In the formation control problem for autonomous robots a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a Lyapunov-based approach. It is well known that there are various other undesired invariant sets of the robots' closed-loop dynamics. This paper addresses a global stability analysis by a differential geometric approach considering invariant manifolds and their local stability properties. The theoretical results are then applied to the well-known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation.
@article{arxiv.1001.4494,
title = {Geometric Analysis of the Formation Problem for Autonomous Robots},
author = {Florian Dorfler and Bruce Francis},
journal= {arXiv preprint arXiv:1001.4494},
year = {2010}
}
Comments
submitted to the IEEE Transaction on Automatic Control