Multi-objective optimization of low-thrust orbit transfers in LEO using Q-law and direct collocation

The increased fuel efficiency makes electric propulsion systems particularly suitable when large $\Delta V$ increments are required, such as during orbital transfers around a central body. On the other hand, low thrust systems operate for a significant amount of mission time, producing long thrusting arcs that have to be designed through appropriate continuous optimization techniques. The corresponding optimal control problem is indeed strongly nonlinear and it is much harder to solve than conventional high-thrust trajectory optimization. In this work, a flexible approach for the optimization of low thrust trajectories is presented. The orbit transfer problem is addressed, introducing a two-stage technique to produce continuous spacecraft trajectories that satisfy initial and terminal conditions defined along two different orbits while minimizing the fuel consumption and/or time of flight (TOF). The devised method takes into account the impact of external perturbations in order to generate a reliable solution. The multi-objective formulation of the optimization problem offers a practical way to trade off fuel consumption and time of flight, providing an adaptable framework able to deal with several use-cases. The proposed optimization strategy relies on a method that combines heuristic guidance algorithms with direct collocation approaches, offering lower computational demands with respect to existing techniques. A peculiar feature of this work is the single-phase formulation of the optimal control problem that requires no prior information about the solution structure. The Q-law results, already close to the global optima, are then used to warm up the optimization routine, that employs direct collocation techniques to transcribe the optimal control problem (OCP) into a nonlinear programming problem (NLP). The transcription process is particularly effective when paired with the Q-law output because of the direct collocation capability of exploiting the entire initial guess, relying on the computed path and controls to produce optimal trajectories while satisfying desired endpoint constraints. The resulting NLP is easily solved with a general-purpose solver such as IPOPT or SNOPT.