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.
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.