Onboard Complete Solution to the Full-Body Relative Orbital Motion Problem

Paper number

IAC-17,C1,9,9,x40627

Author

Prof. Daniel Condurache, Technical University of Iasi, Romania

Year

2017

Abstract

The relative motion between the leader and the deputy is a six-degree of-
freedom (6-DOF) motion, which represents the coupling of the
relative translational motion with the rotational one. In recent years,
increasing attention has been paid to the modeling of the relative 6-DOF motion
of spacecraft . Also, controlling the relative pose of satellite
formation is a very important research subject. The common
approach is to consider the relative translational and rotational dynamics
for the chief–deputy spacecraft formation to be modeled using vector
and tensor formalism. In this paper, we reveal a dual-tensor-based
procedure to obtain exact expressions for the 6-DOF relative orbital law
of motion between two Keplerian confocal orbits. The solution is
obtained by pure analytical methods, and it holds for any leader and
deputy motion, without involving any secular terms or singularities. The
relative orbital motion is reduced, by an adequate change of variables,
into a dual Euler fixed-point problem. Orthogonal dual tensors play a
very important role, with the representation of the solution being, to the
authors’ knowledge, the shortest approach for describing the complete
onboard solution of the 6-DOF orbital motion problem. The solution
does not depend on the local-vertical–local-horizontal (LVLH)
properties involves that is true in any reference frame of the leader with
the origin in its mass center. To obtain this solution, one has to know
only the inertial motion of the leader spacecraft and the initial
conditions of the deputy satellite in the LVLH frame. A representation
theorem is provided for the full-body initial value problem.
Furthermore, the real and imaginary parts are split, and representation
theorems for rotation and translation motion are obtained. Regarding
translation, a closed-form free of coordinate solution is revealed, based of generalised trigonometric function in space at constant curvature. They hold
for all types of reference trajectories of the leader (elliptic, parabolic,
hyperbolic) and deputy (elliptic, parabolic, hyperbolic, rectilinear).

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Abstract document

IAC-17,C1,9,9,x40627.brief.pdf

Manuscript document

IAC-17,C1,9,9,x40627.pdf (🔒 authorized access only).

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