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When nodes in a mobile network use relative noisy measurements with respectto their neighbors to estimate their positions, the overall connectivity andgeometry of the measurement network has a critical influence on the achievablelocalization accuracy. This paper considers the problem of deploying a mobilerobotic network implementing a cooperative localization scheme based on rangemeasurements only, while attempting to maintain a network geometry that isfavorable to estimating the robots' positions with high accuracy. The qualityof the network geometry is measured by a "localizability" function serving aspotential field for robot motion planning. This function is built from theCram\'er-Rao bound, which provides for a given geometry a lower bound on thecovariance matrix achievable by any unbiased position estimator that the robotsmight implement using their relative measurements. We describe gradientdescent-based motion planners for the robots that attempt to optimize orconstrain different variations of the network's localizability function, anddiscuss ways of implementing these controllers in a distributed manner.Finally, the paper also establishes formal connections between our statisticalpoint of view and maintaining a form of weighted rigidity for the graphcapturing the relative range measurements.

Localizability-Constrained Deployment of Mobile Robotic Networks with Noisy Range Measurements