Robust space trajectory design using belief optimal control

This paper presents a novel approach to the robust solution of optimal impulsive control problems under aleatory and epistemic uncertainty. The novel approach uses belief Markov decision processes to reformulate the control problem in terms of uncertainty distributions, called beliefs, rather than the realizations of the system states. This formulation leads to the definition of a belief optimal control problem where the cost function and constraints are functions of the uncertainty distributions. The control formulation encompasses orbit determination arcs as well. The belief optimization is solved with a shooting-like transcription and a nonlinear programming solver to optimize the resulting discretized problem. Both aleatory and epistemic uncertainties are propagated with a nonintrusive polynomial expansion to capture the nonlinearities of the dynamics. Finally, this new approach is applied to the robust optimization of a flyby trajectory of the Europa Clipper mission in a scenario characterized by knowledge, execution, and observation uncertainty.