Abstract
Many space missions require the execution of large-angle attitude slews during which stringent pointing constraints must be satisfied. For example, the pointing direction of a space telescope must be kept away from directions to bright objects, maintaining a prescribed safety margin. In this paper we propose an open-loop attitude control algorithm which determines a rest-to-rest maneuver between prescribed attitudes while ensuring that any of an arbitrary number of body-fixed directions of light-sensitive instruments stays clear of any of an arbitrary number of space-fixed directions. The approach is based on an application of a version of Pontryagin’s Maximum Principle tailor-made for optimal control problems on Lie groups, and the pointing constraints are ensured by a judicious choice of the cost functional. The existence of up to three first integrals of the resulting system equations is established, depending on the number of light-sensitive and forbidden directions. These first integrals can be exploited in the numerical implementation of the attitude control algorithm, as is shown in the case of one light-sensitive and several forbidden directions. The results of the test cases presented confirm the applicability of the proposed algorithm.
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Acknowledgements
The work described here was presented as paper ISSFD-2022-147 at the 28th International Symposium on Space Flight Dynamics, which took place in Beijing (China) from August 29 to September 2, 2022. Partial support for this work by the Klaus Tschira Foundation is gratefully acknowledged.
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David Ailabouni received his Diploma and M.Sc. degree in business engineering with specialization in civil engineering from the University of Kassel and his M.Sc. degree in applied mathematics from the RheinMain University of Applied Sciences. He is currently working as a project manager in the field of tendering and contracting for major construction projects at Drees & Sommer SE and pursuing his Ph.D. degree at the University of Kassel on optimal control problems with geometric structure.
Andreas Meister studied mathematics and computer science at the University of Gättingen and received his Diploma in 1993. From 1993 to 1996 he worked at the German Aerospace Center and got his doctoral degree (Dr. rer. nat.) from the Technical University of Darmstadt in 1996. After working as a research scientist for the Fraunhofer Institute for Industrial Mathematics he became an assistant professor at the University of Hamburg, where he finished his Habilitation in 2001. Afterwards he worked as an assistant professor at the Medical University of Lübeck in 2002 and became a full professor of applied mathematics at the University of Kassel in 2003. He received the Kurt-Hartwig-Siemers Prize for research, the Mentorship Prize of the Claussen-Simon Foundation, the Best Teacher Award of the University of Hamburg, as well as the State of Hesse Award for Excellence in University Teaching. His research area is in the field of numerics of ordinary and partial differential equations with a special focus on real-life applications.
Karlheinz Spindler studied mathematics, mechanics, and history at the Technische Hochschule Darmstadt (Germany). After obtaining his Ph.D. degree in mathematics, he spent two years as a visiting assistant professor at Louisiana State University in Baton Rouge (USA) and then worked for five years in the Flight Dynamics Department of the European Space Operations Centre (ESOC) in Darmstadt. He currently teaches mathematics and data processing at the Hochschule RheinMain (formerly Fachhochschule Wiesbaden). In addition to his research and teaching activities, he is also the founder and co-organizer of a continuing education seminar on technical, didactical, and historical aspects of mathematics. He won the first prize in the Hessian Award for Excellence in Teaching 2022.
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Ailabouni, D., Meister, A. & Spindler, K. Attitude maneuvers avoiding forbidden directions. Astrodyn 7, 351–362 (2023). https://doi.org/10.1007/s42064-023-0163-7
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DOI: https://doi.org/10.1007/s42064-023-0163-7