Thesis
Multi-objective trajectory optimisation under epistemic uncertainty
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2026
- Thesis identifier
- T17583
- Person Identifier (Local)
- 201989971
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- This thesis proposes innovative methodologies for the many-objective optimisation of spacecraft trajectories under epistemic uncertainty, which can also have application outside the domain of trajectory optimisation. Epistemic uncertainty refers to a type of uncertainty that is due to a lack of knowledge, and which cannot be adequately quantified using standard probability theory, making it more challenging to quantify in practice, as computational costs can become prohibitively high, in particular when the number of uncertain variables is increased. Thus, the main challenge addressed by this thesis was reducing the computational cost of quantifying epistemic uncertainty in the context of trajectory optimisation. Several strategies were developed and used in combination. Since the quantification of epistemic uncertainty is an integral part of the objectives being optimised, strategies are developed that reduce the number of evaluations of these objectives. A surrogate model of the lower expectation is combined with a dimensionality reduction technique to contain the computational cost. These dimensionality reduction techniques take the form of control maps, which map the space of control laws to a lower dimensional space, reducing the dimensionality of the search space. Several control maps are tested and compared. The second approach is to reduce the computational cost of quantifying the epistemic uncertainty. Techniques are proposed for some general formulations of epistemic uncertainty. These are accompanied with studies of the scalability of their computational cost with the number of epistemic variables. To optimise trajectories while accounting for the responsiveness of the control law to observations of the state during the trajectory, sampling the uncertain variables and finding the optimal control law for each case can become prohibitively expensive, even in the context of standard probability theory. Dynamic programming strategies have been applied, in the literature, to stochastic optimal control. A key innovation in this work is a dynamic programming formulation for epistemic uncertainty. This allows designing trajectories where the control law responds to observations and corrects for deviations, while still efficiently quantifying the epistemic uncertainty. Additionally, by splitting the trajectory into segments affected by different epistemically uncertain variables, this limits the growth of the computational cost with the number of epistemic variables. Additional key contributions were theoretical proofs that bound the value of this estimate with respect to other epistemic uncertainty quantifications of interest, in a way which is applicable to many commonly used formulations of epistemic uncertainty. These methodologies are incorporated into algorithms which are applied to test cases consisting of spacecraft equipped with low thrust engines, whose parameters are affected by epistemic uncertainty. These consist of an asteroid rendezvous mission, and an asteroid fly-by tour of four asteroids in the asteroid belt. For these, a set of control laws are obtained, describing the evolution of the thrust magnitude and direction over time, and launch parameters, which are robust with respect to epistemic uncertainty in the system parameters. The algorithms used are empirically and theoretically shown to scale well with the number of uncertain variables.
- Advisor / supervisor
- Vasile, Massimiliano
- Resource Type
- DOI
- Funder
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PDF of thesis T17583 | 2026-02-10 | Public | Download |