A rigid-flexible fluid coupling spacecraft attitude and orbit integrated modeling and control method

Abstract

This invention provides an integrated attitude and orbit modeling and control method for rigid-flexible fluid-coupled spacecraft. It establishes a control-oriented integrated kinematic and dynamic model of the rigid-flexible fluid-coupled spacecraft's attitude and orbit, laying the foundation for subsequent controllers; it establishes attitude constraint models and obstacle avoidance constraint models to ensure that attitude and obstacle avoidance constraints are met; and it proposes an adaptive trajectory and attitude integrated controller. This invention employs the aforementioned integrated attitude and orbit modeling and control method for rigid-flexible fluid-coupled spacecraft to achieve integrated trajectory and attitude control of the spacecraft, improving the safety of spacecraft operation.

Description

Technical Field

[0001] This invention relates to the field of integrated control of spacecraft trajectory and attitude, and in particular to a method for integrated modeling and control of rigid-flexible-fluid coupled spacecraft attitude and orbit. Background Technology

[0002] A spacecraft is a space vehicle that operates in space according to the laws of celestial mechanics, responsible for performing complex space exploration, development, and utilization missions involving space and celestial bodies. To accomplish increasingly complex space missions, spacecraft structures are becoming increasingly complex, leading to greater flexible vibrations. To achieve the control objectives of long-term on-orbit operation, spacecraft need to carry more and more liquid fuel, further compromising the stability of the spacecraft system. Furthermore, spacecraft may face the threat of collisions with other spacecraft, targets, and space obstacles; therefore, on-orbit operation also requires meeting attitude angle and obstacle avoidance constraints. Thus, researching related scientific issues has a driving effect, providing new ideas for the safe and stable operation of spacecraft and improving their on-orbit capabilities.

[0003] In terms of attitude control under the influence of flexible attachment vibration, liquid fuel sloshing, and obstacle avoidance constraints, scholars at home and abroad have conducted relevant explorations and research. The current shortcomings are mainly reflected in the following aspects: (1) In the research on spacecraft attitude and orbit control, attitude and orbit are designed separately, and then the controller is designed independently, ignoring the influence of the coupling between orbit dynamics and attitude dynamics; (2) Most existing modeling and control consider rigid-flexible or rigid-liquid spacecraft separately, and the research on rigid-flexible-liquid coupled spacecraft modeling and control is not yet mature; (3) In the spacecraft attitude trajectory control, rigid-flexible-liquid coupling, attitude constraints, obstacle avoidance constraints and other issues are rarely considered in a comprehensive manner. Therefore, the integrated establishment of rigid-flexible-liquid coupled spacecraft orbit dynamics model and attitude dynamics model, and the implementation of attitude and orbit cooperative control are the future development trend and key issues that need to be solved, which have important theoretical significance and engineering value. Summary of the Invention

[0004] The purpose of this invention is to provide an integrated modeling and control method for attitude and orbit of rigid-flexible fluid coupled spacecraft, so as to realize integrated control of trajectory and attitude of rigid-flexible fluid coupled spacecraft and improve the safety of spacecraft operation.

[0005] To achieve the above objectives, this invention provides a method for integrated attitude and orbit modeling and control of rigid-flexible fluid coupled spacecraft, comprising the following steps:

[0006] Based on the momentum conservation theory, the rigid-flexible and rigid-liquid coupling effects are analyzed, and a rigid-flexible and rigid-liquid coupled spacecraft trajectory and attitude integrated dynamic model is established. The three coupling relationships of rigid, flexible and fluid are comprehensively analyzed. Based on the Lie group SE(3) theory, a rigid-flexible fluid coupled spacecraft trajectory and attitude integrated dynamic tracking error model is established, laying the foundation for the following controller design.

[0007] Secondly, attitude constraints, obstacle avoidance constraints, and input constraints of the rigid-flexible fluid coupling spacecraft are established. Based on attitude constraints, obstacle avoidance constraints, and potential function theory, the additional forces exerted on the spacecraft by bright objects and obstacles are obtained. The controller is obtained by combining the additional forces exerted on the spacecraft by bright objects and obstacles.

[0008] Finally, based on the controller, a saturated controller was designed to solve the control input constraint problem and realize the integrated control of the rigid-flexible-fluid coupling spacecraft trajectory and attitude.

[0009] Preferably, based on the theory of momentum conservation and the Lagrange principle, the integrated dynamic model of the rigid-flexible coupled spacecraft trajectory and attitude is established as follows:

[0010]

[0011] Where, m f With J f Let v be the mass and moment of inertia of the rigid-flexible spacecraft, and v be the velocity. m kf For the mass at nominal point k, r bk Let ω be the distance from the spacecraft's center of mass to the connection point between the flexible appendage and the rigid body, ω be the angular velocity, and ω be the rigid-flexible translational coupling matrix. Rotational coupling matrix χ represents flexible vibration. F g and M g M represents the gravitational gradient force and gravitational gradient torque. d and F d For the interfering force and the interfering torque, F is the perturbation force caused by the Earth's oblateness. c and M c For control force and control torque, M g F g and They are respectively J2 = 0.00108263 is the perturbation constant due to the Earth's oblateness disturbance, R∈SO(3) represents the rotation matrix from the spacecraft's body coordinate system to the Earth's inertial frame, I3 is the identity matrix, and μ = 3.9860047 × 10 14 m 3 s -2 R is the standard gravitational parameter for Earth. e =6378.14Km is the radius at the Earth's equator, C0 = diag(

[113] ), p is the position vector of the spacecraft's body coordinate system in the Earth's inertial frame, p z C represents the Z-axis component of the translation vector p; f =diag{2ε i Ωi}and These are the flexibility matrix and stiffness matrix of the flexible attachment, respectively, ε i Let Ω be the damping ratio of the i-th mode. i denoted as the natural frequency of the mode.

[0012] Preferably, the integrated dynamic model of rigid-fluid coupled spacecraft trajectory and attitude is as follows:

[0013]

[0014] Where, m l r is the total mass of the liquid fuel l Let k be the velocity vector at the nominal point k, which is the distance from the center of mass. ω(k) is the angular velocity of point k. and Let M be the rigid-fluid translational coupling matrix and the rigid-fluid rotational coupling matrix. η =[m l1 m l1 m l2 m l2 ] T For the mass matrix of the swaying liquid, C l =[c i1 c i1 c i2 c i2 ] T For a flexible matrix of swaying liquid, K l =[k l1 k l1 k l2 k l2 ] T Let η be the stiffness matrix of the sloshing liquid, and η be the modal value of the sloshing liquid.

[0015] Preferably, based on the Lie group SE(3) theory, a dynamic tracking error model for the trajectory and attitude integration of a rigid-flexible fluid coupled spacecraft is established as follows:

[0016]

[0017] Where Ξ=diag(J,mI3)∈R 6×6 It is a symmetric positive definite matrix, ξ e =ξ-ξ d For spacecraft tracking error, It is the inverse adjoint mapping of the spacecraft's velocity vector ξ, ξ = [v T ω T ] T , It is the adjoint mapping of the spacecraft's velocity vector ξ, the adjoint matrix mapping. Re For the rotation matrix error, p e This represents the position vector error of the spacecraft's body coordinate system in the Earth's inertial frame.

[0018] v d With ω d These are the desired velocity and angular velocity, respectively. Γ d =[M d ,F d ] T ∈R 6 , χ∈R M , γ∈R N These represent the vibration modes of the flexible attachment and the sloshing mode of the liquid fuel, respectively. Let M and N represent the rigid-flexible coupling matrix and the rigid-fluid coupling matrix, respectively. M and N represent the approximate orders of the two modes, respectively. Let M = 3 and N = 4. Let C represent the stiffness matrix. f =diag{2ξ i Ω i ,i=1,2,...,M∈R 3×3 The damping matrix represents the vibration of the flexible attachment, where ξ i and Ω i Let M represent the vibration damping and vibration frequency of the i-th order flexible attachment vibration mode, respectively. l =diag([m1 m1 m2 m2])∈R 4×4 Denotes the mass matrix of the liquid sloshing fuel, where m i This represents the mass of the sloshing fuel in the i-th sloshing mode.

[0019] Preferably, the additional forces exerted on the spacecraft by bright objects and obstacles.

[0020]

[0021] Among them, k3 > 0 and k4 > 0 are positive constants;

[0022] The attitude and obstacle avoidance constraints result in the following controller:

[0023]

[0024] in, Sliding surface S=[S1 S2 S3]=ξ e +ν1η,ν1=diag(ν 11 ,...,ν 16 )∈R 6×6 It is a positive definite diagonal matrix.

[0025] Let K1 ∈ R be a positive definite matrix. 6×6 K is a positive definite diagonal matrix. 2i =diag{K 21 ,K 22 ...K 26} is a positive definite matrix, λ min (K2)>||ΞΓ D ||,

[0026] Preferably, the attitude constraint of the rigid-flexible fluid coupling spacecraft is as follows:

[0027] <a,R T b n >>θ (8);

[0028] Where 'a' represents the unit direction vector of the optical-sensitive spaceborne device in the spacecraft's coordinate system, and θ represents the half-field-of-view angle of the optical-sensitive spaceborne device. p is the unit direction vector of the relative position vector between the bright object and the spacecraft. n This represents the position vector of a bright object in Earth's inertial frame of reference.

[0029] Set a safety angle σ n >θ, when <a,R T b n >≥σ n At that time, the spacecraft attitude constraint problem is not considered;

[0030] In summary, the potential function for attitude constraints is:

[0031]

[0032] Calculate the potential function U n The torque T exerted on the spacecraft by the nth bright object under its influence is equal to the potential function U. n The negative gradient relative to the unit direction vector of the photosensitive spaceborne device is denoted as... The specific expression is:

[0033]

[0034] Where Ra is the unit direction vector of the photosensitive spaceborne device in the Earth's inertial coordinate system;

[0035] Desired attitude of spacecraft g d σ is satisfied at any time. n < <a,R T b n > Unaffected by attitude constraints;

[0036] The obstacle avoidance constraints for rigid-flexible fluid coupled spacecraft are:

[0037] ||p n -p||>d n (11);

[0038] Where, d n p represents the limit distance at which the spacecraft collides with the nth obstacle. n p represents the position vector of a bright object in Earth's inertial frame. n -p represents the relative position vector between the bright object and the spacecraft;

[0039] Set a safe distance when When the spacecraft is far from the obstacle, obstacle avoidance constraints do not need to be considered. Therefore, the potential function of the obstacle avoidance constraint is:

[0040]

[0041] From equation (12), we know that only when the spacecraft's center of mass is taken as the origin and the radius is... The potential function only takes effect when there is an obstacle within the spherical region;

[0042] Calculate the potential function F n The force F exerted on the spacecraft by the nth obstacle under its influence is equal to the potential function F. n The negative gradient relative to the unit direction vector of the photosensitive spaceborne device is denoted as... The specific expression is:

[0043]

[0044] Ensure that obstacle avoidance constraints are met at the desired pose, so that the pose g of the ideal navigation spacecraft is achieved. d Satisfies at any time Unaffected by obstacle avoidance constraints.

[0045] Preferably, the control input constraints for a rigid-flexible fluid-coupled spacecraft are:

[0046]

[0047] in, It is a positive number;

[0048] When the theoretically calculated control torque M c When the actuator exceeds its actual tolerance range, a control input constraint problem arises. Therefore, the following saturation controller is designed:

[0049] Γ=sat(Γ c (15);

[0050] Where sat(·) is the saturation function for vector x = [x1 x2 x3] T The saturation function sat(x) = [sat(x1)sat(x2)sat(x3)] T , where sat(x i )for

[0051]

[0052] Where, x max x min x i The upper and lower bounds of (i = 1, 2, 3).

[0053] Therefore, the present invention employs the above-mentioned integrated modeling and control method for attitude and orbit of rigid-flexible fluid coupled spacecraft, and the technical effects are as follows:

[0054] (1) Establishment of a control model for a rigid-flexible fluid coupled spacecraft: The influence of vibration of the flexible attachments of the spacecraft and liquid fuel sloshing is analyzed. Based on the Lie group SE(3), an integrated kinematic and dynamic model of the trajectory and attitude of the rigid-flexible fluid coupled spacecraft is established to lay the foundation for the subsequent controller.

[0055] (2) Constraint conditions are established: Considering the need for spacecraft onboard equipment to avoid direct exposure to strong light, attitude constraints are established based on the method of setting safe angles; at the same time, considering the threat of collisions between spacecraft and other spacecraft, targets and space obstacles, obstacle avoidance constraints are established based on the method of setting limit distances.

[0056] (3) Trajectory and attitude integrated controller: Based on the spacecraft trajectory and attitude integrated model and the desired trajectory and attitude model, a dynamic model of trajectory and attitude integrated tracking error is established; further, in order to solve the requirements of attitude angle constraint and obstacle avoidance constraint, the additional force of the controller is obtained based on the potential function; finally, the trajectory and attitude integrated controller is obtained, the stability of the system is proved, and the rigid-flexible-fluid coupling spacecraft trajectory and attitude integrated control is realized.

[0057] (4) Finally, to verify the effectiveness of the control algorithm proposed in this invention, a Matlab / Simulink simulation system for the integrated control of the trajectory and attitude of a rigid-flexible fluid coupled spacecraft was built to verify the effectiveness of the algorithm. Attached Figure Description

[0058] Figure 1 A control-oriented modeling and control content structure diagram for a rigid-flexible fluid coupled spacecraft;

[0059] Figure 2 This is a graph showing the attitude tracking error.

[0060] Figure 3 This is a graph showing the angular velocity tracking error.

[0061] Figure 4 This is a graph showing the position tracking error.

[0062] Figure 5 This is a graph showing the speed tracking error.

[0063] Figure 6 For the control force curve;

[0064] Figure 7 For the control torque curve;

[0065] Figure 8 A graph showing the angle between the photosensitive device and a distant luminous object;

[0066] Figure 9 This is a graph showing the angle between the photosensitive device and a nearby luminescent object.

[0067] Figure 10 To track the distance between the spacecraft and three nearby obstacles. Detailed Implementation

[0068] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0069] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0070] This invention provides a method for integrated attitude and orbit modeling and control of rigid-flexible fluid coupled spacecraft, comprising the following steps:

[0071] Step 1: Establish a flexible appendage model. Based on the flexible appendage model, establish a control-oriented model for the rigid-flexible fluid-coupled spacecraft, including the dynamic model of the rigid-flexible fluid-coupled spacecraft and the relative dynamic model of the rigid-flexible fluid-coupled spacecraft. Specifically, this includes...

[0072] Step 1.1 Flexible attachment modeling, specifically including

[0073] Treating the flexible attachment as a cantilever beam, force and moment analysis is performed on each micro-element of the flexible attachment based on the finite element method and modal superposition method, yielding the force and moment balance equations:

[0074]

[0075] Among them, F s Let P(x,t) be the shear force acting on the infinitesimal element, and P(x,t) be the transverse external force per unit length of the cantilever beam. ρ is the mass per unit length of the cantilever beam. wing W represents density. wing H represents the width per unit length. wingLet w(x,t) represent the height per unit length, w(x,t) be the longitudinal displacement at time t at a distance x from the origin of the cantilever beam, M be the torsional moment of the infinitesimal element, EI(x) be the stiffness of the cantilever beam, E be the elastic modulus, and I(x) be the inertia matrix at x.

[0076] Since the influence of dx is relatively small, based on equation (2) we get At the same time, based on Given a lateral external force P(x,t) = 0, we get

[0077]

[0078] make φ n (x) represents the modal function of the natural vibration mode of the spacecraft's solar panel, χ n (t) is a generalized coordinate, and we get

[0079]

[0080] make and but

[0081]

[0082] Based on the method of separation of variables, equation (5) can be rearranged as follows:

[0083]

[0084] Equations (6) and (7) are the standard equations for solving a free beam. Solving them, we get χ(t) = A1sinωt + A2cosωt. The general solution of equation (6) is:

[0085] φ(x)=De rx (8);

[0086] Substituting equation (8) into equation (6), we get r 4 -β 4 =0, the solution is r 1,2 =±β,r 3,4 =±iβ, the general solution of equation (6) is φ(x)=D1e βx +D2e -βx +D3e iβx +D4e -iβx ;

[0087] Based on equation (8), the trigonometric function form of φ(x) is:

[0088] φ(x)=a n [sin(βx)-sinh(βx)-α n (cos(βx)-cosh(βx))] (9);

[0089] in,

[0090] Normalizing equation (9) yields the coefficient a. n

[0091]

[0092] The boundary conditions for the cantilever beam are: w(0,t)=0, w′(0,t)=0, w″(0,t)=0, w″′(0,t)=0; the initial conditions are: w(x,t)| t＝0 =w(x,0), The boundary conditions and initial conditions are as follows:

[0093] φ(x)| x＝0 =0, φ′(x)| x＝0 =0

[0094] φ″(x)| x＝L_wing =0, φ″′(x)| x＝L_wing =0

[0095] Substituting the above boundary conditions and initial conditions into (9), we can obtain

[0096] cos(βL wing )·cosh(βL wing )+1=0 (11);

[0097] Numerical solutions for β were obtained using MATLAB. Furthermore, based on equations (5) and (9), the natural frequencies Ω and mode shapes φ of the flexible attachment were derived. n (x).

[0098] Step 1.2: Based on the theory of momentum conservation and Lagrange's principle, establish an integrated dynamic model of the rigid-flexible coupled spacecraft's trajectory and attitude, specifically including...

[0099] The flexible momentum at nominal point k is

[0100] H fp (k)=m kf v(k) (12);

[0101] Based on equation (12), the flexible angular momentum of the nominal point k is:

[0102] H fc (k)=m kf [r bk +w k ] × v(k) (13);

[0103] Where, r bkw is the distance from the spacecraft's center of mass to the connection point between the flexible appendage and the rigid body. k Let m be the structural displacement at point k of the flexible attachment. kf Let be the mass of point k, and ω(k) and v(k) be the angular velocity and velocity of point k, respectively. For vector x = [x1 x2 x3]... T skew-symmetric matrix x × for

[0104] The velocity vector at nominal point k ω(k) is the angular velocity of point k, which is used in calculating v. b (k) neglects structural displacement ||w k ||. Due to w k =φ k χ, φ k Let χ be the modal function, used to represent the natural mode shape of the spacecraft's solar panel vibration. Further, the momentum H at nominal point k can be obtained. fp (k) and angular momentum H fc (k) is

[0105]

[0106] Based on equation (14), the momentum and angular momentum of the flexible attachment at point k relative to the geocentric coordinate system can be obtained as follows:

[0107]

[0108] Because m kf ω(k) × r bk =-m kf r bk × ω(k), the H of the flexible attachment relative to the Earth's center f for

[0109]

[0110] in, Indicates the quality of flexible accessories. v. The velocity vector of the spacecraft relative to the Earth-centered Earth-fixed coordinate system, and the rigid-flexible translational coupling matrix. Rotational coupling matrix

[0111] The rigid body momentum of the spacecraft is

[0112]

[0113] in, Mass is that of a rigid body.

[0114] The angular momentum of the rigid body is

[0115]

[0116] Based on equation (16), the momentum H of the rigid-flexible coupled spacecraft is obtained. p With angular momentum H c for

[0117]

[0118] in,

[0119] By the law of conservation of angular momentum, we obtain the dynamic equations for rigid-flexible spacecraft:

[0120]

[0121] Where, m f With J f Let v be the mass and moment of inertia of the rigid-flexible spacecraft, and v be the velocity. m kf For the mass at nominal point k, r bk Let ω be the distance from the spacecraft's center of mass to the connection point between the flexible appendage and the rigid body, ω be the angular velocity, and ω be the rigid-flexible translational coupling matrix. Rotational coupling matrix χ represents flexible vibration. F g and M g M represents the gravitational gradient force and gravitational gradient torque. d and F d For the interfering force and the interfering torque, F is the perturbation force caused by the Earth's oblateness. c and M c For control force and control torque, M g F g , The specific expression is:

[0122]

[0123] Where J2=0.00108263 is the perturbation constant due to the Earth's oblateness perturbation, R∈SO(3) represents the rotation matrix from the spacecraft's body coordinate system to the Earth's inertial frame, I3 is the identity matrix, and μ0=3.9860047×10 14 m 3 s -2 R is the standard gravitational parameter for Earth. e =6378.14Km is the radius at the Earth's equator, C0 = diag(

[113] ), p is the position vector of the spacecraft's body coordinate system in the Earth's inertial frame, p z C represents the Z-axis component of the translation vector p;f =diag{2ε i Ω i}and These are the flexibility matrix and stiffness matrix of the flexible attachment, respectively, ε i Let Ω be the damping ratio of the i-th mode. i The natural frequency of the mode;

[0124] The vibration equation of the flexible attachment is established using Lagrange's principle. The vibration equation of the flexible attachment is as follows:

[0125]

[0126] Let the spacecraft's center of mass be O. Divide the liquid in the storage tank into two parts. The first part is a liquid that does not participate in the sloshing, with a mass of m. l0 The distance between the center of mass and the spacecraft's center of mass is r. l0 The second part describes the liquid involved in the sloshing, and the parameters for each order of the sloshing model are: sloshing mass m li Spring stiffness k li Damping c li In equilibrium, the distance from each mass block to the spacecraft's center of mass is r. zi During the swaying state, the distances of each mass block from the spacecraft's center of mass are: η i =[η i1 η i2 ] T , where η i1 η is the sway displacement of the swaying mass along the OX axis. i2 Let i = 1 and 2 be the swaying displacement of the swaying mass along the OY axis, where i = 1 and 2 are the first two swaying displacements taken in the equivalent liquid process.

[0127] The momentum P of the equivalent spring mass l Represented as:

[0128]

[0129] in, The total mass of the liquid fuel, Its distance from the center of mass;

[0130] In the rotating coordinate system, the mass momentum of the spring in the equivalent liquid sloshing is conserved, resulting in the following equation of liquid dynamics:

[0131]

[0132] Among them, based on We can obtain rli, where i = 1, 2, 3…N.

[0133] According to the momentum expression of the equivalent spring mass (26), the angular momentum H of the equivalent spring mass s Represented as:

[0134] H s =J s ω+h s (27);

[0135] in, I is the identity matrix.

[0136]

[0137] In a rotating coordinate system, according to the law of conservation of angular momentum, the dynamic equation of the liquid-filled spacecraft system is:

[0138]

[0139] in,

[0140] Combining equations (26) and (28), let Omitting the second-order minima in equation (26), we get:

[0141]

[0142] Where, m l r is the total mass of the liquid fuel l For its distance from the center of mass, F d and M d These are the disturbance force and the disturbance torque, respectively, F c and M c These represent the control force and control torque, respectively, and the velocity vector at nominal point k. ω(k) is the angular velocity of point k. and Let M be the rigid-fluid translational coupling matrix and the rigid-fluid rotational coupling matrix. η =[m l1 m l1 m l2 m l2 ] T For the mass matrix of the swaying liquid, C l =[c i1 c i1 c i2 c i2 ] T For a flexible matrix of swaying liquid, K l =[k l1 k l1 k l2 k l2 ]T Let η be the stiffness matrix of the sloshing liquid, and η be the modal value of the sloshing liquid.

[0143] Step 1.3, the integrated dynamic model of the rigid-fluid coupled spacecraft trajectory and attitude, includes the following steps:

[0144] Based on the conservation of system momentum and angular momentum, and combining equations (20) and (28), the dynamic model of the trajectory and attitude of the rigid-fluid coupled spacecraft is obtained as follows:

[0145]

[0146] Where J = J l +J2 is the rotational inertia matrix of the spacecraft, m = m f +m l For the mass of the spacecraft;

[0147] The rotation of a rigid body in three-dimensional space is described by a special orthogonal group SO(3), where the elements of the group SO(3) are identity orthogonal matrices in three-dimensional space. In addition, the special Euclidean group SE(3) is used for a unified description of the rotation and translation of rigid bodies in three-dimensional space.

[0148]

[0149] Where R∈SO(3) represents the rotation matrix from the spacecraft's body coordinate system to the Earth's inertial frame, used to describe the spacecraft's attitude; p∈R 3 It is the position vector of the spacecraft's body coordinate system in the Earth's inertial frame;

[0150] Let the spacecraft's velocity vector be:

[0151]

[0152] Where v and ω are the linear velocity and angular velocity of the spacecraft body in the Earth's inertial frame, respectively.

[0153] Based on equations (32) and (33), the integrated attitude and orbit kinematics model of the spacecraft in the Earth's inertial frame is as follows:

[0154]

[0155] Where, ω × It means ω = [ω x ω y ω z ] T The skew-symmetric matrix, i.e.

[0156] The kinematic model of the spacecraft (34) is further simplified to:

[0157]

[0158] Where g represents the actual attitude of the spacecraft;

[0159] Define the adjoint mapping of ξ as:

[0160]

[0161] Then its inverse adjoint mapping is:

[0162]

[0163] Based on the vibration model of the flexible attachments and the sloshing model of the liquid fuel (31), the dynamic equations for the integrated trajectory and attitude of the rigid-flexible fluid coupled spacecraft are obtained:

[0164]

[0165] Where Ξ=diag(J,mI3)∈R 6×6 It is a symmetric positive definite matrix. Γ D =[M d ,F d ] T ∈R 6 , χ∈R M , γ∈R N Let M and N represent the vibration modes of the flexible attachment and the sloshing mode of the liquid fuel, respectively. M and N represent the approximate orders of the two modes, respectively. Let M = 3 and N = 4. These represent the rigid-flexible coupling matrix and the rigid-fluid coupling matrix, respectively. Let C represent the stiffness matrix. f =diag{2ξ i Ω i ,i=1,2,...,M∈R 3×3 The damping matrix represents the vibration of the flexible attachment, where ξ i and Ω i Let M represent the vibration damping and vibration frequency of the i-th order flexible attachment vibration mode, respectively. l =diag([m1 m1 m2 m2])∈R 4×4 Denotes the mass matrix of the liquid sloshing fuel, where m i K represents the mass of the sloshing fuel in the i-th sloshing mode. l =diag([k l1 k l1 k l2 k l2 ])∈R 4×4 C represents the stiffness matrix of the liquid sloshing fuel. l=diag([c i1 c i1 c i2 c i2 ])∈R 4×4 A flexible matrix representing liquid sloshing fuel;

[0166] To achieve integrated tracking and control of the spacecraft's trajectory and attitude, i.e., tracking the desired pose and velocity, let the desired pose of the spacecraft be g. d The desired speed is ξ d According to equation (35), the kinematic equation of the virtual spacecraft at the desired pose is:

[0167]

[0168] Let g e ∈R 4×4 For the actual attitude g and the desired attitude g of the spacecraft d The relative pose matrix, i.e., the tracking error pose matrix, is obtained by taking the spacecraft body coordinate system at the desired pose as the reference frame. Therefore, the tracking error pose matrix is:

[0169]

[0170] Based on the exponential coordinate g of SE(3) e The corresponding tracking error η is shown below:

[0171]

[0172] Where, Φ∈R 3 Indicates attitude tracking error. The position tracking error is represented by the relative pose matrix g. e Calculate Φ and The specific formula is as follows:

[0173]

[0174] Where θ is the rotation matrix g e The corresponding Euler rotation angle, θ=||Φ||=arccos(0.5(tr(R) e )-1)), conversely, Φ and Using the Rodrigues form based on its logarithmic coordinate g e The calculation yielded:

[0175]

[0176] Using the spacecraft's own coordinate system as the reference coordinate system, the tracking error ξ between the spacecraft and the desired velocity is... e for:

[0177]

[0178] In equation (35), the adjoint matrix mapping Ad of g is... g for:

[0179]

[0180] The spacecraft kinematic tracking error model is as follows:

[0181]

[0182] in, It is a positive definite matrix.

[0183] Equation (45) represents the relative velocity between the tracking spacecraft and the virtual navigator spacecraft. Differentiating both sides of equation (45) with respect to time yields:

[0184]

[0185] calculate It is needed at times The derivative with respect to time is

[0186]

[0187] Substituting equations (38) and (49) into equation (48), we obtain the relative dynamics model of the rigid-flexible fluid coupled spacecraft:

[0188]

[0189] Wherein, the adjoint matrix mapping R e For the rotation matrix error, p e This represents the position vector error of the spacecraft's coordinate system in the Earth's inertial frame.

[0190] Step 2: Establish the attitude constraint model, obstacle avoidance constraint model, and input constraint model of the rigid-flexible fluid coupled spacecraft. Based on the attitude constraint model and obstacle avoidance constraint model and potential function theory, obtain the additional forces exerted on the spacecraft by bright objects and obstacles, specifically including...

[0191] Assuming a spacecraft carries light-sensitive onboard equipment, to prevent interference with this equipment, the spacecraft needs to ensure that no brightly emitting objects are within the field of view of the light-sensitive onboard equipment. Let p denote the spacecraft's position vector in the Earth's inertial frame. n p represents the position vector of a bright object in Earth's inertial frame. n -p represents the relative position vector between the bright object and the spacecraft, a represents the unit direction vector of the photosensitive spacecraft in the spacecraft's coordinate system, and θ represents the half field of view of the photosensitive spacecraft.

[0192] When the spacecraft is very far away from a bright object, the condition ||p|| is satisfied. n ||≥200||p||, at this point the relative motion between the spacecraft and the bright object can be ignored, that is, the two are considered to be relatively stationary, and at this point ||p n -p||=||p n When the spacecraft is close to a bright object, the relative motion between them cannot be ignored. Therefore, the unit direction vector of the relative position vector between the bright object and the spacecraft is:

[0193]

[0194] b n After transforming from the Earth's inertial frame to the spacecraft's body coordinate system, we can obtain a and R. T b n The included angle

[0195] <a,R T b n >:

[0196] <a,R T b n >=arccos(a T R T b n (52);

[0197] The attitude constraints of a rigid-flexible fluid coupled spacecraft are:

[0198] <a,R T b n >>θ (53);

[0199] In addition, a safety angle σ is set. n >θ, when <a,R T b n >≥σ n At that time, the spacecraft is considered to be very safe, and there is no need to consider the spacecraft's attitude constraints.

[0200] In summary, the potential function for attitude constraints is:

[0201]

[0202] As can be seen from equation (54), when <a,R T b n >≥σ n When θ < 0, the potential function is 0, and the spacecraft has no attitude constraints; when θ < 0, the potential function is 0, and the spacecraft has no attitude constraints. <a,R T b n >≤σ n At that time, the included angle <a,R T bn The larger the value of U, the greater the potential function. n The smaller the numerator and the larger the denominator, the more the potential function will tend to make the angle between them smaller. <a,R T b n Enlarging the spacecraft achieves the attitude constraint of avoiding direct contact with the light source as much as possible.

[0203] Next, we need to calculate the potential function U. n The torque T exerted on the spacecraft by the nth bright object under its influence is equal to the potential function U. n The negative gradient relative to the unit direction vector of the photosensitive spaceborne device is denoted as... The specific expression is:

[0204]

[0205] Where Ra is the unit direction vector of the photosensitive spaceborne device in the Earth's inertial coordinate system.

[0206] To achieve spacecraft tracking and control, it is necessary to ensure that attitude constraints are met at the desired position, so that the desired spacecraft position g d σ is satisfied at any time. n < <a,R T b n > means that it is not affected by posture constraints.

[0207] Assume the limit distance for the spacecraft to collide with the nth obstacle is d. n p n Let represent the position vector of the nth obstacle in Earth's inertial frame. Then, the obstacle avoidance constraint for the rigid-flexible fluid coupling spacecraft is:

[0208] ||p n -p||>d n (56);

[0209] Similarly, set a safe distance. when That is, when the spacecraft is far from the obstacle, obstacle avoidance constraints do not need to be considered. Therefore, the potential function of the obstacle avoidance constraint is:

[0210]

[0211] From equation (57), it can be seen that only when the spacecraft's center of mass is taken as the origin and the radius is... The potential function only takes effect when there are obstacles within the spherical region.

[0212] Next, we calculate the potential function F. n The force F exerted on the spacecraft by the nth obstacle under its influence is equal to the potential function F. n The negative gradient relative to the unit direction vector of the photosensitive spaceborne device is denoted as... The specific expression is:

[0213]

[0214] Similarly, since this invention discusses the spacecraft tracking and control problem, it is necessary to ensure that the obstacle avoidance constraints are satisfied at the desired pose, so that the pose g of the ideal navigating spacecraft is... d Satisfies at any time That is, it is not affected by obstacle avoidance constraints. Therefore, in the potential function U n and F n Under the influence of bright objects and obstacles, the additional forces exerted on the spacecraft are:

[0215]

[0216] Step 3: For the rigid-flexible fluid-coupled spacecraft, based on the control model and the additional forces exerted on the spacecraft by bright objects and obstacles, the stability of the system is proven using Lyapunov theory. A saturated controller is designed to solve the control input constraint problem, achieving integrated trajectory and attitude control of the rigid-flexible fluid-coupled spacecraft. This includes the following steps:

[0217] Based on the control force (59) obtained from the attitude and obstacle avoidance model, the following controller can be obtained:

[0218]

[0219] in, Sliding surface S=[S1 S2 S3]=ξ e +ν1η,ν1=diag(ν 11 ,...,ν 16 )∈R 6×6 It is a positive definite diagonal matrix. Let K1 ∈ R be a positive definite matrix. 6×6 K is a positive definite diagonal matrix. 2i =diag{K 21 ,K 22 ...K 26} is a positive definite matrix, λ min (K2)>||ΞΓ D ||, λ>0;

[0220] From controller (60):

[0221]

[0222] in, It is an adaptive sliding mode controller The corresponding control system is considered as the nominal system; g(S,t) is regarded as a disturbance outside the nominal system; when the tracked spacecraft reaches the desired pose, i.e., S=0, the spacecraft is not affected by attitude and obstacle avoidance constraints, then g(0,t)=0; where g(S,t) is the nominal system. Disappearable interference;

[0223] The following proves that S=0 is the equilibrium point of system (61). Consider... If the Lyapunov function is V3, then:

[0224]

[0225] Furthermore, we can obtain:

[0226]

[0227] Let β3 = 2λ min (K1), β4=2α, γ=0.5. We will now prove that V3 satisfies the inequality:

[0228]

[0229] Eigenvalue decomposition of the positive definite symmetric matrix Ξ yields: Ξ=QΛQ T Let Q be an orthogonal matrix composed of the eigenvectors of Ξ, and Λ be a positive definite diagonal matrix composed of the eigenvalues ​​of Ξ. Then: ΞS = QΛQ T S. Let y = Q T S, then we have:

[0230] ΞS=QΛy,||y||=||S|| (66);

[0231] therefore:

[0232]

[0233] Since both sides of inequality (67) are squares of positive numbers, taking the square root of both sides of inequality (67) gives:

[0234] ||ΞS||≤λ max (Ξ)||y||=λ max (Ξ)||S|| (68);

[0235] Where β5=λ max (Ξ).

[0236] Next, we prove that g(S,t) satisfies the following equation:

[0237] ||g(S,t)||=||Ξ -1 U PF || (69);

[0238] In equation (69), Ξ -1 It is also a positive definite symmetric matrix, so it can be proved using the same method as equation (65):

[0239] ||g(S,t)||=||Ξ -1 U PF ||≤λ max (Ξ -1 )||U PF || (70);

[0240] Where, λ max (Ξ -1 It is necessary to ensure that:

[0241]

[0242] Since Ξ is a fixed parameter of the spacecraft, it is only necessary to ensure that parameter K1 satisfies:

[0243]

[0244] This ensures that equation (71) holds, and further proves that the vanishable disturbance system (61) is asymptotically stable at S=0.

[0245] Due to physical constraints of the actuator (such as a flywheel), the range of torque that the actuator can generate is limited. When the theoretically calculated control torque exceeds the actual withstand range of the actuator, a control input constraint problem arises. Therefore, the following saturation controller is designed:

[0246] Γ=sat(Γ c (73);

[0247] Where sat(·) is the saturation function. For a vector x = [x1 x2 x3] T The saturation function is sat(x) = [sat(x1)sat(x2)sat(x3)] T , where sat(x i )for

[0248]

[0249] Where, x max x min x i The upper and lower bounds of (i = 1, 2, 3).

[0250] Based on the above three steps, the entire process of integrated trajectory and attitude control of a rigid-flexible fluid coupled spacecraft is completed.

[0251] To verify the effectiveness of the rigid-flexible fluid coupling spacecraft control model and control algorithm established in this invention, the rigid-flexible fluid coupling spacecraft control system was integrated and designed in Matlab / Simulink, and the following simulation verification was performed.

[0252] (1) Parameter settings

[0253] Assume that the mass and inertia matrices of both the ideal spacecraft and the tracking spacecraft are:

[0254]

[0255] The first three vibration frequencies of the flexible attachment's vibration modes are Ω1 = 0.7681 rad·s. -1 Ω2 = 1.1038 rad·s -1 Ω3 = 1.8733 rad·s -1 The vibration damping is ξ1 = 0.0056, ξ2 = 0.0086, and ξ3 = 0.0013; the flexibility matrix of the liquid sloshing mode is C. l =diag(3.334,3.334,0.237,0.237), where the stiffness matrix is ​​K. l =diag(55.21,55.21,7.27,7.27), where the masses of the two equivalent sloshing liquids are m1 = 5 kg and m2 = 0.2 kg, respectively, and their distances from the spacecraft's center of mass are b1 = 1.127 m and b2 = 0.994 m, respectively. The initial values ​​for both modes are zero, δ f With δ l They are respectively

[0256]

[0257] Initial pose g of the virtual navigator spacecraft d (0) and initial velocity vector ξ d (0) are respectively:

[0258]

[0259] Assume the ideal virtual navigator spacecraft is unaffected by external disturbances, vibrations of flexible appendages, and liquid fuel sloshing during operation. The initial attitude and initial angular velocity of the tracked spacecraft at the initial moment are as follows:

[0260]

[0261] The relative positions and relative linear velocities of the tracked spacecraft and the virtual navigator spacecraft at the initial moments are as follows:

[0262]

[0263] Based on the above conditions, the tracking error η(0) at the initial moment can be calculated as follows:

[0264]

[0265] Assuming the upper limit of the actuator's output force and torque are 10N and 0.5N respectively, and the disturbance force and torque are set as follows:

[0266]

[0267] The unit direction vector of the light-sensitive device mounted on the spacecraft is a = [0; 0; 1]. Assume there are three distant luminous objects in the virtual navigation spacecraft's operating environment, and their position information, set warning angle θ, and safety angle σ are given. n As shown in Table 1.

[0268] Table 1 Information on distant luminous objects

[0269] b θ <![CDATA[σ n ]]> [0；-1；0] 20° 35° [0.68；0.67；0.3] 20° 35° [0.38；0；0.925] 20° 35°

[0270] It is also assumed that there are three nearby luminous objects in the operating environment of the virtual navigator spacecraft, and their relative position vectors with respect to the ideal virtual navigator spacecraft are as follows:

[0271]

[0272] For such objects, obstacle avoidance and attitude constraints need to be considered simultaneously. Their warning angles are all set to θ = 15°, and their safety angles are all set to σ. n =30°, warning distance set to d n =30m, safety distance set as

[0273] The parameters of the controller (73) are set as follows:

[0274]

[0275] (2) Results Analysis

[0276] To demonstrate the effectiveness of this method, simulations will be performed under two different conditions:

[0277] Figures 2 to 9 The mathematical simulation results of the controller (73) acting on the rigid-flexible fluid coupling spacecraft are shown. The simulation time is 1000s. Figure 2 The curves showing the attitude tracking error of the tracking spacecraft relative to the ideal virtual navigator spacecraft over time are presented. It can be seen that the attitude tracking error converges at approximately 500s, and calculations show that the subsequent attitude tracking error ||Φ||≤0.05°. Figure 3The curves showing the angular velocity tracking error of the tracking spacecraft relative to the ideal virtual navigator spacecraft over time are presented. It can be seen that the angular velocity tracking error converges at approximately 500 seconds, and the subsequent angular velocity tracking error ||ω is calculated. e ||≤6×10 -4 rad·s -1 . Figure 4 The curves showing the position tracking error of the tracking spacecraft and the ideal virtual navigator spacecraft over time are presented. It can be seen that the position tracking error converges at approximately 400s, and calculations show that the subsequent position tracking error ||Φ||≤0.05°. Figure 5 The curves showing the linear velocity tracking error of the tracking spacecraft relative to the ideal virtual navigator spacecraft over time are presented. It can be seen that the linear velocity tracking error converges at approximately 400 seconds, and the subsequent velocity tracking error ||v is calculated. e ||≤6×10 -3 m·s -1 .

[0278] In summary, the tracking controller (73) can effectively track the ideal virtual navigator spacecraft.

[0279] Figure 6 The simulation shows the curve of the control force output by the controller over time. Note that the control force decays at approximately 400 seconds, indicating that by this time the tracking spacecraft has caught up with the virtual navigator spacecraft in both position and linear velocity. This is consistent with... Figure 4 , Figure 5 The results correspond. Figure 7 The simulation shows the curve of the control torque output by the controller over time. Note that the control torque decays at approximately 500 seconds, indicating that the tracking spacecraft has by this time caught up with the virtual navigator spacecraft in terms of attitude and angular velocity. This is consistent with... Figure 2 , Figure 3 The results correspond. From Figure 6 , Figure 7 As can be seen, there was no severe chattering in the control force and control torque, indicating that the controller used in this patent has a good chattering suppression effect.

[0280] Figure 8 The table shows the curves of the angles between the three luminous objects, which are far from the orbit of the ideal virtual navigator spacecraft, and the photosensitive onboard equipment on the tracking spacecraft, as a function of time. The green and red dashed lines represent the warning angle and the safety angle, respectively. It can be seen that the tracking spacecraft did not exceed the warning angle during the entire operation, and after tracking the ideal virtual navigator spacecraft, the angles between the tracking spacecraft and the luminous objects all exceeded the safety angle, and were not subject to attitude constraints.

[0281] Figure 9 The curves showing the change of the angle between the three luminous objects that are close to the orbit of the ideal virtual navigator spacecraft and the photosensitive onboard equipment on the tracking spacecraft as a function of time are shown in Equation (80). It can also be seen that the tracking spacecraft did not exceed the warning angle during the entire operation process, and the angle between the tracking spacecraft and the luminous objects after tracking the ideal virtual navigator spacecraft exceeded the safe angle and was not subject to attitude constraints.

[0282] Figure 10 The curves showing the Euclidean distances between the tracking spacecraft and three obstacles close to the orbit of the ideal virtual navigator spacecraft over time are presented. It can be seen that the tracking spacecraft did not exceed the set warning distance during the entire motion process, and after the tracking spacecraft tracked the ideal virtual navigator spacecraft, the distance between the tracking spacecraft and the obstacles was greater than the safe distance, and it was not subject to obstacle avoidance constraints.

[0283] In summary, under various constraints, the rigid-flexible fluid coupling spacecraft tracking controller of this patent can complete the tracking of the target spacecraft by the tracking spacecraft within a limited time.

[0284] Therefore, this invention employs the aforementioned integrated modeling and control method for rigid-flexible fluid-coupled spacecraft attitude and orbit. Addressing the spacecraft trajectory and attitude tracking control problem under the influence of flexible vibration and liquid fuel sloshing, it studies the integrated trajectory and attitude tracking control model and algorithm, and obtains the control force and torque based on potential function theory, effectively solving the trajectory and attitude control problem under obstacle avoidance constraints. System stability is proven, and an integrated rigid-flexible fluid-coupled spacecraft trajectory and attitude tracking controller is implemented. Mathematical simulations of the established model and controller are performed using Matlab to verify the effectiveness of the control algorithm.

[0285] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for integrated attitude and orbit modeling and control of rigid-flexible fluid coupled spacecraft, characterized in that, Includes the following steps: Based on the momentum conservation theory, the rigid-flexible and rigid-liquid coupling effects are analyzed, and a rigid-flexible and rigid-liquid coupled spacecraft trajectory and attitude integrated dynamic model is established. The three coupling relationships of rigid, flexible and fluid are comprehensively analyzed. Based on the Lie group SE(3) theory, a rigid-flexible fluid coupled spacecraft trajectory and attitude integrated dynamic tracking error model is established, laying the foundation for the following controller design. Secondly, attitude constraints, obstacle avoidance constraints, and input constraints of the rigid-flexible fluid coupling spacecraft are established. Based on attitude constraints, obstacle avoidance constraints, and potential function theory, the additional forces exerted on the spacecraft by bright objects and obstacles are obtained. The controller is obtained by combining the additional forces exerted on the spacecraft by bright objects and obstacles. The attitude constraints of a rigid-flexible fluid coupled spacecraft are: ； in, This represents the unit direction vector of the photosensitive spaceborne equipment in the spacecraft's coordinate system. This represents the rotation matrix from the spacecraft's own coordinate system to the Earth's inertial frame. Indicates the half field of view of the optically sensitive spaceborne equipment. Let be the unit direction vector of the relative position vector between the bright object and the spacecraft. This represents the position vector of a bright object in Earth's inertial frame of reference. This represents the position vector of the spacecraft's coordinate system in the Earth's inertial frame; Set a safe angle ,when At that time, the spacecraft attitude constraint problem is not considered; The potential function for attitude constraints is: ； Calculate the potential function Under the influence of the first The torque exerted on the spacecraft by a bright object The expression is The specific expression is: ； in, This is the unit direction vector of the photosensitive spaceborne device in the Earth's inertial coordinate system; Desired attitude of spacecraft Satisfies at any time It is not affected by attitude constraints; The obstacle avoidance constraints for rigid-flexible fluid coupled spacecraft are: ； in, Indicates spacecraft and the first The maximum distance at which an obstacle can collide. This represents the relative position vector between a bright object and a spacecraft. Set a safe distance ,when When the spacecraft is far from the obstacle, obstacle avoidance constraints do not need to be considered. Therefore, the potential function of the obstacle avoidance constraint is: ； Only when the spacecraft's center of mass is taken as the origin, and the radius is The potential function only takes effect when there is an obstacle within the spherical region; Calculate the potential function Under the influence of the first The force exerted on the spacecraft by an obstacle The expression is The specific expression is: ； Ensure that obstacle avoidance constraints are met at the desired pose, so that the spacecraft is in the desired pose. Satisfies at any time Unaffected by obstacle avoidance constraints; Additional forces exerted on spacecraft by bright objects and obstacles ； in, and It is a positive number; Finally, based on the controller, a saturated controller was designed to solve the control input constraint problem and realize the integrated control of the rigid-flexible-fluid coupling spacecraft trajectory and attitude.

2. The method for integrated attitude and orbit modeling and control of a rigid-flexible fluid coupled spacecraft according to claim 1, characterized in that, Based on the theory of momentum conservation and the Lagrange principle, the integrated dynamic model of the trajectory and attitude of a rigid-flexible coupled spacecraft is established as follows: ； ； in, and For the mass and moment of inertia of a rigid-flexible spacecraft, For speed, , Nominal point quality This is the distance from the spacecraft's center of mass to the connection point between the flexible attachment and the rigid body. Angular velocity, rigid-flexible translational coupling matrix Rotational coupling matrix , For flexible attachment vibration modes, , and These are the gravitational gradient force and gravitational gradient torque. and For the interfering force and the interfering torque, The perturbation force caused by the Earth's oblateness. and For control force and control torque, , and They are respectively , , , It is the perturbation constant due to the Earth's oblateness perturbation. This represents the rotation matrix from the spacecraft's own coordinate system to the Earth's inertial frame. It is the identity matrix. The standard gravitational parameters for Earth. The radius at the Earth's equator. , It is the position vector of the spacecraft's body coordinate system in the Earth's inertial frame. Represents the translation vector of Axial components; and These are the damping matrix and stiffness matrix of the flexible attachment vibration, respectively. For the first Vibration damping of the vibration modes of the flexible attachment. For the first The vibration frequencies of the flexible attachment's vibration modes. This represents the natural mode shape of vibration of a spacecraft's solar panels.

3. The method for integrated attitude and orbit modeling and control of a rigid-flexible fluid coupled spacecraft according to claim 2, characterized in that, The integrated dynamic model of rigid-fluid coupled spacecraft trajectory and attitude is as follows ； ； in, The total mass of the liquid fuel, The nominal point is the distance from the liquid fuel mass block to the spacecraft's center of mass. velocity vector , For point angular velocity, , For the first The distance from the liquid fuel mass block to the spacecraft's center of mass. It is the identity matrix. and Let the rigid-fluid translational coupling matrix and the rigid-fluid rotational coupling matrix be represented. For the mass matrix of the swaying liquid, For a flexible matrix of swaying liquid, For the stiffness matrix of the swaying liquid, To determine the modal values ​​of the sloshing liquid, Represented as the swaying mass along The derivative of the wobbling displacement of the shaft, Indicates structural displacement. This indicates the mass of the liquid that does not participate in the shaking. This indicates the distance between the center of mass and the spacecraft's center of mass.

4. The method for integrated attitude and orbit modeling and control of a rigid-flexible fluid coupled spacecraft according to claim 3, characterized in that, The integrated dynamic tracking error model for the rigid-flexible fluid coupled spacecraft trajectory and attitude is as follows: ； in, It is a symmetric positive definite matrix. For spacecraft tracking error, It is the velocity vector of the spacecraft. The inverse adjoint mapping, , It is the velocity vector of the spacecraft. The adjoint mapping, the adjoint matrix mapping , For rotation matrix error, This represents the position vector error of the spacecraft's body coordinate system in the Earth's inertial frame. , and These are the desired velocity and angular velocity, respectively. , , , , These represent the vibration modes of the flexible attachment and the sloshing mode of the liquid fuel, respectively. , These represent the rigid-flexible coupling matrix and the rigid-fluid coupling matrix, respectively. and These represent the approximate orders of the two modes, respectively. Represents the stiffness matrix. The damping matrix represents the vibration of the flexible attachment, where and They represent the first Vibration damping and vibration frequency of the first-order flexible attachment vibration modes. The mass matrix of the liquid sloshing fuel is represented, where Indicates the first The mass of the sloshing fuel in the first sloshing mode.

5. The method for integrated attitude and orbit modeling and control of a rigid-flexible fluid coupled spacecraft according to claim 4, characterized in that, The attitude and obstacle avoidance constraints result in the following controller: ； in, Sliding surface , It is a positive definite diagonal matrix. It is a positive definite matrix. It is a positive definite diagonal matrix. It is a positive definite matrix. , , .

6. The method for integrated attitude and orbit modeling and control of a rigid-flexible fluid coupled spacecraft according to claim 5, characterized in that, The control input constraints for a rigid-flexible fluid coupled spacecraft are: ； in, It is a positive number; When the theoretically calculated control torque When the actuator exceeds its actual tolerance range, a control input constraint problem arises. Therefore, the following saturation controller is designed: ； in, For a saturation function, for a vector saturation function ,in for ； in, , They are respectively , The upper and lower bounds.

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