Enumerating the Nonisomorphic Configurations of a Modular Reconfigurable Robot

Abstract

By introducing the modular and reconfigurable design, the limbs of a hexapod robot can be assembled into different configurations to meet various task requirements. Contrary to the fixed configuration system, the task capabilities of the modular reconfigurable robot vary with the configurations. This article addresses the problem of the configuration enumeration and configuration expression of a modular reconfigurable robot. First, by establishing the permutation group of the regular hexagon (the base shape of the modular reconfigurable robot) and adopting the Pólya enumeration theorem, the theoretical formula of the nonisomorphic configuration enumeration is derived. Then, considering the change in structural features, equivalence relations based on structural features are defined and the structural feature method (SFM) is proposed to enumerate the nonisomorphic configurations. In addition, to express configurations more intuitively, a senary vertex identification array with the same dimension as the number of modules is presented, which can be transformed from the decimal index of the configuration. Simulation analysis demonstrates that the result of the SFM is consistent with that of the theoretical calculation, which also confirms the effectiveness and accuracy of the two methods applied in the nonisomorphic configuration enumeration of the modular reconfigurable robot.