Lyapunov-based lunar capture guidance scheme

In this paper, a lunar orbital capture guidance law is presented for a spacecraft with electrical propulsion system using Lyapunov feedback control approach. Construction of the Lyapunov function candidate is based on orbital elements such as equinoctial orbital elements set to avoid the singularities. Unlike the orbit transfer problem between closed orbits, the lunar capture problem has two constraints. One thing is that the spacecraft coming to the planet with hyperbola orbit conditions must be accomplished the closed orbit conditions before passing the first perilune. And the other one is that the perilune altitude of the spacecraft is not smaller than zero to prevent the crashing problem. For this reason, the penalty function approach is used to avoid the lunar surface crashing problem and the orbital energy term instead of the semi-latus rectum in the equinoctial orbit elements set is used to accomplish the closed orbit conditions rapidly.