Control of Contour Formations of Autonomous Vehicles by General Curve Evolution Theory

Abstract

In this paper, we introduce the concept of a contour- shaped formation of autonomous underwater vehicles for the purpose of adaptation to isoclines of environmental fields created as a result of diffusion of chemicals. General curvature-driven curve evolution theory is used as a continuum model for such formations. A collection of robots can act as markers on an imaginary curve moving according to the local curvature and the external environmental force projected unto the normal to the curve. Basic control rules are given, and various strategies for implementation of the scheme are explored. Algorithms are discussed for formation initialization, and simulation runs are presented to demonstrate the behaviour of these types of formations.