Distributed Localization of Modular Robot Ensembles

Internal localization, the problem of estimating relative pose for each module of a modular robot, is a prerequisite for many shape control, locomotion, and actuation algorithms. In this paper, we propose a robust hierarchical approach that uses normalized cut to identify dense sub-regions with small mutual localization error, then progressively merges those sub-regions to localize the entire ensemble. Our method works well in both two and three dimensions, and requires neither exact measurements nor rigid inter-module connectors. Most of the computations in our method can be distributed effectively. The result is a robust algorithm that scales to large ensembles. We evaluate our algorithm in two- and three-dimensional simulations of scenarios with up to 10,000 modules.