  When nodes in a mobile network use relative noisy measurements with respect
to their neighbors to estimate their positions, the overall connectivity and
geometry of the measurement network has a critical influence on the achievable
localization accuracy. This paper considers the problem of deploying a mobile
robotic network implementing a cooperative localization scheme based on range
measurements only, while attempting to maintain a network geometry that is
favorable to estimating the robots' positions with high accuracy. The quality
of the network geometry is measured by a "localizability" function serving as
potential field for robot motion planning. This function is built from the
Cram\'er-Rao bound, which provides for a given geometry a lower bound on the
covariance matrix achievable by any unbiased position estimator that the robots
might implement using their relative measurements. We describe gradient
descent-based motion planners for the robots that attempt to optimize or
constrain different variations of the network's localizability function, and
discuss ways of implementing these controllers in a distributed manner.
Finally, the paper also establishes formal connections between our statistical
point of view and maintaining a form of weighted rigidity for the graph
capturing the relative range measurements.
