Model predictive control for formation reconfiguration exploiting quasi-periodic tori in the cislunar environment

Given the numerous possibilities that formation flying space missions can enable, being able to design and govern relative trajectories in this scenario is fundamental. Particularly interesting, due to the installation and operation of the Lunar Gateway, which will represent the next human outpost in the cislunar environment, will be the exploitation of formation flying missions in the vicinity of this lunar station. The nonlinear dynamics by which the Earth-Moon system is characterised offers the possibility to find bounded relative trajectories which can be used to design the formation. In order to best exploit the formation potential, some reconfiguration manoeuvres can be used, which by changing the relative geometry can increase the versatility and adaptation of the mission. In this paper, a Model Predictive Guidance and Control strategy is proposed and applied to perform rephasing manoeuvres in the harsh environment of the Near Rectilinear Halo Orbits. By including first a limited thrust constraint and then a collision avoidance, a more mission-oriented approach is provided to the system. To further increase the robustness of the on-board algorithms, an adaptive logic is provided to the different tuning weights involved in the Model Predictive Control scheme. In this way, a more flexible system is obtained, which is capable of optimally working also in the presence of a high-fidelity simulation scenario, including discrepancies with the simplified on-board dynamical model.