Ethan R. Burnett

Ethan R. Burnett, Spencer Boone

This paper provides a comparative study of modern uncertainty quantification (UQ) methods. To greatly enhance real-time performance, both differential algebra (DA) and a directional differential algebra (DDA) approach are employed. This can enable fast UQ in the case of non-Gaussian statistics. Higher-order moments, namely skew and kurtosis, can be computed quickly by several means. This motivates their implementation in an analytic approximation of the confidence bounds for the so-called "banana-shaped" non-Gaussian distributions encountered often in nonlinear astrodynamics problems. This method improves greatly on a linear covariance approach, with only 5x its runtime in numerical tests, even before DA methods are employed. Test problems in this work include a restricted three-body cislunar example and an Earth-return aerocapture example.

Ethan Burnett, Hanspeter Schaub

Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite relative motion solutions for linearization about a closed chief orbit. By identifying the analytic relationship between Lyapunov-Floquet transformations of the relative motion dynamics in different coordinate systems, new means are provided for rapid computation and exploration of the types of close-proximity natural relative motion available in various applications. The approach is demonstrated for the Keplerian relative motion problem with general eccentricities in multiple coordinate representations. The Keplerian assumption enables an analytic approach, leads to new geometric insights, and allows for comparison to prior linearized relative motion solutions.