Certifiably Optimal Estimation and Calibration in Robotics via Trace-Constrained Semi-Definite Programming
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916981404336128 |
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| author | Wu, Liangting Tron, Roberto |
| author_facet | Wu, Liangting Tron, Roberto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Certifiably Optimal Estimation and Calibration in Robotics via Trace-Constrained Semi-Definite Programming Wu, Liangting Tron, Roberto Robotics 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. |
| title | Certifiably Optimal Estimation and Calibration in Robotics via Trace-Constrained Semi-Definite Programming |
| topic | Robotics |
| url | https://arxiv.org/abs/2509.23656 |