Distributed reconfiguration of 2D lattice-based modular robotic systems

We prove universal reconfiguration (i.e., reconfiguration between any two robotic systems with the same number of modules) of 2-dimensional lattice-based modular robots by means of a distributed algorithm. To the best of our knowledge, this is the first known reconfiguration algorithm that applies in a general setting to a wide variety of particular modular robotic systems, and holds for both square and hexagonal lattice-based 2-dimensional systems. All modules apply the same set of local rules (in a manner similar to cellular automata), and move relative to each other akin to the sliding-cube model. Reconfiguration is carried out while keeping the robot connected at all times. If executed in a synchronous way, any reconfiguration of a robotic system of n modules is done in O(n) time steps with O(n) basic moves per module, using O(1) force per module, O(1) size memory and computation per module (except for one module, which needs O(n) size memory to store the information of the goal shape), and O(n) communication per module.