Localizability-Constrained Deployment of Mobile Robotic Networks with Noisy Range Measurements
This addresses the challenge of achieving high localization accuracy in mobile robotic networks, which is incremental as it builds on existing statistical and graph rigidity concepts.
The paper tackles the problem of deploying mobile robotic networks to maintain favorable geometries for accurate cooperative localization using noisy range measurements, by designing gradient descent-based motion planners that optimize a localizability function derived from the Cramér-Rao bound.
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 Cramér-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.