CN116203835A - Spacecraft orbit chase-escaping game method based on pulse thrust - Google Patents

Spacecraft orbit chase-escaping game method based on pulse thrust Download PDF

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CN116203835A
CN116203835A CN202211008682.1A CN202211008682A CN116203835A CN 116203835 A CN116203835 A CN 116203835A CN 202211008682 A CN202211008682 A CN 202211008682A CN 116203835 A CN116203835 A CN 116203835A
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党朝辉
肖余之
康志宇
唐生勇
卫国宁
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Northwestern Polytechnical University
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Abstract

The invention provides a spacecraft orbit chase-escaping game method based on pulse thrust, which converts an original extremely-small and extremely-large optimization problem into a double-layer optimization problem by establishing a spacecraft pulse orbit chase-escaping game model, and further adopts a genetic algorithm with global optimizing capability and a mode searching algorithm with rapid convergence characteristic to jointly solve the problem, thereby obviously improving the solving efficiency of the problem, effectively solving the problem of space game by combining a pulse control mode with the spacecraft pulse orbit chase-escaping game model, and laying a theoretical foundation for realizing engineering applications such as space fault spacecraft take-over, space fault spacecraft cleaning and the like.

Description

Spacecraft orbit chase-escaping game method based on pulse thrust
Technical Field
The invention relates to the technical field of aerospace, in particular to a spacecraft orbit chase escaping game method based on pulse thrust, which is used for completing space non-cooperative target chase and threat avoidance tasks with game countermeasure property under the pulse thrust.
Background
Spacecraft orbit chase escaping is a mathematical problem with a wide application background, and is an important implementation step in typical scenes such as space non-cooperative target intersection, space rolling target safe approach, space fault spacecraft on-orbit service and the like. The classical track-following problem is commonly modeled by adopting a continuous force control mode, and is further solved by adopting a differential countermeasure method. However, in the on-orbit movement process of the spacecraft, the existing continuous control cannot be applied to the pulse control problem, but the pulse control is commonly found in the aerospace problem, but does not widely occur in the aerospace game problem, the orbit chase escaping model based on the pulse speed increment control mode is very few, and the corresponding solving method is not clear, so that the aerospace game problem under the pulse control greatly limits the development of the space non-cooperative task based on the pulse control.
Disclosure of Invention
Aiming at the problem that the aerospace game cannot be solved through pulse control in the prior art, the invention provides a spacecraft orbit chase-escaping game method based on pulse thrust.
The invention is realized by the following technical scheme:
a spacecraft orbit chase escaping game method based on pulse thrust comprises the following steps:
step 1, establishing a spacecraft pulse orbit chase escaping game model under the action of pulse thrust;
step 2, acquiring parameter information of the spacecraft chase flight, inputting the parameter information into a spacecraft pulse orbit chase flight game model, and performing inner-outer double-layer optimization on the spacecraft pulse orbit chase flight game model to finish a spacecraft orbit chase flight game.
Preferably, the calculation formula of the spacecraft pulse orbit chase-escaping game model is as follows:
Figure SMS_1
wherein J represents a bilateral optimization index of the chase-escaping game; p represents the subscript of the tracking star; e represents the subscript of the escape star; n represents the total number of pulse speed increment control; x is X P Representing state vectors of tracked satellites, particularlyIs X P ＝[x P ,y P ,z P ,v Px ,v Py ,v Pz ] T ；X E State vector representing escape star, in particular X E ＝[x E ,y E ,z E ,v Ex ,v Ey ,v Ez ] T ；t 0 Indicating the initial moment of the escape; t is t f The terminal moment of the occurrence of the chase back is represented; t is t i The time when each satellite applies pulse rate increment control, i=1, 2, …,5; x represents a radial position component of the track under a relative coordinate system (LVLH system); y represents a position component of the flying direction in the relative coordinate system (LVLH system); z represents a position component of the orbital angular momentum direction in the relative coordinate system (LVLH system); v x Representing the radial velocity component of the track in the relative coordinate system (LVLH system); v y A velocity component representing the direction of orbital flight in a relative coordinate system (LVLH system); v z A velocity component representing the orbital angular momentum direction in the relative coordinate system (LVLH system); deltav P (t i ) In the specific form of Deltav P (t i )＝[Δv Px (t i ),Δv Py (t i ),Δv Pz (t i )] T Representing the tracking star at t i Pulse speed increment control applied at the moment; deltav E (t i ) In the specific form of Deltav E (t i )＝[Δv Ex (t i ),Δv Ey (t i ),Δv Ez (t i )] T Indicating that the escape star is at t i Pulse speed increment control applied at the moment; deltaV P Column vectors formed by pulse speed increment control at all moments of the tracking star are represented; deltaV E Column vectors formed by pulse speed increment control at all moments of escape satellites are represented; psi phi type P (ΔV P ) Representing a constraint function for tracking the increment control of the star pulse speed; psi phi type E (ΔV E ) A constraint function for expressing the escape star pulse speed increment control; s 2 Representing a three-dimensional real vector
Figure SMS_2
2 norms of (2), i.e.)>
Figure SMS_3
Further, the constraint function psi of tracking star pulse speed increment control P (ΔV P ) And a constraint function psi for escape star pulse velocity increment control E (ΔV E ) Modeling is carried out according to the actual maneuvering capability condition of the spacecraft, wherein the actual maneuvering capability condition of the spacecraft comprises the upper limit constraint of a control component of a single pulse speed increment, the upper limit constraint of a control size of the single pulse speed increment, the same size of the single pulse speed increment, and the upper limit of total consumption of the free direction and the pulse speed increment.
Further, there is an upper limit constraint on the control component of the single pulse velocity increment, specifically in the form of:
Figure SMS_4
wherein ,ΔvPxmax -tracking the maximum value of the star single pulse velocity increment in the x-direction;
Δv Pymax -tracking the maximum value of the star single pulse velocity increment in the y-direction;
Δv Pzmax -tracking the maximum value of the star single pulse velocity increment in the z-direction;
Δv Exmax -maximum value of escape star single pulse velocity increment in x direction;
Δv Eymax -maximum value of escape star single pulse velocity increment in y direction;
Δv Ezmax -maximum value of escape star single pulse velocity increment in z direction;
there is an upper limit constraint on the control size of the single pulse velocity increment, and the specific form is as follows:
Figure SMS_5
wherein ：ΔvPmax -tracking the maximum value of the star single pulse speed increment size;
Δv Emax -maximum value of the escape star single pulse speed increment size;
the single pulse speed increment is the same in size and free in direction, and the specific form is as follows:
Figure SMS_6
wherein ：ΔvPmax -tracking the maximum value of the star single pulse speed increment size;
Δv Emax -maximum value of the escape star single pulse speed increment size;
α P (t i ) -tracking pitch angle of the star single pulse velocity increment;
β P (t i ) -tracking the yaw angle of the star single pulse speed increment;
α E (t i ) -pitch angle of escape star single pulse velocity increment;
β E (t i ) -escaping a yaw angle of the star single pulse speed increment;
there is an upper limit on the total consumption of pulse rate increments, in the specific form:
Figure SMS_7
or (b)
Figure SMS_8
wherein ：ΔVPmax -tracking total reserve of star pulse speed increments; deltaV Emax -escape of total reserve of star pulse rate increment.
Preferably, the parameter information of the chase game includes a chase starting time t 0 And terminal time t f The method comprises the steps of carrying out a first treatment on the surface of the N times of pulse application time t 1 ,t 2 ,…,t N The method comprises the steps of carrying out a first treatment on the surface of the Reference satellite orbit semi-major axis a; tracking star initial state X P (t 0 ) The method comprises the steps of carrying out a first treatment on the surface of the Escape star initial state X E (t 0 ) The method comprises the steps of carrying out a first treatment on the surface of the Pulse velocity increment upper limit Deltav of tracking star Pmax The method comprises the steps of carrying out a first treatment on the surface of the Pulse velocity increment upper limit Deltav of escape star Emax 。
Preferably, the calculation formula for performing inner and outer double-layer optimization by the spacecraft pulse orbit chase-escaping game model is as follows:
Figure SMS_9
Figure SMS_10
Figure SMS_11
s.t.G(ΔV P ,ΔV E )≤0
wherein ,
Figure SMS_12
representing an outer layer optimization problem, < >>
Figure SMS_13
Representing an inner layer optimization problem; g (DeltaV) P ,ΔV E ) And less than or equal to 0, integrating all constraints in the spacecraft pulse orbit chase game model into one formalized expression.
Furthermore, the outer layer optimization is carried out on the spacecraft pulse orbit chase game model by adopting a genetic algorithm GA, and the inner layer optimization is carried out by adopting a genetic algorithm mixed mode search algorithm PG.
Further, the specific steps of optimizing the inner layer and the outer layer are as follows:
s1, determining specific parameters of a genetic algorithm GA solver, wherein the specific parameters comprise a population scale L, an evolution algebra D, a crossover coefficient C and a mutation coefficient K; and objective function is performed
Figure SMS_14
As a function of fitness;
s2, regarding independent variable DeltaV P Corresponding sequelaeTransmission algorithm chromosome
Figure SMS_15
Initializing
S3, for each given chromosome
Figure SMS_16
Solving an inner layer optimization problem based on a PGA algorithm to obtain an optimal delta V E Marked as->
Figure SMS_17
Then calculate its objective function value, i.e.>
Figure SMS_18
S4, evaluating chromosome individual by using the objective function value
Figure SMS_19
And for all chromosomes
Figure SMS_20
Performing selection, crossover and mutation operations to generate new population and current optimal result
Figure SMS_21
S5, judging the output result, if the output result does not reach the evolution algebra or other conditions for stopping the GA algorithm, returning to the S3, solving the inner layer optimization problem according to the PGA algorithm, and recalculating the objective function value; otherwise, outputting the individual with the largest fitness in the current result as the optimal solution
Figure SMS_22
Simultaneously marking the corresponding inner layer optimization optimal solution +.>
Figure SMS_23
Will->
Figure SMS_24
Outputting Nash equilibrium solution used as chase-flight game to finish spacecraft orbit chase-flight game。
Furthermore, the specific steps for solving the inner layer optimization problem by the PGA algorithm are as follows:
s31, searching through a genetic algorithm GA to obtain the DeltaV E Is an approximate optimum value of (a)
Figure SMS_25
S32, by
Figure SMS_26
For initial value, a better optimal value is obtained by adopting a mode search algorithm PA
Figure SMS_27
And calculates the objective function value thereof, i.e. +.>
Figure SMS_28
Compared with the prior art, the invention has the following beneficial technical effects:
the invention provides a spacecraft orbit chase-escaping game method based on pulse thrust, which converts an original extremely-small and extremely-large optimization problem into a double-layer optimization problem by establishing a spacecraft pulse orbit chase-escaping game model, and further adopts a genetic algorithm with global optimizing capability and a mode searching algorithm with rapid convergence characteristic to jointly solve the problem, thereby obviously improving the solving efficiency of the problem, effectively solving the problem of space game by combining a pulse control mode with the spacecraft pulse orbit chase-escaping game model, and laying a theoretical foundation for realizing engineering applications such as space fault spacecraft take-over, space fault spacecraft cleaning and the like.
Drawings
FIG. 1 is a flow chart of a spacecraft orbit chase game method based on pulse thrust in the invention;
FIG. 2 is a spacecraft orbit tracking scene based on pulse velocity increment control to which the present invention is applicable;
FIG. 3 is a schematic diagram of a three-dimensional trajectory of a spacecraft chase under 5 pulse velocity increment control in the present invention;
FIG. 4 is a schematic diagram of a two-dimensional trajectory of a spacecraft chase under 5 pulse velocity delta control in the present invention;
FIG. 5 is a graph showing the relative distance change of the chase of a spacecraft under 5 pulse velocity increment control in the present invention;
FIG. 6 is a schematic diagram of a two-dimensional motion trajectory of a chaser approaching an escaping party gradually assuming the escaping party is stationary;
FIG. 7 is a diagram showing the relative distance between the chaser and the escapement provided that the escapement is stationary;
Detailed Description
In order that those skilled in the art will better understand the present invention, a technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and the claims of the present invention and the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the invention described herein may be implemented in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The invention is described in further detail below with reference to the attached drawing figures:
the invention provides a spacecraft orbit chase escaping game method based on pulse thrust, which can effectively solve the problem of the chase escaping of a spacecraft under the action of the pulse thrust and is an effective expansion of a continuous thrust chase escaping game model and a continuous thrust chase escaping game method in the prior art
Specifically, as shown in fig. 1, the pulse thrust-based spacecraft orbit tracking game method comprises the following steps:
step 1, establishing a spacecraft pulse orbit chase escaping game model;
specifically, the calculation formula of the spacecraft pulse orbit chase-escaping game model is as follows:
Figure SMS_29
wherein J represents a bilateral optimization index of the chase-escaping game; p represents the subscript of the tracking star; e represents the subscript of the escape star; n represents the total number of pulse speed increment control; x is X P Representing a state vector of a tracking star, in particular X P ＝[x P ,y P ,z P ,v Px ,v Py ,v Pz ] T ；X E State vector representing escape star, in particular X E ＝[x E ,y E ,z E ,v Ex ,v Ey ,v Ez ] T ；t 0 Indicating the initial moment of the escape; t is t f The terminal moment of the occurrence of the chase back is represented; t is t i The time when each satellite applies pulse rate increment control, i=1, 2, …,5; x represents a radial position component of the track under a relative coordinate system (LVLH system); y represents a position component of the flying direction in the relative coordinate system (LVLH system); z represents a position component of the orbital angular momentum direction in the relative coordinate system (LVLH system); v x Representing the radial velocity component of the track in the relative coordinate system (LVLH system); v y A velocity component representing the direction of orbital flight in a relative coordinate system (LVLH system); v z A velocity component representing the orbital angular momentum direction in the relative coordinate system (LVLH system); deltav P (t i ) In the specific form of Deltav P (t i )＝[Δv Px (t i ),Δv Py (t i ),Δv Pz (t i )] T Representing the tracking star at t i Pulse velocity applied at timeIncremental control; deltav E (t i ) In the specific form of Deltav E (t i )＝[Δv Ex (t i ),Δv Ey (t i ),Δv Ez (t i )] T Indicating that the escape star is at t i Pulse speed increment control applied at the moment; deltaV P Column vectors formed by pulse speed increment control at all moments of the tracking star are represented; deltaV E Column vectors formed by pulse speed increment control at all moments of escape satellites are represented; psi phi type P (ΔV P ) Representing a constraint function for tracking the increment control of the star pulse speed; psi phi type E (ΔV E ) A constraint function for expressing the escape star pulse speed increment control; s 2 Representing a three-dimensional real vector
Figure SMS_30
2 norms of (2), i.e.)>
Figure SMS_31
Wherein: matrix array
Figure SMS_32
The method meets the following conditions:
M＝[I 3×3 ,0 3×3 ]；B＝[0 3×3 ,I 3×3 ] T (2)
in the formula ：
Figure SMS_33
wherein the state transition matrix Φ (t j ,t i ) For implementing the slave t i From time to t j The state transition at the moment is constructed by a CW equation in orbit dynamics, namely:
Figure SMS_34
wherein Δt＝tj -t i ，
Figure SMS_35
The orbital angular velocity of the reference satellite is represented, μ is the earth gravitational field coefficient, and a is the orbit semi-major axis of the reference satellite.
Constraint function psi for tracking star pulse speed increment control P (ΔV P ) And a constraint function psi for escape star pulse velocity increment control E (ΔV E ) Modeling according to the actual maneuvering capability condition of the spacecraft, wherein the actual maneuvering capability condition of the spacecraft comprises upper limit constraint of a control component of a single pulse speed increment, upper limit constraint of a control size of the single pulse speed increment, same size of the single pulse speed increment, freedom in direction and upper limit of total consumption of the pulse speed increment;
wherein, the control component of the single pulse speed increment has an upper limit constraint, and the specific form is as follows:
Figure SMS_36
wherein ,ΔvPxmax -tracking the maximum value of the star single pulse velocity increment in the x-direction;
Δv Pymax -tracking the maximum value of the star single pulse velocity increment in the y-direction;
Δv Pzmax -tracking the maximum value of the star single pulse velocity increment in the z-direction;
Δv Exmax -maximum value of escape star single pulse velocity increment in x direction;
Δv Eymax -maximum value of escape star single pulse velocity increment in y direction;
Δv Ezmax -maximum value of escape star single pulse velocity increment in z direction;
there is an upper limit constraint on the control size of the single pulse velocity increment, and the specific form is as follows:
Figure SMS_37
wherein ：ΔvPmax -tracking star billMaximum value of the secondary pulse velocity increment size;
Δv Emax -maximum value of the escape star single pulse speed increment size;
the single pulse speed increment is the same in size and free in direction, and the specific form is as follows:
Figure SMS_38
wherein ：ΔvPmax -tracking the maximum value of the star single pulse speed increment size;
Δv Emax -maximum value of the escape star single pulse speed increment size;
α P (t i ) -tracking pitch angle of the star single pulse velocity increment;
β P (t i ) -tracking the yaw angle of the star single pulse speed increment;
α E (t i ) -pitch angle of escape star single pulse velocity increment;
β E (t i ) -escaping a yaw angle of the star single pulse speed increment;
there is an upper limit on the total consumption of pulse rate increments, in the specific form:
Figure SMS_39
or:
Figure SMS_40
wherein ：ΔVPmax -tracking total reserve of star pulse speed increments; deltaV Emax -escape of total reserve of star pulse rate increment.
Equation (8) is the same as equation (5) in that there is a limit to pulse rate increment of the thruster of the spacecraft in three directions, except that equation (5) defines the magnitude of the single thrust output and equation (8) defines the magnitude of the total thrust output. Note that equation (5) and equation (8) may also be used in combination, indicating that there are constraints on both single output and total output.
Similarly, the case of equation (9) is the same as equation (6), and there is a limit to the pulse velocity increment of the thruster of the spacecraft in the vector direction, except that equation (6) defines the magnitude of the single thrust output, and equation (9) defines the magnitude of the total thrust output. Equation (6) and equation (9) may also be used in combination to indicate that there are constraints on both single output and total output.
And 2, acquiring parameter information of the chase-after game, inputting the parameter information into a spacecraft pulse orbit chase-after game model, and performing inner-outer double-layer optimization on the spacecraft pulse orbit chase-after game model to finish the spacecraft orbit chase-after game.
Specifically, the parameter information of the chase game includes the chase starting time t 0 And terminal time t f The method comprises the steps of carrying out a first treatment on the surface of the N times of pulse application time t 1 ,t 2 ,…,t N The method comprises the steps of carrying out a first treatment on the surface of the Reference satellite orbit semi-major axis a; tracking star initial state X P (t 0 ) The method comprises the steps of carrying out a first treatment on the surface of the Escape star initial state X E (t 0 ) The method comprises the steps of carrying out a first treatment on the surface of the Pulse velocity increment upper limit Deltav of tracking star Pmax The method comprises the steps of carrying out a first treatment on the surface of the Pulse velocity increment upper limit Deltav of escape star Emax 。
Specifically, the calculation formula for performing the inner and outer double-layer optimization according to the spacecraft pulse orbit chase-escaping game model is as follows:
Figure SMS_41
wherein ,
Figure SMS_42
representing an outer layer optimization problem, < >>
Figure SMS_43
Representing an inner layer optimization problem; g (DeltaV) P ,ΔV E ) And less than or equal to 0, integrating all constraints in the spacecraft pulse orbit chase game model into one formalized expression.
Specifically, the outer layer optimization is carried out on the spacecraft pulse orbit chase game model by adopting a genetic algorithm GA, and the inner layer optimization is carried out by adopting a genetic algorithm mixed mode search algorithm PG, and the specific steps are as follows:
s1, determining specific parameters of a genetic algorithm GA solver, wherein the specific parameters comprise a population scale L, an evolution algebra D, a crossover coefficient C and a mutation coefficient K; and objective function is performed
Figure SMS_44
As a function of fitness;
s2, regarding independent variable DeltaV P Chromosome of corresponding genetic algorithm
Figure SMS_45
Initializing
S3, for each given chromosome
Figure SMS_46
Solving an inner layer optimization problem based on a PGA algorithm to obtain an optimal delta V E Marked as->
Figure SMS_47
Then calculate its objective function value, i.e.>
Figure SMS_48
S4, evaluating chromosome individual by using the objective function value
Figure SMS_49
And for all chromosomes
Figure SMS_50
Performing selection, crossover and mutation operations to generate new population and current optimal result
Figure SMS_51
S5, judging the output result, if the output result does not reach the evolution algebra or other conditions for stopping the GA algorithm, returning to S3, solving the inner layer optimization problem according to the PGA algorithm, and recalculating the objective functionA value; otherwise, outputting the individual with the largest fitness in the current result as the optimal solution
Figure SMS_52
Simultaneously marking the corresponding inner layer optimization optimal solution +.>
Figure SMS_53
Will->
Figure SMS_54
Figure SMS_55
And outputting Nash equilibrium solutions serving as the chase-escaping game to finish the spacecraft orbit chase-escaping game.
The specific steps for solving the inner layer optimization problem by the PGA algorithm are as follows:
s31, searching through a genetic algorithm GA to obtain the DeltaV E Is an approximate optimum value of (a)
Figure SMS_56
S32, by
Figure SMS_57
For initial value, a better optimal value is obtained by adopting a mode search algorithm PA
Figure SMS_58
And calculates the objective function value thereof, i.e. +.>
Figure SMS_59
Examples
Let it be assumed that at some initial time t 0 In the vicinity of a circular orbit having an orbit height of 500km (corresponding to orbit semi-major axis a= 6878.137 km), there are 2 satellites, namely, a chase star P and an escape star E, respectively, whose initial states are shown in table 1. The process of both sides performing escape by pulse thrust is shown in fig. 2. The current escape task requires that the following star be at t f As close as possible to the escape star after =1 hour. Assume that both apply n=5 pulse rate increment control and that pulse is appliedThe inscriptions are uniformly distributed, i.e.: t is t 1 ＝0，t 2 ＝12min，……，t 5 =48 min. It is assumed that there is an upper limit constraint on the control component of the single pulse velocity increment where the chase star does not exceed 10m/s and the escape star does not exceed 1m/s.
j x j (t 0 ) y j (t 0 ) z j (t 0 ) v xj (t 0 ) v yj (t 0 ) v zj (t 0 )
P 0 100 0 0 0 0
E 0 0 0 0 0 0
TABLE 1 initial relative position velocity (km, km/s) of the chase star P and escape star E
Based on the above conditions, specific application steps of the present invention are given below.
1. Firstly, according to the invention step 1, a spacecraft pulse orbit chase-escaping game model under the problem parameters is established as follows:
Figure SMS_60
wherein: matrix array
Figure SMS_61
The method meets the following conditions:
M＝[I 3×3 ,0 3×3 ]，B＝[0 3×3 ,I 3×3 ] T
in the formula ：
Figure SMS_62
wherein the state transition matrix Φ (t j ,t i ) For implementing the slave t i From time to t j The state transition at the moment is constructed by a CW equation in orbit dynamics, namely:
Figure SMS_63
wherein Δt＝tj -t i ，
Figure SMS_64
The orbital angular velocity of the reference satellite is represented, μ is the earth gravitational field coefficient, a= 6878.137km is the orbit semi-major axis of the reference satellite.
Wherein J represents a bilateral optimization index of the chase-escaping game; p tableShowing a subscript of the tracking star; e represents the subscript of the escape star; n represents the total number of pulse speed increment control, and N is 5 in the example; x is X P Representing a state vector of a tracking star, in particular X P ＝[x P ,y P ,z P ,v Px ,v Py ,v Pz ] T ；X E State vector representing escape star, in particular X E ＝[x E ,y E ,z E ,v Ex ,v Ey ,v Ez ] T ；t 0 Indicating the initial moment of the escape; t is t f The terminal moment of the occurrence of the chase back is represented; t is t i The time when each satellite applies pulse rate increment control, i=1, 2, …,5; x represents a radial position component of the track under a relative coordinate system (LVLH system); y represents a position component of the flying direction in the relative coordinate system (LVLH system); z represents a position component of the orbital angular momentum direction in the relative coordinate system (LVLH system); v x Representing the radial velocity component of the track in the relative coordinate system (LVLH system); v y A velocity component representing the direction of orbital flight in a relative coordinate system (LVLH system); v z A velocity component representing the orbital angular momentum direction in the relative coordinate system (LVLH system); deltav P (t i ) In the specific form of Deltav P (t i )＝[Δv Px (t i ),Δv Py (t i ),Δv Pz (t i )] T Representing the tracking star at t i Pulse speed increment control applied at the moment; deltav E (t i ) In the specific form of Deltav E (t i )＝[Δv Ex (t i ),Δv Ey (t i ),Δv Ez (t i )] T Indicating that the escape star is at t i Pulse speed increment control applied at the moment; deltaV P Column vectors formed by pulse speed increment control at all moments of the tracking star are represented; deltaV E Column vectors formed by pulse speed increment control at all moments of escape satellites are represented; psi phi type P (ΔV P ) Representing a constraint function for tracking the increment control of the star pulse speed; psi phi type E (ΔV E ) A constraint function for expressing the escape star pulse speed increment control; s 2 Representing a three-dimensional real vector
Figure SMS_65
2 norms of (2), i.e.)>
Figure SMS_66
2. Then according to the invention step 2, the pulse velocity increment control constraint psi in the escape model P (ΔV P )、ψ E (ΔV E ) The upper limit constraint condition exists in the control component conforming to the single pulse speed increment, specifically:
Figure SMS_67
3. and then, according to the step 3 of the invention, developing the solving of the escape game problem, wherein the specific solving steps are as follows:
s1, inputting relevant parameters of the chase-escaping game, wherein the relevant parameters comprise: time t of flight initiation 0 =0 and terminal time t f =3600 s; time t of 5 pulse application 1 ＝0，t 2 ＝12min，……，t 5 =48 min; reference satellite orbit semi-major axis a= 6878.137km; tracking star initial state X P (t 0 ) The method comprises the steps of carrying out a first treatment on the surface of the Escape star initial state X E (t 0 ) As shown in table 1; single pulse velocity increment component maximum value Deltav of rear-end collision star Pxmax ＝Δv Pymax ＝Δv Pzmax =10m/s, escape star single pulse velocity increment component maximum Δv Exmax ＝Δv Eymax ＝Δv Ezmax ＝1m/s。
S2, a calculation formula for performing inner-outer double-layer optimization by the spacecraft pulse orbit chase-escaping game model is as follows:
Figure SMS_68
Figure SMS_69
Figure SMS_70
s.t.G(ΔV P ,ΔV E )≤0
wherein ,
Figure SMS_71
representing an outer layer optimization problem, < >>
Figure SMS_72
Representing an inner layer optimization problem; g (DeltaV) P ,ΔV E ) And less than or equal to 0, integrating all constraints in the spacecraft pulse orbit chase game model into one formalized expression.
S3, solving the outer layer optimization problem by adopting a Genetic Algorithm (GA), and solving the inner layer optimization problem by adopting a genetic algorithm mixed mode search algorithm (PGA), wherein the outer layer optimization based on the GA comprises the following specific steps:
s31, determining specific parameters of GA solvers such as population size l=10, evolution algebra d=10, crossover coefficient c=0.8, mutation coefficient k=0.2, and the like, and determining an objective function J (Δv P ,ΔV E ) As a function of fitness;
s32, initializing the independent variable DeltaV P Chromosome of corresponding genetic algorithm
Figure SMS_73
S33, for each given chromosome
Figure SMS_74
Solving an inner layer optimization problem based on a PGA algorithm to obtain an optimal delta V E Marked as->
Figure SMS_75
Then calculate its objective function value, i.e.>
Figure SMS_76
Specifically, the solution process using the PGA algorithm can be divided into 2 sub-steps:
s331, searching by GA algorithm to obtain DeltaV E Is an approximate optimum value of (a)
Figure SMS_77
S332, further to
Figure SMS_78
For initial value, a mode search algorithm (PA) is adopted to obtain a better optimal value
Figure SMS_79
And calculates the objective function value thereof, i.e. +.>
Figure SMS_80
S34, evaluating the chromosome individual by using the function value
Figure SMS_81
And for all chromosomes
Figure SMS_82
Performing selection, crossover and mutation operations to generate new population (outer optimization) and current optimal result +.>
Figure SMS_83
S35, if the evolution algebra is not reached or other conditions of GA algorithm termination do not appear, returning to S33; otherwise, outputting the individual with the largest fitness in the current result as the optimal solution
Figure SMS_84
Simultaneously marking the corresponding inner layer optimization optimal solution +.>
Figure SMS_85
Will->
Figure SMS_86
And outputting the Nash equilibrium solution as the chase game. />
Figure SMS_87
The specific calculation results of (2) are shown in tables 2 and 3.
Figure SMS_88
/>
Figure SMS_89
TABLE 2 calculation of 5 pulse speed increment (m/s) for the chase star P and escape star E
And according to the pulse velocity increment calculation results of the two game parties obtained in the table 2, deducing and evolving the motion of the tracking spacecraft and the escape spacecraft, and obtaining the results shown in fig. 3-5. Wherein, figure 3 shows the respective motion trail and motion direction of the chase spacecraft and the escape spacecraft in the three-dimensional relative motion space; FIG. 4 shows a schematic representation of the motion trajectories and motion directions of the escape spacecraft and the chase spacecraft on an xoy plane, respectively; fig. 5 shows the time-dependent distance profile of both sides of the chase.
Figure SMS_90
/>
Figure SMS_91
TABLE 3 calculation of 5 pulse speed increment (m/s) for the chase star when escape star E is stationary
And according to the pulse velocity increment calculation results of the two game parties obtained in the table 3, deducing and evolving the motion of the tracking spacecraft and the escape spacecraft, and obtaining the results shown in fig. 6-7. FIG. 6 is a schematic illustration of the trajectory and direction of motion of a tracking spacecraft and an escape spacecraft on an xoy plane; fig. 7 shows the evolution of the distance between the two sides of the chase over time.
In summary, the invention provides a spacecraft orbit chase-escaping game method based on pulse thrust, which converts an original minimum and maximum optimization problem into a double-layer optimization problem by establishing a spacecraft orbit chase-escaping game model, and further adopts a genetic algorithm with global optimization capability and a mode search algorithm with rapid convergence characteristic to jointly solve, thereby remarkably improving the solving efficiency of the problem, effectively solving the problem of space game by combining a pulse control mode with the spacecraft orbit chase-escaping game model, and laying a theoretical foundation for the realization of engineering applications such as space fault spacecraft takeover, space failure spacecraft cleaning and the like. The optimization index is described by adopting the inter-star distance of the terminal time, the optimization variable is the pulse speed increment of both chase and flight sides at a fixed time interval, the state transition constraint is described by adopting a state transition matrix under a relative motion model, and the pulse motor capability constraint is modeled by adopting the pulse speed increment, the pulse direction and the total consumption. Then, a solving method of the min max optimizing problem is established, and the model also adopts a state transition matrix, so that the evolution calculation of dynamics is simple and convenient; and the model solving adopts a double-layer optimization structure, so that the difficulty of directly solving the min max problem is avoided, and the overall searching and rapid convergence capacity of the problem is improved by further combining a genetic algorithm and a mode searching algorithm.
Finally, it should be noted that: the above embodiments are only for illustrating the technical aspects of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: modifications and equivalents may be made to the specific embodiments of the invention without departing from the spirit and scope of the invention, which is intended to be covered by the claims.

Claims (9)

1. The spacecraft orbit tracking and escaping game method based on the pulse thrust is characterized by comprising the following steps of:
step 1, establishing a spacecraft pulse orbit chase escaping game model under the action of pulse thrust;
step 2, acquiring parameter information of the spacecraft chase flight, inputting the parameter information into a spacecraft pulse orbit chase flight game model, and performing inner-outer double-layer optimization on the spacecraft pulse orbit chase flight game model to finish a spacecraft orbit chase flight game.
2. The spacecraft orbit tracking game method based on pulse thrust according to claim 1, wherein the calculation formula of the spacecraft pulse orbit tracking game model is as follows:
Figure FDA0003810051460000011
Figure FDA0003810051460000012
wherein J represents a bilateral optimization index of the chase-escaping game; p represents the subscript of the tracking star; e represents the subscript of the escape star; n represents the total number of pulse speed increment control; x is X P Representing a state vector of a tracking star, in particular X P ＝[x P ,y P ,z P ,v Px ,v Py ,v Pz ] T ；X E State vector representing escape star, in particular X E ＝[x E ,y E ,z E ,v Ex ,v Ey ,v Ez ] T ；t 0 Indicating the initial moment of the escape; t is t f The terminal moment of the occurrence of the chase back is represented; t is t i The time when each satellite applies pulse rate increment control, i=1, 2, …,5; x represents a radial position component of the track under a relative coordinate system (LVLH system); y represents a position component of the flying direction in the relative coordinate system (LVLH system); z represents a position component of the orbital angular momentum direction in the relative coordinate system (LVLH system); v x Representing the radial velocity component of the track in the relative coordinate system (LVLH system); v y A velocity component representing the direction of orbital flight in a relative coordinate system (LVLH system); v z A velocity component representing the orbital angular momentum direction in the relative coordinate system (LVLH system); deltav P (t i ) In the specific form of Deltav P (t i )＝[Δv Px (t i ),Δv Py (t i ),Δv Pz (t i )] T Representing the tracking star at t i Pulse speed increment control applied at the moment; deltav E (t i ) In the specific form of Deltav E (t i )＝[Δv Ex (t i ),Δv Ey (t i ),Δv Ez (t i )] T Indicating that the escape star is at t i Pulse speed increment control applied at the moment; deltaV P Column vectors formed by pulse speed increment control at all moments of the tracking star are represented; deltaV E Column vectors formed by pulse speed increment control at all moments of escape satellites are represented; psi phi type P (ΔV P ) Representing a constraint function for tracking the increment control of the star pulse speed; psi phi type E (ΔV E ) A constraint function for expressing the escape star pulse speed increment control; s 2 Representing a three-dimensional real vector
Figure FDA0003810051460000021
2 norms of (2), i.e.)>
Figure FDA0003810051460000022
3. The pulse thrust based spacecraft orbit tracking game method according to claim 2, wherein the constraint function ψ of the incremental control of the tracking star pulse velocity is P (ΔV P ) And a constraint function psi for escape star pulse velocity increment control E (ΔV E ) Modeling is carried out according to the actual maneuvering capability condition of the spacecraft, wherein the actual maneuvering capability condition of the spacecraft comprises the upper limit constraint of a control component of a single pulse speed increment, the upper limit constraint of a control size of the single pulse speed increment, the same size of the single pulse speed increment, and the upper limit of total consumption of the free direction and the pulse speed increment.
4. The spacecraft orbit tracking game method based on pulse thrust according to claim 3, wherein the control component of the single pulse velocity increment has an upper limit constraint, and the specific form is as follows:
Figure FDA0003810051460000023
wherein ,ΔvPxmax -tracking the maximum value of the star single pulse velocity increment in the x-direction;
Δv Pymax -tracking the maximum value of the star single pulse velocity increment in the y-direction;
Δv Pzmax -tracking the maximum value of the star single pulse velocity increment in the z-direction;
Δv Exmax -maximum value of escape star single pulse velocity increment in x direction;
Δv Eymax -maximum value of escape star single pulse velocity increment in y direction;
Δv Ezmax -maximum value of escape star single pulse velocity increment in z direction;
there is an upper limit constraint on the control size of the single pulse velocity increment, and the specific form is as follows:
Figure FDA0003810051460000031
wherein ：ΔvPmax -tracking the maximum value of the star single pulse speed increment size;
Δv Emax -maximum value of the escape star single pulse speed increment size;
the single pulse speed increment is the same in size and free in direction, and the specific form is as follows:
Figure FDA0003810051460000032
wherein ：ΔvPmax -tracking the maximum value of the star single pulse speed increment size;
Δv Emax -maximum value of the escape star single pulse speed increment size;
α P (t i ) -tracking pitch angle of the star single pulse velocity increment;
β P (t i ) -tracking the yaw angle of the star single pulse speed increment;
α E (t i ) -pitch angle of escape star single pulse velocity increment;
β E (t i ) -escaping a yaw angle of the star single pulse speed increment;
there is an upper limit on the total consumption of pulse rate increments, in the specific form:
Figure FDA0003810051460000041
or->
Figure FDA0003810051460000042
wherein ：ΔVPmax -tracking total reserve of star pulse speed increments; deltaV Emax -escape of total reserve of star pulse rate increment.
5. The pulse thrust based spacecraft orbit chase flight game method according to claim 1, wherein the parameter information of the chase flight game comprises chase flight start time t 0 And terminal time t f The method comprises the steps of carrying out a first treatment on the surface of the N times of pulse application time t 1 ,t 2 ,…,t N The method comprises the steps of carrying out a first treatment on the surface of the Reference satellite orbit semi-major axis a; tracking star initial state X P (t 0 ) The method comprises the steps of carrying out a first treatment on the surface of the Escape star initial state X E (t 0 ) The method comprises the steps of carrying out a first treatment on the surface of the Pulse velocity increment upper limit Deltav of tracking star Pmax The method comprises the steps of carrying out a first treatment on the surface of the Pulse velocity increment upper limit Deltav of escape star Emax 。
6. The spacecraft orbit chase flight game method based on pulse thrust according to claim 1, wherein the calculation formula of the spacecraft orbit chase flight game model for inner and outer double-layer optimization is as follows:
Figure FDA0003810051460000043
Figure FDA0003810051460000044
Figure FDA0003810051460000045
s.t.G(ΔV P ,ΔV E )≤0
wherein ,
Figure FDA0003810051460000046
representing an outer layer optimization problem, < >>
Figure FDA0003810051460000047
Representing an inner layer optimization problem; g (DeltaV) P ,ΔV E ) And less than or equal to 0, integrating all constraints in the spacecraft pulse orbit chase game model into one formalized expression.
7. The pulse thrust-based spacecraft orbit chase flight game method according to claim 6, wherein the spacecraft pulse orbit chase flight game model is subjected to outer layer optimization by adopting a genetic algorithm GA, and is subjected to inner layer optimization by adopting a genetic algorithm mixed mode search algorithm PG.
8. The spacecraft orbit chase flight game method based on pulse thrust as claimed in claim 7, wherein the specific steps of inner and outer layer optimization are as follows:
s1, determining specific parameters of a genetic algorithm GA solver, wherein the specific parameters comprise a population scale L, an evolution algebra D, a crossover coefficient C and a mutation coefficient K; and objective function is performed
Figure FDA0003810051460000051
As a function of fitness;
s2, regarding independent variable DeltaV P Corresponding toChromosome of genetic algorithm of (a)
Figure FDA0003810051460000052
Initializing
S3, for each given chromosome
Figure FDA0003810051460000053
Solving an inner layer optimization problem based on a PGA algorithm to obtain an optimal delta V E Is recorded as
Figure FDA0003810051460000054
Then calculate its objective function value, i.e.>
Figure FDA0003810051460000055
/>
S4, evaluating chromosome individual by using the objective function value
Figure FDA0003810051460000056
And +.about.all chromosomes->
Figure FDA0003810051460000057
Performing selection, crossover and mutation operations to generate new population and current optimal result ∈ ->
Figure FDA0003810051460000058
S5, judging the output result, if the output result does not reach the evolution algebra or other conditions for stopping the GA algorithm, returning to the S3, solving the inner layer optimization problem according to the PGA algorithm, and recalculating the objective function value; otherwise, outputting the individual with the largest fitness in the current result as the optimal solution
Figure FDA0003810051460000059
Simultaneously marking the corresponding inner layer optimized optimal solution
Figure FDA00038100514600000510
Will->
Figure FDA00038100514600000511
And outputting Nash equilibrium solutions serving as the chase-escaping game to finish the spacecraft orbit chase-escaping game.
9. The spacecraft orbit chase flight game method based on pulse thrust as claimed in claim 8, wherein the specific steps of solving the inner layer optimization problem by the PGA algorithm are as follows:
s31, searching through a genetic algorithm GA to obtain the DeltaV E Is an approximate optimum value of (a)
Figure FDA00038100514600000512
S32, by
Figure FDA0003810051460000061
For initial value, a better optimal value is obtained by adopting a mode search algorithm PA
Figure FDA0003810051460000062
And calculates the objective function value thereof, i.e. +.>
Figure FDA0003810051460000063
/>
CN202211008682.1A 2022-08-22 2022-08-22 Spacecraft orbit chase-escaping game method based on pulse thrust Pending CN116203835A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116750211B (en) * 2023-07-13 2024-01-23 四川大学 Tracking defense method based on tracking target distribution and track planning
CN117485595A (en) * 2023-11-21 2024-02-02 北京易动宇航科技有限公司 Energy management method for electric propulsion system

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116750211B (en) * 2023-07-13 2024-01-23 四川大学 Tracking defense method based on tracking target distribution and track planning
CN117485595A (en) * 2023-11-21 2024-02-02 北京易动宇航科技有限公司 Energy management method for electric propulsion system
CN117485595B (en) * 2023-11-21 2024-04-05 北京易动宇航科技有限公司 Energy management method for electric propulsion system

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