Spacecraft configuration maintenance attitude-orbit coupling collaborative iterative learning control method

Abstract

The invention discloses a spacecraft configuration maintenance attitude-orbit coupling collaborative iterative learning control method, and belongs to the technical field of space. The implementation method comprises the steps that a six-degree-of-freedom kinetic model is established based on a Lie group SE (3) frame, the attitude and orbit coupling problem caused by thruster installation errors in actual engineering is fully considered, the configuration keeping precision is improved, and the unwinding problem caused in a traditional six-degree-of-freedom dual quaternion representation method is avoided. On the basis, a collaborative iterative learning control method is designed, under the condition that an accurate disturbance model is unknown, the influence of disturbance on configuration keeping is counteracted through iterative learning, adjustment time and steady-state errors are considered, the adjustment time is short, meanwhile, the small steady-state errors can be achieved, and the stability of the system is improved. That is to say, the high-precision six-degree-of-freedom configuration of the spacecraft is maintained through attitude and orbit coupling collaborative iterative learning control. The method does not depend on an accurate disturbance model, the adjustment time is shortened, steady-state errors are reduced, and the speed and precision of spacecraft configuration keeping are improved.

Description

Technical Field

[0001] The present invention relates to a spacecraft configuration maintaining control method, in particular to a spacecraft configuration maintaining attitude-orbit coupling collaborative iterative learning control method, and belongs to the field of space technology. Background Art

[0002] In recent years, many commercial aerospace companies have designed and launched constellations with communication, navigation, remote sensing and other functions, providing satellite Internet communication, timing and positioning, earth observation and other services. In order to achieve global coverage of the constellation and reduce the risk of collision between spacecraft within the constellation, spacecraft operating on the same orbital plane need to maintain precise orbital phase and altitude. In addition, in order to achieve uniform observation conditions or antenna pointing requirements on all spacecraft, the attitude of the spacecraft also needs to remain stable and consistent. Therefore, the precise configuration of the spacecraft orbit and attitude is of great significance to improving the working efficiency and operational safety of the constellation.

[0003] Combined with engineering practice, during the maneuvering process of the spacecraft, the gravity gradient torque disturbance related to the orbital position and the thruster installation error cause the spacecraft orbit and attitude to couple motion, which requires six-degree-of-freedom dynamic modeling of the spacecraft. The configuration of the spacecraft is affected by environmental disturbances, which cannot be accurately modeled, and there is little prior information, which increases the difficulty of controller design. In addition, in order to enable the spacecraft to track the target orbital position and attitude, it is difficult to design a suitable controller gain, and it is difficult to take into account the adjustment time and steady-state error. Therefore, it is necessary to design a controller with fast adjustment time, small steady-state error, and independent of accurate disturbance model. Summary of the invention

[0004] In view of the problems that the disturbance model is unknown and the controller gain is difficult to take into account both the adjustment time and the steady-state error during the spacecraft configuration maintenance process, the purpose of the present invention is to provide a spacecraft configuration maintenance attitude and orbit coupling collaborative iterative learning control method, which can achieve high-precision six-degree-of-freedom configuration maintenance while taking into account a shorter adjustment time and a smaller steady-state error.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] The spacecraft configuration maintenance attitude-orbit coupling collaborative iterative learning control method disclosed in the present invention establishes a six-degree-of-freedom dynamic model based on the Lie group SE (3) framework, fully considers the attitude-orbit coupling problem caused by the thruster installation error in actual engineering, improves the configuration maintenance accuracy, and avoids the unwinding problem caused by the traditional six-degree-of-freedom dual quaternion representation method. On this basis, a collaborative iterative learning control method is designed. When the precise disturbance model is unknown, the influence of the disturbance on the configuration maintenance is offset through iterative learning, taking into account the adjustment time and steady-state error. While the adjustment time is short, there can also be a small steady-state error, so as to achieve high-precision six-degree-of-freedom configuration maintenance of the spacecraft. The present invention can be independent of the precise disturbance model, shorten the adjustment time, reduce the steady-state error, and improve the speed and accuracy of configuration maintenance.

[0007] The spacecraft configuration-maintaining attitude-orbit coupling collaborative iterative learning control method disclosed in the present invention comprises the following steps:

[0008] Step 1: Based on the Lie group SE (3) framework, the actual dynamic model and expected dynamic model of the spacecraft with six degrees of freedom are established, and on this basis, the error dynamic model of the spacecraft with six degrees of freedom is established.

[0009] Step 1.1: Establish a six-degree-of-freedom actual dynamic model of the spacecraft.

[0010] For the i-th spacecraft, the position and attitude of the spacecraft can be expressed by the variable g of the Lie group SE(3): i Expressed as

[0011]

[0012] Where R i ∈SO(3) represents the attitude rotation matrix of the i-th spacecraft from its own system to the inertial system along the principal axis of inertia. SO(3) is the Lie group of the special orthogonal matrix representing the attitude of the i-th spacecraft. represents the position vector from the origin of the coordinate system to the center of mass of the i-th spacecraft in the inertial system, represents a three-dimensional real vector set, 0 1×3 represents a 1×3 zero matrix, SE(3) is the Lie group of all translational and rotational motions of the spacecraft. The augmented velocity vector ξ of the i-th spacecraft i Expressed as

[0013]

[0014] in and They represent the inertial angular velocity and translational velocity of the i-th spacecraft in the system, represents a six-dimensional real vector set. In the SE(3) framework, the i-th spacecraft dynamics equation is expressed as

[0015]

[0016] in

[0017]

[0018] ξ i The matrix of the conjugate adjoint mapping is expressed as

[0019]

[0020] symbol(·) × Represents the cross product matrix of a vector. For a three-dimensional vector x=[x1,x2,x3] T , the cross product matrix of x(x) × Defined as

[0021]

[0022] where x1, x2, x3 are the three components of vector x; se(3) is the Lie algebra of the Lie group SE(3), J i is the moment of inertia of the ith spacecraft, m i is the mass of the i-th spacecraft, I3 represents the three-dimensional unit matrix, represents a 6×6 real matrix set, is the gravitational field of the ith spacecraft, is the control torque of the ith spacecraft, is the control force of the ith spacecraft, is the disturbance torque of the ith spacecraft, is the disturbance force of the i-th spacecraft, 0 3×3 Represents a 3×3 zero matrix.

[0023] Step 1.2: Establish the six-degree-of-freedom expected dynamic model of the spacecraft.

[0024] For the i-th spacecraft, in the SE(3) framework, the six-DOF expected dynamics model is expressed as

[0025]

[0026] in

[0027]

[0028] represents the expected attitude rotation matrix of the i-th spacecraft from its own system to the inertial system along the principal axis of inertia, represents the expected position vector from the origin of the coordinate system to the center of mass of the i-th spacecraft in the inertial system, and They represent the expected inertial angular velocity and expected translational velocity of the i-th spacecraft in this system, respectively. is the gravitational field of the i-th spacecraft at the desired position.

[0029] Step 1.3: According to equation (3) obtained in step 1.1 and equation (4) obtained in step 1.2, establish the six-degree-of-freedom error dynamics model of the spacecraft.

[0030] The error h between the actual position and attitude of the i-th spacecraft and the expected position and attitude i Expressed as

[0031]

[0032] The exponential coordinate vector used to represent the position and attitude error of the i-th spacecraft is

[0033]

[0034] in, and The index coordinate vectors representing the attitude tracking error and position tracking error respectively.

[0035] The velocity error of the i-th spacecraft in this system Expressed as

[0036]

[0037] in and They represent the rotational angular velocity error and translational velocity error of the i-th spacecraft system respectively.

[0038]

[0039] (h i ) -1 The matrix representation of the adjoint mapping is

[0040]

[0041] in, Indicates (h i ) -1 A 3×3 block matrix, Indicates (h i ) -1 A 3×1 block matrix.

[0042] The six-degree-of-freedom error kinematic equation of the spacecraft is expressed as

[0043]

[0044] Expressed as

[0045]

[0046] in

[0047]

[0048] and The six-degree-of-freedom error dynamics equation of the spacecraft is expressed as

[0049]

[0050] The matrix of the adjoint mapping is expressed as

[0051]

[0052] Substituting equation (3) into equation (10) and combining equation (8) together, we can obtain the six-DOF error dynamics model of the spacecraft:

[0053]

[0054] Step 2. Based on the six-degree-of-freedom error dynamics model of the spacecraft obtained in step 1, design the spacecraft configuration maintenance attitude-orbit coupling collaborative iterative learning control law, and further determine the parameter conditions of the collaborative iterative learning control law through error analysis, so that the tracking error of the control system converges monotonically, and the spacecraft can be maintained quickly and with high precision without relying on an accurate disturbance model.

[0055] Step 2.1: Design a six-degree-of-freedom configuration-preserving feedback control law to keep the system stable before introducing the collaborative iterative learning control law.

[0056] The control input of the spacecraft consists of two parts: feedback control law and collaborative iterative learning control law. The control input of the i-th spacecraft in the j-th cycle is Feedback Control Law Designed for

[0057]

[0058] Where, the feedback controller gain and is a 6×6 positive definite diagonal matrix.

[0059] Step 2.2: Design a six-degree-of-freedom configuration preserving collaborative iterative learning control law.

[0060] Substituting equation (12) into equation (11), the six-degree-of-freedom error dynamics model of the spacecraft under the feedback control law is:

[0061]

[0062] 0 6×6 represents a 6×6 zero matrix, represents the collaborative iterative learning control law of the i-th spacecraft in the j-th cycle. Formula (13) can be written as

[0063]

[0064] in,

[0065]

[0066] Represents the set of twelve-dimensional real vectors.

[0067] According to the norm of the tracking error, the spacecraft with the smallest tracking error in the jth cycle is determined, denoted as Right now

[0068]

[0069] in represents a natural number, Represents the set of all spacecraft.

[0070] The collaborative iterative learning control law uses the control input and error of the spacecraft with the smallest tracking error in the previous cycle to calculate the control input of the next cycle. represents the jth period spacecraft The control input is

[0071]

[0072] use and denote the spacecraft in the jth period The position and attitude tracking error and the velocity and angular velocity tracking error are:

[0073]

[0074] And define the new system state

[0075]

[0076] For the i-th spacecraft, the collaborative iterative learning control law in the j+1th cycle is for

[0077]

[0078] Among them, the iterative learning controller gain and is a 6×6 positive definite diagonal matrix, △ is a small positive number,

[0079] Step 2.3: Determine the parameter conditions of the collaborative iterative learning control law so that the tracking error of the control system converges monotonically, thereby achieving a short adjustment time and a small steady-state error, and realizing high-precision six-degree-of-freedom configuration maintenance of the spacecraft.

[0080] From equations (14) to (19), we can get the CILC error evolution process equation (20):

[0081]

[0082] in

[0083]

[0084] Represents spacecraft The disturbance in period j is and Represents spacecraft The feedback controller gain, Represents spacecraft The moment of inertia, Represents spacecraft quality.

[0085] In the j+1th period, the tracking error of spacecraft i is obtained by integrating equation (14) from time 0 to t:

[0086]

[0087] Integrate equation (20) from time 0 to t to obtain the j-th period spacecraft Tracking error

[0088]

[0089] Integrate equation (20) from time t to t+△ and substitute it into equation (19), and we get the collaborative iterative learning control law for spacecraft i in the j+1th period:

[0090]

[0091] Substituting equation (22) and equation (23) into equation (21), we can get and are all diagonal matrices, so we get

[0092]

[0093] in

[0094] Since the function f[e i,j(t)] is Lipschitz continuous, so in a cycle time T we have

[0095]

[0096] Taking the norms of both sides of formula (24) and substituting them into formula (25) we get

[0097]

[0098] where b B , b d , b L Respectively represent B i , L i The norm of O(△ 2 ) represents the 2 Apply the Bellman–Gronwall inequality and multiply both sides of equation (26) by e -λt , and λ satisfies

[0099]

[0100] get

[0101]

[0102] in

[0103] From equation (15) and equation (28), we can get

[0104]

[0105] in express The supremum of

[0106]

[0107] Defining variables

[0108]

[0109] Formula (29) can be rewritten as

[0110]

[0111] That is to say

[0112]

[0113] when satisfy

[0114]

[0115] When λ satisfies equation (27), we have and

[0116]

[0117] That is to say

[0118]

[0119] The definition of monotonic convergence of system error is satisfied. Therefore, when equation (35) is satisfied, the tracking error of the control system converges monotonically, thereby achieving a short adjustment time and a small steady-state error, and realizing high-precision six-degree-of-freedom configuration maintenance of the spacecraft.

[0120] Beneficial effects:

[0121] 1. The spacecraft configuration maintenance attitude-orbit coupling collaborative iterative learning control method disclosed in the present invention establishes a spacecraft six-degree-of-freedom error dynamics model under the SE (3) framework, fully considers the attitude-orbit coupling problem caused by thruster installation errors in actual engineering, improves the accuracy of spacecraft configuration maintenance, and avoids the unwinding problem caused by the traditional six-degree-of-freedom dual quaternion representation method.

[0122] 2. The spacecraft configuration maintenance attitude-orbit coupling collaborative iterative learning control method disclosed in the present invention designs a collaborative iterative learning control law. When the precise disturbance model is unknown, it offsets the influence of disturbance on configuration maintenance through iterative learning, takes into account both adjustment time and steady-state error, so that the control process does not rely on the precise disturbance model, and has a small steady-state error while having a short adjustment time, thereby shortening the adjustment time, reducing the steady-state error, and improving the speed and accuracy of configuration maintenance. BRIEF DESCRIPTION OF THE DRAWINGS

[0123] Figure 1 Flowchart of the attitude-orbit coupled collaborative iterative learning control method for spacecraft configuration maintenance;

[0124] Figure 2 This is the graph showing the change of attitude error of spacecraft 1 with iterative learning cycle;

[0125] Figure 3 This is the graph showing the position error of spacecraft 1 changing with the iterative learning cycle;

[0126] Figure 4 This is the graph showing the change of attitude error of spacecraft 2 with iterative learning cycle;

[0127] Figure 5 This is the graph showing the position error of spacecraft 2 changing with the iterative learning cycle;

[0128] Figure 6This is the graph showing the change of attitude error of spacecraft 3 with iterative learning cycle;

[0129] Figure 7 This is the graph showing the position error of spacecraft 3 changing with the iterative learning cycle. DETAILED DESCRIPTION

[0130] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below in conjunction with embodiments and corresponding drawings.

[0131] Example: Problem of high-precision six-degree-of-freedom configuration maintenance for a low-Earth orbit satellite constellation under irregular gravitational field disturbances with unknown precise model

[0132] like Figure 1 As shown, the spacecraft configuration-maintaining attitude-orbit coupling collaborative iterative learning control method disclosed in this embodiment has the following specific implementation steps:

[0133] Step 1: Based on the Lie group SE (3) framework, the actual dynamic model and expected dynamic model of the spacecraft with six degrees of freedom are established, and on this basis, the error dynamic model of the spacecraft with six degrees of freedom is established.

[0134] Step 1.1: Establish a six-degree-of-freedom actual dynamic model of the spacecraft.

[0135] For the i-th spacecraft, the position and attitude of the spacecraft can be expressed by the variable g of the Lie group SE(3): i Expressed as

[0136]

[0137] Where R i ∈SO(3) represents the attitude rotation matrix of the i-th spacecraft from its own system to the inertial system along the principal axis of inertia. SO(3) is the Lie group of the special orthogonal matrix representing the attitude of the i-th spacecraft. represents the position vector from the origin of the coordinate system to the center of mass of the i-th spacecraft in the inertial system, represents a three-dimensional real vector set, 0 1×3 represents a 1×3 zero matrix, SE(3) is the Lie group of all translational and rotational motions of the spacecraft. The augmented velocity vector ξ of the i-th spacecraft i Expressed as

[0138]

[0139] in and They represent the inertial angular velocity and translational velocity of the i-th spacecraft in the system, represents a six-dimensional real vector set. In the SE(3) framework, the i-th spacecraft dynamics equation is expressed as

[0140]

[0141] in

[0142]

[0143] ξ i The matrix of the conjugate adjoint mapping is expressed as

[0144]

[0145] symbol(·) × Represents the cross product matrix of a vector. For a three-dimensional vector x=[x1,x2,x3] T , the cross product matrix of x(x) × Defined as

[0146]

[0147] where x1, x2, x3 are the three components of vector x; se(3) is the Lie algebra of the Lie group SE(3), J i is the moment of inertia of the ith spacecraft, m i is the mass of the i-th spacecraft, I3 represents the three-dimensional unit matrix, represents a 6×6 real matrix set, is the gravitational field of the ith spacecraft, is the control torque of the ith spacecraft, is the control force of the ith spacecraft, is the disturbance torque of the ith spacecraft, is the disturbance force of the i-th spacecraft, 0 3×3 Represents a 3×3 zero matrix.

[0148] Step 1.2: Establish the six-degree-of-freedom expected dynamic model of the spacecraft.

[0149] For the i-th spacecraft, in the SE(3) framework, the six-DOF expected dynamics model is expressed as

[0150]

[0151] in

[0152]

[0153] represents the expected attitude rotation matrix of the i-th spacecraft from its own system to the inertial system along the principal axis of inertia, represents the expected position vector from the origin of the coordinate system to the center of mass of the i-th spacecraft in the inertial system, and They represent the expected inertial angular velocity and expected translational velocity of the i-th spacecraft in this system, respectively. is the gravitational field of the i-th spacecraft at the desired position.

[0154] Step 1.3: According to equation (40) obtained in step 1.1 and equation (41) obtained in step 1.2, a six-degree-of-freedom error dynamics model of the spacecraft is established.

[0155] The error h between the actual position and attitude of the i-th spacecraft and the expected position and attitude i Expressed as

[0156]

[0157] The exponential coordinate vector used to represent the position and attitude error of the i-th spacecraft is

[0158]

[0159] in, and The index coordinate vectors representing the attitude tracking error and position tracking error respectively.

[0160] The velocity error of the i-th spacecraft in this system Expressed as

[0161]

[0162] in and They represent the rotational angular velocity error and translational velocity error of the i-th spacecraft system respectively.

[0163]

[0164] (h i ) -1 The matrix representation of the adjoint mapping is

[0165]

[0166] in, Indicates (h i ) -1 A 3×3 block matrix, Indicates (h i ) -1 A 3×1 block matrix.

[0167] The six-degree-of-freedom error kinematic equation of the spacecraft is expressed as

[0168]

[0169] Expressed as

[0170]

[0171] in

[0172]

[0173] and The six-degree-of-freedom error dynamics equation of the spacecraft is expressed as

[0174]

[0175] The matrix of the adjoint mapping is expressed as

[0176]

[0177] Substituting equation (40) into equation (47) and combining equation (45) in parallel, we can obtain the six-DOF error dynamics model of the spacecraft:

[0178]

[0179] Step 2. Based on the six-degree-of-freedom error dynamics model of the spacecraft obtained in step 1, design the spacecraft configuration maintenance attitude-orbit coupling collaborative iterative learning control law, and further determine the parameter conditions of the collaborative iterative learning control law through error analysis, so that the tracking error of the control system converges monotonically, and the spacecraft can be maintained quickly and with high precision without relying on an accurate disturbance model.

[0180] Step 2.1: Design a six-degree-of-freedom configuration-preserving feedback control law to keep the system stable before introducing the collaborative iterative learning control law.

[0181] The control input of the spacecraft consists of two parts: feedback control law and collaborative iterative learning control law. The control input of the i-th spacecraft in the j-th cycle is Feedback Control Law Designed for

[0182]

[0183] Where, the feedback controller gain and is a 6×6 positive definite diagonal matrix.

[0184] Step 2.2: Design a multi-spacecraft six-degree-of-freedom configuration-preserving collaborative iterative learning control law.

[0185] Substituting equation (49) into equation (48), the six-degree-of-freedom error dynamics model of the spacecraft under the feedback control law is:

[0186]

[0187] 0 6×6 represents a 6×6 zero matrix, represents the collaborative iterative learning control law of the i-th spacecraft in the j-th cycle. Formula (50) can be written as

[0188]

[0189] in,

[0190]

[0191] Represents the set of twelve-dimensional real vectors.

[0192] According to the norm of the tracking error, the spacecraft with the smallest tracking error in the jth cycle is determined, denoted as Right now

[0193]

[0194] in represents a natural number, Represents the set of all spacecraft.

[0195] The collaborative iterative learning control law uses the control input and error of the spacecraft with the smallest tracking error in the previous cycle to calculate the control input of the next cycle. represents the jth period spacecraft The control input is

[0196]

[0197] use and denote the spacecraft in the jth period The position and attitude tracking error and the velocity and angular velocity tracking error are:

[0198]

[0199] And define the new system state

[0200]

[0201] For the i-th spacecraft, the collaborative iterative learning control law in the j+1th cycle is for

[0202]

[0203] Among them, the iterative learning controller gain and is a 6×6 positive definite diagonal matrix, △ is a small positive number,

[0204] Step 2.3: Determine the parameter conditions of the collaborative iterative learning control law so that the tracking error of the control system converges monotonically, thereby achieving a short adjustment time and a small steady-state error, and realizing high-precision six-degree-of-freedom configuration maintenance of the spacecraft.

[0205] From equation (51) to equation (56), we can get the CILC error evolution process equation (57):

[0206]

[0207] in

[0208]

[0209] Represents spacecraft The disturbance in period j is and Represents spacecraft The feedback controller gain, Represents spacecraft The moment of inertia, Represents spacecraft quality.

[0210] In the j+1th period, integrate equation (51) from time 0 to t to obtain the tracking error of spacecraft i:

[0211]

[0212] Integrate equation (57) from time 0 to t to obtain the j-th period spacecraft Tracking error

[0213]

[0214] Integrate equation (57) from time t to t+△ and substitute it into equation (56), and we get the collaborative iterative learning control law for spacecraft i in the j+1th period:

[0215]

[0216] Substituting equation (59) and equation (60) into equation (58), we get and are all diagonal matrices, so we get

[0217]

[0218] in

[0219] Since the function f[e i,j (t)] is Lipschitz continuous, so in a cycle time T we have

[0220]

[0221] Taking the norm of both sides of formula (61) and substituting them into formula (62) we get

[0222]

[0223] where b B , b d , b L Respectively represent B i , L i The norm of O(△ 2 ) represents the 2 Apply the Bellman–Gronwall inequality and multiply both sides of equation (63) by e -λt , and λ satisfies

[0224]

[0225] get

[0226]

[0227] in

[0228] From equation (52) and equation (65), we can get

[0229]

[0230] in express The supremum of

[0231]

[0232] Defining variables

[0233]

[0234] Formula (66) can be rewritten as

[0235]

[0236] That is to say

[0237]

[0238] when satisfy

[0239]

[0240] When λ satisfies equation (64), we have and

[0241]

[0242] That is to say

[0243]

[0244] The definition of monotonic convergence of system error is satisfied. Therefore, when equation (72) is satisfied, the tracking error of the control system converges monotonically, thereby achieving a short adjustment time and a small steady-state error, and realizing high-precision six-degree-of-freedom configuration maintenance of the spacecraft.

[0245] In this embodiment, for the three spacecraft in the low earth orbit constellation, the expected orbital radius r d =7578.137km, orbital inclination i d =87.9°, right ascension of ascending node Ω d = 0, the three spacecraft are equally spaced in the orbital plane with a phase of 120°. The initial orbital radius of the spacecraft is 10 km smaller than the expected radius. The parameters of the Earth are shown in Table 1. The feedback controller gains of the three spacecraft are K p =diag(7×10 -4 I3,5×10 -5 I3), K d =diag(8×10 - 3 I3,1×10 -2 I3), where diag represents a diagonal matrix. The iterative learning controller gains of the three spacecraft are shown in Table 2.

[0246] Table 1 Earth parameters

[0247]

[0248] Table 2 Spacecraft iterative learning controller gains

[0249]

[0250] The attitude error of spacecraft 1 changes with the iterative learning cycle as follows: Figure 2 As shown, the position error of spacecraft 1 changes with the iterative learning cycle as follows Figure 3 As shown in Figure 2, the attitude error and position error of spacecraft 1 can converge when using the classical iterative learning control method and the collaborative iterative learning control method, but the convergence speed is faster when using the collaborative iterative learning control method; the attitude error of spacecraft 2 changes with the iterative learning cycle as shown in Figure 2. Figure 4 As shown, the position error of spacecraft 2 changes with the iterative learning cycle as follows Figure 5 As shown in Figure 2, the attitude error and position error of spacecraft 2 have been oscillating when using the classic iterative learning control method, with the attitude error oscillating at the order of 10° and the position error oscillating at the order of 1000m, but they can converge after using the collaborative iterative learning control method; the attitude error of spacecraft 3 changes with the iterative learning cycle as shown in Figure 2. Figure 6 As shown, the position error of spacecraft 3 changes with the iterative learning cycle as follows Figure 7 As shown in Figure 2, the attitude error and position error of spacecraft 3 diverge when using the classical iterative learning control method, where the attitude error diverges to 100° and the position error diverges to 10 5 m, but it can converge after using the collaborative iterative learning control method. It can be seen that compared with the classical iterative learning control method, the collaborative iterative learning control method can have a smaller steady-state error while shortening the adjustment time, thereby improving the speed and accuracy of spacecraft configuration maintenance.

[0251] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A spacecraft configuration-maintaining attitude-orbit coupling collaborative iterative learning control method, characterized in that: The following steps are included: Step 1: Based on the Lie group SE (3) framework, the actual dynamic model and expected dynamic model of the spacecraft with six degrees of freedom are established, and on this basis, the error dynamic model of the spacecraft with six degrees of freedom is established; Step 2. Based on the six-degree-of-freedom error dynamics model of the spacecraft obtained in step 1, design the spacecraft configuration maintenance attitude-orbit coupling collaborative iterative learning control law, and further determine the parameter conditions of the collaborative iterative learning control law through error analysis, so that the tracking error of the control system converges monotonically, and the spacecraft can be maintained quickly and with high precision without relying on an accurate disturbance model.

2. The spacecraft configuration-maintaining attitude-orbit coupling collaborative iterative learning control method according to claim 1, characterized in that: Step 1 is implemented as follows: Step 1.1: Establish a six-degree-of-freedom actual dynamic model of the spacecraft; For the i-th spacecraft, the position and attitude of the spacecraft can be expressed by the variable g of the Lie group SE(3): i Expressed as Where R i ∈SO(3) represents the attitude rotation matrix of the i-th spacecraft from its own system to the inertial system along the principal axis of inertia. SO(3) is the Lie group of the special orthogonal matrix representing the attitude of the i-th spacecraft. represents the position vector from the origin of the coordinate system to the center of mass of the i-th spacecraft in the inertial system, represents a three-dimensional real vector set, 0 1×3 represents a 1×3 zero matrix, SE(3) is the Lie group of all translational and rotational motions of the spacecraft; the augmented velocity vector ξ of the i-th spacecraft i Expressed as in and They represent the inertial angular velocity and translational velocity of the i-th spacecraft in the system, represents a six-dimensional real vector set; in the SE(3) framework, the i-th spacecraft dynamics equation is expressed as in ξ i The matrix of the conjugate adjoint mapping is expressed as symbol(·) × Represents the cross product matrix of a vector. For a three-dimensional vector x=[x1,x2,x3] T , the cross product matrix of x(x) × Defined as Among them, x1, x2, x3 are the three components of vector x; is the Lie algebra of the Lie group SE(3), J i is the moment of inertia of the ith spacecraft, m i is the mass of the i-th spacecraft, I3 represents the three-dimensional unit matrix, represents a 6×6 real matrix set, is the gravitational field of the ith spacecraft, is the control torque of the ith spacecraft, is the control force of the ith spacecraft, is the disturbance torque of the ith spacecraft, is the disturbance force of the i-th spacecraft, 0 3×3 represents a 3×3 zero matrix; Step 1.2: Establish the six-degree-of-freedom expected dynamic model of the spacecraft; For the i-th spacecraft, in the SE(3) framework, the six-DOF expected dynamics model is expressed as in represents the expected attitude rotation matrix of the i-th spacecraft from its own system to the inertial system along the principal axis of inertia, represents the expected position vector from the origin of the coordinate system to the center of mass of the i-th spacecraft in the inertial system, and They represent the expected inertial angular velocity and expected translational velocity of the i-th spacecraft in this system, respectively. is the gravitational field of the i-th spacecraft at the desired position; Step 1.3: According to equation (3) obtained in step 1.1 and equation (4) obtained in step 1.2, establish a six-degree-of-freedom error dynamics model of the spacecraft; The error h between the actual position and attitude of the i-th spacecraft and the expected position and attitude i Expressed as The exponential coordinate vector used to represent the position and attitude error of the i-th spacecraft is in, and The index coordinate vectors representing the attitude tracking error and position tracking error respectively; The velocity error of the i-th spacecraft in this system Expressed as in and They represent the rotational angular velocity error and translational velocity error of the i-th spacecraft in this system respectively; (h i ) -1 The matrix representation of the adjoint mapping is in, Indicates (h i ) -1 A 3×3 block matrix, Indicates (h i ) -1 3×1 block matrix; The six-degree-of-freedom error kinematic equation of the spacecraft is expressed as Expressed as in and The six-degree-of-freedom error dynamics equation of the spacecraft is expressed as The matrix of the adjoint mapping is expressed as Substituting equation (3) into equation (10) and combining equation (8) together, we can obtain the six-DOF error dynamics model of the spacecraft:

3. The spacecraft configuration-maintaining attitude-orbit coupling collaborative iterative learning control method according to claim 2, characterized in that: Step 2 is implemented as follows: Step 2.1: Design a six-degree-of-freedom configuration-maintaining feedback control law to keep the system stable before introducing the collaborative iterative learning control law; The control input of the spacecraft consists of two parts: feedback control law and collaborative iterative learning control law; the control input of the i-th spacecraft in the j-th cycle is Feedback Control Law Designed for Where, the feedback controller gain and is a 6×6 positive definite diagonal matrix; Step 2.2: Design a six-degree-of-freedom configuration to maintain the collaborative iterative learning control law; Substituting equation (12) into equation (11), the six-degree-of-freedom error dynamics model of the spacecraft under the feedback control law is: 0 6×6 represents a 6×6 zero matrix, represents the collaborative iterative learning control law of the i-th spacecraft in the j-th cycle; Formula (13) is written as in, represents a twelve-dimensional real vector set; According to the norm of the tracking error, the spacecraft with the smallest tracking error in the jth cycle is determined, denoted as Right now in represents a natural number, represents the set of all spacecraft; The collaborative iterative learning control law uses the control input and error of the spacecraft with the smallest tracking error in the previous cycle to calculate the control input of the next cycle; represents the jth period spacecraft The control input is use and denote the spacecraft in the jth period The position and attitude tracking error and the velocity and angular velocity tracking error are: And define the new system state For the i-th spacecraft, the collaborative iterative learning control law in the j+1th cycle is for Among them, the iterative learning controller gain and is a 6×6 positive definite diagonal matrix, △ is a small positive number, Step 2.3: Determine the parameters of the collaborative iterative learning control law so that the tracking error of the system converges monotonically and the high-precision six-degree-of-freedom configuration of the spacecraft is maintained; From equations (14) to (19), we can get the CILC error evolution process equation (20): in Represents spacecraft The disturbance in period j is and Represents spacecraft The feedback controller gain, Represents spacecraft The moment of inertia, Represents spacecraft quality; In the j+1th period, the tracking error of spacecraft i is obtained by integrating equation (14) from time 0 to t: Integrate equation (20) from time 0 to t to obtain the j-th period spacecraft Tracking error Integrate equation (20) from time t to t+△ and substitute it into equation (19), and we get the collaborative iterative learning control law for spacecraft i in the j+1th period: Substituting equation (22) and equation (23) into equation (21), we can get and are all diagonal matrices, so we get in Since the function f[e i,j (t)] is Lipschitz continuous, so in a cycle time T we have Taking the norms of both sides of formula (24) and substituting them into formula (25) we get where b B , b d , b L Respectively represent B i , L i The norm of O(△ 2 ) represents the 2 ; Apply the Bellman–Gronwall inequality and multiply both sides of equation (26) by e -λt , and λ satisfies get where ||e i,j+1 (t)|| λ = ||e i,j+1 (t)||e -λt , ||e i,j (t)|| λ = ||e i,j (t)||e -λt , From equation (15) and equation (28), we can get in express The supremum of Defining variables Formula (29) can be rewritten as That is to say when satisfy When λ satisfies equation (27), we have and That is to say The definition of monotonic convergence of system error is satisfied; therefore, when equation (35) is satisfied, the tracking error of the control system converges monotonically, thereby achieving high-precision six-degree-of-freedom configuration maintenance of the spacecraft.

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