Chance-constraint optimization of interplanetary trajectories with a hybrid multiple-shooting approach

Dynamics uncertainties and stochastic disturbances on a nominal open-loop control law may affect a space mission by deviating the probe from the designed optimal trajectory. To overcome this issue and provide a sufficient level of robustness to the trajectory, additional propellant is usually allocated for correction maneuvers. However, time-consuming and empirical procedures are commonly adopted to estimate these maneuvers, often resulting in the definition of sub-optimal control strategies and over-conservative margins. This manuscript proposes a systematic approach for the design of a closed-loop control law, where quantitative information concerning uncertainty on the system dynamics and stochastic navigation errors are directly accounted for in the optimization process. More in detail, a linear feedback control law is sought to steer the probability distribution of the spacecraft state towards a target distribution at an assigned final time. A hybrid single/multiple-shooting strategy is used to respectively propagate the state mean and probability distribution, resulting in an efficient performance and stability of the numerical method. The results of a test case show the possibility of reducing the final dispersion on the state of several orders of magnitude, with a reasonable increase of fuel consumption.