  This paper presents an approach to externally influencing a team of robots by
means of time-varying density functions. These density functions represent
rough references for where the robots should be located. To this end, a
continuous-time algorithm is proposed that moves the robots so as to provide
optimal coverage given the density functions as they evolve over time. The
developed algorithm represents an extension to previous coverage algorithms in
that time-varying densities are explicitly taken into account in a provable
manner. A distributed approximation to this algorithm is moreover proposed
whereby the robots only need to access information from adjacent robots.
Simulations and robotic experiments show that the proposed algorithms do indeed
exhibit the desired behaviors in practice as well as in theory.
