A Reconstruction Target Determination Method Based on Dimensionally Reduced Energy Control Matrix
Through a method based on dimensionality reduction controllable matrix, the computational complexity and accuracy problems of autonomous reconstruction target determination of spacecraft are solved, and efficient and accurate reconstruction target determination is achieved.
Patent Information
- Application Number
- CN202411503935.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-25
- Publication Date
- 2025-10-28
- Estimated Expiration
- 2044-10-25
AI Technical Summary
Existing technologies are insufficient for efficiently determining reconfiguration targets on spacecraft. Traditional methods are computationally complex and lack precision, failing to meet the requirements for autonomous operation.
A method based on a dimension-reduced controllability matrix is adopted. By determining the controllability Lie derivative of the spacecraft control system, a controllability matrix is established, and matrix transpose and polar coordinate transformation are performed to decompose the common subspace to determine the reconstruction target.
It reduces computational complexity and computational resource requirements, improves the accuracy and efficiency of target determination, and is suitable for autonomous computation on spacecraft with limited computational resources.
Smart Images
Figure CN119512142B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for determining reconstruction targets based on a dimension-reduced energy control matrix, belonging to the field of space autonomous operation technology. Background Technology
[0002] Future deep-space exploration missions will require spacecraft to possess autonomous operation capabilities, and autonomous reconfiguration is crucial to ensuring the safe, reliable, and autonomous operation of spacecraft. To achieve autonomous reconfiguration, the controllability of the system must first be assessed on the spacecraft to uniquely determine the reconfiguration target. Given the severely limited computing resources of spacecraft, the ability to characterize the system's controllability matrix in a reduced-dimensional way is key to determining the reconfiguration target.
[0003] Traditional observability matrix representation methods mainly include differential geometry and Gram matrix methods. Differential geometry methods require calculating higher-order Lie derivatives of the system's controllability to construct a high-dimensional controllability matrix, thus representing the system's controllability. These algorithms involve high-dimensional matrix operations and higher-order Lie derivative calculations, making them difficult to implement on spacecraft. Gram matrix methods are suitable for linear control systems; for nonlinear control systems, linearization is required first, which introduces linearization errors and affects the accuracy of the representation. Summary of the Invention
[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for determining the reconstruction target based on a dimension-reduced controllability matrix, which characterizes the controllability matrix of the system in a dimension-reduced manner and determines the reconstruction target of the spacecraft.
[0005] The technical solution of this invention is:
[0006] A method for determining the reconstruction target based on a dimension-reduced energy control matrix includes the following steps:
[0007] S1. Determine the dynamic equations of the spacecraft control system;
[0008] S2. Determine the controllability Lie derivative calculation rules applicable to the dynamic equations of the spacecraft control system;
[0009] S3. Using the aforementioned Lie derivative calculation rules, establish the controllability matrix of the spacecraft control system;
[0010] S4. By performing matrix transpose on the controllability matrix of the system and then polar coordinate transformation, the common subspace of the controllability matrix is decomposed.
[0011] S5. Determine the reconstruction target using the shared subspace.
[0012] Furthermore, the dynamic equations of the spacecraft control system are as follows:
[0013]
[0014] Where X is the system state variable; t is the time variable; f(X) is the nonlinear function vector related to the system state variable; g(X) is the function vector associated with the system control input; and T is the system control input. It is the first derivative of the system state variables.
[0015] Furthermore, the rule for calculating the controllability Lie derivative is as follows:
[0016]
[0017] Among them, L 0 f For the 0th order Lie derivative of the system, L k f Let f be the k-th order Lie derivative of the system, and f be the abbreviated form of the nonlinear function vector f(X);
[0018] The calculation rules are as follows:
[0019]
[0020] n is the dimension of the system control input.
[0021] Furthermore, the controllability matrix of the spacecraft control system is specifically as follows:
[0022]
[0023] Where C is the controllability matrix.
[0024] Furthermore, the system controllability matrix C is transposed, specifically as follows:
[0025]
[0026] in,(·) T Let C be the transpose operator, and C be the system controllability matrix after the transpose operation.
[0027] Furthermore, the polar coordinate transformation operation is as follows:
[0028]
[0029] in, This represents the new state obtained after polar coordinate transformation of the system state; The common subspace of the decomposed controllability matrix has the same dimension as the system state dimension and is less than the dimension of the observability matrix; The remaining terms in the subspace.
[0030] Furthermore, the method of determining the reconstruction target using the shared subspace specifically includes:
[0031]
[0032] Where e is the reconfiguration target; E is the energy boundary of the spacecraft control system, which is a constant; e f The target vector to be reconstructed is the vector to be optimized.
[0033] Secondly, the present invention also proposes a non-volatile storage medium, comprising: a computer program product, which, when executed, performs the reconstruction target determination method based on the dimension-reduced energy control matrix.
[0034] Thirdly, the present invention also proposes a computer program product that, when executed by a processor, implements the aforementioned method for determining the reconstruction target based on a dimension-reduced energy control matrix.
[0035] The advantages of this invention compared to the prior art are:
[0036] (1) Compared with traditional observability characterization methods, the observability matrix dimensionality reduction characterization method proposed in this invention reflects the attributes of the observability matrix column subspace based on the shared subspace. It realizes the characterization of system controllability with a low-dimensional shared subspace. The related methods can reduce the computational complexity of system controllability analysis.
[0037] (2) The method of the present invention does not linearize or truncate the state equation of the spacecraft, and the given observability matrix dimensionality reduction representation method has better accuracy.
[0038] (3) The common subspace for characterizing the observability matrix of the system given by the method of the present invention does not require complex Lie derivative operations and can obtain an analytical form compared with the traditional method. Therefore, the computational complexity is lower and it is suitable for autonomous operation on spacecraft. Attached Figure Description
[0039] Figure 1 This is a flowchart of the present invention. Detailed Implementation
[0040] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.
[0041] like Figure 1 As shown, this invention proposes a method for determining a reconstruction target based on a dimension-reduced controllable matrix, comprising the following steps.
[0042] S1. Give the dynamic equations of the spacecraft control system;
[0043] S2. Give the rules for calculating the controllability Lie derivative applicable to the system described in S1;
[0044] S3. Using the Lie derivative calculation rules given in S2, establish the controllability matrix of the spacecraft control system.
[0045] S4. By performing matrix transpose on the system controllability matrix in S3 and then polar coordinate transformation, the common subspace of the controllability matrix is decomposed.
[0046] S5. Use the shared subspace obtained in S4 to determine the reconstruction target.
[0047] The system controllability matrix dimensionality reduction representation method obtained in this invention does not require complex Lie derivative operations and reduces the dimension of observability matrix analysis. This algorithm is reliable and consumes few computational resources.
[0048] The following is a detailed description of steps S1 to S6:
[0049] S1. Give the dynamic equations of the spacecraft control system:
[0050]
[0051] Where X is the system state variable; t is the time variable; f(X) is the nonlinear function vector related to the system state variables; g(X) is the function vector associated with the system control input; T is the system control input.
[0052] S2. Give the rule for calculating the controllability Lie derivative applicable to the system described in S1:
[0053]
[0054] The calculation rules are as follows:
[0055]
[0056] n is the dimension of the system control input.
[0057] S3. Using the Lie derivative calculation rules given in S2, establish the controllability matrix of the spacecraft control system:
[0058]
[0059] Where C is the controllability matrix.
[0060] S4. By transposing the system controllability matrix in S3 and then performing polar coordinate transformation, the common subspace of the controllability matrix is decomposed:
[0061]
[0062] Where X is the new state obtained after the polar coordinate transformation of the system state; χ is the common subspace of the decomposed controllability matrix, with the same dimension as the system state dimension, which is generally less than the dimension of the observability matrix; γ is the remaining term of the subspace.
[0063] S5. Determine the reconstruction objective using the shared subspace:
[0064]
[0065] Where e is the reconfiguration target; E is the energy boundary of the spacecraft control system, which is a constant. f The target vector to be reconstructed is the vector to be optimized.
[0066] Using the shared subspace determined in step S4, the system controllability matrix can also be characterized by dimensionality reduction using the obtained shared subspace:
[0067]
[0068] The transpose of the shared subspace χ T The dimension reduction characterizes the controllability matrix C.
[0069] The reconstruction target determination method of this invention is based on the fact that a shared subspace can reflect the column subspace attributes of the observability matrix. It achieves the characterization of system controllability with a low-dimensional shared subspace, and the related methods can reduce the computational complexity of system controllability analysis. This method does not linearize or truncate the state equations of the spacecraft, and the dimensionality reduction characterization method of the observability matrix given by this method has better accuracy. Compared with traditional methods, the shared subspace given by this method for characterizing the system observability matrix does not require complex Lie derivative operations and can obtain an analytical form. Therefore, the computational complexity is lower and it is suitable for autonomous operation on spacecraft.
[0070] The parts of this invention not described in detail are common knowledge to those skilled in the art.
Claims
1. A method for determining a reconstructed target based on a dimension-reduced energy control matrix, characterized in that... include: S1. Determine the dynamic equations of the spacecraft control system; S2. Determine the controllability Lie derivative calculation rules applicable to the dynamic equations of the spacecraft control system; S3. Using the aforementioned Lie derivative calculation rules, establish the controllability matrix of the spacecraft control system; S4. By performing matrix transpose on the controllability matrix of the system and then polar coordinate transformation, the common subspace of the controllability matrix is decomposed. S5. Determine the reconstruction target using the shared subspace; The dynamic equations of the spacecraft control system are as follows: Where X is the system state variable; t is the time variable; f(X) is the nonlinear function vector related to the system state variable; g(X) is the function vector associated with the system control input; and T is the system control input. The first derivative of the system state variables; The rule for calculating the controllability Lie derivative is as follows: in, The 0th-order Lie derivative of the system, Let f be the k-th order Lie derivative of the system, and f be the abbreviated form of the nonlinear function vector f(X); The calculation rules are as follows: n is the dimension of the system control input; The controllability matrix of the spacecraft control system is as follows: in, The controllability matrix; The matrix transpose operation is performed on the system controllability matrix c as follows: in,(·) T For the transpose operator, This is the system controllability matrix after the transpose operation; The polar coordinate transformation operation is as follows: in, This represents the new state obtained after polar coordinate transformation of the system state; The common subspace of the decomposed controllability matrix has the same dimension as the system state dimension and is less than the dimension of the observability matrix; These are the remaining terms in the subspace; The reconstruction target is determined using the shared subspace, specifically as follows: Where e is the reconfiguration target; ε is the energy boundary of the spacecraft control system, which is a constant; e f The target vector to be reconstructed is the vector to be optimized.
2. A non-volatile storage medium, characterized in that, include: A computer program product, when executed, performs the reconstruction target determination method based on a dimension-reduced energy control matrix as described in claim 1.
3. A computer program product, characterized in that, When the computer program is executed by the processor, it implements the reconstruction target determination method based on the dimension-reduced energy control matrix as described in claim 1.