Uncertainty propagation for orbital motion around an asteroid using generalized intrusive polynomial algebra: application to didymos system

The Hera mission plans to release a CubeSat into orbit around the binary asteroid system Didymos to investigate these bodies in more detail. Uncertainties play a key role in designing the trajectory for the CubeSat and thus a method is needed that is able to accurately and efficiently capture all the effects of uncertainties on the dynamics of this system. This paper introduces the Generalised Intrusive Polynomial Algebra (GIPA) as a novel method of producing a surrogate model representing this dynamical system under uncertainties. This method uses an algebra constructed using a basis of orthogonal polynomials that expand the dynamics over a certain set. The algebra is then used to propagate this set over time using conventional numerical integration methods. Both a Taylor polynomial basis and a Chebyshev basis are considered for this study. The results of the GIPA propagation are compared to the results from a Monte Carlo simulation to test its accuracy. GIPA is shown to be able to accurately and efficiently determine how the uncertainties evolve over time for a range of different initial conditions. Which is a useful tool that can be used in the robust design of spacecraft trajectories.