"Small-World" Networks of Mobile Robots

Stergios I. Roumeliotis, Maja J. Mataric

Abstract: In order for a group of robots to coordinate collaboration during multi-robot tasks (Fontan & Mataric 1998), they need to communicate in an intelligent, purposeful way (Gerkey & Mataric 2000). If small groups of robots are involved, global communication (broadcasting, or one-to-all) is usually sufficient. The main advantage is that all the acquired information is available to all the members of the group. However when the number of robots increases so does the amount of data to handle. Information overflow can affect the performance of the separate teams working on different subtasks while limitations of the communication channel can cause interference and reduce the overall performance. A potential alternative to this would be to support local (oneto-a few) communication amongst the robots. The connectivity of such networks (communication topology) is usually assumed to be either completely regular (each robot communicates with its immediate neighbors forming a communication lattice), or completely random (each member of the group communicates with some random other members). However many biological, technological, and social networks lie somewhere between these two extremes (regular lattices vs. random graphs). Recently, a new form of coupled systems called “small-world” networks (Watts & Strogatz 1998), (Collins & Chow 1998), have been used to successfully describe the interactions of systems that can be highly clustered, like regular lattices, yet have small characteristic path lengths like random graphs. Regular networks are also known as “large-world” networks. They are highly clustered while the characteristic path length is large, scaling with the typical dimension n of the network. High clustering is appropriate for certain types of robotic tasks when information produced by individual robots is more likely to be used by neighboring robots. For example, a large number of robots distributed amongst a few teams each performing a different task that requires only local collaboration (e.g. one team is drillingand analyzing soil samples from a certain area while another team is assembling a solar panel) would benefit from such an arrangement of the communication sub-networks between the robots. On the other end, if these teams perform tasks that call for global collaboration (e.g. each team maps neighboring areas) then the size of the characteristic path length results in increased delays for the information to flow from one robot to all the others in the colony. This type of communication topology would reduce the efficiency of the collaboration amongst the sub-groups. In this latter case a random-graph type of connectivity would be ideal. Small characteristic path lengths would ensure that the information gathered by each individ-