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Perturbed State-Transition Matrix for Spacecraft Formation Flying Terminal-Point Guidance

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Abstract

This paper presents a guidance solution of relative motion between two spacecraft using relative classical orbital elements for on-board implementation purposes. The solution is obtained by propagating the relative orbital elements forward in time using a newly formulated state-transition matrix, while taking into account gravitational field up to the fifth harmonic, third-body effects up to the fourth order and drag, then calculating the relative motion in the local-vertical-local-horizontal reference frame at each time-step. Specifically, utilizing Jacobian matrices evaluated at the target spacecraft’s initial orbital elements, the solution proposed in this paper requires only a single matrix multiplication with the initial orbital elements and the desired time to propagate relative orbital elements forward in time. The new solution is shown to accurately describe the relative motion when compared with a numerical simulator, yielding errors on the order of meters for separation distances on the order of thousands of meters. Additionally, the solution maintained accurate tracking performance when used within a back-propagation, or terminal-point, guidance law.

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    Yazan Chihabi & Steve Ulrich

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  1. Yazan Chihabi
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  2. Steve Ulrich
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Correspondence to Yazan Chihabi.

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Chihabi, Y., Ulrich, S. Perturbed State-Transition Matrix for Spacecraft Formation Flying Terminal-Point Guidance. J Astronaut Sci 68, 642–676 (2021). https://doi.org/10.1007/s40295-021-00272-1

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