This paper proposes a method for controlling formations of autonomous nonholonomic vehicles in order to reach a desired target region. The approach is based on utilization of pairs of virtual leaders whose control inputs are obtained in a single optimization process using model predictive control (MPC) methodology. The obtained solution of the optimization includes both a complete plan for the formation including the overall structure of robots' workspace and control inputs for each vehicle. This ensures collision-free trajectories between the robots as well as dynamic obstacles. The proposed method enables to autonomously design arbitrary manoeuvres, like reverse driving or rotations of compact formations of car-like robots. Such a complicated behavior is illustrated by simulations and by experiments. Furthermore, the requirements that guarantee convergence of the group to the target region are formulated.
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