Touring the invariant sets of a two-vortex system using streamline control

This paper presents path planning and control of an intermittently actuated autonomous vehicle for oceanographic sampling based on Lagrangian data. The focus is an idealized ocean-eddy system represented by two point vortices. We partition the model of the underlying flow into distinct invariant regions and use this geometry to plan informative vehicle tours. We propose that crossing boundaries invariant to passive particles and visiting invariant zones increases the overall nonlinear observability of the flow field parameters. We validate the importance of invariant sets and zone boundaries using an existing estimation metric, the unobservability index. To transition between invariant sets, we use a novel control law that drives a vehicle to a desired streamline of a flow field together with another controller based on the idea of inserting a virtual cylinder into the flow. Numerical experiments show the proposed zone-touring algorithm yields planned paths with high observability of the flow field parameters as compared to all possible drifter orbits in a two-vortex system.