Optima localization by vehicle formations imitating the Nelder-Mead simplex algorithm

In this paper, we address the problem of localizing extrema points and iso-contours of ambient environmental fields (specifically, ocean bottom landscape and underwater plumes) using a networked formation of autonomous underwater vehicles. We propose the use of the Nelder-Mead extension to the basic simplex nonlinear optimization algorithm. In these robust gradient-free strategies, decisions are solely made based on field values measured by the individual vehicles, while measurements are fused and actions decided according to the algorithm. A main goal of this paper is to trigger interest in direct search methods as pertains to this type of robotic problem.