Stabilisation of infinitesimally rigid formations of multi-robot networks

Abstract

This article considers the design of a formation control for multivehicle systems that uses only local information. The control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation. A potential function is obtained from the graph, from which a gradient control is derived. Under this controller the target formation becomes a manifold of equilibria for the multivehicle system. It is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold. A complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well. Finally, the controller is validated experimentally.

Keywords:

• cooperative control
• multiagent formations
• graph rigidity

Acknowledgements

The authors thank Manfredi Maggiore for a helpful discussion on centre manifold theory.

Notes

Note

1. The notation e _i is used to refer both to the edge i and as an error vector pointing in the direction of edge i in the framework.