This paper presents a novel algorithm, based on model predictive control
(MPC), for the optimal guidance of a launch vehicle upper stage. The proposed
strategy not only maximizes the performance of the vehicle and its robustness
to external disturbances, but also robustly enforces the splash-down
constraint. Indeed, uncertainty on the engine performance, and in particular on
the burn time, could lead to a large footprint of possible impact points, which
may pose a concern if the reentry points are close to inhabited regions. Thus,
the proposed guidance strategy incorporates a neutral axis maneuver (NAM) that
minimizes the sensitivity of the impact point to uncertain engine performance.
Unlike traditional methods to design a NAM, which are particularly burdensome
and require long validation and verification tasks, the presented MPC algorithm
autonomously determines the neutral axis direction by repeatedly solving an
optimal control problem (OCP) with two return phases, a nominal and a perturbed
one, constrained to the same splash-down point. The OCP is transcribed as a
sequence of convex problems that quickly converges to the optimal solution,
thus allowing for high MPC update frequencies. Numerical results assess the
robustness and performance of the proposed algorithm via extensive Monte Carlo
campaigns.Comment: arXiv admin note: text overlap with arXiv:2210.1461