Finite-Horizon, Energy-Optimal Trajectories in Unsteady Flows

TL;DR

This paper explores finite-horizon model predictive control for energy-efficient mobile sensor trajectories in unsteady flows, revealing how optimal paths leverage flow structures and enabling adaptive, energy-conscious environmental sensing.

Contribution

It introduces a novel connection between finite-time optimal trajectories and flow Lyapunov exponents, demonstrating effective trajectory planning with short prediction horizons in unsteady flows.

Findings

Energy-efficient trajectories exploit invariant flow structures.

Short prediction horizons often achieve near-optimal energy use.

Flow structures guide the design of adaptive sensing paths.

Abstract

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.