Generalizing metamodules to simplify planning in modular robotic systems

In this paper we develop a theory of metamodules and an associated distributed asynchronous planner which generalizes previous work on metamodules for lattice-based modular robotic systems. All extant modular robotic systems have some form of non-holonomic motion constraints. This has prompted many researchers to look to metamodules, i.e., groups of modules that act as a unit, as a way to reduce motion constraints and the complexity of planning. However, previous metamodule designs have been specific to a particular modular robot. By analyzing the constraints found in modular robotic systems we develop a holonomic metamodule which has two important properties: (1) it can be used as the basic unit of an efficient planner and (2) it can be instantiated by a wide variety of different underlying modular robots, e.g., modular robot arms, expanding cubes, hex-packed spheres, etc. Using a series of transformations we show that our practical metamodule system has a provably complete planner. Finally, our approach allows the task of shape transformation to be separated into a planning task and a resource allocation task. We implement our planner for two different metamodule systems and show that the time to completion scales linearly with the diameter of the ensemble.