Analysis of spacecraft disposal solutions from LPO to the Moon with high order polynomial expansions

Abstract

This paper presents the analysis of disposal trajectories from libration point orbits to the Moon under uncertainty. The paper proposes the use of polynomial chaos expansions to quantify the uncertainty in the final conditions given an uncertainty in initial conditions and disposal manoeuvre. The paper will compare the use of polynomial chaos expansions against high order Taylor expansions computed with point-wise integration of the partials of the dynamics, the use of the covariance matrix propagated using a unscented transformation and a standard Monte Carlo simulation. It will be shown that the use of the ellipsoid of uncertainty, that corresponds to the propagation of the covariance matrix with a first order Taylor expansions, is not adequate to correctly capture the dispersion of the trajectories that can intersect the Moon. Furthermore, it will be shown that polynomial chaos expansions better represent the distribution of the final states compared to Taylor expansions of equal order and are comparable to a full scale Monte Carlo simulations but at a fraction of the computational cost.