Hamiltonian-Based Libration Point Orbit Control on Manifold of Constant Energy

© 2021, Springer Nature Switzerland AG. The circular restricted three-body problem (CR3BP) is important from the theoretical as well as a practical viewpoint. In this paper, the objective is to control a spacecraft along stable or unstable libration point orbits. For this purpose, a manifold of constant energy is specified. Then, a Hamiltonian-based state variable feedback control law is designed for regulating the spacecraft to attain the specified level of energy. Through the Lyapunov analysis, asymptotic convergence of the system energy to prescribed level is established. For this multi-dimensional constant energy manifold, a variety of periodic and quasi-periodic libration point orbits can exist. Interestingly, the spacecraft can be controlled using a small control force applied to the spacecraft. Simulation results are presented, which show that in the closed-loop system, the spacecraft follows libration point orbits on the manifold of prescribed energy