FTLE of optimally controlled agents in unsteady flow fields.

Finite-time Lyapunov exponents (FTLE) are used to compute Lagrangian coherent structures of unsteady fluid flow fields. These coherent structures can be used to understand the transport mechanisms of passive tracers advecting with the flow. However, many of the vehicles and mobile sensors we wish to deploy in the ocean or atmosphere are actuated, and some form of intelligent trajectory planning (such as model predictive control) is often adopted to move them optimally in the dynamically changing background flow. In this work, we investigate the use of FTLE on such controlled agents to gain insight into optimal transport routes for navigation in known unsteady flows. We find that these controlled FTLE (cFTLE) coherent structures separate the flow field into different regions based on the cost of transport to the goal location. These separatrices are functions of the planning algorithm's hyper-parameters, such as the optimization time horizon, the maximum actuation amplitude, and the cost of actuation. We can use this information to gain insight into effective deployment locations for mobile agents (which have limitations on actuation and energy capacity) to traverse the ocean or atmosphere.