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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 947843, 11 pages
http://dx.doi.org/10.1155/2015/947843
Research Article

Robust Linear Quadratic Regulator via Sliding Mode Guidance for Spacecraft Orbiting a Tumbling Asteroid

1Department of Control Science and Engineering, Jilin University, Changchun, Jilin 130022, China
2Department of Control Engineering, Changchun University of Technology, Changchun, Jilin 130022, China
3State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China

Received 30 June 2015; Revised 1 September 2015; Accepted 17 September 2015

Academic Editor: Eric Florentin

Copyright © 2015 Peng Zhang et al. 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

Aiming to ensure the stability of the spacecraft with multiuncertainties and mitigate the threat of the initial actuator saturation, a Robust Linear Quadratic Regulator (RLQR) via sliding mode guidance (SMG) for orbiting a tumbling asteroid is proposed in this paper. The orbital motion of the spacecraft near a tumbling asteroid is modelled in the body-fixed frame considering the sun-relative effects, and the orbiting control problem is formulated as a stabilization of a nonlinear time-varying system. RLQR based on the adaptive feedback linearization is proposed to stabilize the spacecraft orbiting with the uncertainties of the asteroid’s rotation and gravitational field. In order to avoid the initial actuator saturation, SMG is applied to generate the transition process trajectory of the closed-loop system. The effectiveness of the proposed control scheme is verified by the simulations of orbiting the asteroid Toutatis 4179.