Stabilizing Motion Relative to an Unstable Orbit: Applications to Spacecraft Formation Flight

Orbit period modulation for relative motion using continuous low thrust in the two-body and restricted three-body problems

“…More recently, Morimoto et al investigated the thrust requirements to turn any arbitrary point in a restricted three-body system into an AEP, finding the regions of stable AEPs in small mass-ratio systems such as the Sun-Earth system which are accessible with small control accelerations (Morimoto et al 2007). Other authors considered the use of active control to stabilise the motion of a spacecraft relative to a reference halo orbit in the Hill and restricted threebody problems, notably producing a circular relative trajectory with applications in formation flight for stellar interferometry (Scheeres et al 2003;Hsiao and Scheeres 2005). Actively controlled formation flight in a two-body system has also been considered by several authors, such as , where full-state feedback control has been used to force a spacecraft onto an arbitrary singly periodic reference orbit relative to an elliptical orbit.…”

“…Whereas past authors have generally used a top-down engineering approach, designing active controllers with which to force a spacecraft onto a predetermined reference trajectory (e.g. Scheeres et al 2003;Hsiao and Scheeres 2005;, this paper instead seeks to generate rich new families of orbits with only position feedback and without a reference trajectory, thereby only minimally intervening into the dynamics of the problem. The assumption of the use of only position feedback instead of full-state feedback is justified by the goal of providing access to useful new trajectories for small, low-cost spacecraft equipped only with position sensing relative to a target spacecraft (e.g.…”

Finite Set Control Transcription for Optimal Control Applications

“…Interest in libration point formations has motivated significant work [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][74][75][76][77] to characterize and negotiate this unstable and highly sensitive regime. For interferometry missions, the formation requirements are even more restrictive, and existing literature highlights the difficulties in designing trajectories and control strategies to effectively operate in this en- In summary, the work to date can be characterized by…”

“…Interest in space-based interferometry has motivated many investigations [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57] into the feasibility of spacecraft formations near the libration points of the SunEarth/Moon system. A survey of many of these efforts is provided for refererence in Appendix B.…”

Canonical Modelling of Coorbital Motion in Hill's Problem Using Epicyclic Orbital Elements

“…Applications of Hill's problem are ubiquitous (see e.g. Vilac & Scheers 2003;Scheeres et al 2003, and the references therein). It has been shown that Hill's problem is characterized by the same generality as that of the restricted three-body problem, in the sense that the mass ration of the coorbiting objects is arbitrary (Hénon 1986).…”