Spacecraft Configuration-Maintaining Attitude-Orbit Coupling Iterative Learning Control Method

Abstract

This invention discloses a spacecraft configuration-maintaining attitude-orbit coupling cooperative iterative learning control method, belonging to the field of space technology. The implementation method of this invention is as follows: a six-degree-of-freedom dynamic model is established based on the Lie group SE(3) framework, fully considering the attitude-orbit coupling problem caused by thruster installation errors in actual engineering, improving configuration-maintaining accuracy, and avoiding the unwinding problem caused by traditional six-degree-of-freedom dual quaternion representation methods. Based on this, a cooperative iterative learning control method is designed to achieve, in the case of an unknown precise perturbation model, offset the influence of perturbation on configuration maintenance through iterative learning, taking into account both adjustment time and steady-state error, achieving a short adjustment time while maintaining a small steady-state error. That is, high-precision six-degree-of-freedom configuration maintenance of the spacecraft is achieved through attitude-orbit coupling cooperative iterative learning control. This invention can shorten the adjustment time, reduce steady-state error, and improve the speed and accuracy of spacecraft configuration maintenance without relying on a precise perturbation model.

Description

Technical Field

[0001] This invention relates to a spacecraft configuration maintenance control method, and more particularly to a spacecraft configuration maintenance attitude-orbit coupling cooperative iterative learning control method, belonging to the field of space technology. Background Technology

[0002] In recent years, numerous commercial space companies have designed and launched constellations with communication, navigation, and remote sensing capabilities, providing services such as satellite internet communication, timing and positioning, and Earth observation. To achieve global coverage and reduce the risk of collisions between spacecraft within the constellation, spacecraft operating in the same orbital plane need to maintain precise orbital phase and altitude. Furthermore, to ensure uniform observation conditions or antenna pointing requirements across all spacecraft, their attitudes must remain stable and consistent. Therefore, maintaining precise orbital and attitude configurations is crucial for improving the constellation's operational efficiency and safety.

[0003] In practical engineering contexts, during spacecraft maneuvers, gravity gradient torque disturbances related to orbital position and thruster installation errors cause coupled motion between the spacecraft's orbit and attitude, necessitating six-degree-of-freedom dynamic modeling. The spacecraft's configuration is affected by environmental disturbances, which cannot be accurately modeled, and limited prior information increases the difficulty of controller design. Furthermore, designing a suitable controller gain to enable the spacecraft to track the target orbital position and attitude is challenging, making it difficult to balance settling time and steady-state error. Therefore, it is necessary to design a controller with fast settling time, small steady-state error, and independence from precise disturbance models. Summary of the Invention

[0004] To address the issues of unknown disturbance models and difficulty in balancing settling time and steady-state error during spacecraft configuration maintenance, this invention aims to provide a spacecraft configuration maintenance attitude-orbit coupled cooperative iterative learning control method that achieves high-precision six-degree-of-freedom configuration maintenance while balancing short settling time and small steady-state error.

[0005] The objective of this invention is achieved through the following technical solution.

[0006] The spacecraft configuration-maintaining attitude-orbit coupling cooperative iterative learning control method disclosed in this invention establishes a six-degree-of-freedom dynamic model based on the Lie group SE(3) framework. It fully considers the attitude-orbit coupling problem caused by thruster installation errors in actual engineering, improving configuration-maintaining accuracy and avoiding the unwinding problem caused by traditional six-degree-of-freedom dual quaternion representation methods. Based on this, a cooperative iterative learning control method is designed. When the precise perturbation model is unknown, iterative learning offsets the influence of perturbations on configuration maintenance, balancing adjustment time and steady-state error. It achieves high-precision six-degree-of-freedom configuration maintenance of the spacecraft while maintaining a short adjustment time and a small steady-state error. This invention can shorten adjustment time, reduce steady-state error, and improve configuration-maintaining speed and accuracy without relying on a precise perturbation model.

[0007] The spacecraft configuration-maintaining attitude-orbit coupling cooperative iterative learning control method disclosed in this invention includes the following steps:

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

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

[0010] For the i-th spacecraft, the spacecraft's position and attitude can be determined by the variable g of the Lie group SE(3). i Represented as

[0011]

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

[0013]

[0014] in and Let represent the inertial angular velocity and translational velocity of the i-th spacecraft in its own system, respectively. Let represent a six-dimensional set of real vectors. Within the SE(3) framework, the i-th spacecraft dynamics equation is expressed as:

[0015]

[0016] in

[0017]

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

[0019]

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

[0021]

[0022] Where x1, x2, and x3 are the three components of vector x; se(3) is the Lie algebra of the Lie group SE(3), and J i Let m be the moment of inertia of the i-th spacecraft. i Let I be the mass of the i-th spacecraft, and let I3 represent the three-dimensional identity matrix. Represents the set of 6×6 real number matrices. Let i be the gravitational field of the i-th spacecraft. Let be the control torque of the i-th spacecraft. For the control force of the i-th spacecraft, Let be the disturbance torque of the i-th spacecraft. For the perturbation force of the i-th spacecraft, 0 3×3 This represents a 3×3 zero matrix.

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

[0024] For the i-th spacecraft, under the SE(3) framework, the six-degree-of-freedom expected dynamics model is expressed as:

[0025]

[0026] in

[0027]

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

[0029] Step 1.3: Based on equation (3) obtained in step 1.1 and equation (4) obtained in step 1.2, establish a six-degree-of-freedom error dynamic model for the spacecraft.

[0030] The error h between the actual position and attitude of the i-th spacecraft and its desired position and attitude i Represented 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 These represent the exponential coordinate vectors of attitude tracking error and position tracking error, respectively.

[0035] Velocity error of the i-th spacecraft in its own system Represented as

[0036]

[0037] in and Let represent the rotational angular velocity error and translational velocity error of the i-th spacecraft's intrinsic system, respectively.

[0038]

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

[0040]

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

[0042] The six-degree-of-freedom error kinematic equations of a spacecraft are expressed as follows:

[0043]

[0044] Represented as

[0045]

[0046] in

[0047]

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

[0049]

[0050] The matrix representation of the adjoint mapping is as follows

[0051]

[0052] Substituting equation (3) into equation (10) and combining them with equation (8), we obtain the six-degree-of-freedom 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 a spacecraft configuration-maintaining attitude-orbit coupling cooperative iterative learning control law. Further, determine the parameter conditions of the cooperative iterative learning control law through error analysis, so that the tracking error of the control system converges monotonically, and realize the spacecraft's rapid and high-precision configuration maintenance without relying on the precise disturbance model.

[0055] Step 2.1: Design a six-degree-of-freedom configuration to maintain feedback control law, so that the system remains stable before the introduction of a cooperative iterative learning control law.

[0056] The control input of a spacecraft consists of two parts: a feedback control law and a cooperative iterative learning control law. The control input of the i-th spacecraft within the j-th period... Feedback control law Designed for

[0057]

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

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

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

[0061]

[0062] 0 6×6 Represents a 6×6 zero matrix. Let represent the cooperative iterative learning control law of the i-th spacecraft in the j-th cycle. Equation (13) can be rewritten as...

[0063]

[0064] in,

[0065]

[0066] This represents a twelve-dimensional set of real number vectors.

[0067] The spacecraft with the smallest tracking error in the j-th period is determined based on the norm of the tracking error, denoted as . Right now

[0068]

[0069] in Represents natural numbers, It represents the collection of all spacecraft.

[0070] The collaborative iterative learning control law uses the spacecraft's control input and error that minimized the tracking error in the previous cycle to calculate the control input for the next cycle. Describes the spacecraft in the j-th period. The control input, i.e.

[0071]

[0072] use and They represent the spacecraft in the j-th period, respectively. Position and attitude tracking error and velocity / angular velocity tracking error, i.e.

[0073]

[0074] And define the new system state.

[0075]

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

[0077]

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

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

[0080] From equations (14) to (19), we obtain equation (20) for the CILC error evolution process.

[0081]

[0082] in

[0083]

[0084] Indicates spacecraft The disturbance experienced during period j and Indicates spacecraft The feedback controller gain, Indicates spacecraft Moment of inertia, Indicates spacecraft The quality.

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

[0086]

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

[0088]

[0089] Integrating equation (20) from time t to t+Δ and substituting it into equation (19), we obtain the cooperative iterative learning control law for spacecraft i in the (j+1)th period.

[0090]

[0091] Substituting equations (22) and (23) into equation (21), since and Both are diagonal matrices, therefore we get

[0092]

[0093] in

[0094] Due to the function f[e i,j[(t)] is Lipschitz continuous, therefore within a periodic time T, we have

[0095]

[0096] Taking the norm of both sides of equation (24) and substituting it into equation (25), we get...

[0097]

[0098] Where b B b d , b L They represent B respectively i , L i The norm, O(△) 2 ) indicates about △ 2 The higher-order minor. 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 equations (15) and (28), we can obtain

[0104]

[0105] in express The supremum, that is

[0106]

[0107] Define variables

[0108]

[0109] Equation (29) is rewritten as

[0110]

[0111] That is to say

[0112]

[0113] when satisfy

[0114]

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

[0116]

[0117] That is to say

[0118]

[0119] The system error is monotonically convergent. Therefore, when equation (35) is satisfied, the tracking error of the control system is monotonically convergent, thus achieving a small steady-state error while having a short adjustment time, 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 cooperative iterative learning control method disclosed in this invention establishes a six-degree-of-freedom error dynamic model of the spacecraft under the SE(3) framework, fully considers the attitude-orbit coupling problem caused by thruster installation error in actual engineering, improves the spacecraft configuration maintenance accuracy, 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 cooperative iterative learning control method disclosed in this invention, by designing a cooperative iterative learning control law, in the case of unknown precise disturbance model, offsets the influence of disturbance on configuration maintenance through iterative learning, taking into account both settling time and steady-state error, so that the control process does not depend on precise disturbance model, and can have a small steady-state error while having a short settling time, thus shortening the settling time, reducing steady-state error, and improving the speed and accuracy of configuration maintenance. Attached Figure Description

[0123] Figure 1 Flowchart of a collaborative iterative learning control method for maintaining attitude and orbit coupling in spacecraft configuration;

[0124] Figure 2 The graph shows the change in the attitude error of spacecraft 1 as a function of the iterative learning cycle.

[0125] Figure 3 The graph shows the change in the position error of spacecraft 1 as a function of the iterative learning cycle.

[0126] Figure 4 The graph shows the change in attitude error of spacecraft 2 as a function of the iterative learning cycle.

[0127] Figure 5 The graph shows the change in the position error of spacecraft 2 as a function of the iterative learning cycle.

[0128] Figure 6The graph shows the change in the attitude error of spacecraft 3 as a function of the iterative learning cycle.

[0129] Figure 7 The graph shows the change in the position error of spacecraft 3 as a function of the iterative learning cycle. Detailed Implementation

[0130] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the embodiments and corresponding drawings.

[0131] Example: Achieving high-precision six-degree-of-freedom configuration maintenance for a near-Earth orbit satellite constellation under irregular gravitational field perturbations with an unknown precise model.

[0132] like Figure 1 As shown in the figure, the specific implementation steps of the spacecraft configuration-maintaining attitude-orbit coupling cooperative iterative learning control method disclosed in this embodiment are as follows:

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

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

[0135] For the i-th spacecraft, the spacecraft's position and attitude can be determined by the variable g of the Lie group SE(3). i Represented as

[0136]

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

[0138]

[0139] in and Let represent the inertial angular velocity and translational velocity of the i-th spacecraft in its own system, respectively. Let represent a six-dimensional set of real vectors. Within the SE(3) framework, the i-th spacecraft dynamics equation is expressed as:

[0140]

[0141] in

[0142]

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

[0144]

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

[0146]

[0147] Where x1, x2, and x3 are the three components of vector x; se(3) is the Lie algebra of the Lie group SE(3), and J i Let m be the moment of inertia of the i-th spacecraft. i Let I be the mass of the i-th spacecraft, and let I3 represent the three-dimensional identity matrix. Represents the set of 6×6 real number matrices. Let i be the gravitational field of the i-th spacecraft. Let be the control torque of the i-th spacecraft. For the control force of the i-th spacecraft, Let be the disturbance torque of the i-th spacecraft. For the perturbation force of the i-th spacecraft, 0 3×3 This represents a 3×3 zero matrix.

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

[0149] For the i-th spacecraft, under the SE(3) framework, the six-degree-of-freedom expected dynamics model is expressed as:

[0150]

[0151] in

[0152]

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

[0154] Step 1.3: Based on equation (40) obtained in step 1.1 and equation (41) obtained in step 1.2, establish a six-degree-of-freedom error dynamic model for the spacecraft.

[0155] The error h between the actual position and attitude of the i-th spacecraft and its desired position and attitude i Represented 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 These represent the exponential coordinate vectors of attitude tracking error and position tracking error, respectively.

[0160] Velocity error of the i-th spacecraft in its own system Represented as

[0161]

[0162] in and Let represent the rotational angular velocity error and translational velocity error of the i-th spacecraft's intrinsic system, respectively.

[0163]

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

[0165]

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

[0167] The six-degree-of-freedom error kinematic equations of a spacecraft are expressed as follows:

[0168]

[0169] Represented as

[0170]

[0171] in

[0172]

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

[0174]

[0175] The matrix representation of the adjoint mapping is as follows

[0176]

[0177] Substituting equation (40) into equation (47) and combining them with equation (45), we obtain the six-degree-of-freedom 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 a spacecraft configuration-maintaining attitude-orbit coupling cooperative iterative learning control law. Further, determine the parameter conditions of the cooperative iterative learning control law through error analysis, so that the tracking error of the control system converges monotonically, and realize the spacecraft's rapid and high-precision configuration maintenance without relying on the precise disturbance model.

[0180] Step 2.1: Design a six-degree-of-freedom configuration to maintain feedback control law, so that the system remains stable before the introduction of a cooperative iterative learning control law.

[0181] The control input of a spacecraft consists of two parts: a feedback control law and a cooperative iterative learning control law. The control input of the i-th spacecraft within the j-th period... Feedback control law Designed for

[0182]

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

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

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

[0186]

[0187] 0 6×6 Represents a 6×6 zero matrix. Let represent the cooperative iterative learning control law of the i-th spacecraft in the j-th cycle. Equation (50) can be rewritten as...

[0188]

[0189] in,

[0190]

[0191] This represents a twelve-dimensional set of real number vectors.

[0192] The spacecraft with the smallest tracking error in the j-th period is determined based on the norm of the tracking error, denoted as . Right now

[0193]

[0194] in Represents natural numbers, It represents the collection of all spacecraft.

[0195] The collaborative iterative learning control law uses the spacecraft's control input and error that minimized the tracking error in the previous cycle to calculate the control input for the next cycle. Describes the spacecraft in the j-th period. The control input, i.e.

[0196]

[0197] use and They represent the spacecraft in the j-th period, respectively. Position and attitude tracking error and velocity / angular velocity tracking error, i.e.

[0198]

[0199] And define the new system state.

[0200] .

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

[0202]

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

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

[0205] From equations (51) to (56), we obtain equation (57) for the CILC error evolution process.

[0206]

[0207] in

[0208]

[0209] Indicates spacecraft The disturbance experienced during period j and Indicates spacecraft The feedback controller gain, Indicates spacecraft Moment of inertia, Indicates spacecraft The quality.

[0210] The tracking error of spacecraft i is obtained by integrating equation (51) from time 0 to t in the (j+1)th period.

[0211]

[0212] Integrating equation (57) from time 0 to t yields the spacecraft in the j-th period. Tracking error

[0213]

[0214] Integrating equation (57) from time t to t+Δ and substituting it into equation (56), we obtain the cooperative iterative learning control law for spacecraft i in the (j+1)th period.

[0215]

[0216] Substituting equations (59) and (60) into equation (58), since and Both are diagonal matrices, therefore we get

[0217]

[0218] in

[0219] Due to the function f[e i,j [(t)] is Lipschitz continuous, therefore within a periodic time T, we have

[0220]

[0221] Taking the norm of both sides of equation (61) and substituting it into equation (62), we get...

[0222]

[0223] Where b B b d , b L They represent B respectively i , L i The norm, O(△) 2 ) indicates about △ 2 The higher-order minor. 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 equations (52) and (65), we can obtain

[0229]

[0230] in express The supremum, that is

[0231]

[0232] Define variables

[0233]

[0234] Equation (66) is rewritten as

[0235]

[0236] That is to say

[0237]

[0238] when satisfy

[0239]

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

[0241]

[0242] That is to say

[0243]

[0244] The system error is monotonically convergent. Therefore, when equation (72) is satisfied, the tracking error of the control system is monotonically convergent, thus achieving a small steady-state error while having a short adjustment time, 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 desired orbital radius r is... d =7578.137km, orbital inclination i d = 87.9°, right ascension of the ascending node Ω d Three spacecraft are positioned in a Keplerian orbit with a phase difference of 120° and evenly spaced within the orbital plane. The initial orbital radius of the spacecraft is 10 km smaller than the desired radius. Earth's parameters are shown in Table 1. The feedback controller gain for the three spacecraft is 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. Gain of Spacecraft Iterative Learning Controller

[0249]

[0250] Spacecraft 1 attitude error changes with 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, the attitude and position errors of spacecraft 1 can converge using both the classical iterative learning control method and the cooperative iterative learning control method, but the convergence speed is faster when using the cooperative iterative learning control method; the attitude error of spacecraft 2 changes with the iterative learning cycle as follows: Figure 4 As shown, the position error of spacecraft 2 changes with the iterative learning cycle as follows: Figure 5 As shown, the attitude and position errors of spacecraft 2 oscillated continuously when using the classical iterative learning control method, with the attitude error oscillating on the order of 10° and the position error on the order of 1000m. However, they converged after using the cooperative iterative learning control method. The attitude error of spacecraft 3 changes with the iterative learning cycle as follows: Figure 6 As shown, the position error of spacecraft 3 changes with the iterative learning cycle as follows: Figure 7 As shown, the attitude error and position error of spacecraft 3 diverge when using the classical iterative learning control method, with the attitude error diverging to 100° and the position error diverging to 10°. 5 The error was on the order of m, but it converged after using the cooperative iterative learning control method. It can be seen that, compared with the classical iterative learning control method, the cooperative iterative learning control method has a shorter settling time and a smaller steady-state error, improving the spacecraft configuration holding speed and accuracy.

[0251] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description 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 within the scope of protection of the present invention.

Claims

1. A spacecraft configuration-maintaining attitude-orbit coupled cooperative iterative learning control method, characterized by: Includes the following steps, Step 1: Based on the Lie group SE(3) framework, establish the actual dynamic model and the expected dynamic model of the spacecraft with six degrees of freedom, and on this basis, establish the error dynamic model of the spacecraft with six degrees of freedom; 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 spacecraft's position and attitude can be determined by the variable g of the Lie group SE(3). i Represented as Where R i ∈SO(3) represents the attitude rotation matrix of the i-th spacecraft from its native frame to the inertial frame along the principal axis of inertia, and SO(3) is a Lie group representing the special orthogonal matrix of the attitude of the i-th spacecraft. This represents the position vector from the origin of the coordinate system in the inertial frame to the center of mass of the i-th spacecraft. Represents a three-dimensional set of real vectors, 0 1×3 Let SE(3) be a 1×3 zero matrix, and let SE(3) be the Lie group of all translational and rotational motions of the spacecraft; let ξ be the augmented velocity vector of the i-th spacecraft. i Represented as in and Let represent the inertial angular velocity and translational velocity of the i-th spacecraft in its own system, respectively. Represents a six-dimensional set of real vectors; within the SE(3) framework, the i-th spacecraft dynamics equation is expressed as in ξ i The matrix representation of the conjugate adjoint mapping is as follows symbol(·) × The matrix representing the cross product of vectors, for a three-dimensional vector x = [x1, x2, x3]. T The cross product matrix (x) of x. × Defined as Where x1, x2, and x3 are the three components of vector x; se(3) is the Lie algebra of the Lie group SE(3), and J i Let m be the moment of inertia of the i-th spacecraft. i Let I be the mass of the i-th spacecraft, and let I3 represent the three-dimensional identity matrix. Represents the set of 6×6 real number matrices, ▽U(r i Let be the gravitational field of the i-th spacecraft. Let be the control torque of the i-th spacecraft. For the control force of the i-th spacecraft, Let be the disturbance torque of the i-th spacecraft. For the perturbation force of the i-th spacecraft, 0 3×3 Represents a 3×3 zero matrix; Step 1.2: Establish the desired six-degree-of-freedom dynamic model of the spacecraft; For the i-th spacecraft, under the SE(3) framework, the six-degree-of-freedom expected dynamics model is expressed as: in Let represent the desired attitude rotation matrix of the i-th spacecraft from its native frame to the inertial frame along the principal axis of inertia. Let represent the desired position vector from the origin of the coordinate system in the inertial frame to the center of mass of the i-th spacecraft. and Let represent the desired inertial angular velocity and desired translational velocity of the i-th spacecraft in its own system, respectively. Let be the gravitational field of the i-th spacecraft at the desired location; Step 1.3: Based on equation (3) obtained in Step 1.1 and equation (4) obtained in Step 1.2, establish a six-degree-of-freedom error dynamic model for the spacecraft; The error h between the actual position and attitude of the i-th spacecraft and its desired position and attitude i Represented as The exponential coordinate vector used to represent the position and attitude error of the i-th spacecraft is: in, and These represent the exponential coordinate vectors of attitude tracking error and position tracking error, respectively. Velocity error of the i-th spacecraft in its own system Represented as in and Let represent the rotational angular velocity error and translational velocity error of the i-th spacecraft's intrinsic system, respectively; for (h i ) -1 The matrix representation of the adjoint mapping is as follows in, (h) i ) -1 A 3×3 block matrix, (h) i ) -1 A 3×1 block matrix; The six-degree-of-freedom error kinematic equations of a spacecraft are expressed as follows: Represented as in and The six-degree-of-freedom error dynamics equation of a spacecraft is expressed as follows: The matrix representation of the adjoint mapping is as follows Substituting equation (3) into equation (10) and combining them with equation (8), we obtain the six-degree-of-freedom error dynamics model of the spacecraft. Step 2: Based on the six-degree-of-freedom error dynamics model of the spacecraft obtained in Step 1, design a configuration-maintaining attitude-orbit coupling cooperative iterative learning control law for the spacecraft. Further, determine the parameter conditions of the cooperative iterative learning control law through error analysis, so that the tracking error of the control system converges monotonically, and realize the spacecraft's rapid and high-precision configuration maintenance without relying on the precise disturbance model. Step 2 is implemented as follows: Step 2.1: Design a six-degree-of-freedom configuration to maintain feedback control law, so that the system remains stable before the introduction of a cooperative iterative learning control law; The control input of a spacecraft consists of two parts: a feedback control law and a cooperative iterative learning control law; the control input of the i-th spacecraft in the j-th period. Feedback control law Designed for Among them, the feedback controller gain and It is a 6×6 positive definite diagonal matrix; Step 2.2: Design a six-DOF configuration-preserving cooperative iterative learning control law; Substituting equation (12) into equation (11), the six-degree-of-freedom error dynamics model of the spacecraft under the action of the feedback control law is: 0 6×6 Represents a 6×6 zero matrix. This represents the cooperative iterative learning control law for the i-th spacecraft in the j-th cycle; Equation (13) is written as in, Represents a twelve-dimensional set of real vectors; The spacecraft with the smallest tracking error in the j-th period is determined based on the norm of the tracking error, denoted as . Right now in Let I represent a natural number and 1 represent the set of all spacecraft. The collaborative iterative learning control law uses the spacecraft's control input and error that minimized the tracking error in the previous cycle to calculate the control input for the next cycle; Describes the spacecraft in the j-th period. The control input, i.e. use and They represent the spacecraft in the j-th period, respectively. Position and attitude tracking error and velocity / angular velocity tracking error, i.e. And define the new system state. For the i-th spacecraft, the collaborative iterative learning control law in the j+1-th cycle for Among them, the iterative learning controller gain and It is a 6×6 positive definite diagonal matrix, where Δ is a small positive number. Step 2.3: Determine the parameters of the cooperative iterative learning control law so that the tracking error of the system converges monotonically, thereby achieving high-precision six-degree-of-freedom configuration maintenance of the spacecraft; From equations (14) to (19), we obtain equation (20) for the CILC error evolution process. in Indicates spacecraft The disturbance experienced during period j and Indicates spacecraft The feedback controller gain, Indicates spacecraft Moment of inertia, Indicates spacecraft The quality; The tracking error of spacecraft i is obtained by integrating equation (14) from time 0 to t in the (j+1)th period. Integrating equation (20) from time 0 to t yields the j-th period spacecraft. Tracking error Integrating equation (20) from time t to t+Δ and substituting it into equation (19), we obtain the cooperative iterative learning control law for spacecraft i in the (j+1)th period. Substituting equations (22) and (23) into equation (21), since and Both are diagonal matrices, therefore we get in Due to the function f[e i,j [(t)] is Lipschitz continuous, therefore within a periodic time T, we have Taking the norm of both sides of equation (24) and substituting it into equation (25), we get... Where b B b d , b L They represent B respectively i , L i The norm, O(Δ) 2 ) represents about Δ 2 The higher-order small quantity; 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 equations (15) and (28), we can obtain in express The supremum, that is Define variables Equation (29) is rewritten as That is to say when satisfy And when λ satisfies equation (27), we have and That is to say The system error is monotonically convergent, so when equation (35) is satisfied, the tracking error of the control system is monotonically converged, thereby achieving high-precision six-degree-of-freedom configuration maintenance of the spacecraft.

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