Design of robust maneuvers for the MMX mission: a chance-constraint optimization perspective

The design of spacecraft trajectories in nonlinear dynamical systems subject to model uncertainty and disturbances is a complex and demanding task. Methods based on robust optimization consist in accounting, within the optimization process, for the possibility of having an imperfect knowledge of state and control variables. This allows to obtain a solution in which, a priori, a small amount of propellant is traded for reduced sensitivity to uncertainties and state errors, mitigating in this way the risk of partial or complete mission failure. In this manuscript, a chance-constraint optimization method is conceived and applied to design a robust impulsive approaching trajectory for a spacecraft aimed at the Martian moon Phobos. The trajectory starts at the end of the heliocentric journey from the Earth with given uncertainty on initial conditions. Spacecraft states and control are regarded as probability distributions over time while unscented transformation is used for efficient propagation of these distributions through nonlinear stochastic system dynamics. Numerical results are presented for a case study related to the future sample return mission MMX of the Japanese Aerospace Explorations Agency (JAXA).