  Intelligent mobile sensors, such as uninhabited aerial or underwater
vehicles, are becoming prevalent in environmental sensing and monitoring
applications. These active sensing platforms operate in unsteady fluid flows,
including windy urban environments, hurricanes, and ocean currents. Often
constrained in their actuation capabilities, the dynamics of these mobile
sensors depend strongly on the background flow, making their deployment and
control particularly challenging. Therefore, efficient trajectory planning with
partial knowledge about the background flow is essential for teams of mobile
sensors to adaptively sense and monitor their environments. In this work, we
investigate the use of finite-horizon model predictive control (MPC) for the
energy-efficient trajectory planning of an active mobile sensor in an unsteady
fluid flow field. We uncover connections between the finite-time optimal
trajectories and finite-time Lyapunov exponents (FTLE) of the background flow,
confirming that energy-efficient trajectories exploit invariant coherent
structures in the flow. We demonstrate our findings on the unsteady double gyre
vector field, which is a canonical model for chaotic mixing in the ocean. We
present an exhaustive search through critical MPC parameters including the
prediction horizon, maximum sensor actuation, and relative penalty on the
accumulated state error and actuation effort. We find that even relatively
short prediction horizons can often yield nearly energy-optimal trajectories.
These results are promising for the adaptive planning of energy-efficient
trajectories for swarms of mobile sensors in distributed sensing and
monitoring.
