Metamorphic Robots: Enumeration of Configurations and Motion Planning

This paper considers how to enumerate the basic set of all the non-isomorphic configurations of a planar metamorphic robotic system. Metamorphic robotic systems are being widely studied because their shape changing abilities make them potentially useful for a larger set of tasks that conventional robotic systems are unable to develop, for example reconnaissance, exploration, satellite recovery, or operation in constrained environments inaccessible to humans, (e.g., nuclear reactors, space or deep water). 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. Another issue considered in this paper is the motion planning of a metamorphic robot system, i.e., how to determine a sequence of module movements required to go from a given initial configurations to a desired final configuration. The paper solved the fundamental problem which is to determine the set of all possible configurations. Knowing all the possible configurations, the motion planning is solved with algorithms proposed in the literature.