This paper is concerned with the decentralized formation control of multi-agent systems moving in the plane using rigid graph theory. Using a double-integrator agent model (as opposed to the simpler, single-integrator model), we propose a new control law to asymptotically stabilize the interagent distance error dynamics. Our approach uses simple backstepping and Lyapunov arguments. The control, which is explicitly dependent on the rigidity matrix of the undirected graph that models the formation, is derived for a class of potential functions. Specific potential functions are then used as a demonstration inclusive of simulation results.

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