Active Singularities for Multivehicle Motion Planning in an N-Vortex System

This paper presents a path-planning paradigm for distributed control of multiple sensor platforms in a geophysical flow well-approximated by a point-vortex model. We utilize Hamiltonian dynamics to generate control vector fields for vehicle motion in N -vortex flows using the concept of an active singularity whose strength is a tunable control input. We introduce active singularities that are virtual point vortices possibly collocated with virtual point sources or sinks. We provide a principled method to stabilize relative equilibria of these virtual vortices in the presence of the actual point vortices, which represent the underlying geophysical flow. We illustrate how these relative equilibria may be useful for vehicle path planning and sampling in a geophysical flow. Preliminary results presented here are based on an adaptive control design.