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.
| Date of Award | 22 Jan 2026 |
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| Original language | English |
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| Awarding Institution | - University Of Strathclyde
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| Sponsors | University of Strathclyde |
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| Supervisor | Massimiliano Vasile (Supervisor) & Christie Maddock (Supervisor) |
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