Design of sliding mode controllers for formation flying along unstable periodic orbits in CR3BP

This paper studies a control law to stabilize the orbital motion in the vicinity of an unstable equilibrium point and periodic orbits in the circular-restricted three-body problem (CR3BP). Since the libration point orbits especially around collinear points are highly unstable, time-delay in sensor and/or acutor might cause instability. In this paper, we derive a continuous sliding mode controller (Cont. SMC) to achieve robust fuel-efficient periodic motion based upon a new Lyapunov function to smooth the control input. Then, the total velocity change is investigated to reach and maintain a halo orbit in the Sun-Earth CR3BP. Simulation results show that the proposed Cont. SMC has good performance and robustness in the presence of unmodeled time-delay.