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

Abstract. 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 con-cept 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 geo-physical 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