  Volumetric objectives for exploration and perception tasks seek to capture a
sense of value (or reward) for hypothetical observations at one or more camera
views for robots operating in unknown environments. For example, a volumetric
objective may reward robots proportionally to the expected volume of unknown
space to be observed. We identify connections between existing
information-theoretic and coverage objectives in terms of expected coverage,
particularly that mutual information without noise is a special case of
expected coverage. Likewise, we provide the first comparison, of which we are
aware, between information-based approximations and coverage objectives for
exploration, and we find, perhaps surprisingly, that coverage objectives can
significantly outperform information-based objectives in practice.
Additionally, the analysis for information and coverage objectives demonstrates
that Randomized Sequential Partitions -- a method for efficient distributed
sensor planning -- applies for both classes of objectives, and we provide
simulation results in a variety of environments for as many as 32 robots.
