Contour shaped formation control for autonomous underwater vehicles using canonical shape descriptors and deformable models

Cooperative tasks such as swarms following gradients, detecting environmental boundaries (defining natural features) and exploration by aggregates of mobile autonomous robots have gained much attention in the past few years. Aggregates come in various forms including rigid formations, involving a few robots, with clearly-defined simple shapes or swarms, with up to hundreds of robots, but with no particular shape characteristics. In the afore-mentioned tasks, a large aggregate is required to form complex shapes. When the number of robots increases, it is very difficult or even senseless to manually determine the position of each and every agent within the formation. In this paper, we concentrate on a special kind of geometric formation (open and closed contours). We use Fourier descriptors, as one of the most natural ways of representing curves, and active contour models, to make the aggregate exhibit desirable physical behaviours. We apply these kinds of formations to the case of autonomous underwater vehicles collectively exploring, mapping, and adapting to environmental features. Many of the features found in underwater landscapes are shaped as open or closed contours so that the proposed combination makes sense. In our approach, a group of mobile agents can synthesize a curve given a small set of canonical invariant descriptors.