In this work, we develop a new method to design energy minimum low-thrust missions (-minimization). In the Circular Restricted Three Body Problem, the knowledge of invariant manifolds helps us initialize an indirect method solving a transfer mission between periodic Lyapunov orbits. Indeed, using the PMP, the optimal control problem is solved using Newton-like algorithms finding the zero of a shooting function. To compute a Lyapunov to Lyapunov mission, we first compute an admissible trajectory using a heteroclinic orbit between the two periodic orbits. It is then used to initialize a multiple shooting method in order to release the constraint. We finally optimize the terminal points on the periodic orbits. Moreover, we use continuation methods on position and on thrust, in order to gain robustness. A more general Halo to Halo mission, with different energies, is computed in the last section without heteroclinic orbits but using invariant manifolds to initialize shooting methods with a similar approach.
Accepté le :
DOI : 10.1051/m2an/2016044
Mots clés : Three body problem, optimal control, low-thrust transfer, Lyapunov orbit, Halo orbit, continuation method
@article{M2AN_2017__51_3_965_0, author = {Chupin, Maxime and Haberkorn, Thomas and Tr\'elat, Emmanuel}, title = {Low-thrust {Lyapunov} to {Lyapunov} and {Halo} to {Halo} missions with $L^{2}$-minimization}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {965--996}, publisher = {EDP-Sciences}, volume = {51}, number = {3}, year = {2017}, doi = {10.1051/m2an/2016044}, mrnumber = {3666653}, zbl = {1370.49024}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2016044/} }
TY - JOUR AU - Chupin, Maxime AU - Haberkorn, Thomas AU - Trélat, Emmanuel TI - Low-thrust Lyapunov to Lyapunov and Halo to Halo missions with $L^{2}$-minimization JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 965 EP - 996 VL - 51 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016044/ DO - 10.1051/m2an/2016044 LA - en ID - M2AN_2017__51_3_965_0 ER -
%0 Journal Article %A Chupin, Maxime %A Haberkorn, Thomas %A Trélat, Emmanuel %T Low-thrust Lyapunov to Lyapunov and Halo to Halo missions with $L^{2}$-minimization %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 965-996 %V 51 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016044/ %R 10.1051/m2an/2016044 %G en %F M2AN_2017__51_3_965_0
Chupin, Maxime; Haberkorn, Thomas; Trélat, Emmanuel. Low-thrust Lyapunov to Lyapunov and Halo to Halo missions with $L^{2}$-minimization. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 965-996. doi : 10.1051/m2an/2016044. http://www.numdam.org/articles/10.1051/m2an/2016044/
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