Trajectory optimization with gradient descent for a variable-volume float

Abstract

In the realm of fluid dynamics and particle transport, the control of particle trajectories represents a formidable challenge. It would be useful to be able to optimally navigate an oceanographic float from one pre-set location to another by solely changing its buoyancy. In this thesis, a first step in discovering whether this is possible and what optimization strategy can be used is taken.
To do so, first, the physical situation is translated into a mathematical model. Then, an optimization strategy for changing the buoyancy to optimally travel to a set location is constructed. The strategy is based on gradient descent and implemented in Python. Four different definitions of an optimal trajectory to a target location are considered, those are 1) any trajectory that leads to the target location, 2) the most time-efficient trajectory, 3) the most energy-efficient trajectory, and 4) a trajectory that is both time and energy-efficient.
The optimization strategy is tested for five different starting and target locations for a small spherical float in an idealized two-dimensional linear flow field. It is concluded that it is possible to use the optimization strategy to navigate a float using buoyancy changes for all four optimization objectives, although the current implementation is not efficient enough for targets far away.
The first objective of future research should be to increase the coding efficiency. Thereafter, other steps toward a more realistic situation can be taken, such as testing for non-linear flow fields, three-dimensional fields, and bigger floats.