Enumeration of planar metamorphic robots configurations

This paper considers how to enumerate all the non-isomorphic configurations of a planar metamorphic robotic system. A metamorphic robotic system is a collection of mechatronic modules that can dynamically self-reconfigure in a variety of configurations, kinematic chains, to meet different or changing task requirements. However, due to typical symmetries in module design, different assemblies may generate isomorphic robotic structures. To solve this problem, we use group theory tools for the identification of symmetries of metamorphic robotic systems. In particular, we define the concept of binary orbits of the automorphism group of the graphs associated with the metamorphic robot configurations.