Constrained trajectory optimization for lunar landing

As a first step towards exploration of Mars and beyond, humanity will again be landing on the surface of the Moon. The increase in computational capability since Apollo allows more capable on-board G&C algorithms to be implemented, both for manned and unmanned missions. This paper explores the trade-space of fuel-optimal trajectories from a Lunar parking orbit to soft landing, constraining both translational and attitude states in selected phases of the decent trajectory. A Legendre pseudospectral method is used to discretize and optimize the entire trajectory. Operational constraints include continuous (i.e., finite non-zero) thrust during braking, de-orbit perigee height specifications, and final vertical descent.