Robust trajectory optimization with chance-constrained formulation

This thesis investigates the chance-constraint formulation of robust trajectory optimization for space applications. The importance of robustness in space trajectory optimization is growing significantly as the modern mission design approach prioritizes lightweight satellite architectures and cost reduction. However, this emphasis also raises the risk of deviating from a nominal path due to errors in navigation or incorrect maneuvers. Consequently, it is crucial to compute control laws that directly incorporate quantitative information about uncertainty in system dynamics and stochastic navigation errors during the optimization process. This works aims to formulate a stochastic framework for trajectory optimization with the goal of increasing intrinsic robustness of space flight, in both impulsive and low-thrust transfers. Two different approaches are considered in this regard: open-loop control, assessing the possibility of reducing the state dispersion by optimizing a sequence of deterministic maneuvers, and closed-loop control, defining a linear feedback control law that computes the corrective maneuver during the flight, limiting in this way the state dispersion. In order to deal with the stochastic formulation of the state, chance-constraint theory is employed when expressing the cost function and the constraints on control magnitude. As assessments of the validity and performance capability of the proposed robust trajectory optimization methodologies, test cases involving potential space applications are employed, involving interplanetary transfers and station-keeping control strategies.