Beacon Election and Path Planning for Heterogeneous Underwater Vehicles

Navigation error for swarming vehicles grows as a function of time, especially in GPS-denied environments, such as underwater. We seek to address this problem by minimizing the swarm navigation error of underwater vehicles using a dynamic selection of a single vehicle, known as a beacon, to intermittently surface for navigation corrections. We propose an auction-based algorithm that maximizes Kullback-Leibler (KL) divergence while minimizing surfacing duration using a receding horizon control approach. The algorithm is novel as it minimizes surfacing of vehicles, thereby saving energy and reducing the incidence of surface collisions. Our algorithm is compared to several alternative strategies including a scheduled surfacing approach, constrained surfacing duration, and constrained beacon behavior using numerical simulations.