CN114996841B - Optimal coplanarity transfer search method based on tangent initial value - Google Patents

Abstract

The invention discloses an optimal coplanarity transfer search method based on a tangent initial value, and relates to an optimal coplanarity transfer search method based on a tangent initial value. The invention aims to solve the problems that the existing method is limited by optimization variables, has long calculation time and low solving efficiency and is difficult to meet the large-scale track transfer requirement. The process is as follows: 1. completing initial condition setting of pulse optimization; 2. limiting the thrust direction in the velocity tangent direction, setting an optimization index as the optimal fuel, and performing global search on 2n-3 variables needing to be optimized for the optimal solution of the tangential impulse fuel by utilizing a genetic algorithm to obtain the optimal solution of the global fuel under the condition of the tangential impulse; 3. completing initialization of the fmincon algorithm; 4. and limiting the pulse direction in a track plane, setting an optimization index as the optimal fuel, and carrying out local optimization on 3n-4 optimization variables by using an fmincon algorithm to obtain the optimal local fuel solution. The invention is used in the field of spacecraft orbit transfer.

Description

An optimal coplanar transfer search method based on tangent initial value

Technical Field

The invention relates to an optimal coplanar transfer searching method based on tangent initial value.

Background Art

The orbital dynamics of spacecraft is the basic science of aerospace engineering. The orbital design of spacecraft is the key to ensure the smooth execution of spacecraft missions. Since humans entered the space age, orbital design theory has developed rapidly, and related methods and technologies have been verified by a large number of actual projects. Orbital transfer is a basic problem in orbital design, which refers to the active transfer of a spacecraft from its original orbit to its target orbit through a maneuvering process, usually taking into account design indicators such as fuel consumption, transfer time, and control accuracy.

At present, the number of satellites in orbit is increasing, and the demand for orbit design of transfer missions is increasing accordingly. This puts higher requirements on the efficiency of solving transfer missions. When solving the optimal fuel transfer orbit, the global optimal pulse transfer scheme is usually obtained based on the number of pulses required by the mission through global search algorithms such as genetic algorithms. However, the traditional method is limited by the optimization variables (3n-4 optimization variables), the calculation time is long, the solution efficiency is low, and it is difficult to cope with large-scale orbit transfer needs.

Summary of the invention

The purpose of the present invention is to solve the problems that the existing methods are limited by optimization variables (3n-4 optimization variables), have long calculation time, low solution efficiency, and are difficult to cope with large-scale orbit transfer needs, and to propose an optimal coplanar transfer search method based on tangent initial values.

An optimal coplanar transfer search method based on tangent initial value has the following specific process:

Step 1: Complete the initial condition setting for pulse optimization:

According to the initial orbit parameters of the spacecraft, the target orbit parameters and the number of pulses n required by the mission, the number of iterations and population size parameters of the genetic algorithm are set;

Step 2: Genetic algorithm is used to find the global optimal solution of tangent pulse:

Based on step 1, the thrust direction is limited to the speed tangent direction, the optimization index is set to the fuel optimality, and the genetic algorithm is used to perform a global search for the 2n-3 variables that need to be optimized for the tangent pulse fuel optimal solution, and the global fuel optimal solution under the tangent pulse condition is obtained;

Step 3: Complete the initialization of the fmincon algorithm:

The radial value of each pulse of the global optimal solution under the tangent pulse condition obtained by the genetic algorithm is set to 0 and then substituted into the fmincon algorithm as the initial guess;

Step 4: Use the fmincon algorithm to find the local optimal solution of the free direction pulse:

Based on the initial conditions given in step 1, the pulse direction is restricted to the orbital plane, the optimization index is set to fuel optimality, and the fmincon algorithm is used to perform local optimization on 3n-4 optimization variables to obtain the local fuel optimal solution under the free direction pulse condition.

The beneficial effects of the present invention are:

The present invention proposes an optimal rapid search algorithm for coplanar orbit transfer fuel based on the initial guess of tangent pulse. Tangent pulse refers to a pulse whose thrust direction is colinear with the velocity direction. It is easy to implement, highly safe, easy to solve, and has the characteristics of approximately optimal energy in engineering. The tangent direction is the thrust direction that changes the orbit energy the fastest. The algorithm searches for the global optimal solution of the tangent pulse, and utilizes the characteristics of the tangent pulse with few optimization variables (2n-3 optimization variables) and approximately optimal fuel, which effectively improves the calculation efficiency. This solution is used as the initial guess of the local optimization algorithm, and then the local optimization algorithm is used to obtain the final solution, which ensures the optimal fuel while saving calculation time.

In the present invention, the pulse is first directly limited to a tangent pulse, thereby reducing the optimization variables, and after obtaining the global optimal solution under the tangent condition, this solution is used as the initial guess of the local optimization algorithm, and then the local optimization algorithm is used to obtain the final solution. The algorithm takes advantage of the fact that the tangent pulse has few optimization variables, effectively improves the calculation efficiency, and can converge to the same set of fuel optimal solutions as the original free pulse global search method, saving calculation time, and can be used for any number of pulses.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of the optimal search algorithm for coplanar orbit transfer fuel based on tangent initial value;

FIG2 is a conventional method for solving the optimal flow chart of coplanar orbital fuel transfer;

FIG3 is a schematic diagram of the orbit transfer process;

Figure 4 is a comparison of two pulse fuels;

Figure 5 is a comparison chart of three-pulse fuels.

DETAILED DESCRIPTION

Specific implementation method 1: This implementation method is an optimal coplanar transfer search method based on tangent initial value. The specific process is as follows:

Step 1: Complete the initial condition setting for pulse optimization:

According to the initial orbit parameters of the spacecraft, the target orbit parameters and the number of pulses n required by the mission, the number of iterations and the number of populations of the genetic algorithm are set;

Step 2: Genetic algorithm is used to find the global optimal solution of tangent pulse:

Based on step 1, the thrust direction is limited to the speed tangent direction, the optimization index is set to the fuel optimality, and the genetic algorithm is used to perform a global search for the 2n-3 variables that need to be optimized for the tangent pulse fuel optimal solution, and the global fuel optimal solution under the tangent pulse condition is obtained;

Step 3: Complete the initialization of the fmincon algorithm:

According to the initial conditions such as the number of pulses, the maximum number of iterations of the fmincon algorithm, the convergence error limit and other parameters are reasonably set to ensure that the convergence accuracy meets the simulation requirements. The radial value of each pulse of the global optimal solution under the tangent pulse condition obtained by the genetic algorithm is set to 0 and then substituted into the fmincon algorithm as the initial guess; the maximum number of iterations of the fmincon algorithm can be increased, and the convergence conditions can be reasonably set to obtain the optimal solution that meets the convergence conditions;

Step 4: Use the fmincon algorithm to find the local optimal solution of the free direction pulse:

Based on the initial conditions given in step 1, the pulse direction is restricted to the orbital plane, the optimization index is set to fuel optimality, and the fmincon algorithm is used to perform local optimization on 3n-4 optimization variables to obtain the local fuel optimal solution under the free direction pulse condition.

Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the initial condition setting for pulse optimization is completed in step 1:

According to the initial orbit parameters of the spacecraft, the target orbit parameters and the number of pulses n required by the mission, the number of iterations and the number of populations of the genetic algorithm are set;

The specific process is:

The orbital parameters of the spacecraft at the initial moment are given in the J2000 geocentric inertial coordinate system. The initial orbital parameters of the spacecraft include: semi-major axis a ₀ , eccentricity e ₀ , orbital inclination i ₀ , ascending node right ascension Ω ₀ , pericenter angular distance ω ₀ ;

The target orbit parameters include: semi-major axis a _f , eccentricity e _f , orbit inclination i _f , ascending node right ascension Ω _f , pericenter angular distance ω _f ; among which, the orbit inclination and ascending node right ascension should be the same as those of the spacecraft at the initial moment, i ₀ = _if , Ω ₀ = Ω _f , that is, the initial orbit of the spacecraft and the target orbit meet the coplanar condition;

When the eccentricity of the initial orbit and the target orbit in the initial condition is large, there will be a large gap between the global optimal solution of the tangent pulse and the global optimal solution of the free direction pulse, that is, the location where the tangent pulse global optimal solution applies the pulse is not near the location where the free direction pulse global optimal solution applies the pulse. There is a certain possibility of obtaining a local optimal solution using the method of the present invention; the population size and the number of iterations of the genetic algorithm should be reasonably set to ensure convergence and convergence speed;

The dynamic models used in the whole process of the present invention are all two-body models, that is, the perturbation factors such as the non-spherical perturbation of the earth, the solar light pressure, and the atmospheric resistance are not considered;

表示r的一阶导数，

表示v的一阶导数。Where, μ represents the gravitational constant of the Earth, r and v represent the position vector and velocity vector of the spacecraft in the J2000 geocentric inertial coordinate system, respectively, and |r| represents the magnitude of the corresponding position vector;

represents the first-order derivative of r,

represents the first derivative of v.

The other steps and parameters are the same as those in the first embodiment.

Specific implementation method three: This implementation method is different from specific implementation methods one or two in that the genetic algorithm in step two solves the tangent pulse global fuel optimal solution:

Based on step 1, the thrust direction is limited to the tangential direction, the optimization index is set to the optimal fuel, and the genetic algorithm is used to perform a global search for the 2n-3 variables that need to be optimized for the tangential pulse fuel optimal solution, and the global fuel optimal solution under the tangential pulse condition is obtained;

The specific process is:

In step 2, the calculation and optimization process of fuel consumption is as follows:

Step 21: Assuming that the number of pulses is n, the number of state variables to be optimized to obtain the optimal fuel solution is at least 2n-3, and the state variables to be optimized are selected as X=[θ ₁ ,θ ₂ ,...,θ _n-1 ,Δv ₁ ,Δv ₂ ,...,Δv _n-2 ];

Among them, θ _i represents the angle between the position of the spacecraft at the time of the i-th pulse and the radial direction OX of the ascending node of the initial orbit, and the value range is [0,2π]; _Δvi is the size of the i-th pulse. Considering the speed of the earth satellite's elliptical orbit, the pulse does not need to be too large. The value range is set to [-10,10], with the same direction as the original speed direction as positive, and the unit is km/s;

Step 22: According to the initial orbital parameters [a ₀ , e ₀ , i ₀ , Ω ₀ , ω ₀ ] and the state variables to be optimized, orbital recursion can be performed. Taking the first pulse process as an example, the orbital recursion process is expressed as follows:

The six orbital elements [a ₁ ,e ₁ ,i ₁ ,Ω ₁ ,ω ₁ ,f ₁ ] of the spacecraft at θ ₁ before the first pulse is applied can be obtained from the initial orbital parameters and θ ₁ , where the first five orbital parameters are the same as the initial orbital parameters, that is, they satisfy a ₁ ＝a ₀ , e ₁ ＝e ₀ , i ₁ ＝i ₀ , Ω ₁ ＝Ω ₀ , ω ₁ ＝ω ₀ , and the true anomaly f ₁ ＝θ ₁ -ω ₁ ; the six orbital elements [a ₁ ′,e ₁ ′,i 1 ′,Ω 1 ′,ω ₁ ′ _, f ₁ ′] at θ ₁ after the first pulse is applied can be solved by the six orbital elements before the pulse is applied at θ ₁ and the pulse size _{Δv 1} ;

Step 23: It is easy to know that for the first five items of the six orbital numbers, a ₁ ′＝a ₂ , e ₁ ′＝e ₂ , i ₁ ′＝i ₂ , Ω ₁ ′＝Ω ₂ , ω ₁ ′＝ω ₂ ; f ₂ ＝θ ₂ -ω ₂ can be obtained through θ ₂ ; thus, the six orbital numbers [a ₂ ,e ₂ ,i ₂ ,Ω ₂ ,ω ₂ ,f ₂ ] before the second pulse Δv ₂ is applied can be obtained, and the six orbital numbers [a ₂ ′,e ₂ ′,i ₂ ′,Ω 2 ′,ω ₂ ′,f ₂ ′] at θ ₂ after the second pulse is applied can be solved by the six orbital numbers before the pulse is applied at θ ₂ and the pulse _{Δv 2} ;

The orbital recursion is performed in this way until the orbital parameters [a n _{- 2} ′,e _n-2 ′,i n-2 ′,Ω _n-2 ′,ω _{n -2} ′,f _{n-2 ′} ] are obtained after the pulse Δv n-2 is applied at θ n-2. Through the known orbital parameters of the target orbit [a _f ,e _f , _if ,Ω _f ,ω _f ] and θ _n-1 among the state variables to be optimized, the sizes of the last two tangent pulses Δv _n-1 and Δv _n can be obtained by using existing methods.

Therefore, there are a total of 2n-3 state variables to be optimized in the entire solution process, that is, by optimizing X=[θ ₁ ,θ ₂ ,...,θ _n-1 ,Δv ₁ ,Δv ₂ ,...,Δv _n-2 ], the optimal fuel transfer orbit under tangent pulse conditions can be solved; through the genetic algorithm, a global search is performed on the 2n-3 variables that need to be optimized to obtain the optimal fuel transfer orbit under tangent pulse conditions, and the global fuel optimal solution under tangent pulse conditions is obtained.

The other steps and parameters are the same as those in the first or second embodiment.

Specific implementation mode 4: This implementation mode is different from the specific implementation modes 1 to 3 in that in step 22, orbit recursion can be performed according to the initial orbit parameters [a ₀ , e ₀ , i ₀ , Ω ₀ , ω ₀ ] and the state variables to be optimized. Taking the first pulse process as an example, the orbit recursion process is expressed as follows:

The six orbital elements [a ₁ ,e ₁ ,i ₁ ,Ω ₁ ,ω ₁ ,f ₁ ] of the spacecraft at θ ₁ before the first pulse is applied can be obtained from the initial orbital parameters and θ ₁ , where the first five orbital parameters are the same as the initial orbital parameters, that is, they satisfy a ₁ ＝a ₀ , e ₁ ＝e ₀ , i ₁ ＝i ₀ , Ω ₁ ＝Ω ₀ , ω ₁ ＝ω ₀ , and the true anomaly f ₁ ＝θ ₁ -ω ₁ ; the six orbital elements [a ₁ ′,e ₁ ′,i 1 ′,Ω 1 ′,ω ₁ ′ _, f ₁ ′] at θ ₁ after the first pulse is applied can be solved by the six orbital elements before the pulse is applied at θ ₁ and the pulse size _{Δv 1} ;

The specific process is:

The position vector and velocity vector [r ₁ ,v ₁ ] of the spacecraft when the first pulse is applied can be expressed as

r ₁ =C ₃ (Ω ₁ )C ₁ (i ₁ )C ₃ (ω ₁ )[|r ₁ |sinf ₁ ; |r ₁ |cosf ₁ ; 0]

In the formula, C ₁ and C ₃ represent rotation matrices, and the form of the rotation matrix is:

where α represents Ω ₁ , i ₁ or ω ₁ ;

After applying pulse Δv ₁ at θ ₁ , the position vector remains unchanged, but the velocity vector changes. At this time, the position vector and velocity vector of the spacecraft [r ₁ ′,v ₁ ′] can be expressed as

r ₁ ′＝r ₁

Therefore, the position and velocity vectors r ₁ ′ and v ₁ ′ after the pulse is applied can be used to solve the six _orbital elements [a ₁ ′, e ₁ ′, i ₁ ′, Ω ₁ ′, ω ₁ ′, f ₁ ′] after the pulse Δv 1 is applied at θ ₁ .

The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

Specific implementation mode five: This implementation mode is different from specific implementation modes one to four in that, in steps two and three, it is easy to know that for the first five items of the six orbital numbers, a ₁ ′＝a ₂ , e ₁ ′＝e ₂ , i ₁ ′＝i ₂ , Ω ₁ ′＝Ω ₂ , ω ₁ ′＝ω ₂ ; f ₂ ＝θ ₂ -ω ₂ can be obtained through θ ₂ ; thus, the six orbital numbers [a ₂ ,e ₂ ,i ₂ ,Ω ₂ ,ω ₂ ,f ₂ ] before the second pulse Δv ₂ is applied can be obtained, and the six orbital numbers [a ₂ ′,e ₂ ′,i _{2 ′,Ω 2} ′,ω ₂ ′,f ₂ ′ _] at θ ₂ after the second pulse is applied can be solved by the six orbital numbers before the pulse is applied at θ ₂ and the pulse Δv ₂ ;

The orbital recursion is performed in this way until the orbital parameters [a n _{- 2} ′,e _n-2 ′,i n-2 ′,Ω _n-2 ′,ω _n-2 ′,f n- ₂ ′] after applying the pulse Δv _n-2 at θ _n-2 are obtained. The sizes Δv n-1 , Δv n of the last two tangent pulses can be obtained by using the known orbital parameters [a _f ,e _f , _if ,Ω _f ,ω _{f ]} of the target orbit and θ _{n -1} among the state variables to be optimized using the existing method.

The process is as follows:

θ＝θ _n -θ _n-1

Where θ represents the difference between the angle θ _n and the angle θ _n-1 ; λ represents the intermediate variable;

Using the relationship between the flight direction angle γ and the true anomaly angle, we can get

Where γ _j represents the flight direction angle before applying the jth pulse Δv _j , |r _j | represents the position vector size when applying the jth pulse Δv _j , and p _j represents the semi-path of the orbit;

Multiply both sides by p _n sinθ,

Arrangement available

则

make

but

表示中间变量；Where k ₁ and k ₂ represent intermediate variables,

represents an intermediate variable;

The semi-diameter and angular momentum of the transfer orbit in the process are

Thus, the magnitudes of the last two pulses Δv _n-1 and Δv _n can be obtained.

The total fuel consumption can be expressed as

The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

Specific implementation method 6: This implementation method is different from any one of specific implementation methods 1 to 5 in that the fmincon algorithm in step 4 solves the local fuel optimal solution of the free direction pulse:

Based on the initial conditions given in step 1, the pulse direction is restricted to the orbital plane, the optimization index is set to the optimal fuel, and the fmincon algorithm is used to perform local optimization on 3n-4 optimization variables to obtain the local optimal fuel solution under the free direction pulse condition;

In step 4, when the pulse directions are all in the free direction, the calculation and optimization process of fuel consumption is as follows:

Assuming that the number of pulses is n, the number of state variables to be optimized required to obtain the optimal solution is at least 3n-4, and the state variable is selected as X=[ _θ1 , _θ2 ,..., _θn , _Δvi1 , _Δvi2 ,...,Δvi _(n-2) , _Δvj1 , _Δvj2 ,..., _Δvj(n-2) ], where _θk represents the angle between the position of the spacecraft at the kth pulse and the radial direction OX of the ascending node of the initial orbit, and its value range is [0,2π]; _Δvik is the magnitude of the radial component of the kth pulse, and its value range is [-10,10]; _Δvjk is the magnitude of the circumferential component of the kth pulse, and its value range is [-10,10], with the same direction as the original velocity direction being positive, and the unit is km/s;

Similar to the tangent orbit recursion process, taking the first pulse process as an example, the position velocity vector r ₁ ′, v ₁ ′ after the pulse is applied can be recursively obtained through the initial orbit parameters and θ ₁ , Δv _i1 , Δv _j1 , so as to solve the six orbital numbers after the pulse is applied, and then f ₂ is obtained through θ _2. The six orbital numbers [a ₂ ′, e ₂ ′, i ₂ ′, Ω 2 _′ , ω 2 ′, f ₂ ′ _] at θ ₂ after the second pulse is applied can be solved through the six orbital numbers before the pulse is applied at θ ₂ and the pulse _{Δv i2} , Δv j2, and the next step of orbital recursion can be carried out;

Finally, the six orbit numbers after the n-2th pulse is applied are obtained. Given the orbital parameters of the target orbit and considering the variables to be optimized θ _n-1 , θ _n , the problem is transformed into the traditional optimal double-pulse transfer problem. The optimal double-pulse transfer can be used to obtain the analytical solutions of Δvi _(n-1) , _Δvj(n-1) , Δv _in , Δv _jn . Therefore, the whole process requires 3n-4 state variables to be optimized, that is, the total fuel consumption of the whole transfer process can be obtained.

The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

The following examples are used to verify the beneficial effects of the present invention:

Embodiment 1:

Two-pulse example

The following is a specific example of two pulses. The orbital parameters of the example are shown in Table 1:

Table 1 Orbital parameters of Example 1

The genetic algorithm sets PopulationSize to 150 and Generations to 100. The fmincon algorithm sets MaxFunEvals to 6000, MaxIter to 5000, and TolCon to 1e-6.

The simulation results are shown in Table 2:

Table 2 Simulation results of example 1

It can be seen that the method of the present invention and the traditional method converge to the same set of solutions and have a huge advantage in computational efficiency.

Three-pulse example

The following is a specific example of a set of three pulses. The orbital parameters of the example are shown in Table 3:

Table 3 Orbital parameters of Example 2

The algorithm parameter settings are the same as in Example 1. The simulation results are shown in Table 4:

Table 4 Simulation results of example 2

It can be seen that the method of the present invention and the traditional method converge to the same set of solutions and have a huge advantage in computational efficiency.

Overall effect of the method

To obtain reliable conclusions, a large number of simulation examples are carried out:

The initial orbit perigee height is a random number between 300 and 2000 km, and the target orbit perigee height is 0.3 to 3 times the initial orbit perigee height, and the multiple is a random number. The initial orbit eccentricity e ₀ and the target orbit eccentricity e _f are random numbers between 0 and 1. _{ω 0} and ω _f are random numbers between 0 and 2π. The above random numbers are uniformly distributed. 600 groups of two pulses are taken for simulation, and 250 groups of three pulses are taken for simulation. The algorithm parameter settings are the same as above.

The comparison between the traditional method and the calculation time is shown in Table 5.

Table 5 Comparison of calculation time

The fuel optimal solution obtained by the method used in the present invention is compared with the fuel optimal solution obtained by the traditional method, and the comparison results are shown in Figures 4 and 5. The percentage in the legend is the percentage of fuel consumed by the present method compared with the traditional method. Since the fuel consumed by the transfer between the two tracks is the same, for the convenience of drawing, it is assumed that e ₀ is less than e _f . The height of the vertical axis represents the number of simulation groups that meet the classification of e ₀ and e _f .

As shown in Figures 4 and 5, when the eccentricity is small, the fuel index obtained by the method used in the present invention and the traditional method is almost the same. Since earth orbit satellites are generally not designed with large eccentricity orbits, the method used in the present invention is universal.

It can be seen that a large number of examples show that the method proposed in the present invention can usually converge to the same set of solutions as the traditional method, and has an advantage of 1 to 2 orders of magnitude in calculation time.

The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims (5)

1. An optimal coplanarity transfer search method based on tangent initial values is characterized in that: the method comprises the following specific processes:

step one, finishing initial condition setting of pulse optimization:

setting iteration times and population quantity parameters of a genetic algorithm according to initial orbit parameters, target orbit parameters and pulse number n required by a task of the spacecraft;

step two, solving a tangent pulse global optimal solution by a genetic algorithm:

based on the first step, the thrust direction is limited in the speed tangential direction, optimization indexes are set as fuel optimum, 2n-3 variables needing to be optimized for the tangential pulse fuel optimum solution are searched globally by utilizing a genetic algorithm, and the global fuel optimum solution under the tangential pulse condition is obtained;

step three, completing initialization of the fmincon algorithm:

setting the radial value of the global optimal solution under the tangent pulse condition obtained by the genetic algorithm to 0, and substituting the radial value into the fmincon algorithm as an initial guess;

step four, solving the local optimal solution of the free direction pulse by using an fmincon algorithm:

limiting the pulse direction in the plane of the track according to the initial conditions given in the step one, setting optimization indexes as fuel optimization, and carrying out local optimization on 3n-4 optimization variables by using an fmincon algorithm to obtain a local fuel optimal solution under the pulse condition in the free direction;

solving the local fuel optimal solution of the free direction pulse by using an fmincon algorithm in the fourth step:

limiting the pulse direction in the plane of the track according to the initial conditions given in the step one, setting optimization indexes as fuel optimization, and carrying out local optimization on 3n-4 optimization variables by using an fmincon algorithm to obtain a local fuel optimal solution under the pulse condition in the free direction; the process is as follows:

assuming that the number of pulses is n, the state variable is selected to be X = [ theta ] ₁ ,θ ₂ ,...,θ _n ,Δv _i1 ,Δv _i2 ,...,Δv _i(n-2) ,Δv _j1 ,Δv _j2 ,...,Δv _j(n-2) ]Wherein, θ _k The included angle between the position of the spacecraft and the rise point radial direction OX of the initial orbit at the kth pulse is represented, and the value range is [0,2 pi ]]；Δv _ik Is the radial component of the kth pulse and has the value range of [ -10]，Δv _jk Is the size of the circumferential component of the kth pulse and has the value range of [ -10,10,]the direction same as the original speed direction is taken as positive, and the unit is km/s;

by initial orbit parameter and theta ₁ ，Δv _i1 ，Δv _j1 Recursion is carried out to obtain a position velocity vector r after pulse is applied ₁ ′，v ₁ ' to find out six tracks after pulse application, and then passing through theta ₂ To obtain f ₂ Disclosure of the inventionOver at theta ₂ Six number of tracks and pulse Δ v before applying pulse _i2 ,Δv _j2 Solving for second applied pulse at θ ₂ Six number of tracks [ a ] ₂ ′,e ₂ ′,i ₂ ′,Ω ₂ ′,ω ₂ ′,f ₂ ′]；

Finally, solving to obtain six tracks after the pulse is applied for the (n-2) th time, knowing the track parameters of the target track, and considering the variable theta to be optimized _n-1 ，θ _n Obtaining Δ v using optimal dipulse transfer _i(n-1) ，Δv _j(n-1) ，Δv _in ，Δv _jn So that the whole process requires 3n-4 state variables to be optimized, i.e. the total fuel consumption of the whole transfer process can be obtained

2. The optimal coplanar transition search method based on the tangent initial value as claimed in claim 1, wherein: the initial condition setting for completing the pulse optimization in the first step is as follows:

setting iteration times and population quantity parameters of a genetic algorithm according to initial orbit parameters, target orbit parameters and pulse number n required by a task of the spacecraft; the specific process is as follows:

the orbit parameters of the spacecraft at the initial moment are given under a J2000 geocentric inertial coordinate system, and the initial orbit parameters of the spacecraft comprise: semi-major axis a ₀ Eccentricity e ₀ Track inclination i ₀ The right ascension channel omega ₀ Angle distance omega from the proximal point ₀ ；

The target orbit parameters include: semi-major axis a _f Eccentricity e _f Track inclination i _f And the right ascension omega _f Angle distance omega from the proximal point _f (ii) a Where the orbital inclination and ascent intersection declination should be the same as for the spacecraft at the initial moment, i ₀ ＝i _f ，Ω ₀ ＝Ω _f I.e. the initial orbit of the spacecraft is full of the target orbitA foot coplanarity condition;

the adopted dynamic model is a two-body model, namely factors such as earth non-spherical perturbation, sunlight pressure and atmospheric resistance perturbation are not considered;

wherein mu represents the gravitational constant of the earth, r and v represent the position vector and the velocity vector of the spacecraft under the J2000 geocentric inertial coordinate system, and | r | represents the size of the position vector;

denotes the first derivative of r,. Sup.>

Representing the first derivative of v.

3. The optimal coplanar transition search method based on tangent initial value as claimed in claim 2, wherein: solving the tangent pulse global fuel optimal solution by the genetic algorithm in the step two:

based on the first step, limiting the thrust direction in the tangential direction, setting an optimization index as the optimal fuel, and performing global search on 2n-3 variables needing to be optimized for the optimal solution of the tangential impulse fuel by utilizing a genetic algorithm to obtain the optimal solution of the global fuel under the condition of the tangential impulse; the specific process is as follows:

step two, assuming that the pulse number is n, the number of state variables needing to be optimized for obtaining the fuel optimal solution is at least 2n-3, and selecting the state variable to be optimized as X = [ theta ] = ₁ ,θ ₂ ,...,θ _n-1 ,Δv ₁ ,Δv ₂ ,...,Δv _n-2 ]；

Wherein, theta _i Is shown asThe included angle between the position of the spacecraft and the rise-intersection point of the initial orbit in the radial direction OX during the i-time pulse is in the value range of [0,2 pi]；Δv _i The value range of the ith pulse is set to be [ -10,10]The direction same as the original speed direction is taken as positive, and the unit is km/s;

step two, according to the initial orbit parameter [ a ] ₀ ,e ₀ ,i ₀ ,Ω ₀ ,ω ₀ ]And carrying out track recursion on the state variable to be optimized, wherein the track recursion process is represented as follows:

from initial orbit parameters and theta ₁ It can be obtained that the spacecraft is at theta before the first pulse is applied ₁ Six number of tracks [ a ] ₁ ,e ₁ ,i ₁ ,Ω ₁ ,ω ₁ ,f ₁ ]Wherein the first five orbital parameters are the same as the initial orbital parameters, i.e. satisfy a ₁ ＝a ₀ 、e ₁ ＝e ₀ 、i ₁ ＝i ₀ 、Ω ₁ ＝Ω ₀ 、ω ₁ ＝ω ₀ True proximal angle f ₁ ＝θ ₁ -ω ₁ (ii) a By passing at theta ₁ Six tracks before applying pulse and pulse size Deltav ₁ Solving for θ after the first applied pulse ₁ Six number of tracks [ a ] ₁ ′,e ₁ ′,i ₁ ′,Ω ₁ ′,ω ₁ ′,f ₁ ′]；

Step two and step three, for the first five items of six track numbers, there is a ₁ ′＝a ₂ 、e ₁ ′＝e ₂ 、i ₁ ′＝i ₂ 、Ω ₁ ′＝Ω ₂ 、ω ₁ ′＝ω ₂ (ii) a Through theta ₂ Can find f ₂ ＝θ ₂ -ω ₂ (ii) a From which the second pulse av can be applied ₂ Six number of front tracks [ a ₂ ,e ₂ ,i ₂ ,Ω ₂ ,ω ₂ ,f ₂ ]By passing at theta ₂ Six number of tracks and pulse Δ v before applying pulse ₂ Solving for second applied pulse at θ ₂ Six number of tracks [ a ] ₂ ′,e ₂ ′,i ₂ ′,Ω ₂ ′,ω ₂ ′,f ₂ ′]；

Until obtaining at theta _n-2 To apply a pulse Δ v _n-2 Rear orbital parameter [ a _n-2 ′,e _n-2 ′,i _n-2 ′,Ω _n-2 ′,ω _n-2 ′,f _n-2 ′]By knowing the orbital parameters of the target orbit [ a ] _f ,e _f ,i _f ,Ω _f ,ω _f ]And theta in the state variable to be optimized _n-1 The magnitude Deltav of the last two tangent pulses is obtained _n-1 ，Δv _n 。

4. The optimal coplanar transition search method based on the tangent initial value as claimed in claim 3, wherein: in the second step, the initial orbit parameter [ a ] is used as the basis ₀ ,e ₀ ,i ₀ ,Ω ₀ ,ω ₀ ]And the state variables to be optimized can be subjected to track recursion, and the track recursion process is expressed as follows:

from initial orbit parameters and theta ₁ The first time before pulse is applied can be obtained that the spacecraft is at theta ₁ Six number of tracks [ a ] ₁ ,e ₁ ,i ₁ ,Ω ₁ ,ω ₁ ,f ₁ ]Wherein the first five orbital parameters are the same as the initial orbital parameters, i.e. satisfy a ₁ ＝a ₀ 、e ₁ ＝e ₀ 、i ₁ ＝i ₀ 、Ω ₁ ＝Ω ₀ 、ω ₁ ＝ω ₀ True proximal angle f ₁ ＝θ ₁ -ω ₁ (ii) a By passing at theta ₁ Six tracks before pulse application and pulse size Δ v ₁ Solving for theta after the first applied pulse ₁ Six number of tracks [ a ] ₁ ′,e ₁ ′,i ₁ ′,Ω ₁ ′,ω ₁ ′,f ₁ ′]；

The specific process is as follows:

position and velocity vectors r of the spacecraft on the first pulse application ₁ ,v ₁ ]Can be expressed as

r ₁ ＝C ₃ (Ω ₁ )C ₁ (i ₁ )C ₃ (ω ₁ )[|r ₁ |sinf ₁ ；|r ₁ |cosf ₁ ；0]

In the formula, C ₁ 、C ₃ Representing a rotation matrix of the form:

at theta ₁ To apply a pulse Δ v ₁ Then, the position vector is not changed, the speed vector is changed, and the position vector and the speed vector [ r ] of the spacecraft are changed at the moment ₁ ′,v ₁ ′]Can be expressed as

r ₁ ′＝r ₁

So that the position and velocity vector r after the pulse is applied can be used ₁ ′，v ₁ Solving at θ ₁ To apply a pulse Δ v ₁ Six number of rear tracks [ a ] ₁ ′,e ₁ ′,i ₁ ′,Ω ₁ ′,ω ₁ ′,f ₁ ′]。

5. The optimal coplanar transition search method based on tangent initial value as claimed in claim 4, wherein: in the second step and the third step, the first five items of six orbits are known to have a ₁ ′＝a ₂ 、e ₁ ′＝e ₂ 、i ₁ ′＝i ₂ 、Ω ₁ ′＝Ω ₂ 、ω ₁ ′＝ω ₂ (ii) a Through theta ₂ Can find f ₂ ＝θ ₂ -ω ₂ (ii) a From which the second pulse av can be applied ₂ Six number of front tracks [ a ₂ ,e ₂ ,i ₂ ,Ω ₂ ,ω ₂ ,f ₂ ]By at θ ₂ Six number of tracks and pulse Δ v before applying pulse ₂ Solving for θ after second pulse application ₂ Six number of tracks [ a ] ₂ ′,e ₂ ′,i ₂ ′,Ω ₂ ′,ω ₂ ′,f ₂ ′]；

Until obtaining at theta _n-2 To apply a pulse Δ v _n-2 Rear orbital parameter [ a ] _n-2 ′,e _n-2 ′,i _n-2 ′,Ω _n-2 ′,ω _n-2 ′,f _n-2 ′]By knowing the orbital parameters of the target orbit [ a ] _f ,e _f ,i _f ,Ω _f ,ω _f ]And theta in the state variable to be optimized _n-1 The magnitude Deltav of the last two tangent pulses is obtained _n-1 ，Δv _n ；

The process is as follows:

θ＝θ _n -θ _n-1

in which theta represents theta _n Angle of included angle and theta _n-1 The difference of the included angles; λ represents an intermediate variable;

the relationship between the flight direction angle gamma and the true approach point angle can be used to obtain

In the formula of gamma _j Indicating the application of the j-th pulse av _j Front flight direction angle, | r _j L denotes the application of the jth pulse Δ v _j Position vector magnitude of time, p _j Representing the radius of the track;

multiplication of both sides by p _n sinθ，

Can be obtained by finishing

Order to

Then->

In the formula k ₁ 、k ₂ The intermediate variable is represented by a number of variables,

representing an intermediate variable;

the transfer orbit has a radius and an angular momentum of

The magnitude Deltav of the last two pulses can thus be determined _n-1 ，Δv _n

The total fuel consumption can be expressed as

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