Abstract
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.
Highlights
Large self-reconfigurable modular robots have received a growing interest from the robotics community
We demonstrate that the computational complexity of the approach is nearly linear in the size of the ensemble for a fixed ensemble structure, and outperforms methods from wireless sensor network localization based on classical multidimensional scaling [12] and semidefinite programming (SDP) relaxations [9, 10], as well as simpler incremental heuristics
We examine large-scale localization in modular robot ensembles using uncertain, local observations
Summary
Large self-reconfigurable modular robots have received a growing interest from the robotics community. Constraint-based approaches [4, 3, 5] rely on strong prior assumptions about ensemble structure (e.g., lattices) or require exact observations to scale up to large ensembles They are neither robust to noise nor well suited to irregular, non-lattice structures, common in some SRMRs. Local probabilistic approaches have been shown to be effective in localization of relatively small modular robots, such as PolyBot[6], but require assumptions of strong sensing, or robust mechanical latching to reduce errors in larger systems. A key challenge in internal localization is that observations are not stored centrally, and it is not feasible to collect the observations to a single node This calls for a distributed approach, but the recursive nature of our algorithm and top-down partitioning make a distributed implementation difficult to achieve. We demonstrate that the computational complexity of the approach is nearly linear in the size of the ensemble for a fixed ensemble structure, and outperforms methods from wireless sensor network localization based on classical multidimensional scaling [12] and semidefinite programming (SDP) relaxations [9, 10], as well as simpler incremental heuristics
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