Reconfigurability in versatile systems of modular robots is achieved by appropriately actuating individual modular units. Optimizing the distribution of active and passive modules in modular architecture can significantly reduce both cost and energy of a reconfiguration task. This paper presents a methodology for planning this distribution in modular robots, resulting in a minimum number of active modules that guarantees the capability to reconfigure. We discuss the optimal distribution problem in layout-based and target-based planning schemes such that modular robots can instantly respond to reconfiguration commands with either an initial planar layout or a target configuration as input. We propose heuristic algorithms as solutions for the different scenarios, which we demonstrate by applying them to Mori, a modular origami robot, in simulation. The results show that our algorithms yield high-quality distribution schemes in reduced time, and are thus viable for real-time applications in modular robotic systems.

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