High speed formations of reconfigurable modular robotic systems

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