Toward efficient navigation in uncertain gyre-like flows

Abstract

We present the development and experimental validation of an autonomous surface/underwater vehicle control strategy that leverages the environmental dynamics and uncertainty to navigate in a stochastic fluidic environment. We assume that the workspace is composed of the union of a collection of disjoint regions, each bounded by Lagrangian coherent structures (LCSs). LCSs are dynamical features in the flow field that behave like invariant manifolds in general time-invariant dynamical systems and delineate the boundaries of attraction basins. We analyze a passive particle’s noise-induced transition between adjacent LCS-bounded regions and show how most probable escape trajectories with respect to the transition probability between adjacent LCS-bounded regions can be determined. Additionally, we show how the likelihood of transition can be controlled through minimal actuation. The result is an energy efficient navigation strategy that leverages the inherent dynamics of the surrounding flow field for mobile sensors operating in a noisy fluidic environment. We experimentally validate the proposed vehicle control strategy and analyze its theoretical properties. Our results show that the single vehicle control parameter exhibits a predictable exponential scaling with respect to the escape times and is effective even in situations where the structure of the flow is not fully known and control effort is costly.