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Time‐optimal reorientation of the rigid spacecraft using a pseudospectral method integrated homotopic approach
Author(s) -
Li Jing,
Xi Xiaoning
Publication year - 2014
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2145
Subject(s) - pseudospectral optimal control , spacecraft , pseudo spectral method , convergence (economics) , mathematics , optimal control , control theory (sociology) , homotopy , maximum principle , pontryagin's minimum principle , trajectory , mathematical optimization , computer science , mathematical analysis , physics , engineering , control (management) , aerospace engineering , fourier transform , fourier analysis , artificial intelligence , astronomy , economic growth , pure mathematics , economics
Summary This paper proposes a robust algorithm for time‐optimal rigid spacecraft reorientation trajectory generation. Based on the Pontryagin's maximum principle, the first‐order necessary optimality conditions are derived. These optimality conditions are numerically satisfied by adopting a pseudospectral method integrated homotopic approach to solve the associated shooting functions. First, the energy‐optimal reorientation solution is obtained using the Radau pseudospectral method, which has a spectral convergence speed and can give a precise estimation of the initial costates used to start the homotopic approach. Then, a modified homotopy scheme is given to deform the associated energy‐optimal solution to the desired time‐optimal solution continuously. Finally, for the inertially symmetric spacecraft reorientation problem, the newly found time‐optimal solutions are presented. The performance of the algorithm is illustrated by simulating a general asymmetric rigid spacecraft time‐optimal reorientation problem. Copyright © 2014 John Wiley & Sons, Ltd.