its recuperative heat exchanger, the output of the channel of the cold gaseous working medium of each recuperative heat exchanger with the input of the heater - gas-cooled nuclear reactor.

EFFECT: high efficiency and reliability of the spacecraft nuclear propulsion system.

19 cl, 2 dwg

FIELD: transport.

SUBSTANCE: invention relates to space engineering and can be used in carrier rockets.. Proposed rocket comprises head unit with payload, parallel separable rocket stages with multichamber engines with fuel tanks shaped to torus, tapered tail, short central body at first stage, single trough-like nozzle at second stage, bottom part composed of outer and inner cones composed by outer and inner surfaces of short central body shell and inner surface of single trough-like nozzle shell. Fuel tanks and single trough-like nozzle are arranged inside short central body between first-stage tanks.

EFFECT: decreased bottom resistance, higher specific pulse.

5 cl, 9 dwg

FIELD: transport.

SUBSTANCE: invention relates to space engineering, particularly, to astronaut operation in weightlessness. Proposed holder comprises retainer composed by wire (made of afterflow material) in non-metallic sheath, ring at retainer end in diameter comparable with sized of fingers of inflated space-suit glove, lever with opening in diameter comparable with retainer diameter.

EFFECT: higher safety of articles retention in open space.

3 dwg

FIELD: transport.

SUBSTANCE: invention relates to space engineering, particularly, to astronaut operation in weightlessness. Proposed holder comprises retainer composed by wire (made of afterflow material) in non-metallic sheath, rings at retainer end in diameter comparable with sized of fingers of inflated space-suit glove.

EFFECT: higher safety of articles retention in open space.

3 dwg

FIELD: engines and pumps.

SUBSTANCE: pulse is obtained by ejection of gasified liquid residues of unused components of rocket propellants (RP). Pulse is generated by combustion of unused components of rocket propellants (RP) on rocket gas engine combustion chamber. Volume of unused propellant residues is limited to divide a second heat carrier mass flow rate into parts, one being fed in tank section confined by the screen while another portion being fed into tank second part. Amount of fed heat carrier is defined proceeding from evaporation of residual propellant component drops. Device for withdrawal of separable carrier rocket section comprises oxidiser and propellant tanks, tank supercharging system, rocket gas engine with feed and gasification systems. It incorporates feed lines with acoustic radiators (calculated proceeding from minimum mass loses for gasification by preset amounts of propellant and pressure). Said separation screen is calculated proceeding from surface tension force.

EFFECT: reduced power consumption for gasification.

3 cl, 4 dwg

FIELD: transport.

SUBSTANCE: invention relates to space engineering and can be used for attachment and separation of cluster-configuration of carrier rocket. Proposed device comprises air operated pusher, attachment assembles and lock. Air operated pusher comprises cylinder with rod equipped with turn keys, spherical joint with ball lock and retainer piston, structural rod secured at bearing structure nearby wall second stage. Cylinder comprises extra cavity for rod pull-in.

EFFECT: higher reliability, decreased weight.

3 cl, 9 dwg

FIELD: aircraft engineering.

SUBSTANCE: invention relates to design and thermal control of spacecraft in weight of up to 100 kg launched as parallel payloads. Spacecraft unpressurised parallelepiped-like container has cellular panels (3, 4, 5) with instruments (2) installed threat. Heat from instruments (2) is uniformly distributed over said cellular panels by means of manifold heat pipes (6). Note here that instruments are stabilised thermally. Notable decrease in instrument heat release switches on the electric heaters at upper cellular panel (3). This allows a tolerable temperature of instruments to be ensured by cellular panel and heat pipes (6). Lower cellular panel (4) is directed towards the Earth and represents a radiator design. Upper and lower panels are interconnected by adjustable diagonal struts (8). Shield-vacuum heat insulation (9) is arranged at lateral faces of instrument container without cellular panel. Said insulation is arranged at screen structure secured at cellular panel, on inner side of solar battery panes (1).

EFFECT: decreased weight, enhanced performances on mini- and micro-spacecraft.

3 dwg

FIELD: transport.

SUBSTANCE: invention relates to cosmonautics and can be used for safeguarding Earth against collision with dangerous cosmic body. Moon launch missile system comprises launching table located directly on the Moon surface, thermal casing placed on launching table and having opening cover at the top, mirrored outer surface and inner surface covered with heat insulating material (teflon, polytetrafluoroethylene, polychlorotrifluoroethylene, crystalline copolymer of ethane with tetrafluoroethylene), temperature-control system with heat accumulators and heater, power source, jet-propulsion solid-fuel missile with payload of 5-9 tons and takeoff mass of 20-30 tons. The launching table in the central part has translating cover to exhaust gases during missile takeoff.

EFFECT: invention permits to improve the Earth safety against collision with dangerous cosmic body.

6 cl

FIELD: transport.

SUBSTANCE: invention relates to space engineering and can be used for increasing the radiation safety of manned spaceship crew. Spaceship comprises shuttle unit, working compartment, power plat with fuel store and adaptor stage. The latter is provided with hatches with tight covers and is arranged inside fuel tank to communicated working compartment with shuttle unit. At increased radiation level the crew moves into adapter stage to be isolated by covers.

EFFECT: higher radiation safety.

2 cl, 1 dwg

FIELD: transport.

SUBSTANCE: invention relates to aerospace engineering and can be used at lunar rocket launching complexes (LLC). Nearby LCC, on lunar surface, arranged are thermal jacket with heat accumulators, pump station, solar batteries and storage battery, thermal jacket outer surface being coated with light-reflecting film while outer surface with heat-insulation panels. Heat accumulators are filled with liquid heat carrier to half of their volume to heat its by the heat of celestial bodies at opening the covers of said thermal jacket with the help of open/close system light sensors during natural lunar day. Temperature of LCC structure elements and rocket liquid propellant components is measured during natural lunar night LCC structure elements and rocket liquid propellant components are heated by pumping liquid heat carrier heated from celestial bodies via said components and elements from charged thermal accumulators into empty thermal accumulators during the entire natural lunar night with the help of pump station pumps supplied from solar batteries or storage battery.

EFFECT: higher reliability of heating system during long-term operation of LCC.

5 cl

FIELD: rocketry and space engineering; cryogenic stages of space rockets.

SUBSTANCE: according for first version, oxidizer supply unit is shifted in transversal direction and is secured in lower point of convex part of lower head plate of oxidizer tank, thus forming additional space in inter-tank compartment in axial direction; this space is used for displacement of cruise engine together with fuel tank towards oxidizer tank. According to second version, oxidizer supply unit is secured on concave part of lower head plate of oxidizer tank. Full suction of oxidizer from tank is performed by means of passages of intake unit introduced into concave part of lower head plate of oxidizer tank and used for coupling the lower zone of oxidizer tank with oxidizer supply unit inlet.

EFFECT: improved mass characteristics due to reduction of overall dimensions in length.

2 dwg