{"ID":2864156,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.23656","arxiv_id":"2509.23656","title":"Certifiably Optimal Estimation and Calibration in Robotics via Trace-Constrained Semi-Definite Programming","abstract":"Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them to rank-1 matrices, a condition that can be challenging to achieve. In this work, we focus on trace-constrained SDPs (TCSDPs), where the decision variables are Positive Semi-Definite (PSD) matrices with fixed trace values. We show that the latter can be used to design a gradient-based refinement procedure that projects relaxed SDP solutions toward rank-1, low-cost candidates. We also provide fixed-trace SDP relaxations for common robotic quantities, such as rotations and translations, and a modular virtual robot abstraction that simplifies modeling across different problem settings. We demonstrate that our trace-constrained SDP framework can be applied to many robotics tasks, and we showcase its effectiveness through simulations in Perspective-n-Point (PnP) estimation, hand-eye calibration, and dual-robot system calibration.","short_abstract":"Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them to rank-1 matrices, a condition that can be challenging to achieve. In this work...","url_abs":"https://arxiv.org/abs/2509.23656","url_pdf":"https://arxiv.org/pdf/2509.23656v2","authors":"[\"Liangting Wu\",\"Roberto Tron\"]","published":"2025-09-28T05:46:35Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[]","has_code":false}