Abstract
In this paper, we present CPL-Sync, a certifiably correct algorithm to solve planar pose graph optimization (PGO) using the complex number representation. We formulate planar PGO as the maximum likelihood estimation (MLE) on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to complex semidefinite programming (SDP). Furthermore, we simplify the corresponding semidefinite programming to Riemannian staircase optimization (RSO) on complex oblique manifolds that can be solved with the Riemannian trust region (RTR) method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through comparisons with existing methods as well as applications on planar PGO in simultaneous localization and mapping (SLAM), which indicates that the proposed algorithm is capable of solving planar PGO certifiably, and is more efficient in numerical computation and more robust to measurement noises than existing state-of-the-art methods. The C++ code for CPL-Sync is available at https://github.com/fantaosha/CPL-Sync.
Original language | English (US) |
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Title of host publication | 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2019 |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 1904-1911 |
Number of pages | 8 |
ISBN (Electronic) | 9781728140049 |
DOIs | |
State | Published - Nov 2019 |
Event | 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2019 - Macau, China Duration: Nov 3 2019 → Nov 8 2019 |
Publication series
Name | IEEE International Conference on Intelligent Robots and Systems |
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ISSN (Print) | 2153-0858 |
ISSN (Electronic) | 2153-0866 |
Conference
Conference | 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2019 |
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Country/Territory | China |
City | Macau |
Period | 11/3/19 → 11/8/19 |
Funding
This material is based upon work supported by the National Science Foundation under award DCSD-1662233.
ASJC Scopus subject areas
- Control and Systems Engineering
- Software
- Computer Vision and Pattern Recognition
- Computer Science Applications