Optimal formation reconfiguration by using generating functions: Applications to the hill three-body problem

Chandeok Park, Ji Hyun Yang, Daniel J. Scheeres

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


This paper presents a unified methodology to studying optimal continuous-thrust formation flying maneuvers by employing the generating functions appearing in the theory of Hamiltonian dynamics. It begins by defining an optimal control problem subject to a relative dynamical system with respect to a known reference trajectory, and applying the Pontryagin principle to compose a two point boundary value problem for a standard Hamiltonian system. Then, as the Hamiltonian phase flow is viewed as a canonical transformation, the associated generating functions are obtained in the form of series expansion. This enables us to determine the initial adjoints and the optimal cost as algebraic functions of initial and final states, and to develop the optimal control in feedback form. This analytic nature of our approach provides a more computationally tractable procedure than the conventional shooting technique, especially when it is necessary to analyze multiple spacecraft maneuvers for substantially many varying boundary conditions and time spans. Furthermore, compared with the linear solution, our higher order solution shows better convergence to the nonlinear reference solution both temporally and spatially. These favorable properties are demonstrated by applying the proposed methodology to a fuel-optimal formation reconfiguration maneuvers near the L2 Lagrangian point in the frame of Hill three-body problem. Finally, our continuous-thrust optimal solutions are compared qualitatively with the impulsive-thrust solutions developed by Guibout and Scheeres.

Original languageEnglish
Title of host publicationAIAA/AAS Astrodynamics Specialist Conference 2012
Publication statusPublished - 2012
EventAIAA/AAS Astrodynamics Specialist Conference 2012 - Minneapolis, MN, United States
Duration: 2012 Aug 132012 Aug 16

Publication series

NameAIAA/AAS Astrodynamics Specialist Conference 2012


OtherAIAA/AAS Astrodynamics Specialist Conference 2012
Country/TerritoryUnited States
CityMinneapolis, MN

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A1012351).

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Astronomy and Astrophysics


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