Robust optimal powered descent guidance via model predictive convex programming

This paper investigates the robust fuel-optimal guidance problem for powered descent landing under uncertainty. A robust optimal control problem (OCP) with stochastic dynamics and constraints is first constructed to ensure both optimality and safety. The polynomial chaos expansion (PCE)-based uncertainty quantification technique is then employed to convert the stochastic OCP into a high-dimensional deterministic OCP, which, while tractable, involves a large number of decision variables and is computationally intensive. To mitigate this issue, the dynamics are convexified within the model predictive convex programming (MPCP) framework, reducing the number of decision variables by establishing the sensitivity relationship between state and control corrections. Furthermore, convexification techniques including lossless convexification and successive convexification are applied to convexify the nonlinear inequality constraints. To enhance computational efficiency, a dimension reduction method is also introduced. After solving the robust OCP through convex optimization, a closed-loop guidance algorithm based on receding horizon strategy is proposed to address navigational errors. Numerical simulations demonstrate the advantages of this guidance algorithm.