Orbital Station-Keeping in the Circular and Elliptic Restricted Three-Body Problems

11/18/2024

Periodic orbits of the circular and elliptic versions of the Restricted Three-Body Problem (R3BP) are targeted by many contemporary space missions within the Earth-Moon system. Given their unstable nature, control is mandatory to ensure accurate tracking of these trajectories, which formally constitutes an orbital station-keeping problem. In this work, different control alternatives to tackle a general formulation of this problem are developed. On the one hand, a nonlinear (NL) approach is established via a backstepping technique, which is shown to provide global guarantees in terms of asymptotic stability, evoking Lyapunov's theory. To adhere to possible physical constraints, an adaption including actuation saturation is similarly proposed, ensuring these guarantees are maintained, at least locally, in the occurrence of saturation. On the other hand, an optimal control law is derived for a linearised version of the dynamics by solving a periodic Linear Quadratic Regulator (LQR) problem which minimises a cost function incorporating the linear stability properties of the nominal orbit, obtained through Floquet theory. Additionally, a combined alternative coupling the two base approaches is also proposed. Numerical simulations show that the NL control law is most adequate for tackling large deviations, being however outperformed by the LQR alternative when in close proximity to the nominal orbit, attesting to the meaningfulness of a combined controller. The adapted NL law considering actuation saturation is also validated numerically, where the inclusion of such guarantees is shown to considerably limit the controller gain selection.

Authors in the community:

• 

  A

  António Maria Wergikosky Nunes

  ist195770

Supervisors of this institution:

• 

  P

  Pedro Tiago Martins Batista

  ist14388

mechanical-engineering - Mechanical engineering

eng - English

Instituto Superior Técnico