Optimal state estimation and control of space systems under severe uncertainty

Student thesis: Doctoral Thesis

Abstract

This thesis presents novel methods and algorithms for state estimation and optimal control under generalised models of uncertainty. Tracking, scheduling, conjunction assessment, as well as trajectory design and analysis, are typically carried out either considering the nominal scenario only or under assumptions and approximations of the underlying uncertainty to keep the computation tractable. However, neglecting uncertainty or not quantifying it properly may result in lengthy design iterations, mission failures, inaccurate estimation of the satellite state, and poorly assessed risk metrics. To overcome these challenges, this thesis proposes approaches to incorporate proper uncertainty treatment in state estimation, navigation and tracking, and trajectory design. First, epistemic uncertainty is introduced as a generalised model to describe partial probabilistic models, ignorance, scarce or conflicting information, and, overall, a larger umbrella of uncertainty structures. Then, new formulations for state estimation, optimal control, and scheduling under mixed aleatory and epistemic uncertainties are proposed to generalise and robustify their current deterministic or purely aleatory counterparts. Practical solution approaches are developed to numerically solve such problems efficiently. Specifically, a polynomial reinitialisation approach for efficient uncertainty propagation is developed to mitigate the stochastic dimensionality in multi-segment problems. For state estimation and navigation, two robust filtering approaches are presented: a generalisation of the particle filtering to epistemic uncertainty exploiting samples' precomputations; a sequential filtering approach employing a combination of variational inference and importance sampling. For optimal control under uncertainty, direct shooting-like transcriptions with a tunable high-fidelity polynomial representation of the dynamical flow are developed. Uncertainty quantification, orbit determination, and navigation analysis are incorporated in the main optimisation loop to design trajectories that are simultaneously optimal and robust. The methods developed in this thesis are finally applied to a variety of novel test cases, ranging from LEO to deep-space missions, from trajectory design to space traffic management. The epistemic state estimation is employed in the robust estimation of debris' conjunction analyses and incorporated in a robust Bayesian framework capable of autonomous decision-making. An optimisation-based scheduling method is presented to efficiently allocate resources to heterogeneous ground stations and fusing information coming from different sensors, and it is applied to the optimal tracking of a satellite in highly perturbed very-low Earth orbit, and a low-resource deep-space spacecraft. The optimal control methods are applied to the robust optimisation of an interplanetary low-thrust trajectory to Apophis, and to the robust redesign of a leg of the Europa Clipper tour with an initial infeasibility on the probability of impact with Jupiter's moon.
Date of Award15 Sep 2021
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SupervisorMassimiliano Vasile (Supervisor) & Christie Maddock (Supervisor)

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