Copyright © 2013 E. G. Hernandez-Martinez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Inspired from the collective behavior of biological entities for the group motion coordination, this paper analyzes the formation control of mobile robots in discrete time where each robot can sense only the position of certain team members and the group behavior is achieved through the local interactions of robots. The main contribution is an original formal proof about the global convergence to the formation pattern represented by an arbitrary Formation Graph using attractive potential functions. The analysis is addressed for the case of omnidirectional robots with numerical simulations.