  This paper addresses an Optimal Transport (OT)-based efficient multi-robot
exploration problem, considering the energy constraints of a multi-robot
system. The efficiency in this problem implies how a team of robots (agents)
covers a given domain, reflecting a priority of areas of interest represented
by a density distribution, rather than simply following a preset of uniform
patterns. To achieve an efficient multi-robot exploration, the optimal
transport theory that quantifies a distance between two density distributions
is employed as a tool, which also serves as a means of performance measure. The
energy constraints for the multi-robot system is then incorporated into the
OT-based multi-robot exploration scheme.
  The proposed scheme is decoupled from robot dynamics, broadening the
applicability of the multi-robot exploration plan to heterogeneous robot
platforms. Not only the centralized but also decentralized algorithms are
provided to cope with more realistic scenarios such as communication range
limits between agents. To measure the exploration efficiency, the upper bound
of the performance is developed for both the centralized and decentralized
cases based on the optimal transport theory, which is computationally tractable
as well as efficient. The proposed multi-robot exploration scheme is also
applicable to a time-varying distribution, where the spatio-temporal evolution
of the given reference distribution is desired. To validate the proposed
method, multiple simulation results are provided.
