This paper transforms the problem of droplet routing for digital microfluidic biochips (DMFBs) from the discrete into the continuous domain, based on the observation that droplet transport velocity is a function of the actuation voltage applied to electrodes that control the devices. A new formulation of the DMFB droplet routing problem is introduced for the continuous domain, which attempts to minimize total energy consumption while meeting a timing constraint. Henceforth, DMFBs should be viewed as continuous, highly integrated cyber-physical systems that interact with and manipulate physical quantities, as opposed to inherently discrete and fully synchronized devices. © 2014 IEEE.