  In robotic networks relying on noisy range measurements between agents for
cooperative localization, the achievable positioning accuracy strongly strongly
depends on the network geometry. This motivates the problem of planning robot
trajectories in such multi-robot systems in a way that maintains high
localization accuracy. We present potential-based planning methods, where
localizability potentials are introduced to characterize the quality of the
network geometry for cooperative position estimation. These potentials are
based on Cramer Rao Lower Bounds (CRLB) and provide a theoretical lower bound
on the error covariance achievable by any unbiased position estimator. In the
process, we establish connections between CRLBs and the theory of graph
rigidity, which has been previously used to plan the motion of robotic
networks. We develop decentralized deployment algorithms appropriate for large
networks, and we use equality-constrained CRLBs to extend the concept of
localizability to scenarios where additional information about the relative
positions of the ranging sensors is known. We illustrate the resulting robot
deployment methodology through simulated examples and an experiment.
