A hybrid multiple-shooting approach for covariance control of interplanetary missions with navigation errors

During interplanetary flight, several sources of stochastic disturbances and dynamical uncertainties may deviate a spacecraft from its nominal trajectory. This manuscript proposes a systematic robust trajectory design method, where quantitative information concerning uncertainty on the system dynamics and stochastic navigation errors are directly accounted for in the mission-planning process. A linear feedback control law is designed to steer the probability distribution of the spacecraft state towards a target distribution at an assigned final time, minimizing the propellant consumption while guaranteeing robustness to disturbance and uncertainties. A hybrid multiple-shooting approach is adopted, where the mean trajectory and the open-loop controls are optimized according to a multiple-shooting scheme, while a single-shooting scheme is adopted for propagating higher-order statistical moments of the spacecraft state distribution. The proposed approach is applied to the analysis of the extended mission phase of the future JAXA mission DESTINY+. The final dispersion on the state is expected to be reduced by a few orders of magnitude, with a small increase in fuel consumption.