An integrated attitude, orbit and vibration modeling method for on-orbit assembly of large spacecraft

Abstract

The present invention discloses an attitude-orbit-vibration integrated modeling method for on-orbit assembly of large spacecraft, including: S1, analyzing the dynamic evolution characteristics of structural vibration; S2, making modeling assumptions and defining required vectors; S3, analyzing the coupling mechanism of large-scale structural vibration characteristic changes and attitude-orbit motion according to the results of the dynamic evolution characteristic analysis; S4, establishing a group of dynamic equations in the body coordinate system based on the required vectors and the coupling effects of vibration, attitude and orbit; S5, defining a dual matrix, and constructing a spacecraft orbit-attitude-vibration integrated dynamic model based on dual quaternions when the spacecraft is assembled on-orbit according to the group of dynamic equations. The present invention fully analyzes the interaction mechanism between the vibration characteristic changes and attitude-orbit motion to establish an orbit-attitude-vibration integrated model, fully highlighting the dynamic characteristics of the mutual coupling of orbit-attitude-vibration of large spacecraft, making it easier to analyze the dynamic characteristics, and thus producing a better control effect.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology, and in particular relates to an attitude, orbit and vibration integrated modeling method for on-orbit assembly of a large spacecraft. Background Art

[0002] Large spacecraft are important strategic aerospace equipment for future space resource utilization, exploration of the mysteries of the universe, and long-term in-orbit residence. They cannot be constructed through a single launch and orbital deployment, and often require multiple launches and in-orbit assembly for construction. During the assembly process, the nonlinear coupling effect between the attitude and orbit motion of large spacecraft and the vibration of large structures makes it difficult to model the integrated modeling of large spacecraft, which is the core technical difficulty hindering the in-orbit assembly of large spacecraft.

[0003] Existing spacecraft attitude and orbit integrated modeling methods can be divided into three categories. The first category is to describe the orbit and attitude motion of the spacecraft separately, and then combine them to form an attitude and orbit integrated dynamic model; the second category is to establish an attitude and orbit integrated dynamic model based on dual quaternions; the third category is to model based on exponential coordinates on the Lie group SE (3), which describes the rotation and translation of the rigid body in three-dimensional space without singularity, and then describes the six-degree-of-freedom motion of the spacecraft. Based on this modeling idea, an attitude and orbit integrated dynamic model is established. There are two main existing spacecraft attitude and vibration integrated modeling methods, namely, integrated models based on active vibration suppression and passive vibration suppression. However, in theory, for the above attitude and orbit integrated modeling and attitude vibration integrated modeling methods, the former does not consider structural vibration, and the latter does not consider the influence of orbital motion. They cannot fully highlight the dynamic characteristics of the mutual coupling between orbit, attitude, and vibration of large spacecraft, resulting in difficulty in achieving integrated control or failing to meet the requirements of high-precision and high-stability control due to unclear dynamic coupling mechanism.

[0004] Existing integrated orbit-attitude-vibration modeling approaches mostly consider the effects of gravity gradients, establishing an on-orbit dynamics model in the Hamiltonian system and then using the Symplectic Runge-Kutta method to determine the dynamic response under the influence of different parameters. However, this approach does not analyze the dynamic evolution of vibrations of large flexible structures under multi-source perturbations. Instead, it focuses on analyzing the coupling between attitude and structural vibrations, as well as the effects of gravity gradients on attitude and orbital motion, without in-depth analysis of the coupling between structural vibration and orbital motion. Summary of the Invention

[0005] In response to the above-mentioned deficiencies in the prior art, the present invention provides an attitude, orbit and vibration integrated modeling method for on-orbit assembly of large spacecraft, which solves the problem that the existing attitude and orbit integrated dynamics model does not consider the influence of structural vibration and the attitude and vibration integrated model does not consider the influence of orbital motion, and cannot fully highlight the dynamic characteristics of the mutual coupling of orbit, attitude and vibration of large spacecraft.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: a method for integrating attitude, orbit and vibration modeling for on-orbit assembly of a large spacecraft, comprising the following steps:

[0007] S1. Analyze the dynamic evolution characteristics of vibration of large flexible structures under multi-disturbance excitation;

[0008] S2. Make modeling assumptions in the spacecraft body coordinate system and define the required vectors;

[0009] S3. Based on the results of dynamic evolution characteristics analysis, analyze the coupling mechanism between the changes in large-scale structural vibration characteristics and attitude and orbit motion;

[0010] S4. Based on the required vectors and the coupling effects of vibration, attitude, and trajectory obtained from the coupling mechanism analysis, a set of dynamic equations in the body coordinate system is established;

[0011] S5. Define the dual matrix and construct a spacecraft orbit-attitude-vibration integrated dynamic model based on the dual quaternion during on-orbit assembly of the spacecraft according to the dynamic equations.

[0012] Furthermore, the step S1 is specifically as follows:

[0013] On a large flexible structure, a piezoelectric actuator is bonded to the surface of a flexible attachment. The voltage generated by the actuator is used to generate deformation that leads to torque. The structural vibration characteristics are analyzed based on active vibration suppression under multi-disturbance excitation.

[0014] Furthermore, in step S2, the modeling assumption in the spacecraft body coordinate system is:

[0015] l i +r i ≈r i

[0016] Where, l i The perturbation part Δm of the nominal mass m0 that changes due to on-orbit assembly is at position r in this system before the structural vibration occurs. i The mass element m i Mass element m after structural vibration occurs i moving distance.

[0017] Furthermore, in step S4, the dynamic equations in the body coordinate system are:

[0018]

[0019] Where F is the net external force, v is the spacecraft velocity vector, is the spacecraft acceleration vector, ω is the attitude angular velocity vector, δ a is the orbital coupling coefficient matrix, is the acceleration vector of the modal coordinates after structural vibration occurs, is the velocity vector of the modal coordinates after structural vibration occurs;

[0020] T is the moment of momentum, J0 is the nominal inertia matrix, ΔJ is the perturbation part of the moment of inertia caused by on-orbit assembly, is the attitude angular acceleration, δ b is the coupling coefficient matrix of vibration to spacecraft attitude;

[0021] Β is the modal damping matrix, K is the stiffness matrix, η is the modal coordinate, u p and Δ p are the piezoelectric input and the corresponding coupling matrix, respectively.

[0022] Furthermore, the dual matrix in step S5 is:

[0023]

[0024] Where, is the coupling coefficient matrix of vibration to spacecraft, ε is an infinitesimal quantity;

[0025] The equivalent dual matrix of the dual matrix for:

[0026]

[0027] Where I is the identity matrix.

[0028] Furthermore, the spacecraft orbit-attitude-vibration integrated dynamic model in step S5 is:

[0029]

[0030] Where,

[0031]

[0032] in,

[0033] The beneficial effects of the present invention are:

[0034] The present invention fully analyzes the interaction mechanism between the changes in vibration characteristics and attitude-orbit motion, considers the coupling effect between orbit, attitude and vibration, and establishes an orbit-attitude-vibration integrated model, which fully highlights the dynamic characteristics of the mutual coupling between orbit, attitude and vibration of large spacecraft, makes it easier to analyze the dynamic characteristics, and thus produces better control effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of the attitude, orbit and vibration integrated modeling method for on-orbit assembly of large spacecraft provided by the present invention. DETAILED DESCRIPTION

[0036] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0037] Large spacecraft are significantly affected by complex perturbations such as environmental forces. Large-scale and configurational changes during assembly can easily trigger structural vibrations, and attitude-orbit motion exhibits strong kinematic coupling with elastic deformation. Considering only the coupling of orbit and attitude to establish an integrated attitude-orbit dynamics model, under the influence of structural vibration, the dynamic coupling mechanism is unclear, resulting in the final results failing to meet high-precision requirements. Furthermore, considering only the coupling of attitude and vibration without considering orbital motion can significantly deviate from the actual dynamic characteristics, making integrated control difficult.

[0038] Therefore, an embodiment of the present invention provides an attitude, orbit, and vibration integrated modeling method for on-orbit assembly of a large spacecraft. The method selects four elements to represent the integrated dynamic model of the orbit, attitude, and vibration of the large spacecraft during on-orbit assembly. Considering the coupling effect of the orbit, attitude, and vibration, the dynamic equations are derived in the body coordinate system. Based on the equations, the spacecraft orbit-attitude-vibration integrated dynamic model based on the dual four elements during on-orbit assembly is obtained, such as Figure 1 As shown, the following steps are included:

[0039] S1. Analyze the dynamic evolution characteristics of vibration of large flexible structures under multi-disturbance excitation;

[0040] S2. Make modeling assumptions in the spacecraft body coordinate system and define the required vectors;

[0041] S3. Based on the results of dynamic evolution characteristics analysis, analyze the coupling mechanism between the changes in large-scale structural vibration characteristics and attitude and orbit motion;

[0042] S4. Based on the required vectors and the coupling effects of vibration, attitude, and trajectory obtained from the coupling mechanism analysis, a set of dynamic equations in the body coordinate system is established;

[0043] S5. Define the dual matrix and construct a spacecraft orbit-attitude-vibration integrated dynamic model based on the dual quaternion during on-orbit assembly of the spacecraft according to the dynamic equations.

[0044] In step S1 of this embodiment, the method for performing dynamic evolution characteristic analysis is specifically as follows: on a large flexible structure, a piezoelectric brake is bonded to the surface of a vibration attachment, and its voltage is used to generate structural vibration, and then the structural vibration characteristic analysis under active suppression is performed.

[0045] In step S2 of this embodiment, the modeling assumption in the spacecraft body coordinate system is:

[0046] l i +r i ≈r i (1)

[0047] Where, l i The perturbation part Δm of the nominal mass m0 that changes due to on-orbit assembly is at position r in this system before the structural vibration occurs. i The mass element m i Mass element m after structural vibration occurs i moving distance.

[0048] In step S4 of this embodiment, the dynamic equations in the body coordinate system include the calculation formulas for the total external force and angular momentum of the spacecraft, and the motion equations of the vibration part. The equations are specifically:

[0049]

[0050] Where F is the net external force, v is the spacecraft velocity vector, is the spacecraft acceleration vector, ω is the attitude angular velocity vector, δ a is the orbital coupling coefficient matrix, is the acceleration vector of the modal coordinates after structural vibration occurs, is the velocity vector of the modal coordinates after structural vibration occurs;

[0051] T is the moment of momentum, J0 is the nominal inertia matrix, ΔJ is the perturbation part of the moment of inertia caused by on-orbit assembly, is the attitude angular acceleration, δ b is the coupling coefficient matrix of vibration to spacecraft attitude;

[0052] Β is the modal damping matrix, K is the stiffness matrix, η is the modal coordinate, u p and Δ p are the piezoelectric input and the corresponding coupling matrix, respectively.

[0053] In this embodiment, the method for constructing the dynamic equations in step S4 is specifically as follows:

[0054] Keep the second-order small quantity, according to Newton's second law:

[0055]

[0056] After finite element analysis, we get:

[0057]

[0058] Similarly, we get:

[0059]

[0060] After further finite element analysis, we get:

[0061]

[0062] Reintroduction:

[0063]

[0064] Therefore, the orbit-attitude-vibration integrated dynamic equations of large spacecraft in the body coordinate system are obtained:

[0065]

[0066] Furthermore, the above equations Substituting into F and T we get:

[0067]

[0068] Further sorting out and

[0069]

[0070] Will get and Substituting back and sorting it out we get:

[0071]

[0072] In step S5 of this embodiment, according to the dual number Dual Quaternion The resulting dual matrix is:

[0073]

[0074] middle, is the coupling coefficient matrix of vibration to spacecraft, ε is an infinitesimal quantity;

[0075] According to formula (11), the equivalent dual matrix of the dual matrix is ​​obtained for:

[0076]

[0077] Where I is the identity matrix.

[0078] Based on the defined dual matrix, the spacecraft orbit-attitude-vibration integrated dynamic model in step S3 is obtained as:

[0079]

[0080] Where,

[0081]

[0082] in, In the description of the present invention, it should be understood that the terms "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only and cannot be understood as indicating or implying the relative importance or the number of technical features implicitly specified. Therefore, the features defined by "first", "second", and "third" may explicitly or implicitly include one or more of such features.

Claims

1. A method for integrating attitude, orbit and vibration modeling for on-orbit assembly of large spacecraft, characterized in that: The following steps are involved: S1. Analyze the dynamic evolution characteristics of vibration of large flexible structures under multi-disturbance excitation; S2. Make modeling assumptions in the spacecraft body coordinate system and define the required vectors; S3. Based on the results of dynamic evolution characteristics analysis, analyze the coupling mechanism between the vibration characteristics of large structures and attitude and track motion; S4. Based on the required vector and the coupling effects of vibration, attitude and orbit obtained by coupling mechanism analysis, a group of dynamic equations in the body coordinate system is established; S5. Define the dual matrix and construct the spacecraft orbit-attitude-vibration integrated dynamics model based on the dual quaternion when assembling the spacecraft on-orbit according to the dynamics equations; In step S4, the dynamic equations in the body coordinate system are: Where F is the resultant external force, v is the spacecraft velocity vector, is the spacecraft acceleration vector, ω is the attitude angular velocity vector, δ a is the orbital coupling coefficient matrix, is the acceleration vector of the modal coordinates after structural vibration occurs, is the velocity vector of the modal coordinates after the structural vibration occurs; T is the momentum, J0 is the nominal inertia matrix, ΔJ is the perturbation part of the change in the moment of inertia due to on-orbit assembly, is the attitude angular acceleration, δ b is the coupling coefficient matrix of vibration to spacecraft attitude; Β is the modal damping matrix, K is the stiffness matrix, η is the modal coordinate, u p and Δ p are the piezoelectric input and the corresponding coupling matrix, respectively; The dual matrix in step S5 is: In the formula, is the coupling coefficient matrix of vibration to spacecraft, ε is an infinitesimal quantity; The equivalent dual matrix of the dual matrix is for: Where I is the unit matrix; The spacecraft orbit-attitude-vibration integrated dynamics model in step S5 is: In the formula, in, 2. The attitude, orbit and vibration integrated modeling method for on-orbit assembly of large spacecraft according to claim 1 is characterized in that: The step S1 is specifically as follows: On large flexible structures, piezoelectric actuators are bonded to the surface of flexible attachments, and their voltage is used to generate deformation that leads to torque. The structural vibration characteristics are analyzed based on active vibration suppression under multi-disturbance excitation.

3. The attitude, orbit and vibration integrated modeling method for on-orbit assembly of large spacecraft according to claim 1 is characterized in that: In step S2, the modeling assumption in the spacecraft body coordinate system is: l i +r i ≈r i In the formula, l i is the perturbation part Δm of the nominal mass m0 that changes due to on-orbit assembly and is located at position r in the system before structural vibration occurs. i The mass element m i Mass element m after structural vibration i moving distance.

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