1. Corporate Communications April 2007 3rd Global Trajectory Optimization Competition Team 13 : Thierry Dargent* Vincent Martinot* Joris Olympio ** Thierry.dargent@thaleslaleniaspace.com * Thales Alenia Space ** Centre de Mathématiques Appliquées de L’Ecole des Mines de Paris

2. All rights reserved © 2008, Thales Alenia Space Corporate Communications April 2007 2 Introduction The third Global Trajectory Optimization Competition has been handled in Thales Alenia Space by a team of 3 persons: Thierry Dargent in charge of the research group on Platform & Satellite in the Thales Alenia Space Research Directorate Vincent Martinot in charge of mission analysis in the Advanced Project Department of the Science and Observation Directorate in Thales Alenia Space Joris Olympio Phd Student at “Centre de mathématique appliqué de l’Ecole des mines de Paris” (CMA) co-financed by CNES and Thales Alenia Space

3. All rights reserved © 2008, Thales Alenia Space Corporate Communications April 2007 3 Main method used The proposed final solution is based on: Step 1a: the use of dynamic programming for the global search on a simple criteria Step 1b: Use of simplified low trust dynamic model Step 2: Indirect method for local optimization running: T_3D software, an internal Thales Alenia Space tool providing solutions for the optimal orbit transfer problem. allowing to design minimum time or maximum mass transfers for a large sets of initial or final conditions (departure with a given or free departure infinite velocity, transfers, rendez-vous…) The theory behind T_3D is the application of the maximal principle and the utilization of continuation and smoothing techniques.

4. All rights reserved © 2008, Thales Alenia Space Corporate Communications April 2007 4 The problem requires to handle a very large combinatorial problem The first step objective was to decrease this combinatorial problem by removing asteroids with an energy criteria (ephemeris-free transfer): We have computed the  V needed to remove eccentricity and inclination on asteroid orbit and selected around the 20 best asteroids. The second step was to create a sequence [Earth, Ast1, Ast2, Ast3, Earth] with a reasonable phasing: A dynamic programming with 4 steps has been performed on the selected asteroids using a simple and quick criteria J: with all the t i respecting the date constraint. The minimization of this criteria gives an asteroid sequence and the potential dates of transfer How we proceed (1/3): step 1a

5. All rights reserved © 2008, Thales Alenia Space Corporate Communications April 2007 5 How we proceed (2/3): step 1b (1/2) In parallel we focused only on simple sub-sequences: Asteroid to Asteroid, Earth to Asteroid and Asteroid to Earth legs. We used an extended low-thrust model (assuming a thrust-ballisic-thrust sequence) to quickly assess these possible sub-sequences. A simplified objective function allows constructing complete sequences, by patching these sub-sequences. The construction step considers a sorting procedure and dynamic programming, to minimise the consumption and satisfy minimum rest-time condition at each asteroid. The computationnal cost of constructing complete sequences is limited Thanks to that, we could quickly consider different schemes: E-A-A-A-E E-E-A-......-A-E-E...A-E-A-...

6. All rights reserved © 2008, Thales Alenia Space Corporate Communications How we proceed (3/3) step 1b (2/2) The extended low-thrust model includes both thrust and coast segments. We have a quick and fair evaluation of the optimal cost. -For each sub-sequence, we considered 1 and 2 revolutions transfers, with 1 or 2 coast segments. -Test of the best complete solutions with T3D shows the model to be close to the optimal solution. April 2007 6 The E-A-A-A-E scheme, with the best asteroid selection, immediately produces a solution around 0.81. We concluded that swing-bys are necessary to increase further the cost criterion

7. All rights reserved © 2008, Thales Alenia Space Corporate Communications April 2007 7 Solution Overview The proposed solution is a sequence Earth-96-Earth-88-49-Earth lasting close to the maximum mission duration of 10 years

8. All rights reserved © 2008, Thales Alenia Space Corporate Communications April 2007 8 Overall trajectory

9. All rights reserved © 2008, Thales Alenia Space Corporate Communications April 2007 9 Earth to 2001 GP2 (GTOC n°96)

10. All rights reserved © 2008, Thales Alenia Space Corporate Communications April 2007 10 2001 GP2 (GTOC n°96) to 1991 VG(GTOC n°88)

11. All rights reserved © 2008, Thales Alenia Space Corporate Communications April 2007 11 1991 VG (GTOC n°88) to 2000 SG344 (GTOC n°49)

12. All rights reserved © 2008, Thales Alenia Space Corporate Communications April 2007 12 2000 SG344 (GTOC n°49) to Earth