Numerical optimal control for satellite attitudes
DOI:
https://doi.org/10.24193/subbmath.2019.2.11Keywords:
49J15, 70Q05, 93C10, 93C15Abstract
In this paper we will present a new approach for optimal control of slews and attitude profiles. After the description of a set of the considered Hamiltonian functions and the respective slew maneuvers some analytical consequences of the choices are given. A comparison with the actual operational Euler angle slew is given and shows a close match. The performed numerical investigations of direct solutions help to gain a clearer picture on the underlaying analytical problem. By applying the Pontryagin maximum principle to the Hamiltonian equation, a family of closed dynamics ordinary differential equation for the direct optimal control problem is presented and their solutions and properties are investigated.
References
Joel A E Andersson, Joris Gillis, Greg Horn, James B Rawlings and Moritz Diehl, CasADi - A software framework for nonlinear optimization and optimal control Mathematical Programming Computation, 2018.
A. E. Bryson & Y. C. Ho, Applied Optimal Control: Optimization, Estimation and Control 1981.
E. Frazzoli, M. A. Dahleh, E. Feron, A randomized attitude slew planning algorithm for autonomous spacecraft AIAA Conference, Montreal, 2001.
J.L. Junkins and J.D.Turner, Optimal Continuous Torque Attitude Maneuvers Virginia Polytechnic Institute and State University, Blacksburg, Va. 1980.
K. Spindler, Optimal control on Lie groups with applications to attitude control Math. Control Signals and Systems 11 (1998), No. 3, 197-219.
K. Spindler, Attitude Maneuvers which avoid a forbidden direction Journal of Dynamical and Control Systems, Vol. 8, No. 1, 2002.
D. E. Kirk, Optimal Control Theory, 1970 / Dover 2016.
R. Rigger, J. Yde, M. Mueller, V. Companys, The Optimization of Attitude profiles for SMART-1: A highly constrained Problem. Proceedings of the 18th International Symposium on Space Flight Dynamics, 2004.
J. Wertz, Spacecraft attitude determination and control Kluwer Academic Publishers, 1990.
Rafal Wisniewski and Piotr Kulczycki, Slew Maneuver Control for Spacecraft Equipped with Star Camera and Reaction Wheels Preprint submitted to Elsevier Science, 2003.
Liuping Wang, Model Predictive Control System Design and Implementation Springer - Advances in Industrial Control, 2009.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.
