Optimal control of attitude for coupled-rigid-body spacecraft via Chebyshev-Gauss pseudospectral method

doi:10.1007/s10483-017-2236-8

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (9): 1257-1272.doi: https://doi.org/10.1007/s10483-017-2236-8

Optimal control of attitude for coupled-rigid-body spacecraft via Chebyshev-Gauss pseudospectral method

Xinsheng GE¹, Zhonggui YI², Liqun CHEN³

1. College of Science, Beijing Information Science and Technology University, Beijing 100192, China;
2. College of Mechanical and Electrical Engineering, Beijing Information Science and Technology University, Beijing 100192, China;
3. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

收稿日期:2016-09-01 修回日期:2016-12-28 出版日期:2017-09-01 发布日期:2017-09-01
通讯作者: Xinsheng GE,E-mail:gebim@vip.sina.com E-mail:gebim@vip.sina.com
基金资助:
Project supported by the National Natural Science Foundation of China (No.11472058)

Optimal control of attitude for coupled-rigid-body spacecraft via Chebyshev-Gauss pseudospectral method

Xinsheng GE¹, Zhonggui YI², Liqun CHEN³

1. College of Science, Beijing Information Science and Technology University, Beijing 100192, China;
2. College of Mechanical and Electrical Engineering, Beijing Information Science and Technology University, Beijing 100192, China;
3. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Received:2016-09-01 Revised:2016-12-28 Online:2017-09-01 Published:2017-09-01
Contact: Xinsheng GE E-mail:gebim@vip.sina.com
Supported by:
Project supported by the National Natural Science Foundation of China (No.11472058)

摘要/Abstract

摘要：

The attitude optimal control problem (OCP) of a two-rigid-body spacecraft with two rigid bodies coupled by a ball-in-socket joint is considered. Based on conservation of angular momentum of the system without the external torque, a dynamic equation of three-dimensional attitude motion of the system is formulated. The attitude motion planning problem of the coupled-rigid-body spacecraft can be converted to a discrete nonlinear programming (NLP) problem using the Chebyshev-Gauss pseudospectral method (CGPM). Solutions of the NLP problem can be obtained using the sequential quadratic programming (SQP) algorithm. Since the collocation points of the CGPM are Chebyshev-Gauss (CG) points, the integration of cost function can be approximated by the Clenshaw-Curtis quadrature, and the corresponding quadrature weights can be calculated efficiently using the fast Fourier transform (FFT). To improve computational efficiency and numerical stability, the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of state and control variables. Furthermore, numerical float errors of the state differential matrix and barycentric weights can be alleviated using trigonometric identity especially when the number of CG points is large. A simple yet efficient method is used to avoid sensitivity to the initial values for the SQP algorithm using a layered optimization strategy from a feasible solution to an optimal solution. Effectiveness of the proposed algorithm is perfect for attitude motion planning of a two-rigid-body spacecraft coupled by a ball-in-socket joint through numerical simulation.

关键词: Hausdorff dimensions, Hausdorff measures, Box dimensions, girth to area normal ratio, SIM, Chebyshev-Gauss (CG) point, spacecraft, coupled rigid body, pseudospectral method (PM), optimal control

Abstract:

Key words: optimal control, Hausdorff dimensions, Hausdorff measures, Box dimensions, girth to area normal ratio, SIM, spacecraft, Chebyshev-Gauss (CG) point, pseudospectral method (PM), coupled rigid body

中图分类号:

37N30

Xinsheng GE, Zhonggui YI, Liqun CHEN. Optimal control of attitude for coupled-rigid-body spacecraft via Chebyshev-Gauss pseudospectral method[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(9): 1257-1272.

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Optimal control of attitude for coupled-rigid-body spacecraft via Chebyshev-Gauss pseudospectral method

Optimal control of attitude for coupled-rigid-body spacecraft via Chebyshev-Gauss pseudospectral method

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