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Given a multi-robot system, in order to preserve its geometric shape in a formation, the minimal persistence control addresses questions: (1) what pairwise communication connections have to be prescribed to minimize communication channels, and (2) which orientations of communication links are to be placed between robots. In this paper, we propose a minimal persistence control problem on multi-robot systems with underlying graphs, being directed and dynamically switching. We develop distributed algorithms based on the rank of the rigidity matrix and the pebble game method. The feasibility of the proposed methods is validated by simulations on the robotic simulator Webots and experiments on e-puck robot platform.

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