A control method for frontlight grabbing position orbit game based on genetic algorithm

Abstract

The present invention relates to the field of game control of space vehicles, in particular to an optimal control algorithm considering information delay and impulsive control. It discloses a sunlight-facing position-grabbing orbit game control method based on a genetic algorithm. The established model of the sunlight-facing position-grabbing orbit game takes into account this new game form of sunlight-facing position-grabbing, as well as the information delay of both parties and the maneuvers of both parties are in the form of impulsive maneuvers, which conforms to the real space scenario. At the same time, the optimal control solution method based on the genetic algorithm proposed by the present invention can ensure the optimality of the system performance. The present invention can quickly and efficiently give the optimal impulsive control sequence of the participants in the sunlight-facing position-grabbing orbit game scenario.

Description

Technical Field

[0001] The present invention relates to the field of space vehicle game control, and particularly to an optimal control algorithm considering information delay and impulse control, specifically a sunward position seizure orbit game control method based on a genetic algorithm. Background Art

[0002] With the rapid development of spacecraft rendezvous and docking technology, traditional cooperative rendezvous control methods have become relatively mature. Currently and for some time to come, for the game problems of non-cooperative targets, such as approaching and operating on out-of-control, failed spacecraft and space debris, etc., will be an important research direction in the field of spacecraft control. The spacecraft game problem mainly refers to the spacecraft pursuit-evasion problem at the present stage. For example, the approaching control problem of an active spacecraft is a typical orbit pursuit-evasion game problem. Currently, the most commonly used method for the spacecraft orbit pursuit-evasion problem is the differential game method. The literature 1 "Research Review on Differential Games of Spacecraft Orbit Pursuit-Evasion" details the current research status of differential games of spacecraft orbit pursuit-evasion, divides the solution methods of the spacecraft pursuit-evasion problem into qualitative differential games and quantitative differential games, and can solve the saddle point solution of the spacecraft pursuit-evasion problem under continuous control by using differential games, and achieve good results.

[0003] In view of the increasing complexity of space missions, the game problems of spacecraft are not limited to the pursuit-evasion form. The literature 2 "Space Orbit Games: Concepts, Principles and Methods" gives 9 types of orbit games such as lurking, camouflage, pursuit-evasion, interception, defense, blockade, encirclement, attachment, takeover, etc., and conducts detailed descriptions and classifications, analyzes the principles and difficulties of each orbit game, and completes the design of the general orbit game task process. During the process of approaching and detecting non-cooperative targets, the sunlight illumination is a factor that has a great impact on the detection equipment. For example, when using an on-board camera on one's own side to image the other side under sunward conditions, the imaging quality will be clearer. At the same time, if the other side wants to detect one's own side, one's own side is also in the high-brightness background of sunlight illumination in its field of view, which will cause great obstacles to its detection. Therefore, the process of both sides seizing the sunward position is also a game process, which is not reflected in the literature 1 and the literature 2. Moreover, there is currently no systematic research on the modeling and solution of sunward position seizure games in the field of spacecraft orbital dynamics. Summary of the Invention

[0004] Aiming at the problem of how to control the game of both sides seizing the sunward position during the process of approaching and detecting non-cooperative targets in the prior art, the present invention provides a sunward position seizure orbit game control method based on a genetic algorithm, which can quickly and efficiently give the optimal impulse control sequence of the participants in the sunward position seizure orbit game scenario.

[0005] The present invention is realized through the following technical solutions:

[0006] A head-on sunlight occupation orbit game control method based on genetic algorithm, comprising the following steps:

[0007] Obtain the head-on sunlight occupation game parameters of two non-cooperative targets;

[0008] Establish a head-on sunlight occupation orbit game model, and input the head-on sunlight occupation game parameters of the two non-cooperative targets into the head-on sunlight occupation orbit game model;

[0009] According to the shortest time performance index, design the optimal control strategies for the two non-cooperative targets in the head-on sunlight occupation orbit game model, and calculate the transfer time of the head-on sunlight occupation of both sides and the pulse speed increments for two times in the optimal control strategies of both sides;

[0010] Calculate the pulse sequence of the optimal control strategies of both sides through genetic algorithm to obtain the optimal pulse sequences of both sides, and complete the head-on sunlight occupation orbit game control.

[0011] Preferably, the head-on sunlight occupation game parameters of the two non-cooperative targets include the initial state information X P (t0) = [x P0 , y P0 , z P0 , vx P0 , vy P0 , vz P0 and X E (t0) = [x E0 , y E0 , z E0 , vx E0 , vy E0 , vz E0 , the game maneuvering capabilities of the two game sides, the orbital radius a of the virtual spacecraft at the origin of the LVLH coordinate system, the control information delay time ΔT of the two game sides, and; the unit vector ρ of the initial light direction of the two game sides in the LVLH coordinate system;

[0012] The initial state information of the two game sides includes the initial position and velocity information of both sides; the game maneuvering capabilities of the two game sides include the maximum speed increment magnitude Δv of a single pulse Pmax , Δv Emax ;

[0013] Among them, X P (t0) represents the initial state information of Party P, and X E (t0) represents the initial state information of Party E, where x, y, and z are the initial position coordinates and v is the initial velocity condition.

[0014] Furthermore, the establishment process of the head-on sunlight occupation orbit game model is as follows:

[0015] Taking a non - maneuvering virtual spacecraft as the origin, an LVLH coordinate system is established. The dynamic equations of two non - cooperative targets are determined by combining the parameters of the sun - light preemptive game of the two non - cooperative targets in the LVLH coordinate system;

[0016] According to the dynamic equations of the two non - cooperative targets, the pulse control method is adopted to determine the control equations of the two non - cooperative targets;

[0017] Based on the control equations of the two non - cooperative targets, the trajectory of the other party is predicted to obtain the orbit prediction equations of the two non - cooperative targets;

[0018] According to the orbit prediction equations of the two non - cooperative targets, the sun - light preemptive game target sets, performance indexes and control domains of the two non - cooperative targets are obtained;

[0019] According to the control delay time of the two non - cooperative targets, combined with the sun - light preemptive game target sets, performance indexes and control domains of the two non - cooperative targets, the sun - light position state deviation amounts of the two non - cooperative targets are determined, and the establishment of the sun - light preemptive orbit game model is completed.

[0020] Furthermore, in the LVLH coordinate system, the dynamic equations of the two non - cooperative targets are determined by combining the parameters of the sun - light preemptive game of the two non - cooperative targets as follows:

[0021] X P (t)=Φ(t,t0)X P (t0)

[0022] X E (t)=Φ(t,t0)X E (t0)

[0023] Among them, Φ(t,t0) is the state transition matrix, and its expression is as follows:

[0024]

[0025] Among them, respectively represent the state quantities of the two spacecrafts; the first three dimensions are the position coordinates in the LVLH coordinate system; the last three dimensions are the corresponding velocity components of each axis; t0 represents the initial time, X P (t0),X E (t0) represent the state quantities at the initial time; n is the angular velocity of the virtual spacecraft, and its value near the earth is μ=3.986×10 14 m 3 s -2 =3.986×10 5 km 3 s -2 , and a is the revolution radius of the virtual spacecraft.

[0026] Furthermore, the pulse control method is adopted according to the dynamic equations of two non-cooperative targets, and the control equations of the two non-cooperative targets are determined as follows:

[0027] X(t f )=Φ(t f ,t0)X(t0)+Φ v (t f ,t0)Δv0+Φ v (t f ,t f )Δv1

[0028] where Φ v is the state transition matrix, and the expression is as follows:

[0029]

[0030] where t f represents the terminal time; Δv1, Δv2 represent the velocity change amounts of two pulses; t0 represents the initial time; and n is the angular velocity of the virtual spacecraft.

[0031] Furthermore, the trajectory prediction of each other is performed according to the control equations of the two non-cooperative targets, and the orbit prediction equations of the two non-cooperative targets are as follows:

[0032] X(t f )=Φ(t f ,t0)X(t0)

[0033] where t f represents the terminal time; t0 represents the initial time.

[0034] Furthermore, the sunward position-grabbing game target sets of the two non-cooperative targets are obtained according to the orbit prediction equations of the two non-cooperative targets:

[0035] X P (t f )∈S P ,X E (t f )∈S E

[0036] S P ={X P (t f )||X P (t f )-X E (t f )-δX|<ξ}

[0037] S E ={X E (t f )||XE (t f ) - X P (t f ) - δX | < ξ

[0038] where ξ represents an extremely small quantity; S E represents the target set of Party E at the terminal time; S P represents the target set of Party P at the terminal time;

[0039] The performance indexes of two non - cooperative targets are as follows

[0040] J P = J E = t f ;

[0041] where, J P represents the performance index of Party P's target; J E represents the performance index of Party E's target; t f represents the terminal time;

[0042] The control domains of two non - cooperative targets:

[0043] Among them, the control domain of Party P's target is as follows:

[0044]

[0045] The control domain of Party E's target is as follows:

[0046]

[0047] where, u P represents the control vector of Party P; U P represents the set of ranges that the control vector of Party P can take; Δv Px represents the component of the pulse velocity increment of Party P along the x - axis; Δv Py represents the component of the pulse velocity increment of Party P along the y - axis; Δv Pz represents the component of the pulse velocity increment of Party P along the z - axis; Δv Pmax represents the maximum value that the modulus of the pulse velocity increment of Party P can take; u E represents the control vector of Party E; U E represents the set of ranges that the control vector of Party E can take; Δv Ex represents the component of the pulse velocity increment of Party E along the x - axis; Δv Ey represents the component of the pulse velocity increment of Party E along the y - axis; Δv Ez represents the component of the pulse velocity increment of Party E along the z - axis; Δv Emax represents the maximum value that the modulus of the pulse velocity increment of Party E can take.

[0048] Furthermore, according to the control delay times of two non-cooperative targets, combining the sunward position capture game target sets, performance indicators and control domains of the two non-cooperative targets, the sunward position state deviation of the two non-cooperative targets is determined, where the sunward position state deviation is δX, and its magnitude is d δX , and the direction is the direction of the spacecraft pointing to the sun, that is, the opposite direction of ρ.

[0049] Preferably, the design process of the optimal control strategy for the two non-cooperative targets is as follows:

[0050] After the two non-cooperative targets detect each other's state information, they perform orbit prediction, predict the estimates of each other in the next period of time, and perform maneuvers after obtaining the trajectories, and reach the sunward positions of each other in the least time;

[0051] One of the non-cooperative targets reaches the sunward position of the other in the least time. In a single round, its transfer time and the two pulse velocity increments should satisfy the following equations:

[0052] Among them, the transfer time equation of one non-cooperative target in a single round is as follows:

[0053]

[0054] The equation of the two pulse velocity increments of one non-cooperative target in a single round is as follows:

[0055]

[0056] Among them, t fP , t fE is the transfer time of both sides; [Δv P0 , Δv P1 T , [Δv E0 , Δv E1 T is the two-pulse sequence of both sides at this transfer time.

[0057] Furthermore, the steps to obtain the optimal pulse sequences of both sides by calculating the pulse sequences of the optimal control strategies of both sides through the genetic algorithm are as follows:

[0058] L1. Input the orbital radius a of the virtual spacecraft, input the initial states X P (t0), X E (t0) of the two non-cooperative targets, input the control delay time ΔT of the two non-cooperative targets, input the maximum velocity increment constraints Δv Pmax , Δv Emax , and input the position of the sun in the LVLH coordinate system at the initial moment;

[0059] ​​L2. Determine the direction of the sunward position deviation δX based on the initial states X P (t0), X E (t0) and the position of the sun at the initial moment in the LVLH coordinate system, and determine the specific component form of the sunward position deviation δX;

[0060] L3. Solve for the shortest transfer time and the corresponding pulse velocity increment of one of the non - cooperative targets in the first round according to the sunward position deviation δX. According to the transfer - time equation constraint of one non - cooperative target within a single round, use the genetic algorithm to optimize the time under the constraint of the control domain. The population is set as t fP , and the fitness function is J = |t fP |, so as to obtain the shortest transfer time t fP and record the corresponding pulse increment. If t fP > ΔT, then enter L4; otherwise, the game ends and the optimal pulse sequences of both sides are output;

[0061] L4. Solve for the shortest transfer time and the corresponding pulse velocity increment of the other non - cooperative target in the first round according to the sunward position deviation δX. According to the equation constraint of the two - pulse velocity increments of one non - cooperative target within a single round, use the genetic algorithm to optimize the time under the constraint of the control domain. The population is set as t fE , and the fitness function is J = |t fE |, so as to obtain the shortest transfer time t fE and record the corresponding pulse increment. If t fE > ΔT, then return to L3; otherwise, the game ends;

[0062] L5. Output the optimal pulse sequences of both sides to complete the sunward position - grabbing orbit game control.

[0063] Compared with the prior art, the present invention has the following beneficial technical effects:

[0064] The present invention provides a sunward position - grabbing orbit game control method based on the genetic algorithm. The established sunward position - grabbing orbit game model takes into account this new game form of sunward position - grabbing, as well as the information delay of both sides and the maneuver of both sides using the pulse maneuver method, which conforms to the real - space scenario. At the same time, the optimal control solution method based on the genetic algorithm proposed by the present invention can ensure the optimality of the system efficiency. The present invention can quickly and efficiently give the optimal pulse control sequences of the participants in the sunward position - grabbing orbit game scenario. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 is a flowchart of the sunward position - grabbing orbit game control method based on the genetic algorithm in the present invention;

[0066] Figure 2Flow chart for establishing the head-on light grabbing position orbit game model in the present invention;

[0067] Figure 3 Scene schematic diagram of the present invention;

[0068] Figure 4 Simulation trajectory diagram of the present invention;

[0069] Figure 5 Simulation diagram of the change in the relative distance between both sides of the present invention;

[0070] Figure 6 Pulse sequence diagram in the example of the present invention. Detailed implementation manners

[0071] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0072] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and do not have to be used to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0073] The present invention will be further described in detail below in conjunction with the accompanying drawings:

[0074] Refer to Figure 1 , the present invention provides a head-on light grabbing position orbit game control method based on a genetic algorithm, which can quickly and efficiently give the optimal pulse control sequence of participants in the head-on light grabbing position orbit game scenario.

[0075] Specifically, the head-on light grabbing position orbit game control method based on a genetic algorithm includes the following steps:

[0076] Obtain the head-on light grabbing position game parameters of two non-cooperative targets;

[0077] Establish a headlight position - grabbing orbital game model, and input the headlight position - grabbing game parameters of two non - cooperative targets into the headlight position - grabbing orbital game model;

[0078] According to the performance index of the shortest time, design the optimal control strategies for two non - cooperative targets in the headlight position - grabbing orbital game model, and calculate the transfer time of the headlight position - grabbing for both sides and the two - pulse velocity increments in the optimal control strategies of both sides;

[0079] Calculate the pulse sequences of the optimal control strategies of both sides through the genetic algorithm to obtain the optimal pulse sequences of both sides, and complete the headlight position - grabbing orbital game control.

[0080] Specifically, the headlight position - grabbing game parameters of the two non - cooperative targets include the initial state information \(X\) P (t0) = [x P0 , y P0 , z P0 , vx P0 , vy P0 , vz P0 and \(X\) E (t0) = [x E0 , y E0 , z E0 , vx E0 , vy E0 , vz E0 , the maneuvering capabilities of both sides of the game, the orbital radius \(a\) of the virtual spacecraft at the origin of the LVLH coordinate system, the control information delay time \(\Delta T\) of both sides of the game; and the unit vector \(\rho\) of the initial illumination direction of both sides of the game in the LVLH coordinate system;

[0081] The initial state information of both sides of the game includes the initial position and velocity information of both sides; the maneuvering capabilities of both sides of the game include the maximum velocity increment magnitude \(\Delta v\) of a single pulse Pmax , \(\Delta v\) Emax ;

[0082] Among them, \(X\) P (t0) represents the initial state information of Party P, and \(X\) E (t0) represents the initial state information of Party E, \(x\), \(y\), \(z\) are the initial position coordinates, and \(v\) is the initial velocity situation.

[0083] Specifically, the establishment of the headlight position - grabbing orbital game model includes game participants, the dynamic equations of the participants, the initial state, the target set, the performance index, the control domain, the control delay time \(\Delta T\) of both sides, and the headlight position deviation \(\delta X\); According to Figure 2 As shown, the establishment process of the headlight position - grabbing orbital game model is as follows:

[0084] Taking an immobile virtual spacecraft as the origin, an LVLH coordinate system is established. The LVLH coordinate system combines the parameters of the sunlight-grabbing position game of two non-cooperative targets to determine the dynamic equations of the two non-cooperative targets. The dynamic equations adopt the CW equations;

[0085] According to the dynamic equations of the two non-cooperative targets, the pulse control method is adopted to determine the control equations of the two non-cooperative targets;

[0086] According to the control equations of the two non-cooperative targets, the trajectory prediction of the other party is used to obtain the orbit prediction equations of the two non-cooperative targets;

[0087] According to the orbit prediction equations of the two non-cooperative targets, the sunlight-grabbing position game target sets, performance indicators and control domains of the two non-cooperative targets are obtained;

[0088] According to the control delay time of the two non-cooperative targets, combined with the sunlight-grabbing position game target sets, performance indicators and control domains of the two non-cooperative targets, the sunlight position state deviation amounts of the two non-cooperative targets are determined, and the establishment of the sunlight-grabbing position orbit game model is completed.

[0089] Among them, in the LVLH coordinate system, the dynamic equations of the two non-cooperative targets are determined by combining the parameters of the sunlight-grabbing position game of the two non-cooperative targets as follows:

[0090] X P (t)=Φ(t,t0)X P (t0)

[0091] X E (t)=Φ(t,t0)X E (t0)

[0092] Among them, Φ(t,t0) is the state transition matrix, and the expression is as follows:

[0093]

[0094] Among them, respectively represent the state quantities of the two spacecraft; the first three dimensions are the position coordinates in the LVLH coordinate system; the last three dimensions are the corresponding axis velocity components; t0 represents the initial time, X P (t0),X E (t0) represents the state quantity at the initial time; n is the angular velocity of the virtual spacecraft, and its value near the earth is μ=3.986×10 14 m 3 s -2 =3.986×10 5 km 3 s -2 , and a is the revolution radius of the virtual spacecraft.

[0095] Among them, according to the dynamic equations of two non-cooperative targets, the pulse control method is adopted to determine the control equations of the two non-cooperative targets as follows:

[0096] X(t f )=Φ(t f ,t0)X(t0)+Φ v (t f ,t0)Δv0+Φ v (t f ,t f )Δv1

[0097] Among them, Φ v is the state transition matrix, and the expression is as follows:

[0098]

[0099] Among them, t f represents the terminal time; Δv1, Δv2 represent the velocity change amounts of two pulses; t0 represents the initial time; n is the angular velocity of the virtual spacecraft.

[0100] Among them, according to the control equations of the two non-cooperative targets, the orbit prediction equations of the two non-cooperative targets are obtained by predicting each other's trajectories as follows:

[0101] X(t f )=Φ(t f ,t0)X(t0)

[0102] Among them, t f represents the terminal time; t0 represents the initial time.

[0103] Among them, according to the orbit prediction equations of the two non-cooperative targets, the sunlit position snatching game target sets of the two non-cooperative targets are obtained as follows:

[0104] X P (t f )∈S P ,X E (t f )∈S E

[0105] S P ={X P (t f )||X P (t f )-X E (t f )-δX|<ξ}

[0106] S E ={X E (t f )||XE (t f ) - X P (t f ) - δX | < ξ

[0107] where ξ represents an extremely small quantity; S E represents the target set of Party E at the terminal time; S P represents the target set of Party P at the terminal time;

[0108] The performance indexes of two non - cooperative targets are as follows

[0109] J P = J E = t f ;

[0110] where, J P represents the performance index of Party P's target; J E represents the performance index of Party E's target; t f represents the terminal time;

[0111] The control domains of two non - cooperative targets:

[0112] Among them, the control domain of Party P's target is as follows:

[0113]

[0114] The control domain of Party E's target is as follows:

[0115]

[0116] where, u P represents the control vector of Party P; U P represents the set of ranges that the control vector of Party P can take; Δv Px represents the component of the pulse velocity increment of Party P along the x - axis; Δv Py represents the component of the pulse velocity increment of Party P along the y - axis; Δv Pz represents the component of the pulse velocity increment of Party P along the z - axis; Δv Pmax represents the maximum value that the modulus of the pulse velocity increment of Party P can take; u E represents the control vector of Party E; U E represents the set of ranges that the control vector of Party E can take; Δv Ex represents the component of the pulse velocity increment of Party E along the x - axis; Δv Ey represents the component of the pulse velocity increment of Party E along the y - axis; Δv Ez represents the component of the pulse velocity increment of Party E along the z - axis; Δv Emax represents the maximum value that the modulus of the pulse velocity increment of Party E can take.

[0117] The control delay time of both sides is ΔT, which represents the time required for one side to make a corresponding maneuver after perceiving the other side's maneuver.

[0118] The deviation of the position state in the front-light direction is δX, and its magnitude is d δX , and the direction is related to the direction of the light, specifically the direction of the spacecraft pointing to the sun, that is, the opposite direction of ρ. Due to the influence of the earth's revolution, the direction of the sun's rays is constantly changing for the orbital spacecraft around the earth. However, considering that the influence of the change in the direction of the sun's rays caused by the earth's revolution is very small in a short period of time, it is assumed that the direction of the sun's rays is fixed in the model proposed in the present invention.

[0119] Specifically, the design process of the optimal control strategy for two non-cooperative targets is as follows:

[0120] After two non-cooperative targets detect the state information of each other, they perform orbit prediction, estimate the other party in the future for a period of time, and after obtaining the trajectory, they perform maneuvers and reach the front-light position of the other party in the shortest time;

[0121] One of the non-cooperative targets reaches the front-light position of the other party in the shortest time. In a single round, its transfer time and the two-pulse velocity increment should satisfy the following equations:

[0122] Among them, the transfer time equation of one non-cooperative target in a single round is as follows:

[0123]

[0124] The two-pulse velocity increment equation of one non-cooperative target in a single round is as follows:

[0125]

[0126] Among them, t fP , t fE are the transfer times of both sides; [Δv P0 , Δv P1 T , [Δv E0 , Δv E1 T are the two-pulse sequences of both sides at this transfer time.

[0127] ​​In this way, a series of solution families that satisfy the initial state and the target set for both sides are obtained. Considering the optimality of the performance index, the optimal strategy is to find the solution with the shortest time among these solutions. Since the head-on position snatching game is a multi-round game process, the maneuvers of both sides alternate. If the shortest transfer time found by one side using the optimal strategy in a certain round is longer than the control delay time ΔT of both sides, then it is the turn of the other side to maneuver. This process repeats until the shortest transfer time of one side in a certain round is shorter than the control delay time ΔT, indicating that it can successfully reach the head-on position of the other side and the game ends.

[0128] Specifically, the steps to obtain the optimal pulse sequences of the optimal control strategies for both sides by calculating through the genetic algorithm are as follows:

[0129] L1. Input the orbital radius a of the virtual spacecraft, and input the initial states X P (t0), X E (t0) of the two non-cooperative targets, input the control delay time ΔT of the two non-cooperative targets, input the maximum velocity increment constraint Δv Pmax , Δv Emax , and input the position of the sun in the LVLH coordinate system at the initial moment;

[0130] L2. Determine the direction of the head-on position deviation δX according to the initial states X P (t0), X E (t0) of the two non-cooperative targets and the position of the sun in the LVLH coordinate system at the initial moment, and determine the specific component form of the head-on position deviation δX;

[0131] L3. Solve the shortest transfer time and the corresponding pulse velocity increment of one of the non-cooperative targets in the first round according to the head-on position deviation δX. According to the transfer time equation constraint of a non-cooperative target within a single round, use the genetic algorithm to optimize the time under the constraint of the control domain. The population is set as t fP , and the fitness function is J = |t fP |, so as to obtain the shortest transfer time t fP and record the corresponding pulse increment. If t fP > ΔT, then enter L4; otherwise, the game ends and the optimal pulse sequences of both sides are output;

[0132] L4. Solve the shortest transfer time and the corresponding pulse velocity increment of the other non-cooperative target in the first round according to the head-on position deviation δX. According to the two-pulse velocity increment equation constraint of a non-cooperative target within a single round, use the genetic algorithm to optimize the time under the constraint of the control domain. The population is set as t fE , and the fitness function is J = |t fE |, so as to obtain the shortest transfer time tfE And record the corresponding pulse increment. If t fE > ΔT, then return L3; otherwise, the game ends.

[0133] L5. Output the optimal pulse sequences of both sides to complete the control of the headlight position-grabbing orbit game.

[0134] Embodiment

[0135] A headlight position-grabbing orbit game control method based on the genetic algorithm is proposed. According to Figure 3 the schematic diagram of the scenario of two non-cooperative targets shown, its steps are as follows:

[0136] S1. Input the relevant parameters involved in the headlight position-grabbing game problem, including the initial states, game capabilities, orbits, information delay time, and environmental factors of both game sides. Among them, input the initial states X P (t0) = [50 km, -100 km, 0, -5 m / s, -5 m / s, 5 m / s, 0], X E (t0) = [20 km, 0, 0, 0, -4 m / s, 0], input the maximum speed increment constraints Δv Pmax = 15 m / s, Δv Emax = 15 m / s, input the orbital radius a = 36000 km of the virtual spacecraft, input the control delay time ΔT = 1800 s of both sides, and input the position of the sun at the initial moment in the LVLH coordinate system, and its illumination direction is along the negative x-axis of the LVLH coordinate system, that is, ρ = [-1, 0, 0];

[0137] S2. Establish a headlight position-grabbing orbit game model, including game participants, the dynamic equations of the participants, initial states, target sets, performance indicators, control domains, the control delay time ΔT = 1800 s of both sides, and the headlight position deviation amount δX. First, the game participants are two non-cooperative targets competing for positions. Its dynamic equations adopt the CW equations. A local coordinate system, that is, the LVLH coordinate system, is established with a non-maneuvering virtual spacecraft as the origin. In the LVLH coordinate system, the spacecraft state equation is as follows:

[0138]

[0139] Among them respectively represent the state quantities of the spacecrafts on both sides. The first three dimensions are the position coordinates in the LVLH coordinate system, and the last three dimensions are the corresponding velocity components of each axis. t0 represents the initial moment, X P (t0), X E (t0) represent the state quantities at the initial moment. Among them, the state transition matrix is:

[0140]

[0141] Δt = t - t0 (2)

[0142] where n is the angular velocity of the virtual spacecraft, and its value near the Earth is μ = 3.986×10 14 m 3 s -2 = 3.986×10 5 km 3 s -2 , and a = 36000 km is the revolution radius of the virtual spacecraft.

[0143] Furthermore, considering that both sides are under impulse control, their control equations are as follows:

[0144] X(t f ) = Φ(t f , t0)X(t0) + Φ v (t f , t0)Δv0 + Φ v (t f , t f )Δv1 (3)

[0145] where t f represents the terminal time, and Δv1, Δv2 represent the velocity changes of the two impulses. The state transition matrix Φ v is:

[0146]

[0147] In addition, both sides need to predict the trajectories of the other side, and the orbit recurrence prediction model is:

[0148] X(t f ) = Φ(t f , t0)X(t0) (4)

[0149] where t f represents the terminal time, and t0 represents the initial time.

[0150] The initial states of both sides are X P (t0), X E (t0), where the specific values are known from S1 to be X P (t0) = [50 km, -100 km, 0, -5 m / s, -5 m / s, 5 m / s, 0], X E (t0) = [20 km, 0, 0, 0, -4 m / s, 0].

[0151] The set of goals for the direct sunlight position-grabbing game corresponding to both sides is X P (t f ) ∈ SP , X E (t f ) ∈ S E , S P = {X P (t f ) || X P (t f ) - X E (t f ) - δX | < ξ}, S E = {X E (t f ) || X E (t f ) - X P (t f ) - δX | < ξ}, where ξ represents an extremely small quantity.

[0152] The performance indexes of both sides are J P = J E = t f .

[0153] The control domain of Party P is Similarly, the control domain of Party E is:

[0154] The control delay time of both sides is ΔT = 1800 s, which represents the time required for one side to make a corresponding maneuver after perceiving the maneuver of the other side.

[0155] The deviation of the sunlit position state is δX, and its magnitude d δX = 10 km, and the direction is related to the direction of sunlight. Specifically, it is the direction of the spacecraft pointing to the sun, that is, the opposite direction of ρ = [-1, 0, 0]. Due to the influence of the earth's revolution, the direction of sunlight for an orbiting spacecraft around the earth is constantly changing. However, considering that the influence of the change in the direction of sunlight caused by the earth's revolution is very small in a short period of time, it is assumed that the direction of sunlight is fixed in the model proposed in the present invention.;

[0156] S3. Considering the performance index of the shortest time, design the optimal control strategy for seizing the sunlit position, as follows:

[0157] The designed strategy is that after both sides detect the state information of the other side, they perform orbit prediction, predict the trajectory of the other side in the future for a period of time, and after obtaining the trajectory, they make maneuvers, aiming to reach the sunlit position of the other side at a certain future moment with the least possible time.

[0158] In order for a certain spacecraft to reach the sunlit position of the other spacecraft, its transfer time and the two pulse velocity increments should satisfy the following equations within a single round:

[0159]

[0160]

[0161] where t fP , t fE is the transfer time of both sides, [Δv P0 , Δv P1 T , [Δv E0 , Δv E1 T are the two pulse sequences of both sides at the transfer time.

[0162] In this way, a series of solution families that satisfy the initial state and the target set for both sides are obtained. Considering the optimality of the performance index, the optimal strategy is to find the solution with the shortest time among these solutions. Since the head-on position snatching game is a multi-round game process, the maneuvers of both sides alternate. If the shortest transfer time found by one side using the optimal strategy in a certain round is longer than the control delay time of 1800 s for both sides, then it is the turn of the other side to maneuver. This process repeats until the shortest transfer time of one side in a certain round is shorter than the control delay time of 1800 s, which means it can successfully reach the head-on position of the other side and the game ends;

[0163] S4. Based on the genetic algorithm, solve the pulse sequence of the optimal strategy, and the specific steps are as follows:

[0164] STEP1. Input the orbital radius a = 36000 km of the virtual spacecraft, and input the initial states X P (t0) = [50 km, -100 km, 0, -5 m / s, -5 m / s, 5 m / s, 0], X E (t0) = [20 km, 0, 0, 0, -4 m / s, 0], input the control delay time ΔT = 1800 s of both sides, and input the maximum velocity increment constraints Δv Pmax = 15 m / s, Δv Emax = 15 m / s, and input the position of the sun at the initial moment in the LVLH coordinate system, and its illumination direction is along the negative x-axis of the LVLH coordinate system.

[0165] STEP2. Determine the direction of the head-on position deviation δX according to the initial state and the sun position. Its direction is at a distance d δX = 10 km along the x-axis direction from the actual positions of both spacecraft, and further determine its specific component form, and the expression is δX = [10 km, 0, 0, 0, 0, 0].

[0166] ​​STEP3. Solve for the shortest transfer time of Party P in the first round and the corresponding pulse velocity increment. According to the constraints of formula (5), use the genetic algorithm to optimize the time under the constraints of the control domain to obtain the shortest transfer time t fP = 6660.2 s > 1800 s. Record the pulse velocity increment of this time as Δv P0 = [-7.9044 m / s, 2.1015 m / s, 0]. Enter STEP4.

[0167] STEP4. Solve for the shortest transfer time of Party E in the first round and the corresponding pulse velocity increment. According to the constraints of formula (6), use the genetic algorithm to optimize the time under the constraints of the control domain to obtain the shortest transfer time t fE = 5463.55 s > 1800 s. Record the pulse velocity increment of this time as Δv E0 = [2.8761 m / s, 3.6155 m / s, 0]. Enter STEP3* for the second time.

[0168] STEP3*. Solve for the shortest transfer time of Party P in the second round and the corresponding pulse velocity increment. According to the constraints of formula (5), use the genetic algorithm to optimize the time under the constraints of the control domain to obtain the shortest transfer time t fP = 3357.5 s > 1800 s. Record the pulse velocity increment of this time as Δv P1 = [0.0307 m / s, 0.1276 m / s, 0]. Enter STEP4*.

[0169] STEP4*. Solve for the shortest transfer time of Party E in the second round and the corresponding pulse velocity increment. According to the constraints of formula (6), use the genetic algorithm to optimize the time under the constraints of the control domain to obtain the shortest transfer time t fE = 1755 s < 1800 s. Therefore, the game ends and Party E successfully reaches the backlight position of Party P. Record the pulse velocity increment of this time as Δv E1 = [11.939 m / s, 3.63 m / s, 0].

[0170] STEP5. Output the pulse control sequences of both sides, Δv P = [Δv P0 , Δv P1 , Δv E = [Δv E0 , Δv E1 . Output the trajectory diagrams of both sides, as shown in Figure 4 shown. The change in the relative distance between the two sides is as shown in Figure 5 shown, and the pulse control sequences of both sides over time are as shown in Figure 6 shown.

[0171] In summary, the present invention provides a control method for head-on light-grabbing orbit game based on genetic algorithm, and gives a method for modeling analysis and solution in a new orbit game scenario. The purpose of the present invention is to establish a head-on light-grabbing orbit game model and propose its corresponding solution method to overcome the deficiencies of the prior art. The established head-on light-grabbing orbit game model of the present invention takes into account this new game form of head-on light-grabbing, as well as the information delay of both parties and the maneuvers of both parties are in the form of impulsive maneuvers, which conforms to the real space scenario. At the same time, the optimal control solution method based on genetic algorithm proposed by the present invention can ensure the optimality of the system efficiency. The present invention can quickly and efficiently give the optimal impulsive control sequence of the participants in the head-on light-grabbing orbit game scenario.

[0172] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the specific implementation manners of the present invention can still be modified or equivalently replaced, and any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the protection scope of the claims of the present invention.

Claims

1. A control method for the head-on light-grabbing orbit game based on the genetic algorithm, characterized in that, It includes the following steps: Obtain the headlight position seizure game parameters of two non-cooperative targets; The parameters of the headlight position grabbing game between the two non-cooperative targets include the initial state information X of both sides of the game P (t0) = [x P0 , y P0 , z P0 , vx P0 , vy P0 , vz P0 and X E (t0) = [x E0 , y E0 , z E0 , vx E0 , vy E0 , vz E0 , the maneuvering capabilities of both sides of the game, the orbital radius a of the virtual spacecraft at the origin of the LVLH coordinate system, the control information delay time ΔT of both sides of the game, and the unit vector ρ of the initial illumination direction of both sides of the game in the LVLH coordinate system; The initial state information of the two gaming parties includes their initial positions and velocity information; the gaming maneuverability of the two gaming parties includes the magnitude of the maximum velocity increment Δv of a single pulse Pmax , Δv Emax ; Among them, X P (t0) represents the initial state information of Party P, and X E (t0) represents the initial state information of Party E, where x, y, and z are the initial position coordinates, and v is the initial velocity condition; Establish a headlight position seizure orbital game model, and input the headlight position seizure game parameters of the two non-cooperative targets into the headlight position seizure orbital game model; The establishment process of the headlight position seizure orbital game model is as follows: Establish a LVLH coordinate system with a non-maneuvering virtual spacecraft as the origin. The LVLH coordinate system combines the headlight position seizure game parameters of the two non-cooperative targets to determine the dynamic equations of the two non-cooperative targets; According to the dynamic equations of the two non-cooperative targets, adopt a pulse control method to determine the control equations of the two non-cooperative targets; According to the control equations of the two non-cooperative targets, predict the trajectories of each other to obtain the orbital prediction equations of the two non-cooperative targets; According to the orbital prediction equations of the two non-cooperative targets, obtain the headlight position seizure game target sets, performance indicators and control domains of the two non-cooperative targets; According to the control delay times of the two non-cooperative targets, combine the headlight position seizure game target sets, performance indicators and control domains of the two non-cooperative targets to determine the headlight position state deviation amounts of the two non-cooperative targets, and complete the establishment of the headlight position seizure orbital game model; According to the shortest time performance indicator, design the optimal control strategies of the two non-cooperative targets in the headlight position seizure orbital game model, and calculate the transfer time and the two pulse velocity increments of the two non-cooperative targets during the headlight position seizure in the optimal control strategies of both sides; The design process of the optimal control strategies of the two non-cooperative targets is as follows: After the two non-cooperative targets detect the state information of each other, they perform orbital prediction, predict the estimation of the other party in the future period of time, and after obtaining the trajectory, they perform maneuvering and reach the headlight position of the other party in the shortest time; One of the non-cooperative targets reaches the headlight position of the other party in the shortest time. In a single round, its transfer time and the two pulse velocity increments should satisfy the following equations: Among them, the transfer time equation of one non-cooperative target in a single round is as follows: The two pulse velocity increment equations of one non-cooperative target in a single round are as follows: where t fP , t fE is the transfer time of both parties; [Δv P0 , Δv P1 T , [Δv E0 , Δv E1 T are the two pulse sequences of both parties at this transfer time;​​ Calculate the pulse sequences of the optimal control strategies of both sides through the genetic algorithm to obtain the optimal pulse sequences of both sides, and complete the headlight position seizure orbital game control; The steps of calculating the pulse sequences of the optimal control strategies of both sides through the genetic algorithm are as follows: Input the orbital radius a of the virtual spacecraft, and input the initial states X P (t0), X E (t0) of the two non-cooperative targets. Input the control delay time ΔT of the two non-cooperative targets, and input the maximum velocity increment constraint Δv Pmax , Δv Emax , and input the position of the sun in the LVLH coordinate system at the initial moment; L2. Determine the direction of the sunward position deviation δX based on the initial states X P (t0), X E (t0) of two non - cooperative targets and the position of the sun at the initial moment in the LVLH coordinate system, and determine the specific component form of the sunward position deviation δX; L3. Solve the shortest transfer time of one of the non - cooperative targets and the corresponding pulse velocity increment in the first round according to the front - light position deviation amount δX. According to the transfer - time equation constraint of a non - cooperative target within a single round, use the genetic algorithm to optimize the time under the constraint of the control domain. The population is set as t fP , and the fitness function is J = |t fP |, so as to obtain the shortest transfer time t fP and record the corresponding pulse increment. If t fP >ΔT, then enter L4; otherwise, the game ends and the optimal pulse sequences of both sides are output. L4. Solve for the shortest transfer time of the other non - cooperative target in the first round and the corresponding pulse velocity increment according to the front - light position deviation amount δX. According to the constraint of the two - pulse velocity increment equations of a non - cooperative target within a single round, use the genetic algorithm to optimize the time under the constraints of the control domain, and set the population as t fE , and the fitness function is J = |t fE |, so as to obtain the shortest transfer time t fE and record the corresponding pulse increment. If t fE > ΔT, then return to L3; otherwise, the game ends. L5. Output the optimal pulse sequences of both sides to complete the headlight position seizure orbital game control.

2. The method for controlling the head-on light-grabbing orbit game based on the genetic algorithm according to claim 1, wherein In the LVLH coordinate system, combine the headlight position seizure game parameters of the two non-cooperative targets to determine the dynamic equations of the two non-cooperative targets as follows: X P \(\mathbf{X}(t)=\varPhi(t,t_0)\mathbf{X}(t_0)\) P (t0) X E X(t) = Φ(t, t0)X(t0) E (t0) Among them, Φ(t,t0) is the state transition matrix, and the expression is as follows: Among them, respectively represent the state variables of the two spacecraft; the first three dimensions are the position coordinates in the LVLH coordinate system; the last three dimensions are the velocity components of each axis; t0 represents the initial time, X P (t0), X E (t0) represents the state variable at the initial time; n is the angular velocity of the virtual spacecraft, and its value is μ = 3.986×10 14 m 3 s -2 = 3.986×10 5 km 3 s -2 , and a is the revolution radius of the virtual spacecraft.

3. The method for controlling the game of the front-light position-grabbing orbit based on the genetic algorithm according to claim 2, wherein According to the dynamic equations of the two non-cooperative targets, adopt a pulse control method to determine the control equations of the two non-cooperative targets as follows: X(t f ) = Φ(t f , t0)X(t0) + Φ v (t f , t0)Δv0 + Φ v (t f , t f )Δv1 where, Φ v is the state transition matrix, and the expression is as follows: where t f represents the terminal time; Δv1 and Δv2 represent the velocity changes of two pulses; t0 represents the initial time; and n is the angular velocity of the virtual spacecraft.

4. The method for controlling the game of the frontlight grabbing position orbit based on the genetic algorithm according to claim 3, characterized in that, According to the control equations of the two non-cooperative targets, predict the trajectories of each other to obtain the orbital prediction equations of the two non-cooperative targets as follows: X(t f ) = Φ(t f , t0)X(t0) Among them, t f represents the terminal time; t0 represents the initial time.

5. A method for controlling the game of the front-light grabbing position orbit based on the genetic algorithm according to claim 4, characterized in that, According to the orbital prediction equations of the two non-cooperative targets, obtain the headlight position seizure game target sets of the two non-cooperative targets as follows: X P (t f )∈S P ,X E (t f )∈S E S P = {X P (t f ) || X P (t f ) - X E (t f ) - δX | < ξ} S E = {X E (t f ) || X E (t f ) - X P (t f ) - δX | < ξ} where ξ represents an infinitesimal quantity; S E represents the target set of Party E at the terminal time; S P represents the target set of Party P at the terminal time; The performance indicators of the two non-cooperative targets are as follows J P = J E = t f ; Among them, J P represents the performance index of the P - side target; J E represents the performance index of the E - side target; t f represents the terminal time; The control domains of the two non-cooperative targets: Among them, the control domain of the P-side target is as follows: The control domain of the E-side target is as follows: where, u P represents the control vector of Party P; U P represents the set of ranges that the control vector of Party P can take; Δv Px represents the component of the pulse velocity increment of Party P along the x-axis; Δv Py represents the component of the pulse velocity increment of Party P along the y-axis; Δv Pz represents the component of the pulse velocity increment of Party P along the z-axis; Δv Pmax represents the maximum value that the magnitude of the pulse velocity increment of Party P can take; u E represents the control vector of Party E; U E represents the set of ranges that the control vector of Party E can take; Δv Ex represents the component of the pulse velocity increment of Party E along the x-axis; Δv Ey represents the component of the pulse velocity increment of Party E along the y-axis; Δv Ez represents the component of the pulse velocity increment of Party E along the z-axis; Δv Emax represents the maximum value that the magnitude of the pulse velocity increment of Party E can take.

6. The method for controlling the head-on light grabbing position orbit game based on the genetic algorithm according to claim 5, wherein According to the control delay times of two non-cooperative targets, combining the sunward position seizure game target sets, performance indicators, and control domains of the two non-cooperative targets, determine the sunward position state deviation of the two non-cooperative targets, where the sunward position state deviation is δX, and its magnitude is d δX , and the direction is the direction of the spacecraft pointing to the sun, that is, the opposite direction of ρ.

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