Configuration Enumeration of Multi-Limb Reconfigurable Modular Robots

By introducing modular and reconfigurable designs, the Multi-limb Reconfigurable Modular Robots (MLRMR) have many different configurations instead of a single fixed configuration, which greatly expands the boundaries of the operation. However, the number of non-isomorphic configurations increases exponentially with the number of modules, making it necessary to explore the enumeration method theoretically. Based on the group theory, the permutation groups of the Multi-limb (including three-limb, four-limb, and five-limb) Reconfigurable Modular Robots are established in this paper, and the theoretical formulas of configuration enumeration are derived by applying the Pólya enumeration theorem. This work can be used as the basis of configuration analysis.