Rigid-flexible liquid coupling spacecraft attitude and orbit integrated modeling and control method

Abstract

The invention provides a rigid-flexible-liquid coupling spacecraft attitude and orbit integrated modeling and control method, which establishes a control-oriented attitude and orbit integrated kinematics and dynamics model of a rigid-flexible-liquid coupling spacecraft, and lays a foundation for the following controllers; establishing an attitude constraint model and an obstacle avoidance constraint model, and ensuring that attitude constraint and obstacle avoidance constraint requirements are met; and a self-adaptive track and attitude integrated controller is provided. According to the rigid-flexible-liquid coupling spacecraft attitude and orbit integrated modeling and control method, rigid-flexible-liquid coupling spacecraft orbit and attitude integrated control is achieved, and the spacecraft operation safety is improved.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft trajectory and attitude integrated control, and in particular to a rigid-flexible-liquid coupled spacecraft attitude and trajectory integrated modeling and control method. Background Art

[0002] A spacecraft is a space vehicle that operates in space according to the laws of celestial mechanics and is responsible for carrying out complex aerospace missions such as exploring, developing, and utilizing space and celestial bodies. In order to complete increasingly complex aerospace missions, the structure of spacecraft is becoming increasingly complex, resulting in increasingly larger flexible vibrations. In order to achieve the control goal of long-term on-orbit operation, spacecraft need to carry more and more liquid fuel, which further undermines the stability of the spacecraft system. In addition, spacecraft may also face the threat of collision with other spacecraft, targets, and space obstacles, so attitude angles and obstacle avoidance constraints need to be met during on-orbit operation. Therefore, research on related scientific issues is of driving significance and provides new ideas for the safe and stable operation of spacecraft and improving on-orbit operation capabilities.

[0003] Domestic and foreign scholars have conducted relevant explorations and research on attitude control under the influence of flexible appendage vibration, liquid fuel sloshing and obstacle avoidance constraints. The current deficiencies are mainly reflected in the following aspects: (1) In the research work on spacecraft attitude and orbit control, the 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 of the existing modeling and control consider rigid-flexible or rigid-liquid spacecraft separately, and the modeling and control of rigid-flexible-liquid coupled spacecraft is not yet mature; (3) In the control of spacecraft attitude trajectory, the rigid-flexible-liquid coupling, attitude constraints, obstacle avoidance constraints and other issues are rarely considered comprehensively. Therefore, the integrated establishment of rigid-flexible-liquid coupled spacecraft orbit dynamics model and attitude dynamics model, and the attitude-orbit coordinated control are the future development trends and key issues that need to be solved, which have important theoretical significance and engineering value. Summary of the invention

[0004] The purpose of the present invention is to provide a rigid-flexible-liquid coupled spacecraft attitude and orbit integrated modeling and control method, to achieve rigid-flexible-liquid coupled spacecraft trajectory and attitude integrated control, and to improve the safety of spacecraft operation.

[0005] To achieve the above object, the present invention provides a rigid-flexible-liquid coupled spacecraft attitude and orbit integrated modeling and control method, comprising the following steps:

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

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

[0008] Finally, based on the controller, a saturation controller is designed to solve the control input constraint problem and realize the integrated control of the trajectory and attitude of the rigid-flexible-liquid coupled spacecraft.

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

[0010]

[0011] Among them, m f With J f is the mass and moment of inertia of the rigid-flexible spacecraft, v is the velocity, m kf is the mass of the nominal point k, r bk is the distance from the center of mass of the spacecraft to the connection between the flexible attachment and the rigid body, ω is the angular velocity, and the rigid-flexible translation coupling matrix Rotational coupling matrix χ is flexible vibration, F g and M g is the gravity gradient force and gravity gradient moment, M d and F d are the disturbance force and disturbance torque, is the disturbance force caused by the Earth's oblateness, F c and M c is the control force and control torque, M g 、F g and They are 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 coordinate system to the Earth’s inertial system, I3 is the unit matrix, μ = 3.9860047 × 10 14 m 3 s -2 is the standard gravitational parameter of the Earth, R e =6378.14 km is the radius at the Earth’s equator, C0 = diag(

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

[0012] Preferably, the rigid-fluid coupled spacecraft trajectory attitude integrated dynamics model is:

[0013]

[0014] Among them, m l is the total mass of liquid fuel, r l The velocity vector of the nominal point k is its distance to the center of mass. ω(k) is the angular velocity of point k, and is the rigid-fluid translation coupling matrix and the rigid-fluid rotation coupling matrix, M η =[m l1 m l1 m l2 m l2 ] T is the mass matrix of the sloshing liquid, C l =[c i1 c i1 c i2 c i2 ] T is the flexible matrix of the shaking liquid, K l =[k l1 k l1 k l2 k l2 ] T is the sloshing liquid stiffness matrix, and η is the sloshing liquid modal value.

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

[0016]

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

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

[0023]

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

[0025] is a positive definite matrix, K1∈R 6×6 is a positive definite diagonal matrix, K2=diag{K 21 ,K 22 ...K 26} is a positive definite matrix, λ min (K2)>||ΞΓ D ||, λ>0.

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

[0027] <a,R T b n > >θ (8);

[0028] Where a represents the unit direction vector of the photosensitive satellite-borne device in the spacecraft coordinate system, θ represents the half field of view angle of the photosensitive satellite-borne device, is the unit direction vector of the relative position vector between the bright object and the spacecraft, p n represents the position vector of the bright object in the Earth's inertial frame;

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

[0030] In summary, the potential function of the attitude constraint is:

[0031]

[0032] Calculate the potential function U n The nth bright object exerts a torque T on the spacecraft under the action of the potential function U n The negative gradient relative to the unit direction vector of the photosensitive satellite-borne equipment is denoted as The specific expression is:

[0033]

[0034] Wherein, Ra is the unit direction vector of the photosensitive satellite-borne equipment in the Earth's inertial coordinate system;

[0035] The desired position of the spacecraft g d At any time, σ n < <a,R T b n >, not affected by posture constraints;

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

[0037]

[0038] Among them, d n represents the limit distance of collision between the spacecraft and the nth obstacle, p n represents the position vector of the bright object in the Earth's inertial system, p n -p represents the relative position vector of the bright object and the spacecraft;

[0039] Set a safe distance when When the spacecraft is far away from the obstacle, there is no need to consider the obstacle avoidance constraint. Therefore, the potential function of the obstacle avoidance constraint is:

[0040]

[0041] From formula (12), we know that only when the center of mass of the spacecraft is taken as the origin and the radius is The potential function takes effect only when there are obstacles in the spherical region;

[0042] Calculate the potential function F n The force F exerted by the nth obstacle on the spacecraft under the action of n The negative gradient relative to the unit direction vector of the photosensitive satellite-borne equipment is denoted as The specific expression is:

[0043]

[0044] Ensure that the desired position satisfies the obstacle avoidance constraint, so that the position of the ideal pilot spacecraft g d Satisfied at any time Not affected by obstacle avoidance constraints.

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

[0046]

[0047] in, is a positive constant;

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

[0049] Γ=sat(Γ c ) (15);

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

[0051]

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

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

[0054] (1) Establishment of control model for rigid-flexible-liquid coupling spacecraft: Analyze the influence of the vibration of the spacecraft's flexible attachments and the sloshing of liquid fuel, and establish an integrated kinematic and dynamic model of the trajectory and attitude of the rigid-flexible-liquid coupling spacecraft based on the Lie group SE (3), laying the foundation for the subsequent controller.

[0055] (2) Establishment of constraint conditions: Considering the need for spacecraft-borne equipment to avoid direct exposure to strong light, attitude constraints are established based on the method of setting a safe angle. At the same time, considering the threat of collision between the spacecraft and other spacecraft, targets, and space obstacles, obstacle avoidance constraints are established based on the method of setting a limit distance.

[0056] (3) Trajectory and attitude integrated controller: Based on the spacecraft trajectory and attitude integrated model and the expected trajectory and attitude model, a trajectory and attitude integrated tracking error dynamic model is established. Furthermore, in order to meet the requirements of attitude angle constraint and obstacle avoidance constraint, the controller additional force is obtained based on the potential function. Finally, the trajectory and attitude integrated controller is obtained, and the stability of the system is proved to realize the rigid-flexible-liquid coupled spacecraft trajectory and attitude integrated control.

[0057] (4) Finally, in order 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-liquid coupled spacecraft was built to verify the effectiveness of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Provide control modeling and control content structure diagram for rigid-flexible-liquid coupling spacecraft;

[0059] Figure 2 is the attitude tracking error curve;

[0060] Figure 3 is the angular velocity tracking error curve;

[0061] Figure 4is the position tracking error curve;

[0062] Figure 5 It is the speed tracking error curve;

[0063] Figure 6 It is the control force curve diagram;

[0064] Figure 7 is the control torque curve;

[0065] Figure 8 It is a curve diagram of the angle between the photosensitive device and the distant luminous object;

[0066] Fig. 9 It is a curve diagram of the angle between the photosensitive device and the nearest luminous object;

[0067] Fig.10 To track the distance between the spacecraft and three closer obstacles. DETAILED DESCRIPTION

[0068] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0069] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0070] The present invention provides a rigid-flexible-liquid coupled spacecraft attitude-orbit integrated modeling and control method, comprising the following steps:

[0071] Step 1: Establish a flexible attachment model. According to the flexible attachment model, establish a rigid-flexible-liquid coupling spacecraft control model, including a rigid-flexible coupling spacecraft dynamics model and a rigid-flexible-liquid coupling spacecraft relative dynamics model.

[0072] Step 1.1 Flexible attachment modeling, including

[0073] The flexible attachment is treated as a cantilever beam, and the force and moment analysis of each microelement of the flexible attachment is performed based on the finite element and modal superposition method. The force and moment balance equation is obtained as follows:

[0074]

[0075] Among them, F s is the shear force on the microelement, P(x,t) is the lateral external force per unit length of the cantilever beam, m f1 =ρ wing W wing H wing is the mass per unit length of the cantilever beam, ρ wing represents density, W wing Indicates the width per unit length, H wingrepresents the height per unit length, w(x,t) is the longitudinal displacement at time t from the origin x of the cantilever beam, M is the infinitesimal torsional moment, EI(x) is the stiffness of the cantilever beam, E is the elastic modulus, and I(x) is the inertia matrix at x;

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

[0077]

[0078] make φ n (x) is the modal function of the natural vibration mode of the spacecraft sailboard, χ n (t) is the generalized coordinate, we have

[0079]

[0080] make and but

[0081]

[0082] Based on the separation of variables method, formula (5) is organized as follows:

[0083]

[0084] Formula (6) and Formula (7) are standard equations for solving free beams. The solution is χ(t) = A1sinωt + A2cosωt. The general solution of Formula (6) is:

[0085] φ(x)=De rx (8);

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

[0087] Based on formula (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] Normalize equation (9) to get coefficient a n

[0091]

[0092] The boundary conditions of 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

[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] MATLAB is used to obtain the numerical solution of β. At the same time, based on equations (5) and (9), the natural frequency Ω and natural vibration mode φ of the flexible attachment are obtained. n (x).

[0098] Step 1.2: Based on the momentum conservation theory and Lagrangian principle, establish an integrated dynamic model of the rigid-flexible coupling spacecraft trajectory and attitude, including

[0099] The flexible momentum of the nominal point k is

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

[0101] Based on formula (12), the flexible momentum moment of the nominal point k is

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

[0103] Among them, r bkis the distance from the center of mass of the spacecraft to the connection between the flexible attachment and the rigid body, w k is the structural displacement of the flexible attachment point k, m kf is the mass of point k, ω(k) and v(k) are the angular velocity and speed of point k respectively. For vector x = [x1 x2 x3] T , the skew-symmetric matrix x × for

[0104] Velocity vector at nominal point k ω(k) is the angular velocity of point k. b (k) Ignore the structural displacement ||w k ||. Due to w k =φ k χ,φ k is the modal function, which is used to represent the natural vibration mode of the spacecraft sailboard vibration, and χ is the vibration mode. Further, the momentum H of the nominal point k can be obtained fp (k) and angular momentum H fc (k)

[0105]

[0106] Based on formula (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] Due to m kf ω(k) × r bk =-m kf r bk × ω(k), H of the flexible attachment relative to the center of the earth f for

[0109]

[0110] in, represents the quality of the flexible attachment, v The velocity vector of the spacecraft relative to the Earth-centered Earth-fixed coordinate system, the rigid-flexible translation coupling matrix Rotational coupling matrix

[0111] The rigid body momentum of the spacecraft is

[0112]

[0113] in, is the rigid body mass;

[0114] The moment of momentum of the rigid body is

[0115]

[0116] Based on formula (16), the momentum H of the rigid-flexible coupling spacecraft is obtained p and angular momentum H c for

[0117]

[0118] in,

[0119] According to the conservation theorem of momentum, the dynamic equation of rigid-flexible spacecraft is obtained:

[0120]

[0121] Among them, m f With J f is the mass and moment of inertia of the rigid-flexible spacecraft, v is the velocity, m kf is the mass of the nominal point k, r bk is the distance from the center of mass of the spacecraft to the connection between the flexible attachment and the rigid body, ω is the angular velocity, and the rigid-flexible translation coupling matrix Rotational coupling matrix χ is flexible vibration, F g and M g is the gravity gradient force and gravity gradient moment, M d and F d are the disturbance force and disturbance torque, is the disturbance force caused by the Earth's oblateness, F c and M c is the 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 coordinate system to the Earth’s inertial system, I3 is the unit matrix, and μ0 = 3.9860047 × 10 14 m 3 s -2 is the standard gravitational parameter of the Earth, R e =6378.14 km is the radius at the Earth’s equator, C0 = diag(

[113] ), p is the position vector of the spacecraft’s coordinate system in the Earth’s inertial system, p z represents the Z-axis component of the translation vector p; Cf =diag{2ε i Ω i}and are the flexibility matrix and stiffness matrix of the flexible attachment, ε i is the damping ratio of the i-th mode, Ω i is the natural frequency of the mode;

[0124] The Lagrange principle is used to establish the vibration equation of the flexible attachment. The vibration equation of the flexible attachment is:

[0125]

[0126] Let the coordinate of the center of mass of the spacecraft be O, and divide the liquid in the tank into two parts. The first part is the liquid that does not participate in the sloshing, with a mass of m l0 , the distance between the center of mass and the center of mass of the spacecraft is r l0 ; The second part is the liquid involved in the sloshing. The parameters of each order sloshing model are: sloshing mass m li , spring stiffness k li , damping c li , the distance between each order mass block and the center of mass of the spacecraft in the equilibrium state is r zi , the distance between each order mass block and the center of mass of the spacecraft in the shaking state is η i =[η i1 η i2 ] T , where η i1 is the sway displacement of the sway mass along the OX axis, η i2 is the sloshing displacement of the sloshing mass along the OY axis, i=1, 2 is the first two order sloshing displacements in the liquid equivalent process;

[0127] Momentum P of the equivalent spring mass l It is expressed as:

[0128]

[0129] in, is the total mass of liquid fuel, is the distance to the centroid;

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

[0131]

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

[0133] According to the momentum expression of the equivalent spring mass (26), the momentum moment of the equivalent spring mass H s It is expressed as:

[0134] H s =J s ω+h s (27);

[0135] in, I is the identity matrix,

[0136]

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

[0138]

[0139] in,

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

[0141]

[0142] Among them, m l is the total mass of liquid fuel, r l is the distance to the center of mass, F d and M d are the disturbance force and disturbance torque respectively, F c and M c They are the control force and control torque respectively, and the velocity vector of the nominal point k ω(k) is the angular velocity of point k, and is the rigid-fluid translation coupling matrix and the rigid-fluid rotation coupling matrix, M η =[m l1 m l1 m l2 m l2 ] T is the mass matrix of the sloshing liquid, C l =[c i1 c i1 c i2 c i2 ] T is the flexible matrix of the shaking liquid, K l =[k l1 k l1 k l2 k l2 ]T is the sloshing liquid stiffness matrix, and η is the sloshing liquid modal value.

[0143] Step 1.3, the rigid-liquid coupled spacecraft trajectory attitude integrated dynamics model, includes the following steps:

[0144] Based on the conservation of system momentum and angular momentum, the trajectory attitude dynamics model of the rigid-fluid coupled spacecraft is obtained by combining equation (20) with equation (28):

[0145]

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

[0147] The rotation of a rigid body in three-dimensional space is described based on the special orthogonal group SO(3), where the elements of the group SO(3) are the unit orthogonal matrices in three-dimensional space. In addition, the special Euclidean group SE(3) is used to uniformly describe the rotation and translation of rigid bodies in three-dimensional space, g∈SE(3)=R 3 ×SO(3):

[0148]

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

[0150] Let the velocity vector of the spacecraft be:

[0151]

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

[0153] Based on equations (32) and (33), the attitude-orbit integrated kinematic model of the spacecraft in the Earth inertial system is obtained as follows:

[0154]

[0155] Among them, ω × It means ω=[ω x ω y ω z ] T The skew-symmetric matrix is

[0156] The kinematic model of the spacecraft (34) is further organized as follows:

[0157]

[0158] Among them, g represents the actual position of the spacecraft;

[0159] Define the adjoint map of ξ as:

[0160]

[0161] Then its anti-adjoint mapping is:

[0162]

[0163] Based on the flexible attachment vibration model and the liquid fuel sloshing model (31), the dynamic equations of the rigid-flexible-liquid coupling spacecraft trajectory and attitude integration are obtained:

[0164]

[0165] Where Ξ=diag(J,mI3)∈R 6×6 is a symmetric positive definite matrix, Γ D =[M d ,F d ] T ∈R 6 ,χ∈R M ,γ∈R N They represent the vibration mode 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. M=3, N=4; They represent the rigid-flexible coupling matrix and the rigid-fluid coupling matrix respectively. represents the stiffness matrix, C f =diag{2ξ i Ω i ,i=1,2,...,M}∈R 3×3 represents the damping matrix of the flexible attachment vibration, where ξ i and Ω i They represent the vibration damping and vibration frequency of the i-th order flexible attachment vibration mode, M l =diag([m1 m1 m2 m2])∈R 4×4 represents the mass matrix of the liquid sloshing fuel, where m i represents the mass of the sloshing fuel of the i-th sloshing mode, K l =diag([k l1 k l1 k l2 k l2 ])∈R4×4 represents the stiffness matrix of the liquid sloshing fuel, C l =diag([c i1 c i1 c i2 c i2 ])∈R 4×4 A flexibility matrix representing the liquid sloshing fuel;

[0166] In order to realize the integrated tracking control of the trajectory attitude of the spacecraft, that is, the spacecraft tracks the expected posture and expected velocity, let the expected posture of the spacecraft be g d , the expected speed is ξ d According to formula (35), the kinematic equation of the virtual spacecraft at the desired position is:

[0167]

[0168] Let g e ∈R 4×4 is the actual position g and expected position g of the spacecraft d The relative pose matrix of the tracking error pose matrix is ​​taken as the reference system, and the tracking error pose matrix is

[0169]

[0170] Exponential coordinate g based on SE(3) e The corresponding tracking error η is as follows:

[0171]

[0172] Among them, Φ∈R 3 represents the attitude tracking error, Represents the position tracking error, which 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)), on the contrary, Φ and Using the Rodriguez formula according to its logarithmic coordinates g e The calculation results are:

[0175]

[0176] Taking the spacecraft body coordinate system as the reference coordinate system, the tracking error ξ between the spacecraft and the desired velocity ise for:

[0177]

[0178] The adjoint matrix mapping Ad of g in formula (35) g for:

[0179]

[0180] Then the spacecraft kinematic tracking error model is:

[0181]

[0182] in, is a positive definite matrix,

[0183] Formula (45) is the relative speed between the tracking spacecraft and the virtual pilot spacecraft. The derivative of both sides of formula (45) with respect to time is:

[0184]

[0185] calculate Need to use The derivative with respect to time is

[0186]

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

[0188]

[0189] Among them, the adjoint matrix mapping R e is the rotation matrix error, p e is the position vector error of the spacecraft body coordinate system in the Earth's inertial system.

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

[0191] Assuming that there is a light-sensitive onboard device on the spacecraft, in order to avoid interference with the device, the spacecraft needs to ensure that there are no bright luminous objects within the field of view of the light-sensitive onboard device. Let p represent the position vector of the spacecraft in the Earth's inertial system, p n represents the position vector of the bright object in the Earth's inertial system, p n-p represents the relative position vector of the bright object and the spacecraft, a represents the unit direction vector of the photosensitive satellite-borne equipment in the spacecraft body coordinate system, and θ represents the half field of view angle of the photosensitive satellite-borne equipment.

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

[0193]

[0194] b n After converting from the Earth's inertial system to the spacecraft's coordinate system, we can get a and R T b n Angle

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

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

[0197] Then the attitude constraint of the rigid-flexible-fluid coupled spacecraft is:

[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 When , the spacecraft is considered to be very safe and there is no need to consider the spacecraft attitude constraint problem.

[0200] In summary, the potential function of the attitude constraint is:

[0201]

[0202] It can be seen from formula (54) that when <a,R T b n >≥σ n When θ < <a,RT b n >≤σ n When <a,R T b n >The larger the potential function U n The smaller the numerator, the larger the denominator, so the potential function tends to make the angle <a,R T b n >becomes bigger, thus achieving the attitude constraint of allowing the spacecraft to avoid facing the light source as much as possible.

[0203] Next, we need to calculate the potential function U n The nth bright object exerts a torque T on the spacecraft under the action of the potential function U n The negative gradient relative to the unit direction vector of the photosensitive satellite-borne equipment is denoted as The specific expression is:

[0204]

[0205] Wherein, Ra is the unit direction vector of the photosensitive satellite-borne equipment in the Earth's inertial coordinate system.

[0206] In order to achieve spacecraft tracking control, it is necessary to ensure that the desired position satisfies the attitude constraints, so that the spacecraft desired position g d At any time, σ n < <a,R T b n >, that is, it is not affected by posture constraints.

[0207] Assume that the limit distance for the spacecraft to collide with the nth obstacle is d n , p n represents the position vector of the nth obstacle in the Earth's inertial system, then the obstacle avoidance constraint of the rigid-flexible-liquid coupling spacecraft is:

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

[0209] Similarly, set a safe distance when That is, when the spacecraft is far away from the obstacle, there is no need to consider the obstacle avoidance constraint. Therefore, the potential function of the obstacle avoidance constraint is:

[0210]

[0211] From formula (57), we can see that only when the center of mass of the spacecraft is taken as the origin and the radius is The potential function takes effect only when there are obstacles in the spherical region.

[0212] Next, calculate the potential function F nThe force F exerted by the nth obstacle on the spacecraft under the action of n The negative gradient relative to the unit direction vector of the photosensitive satellite-borne equipment is denoted as The specific expression is:

[0213]

[0214] Similarly, since the present invention discusses the problem of spacecraft tracking control, it is necessary to ensure that the desired position satisfies the obstacle avoidance constraint, so that the position g of the ideal pilot spacecraft is d Satisfied at any time That is, it is not affected by the obstacle avoidance constraint. Therefore, in the potential function U n and F n Under the action of , the additional force exerted on the spacecraft by bright objects and obstacles is:

[0215]

[0216] Step 3: Based on the control model of the rigid-flexible-liquid coupling spacecraft, the stability of the system is proved by Lyapunov theory based on the additional forces exerted on the spacecraft by bright objects and obstacles. A saturation controller is designed to solve the control input constraint problem and realize the integrated control of the trajectory and attitude of the rigid-flexible-liquid coupling spacecraft, which 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 is a positive definite diagonal matrix, is a positive definite matrix, K1∈R 6×6 is a positive definite diagonal matrix, K2=diag{K 21 ,K 22 ...K 26} is a positive definite matrix, λ min (K2)>||ΞΓ D ||, λ>0;

[0220] From the controller (60), we get:

[0221]

[0222]

[0223] in, It is an adaptive sliding mode controller The corresponding control system is regarded as the nominal system; g(S,t) is regarded as a disturbance outside the nominal system; when the tracking spacecraft reaches the desired posture, that is, S = 0, the spacecraft is not affected by the attitude and obstacle avoidance constraints, then: g(0,t) = 0; where g(S,t) is the nominal system The disappearing interference;

[0224] Next, we prove that S = 0 is the equilibrium point of system (61). Consider The Lyapunov function of is V3, then:

[0225]

[0226] Further we can get:

[0227]

[0228] Let β3=2λ min (K1), β4=2α, γ=0.5. The following proves that V3 satisfies the inequality:

[0229]

[0230] Perform eigenvalue decomposition on the positive definite symmetric matrix Ξ and obtain: Ξ=QΛQ T , where Q is an orthogonal matrix consisting of the eigenvectors of Ξ, and Λ is a positive definite diagonal matrix consisting of the eigenvalues ​​of Ξ. Then: ΞS=QΛQ T S. Let y = Q T S, then:

[0231] ΞS=QΛy,||y||=||S|| (66);

[0232] therefore:

[0233]

[0234] Both sides of inequality (67) are squares of positive numbers, so taking the square root of both sides of inequality (67) yields:

[0235] ||ΞS||≤λ max (Ξ)||y||=λ max (Ξ)||S|| (68);

[0236] Where β5 = λ max (Ξ).

[0237] Next, we prove that g(S,t) satisfies the following equation:

[0238] ||g(S,t)||=||Ξ -1 U PF || (69);

[0239] In formula (69), -1 It is also a positive definite symmetric matrix, so we can use the same method as equation (65) to prove:

[0240] ||g(S,t)||=||Ξ -1 U PF ||≤λ max (Ξ -1 )||U PF || (70);

[0241] Among them, λ max (Ξ -1 ) need to ensure:

[0242]

[0243] Since Ξ is a fixed parameter of the spacecraft, we only need to ensure that parameter K1 satisfies:

[0244]

[0245] This ensures that equation (71) holds true, and further proves that the vanishing perturbation system (61) is asymptotically stable at S=0.

[0246] Affected by the physical constraints of the actuator (such as flywheel, etc.), the range of torque that the actuator can generate is limited. When the theoretically calculated control torque exceeds the actual range that the actuator can bear, a control input constraint problem will occur. Therefore, the following saturation controller is designed:

[0247] Γ=sat(Γ c ) (73);

[0248] Among them, sat(·) is the saturation function. For vector x=[x1 x2 x3] T , saturation function sat(x) = [sat(x1)sat(x2)sat(x3)] T , where sat(x i )for

[0249]

[0250] Among them, x max , x min x i The upper and lower bounds of (i=1,2,3).

[0251] Based on the above three steps, the entire rigid-flexible-liquid coupled spacecraft trajectory and attitude integrated control process is completed.

[0252] In order to verify the effectiveness of the rigid-flexible-liquid coupling spacecraft control model and control algorithm established by the present invention, the rigid-flexible-liquid coupling spacecraft control system is integrated and designed in Matlab / Simulink, and the following simulation verification is performed.

[0253] (1) Parameter setting

[0254] Assume that the mass and inertia matrices of the ideal spacecraft and the tracking spacecraft are:

[0255]

[0256] The first three vibration frequencies of the vibration mode of the flexible attachment are Ω1 = 0.7681 rad·s -1 ,Ω2=1.1038rad·s -1 ,Ω3=1.8733rad·s -1 , r = 0.8m, vibration damping is ξ1 = 0.0056, ξ2 = 0.0086, ξ3 = 0.0013; the flexibility matrix of the liquid sloshing mode is C l =diag(3.334,3.334,0.237,0.237), the stiffness matrix is ​​K l =diag(55.21,55.21,7.27,7.27), the masses of the two-order equivalent sloshing liquids are m1=5kg and m2=0.2kg, and the distances from the center of mass of the spacecraft are b1=1.127m and b2=0.994m, respectively. The initial values ​​of the two modes are both zero, δ f With δ l They are

[0257]

[0258] The initial position g of the virtual pilot spacecraft d (0) and the initial velocity vector ξ d (0) are:

[0259]

[0260] Assume that the ideal virtual pilot spacecraft is not affected by external interference, vibration of flexible accessories, and sloshing of liquid fuel during operation. The initial attitude and initial angular velocity of the tracking spacecraft at the initial moment are:

[0261]

[0262] The relative positions and relative linear velocities of the tracking spacecraft and the virtual pilot spacecraft at the initial moment are:

[0263]

[0264] According to the above conditions, the tracking error η(0) at the initial moment can be calculated as:

[0265]

[0266] Assuming that the output upper limit force and torque of the actuator are 10N and 0.5N respectively, the interference force and torque are set as:

[0267]

[0268] The unit direction vector of the light-sensitive device on the spacecraft is a = [0; 0; 1]; Assume that there are three luminous objects at a relatively long distance in the operating environment of the virtual pilot spacecraft, and their position information, the set warning angle θ and the safety angle σ n As shown in Table 1.

[0269] Table 1 Information on distant luminous objects

[0270] <![CDATA[b n ]]> θ <![CDATA[σ n ]]> [0；-1；0] 20° 35° [0.68；0.67；0.3] 20° 35° [0.38；0；0.925] 20° 35°

[0271] At the same time, it is assumed that there are three relatively close luminous objects in the operating environment of the virtual pilot spacecraft, and their relative position vectors to the ideal virtual pilot spacecraft are:

[0272]

[0273] For such objects, obstacle avoidance and posture 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°, the warning distance is set to d n =30m, the safety distance is set to

[0274] The parameters of the controller (73) are set as:

[0275]

[0276] (2) Results Analysis

[0277] To illustrate the effectiveness of this method, two simulations are performed below:

[0278] Figures 2 to 9 The mathematical simulation results of applying the controller (73) to a rigid-flexible-fluid coupled spacecraft are shown, with a simulation time of 1000 seconds. Figure 2The curve of the attitude tracking error of the tracking spacecraft relative to the ideal virtual pilot spacecraft over time is shown. It can be seen that the attitude tracking error converges in about 500s, and after calculation, the attitude tracking error ||Φ||≤0.05°. Figure 3 The curve of the angular velocity tracking error of the tracking spacecraft relative to the ideal virtual pilot spacecraft over time is shown. It can be seen that the angular velocity tracking error converges at about 500s, and the angular velocity tracking error ||ω is obtained after calculation. e ||≤6×10 -4 rad·s -1 . Figure 4 The curve of the position tracking error between the tracking spacecraft and the ideal virtual pilot spacecraft over time is shown. It can be seen that the position tracking error converges in about 400s, and after calculation, the position tracking error ||Φ||≤0.05°. Figure 5 The curve of the linear velocity tracking error of the tracking spacecraft relative to the ideal virtual pilot spacecraft over time is shown. It can be seen that the linear velocity tracking error converges at about 400s, and the velocity tracking error ||v e ||≤6×10 -3 m·s -1 .

[0279] In summary, the tracking controller (73) can well implement the tracking spacecraft's tracking of the ideal virtual pilot spacecraft.

[0280] Figure 6 The curve of the control force output by the controller during the simulation is shown. It is noted that the control force decays around 400s, which means that the tracking spacecraft has tracked the virtual pilot spacecraft in terms of position and linear velocity. This is also consistent with Figure 4 , Figure 5 The results correspond. Figure 7 The curve of the control torque output by the controller during the simulation is shown. It is noted that the control torque decays at about 500s, which means that the tracking spacecraft has tracked the virtual pilot spacecraft in terms of attitude and angular velocity. This is also consistent with Figure 2 , Figure 3 The result corresponds to. Figure 6 , Figure 7 It can be seen that there is no serious chattering phenomenon in the control force and control torque, which shows that the controller used in this patent has a good effect of suppressing chattering.

[0281] Figure 8The time-varying curves of the angles between the three luminous objects that are far from the orbit of the ideal virtual pilot spacecraft in Table 1 and the photosensitive onboard equipment on the tracking spacecraft are shown, where the green and red dotted lines represent the warning angle and the safety angle, respectively. It can be seen that the tracking spacecraft did not cross the warning angle during the entire operation, and the angles between the ideal virtual pilot spacecraft and the luminous objects exceeded the safety angle after tracking, and were not subject to attitude constraints.

[0282] Fig. 9 The time-varying curves of the angles between the three luminous objects that are close to the orbit of the ideal virtual pilot spacecraft in equation (80) and the photosensitive onboard equipment on the tracking spacecraft are shown. It can also be seen that the tracking spacecraft did not cross the warning angle during the entire operation process, and the angles between the ideal virtual pilot spacecraft and the luminous objects on the tracking spacecraft all exceeded the safety angle and were not subject to attitude constraints.

[0283] Fig.10 The Euclidean distance curve between the three obstacles close to the orbit of the ideal virtual pilot spacecraft and the tracking spacecraft is given. It can be seen that the tracking spacecraft did not cross the set warning distance during the entire movement process, and the distance between the tracking spacecraft and the obstacles after tracking the ideal virtual pilot spacecraft was greater than the safety distance and was not subject to obstacle avoidance constraints.

[0284] In summary, under various constraints, the rigid-flexible-liquid coupled spacecraft tracking controller of this patent can complete the tracking of the target spacecraft by the tracking spacecraft within a limited time.

[0285] Therefore, the present invention adopts the above-mentioned rigid-flexible-liquid coupled spacecraft attitude and trajectory integrated modeling and control method, and studies the trajectory attitude integrated tracking control model and control algorithm for the spacecraft trajectory attitude tracking control problem under the influence of flexible vibration and liquid fuel sloshing, and obtains the control force and torque based on the potential function theory, effectively solving the trajectory attitude control problem under obstacle avoidance constraints. The system stability proof is completed, the rigid-flexible-liquid coupled spacecraft trajectory attitude integrated tracking controller is realized, and the established model and controller are mathematically simulated by Matlab to verify the effectiveness of the control algorithm.

[0286] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A rigid-flexible-liquid coupled spacecraft attitude and orbit integrated modeling and control method, characterized in that: The following steps are involved: Based on the theory of conservation of momentum, the rigid-flexible and rigid-liquid coupling effects are analyzed, and the trajectory and attitude integrated dynamics model of rigid-flexible and rigid-liquid coupling spacecraft is established. The three coupling relationships of rigid-flexible and liquid are comprehensively analyzed, and based on the Lie group SE (3) theory, the trajectory and attitude integrated dynamics tracking error model of rigid-flexible and liquid coupling spacecraft is established, laying the foundation for the following controller design; Secondly, the attitude constraint, obstacle avoidance constraint and input constraint of the rigid-flexible-fluid coupling spacecraft are established. Based on the attitude constraint, obstacle avoidance constraint and potential function theory, the additional force exerted on the spacecraft by bright objects and obstacles is obtained. Combined with the additional force exerted on the spacecraft by bright objects and obstacles, the controller is obtained. Finally, based on the controller, a saturation controller is designed to solve the control input constraint problem and realize the integrated control of the trajectory and attitude of the rigid-flexible-liquid coupled spacecraft.

2. The method for integrating attitude and orbit modeling and control of a rigid-flexible-liquid coupled spacecraft according to claim 1, characterized in that: Based on the momentum conservation theory and Lagrangian principle, the trajectory and attitude integrated dynamics model of rigid-flexible coupling spacecraft is established as follows: Among them, m f With J f is the mass and moment of inertia of the rigid-flexible spacecraft, v is the velocity, m kf is the mass of the nominal point k, r bk is the distance from the center of mass of the spacecraft to the connection between the flexible attachment and the rigid body, ω is the angular velocity, and the rigid-flexible translation coupling matrix Rotational coupling matrix χ is flexible vibration, F g and M g is the gravity gradient force and gravity gradient moment, M d and F d is the disturbance force and disturbance torque, a J2 is the disturbance force caused by the Earth's oblateness, F c and M c is the control force and control torque, M g 、F g with a J2 They are 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 coordinate system to the Earth’s inertial system, I3 is the unit matrix, μ = 3.9860047 × 10 14 m 3 s -2 is the standard gravitational parameter of the Earth, R e =6378.14 km is the radius at the Earth’s equator, C0 = diag([113]), p is the position vector of the spacecraft’s coordinate system in the Earth’s inertial system, p z represents the Z-axis component of the translation vector p; C f =diag{2ε i Ω i }and are the flexibility matrix and stiffness matrix of the flexible attachment, ε i is the damping ratio of the i-th mode, Ω i is the natural frequency of the mode.

3. The method for integrating attitude and orbit modeling and control of a rigid-flexible-liquid coupled spacecraft according to claim 1, characterized in that: The integrated dynamic model of rigid-fluid coupled spacecraft trajectory and attitude is: Among them, m l is the total mass of liquid fuel, r l The velocity vector of the nominal point k is its distance to the center of mass. ω(k) is the angular velocity of point k, and is the rigid-fluid translation coupling matrix and the rigid-fluid rotation coupling matrix, M η =[m l1 m l1 m l2 m l2 ] T is the mass matrix of the sloshing liquid, C l =[c i1 c i1 c i2 c i2 ] T is the flexible matrix of the shaking liquid, K l =[k l1 k l1 k l2 k l2 ] T is the sloshing liquid stiffness matrix, and η is the sloshing liquid modal value.

4. The method for integrating attitude and orbit modeling and control of a rigid-flexible-liquid coupled spacecraft according to claim 1, characterized in that: Based on the Lie group SE (3) theory, the trajectory and attitude integrated dynamic tracking error model of rigid-flexible-fluid coupling spacecraft is established as follows: Where Ξ=diag(J,mI3)∈R 6×6 is a symmetric positive definite matrix, ξ e =ξ-ξ d is the spacecraft tracking error, is the anti-adjoint mapping of the spacecraft's velocity vector ξ, ξ=[v T ω T ] T ,ad ξe is the adjoint mapping of the spacecraft's velocity vector ξ, and the adjoint matrix mapping R e is the rotation matrix error, p e is the position vector error of the spacecraft body coordinate system in the Earth’s inertial system, v d With ω d are the expected velocity and angular velocity respectively, Γ d =[M d ,F d ] T ∈R 6 ,χ∈R M ,γ∈R N represent the vibration mode of the flexible attachment and the sloshing mode of the liquid fuel, respectively. They represent the rigid-flexible coupling matrix and the rigid-fluid coupling matrix respectively, and M and N represent the approximate orders of the two modes respectively. represents the stiffness matrix, C f =diag{2ξ i Ω i ,i=1,2,...,M}∈R 3×3 represents the damping matrix of the flexible attachment vibration, where ξ i and Ω i They represent the vibration damping and vibration frequency of the i-th order flexible attachment vibration mode, M l =diag([m1 m1 m2 m2])∈R 4×4 represents the mass matrix of the liquid sloshing fuel, where m i represents the mass of sloshing fuel of the i-th sloshing mode.

5. The method for integrating attitude and orbit modeling and control of a rigid-flexible-liquid coupled spacecraft according to claim 1, characterized in that: Additional forces exerted on the spacecraft by bright objects and obstacles Among them, k3>0 and k4>0 are positive constants; The attitude and obstacle avoidance constraints give the following controller: in, Sliding surface S = [S1 S2 S3] = ξ e +ν1η,ν1=diag(ν 11 ,...,ν 16 )∈R 6×6 is a positive definite diagonal matrix, is a positive definite matrix, K1∈R 6×6 is a positive definite diagonal matrix, K2=diag{K 21 ,K 22 ...K 26 } is a positive definite matrix, λ min (K2)>||ΞΓ D ||, λ>

0.

6. The method for integrating attitude and orbit modeling and control of a rigid-flexible-liquid coupled spacecraft according to claim 5, characterized in that: The attitude constraint of the rigid-flexible-fluid coupled spacecraft is: <a,R T b n >>θ (8); Where a represents the unit direction vector of the photosensitive satellite-borne device in the spacecraft coordinate system, θ represents the half field of view angle of the photosensitive satellite-borne device, is the unit direction vector of the relative position vector between the bright object and the spacecraft, p n represents the position vector of the bright object in the Earth's inertial frame; Set a safety angle σ n >θ, when <a,R T b n >≥σ n When , the spacecraft attitude constraint problem is not considered; In summary, the potential function of the attitude constraint is: Calculate the potential function U n The nth bright object exerts a torque T on the spacecraft under the action of the potential function U n The negative gradient relative to the unit direction vector of the photosensitive satellite-borne equipment is denoted by T = -▽U n , the specific expression is: Wherein, Ra is the unit direction vector of the photosensitive satellite-borne equipment in the Earth's inertial coordinate system; The desired position of the spacecraft g d At any time, σ n < <a,R T b n >, not affected by posture constraints; The obstacle avoidance constraints of the rigid-flexible-fluid coupled spacecraft are: ||p n -p||>d n (11); Among them, d n represents the limit distance of collision between the spacecraft and the nth obstacle, p n represents the position vector of the bright object in the Earth's inertial system, p n -p represents the relative position vector of the bright object and the spacecraft; Set a safe distance when When the spacecraft is far away from the obstacle, there is no need to consider the obstacle avoidance constraint. Therefore, the potential function of the obstacle avoidance constraint is: From formula (12), we know that only when the center of mass of the spacecraft is taken as the origin and the radius is d n The potential function takes effect only when there are obstacles in the spherical region of s; Calculate the potential function F n The force F exerted by the nth obstacle on the spacecraft under the action of n The negative gradient relative to the unit direction vector of the photosensitive satellite-borne equipment is denoted as F = -▽F n , the specific expression is: Ensure that the desired position satisfies the obstacle avoidance constraint, so that the position of the ideal pilot spacecraft g d Satisfied at any time Not affected by obstacle avoidance constraints.

7. The method for integrating attitude and orbit modeling and control of a rigid-flexible-liquid coupled spacecraft according to claim 5, characterized in that: The control input constraints of the rigid-flexible-fluid coupled spacecraft are: in, is a positive constant; When the theoretically calculated control torque M c When the value exceeds the actual tolerance of the actuator, a control input constraint problem occurs. Therefore, the following saturation controller is designed: C=sat(C c ) (15); Among them, sat(·) is the saturation function, for vector x = [x1 x2 x3] T , saturation function sat(x) = [sat(x1) sat(x2) sat(x3)] T , where sat(x i )for Among them, x max , x min x i The upper and lower bounds of (i=1,2,3).

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