XIX CONGRESSO NAZIONALE AIDAA 17 – 21 settembre 2007 FORLÌ (FC) REACHING NEOS: SOLUTION FOR THE SECOND GLOBAL TRAJECTORY OPTIMIZATION COMPETITION M. MASSARI 1 , R. ARMELLIN 1 , P. DI LIZIA 1 AND F. TOPPUTO 1 1 Aerospace Engineering Department, Politecnico di Milano, Italy ABSTRACT The second global trajectory optimization competition was organized by the Outer Planets Mission Analysis Group of the Jet Propulsion Laboratory and was announced in October 2006. The competition objective was to find the global optimal low-thrust trajectory, maximizing a complex objective function over a huge search space. The problem was a multiple asteroid rendezvous: a trajectory had to be designed for a low-thrust spacecraft which departs from the Earth and subsequently performs a rendezvous with one asteroid chosen within each of four defined groups of asteroids. In this paper we present the results obtained by the Aerospace Engineering Department of Politecnico di Milano. The problem has been approached by means of a two-phase solution process. The first phase aims at determining a preliminary solution close to the global optimum that is refined in the second phase through a local optimization. In this work the two-phase approach is presented together with the obtained solution. 1. INTRODUCTION The Global Trajectory Optimization Competition was inaugurated in 2005 by the Advanced Concepts Team, Eu- ropean Space Agency. The second competition was organized by the Outer Planets Mission Analysis Group of the Jet Propulsion Laboratory and was announced in October 2006. The competition objective is to find the global optimal low-thrust trajectory, minimizing or maximizing a complex objective function over a huge search space. The problem is described below. For further details see [1]. The problem to be solved in the second competition is a multiple asteroid rendezvous. A trajectory must be designed for a low-thrust spacecraft which launches from Earth and subsequently performs a rendezvous with one asteroid from each of four defined groups of asteroids. Maximization of the ratio of final spacecraft mass to flight time is sought. The asteroid groups are chosen such that they are sufficiently well populated and sufficiently diverse between themselves (in terms of orbital elements) so as to ensure that there is no obvious best solution and that the trajectories necessarily exhibit large excursions in most of the orbital elements. Moreover the total number of asteroids composing the groups amount to 910, assuring that the search space is quite big. The whole optimization problem has been approached by means of a two-phase solution process. The first phase aims at determining a preliminary solution which is refined in the second phase using a local optimization method. One of the issues to be solved in the first phase is represented by the determination of the sequence of the groups of the asteroids to be visited. This choice has been mainly driven by some physical considerations. Analyzing the mean energy level of the asteroids belonging to the same group and the mean time required to transfer from one group to another, we have estimated the global optimum to be associated to a particular group sequence from inner asteroids to outer ones. This means that the spacecraft will gradually move from the group closest to the Earth to the farthest. In this way, the spacecraft’s energy monotonically increases. Once the groups sequence has been identified, the following problems has been addressed: the determination of the asteroids to be visited within each group, the proper modelization of each transfer trajectory, and the solution of the resulting hybrid global optimization problem (continuous and discrete variables).