Scale-Adaptive Polygonal Formations of Submersible Vehicles and Tracking Isocontours

Building on the assumption that identification of a sufficient number of isoclines of an environmental field (such as the ocean bottom terrain) allows efficient reconstruction of the field, in this paper, a sequel to [1], we describe a system where a group of robots in a spacial arrangement (a regular polygon centred around a lead robot) locally construct the field (measured at the locations of the robots) inside the polygonal area using interpolation by barycentric coordinates. If the error of interpolation is small enough, the corresponding isocline of the interpolated field will match the real isocline accurately enough. Tracking this isocline in a certain direction will then allow robust traversal of field isoclines. We use the measurement at the centre of the formation to adjust the size of the polygon to obtain desired accuracy.