Design of a Formation Flying Demonstration Mission In GTO based on Optimal Guidance Profiles
- Paper number
IAC-05-C1.1.02
- Author
Dr. Luis F. Penin, DEIMOS Space S.L., Spain
- Coauthor
Mr. Joao Araujo, DEIMOS Engenharia, Portugal
- Coauthor
Mr. Juan-Carlos Bastante, DEIMOS Space, Spain
- Coauthor
Mr. Augusto Caramagno, DEIMOS Space, Spain
- Coauthor
Mr. Bogdan Udrea, European Space Agency (ESA)/ESTEC, The Netherlands
- Year
2005
- Abstract
Optical interferometry in space is identified as the critical technology for ESA’s 21st century science mission Darwin. The goal is to ultimately study Earth-like planets around nearby stars, and to determine their capability to host life, as we know it. To also provide imaging that could probe the Universe at spatial scales one or more orders of magnitudes better than the monolithic telescopes planned for the near future is a secondary goal.
In the case of a fully-fledged system study, the review of the demonstration requirements would set the framework for selecting the most suitable orbit. The possibility of deploying such a technology demonstration mission into a Geostationary Transfer Orbit (GTO) by searching for stable formation configurations around the apogee of this reference orbit has been previously demonstrated by the authors in [Bastante-05]. Attending to the typical set of pointing requirements for Darwin–like missions, stability is understood as: minimum variance of distances; minimum variance of angles between satellites; and minimum variance of satellites plane orientation. These configurations allow for a certain time interval for experimentation around apogee where minimum control action is required.
In this context the paper focuses on the design of analytical and numerical optimal guidance low-thrust profiles for a three spacecraft formation during observation phase around apogee. The objective is to maximise the observation time in which the constrained formation configuration shall remain stable, while minimising fuel consumption. The design method pays also special attention to loose and safe configurations away from the apogee, allowing the sequential execution of an experimentation timeline to be completed in several orbits with minimum cost. This is accomplished by bringing back together the satellites at apogee entrance with no excessive divergence close to perigee.
The analytical design methodology is based on a formulation relating the relative evolution of the Cartesian coordinates on a local frame with the corresponding differences in the Keplerian elements between the satellites. After obtaining the satellites Keplerian elements desired evolution, Gauss equations allow for an analytical derivation of low thrust profiles for the objective guidance laws.
An alternative approach based on the numerical optimisation of such profiles through a Gradient Restoration Algorithm, solving a full optimal control problem, is followed for comparison purposes. In this case, J2 perturbation is taken into account, allowing the assessment of the most relevant perturbation effect.
Finally, both approaches are tested and compared on a simulator considering detailed perturbation models (high order gravitational harmonics, Solar radiation pressure and third bodies).
The work presented in this paper was done under the ESA/ESTEC contract number 17529/03/NL/LvH/bj, for the study of Formation Estimation Methodologies for Distributed Spacecraft (FEMDIS). The project team was led by Pedro Lima, from ISR/IST (Portugal) and managed by Bogdan Udrea (ESA/ESTEC) as Technical Officer.
References[Bastante-05] J.C. Bastante et al, "Formation Design for Technology Demonstration Missions in GTO", 4th International Workshop on Satellite Constellations and Formation Flying, Sao José dos Campos, Brazil, February 2005.
- Abstract document
- Manuscript document
IAC-05-C1.1.02.pdf (🔒 authorized access only).
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