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In this work, we develop a new method to design energy minimum low-thrustmissions (L2-minimization). In the Circular Restricted Three Body Problem, theknowledge of invariant manifolds helps us initialize an indirect method solvinga transfer mission between periodic Lyapunov orbits. Indeed, using the PMP, theoptimal control problem is solved using Newton-like algorithms finding the zeroof a shooting function. To compute a Lyapunov to Lyapunov mission, we firstcompute an admissible trajectory using a heteroclinic orbit between the twoperiodic orbits. It is then used to initialize a multiple shooting method inorder to release the constraint. We finally optimize the terminal points on theperiodic orbits. Moreover, we use continuation methods on position and onthrust, in order to gain robustness. A more general Halo to Halo mission, withdifferent energies, is computed in the last section without heteroclinic orbitsbut using invariant manifolds to initialize shooting methods with a similarapproach.

Low-Thrust Lyapunov to Lyapunov and Halo to Halo with $L^2$-Minimization