Stochastic Optimization Through Nonlinear Covariance Mapping: Application to Weak Stability Boundary Transfers

The advent of CubeSats for space exploration has underscored the need for a more stochastic-oriented mission analysis. Due to their limited orbital control authority and significant command execution errors, CubeSat missions are more vulnerable to space flight uncertainty. As a result, mission analysts are increasingly seeking optimal solutions from a stochastic perspective by embedding uncertainties into the optimization phase. In this work, uncertainties related to initial conditions, maneuver executions, and navigation are incorporated into a stochastic trajectory optimization process. The proposed method leverages a novel implementation of the unscented transformation, where a continuous propagation map avoids the simplification associated with sigma point resampling. With this approach, the problem is formulated as a nonlinear programming problem. The method is applied to weak stability boundary transfers, using the LUMIO CubeSat mission as the case study. This marks a novel and significant application. Results show that stochastic optimization can generate new nominal trajectories that require less fuel and are more robust if compared to those obtained through deterministic optimization only. Monte Carlo analyses with higher-fidelity sources of uncertainties, such as process-noise, validate the proposed approach in a more general framework.