  This paper considers deployment problems where a mobile robotic network must
optimize its configuration in a distributed way in order to minimize a
steady-state cost function that depends on the spatial distribution of certain
probabilistic events of interest. Moreover, it is assumed that the event
location distribution is a priori unknown, and can only be progressively
inferred from the observation of the actual event occurrences. Three classes of
problems are discussed in detail: coverage control problems, spatial
partitioning problems, and dynamic vehicle routing problems. In each case,
distributed stochastic gradient algorithms optimizing the performance objective
are presented. The stochastic gradient view simplifies and generalizes
previously proposed solutions, and is applicable to new complex scenarios, such
as adaptive coverage involving heterogeneous agents. Remarkably, these
algorithms often take the form of simple distributed rules that could be
implemented on resource-limited platforms.
