This paper is concerned with the decentralized formation control of multi-agent systems moving in the plane. Using a single-integrator agent model, we propose a new distributed control law to asymptotically stabilize the inter-agent distance error dynamics. Our approach exploits the infinitesimal and minimal rigidity of the undirected graph that models the formation. A Lyapunov-based analysis shows that these two properties are necessary conditions for asymtptotic stability. The control, which is explicitly dependent on the graph rigidity matrix, is derived for a class of potential functions.

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