A spacecraft control method for close-range spacecraft orbital impulse game

Abstract

A spacecraft control method for close-range spacecraft orbital pulse game, relating to the field of spacecraft orbital game. The present invention is to solve the problem that the existing spacecraft control method does not meet the actual working environment requirements, resulting in the spacecraft engine being unable to work normally under the spacecraft orbital game countermeasures. The present invention includes: obtaining spacecraft state information, establishing an inertial coordinate system and an orbital coordinate system, and obtaining the position and velocity information of the spacecraft in the inertial coordinate system and the orbital coordinate system; using the position and velocity information to establish a C‑W equation, converting the C‑W equation into a Ricaati equation, and obtaining the optimal closed-loop feedback control rate; obtaining the thrust received by the spacecraft, converting the thrust received by the spacecraft to the inertial coordinate system, and obtaining the real-time position information of the spacecraft using the thrust change in the inertial coordinate system; calculating the pulse thrust differential countermeasure of Lambert orbit transfer according to the real-time position information of the spacecraft, and obtaining the velocity increment required for the rendezvous process. The present invention is used to realize spacecraft orbital game.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft orbit game, and in particular to a spacecraft control method for close-range spacecraft orbit pulse game. Background Art

[0002] With the continuous development and progress of human civilization, the scope of human exploration has become larger and larger. So far, more than 30 countries have successively developed and launched various launch vehicles, meteorological satellites, communication satellites, scientific experimental satellites, space shuttles and space stations, which have undertaken multiple tasks such as transportation, communication, command, early warning, real-time monitoring, mapping, navigation and positioning. Low-Earth satellites have the characteristics of wide observation range and fast information transmission speed, and their military value is becoming increasingly prominent. Military satellites undertake many tasks such as enemy reconnaissance, communication, weather forecasting, monitoring and early warning, and are an important part of the modern joint combat system.

[0003] Due to the needs of military strategy, the research team led by Dr. Isaacs of the Rand Corporation in the United States conducted research on the pursuit problem in which both sides of the confrontation can make free decisions and actions. The formation of differential game theory has two roots: game theory and control theory. Starr and Ho studied the concepts of three different types of solutions for multi-person non-zero-sum differential games: maximum and minimum, Nash equilibrium and non-inferiority group strategy. Subsequently, Leitmann, MelMan and Friedman also made a lot of research in this regard. Elliot, Bensoussan and many other scholars used variational methods and martingale theory to give a rigorous mathematical proof of the existence and uniqueness of solutions to random differential games. Stackelberg master-slave differential games have become a new research hotspot. Lasry and Lions studied non-zero-sum differential games with a large number of players, which are called mean field games. Aumann, Maschler and Harsanyi studied static incomplete information differential games, in which Harsanyi transformed the game under incomplete information into a complete but imperfect game, and then solved it using the method of processing complete information. Kreps and Wilson studied dynamic incomplete information differential games, and introduced the solution ideas of perfect Bayesian equilibrium and sequential equilibrium into discrete dynamic games. However, there is currently less attention paid to the study of incomplete information continuous dynamic games. Sha Jichang conducted in-depth research on the firepower allocation problem of multi-service operations based on differential game theory for various military confrontations, and Li Dengfeng systematically studied differential games. In recent years, more and more scholars have participated in the study of differential games.

[0004] The existing spacecraft orbit game mainly uses continuous thrust to pursue and escape. The control strategy of optimal control theory is used to find the construction of the boundary fence of the pursuit and escape game and the solution of the optimal control law of the saddle point. The traditional linear quadratic differential game is a widely used differential game with a simple form. It describes the relative motion of the spacecraft in the Hill coordinate system and converts the HJB equation into the Ricaati equation to solve the closed-loop optimal feedback control rate. However, the thrust obtained is a continuously changing quantity, while the actual spacecraft thrust is a pulse thrust. Therefore, the current spacecraft control method does not meet the actual working environment requirements. Therefore, the spacecraft engine cannot work normally under the existing spacecraft orbit game game. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that the existing spacecraft control method does not meet the actual working environment requirements, resulting in the spacecraft engine being unable to work normally under the spacecraft orbit game strategy, and a spacecraft control method for close-range spacecraft orbit pulse game is proposed.

[0006] A spacecraft control method for close-range spacecraft orbital impulse game. The specific process is:

[0007] Step 1: Obtain the status information of the spacecraft, establish an inertial coordinate system and an orbital coordinate system, and use the status information of the spacecraft to obtain the position and velocity information of the spacecraft in the inertial coordinate system and the orbital coordinate system;

[0008] The spacecraft includes: pursuit spacecraft and escape spacecraft;

[0009] Step 2: Use the position and velocity information of the spacecraft in the orbital coordinate system and inertial coordinate system obtained in step 1 to establish the CW equation, convert the CW equation into the Ricaati equation through the optimal control strategy, and obtain the optimal closed-loop feedback control rate;

[0010] Step 3: Use the optimal closed-loop feedback control rate obtained in step 2 to obtain the thrust of the spacecraft, convert the thrust of the spacecraft into an inertial coordinate system, and use the thrust change in the inertial coordinate system to obtain the real-time position information of the spacecraft;

[0011] Step 4: Calculate the pulse thrust differential strategy for Lambert orbit transfer based on the real-time position information of the spacecraft obtained in step 3 to obtain the speed increment required for the pursuit spacecraft during the rendezvous process.

[0012] Furthermore, the step of obtaining the spacecraft status information, establishing an inertial coordinate system and an orbital coordinate system, and using the spacecraft status information to obtain the position and velocity information of the spacecraft in the inertial coordinate system and the orbital coordinate system includes the following steps:

[0013] Step 11: Get spacecraft status information

[0014] Among them, r i , i , γ i 、v i , i They are the distance from the spacecraft to the Earth, geographical longitude, geographical latitude, flight path angle, flight speed and azimuth, i = P for the pursuing spacecraft, and i = E for the escaping spacecraft;

[0015] Step 1 and 2: Establish the inertial coordinate system and orbital coordinate system;

[0016] The inertial coordinate system takes the center of mass of the earth O as its origin, OX points to the vernal equinox, OZ points to the North Pole, and OY points to the right-hand screw rule;

[0017] The orbital coordinate system takes the center of mass o of the spacecraft rendezvous target as its origin, the ox axis is the direction from the center of the earth to the center of mass of the spacecraft, the oy axis is the direction of motion of the spacecraft, and the oz axis is determined according to the right-hand screw rule;

[0018] Step 13: Use the spacecraft's status information to obtain the spacecraft's position and velocity information in the inertial coordinate system and orbital coordinate system.

[0019] Furthermore, the step 13 of obtaining the position and velocity information of the spacecraft in the inertial coordinate system and the orbital coordinate system by using the state information of the spacecraft comprises the following steps:

[0020] Step 131: Obtain the position and velocity information of the spacecraft in the inertial coordinate system And use Get the position and velocity difference between the pursuing and escaping spacecraft:

[0021] First, obtain the position information of the spacecraft in the inertial coordinate system:

[0022]

[0023] Among them, (x i ,y i , z i ) is the coordinate of the spacecraft in the inertial coordinate system;

[0024] Then, use formula (2) to calculate x i ,y i , z i Take the derivative and obtain the velocity information of the spacecraft in the inertial coordinate system, which is formula (3);

[0025]

[0026]

[0027] in, is the velocity of the spacecraft in the x, y, and z directions of the inertial coordinate system;

[0028] Finally, using Get the position and velocity difference between the pursuing spacecraft and the escaping spacecraft

[0029] Among them, Δx, Δy, Δz are the position differences in the x, y, and z directions between the pursuing spacecraft and the escaping spacecraft. is the velocity difference in the x, y, and z directions between the pursuing spacecraft and the escaping spacecraft;

[0030] Step 132: Obtain the transformation matrix of the pursuit spacecraft from the orbital coordinate system to the inertial coordinate system according to the position and velocity information of the pursuit spacecraft in the inertial coordinate system;

[0031] Step 133. Use the position and velocity difference between the pursuit spacecraft and the escape spacecraft and the transformation matrix of the pursuit spacecraft from the orbital coordinate system to the inertial coordinate system to obtain the position and velocity vector of the escape spacecraft in the orbital coordinate system.

[0032] Furthermore, in step 132, the conversion matrix of the pursuit spacecraft from the orbital coordinate system to the inertial coordinate system is obtained according to the position and velocity information of the pursuit spacecraft in the inertial coordinate system, as shown in the following formula:

[0033] M E =[i x i y i z ](4)

[0034]

[0035] Among them, i x 、i y 、i z is the transformation matrix M E The parameters in r p is the position vector of the pursuit spacecraft in the inertial coordinate system, v p is the pursuit spacecraft flight velocity vector.

[0036] Furthermore, in step 133, the position and velocity difference between the pursuit spacecraft and the escape spacecraft and the transformation matrix of the pursuit spacecraft from the orbital coordinate system to the inertial coordinate system are used to obtain the position and velocity vector of the escape spacecraft in the orbital coordinate system, as shown in the following formula:

[0037]

[0038] Among them, r pe =[Δx Δy Δz], They are respectively the position vector and velocity vector of the escaping spacecraft in the orbital coordinate system.

[0039] Furthermore, the step 2 uses the position and velocity information of the spacecraft in the orbital coordinate system and the inertial coordinate system obtained in the step 1 to establish a CW equation, converts the CW equation into a Ricaati equation through an optimal control strategy, and obtains an optimal closed-loop feedback control rate, including the following steps:

[0040] Step 21: Use the position and velocity information of the spacecraft in the orbital coordinate system and inertial coordinate system obtained in step 1 to establish the CW equation as follows:

[0041]

[0042]

[0043]

[0044]

[0045] in, represents the position and velocity of the pursuing spacecraft relative to the escaping spacecraft, U = [u x u y u z ] T is the acceleration difference between the escaping spacecraft and the pursuing spacecraft, r = [δx δyδz] represents the position vector of the pursuing spacecraft relative to the escaping spacecraft, represents the velocity vector of the pursuing spacecraft relative to the escaping spacecraft, A and B are intermediate matrices, is the derivative of X, B P , B E is an intermediate variable, U e is the acceleration of the force on the escaping spacecraft, U p is the acceleration of the force on the pursuing spacecraft; is the angular velocity of the spacecraft in the inertial coordinate system, μ is the gravitational constant;

[0046] Step 22: Convert the CW equation into the Ricaati equation through the optimal control strategy to obtain the optimal closed-loop feedback control rate.

[0047] Furthermore, the step 22 converts the CW equation into the Ricaati equation through the optimal control strategy to obtain the optimal closed-loop feedback control rate, including the following steps:

[0048] Step 221: Convert the CW equation into the Ricaati equation through the optimal control strategy, as shown below:

[0049]

[0050] Among them, R p , R e , Q is a positive semidefinite matrix, P(t) is a Ricatti matrix, is the derivative of P(t), where t is time;

[0051] Step 222: The time t in the Ricaati equation obtained in step 221 is tended to infinity to obtain the optimal closed-loop feedback control rate:

[0052]

[0053] Among them, u i (t) is the optimal thrust magnitude and direction of the spacecraft, R i , B i It is a semi-positive definite matrix, and P(t) = P' when time t tends to infinity.

[0054] Furthermore, the step of step 3 using the optimal closed-loop feedback control rate obtained in step 2 to obtain the thrust of the spacecraft, converting the thrust of the spacecraft to an inertial coordinate system, and obtaining the real-time position information of the spacecraft using the thrust change in the inertial coordinate system includes the following steps:

[0055] Step 31: Obtain the gravitational force on the spacecraft:

[0056]

[0057]

[0058] Among them, u ri is the inertial coordinate system r i Unit vector in the direction, r i Yes i The modulus length, M and m are the masses of the pursuit spacecraft and the escape spacecraft, G is the gravity, r i is the spacecraft position vector;

[0059] Step 32: Use the gravitational force on the spacecraft to obtain the acceleration of the spacecraft

[0060]

[0061] Step 3.3. Use the acceleration of the spacecraft obtained in step 3.2 to obtain the relative motion formula of the two-body system:

[0062]

[0063] μ=G(M+m) (14)

[0064] Wherein, μ represents the gravitational constant;

[0065] Step 3 and 4: Analyze the forces on the pursuit spacecraft according to the relative application formula of the two-body system and establish the dynamic equation of the pursuit spacecraft:

[0066]

[0067]

[0068]

[0069] In the formula, u' x ,u' y ,u' z It indicates the thrusts in the x, y, and z directions on the pursuit spacecraft in the inertial coordinate system, and R indicates the position of the pursuit spacecraft from the center of the earth;

[0070] Step 35: Change the thrust u' in real time x 、u' y 、u' z The real-time position information of the pursuing spacecraft is obtained by the size of R and the size of R, and the real-time position information of the escaping spacecraft is obtained according to the relative position relationship between the pursuing spacecraft and the escaping spacecraft.

[0071] Furthermore, in step 4, the pulse thrust differential strategy for Lambert orbit transfer is calculated based on the real-time position information of the spacecraft obtained in step 3 to obtain the velocity increment required for the spacecraft rendezvous process, as shown in the following formula:

[0072]

[0073]

[0074] Among them, v c v is the velocity vector of the spacecraft at the starting point of the original orbit at the start of the rendezvous; t is the velocity vector of the spacecraft at the rendezvous point at the end of the rendezvous, and Δv1 is the velocity vector of the spacecraft from 0 to N revolutions during the rendezvous process. max The velocity increment corresponding to all prograde orbits of the circle, Δv2 is the velocity increment of the spacecraft from 0 circles to N circles during the rendezvous process. max The velocity increment corresponding to all the retrograde orbits of the loop, v1 and v2 are the velocity vectors of the pursuit spacecraft and the escape spacecraft on the transfer orbit, r1 and r2 are the position vectors of the starting and ending points of the spacecraft rendezvous, f and g are the Lagrangian coefficients, is the derivative of the Lagrange coefficient, is the maximum number of cycles, T m is the orbital period of the serviced spacecraft;

[0075] Among them, f, g, Satisfies the following expression:

[0076]

[0077] Where r1 and r2 represent the position vector moduli of the starting and ending points of the spacecraft, Δθ represents the true anomaly angle of the spacecraft on the transfer orbit, and h represents the modulus of the orbital angular momentum.

[0078] Furthermore, (Δv1, Δv2) satisfies the following Lambert strategy:

[0079] (Δv1,Δv2)=Lambert(x1,x2,t') (21)

[0080] Among them, x1 is the velocity vector of the pursuing spacecraft at the initial position, x2 is the velocity vector of the escaping spacecraft at the rendezvous point, and t' is the transfer time.

[0081] Beneficial effects:

[0082] The present invention is based on an inertial coordinate system, and obtains the position and velocity information of a spacecraft in an orbital coordinate system and an inertial coordinate system by converting between variables. The present invention uses the position and velocity information of the spacecraft to establish a CW dynamic equation, uses an optimal control strategy to convert it into a Ricaati equation, and uses differential recursion to calculate the relative distance change. After using the optimal control strategy for the pursuit spacecraft, the dynamic equation of the spacecraft is established to obtain the position information in the inertial coordinate system; the present invention uses the CW equation to obtain the distance between the pursuit spacecraft and the escape spacecraft, thereby obtaining the position information of the escape spacecraft; the Lambert orbit change formula is used for the positions of the pursuit spacecraft and the escape spacecraft to obtain a pulse thrust differential strategy. The present invention solves the defects of the traditional continuous thrust differential strategy, proposes an open-loop pulse thrust differential strategy, discretizes the closed-loop differential game, and then uses Lambert orbit change, so that this strategy can be actually applied to the orbit game of the spacecraft, which is more in line with the actual working environment requirements, so that the spacecraft engine can work normally under the spacecraft orbit game strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 It is a flow chart of the present invention;

[0084] Figure 2 It is a schematic diagram of the geocentric inertial system;

[0085] Figure 3 It is a schematic diagram of the inertial system;

[0086] Figure 4 This is a schematic diagram of Lambert's track change;

[0087] Figure 5 Schematic diagram of path angle and azimuth angle;

[0088] Figure 6 is a schematic diagram of thrust acceleration vector;

[0089] Figure 7 Schematic diagram of Lambert coplanar transfer;

[0090] Figure 8 is the distance between the pursuit and escape satellites at 200s;

[0091] Fig. 9 Motion trajectories for pursuing spacecraft using closed-loop continuous differential games and open-loop impulsive differential games;

[0092] Fig.10 Motion trajectories for escaping spacecraft using closed-loop continuous differential games and open-loop impulsive differential games;

[0093] Fig.11 Motion trajectories for pursuit and escape spacecraft using closed-loop continuous differential games and open-loop impulsive differential games. DETAILED DESCRIPTION

[0094] Specific implementation method 1: Figure 1 As shown, the specific process of a spacecraft control method for close-range spacecraft orbit pulse game in this embodiment is as follows:

[0095] Step 1: Obtain the status information of the spacecraft, establish an inertial coordinate system and an orbital coordinate system, and use the status information of the spacecraft to obtain the position and velocity information of the spacecraft in the inertial coordinate system and the orbital coordinate system, including the following steps:

[0096] Step 11: Get spacecraft status information

[0097] Among them, r i , i , γ i 、v i , i They are the distance from the spacecraft to the Earth, geographic longitude, geographic latitude, flight path angle, flight speed and azimuth, i represents the spacecraft, i=P represents the pursuit spacecraft, and i=E represents the escape spacecraft, such as Figure 5-6 As shown;

[0098] Step 1 and 2: Establish the inertial coordinate system and orbital coordinate system:

[0099] like Figure 2 As shown, the present invention describes the entire rendezvous process based on the inertial coordinate system and the orbital coordinates (LVLH) of the rendezvous target.

[0100] The inertial coordinate system takes the Earth's center of mass O as its origin, OX points to the vernal equinox, OZ points to the North Pole, and OY points according to the right-hand screw rule. Figure 3 As shown, the orbital coordinate system (LVLH) takes the center of mass o of the spacecraft rendezvous target as its origin, the ox axis is the direction from the center of the earth to the center of mass of the spacecraft, the oy axis is the direction of spacecraft motion (located in the orbital plane and perpendicular to the ox axis), and the oz axis is determined according to the right-hand screw rule.

[0101] Step 13: Use the spacecraft's status information to obtain the spacecraft's position and velocity information in the inertial coordinate system and orbital coordinate system:

[0102] Step 131: Obtain the position and velocity information of the spacecraft in the inertial coordinate system And use Get the position and velocity difference between the pursuing and escaping spacecraft:

[0103] First, obtain the position and velocity information of the spacecraft in the inertial coordinate system

[0104]

[0105]

[0106] in, is the change in distance from the spacecraft to the Earth, is the change in geographic latitude, is the change in geographic longitude. Using formula (2) i ,y i , z i Taking the derivative, we get:

[0107]

[0108] The simplified form is:

[0109]

[0110] Among them, (x i ,y i , z i ) is the coordinate of the spacecraft in the inertial coordinate system, is the velocity of the spacecraft in the x, y, and z directions of the inertial coordinate system;

[0111] Then, use Get the position and velocity difference between the pursuing spacecraft and the escaping spacecraft

[0112] Step 132: Obtain the transformation matrix of the pursuit spacecraft from the orbital coordinate system to the inertial coordinate system based on the position and velocity information of the pursuit spacecraft in the inertial coordinate system:

[0113] M E =[i x i y i z ] (5)

[0114]

[0115] Among them, i x 、i y 、i z is the transformation matrix M E The parameters in r p is the position vector of the pursuit spacecraft in the inertial coordinate system, v p is the pursuit spacecraft flight velocity vector;

[0116] Step 133: Use the position and velocity difference between the pursuit spacecraft and the escape spacecraft and the transformation matrix of the pursuit spacecraft from the orbital coordinate system to the inertial coordinate system to obtain the position and velocity vector of the escape spacecraft in the pursuit spacecraft orbital coordinate system (the orbital coordinate system with the pursuit spacecraft as the reference) as shown below:

[0117]

[0118] Among them, r pe =[Δx Δy Δz], They are respectively the position and velocity vector of the escaping spacecraft in the orbital coordinate system of the pursuing spacecraft (the position and velocity of the escaping spacecraft relative to the pursuing spacecraft).

[0119] Step 2: Use the position and velocity information of the spacecraft in the orbital coordinate system and inertial coordinate system obtained in step 1 to establish the CW equation, convert the CW equation into the Ricaati equation through the optimal control strategy, and obtain the optimal closed-loop feedback control rate:

[0120] The CW equation is a dynamic equation describing two spacecraft in the orbital coordinate system. It can obtain the position and velocity state information of the pursuing and escaping spacecraft at different times. If the game time is infinite, the payment function is introduced and converted into the Ricaati equation for solution to obtain the closed-loop optimal feedback control law. Solving this equation can obtain the optimal closed-loop feedback control law.

[0121] Step 21: Use the position and velocity information of the spacecraft in the orbital coordinate system and inertial coordinate system obtained in step 1 to establish the CW equation:

[0122] The position vector of the escape spacecraft in the inertial coordinate system can be expressed as r e =[x e y e z e ] T , the position vector of the pursuit spacecraft in the inertial coordinate system is r p =[x p y p z p ] T , get the acceleration of the pursuing spacecraft and the escaping spacecraft:

[0123]

[0124]

[0125] in, is the acceleration of the pursuing spacecraft and the escaping spacecraft, a e and a p They represent the acceleration of the forces acting on the escaping spacecraft and the pursuing spacecraft, respectively, and μ is the gravitational constant;

[0126] Then the position vector r of the pursuing spacecraft relative to the escaping spacecraft can be expressed as:

[0127] r=r p -r e =[x p y p z p ] T -[x e y e z e ] T =[δx δy δz] (10)

[0128] Among them, δx, δy, and δz are the values ​​of the pursuing spacecraft in the x, y, and z directions relative to the escaping spacecraft, respectively;

[0129] Assume that u is represented as follows

[0130] a p -a e =U p -U e =[u x u y u z ] (11)

[0131] Among them, u x 、u y 、u zare the differences in the accelerations in the x, y, and z directions of the forces acting on the escaping spacecraft and the pursuing spacecraft, respectively;

[0132] Taking the second derivative of the above formula, we can get:

[0133]

[0134] Where t is time;

[0135] According to the vector derivative operation, we have:

[0136]

[0137] Among them, ω and They represent the angular velocity vector and angular acceleration vector of the spacecraft in the inertial coordinate system, respectively, and δ is the symbol of the partial derivative;

[0138] Assuming that the trajectory of the spacecraft is approximately circular, we can get:

[0139]

[0140] The above formula can be simplified as:

[0141]

[0142] The cross multiplication rule in mathematics can be further simplified to:

[0143]

[0144] Substituting formula (12) into formula (15) yields:

[0145]

[0146] Since the orbit of the spacecraft is assumed to be a circular orbit, according to the law of universal gravitation:

[0147]

[0148] By deduction, we can get:

[0149]

[0150]

[0151]

[0152] in, is the second-order partial derivative with respect to δx, is the second-order partial derivative of δz;

[0153] Assuming the intermediate variable U=[ux u y u z ] T System modeling can obtain:

[0154]

[0155] in, is the derivative of X, B P , B E is an intermediate variable;

[0156]

[0157]

[0158]

[0159] In the formula, It represents the position and velocity of the pursuing spacecraft relative to the escaping spacecraft, usually a 6-dimensional vector, U = [u x u y u z ] T is the acceleration difference between the escaping spacecraft and the pursuing spacecraft, r represents the position vector of the pursuing spacecraft relative to the escaping spacecraft, v represents the velocity vector of the pursuing spacecraft relative to the escaping spacecraft, r = [δxδyδz] is the position of the pursuing spacecraft relative to the escaping spacecraft, is the position and velocity of the pursuing spacecraft relative to the escaping spacecraft, A and B are intermediate matrices, is the angular velocity scalar of the spacecraft in the inertial coordinate system;

[0160] Step 22: Convert the CW equation into the Ricaati equation through the optimal control strategy to obtain the optimal closed-loop feedback control rate:

[0161] Consider the general game of pursuit and escape between two spacecraft. Both parties pursue their own optimal control amount and minimize their own payment function (usually related to time, distance, energy parameters, using Bolza performance index):

[0162]

[0163] If there exists a set of optimal maneuver strategies and For any maneuver strategy U of the two parties in pursuit P and U E The following formula is established

[0164] J E (U * p ,UE )≥J E (U * p ,U * E )(twenty four)

[0165] J P (U * p ,U * E )≤J P (U * p ,U E )(25)

[0166] So say and The Nash equilibrium of the game.

[0167] If the game is time-given, according to the optimal control principle, the spacecraft payment function J at the equilibrium point can be expressed as

[0168]

[0169] Where Q pf ,Q P is a semi-positive definite matrix, representing the weight of the relative distance, R p ,R e is a semi-positive definite matrix, representing the energy weight.

[0170] If the game function time is infinite, the payment function can be

[0171]

[0172] A fixed stay differential game is constructed, and formula (27) is transformed into the Ricaati equation to solve the closed-loop optimal feedback control law. The constructed Ricaati equation is as follows:

[0173]

[0174] in, is the derivative of P(t), P(t) is the Ricatti matrix;

[0175] P(t) in the above formula is the Ricatti matrix, which is:

[0176] Q=Q P

[0177] When time tends to infinity, this strategy becomes a differential strategy in infinite time domain:

[0178]

[0179] Among them, when time tends to infinity, P(t) is P' in formula (29);

[0180] The optimal closed-loop feedback control rate can be obtained as:

[0181]

[0182] Among them, u i (t) is the thrust magnitude and direction of the spacecraft under the optimal conditions of the payoff function, x(t) is the relative distance between the escaping spacecraft and the pursuing spacecraft in the orbital coordinate system, R i is a positive semidefinite matrix;

[0183] Step 3: Use the optimal closed-loop feedback control rate obtained in step 2 to obtain the thrust of the spacecraft, convert the thrust of the spacecraft to the inertial coordinate system, and use the thrust change in the inertial coordinate system to obtain the real-time position information of the spacecraft:

[0184] The thrust obtained in step 2 is converted to the inertial system through the conversion between orbital systems. The dynamic equation of the satellite in the inertial system is established. According to the thrust change and the coordinate system conversion matrix transformation, the real-time position and velocity information of the satellite can be calculated.

[0185] Step 31: Obtain the gravitational force on the spacecraft:

[0186] In the case of an ideal two-body system considering only gravity, let the spacecraft position vector r in the inertial coordinate system i , the modulus length is r i ; The mass of the pursuing spacecraft and the mass of the escaping spacecraft are M and m respectively, and the gravitational force on the spacecraft is:

[0187]

[0188]

[0189] Among them, u ri Yes i The unit vector in the direction, G represents the magnitude of gravity;

[0190] Step 32: Use the gravitational force on the spacecraft to obtain the acceleration of the spacecraft:

[0191]

[0192] Step 3.3. Use the acceleration of the spacecraft obtained in step 3.2 to obtain the relative motion formula of the two-body system:

[0193]

[0194] μ=G(M+m) (35)

[0195] But at this point the spacecraft will be affected by the thrust of the engine;

[0196] Step 3 and 4: Analyze the force on the spacecraft. It can be found that the spacecraft is affected by gravity and the thrust of the engine, and the dynamic equation of the spacecraft is established:

[0197]

[0198]

[0199]

[0200] In the formula, μ represents the gravitational constant, u' x ,u' y ,u' z It indicates the thrusts in the x, y, and z directions on the pursuit spacecraft in the inertial coordinate system, and R indicates the position of the pursuit spacecraft from the center of the earth;

[0201] Step 35: Change the thrust u' in real time x 、u' y 、u' z The size of R and the size of R are used to obtain the real-time position information of the pursuing spacecraft, and the real-time position information of the escaping spacecraft is obtained according to the relative position of the pursuing spacecraft and the escaping spacecraft.

[0202] Step 4: Calculate the pulse thrust differential strategy for Lambert orbit transfer based on the real-time position information of the spacecraft obtained in step 3 to obtain the required velocity increment of the spacecraft during the rendezvous process:

[0203] Taking 200 seconds as a time interval, the change of the spaceflight position at the beginning and after 200 seconds is calculated, and then the Lambert orbit change method is used. The calculated result is the size and direction information of the engine thrust, thus obtaining an open-loop pulse thrust differential strategy.

[0204] After the initial position velocity x1 of the pursuit spacecraft, the position velocity x2 of the escape at the rendezvous point, and the transfer time t', there may be multiple Lambert transfer strategies. The strategy with the smallest required velocity increment (optimal fuel) is selected as the rendezvous maneuver. Assume that the orbital period of the service spacecraft is T m ,Will Set as the maximum round. Traverse from round 0 to round N max The velocity increments corresponding to all the prograde and retrograde orbits are taken as the output of Lambert transfer. The optimal two-pulse Lambert transfer under fixed time is obtained. Figure 7 , the above process is expressed as:

[0205] (Δv1,Δv2)=Lambert(x1,x2,t') (39)

[0206] Where x1 is the velocity vector of the pursuing spacecraft at the initial position, x2 is the velocity vector of the escaping spacecraft at the rendezvous point, t' is the transfer time, and Δv1 is from lap 0 to lap N. max The velocity increment corresponding to all the prograde orbits is Δv2, which is the velocity increment from cycle 0 to cycle N. max The velocity increment corresponding to all retrograde orbits;

[0207] like Figure 4 As shown in the figure, the calculation formula of Lambert track change is as follows:

[0208]

[0209] Among them, v c v is the velocity vector of the spacecraft at point P1 on the original orbit at the start of the rendezvous; t It is the velocity vector at the intersection point P2 at the intersection end time on the target orbit.

[0210] Using the Lagrange coefficients f, g and their derivatives The velocities v1 and v2 of the spacecraft transfer orbit can be expressed as:

[0211]

[0212] Among them, v1 and v2 are the velocity vectors of the pursuit spacecraft and the escape spacecraft in the transfer orbit;

[0213] According to orbital mechanics theory, f, g, Satisfies the following expression:

[0214]

[0215] Where r1 and r2 represent the position vector modulus of the spacecraft’s starting point P1 and ending point P2, Δθ represents the true anomaly angle passed on the transfer orbit, and h represents the modulus of the orbital angular momentum (when calculating the velocity increment of the pursuing spacecraft, P1 and P2 are the starting point and ending point of the pursuing spacecraft; when calculating the velocity increment of the escaping spacecraft, P1 and P2 are the starting point and ending point of the escaping spacecraft).

[0216] Embodiment: In order to verify the beneficial effects of the present invention, the following experiments were carried out:

[0217] The initial spacecraft position and attitude information is shown in Table 1:

[0218] Table 1 Initial spacecraft position and attitude information

[0219]

[0220] Calculations show that the pursuing and escaping spacecraft will rendezvous at around 3500s. Figure 8 is the absolute distance between the spacecraft within 200s. We control the maximum thrust of the spacecraft in each direction to not exceed 5 / 2 ,After 200s, the position movement of the pursuit spacecraft and the position change of the spacecraft using the discrete differential decision are as follows Fig. 9 As shown in the figure, the position movement of the escaping spacecraft after 200s and the position change of the spacecraft using the discrete differential decision are as follows: Fig.10 As shown in the figure, after 200s, the position movement of the chasing and escaping spacecraft using the continuous differential strategy and the position change of the spacecraft using the discrete differential strategy are as follows Fig.11 As shown in Figure 2, it can be seen that discretization has a good control effect.

[0221] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A spacecraft control method for close-range spacecraft orbital impulse game, characterized in that The specific process of the method is: Step 1: Obtain the status information of the spacecraft, establish an inertial coordinate system and an orbital coordinate system, and use the status information of the spacecraft to obtain the position and velocity information of the spacecraft in the inertial coordinate system and the orbital coordinate system; The spacecraft includes: pursuit spacecraft and escape spacecraft; Step 2: Use the position and velocity information of the spacecraft in the orbital coordinate system and inertial coordinate system obtained in step 1 to establish the CW equation, convert the CW equation into the Ricaati equation through the optimal control strategy, and obtain the optimal closed-loop feedback control rate, including the following steps: Step 21: Use the position and velocity information of the spacecraft in the orbital coordinate system and inertial coordinate system obtained in step 1 to establish the CW equation as follows: in, represents the position and velocity of the pursuing spacecraft relative to the escaping spacecraft, U = [u x u y u z ] T is the acceleration difference between the escaping spacecraft and the pursuing spacecraft, r = [δxδyδz] represents the position vector of the pursuing spacecraft relative to the escaping spacecraft, represents the velocity vector of the pursuing spacecraft relative to the escaping spacecraft, A and B are intermediate matrices, is the derivative of X, B P , B E is an intermediate variable, U e is the acceleration of the force acting on the escaping spacecraft, U p is the acceleration of the force on the pursuing spacecraft; is the angular velocity of the spacecraft in the inertial coordinate system, μ is the gravitational constant; Step 22: Convert the CW equation into the Ricaati equation through the optimal control strategy to obtain the optimal closed-loop feedback control rate, including the following steps: Step 221: Convert the CW equation into the Ricaati equation through the optimal control strategy, as shown below: Among them, R p , R e , Q is a positive semidefinite matrix, P(t) is a Ricatti matrix, is the derivative of P(t), where t is time; Step 222: The time t in the Ricaati equation obtained in step 221 is tended to infinity to obtain the optimal closed-loop feedback control rate: Among them, u i (t) is the optimal thrust magnitude and direction of the spacecraft, R i , B i It is a semi-positive definite matrix, when time t tends to infinity, P(t) = P'; Step 3: Use the optimal closed-loop feedback control rate obtained in step 2 to obtain the thrust of the spacecraft, convert the thrust of the spacecraft into an inertial coordinate system, and use the thrust change in the inertial coordinate system to obtain the real-time position information of the spacecraft; Step 4: Calculate the pulse thrust differential strategy for Lambert orbit transfer based on the real-time position information of the spacecraft obtained in step 3 to obtain the velocity increment required for the pursuit spacecraft during the rendezvous process, as shown in the following formula: Among them, v c v is the velocity vector of the spacecraft at the starting point of the original orbit at the start of the rendezvous; t is the velocity vector of the spacecraft at the rendezvous point at the end of the rendezvous, and Δv1 is the velocity vector of the spacecraft from 0 to N revolutions during the rendezvous process. max The velocity increment corresponding to all prograde orbits of the circle, Δv2 is the velocity increment of the spacecraft from 0 circles to N circles during the rendezvous process. max The velocity increment corresponding to all the retrograde orbits of the loop, v1 and v2 are the velocity vectors of the pursuit spacecraft and the escape spacecraft on the transfer orbit, r1 and r2 are the position vectors of the starting and ending points of the spacecraft rendezvous, f and g are the Lagrangian coefficients, is the derivative of the Lagrange coefficient, is the maximum number of cycles, T m is the orbital period of the serviced spacecraft; Among them, f, g, Satisfies the following expression: Where r1 and r2 represent the position vector modulus of the spacecraft’s starting and ending points, Δθ represents the true anomaly angle that the spacecraft passes through on the transfer orbit, and h represents the modulus of the orbital angular momentum. (Δv1, Δv2) satisfies the following Lambert strategy: (Δv1,Δv2)=Lambert(x1,x2,t') (21) Among them, x1 is the velocity vector of the pursuing spacecraft at the initial position, x2 is the velocity vector of the escaping spacecraft at the rendezvous point, and t' is the transfer time.

2. A spacecraft control method for close-range spacecraft orbital impulse game according to claim 1, characterized in that: The step 1 of obtaining the state information of the spacecraft, establishing an inertial coordinate system and an orbital coordinate system, and using the state information of the spacecraft to obtain the position and velocity information of the spacecraft in the inertial coordinate system and the orbital coordinate system includes the following steps: Step 11: Get spacecraft status information (i=P,E); Among them, r i , i , γ i 、v i , i They are the distance from the spacecraft to the Earth, geographical longitude, geographical latitude, flight path angle, flight speed and azimuth, i = P for the pursuing spacecraft, and i = E for the escaping spacecraft; Step 1 and 2: Establish the inertial coordinate system and orbital coordinate system; The inertial coordinate system takes the center of mass of the earth O as its origin, OX points to the vernal equinox, OZ points to the North Pole, and OY points to the right-hand screw rule; The orbital coordinate system takes the center of mass o of the spacecraft rendezvous target as its origin, the ox axis is the direction from the center of the earth to the center of mass of the spacecraft, the oy axis is the direction of motion of the spacecraft, and the oz axis is determined according to the right-hand screw rule; Step 13: Use the spacecraft's status information to obtain the spacecraft's position and velocity information in the inertial coordinate system and orbital coordinate system.

3. A spacecraft control method for close-range spacecraft orbital impulse game according to claim 2, characterized in that: The step 1-3 of using the state information of the spacecraft to obtain the position and velocity information of the spacecraft in the inertial coordinate system and the orbital coordinate system includes the following steps: Step 131: Obtain the position and velocity information of the spacecraft in the inertial coordinate system (i=P,E), and use (i=P,E) Get the position and velocity difference between the pursuing spacecraft and the escaping spacecraft: First, obtain the position information of the spacecraft in the inertial coordinate system: Among them, (x i ,y i , z i ) is the coordinate of the spacecraft in the inertial coordinate system; Then, use formula (2) to calculate x i ,y i , z i Take the derivative and obtain the velocity information of the spacecraft in the inertial coordinate system, which is formula (3); in, is the velocity of the spacecraft in the x, y, and z directions of the inertial coordinate system; Finally, using (i=P,E) Obtain the position and velocity difference between the pursuing spacecraft and the escaping spacecraft Among them, Δx, Δy, Δz are the position differences in the x, y, and z directions between the pursuing spacecraft and the escaping spacecraft. is the velocity difference in the x, y, and z directions between the pursuing spacecraft and the escaping spacecraft; Step 132: Obtain the transformation matrix of the pursuit spacecraft from the orbital coordinate system to the inertial coordinate system according to the position and velocity information of the pursuit spacecraft in the inertial coordinate system; Step 133. Use the position and velocity difference between the pursuit spacecraft and the escape spacecraft and the transformation matrix of the pursuit spacecraft from the orbital coordinate system to the inertial coordinate system to obtain the position and velocity vector of the escape spacecraft in the orbital coordinate system.

4. A spacecraft control method for close-range spacecraft orbital impulse game according to claim 3, characterized in that: In the step 132, the conversion matrix of the pursuit spacecraft from the orbital coordinate system to the inertial coordinate system is obtained according to the position and velocity information of the pursuit spacecraft in the inertial coordinate system, as shown in the following formula: M E =[i x i y i z ](4) Among them, i x 、i y 、i z is the transformation matrix M E The parameters in r p is the position vector of the pursuit spacecraft in the inertial coordinate system, v p is the pursuit spacecraft flight velocity vector.

5. A spacecraft control method for close-range spacecraft orbital impulse game according to claim 4, characterized in that: In step 133, the position and velocity difference between the pursuit spacecraft and the escape spacecraft and the transformation matrix of the pursuit spacecraft from the orbital coordinate system to the inertial coordinate system are used to obtain the position and velocity vector of the escape spacecraft in the orbital coordinate system, as shown in the following formula: Among them, r pe =[ΔxΔyΔz], They are respectively the position vector and velocity vector of the escaping spacecraft in the orbital coordinate system.

6. A spacecraft control method for close-range spacecraft orbital impulse game according to claim 5, characterized in that: The method of obtaining the thrust of the spacecraft by using the optimal closed-loop feedback control rate obtained in step 2 in step 3, converting the thrust of the spacecraft to an inertial coordinate system, and obtaining the real-time position information of the spacecraft by using the thrust change in the inertial coordinate system, comprises the following steps: Step 31: Obtain the gravitational force on the spacecraft: Among them, u ri is the inertial coordinate system r i Unit vector in the direction, r i Yes i , M and m are the masses of the pursuing and escaping spacecraft, G is gravity, and ri is the position vector of the spacecraft; Step 32: Use the gravitational force on the spacecraft to obtain the acceleration of the spacecraft Step 3.

3. Use the acceleration of the spacecraft obtained in step 3.2 to obtain the relative motion formula of the two-body system: μ=G(M+m)(14) Among them, μ represents the gravitational constant; Step 3 and 4: Analyze the forces on the pursuit spacecraft according to the relative application formula of the two-body system and establish the dynamic equation of the pursuit spacecraft: In the formula, u' x ,u' y ,u' z It indicates the thrusts in the x, y, and z directions on the pursuit spacecraft in the inertial coordinate system, and R indicates the position of the pursuit spacecraft from the center of the earth; Step 35: Change the thrust u' in real time x 、u' y 、u' z The real-time position information of the pursuing spacecraft is obtained by the size of R and the size of R, and the real-time position information of the escaping spacecraft is obtained according to the relative position relationship between the pursuing spacecraft and the escaping spacecraft.

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