Attainable Landing Area Computation of Lunar Landers with Pseudo-Spectral and Polynomial Based Guidance Methods

In this paper, we introduce two methods for computing reachable sets, namely, via Pseudo-Spectral based optimal control techniques and via a modified form of the Apollo guidance algorithm. Specifically, in the latter case, we use the Apollo guidance to generate a reference trajectory, and a Lyapunov-based PD controller to track it. We then demonstrate the effectiveness of both approaches on the soft-landing problem for a Moon mission, where we show that although both algorithms achieve similar propellant requirements, the optimal control approach generates larger reachable sets at the expense of higher computational cost