Digraphs based algorithms for formation flight control
- Paper number
IAC-23,C1,4,4,x78605
- Author
Dr. Sergey Shestakov, Keldysh Institute of Applied Mathematics of RAS, Russian Federation
- Coauthor
Mr. Rolan Dadashev, Keldysh Institute of Applied Mathematics of RAS, Russian Federation
- Year
2023
- Abstract
The addressed problem is the construction and maintenance of a satellite formation. Given a group of tens of small satellites or a swarm with relatively small relative distances, achieving and maintaining a desired geometric configuration is not an easy task. A simultaneous relative drift elimination faces the problem of bandwidth restriction, i.e., a small satellite cannot receive a signal from all of its partners. Instead, a communication constraint of some sort must be implemented, and therefore, only the local information of the closest satellites is obtainable for a control algorithm. We propose a control algorithm construction approach based on the use of directed graphs. These graphs represent the possible one- or two-way connections between satellites, and allow us to study formations with one `mothership' or several `shepherd' satellites. An analytical study of the proposed controlled system is performed. It is shown that the linearized dynamic equations of a system have a close connection with a generalized Laplacian matrix, and accordingly, the spectral properties of a digraph determine the behavior of the controlled motion. The spectral properties of the aforementioned graphs are studied. Different modifications (i.e., weighted digraphs) to a proposed technique are also considered. Several strategies for `shepherd' satellites to prevent formation degradation and maintain relative drift are considered. The resulting control algorithms were validated using Monte-Carlo simulations.
- Abstract document
- Manuscript document
IAC-23,C1,4,4,x78605.pdf (🔒 authorized access only).
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