Formations for fast locomotion of metamorphic robotic systems

In this paper, we examine the problem of dynamic self-reconfiguration of a modular robotic system (frequently referred to as a self-reconfigurable or metamorphic system), to a formation aimed at reaching a specified target position as quickly as possible. We present a number of fast formations for both rectangular and hexagonal systems, and prove upper and lower bounds on the speed of locomotion. In particular, the formations presented here achieve a constant ratio guarantee on the time to reach a given target in the asymptotic sense.