{"paper":{"title":"Rigidity Theory in SE(2) for Unscaled Relative Position Estimation using only Bearing Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Antonio Franchi, Daniel Zelazo, Paolo Robuffo Giordano","submitted_at":"2013-11-05T13:12:10Z","abstract_excerpt":"This work considers the problem of estimating the unscaled relative positions of a multi-robot team in a common reference frame from bearing-only measurements. Each robot has access to a relative bearing measurement taken from the local body frame of the robot, and the robots have no knowledge of a common or inertial reference frame. A corresponding extension of rigidity theory is made for frameworks embedded in the \\emph{special Euclidean group} $SE(2) = \\mathbb{R}^2 \\times \\mathcal{S}^1$. We introduce definitions describing rigidity for $SE(2)$ frameworks and provide necessary and sufficient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1044","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}