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International Journal of Aerospace Engineering
Volume 2018 (2018), Article ID 5947521, 14 pages
https://doi.org/10.1155/2018/5947521
Research Article

Time-Optimal Attitude Scheduling of a Spacecraft Equipped with Reaction Wheels

Universidad Rey Juan Carlos, Camino del Molino s/n, 28943 Fuenlabrada, Madrid, Spain

Correspondence should be addressed to Ernesto Staffetti; se.cjru@itteffats.otsenre

Received 7 August 2017; Accepted 7 December 2017; Published 8 April 2018

Academic Editor: Kenneth M. Sobel

Copyright © 2018 Alberto Olivares and Ernesto Staffetti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The time-optimal control problem of a spacecraft equipped with reaction wheels has been studied, in which the spacecraft is constrained to sequentially assume a set of attitudes, whose order is not specified. This attitude scheduling problem has been solved as a multiphase mixed-integer optimal control problem in which binary functions have been introduced to model the choice of the optimal sequence of target attitudes and to enforce the constraint of adopting once and only once each attitude. Given the dynamic model of the spacecraft, the initial and final attitudes, and a set of target attitudes, solving this problem consists in finding the control inputs, the sequence of attitudes with the corresponding passage times, and the resulting trajectory of the spacecraft that minimize the time of the maneuver. The multiphase mixed-integer optimal control problem has been converted into a mixed-integer nonlinear programming problem first making the unknown passage times through the target attitudes part of the state, then introducing binary variables to discretize the binary functions, and finally applying a fifth-degree Gauss-Lobatto direct collocation method to tackle the dynamic constraints. The resulting problem has been solved using a nonlinear programming-based branch-and-bound algorithm.