Olympio, Joris T. (2008) Optimisation and Optimal Control Methods for Planet Sequence Design of Low-Thrust Interplanetary Transfer Problems with Gravity-Assists. PhD thesis Informatique temps réel, robotique et automatique, CMA - Centre de Mathématiques Appliquées, ENSMP p.147.

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Abstract

Electrical propulsion systems allow broader a class of spacecraft trajectories than conventional chemical propulsion. But because low-thrust propulsion systems induce limited controllability for the spacecraft and increase overall trajectory transfer duration, it is generally useful to use gravitational assistances. Gravity assists allow reducing both the consumption and the mission duration. The optimisation of continuous thrust trajectory remains a terrible task. General methods may be difficult to converge. In addition, the optimisation of the scenario, i.e. seeking the optimal planet sequence for the gravity assists, is never included in the optimisation process. The planet sequence is very likely not optimal. Mission analysts usually consider several different planet sequences. The trade-off between the different solutions permit identifying a promising planet sequence. This approach is however time consuming. The purpose of this thesis is to provide method to design optimal scenarios. This thesis proposes methods for the determination of the optimal scenario. Two approaches have been considered. The first approach considers the problem as an integer programming problem, when many sequences are considered a-priori. A low-thrust trajectory model has been designed, using inversion dynamics approach, to compute efficiently approximate solutions to the low-thrust trajectory transfer problem. This low-thrust model uses coast arcs to minimise the consumption, but also to increase the degree of freedom for satisfying terminal constraints. We set up an algorithm with polynomial complexity to solve the multi-gravity-assist low-thrust problem. The computational cost is limited using pruning constraints to reduce the size of the search boxes. The second approach formulates the problem as an indirect continuous optimal control problem. The dynamic includes all major gravitational bodies. Swing-bys are not introduced with intermediate constraint, but implicit with the dynamic and the appropriate control. We show that usual direct and indirect methods have difficult convergence for this problem. Using a second order gradient method, we seek the optimal control that transfers the spacecraft to its destination while in a multi-body dynamics. In some case, the optimal control manages to introduce gravity assist on the trajectory. The scenario is then given a posteriori, once an optimal control has been found.

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