Optimization of Low-Thrust Trajectories for Formation Flying with Parallel Multiple Shooting

In this work the problem of optimization of low-thrust space trajectory is addressed. The problem can be stated as the solution of an optimal control problem in which an objective function related to controls is minimized satisfying a series of constraints on the trajectory which are both differential and algebraic. The problem has been faced transcribing the differential constraints with a parallel multiple shooting transcription method into a NLP problem which has been solved with an interior point method. The method that has been developed is particularly suited for the solution of problems in which the trajectory is constrained with a great number of inequalities both on states and controls. As an example of such kind of problem, the method has been applied to the design of reconfiguration maneuvers for spacecrafts flying in formation, where the collision avoidance issue leads to the imposition of a large number of inequalities on states.