Exploring Grammar-Guided Design and Evolution of Polyominoes with Modular Soft Robots

Languages for describing two-dimensional (2-D) structures have become powerful tools across multiple fields, including pattern recognition, image processing, and the modeling of physical and chemical phenomena. One of such structures is labeled polyominoes, i.e., geometric shapes formed by connected unit squares arranged on a 2-D grid. In previous work, we introduced: (a) a novel grammar-based approach for defining sets of labeled polyominoes that satisfy predefined requirements, and (b) an algorithm to develop labeled polyominoes following the rules of the proposed grammar. We demonstrated that these two components enable optimization within the space of labeled polyominoes, similarly to how grammatical evolution and its extensions operate in string-based search spaces. In this work, we extend our previous approach to a new domain: the evolution of modular soft robots, namely, voxel-based soft robots (VSRs). We evolve VSRs for the task of energy-efficient locomotion, while constraining their physical structure to adhere to a given grammar. We show that the evolved robots successfully perform their assigned tasks and do have the required structure. These results highlight the potential of integrating domain knowledge through grammars to guide the evolutionary design of complex structure as modular soft robots.