Robust Space Trajectory Design Using Belief Optimal Control

Abstract

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 realisations 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 optimisation is solved with a shooting-like transcription and a nonlinear programming solver to optimise the resulting discretised problem. Both aleatory and epistemic uncertainties are propagated with a non-intrusive polynomial expansion to capture the nonlinearities of the dynamics. Finally, this new approach is applied to the robust optimisation of a flyby trajectory of the Europa Clipper mission in a scenario characterised by knowledge, execution and observation uncertainty.

Robust Trajectory Design for Ballistic Landings on Dimorphos

“…These polynomials have been previously used in an astrodynamics setting as well in [35] and [36]. This work follows a similar approach as [35] and [37], and uses a Chebyshev polynomial basis together with a Smolyak sparse grid sampling approach to obtain the polynomial from Eq. ( 11), which is hereafter called the non-intrusive Chebyshev Interpolation (NCI) method.…”