Fuel-efficient navigation in complex flows

In realistic time-chaotic flows, the time-dependent separatrices are revealed by Lagrangian coherent structures (LCS). The LCS surfaces organize complex flows, revealing dynamical channels useful for weakly propelled mobile agents. We propose a feedback control strategy to explicitly incorporate LCS, which are in general evolving. Inanc et al. (2005) observed that the fuel optimal trajectory in ocean flow seems to lie on a moving LCS surface. We take this observation a step further by explicitly incorporating the moving LCS location into the control strategy. We have the vehicle track an LCS surface, considering this a time-dependent boundary following problem, with the aim of following lanes of fuel-efficient motion delineated by LCS surfaces. We demonstrate this strategy in a double-gyre flow and find that indeed a strategy using LCS is feasible and uses less fuel than a naive direct targeting approach.