This paper proposes a novel algorithm, based on model predictive control (MPC), for the optimal guidance of a launch vehicle upper stage. The guidance algorithm must take into account a realistic dynamical model and several nonconvex constraints, such as the maximum heat flux after fairing jettisoning and the splash-down of the burned-out stage, to properly predict and optimize the system performance. Convex optimization is embedded into the MPC framework to allow for high update frequencies. Specifically, state-of-the-art convexification methods and a hp pseudospectral discretization scheme are used to formulate the optimal control problem as a sequence of second-order cone programming problems that quickly converges to an optimal solution. Convergence is further enhanced via a soft trust region and an improved strategy for updating the reference solution. Also, virtual controls and proper constraint relaxations are introduced to guarantee the recursive feasibility of the algorithm. Numerical results relative to the autonomous guidance of the third stage of a VEGA-like vehicle are presented to prove the validity of the MPC approach. The computational efficiency and robustness of the algorithm are discussed on the basis of extensive Monte Carlo campaigns that account for off-nominal initial conditions and random in-flight disturbances.
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