Curve shortening-inspired self-reconfiguration of heterogenous hexagonal-shaped modules toward a straight chain

This study deals with a self-reconfiguration problem of hexagonal-shaped modules from an arbitrary initial configuration to a straight chain. Modules are modeled as the same-sized rigid bodies. Two categories of modules with different functionalities are used. One category comprises two powerful modules, which are expected to play the role of terminal modules in a goal configuration. The other category comprises several ordinary modules, which are expected to fill in the middle portion in a goal configuration. A distributed control strategy, inspired by the idea of curve shortening, is developed for each module to act cooperatively to attain a goal configuration. It is verified that under the proposed strategy, modules eventually converge to a straight chain.