| This thesis designs a formation control for multivehicle systems that uses only local information. Formation control of this type can be applied in mobile sensor networks applications.;The control is derived from a potential function based on an undirected infinitesimally rigid graph. This graph specifies the target formation. Then the potential function is used to specify a gradient control, under with the target formation then becomes a manifold of equilibria for the multivehicle system. The stability of this manifold is studied using a nonlinear coordinate transformation and linearization techniques.;Using these techniques, we show that the infinitesimal rigidity condition of the formation graph provides a sufficient condition to show that the equilibrium manifold is locally asymptotically stable. Finally, a complete study of the stability of the regular polygon formation is presented. These results were validated experimentally. |
