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Automated stable region generation, detection, and representation for applications to mission design

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Abstract

This paper presents an automated algorithm to extract dynamical features, such as stability constraints, from phase space maps. The functional representation of these constraints allows their inclusion in optimization problems and thus expands the use of dynamical tools in space mission design. The challenge to autonomously detect the regions of interest in stability maps is discussed through utilizing image processing algorithms to cluster map data. Additionally, to use the detected regions, both discrete and smooth functional representations are studied. Based on similar clustering techniques that have been considered in extracting and representing features of phase space maps, we proposed an adaptively map generation algorithm. It creates a nonuniform grid of points on a map which is denser near the boundaries of the regions of interest. Both representation and map generation algorithms provide significant performance enhancements in phase space analysis. All these techniques are illustrated on examples of stability maps in small body dynamics.

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Notes

  1. An end node or leaf is a node with no children.

  2. Note that neighbors in a quadtree structure refers to the spatial neighboring blocks, and not to the adjacent nodes as in an abstract tree.

  3. The depth of the tree is equivalent to the level of the tree where all nodes are end nodes (leaves).

  4. In Sect. 2, we mentioned that the trend of change in FLI value indicates the stability property of the trajectory.

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Acknowledgments

Partial support for this research has been provided by the National Aeronautics and Space Administration, Astrodynamics Research Grant, In-Space Propulsion Technology Development program (Grant No. NNX13AH03G) and is gratefully acknowledged.

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Authors and Affiliations

  1. California State Polytechnic University, Pomona, 3801 W Temple Ave, Pomona, CA, 91768, USA

    Navid Nakhjiri

  2. University of California, Irvine, 4200 Engineering Gateway, Irvine, CA, 92697, USA

    Benjamin Villac

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  1. Navid Nakhjiri
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  2. Benjamin Villac
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Correspondence to Navid Nakhjiri.

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Nakhjiri, N., Villac, B. Automated stable region generation, detection, and representation for applications to mission design. Celest Mech Dyn Astr 123, 63–83 (2015). https://doi.org/10.1007/s10569-015-9629-0

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  • DOI: https://doi.org/10.1007/s10569-015-9629-0

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