Convex Formulation and Efficiency Enhancement for Powered Landing Guidance With Second-Order Cone Probability Constraints

Real-time trajectory optimization is crucial for achieving autonomous guidance in powered landing. However, the existing algorithms often struggle with uncertainties and are unable to handle second-order cone probability constraints, such as control magnitude and direction constraints. In addition, the large-scale and complex nature of these optimization problems hampers real-time performance. This study addresses these shortcomings by presenting a convex formulation suitable for general second-order cone probability constraints and proposing two strategies, conservative approximation and variable reduction, to improve real-time performance. Specifically, the conservative approximation converts spectral norm constraints into second-order cone constraints, while the variable reduction reduces the number of optimization variables. Applied to a powered landing simulation scenario, the proposed approaches effectively handle second-order cone probability constraints and improve real-time performance by two to three orders of magnitude.