In this paper, we study the Online Network Formation Problem (ONFP) for a
mobile multi-robot system. Consider a group of robots with a bounded
communication range operating in a large open area. One of the robots has a
piece of information which has to be propagated to all other robots. What
strategy should the robots pursue to disseminate the information to the rest of
the robots as quickly as possible? The initial locations of the robots are
unknown to each other, therefore the problem must be solved in an online
fashion.
For this problem, we present an algorithm whose competitive ratio is O(Hβ max{M,MHβ}) for arbitrary robot deployments, where M is the
largest edge length in the Euclidean minimum spanning tree on the initial robot
configuration and H is the height of the tree. We also study the case when
the robot initial positions are chosen uniformly at random and improve the
ratio to O(M). Finally, we present simulation results to validate the
performance in larger scales and demonstrate our algorithm using three robots
in a field experiment