Deformation of FTLE ridges under the action of control in unsteady fluid flows

Finite-time Lyapunov Exponent fields allow us to visualize transport barriers and regions of strong attraction or repulsion for passive particles in an unsteady fluid flow. It is also possible to extract FTLE from data generated by active agents that use actuation to move through the flow. The effect of actuation and control may be viewed as resulting in a new effective background vector field in which the active agent appears to be a passive particle. Therefore, when FTLE is computed for active agents, the resulting control FTLE (cFTLE) field deviates from the passive FTLE field. In our work, we investigate the deformation of the cFTLE field from the passive FTLE on agents using model predictive control (MPC) to move through the flow. In particular, we investigate how changes in the control parameters produce deformations in the cFTLE ridges; these parameters include time horizon, energy penalty, and location of the goal target. These results could be useful in the context of agents navigating in the ocean, for example to generate high-level control policies or to decide where to deploy agents.