Enumeration of Configurations and Their Kinematics for ModRED II Modular Robots

Modular robotics is a popular topic for robotic applications and design. The reason behind this popularity is the ability to use and reuse the same robot modules for accomplishing different tasks through reconfiguration. The robots are capable of self-reconfiguration based on the requirements of the task and environmental constraints. It is possible to have a large number of configuration combinations for the same set of modules. Therefore, it is important to identify unique configurations from among the full set of possible configurations and establish a kinematic strategy for each before reconfiguring the robots into a new shape. This becomes more difficult for robot units having more than one connection type and more degrees of freedom (DOF) For example, ModRED II modules have two types of connections and four DOF per module. In this paper, the set of configurations is enumerated, and determination of configuration isomorphism is accomplished for ModRED II modules using graph theory. Kinematic equations are then derived for unique configurations. The kinematic method is then demonstrated for certain example configurations using ModRED II modules.