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

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Abstract

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.

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Authors and Affiliations

  1. College of Science, Beijing Information Science and Technology University, Beijing, 100192, China

    Xinsheng Ge

  2. College of Mechanical and Electrical Engineering, Beijing Information Science and Technology University, Beijing, 100192, China

    Zhonggui Yi

  3. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China

    Liqun Chen

Authors
  1. Xinsheng Ge
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  2. Zhonggui Yi
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  3. Liqun Chen
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Corresponding author

Correspondence to Xinsheng Ge.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11472058)

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Ge, X., Yi, Z. & Chen, L. Optimal control of attitude for coupled-rigid-body spacecraft via Chebyshev-Gauss pseudospectral method. Appl. Math. Mech.-Engl. Ed. 38, 1257–1272 (2017). https://doi.org/10.1007/s10483-017-2236-8

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  • DOI: https://doi.org/10.1007/s10483-017-2236-8

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