CN112016187B - Hybrid power-based ground-near asteroid rendezvous mission orbit optimization method - Google Patents
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Abstract
The invention relates to a hybrid-based ground-near asteroid rendezvous mission orbit optimization method, which comprises the following steps of: establishing a dynamic model of a minor planet detector of the solar photovoltaic and solar photovoltaic hybrid propulsion power; an optimization method for the asteroid exploration orbit is designed based on physical planning and a Gaussian pseudo-spectral method. The invention has the advantages that: by adopting a physical programming framework, the multi-objective track optimization problem can be converted into a single-objective optimization problem reflecting the preference of a designer. An iterative optimization strategy based on a Gaussian pseudo-spectrum method can effectively solve the initial value problem of a plurality of variables in intersection orbit optimization. The multi-objective optimization simulation result shows that the hybrid power small-row detector can generate different track forms to realize minimum fuel consumption and minimum flight time. The simulation also shows that the task period of the hybrid power detector for continuously meeting the four small near-earth planets is about five years, and the task is saved by about one year and half compared with the task of completing the same meeting by the solar sail detector.
Description
Technical Field
The invention relates to the technical field of near-earth asteroid detection, in particular to a hybrid power-based method for optimizing an intersection task orbit of a near-earth asteroid detector.
Background
The detection of the asteroid in the near field is of great significance for researching the origin of the solar system, in addition, the asteroid in the near field also has the risk of colliding with the earth, and in order to remove the potential collision risk, in recent years, the detection research of the asteroid is carried out in many countries; even a plurality of continuous detection plans of the asteroids and observation tasks of the asteroids in the near field are provided, so that the knowledge of the asteroids in the near field is improved, and the collision threat to the earth is eliminated. However, the current detection aspect of the multi-planet intersection has the defects of high cost and low feasibility, so how to solve the problems existing in the multi-planet intersection by using an orbit optimization method is urgently needed.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a hybrid-based ground-near asteroid rendezvous mission orbit optimization method, which adopts a physical programming framework to convert a multi-objective optimization problem into a single-objective optimization problem reflecting the preference of a designer. An iterative optimization strategy based on a Gaussian pseudo-spectrum method can effectively solve the initial value problem of a plurality of variables in the orbit optimization.
The purpose of the invention is realized by the following technical scheme: a hybrid-based ground approaching asteroid rendezvous mission orbit optimization method comprises the following steps:
establishing a detector dynamic model based on the solar light pressure and the hybrid propulsive power generated by the solar light and the electricity;
the multi-objective optimization method based on physical planning is combined with an iterative optimization method of a Gaussian pseudo-spectral method to achieve multi-objective intersection orbit optimization, and an optimal orbit and an optimal control variable are obtained.
Further, the establishing of the hybrid power detector dynamic model through the hybrid propulsive power generated by the sunlight pressure and the sunlight electricity comprises the following steps:
according to a conversion relation
The Kepler orbit six elements [ ae i omega v ] are processed] T Conversion to MEE variable y ═ p, f, g, h, k, L] T ；
Controlling sunlight pressure and the thrust direction of sunlight electricity by adjusting the posture of the hybrid power detector, so as to define the control variable of the hybrid power detector in an RTH reference coordinate system;
the acceleration caused by the sunlight pressure is described in the RTH coordinate system as a function of the control variable of the sunlight pressure
The acceleration of the solar photovoltaic in the RTH coordinate system is described as the propulsion variable of the solar photovoltaic
Adding a quality variable to the state variable and letting X ═ y; m is]To obtain a kinetic equation
Further, the control variables of the sunlight pressure comprise a cone angle alpha and an azimuth angle delta; the propulsion variable of the sunlight comprises a thrust cone angle alpha T Azimuthal angle delta T And a thrust magnitude T.
Further, the physical programming-based multi-objective optimization method and the Gaussian pseudo-spectral method combined iterative optimization method comprise the following steps:
introducing a preference function into the physical planning of the multi-target problem to obtain a design point with optimal comprehensive target satisfaction as an optimal solution of the problem, and further converting the multi-target problem into a single-target optimization problem;
and solving a single-target optimization problem through a Gaussian pseudo-spectrum method to convert the control variable and the state variable, and optimizing the initial value of the state variable and the control ratio variable in the Gaussian pseudo-spectrum method by adopting an iterative optimization strategy of the Gaussian pseudo-spectrum method.
Further, the introducing a preference function into the physical planning of the multi-objective problem to obtain a design point with optimal comprehensive objective satisfaction as an optimal solution of the problem, and further converting the multi-objective problem into a single-objective optimization problem includes:
introducing a function of the design index into a physical planning problem as a preference function so as to reflect the preference degree of a designer to each design target;
designing various preference functions as a preference function of a design target according to the track optimization, and further obtaining an optimization model of the physical planning problem, wherein the optimization model comprises the following steps:
and optimizing the preference function, and seeking a design point with optimal comprehensive target satisfaction as an optimal solution of the physical planning problem.
Further, the types of the preference function of the design include a soft-type preference function with a smaller design index and a soft-type preference function with a larger design index.
Further, the step of solving the single-target optimization problem by the gaussian pseudo-spectrum method to perform the conversion of the control variables and the state variables comprises the following steps:
all state variables in the dynamic equation have lagrangian polynomials at N Gaussian points and initial time points
Control variable adoption
Dispersing the formula;
in the same timeDesigning a state variable x (tau) of a Gaussian point under various constraint conditions of satisfying a kinetic equation i ) And a control variable U (τ) i ) To make the performance index
And (4) minimizing, thereby converting the orbit optimization problem into a nonlinear programming problem.
Further, the plurality of constraint conditions satisfying the kinetic equation comprise constraints satisfying the kinetic equation at the assembly point, terminal state constraints, boundary constraints and process constraints.
Further, the optimization of the state and control ratio variable initial value in the gaussian pseudo-spectrum method by the iterative optimization strategy of the gaussian pseudo-spectrum method comprises:
a1, extracting the orbit parameter on the Gaussian point from the plane orbit and the estimation value as the initial value;
a2, solving an orbit optimization problem based on a Gaussian pseudo-spectrum method, and obtaining the current optimal control variable;
a3, substituting the current optimal control variable into the kinetic equation integral, judging whether the obtained intersection track meets the requirement of terminal constraint, if so, turning to the step A5, otherwise, turning to the step A4;
a4, increasing the number of distribution points by using the current optimal orbit as a new initial value, obtaining a new initial value guess through interpolation, solving the optimal orbit after increasing the number of distribution points by adopting a Gaussian pseudo-spectrum method, and then turning to the step A2;
and A5, saving the current optimal track and the control variable.
The beneficial effects of the invention are as follows: a hybrid-based ground-near asteroid rendezvous mission orbit optimization method adopts a physical planning framework, and a multi-objective optimization problem can be converted into a single-objective optimization problem reflecting the preference of a designer. An iterative optimization strategy based on a Gaussian pseudo-spectrum method can effectively solve the initial value problem of a plurality of variables in the orbit optimization. The multi-objective optimization simulation result shows that the hybrid power can generate different track forms to realize the minimum fuel consumption and the minimum flight time. Then a number of asteroid rendezvous mission plans were studied. Simulation shows that the task period of the hybrid power detector for continuously crossing four small near-earth planets is about five years, and the hybrid power detector saves about one year and half compared with a solar sail detector for completing the same crossing task. Simulation results also show that the hybrid probe can generate various forms of intersection orbits when the minor planet intersects.
Drawings
FIG. 1 is a schematic diagram of control variables of an RTH reference coordinate system;
FIG. 2 is a schematic flow chart of the optimization method of the present invention;
FIG. 3 is a diagram illustrating basic types of preference functions;
FIG. 4 is a schematic diagram illustrating the Class1-S type preference function interval division;
FIG. 5 is a schematic view of a rendezvous track;
FIG. 6 is a schematic diagram of a control variable history;
FIG. 7 is a two-dimensional intersection orbit comparison of hybrid power and solar sail power;
FIG. 8 is a schematic diagram of a three-dimensional intersection trajectory;
fig. 9 is a control variable map of the hybrid.
Detailed Description
In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, but not all the embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, as presented in the figures, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application. The invention is further described below with reference to the accompanying drawings.
Dynamic model adoption for rendezvous orbit optimizationMEE variable (Modified electronic Elements) variables which have no physical significance and are functions of Keplerian orbit six-element variables are adopted, but the method for using the variables to carry out orbit optimization design is superior to Keplerian orbit Elements because of no singularity and superior to position parameter variables of a Cartesian coordinate system because the magnitude difference of the motion variables of the Cartesian coordinate system in the orbit equation set is large, and the optimization design is not facilitated. MEE variable and Kepler orbit six elements [ ae i omega [ nu ]] T The conversion relationship is as follows:
y＝[p,f,g,h,k,L] T
wherein the content of the first and second substances,
in the formula, p, f, g, h, k and L are nonsingular orbital element variables, a is a semi-major axis of an elliptical orbit, e is an eccentricity, i is an orbit inclination angle, omega is a ascension of a rising intersection point, omega is an amplitude angle of an apogee, ν is a flat apogee angle, and p is a radius.
As shown in fig. 1, the hybrid probe acceleration comes from two parts: thrust generated by sunlight pressure and thrust generated by sunlight electricity. In the dynamic equation, the sunlight pressure model is an ideal plane, so that the thrust direction can be controlled by adjusting the posture. Meanwhile, the solar photoelectric thrust direction is also determined by the detector attitude. Thus, the hybrid probe control variables may be defined in a Radial-Transversal-h (RTH) reference coordinate system.
According to the coordinate system and the previous assumptions, the solar light pressure control variable includes two angles: cone angle α and azimuth angle δ. The solar photovoltaic propulsion variables include three: thrust cone angle alpha T Azimuthal angle delta T And a thrust magnitude T.
The acceleration due to the sunlight pressure is described in the RTH coordinate system as:
wherein m is 0 And m is the initial and current mass, beta, respectively, of the hybrid aircraft mass 0 Is the constant of the brightness coefficient of the solar sail, and takes beta in the simulation calculation 0 0.1 r is taken approximately as a distance unit of day, i.e., 1AU, and μ is the solar attraction constant.
Acceleration a generated by sunlight in RTH coordinate system T Comprises the following steps:
adding the quality variable to the state variable, and enabling X to be [ y; m ], the kinetic equation can be written as:
wherein the content of the first and second substances,
the vector b is
Wherein v is e ＝I sp g 0 Exhaust velocity, specific impulse value I sp 3200s is determined according to current engine technology.
Orbital optimization is to provide a theoretical orbit that intersects the detector and asteroid, and mathematically the problem can be described as: design the following control variables
U T ＝[α δ α T δ T T]
Fuel consumption and task time are minimized, namely:
meanwhile, a kinetic equation is satisfied, and the control variable constraint is as follows:
and terminal state variable constraints, e.g. relative position constraints
Or a relative velocity constraint.
Formula (II)
The constraints on the control variables are to take into account the smoothness of the angular variations and the direction of the acceleration produced by the solar sail as compared to the direction away from the sun. The mission planning phase considers the relative position constraint of the terminal.
In order to solve the multi-objective optimization problem with different physical meanings, the invention adopts a physical programming method to replace a weight method; the basic idea is as follows: preference functions are introduced to convert design goals of different physical significance into dimensionless satisfaction goals of the same order of magnitude. And (4) through optimizing the preference function, seeking a design point with optimal comprehensive target satisfaction as an optimal solution of the problem. Therefore, establishing a preference function is a key to the physical planning problem, which reflects the degree of preference of the designer for each design objective.
The preference function is a function of the design index, i-th design index g i Has a preference function of
The more satisfied the design criteria, the smaller the preference function value. As shown in fig. 3, the preferences for design criteria in physical planning are divided into the following four types: class 1: the smaller the design index is, the better; (ii) Class 2: the larger the design index is, the better; (iii) Class 3: the design index tends to be the best value; (iv) Class 4: the design index is best in a certain value range. Each of the above preferences is further classified into soft and hard (S, H)And (4) molding. The soft preference function means that the preference function value changes along with the design index in a feasible region, and different preference degrees of different values of the design index are reflected. For the hard preference function, the function value of the design index in the feasible domain is minimum, and the design index is only feasible.
As shown in fig. 4, in order to more specifically and flexibly reflect the preference of the designer, the physical planning divides the design target of the soft preference function into several continuous intervals with different satisfaction degrees. Taking Class1-S as an example, a certain design target is subjected to interval division:
(1) very desirable field (g) i ≤g i1 ): an acceptable range, and a target value within the range is desired;
(2) expectation domain (g) i1 ≤g i ≤g i2 ): acceptable range desired by the designer;
(3) tolerable domain (g) i2 ≤g i ≤g i3 ): an acceptable range;
(4) undesired field (g) i3 ≤g i ≤g i4 ): acceptable but undesirable ranges;
(5) very undesirable domain (g) i4 ≤g i ≤g i5 ): the target is acceptable but highly undesirable in this interval;
(6) unacceptable Domain (g) i ≥g i5 ): the target is not acceptable within this range.
Wherein g is i1 ～g i5 Is the interval endpoint value for the ith design objective given by the designer according to his preferences.
Generally, the common logarithm of the average value of the preference function of each design target is taken as a comprehensive preference function; in the orbit optimization problem of the invention, the preference functions of the design targets are only Class1-S and Class2-S, so the optimization model of the physical planning problem is as follows:
g i (x)≤g i5 (for class 1-S objective)
z jm ≤z j ≤z jM
wherein z is jm z jM To design the boundary values of the variables.
As shown in FIG. 2, after the comprehensive performance index function is obtained, the multi-objective problem is converted into a single-objective optimization problem, the single-objective optimization problem can be solved by a Gaussian pseudo-spectrum method, and the iterative optimization strategy based on the Gaussian pseudo-spectrum method is adopted to solve a large number of problems related to variable initial value guessing.
All state variables in the dynamic equation are approximated by a series of Lagrange polynomials at N Gaussian points and initial time points, so that
Wherein
For consistency, the control variables are discretized in the following format
By adopting the numerical discrete method, the continuous optimal control problem of the track optimization is converted into a nonlinear programming problem. Namely: state variable x (tau) of design Gaussian point i ) And a control variable U (τ) i ) Minimizing performance indicators
Simultaneously satisfying the constraint of the kinetic equation at the collocation point
Terminal state constraints
And boundary constraint
φ(X 0 ,t 0 ,X f ,t f )＝0
And process constraints
C(X k ,U k ,τ k ；t 0 ,t f )≤0(k＝1,…,N)
Thereby converting the orbit optimization problem into a nonlinear programming problem
s.t.g i (z)≥0,j＝1,2,…,p
h i (z)＝0,j＝1,2,…,p
The iterative optimization strategy is used for solving the problem of initial value setting of state and control ratio variables in the Gaussian pseudo-spectral method, and the basic strategy is as follows:
step I, extracting the track parameters on Gaussian points from the plane track and the estimated value as initial values;
StepII, solving the problem of track optimization based on a Gaussian pseudo-spectrum method to obtain the current optimal control variable;
StepIII, namely substituting the current optimal control variable into a kinetic equation integral to see whether the obtained intersection orbit meets the terminal precision requirement or not, and if so, turning to the V step; otherwise, go to step IV;
StepIV, namely, taking the current most-tracked track as a new initial value, increasing the number of distribution points, obtaining a new initial value guess through interpolation, solving the optimal track after increasing the number of the distribution points by adopting a Gaussian pseudo-spectral method, and then turning to the step II;
and StepV, storing the current optimal track and the control variable.
The method is simulated through a simulation experiment, and the background of a simulation example is the optimization of the intersection orbit of the asteroid. The hybrid probe starts from the earth orbit and meets a certain asteroid in the ground. Three conditions with different preferences for two optimization targets are considered in the simulation example. The example favors 1 less fuel consumption, the example 3 favors less meeting time, and the example 2 favors a compromise. Table 1 defines the preference function interval values for three simulation examples.
TABLE 1 preference function Interval endpoint values
The performance indicators and terminal constraints for the three cases of the simulation are listed in table 2. The obtained orbit is the control variable integral result. The trajectory versus control variable curves are shown in fig. 5 and 6. In fig. 5, the curves with black circles represent the earth orbit, the curves with triangles represent the minor planet orbit, and the curves with gray circles represent the transfer orbit. The first two graphs in fig. 6 are the controlled variable curves of the solar photovoltaic power, and the last three graphs are the controlled variable curves of the solar photovoltaic power.
TABLE 2 comparison of simulation calculation results
From the results of Table 2, the fuel consumption of example 1 is much less than the other two examples, which reflects exactly the designer's preference. Meanwhile, the flight time of example 3 is less than that of examples 1 and 2. The performance indexes of the simulation examples show that the result obtained by the multi-objective optimization method based on the physical planning can reflect the preference of a designer.
It can be seen from the simulation results that the track shape obtained in the example 3 is different from the track shapes obtained in the examples 1 and 2, and the crossing track of the example 3 is 2 circles. This shows that the hybrid probe is capable of forming a variety of possible intersecting track shapes. In these three examples, different numbers of intersection turns are possible.
In a simulation example for optimizing a plurality of minor planet rendezvous orbits, the result of the method is compared with the result of a solar sail detector; the kinetic equation of the solar sail vehicle is obtained by removing the acceleration term and the mass change equation of the solar photovoltaic from the hybrid equation. The asteroid access sequence in the mission plan is:
Leg1:Earth-2011 AU4
Leg2:2011AU4-2012AQ
Leg3:2012AQ-2005LC
Leg4:2005LC-Apophis
the track optimization method is the same as above, except that the set optimization goal is the shortest task time. The single target is set in order to compare the optimal trajectory of the intersection of the hybrid detector with the solar sail navigation detector. The calculated orbit is the result of the control variable integration obtained by adopting a pseudo-spectral method.
In comparing the hybrid simulation results with those of the solar sail vehicle simulation, the schedule of tasks performed by the hybrid and solar sail vehicle is shown in table 3, the time constraint of stay on the asteroid between two intersections is [20,100] days, and the task schedule of the hybrid detector is shown on the left side of table 3. The total mission time was 1773 days or 4.86 years. The track transfer time was 1698 days. The right side of table 3 is a mission schedule for a solar sail vehicle. The total mission time was 2393 days or 6.56 years, and the track transfer time was 2077 days. From the results, it can be seen that the hybrid probe saves the mission time by 1.7 years in the mission, consuming 417kg of the working fluid. As shown in fig. 7, a comparison of hybrid power versus 2-dimensional intersection orbit for a solar sail vehicle. It can be seen from the results that the hybrid detector has a shorter task time than the solar sail detector at each of the meeting phases. Particularly, in the fourth intersection stage, the shape difference between the initial track and the target track is large, the transfer track of the hybrid power detector is only one circle, and the transfer track of the solar sail detector is two circles.
TABLE 3 rendezvous task Schedule
Solar light pressure power detector of hybrid power detector
Table 4 shows characteristic parameters of the hybrid probe mission, including transit time, fuel consumption, and terminal constraints. The transfer time and fuel consumption of the fourth cross is greater than those of the other three crosses. As shown in fig. 8, the hybrid detector detects a 3-bit orbit of the task. The track of the exploration task is described more intuitively. As shown in fig. 9, the control variable curve of the hybrid indicates that the control variables meet the boundary requirements and the mission plan is feasible.
TABLE 4 characteristic parameters of hybrid mission
The sunlight pressure and sunlight-electricity hybrid power detector has the potential of being applied to the detection task of the asteroid in the near field; a multi-objective orbit optimization method adopting physical planning and iterative optimization based on a Gaussian pseudo-spectrum method is provided. With the physical programming framework, the multi-objective optimization problem can be transformed into a single-objective optimization problem that reflects the preferences of designers. An iterative optimization strategy based on a Gaussian pseudo-spectrum method can effectively solve the initial value problem of a plurality of variables in the orbit optimization.
According to simulation results, the intersection orbit forms obtained are different under the conditions that the same intersection task is heavy and the designers expect different task time and fuel consumption. At the same time, the hybrid probe can obtain more possible forms of rendezvous trajectory, such as different numbers of turns of transfer trajectory in the same rendezvous mission. Finally, a simulation result of a multi-asteroid rendezvous task shows that the hybrid power detector is more advantageous in saving task time compared with a solar sail detector, and has the potential of being applied to future asteroid detection tasks.
The foregoing is illustrative of the preferred embodiments of this invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and that various other combinations, modifications, and environments may be resorted to, falling within the scope of the concept as disclosed herein, either as described above or as apparent to those skilled in the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (3)
1. A method for optimizing an intersection task orbit of a near-earth asteroid based on hybrid power is characterized by comprising the following steps: the track optimization method comprises the following steps:
establishing a detector dynamic model for hybrid propulsion generated by sunlight pressure and sunlight electricity;
the multi-objective optimization method based on physical planning is combined with an iterative optimization method of a Gaussian pseudo-spectral method to realize multi-objective track optimization, and an optimal rendezvous track and an optimal control variable are obtained;
the establishment of the dynamic model of the hybrid propulsion power detector generated by the sunlight pressure and the sunlight electricity comprises the following steps:
according to a conversion relation
The Kepler orbit six elements [ ae i omega v ] are processed] T Conversion to MEE variable y ═ p, f, g, h, k, L] T Wherein p, f, g, h, k and L are nonsingular track element variables, a is a semi-major axis of an elliptical track, e track is eccentricity, i is a track inclination angle, omega is a ascension of a rising intersection point, omega is an amplitude angle of a near place, ν is a flat near point angle, and p is a radius;
controlling sunlight pressure and the thrust direction of sunlight electricity by adjusting the posture of the hybrid power detector, so as to define the control variable of the hybrid power detector in an RTH reference coordinate system;
the acceleration caused by the solar light pressure is described in the RTH coordinate system by the control variable of the solar light pressure as
The acceleration of the solar photovoltaic in the RTH coordinate system is described by the propulsion variable of the solar photovoltaic
Adding a quality variable to the state variable and letting X ═ y; m is]To obtain a kinetic equation
Wherein m is 0 And m represents the initial and current masses, beta, respectively, of the hybrid aircraft 0 The method comprises the steps of expressing a solar sail brightness coefficient constant, | | r | | | expresses a day-ground unit distance, and mu expresses a solar attraction constant;
the control variables of the sunlight pressure comprise a conical angle alpha and an azimuth angle delta; the propulsion variable of the sunlight comprises a thrust cone angle alpha T Azimuthal angle delta T And the magnitude of the thrust T;
the physical programming-based multi-objective optimization method combines an iterative optimization method of a Gaussian pseudo-spectral method, and comprises the following steps:
introducing a preference function into the physical planning of the multi-target problem to obtain a design point with optimal comprehensive target satisfaction as an optimal solution of the problem, and further converting the multi-target problem into a single-target optimization problem;
solving a single-target optimization problem through a Gaussian pseudo-spectrum method to carry out conversion of control variables and state variables, and optimizing the state and the control variables by adopting an iterative optimization strategy of the Gaussian pseudo-spectrum method;
the method for converting the multi-target problem into the single-target optimization problem comprises the following steps of introducing a preference function into physical planning of the multi-target problem to obtain a design point with optimal comprehensive target satisfaction as an optimal solution of the problem, and further converting the multi-target problem into the single-target optimization problem:
introducing a function of the design index into a physical planning problem as a preference function so as to reflect the preference degree of a designer to each design target;
designing various preference functions as a preference function of a design target according to the track optimization, and further obtaining an optimization target of a physical planning problem, wherein the optimization target is as follows:
optimizing the preference function, and seeking a design point with optimal comprehensive target satisfaction as an optimal solution of the physical planning problem;
the method for solving the single-target optimization problem by the Gaussian pseudo-spectrum method to carry out the conversion of the control variables and the state variables comprises the following steps:
all state variables in the dynamic equation are approximated on N Gaussian points and initial time points by adopting a column Lagrange polynomial
Control variable adoption
Discretizing a formula, wherein X (tau) represents a state variable of the hybrid detection dynamical model, X (tau) represents a discrete value of the state variable of the hybrid detection dynamical model, U (tau) represents a control variable of the hybrid detection dynamical model, and U (tau) represents a discrete value of the control variable of the hybrid detection dynamical model;
designing a state variable x (tau) of a Gaussian point under the condition of simultaneously satisfying multiple constraint conditions of a kinetic equation i ) And a control variable U (τ) i ) To make the performance index
Minimum, thereby converting the orbit optimization problem into a nonlinear programming problem;
the given of the initial values of the optimization state and the control ratio variable of the iterative optimization strategy adopting the Gaussian pseudo-spectrum method comprises the following steps:
a1, extracting the orbit parameter on the Gaussian point from the plane orbit and the estimation value as the initial value;
a2, solving an orbit optimization problem based on a Gaussian pseudo-spectrum method, and obtaining the current optimal control variable;
a3, substituting the current optimal control variable into the kinetic equation integral, judging whether the obtained intersection track meets the requirement of terminal constraint, if so, turning to the step A5, otherwise, turning to the step A4;
a4, increasing the number of distribution points by using the current optimal orbit as a new initial value, obtaining a new initial value guess through interpolation, solving the optimal orbit after increasing the number of distribution points by adopting a Gaussian pseudo-spectrum method, and then turning to the step A2;
and A5, saving the current optimal track and the control variable.
2. The hybrid-based ground approaching asteroid rendezvous mission orbit optimization method of claim 1, wherein: the types of the preference function of the design include a soft-type preference function with a smaller design index and a soft-type preference function with a larger design index.
3. The hybrid-based ground approaching asteroid rendezvous mission orbit optimization method of claim 1, wherein: the multiple constraint conditions satisfying the kinetic equation comprise constraint satisfying the kinetic equation at the assembly point, terminal state constraint, boundary constraint and process constraint.
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