TY - GEN
T1 - Efficient and Guaranteed Planar Pose Graph optimization Using the Complex Number Representation
AU - Fan, Taosha
AU - Wang, Hanlin
AU - Rubenstein, Michael
AU - Murphey, Todd
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under award DCSD-1662233.
Publisher Copyright:
© 2019 IEEE.
PY - 2019/11
Y1 - 2019/11
N2 - 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.
AB - 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.
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U2 - 10.1109/IROS40897.2019.8968044
DO - 10.1109/IROS40897.2019.8968044
M3 - Conference contribution
AN - SCOPUS:85081157208
T3 - IEEE International Conference on Intelligent Robots and Systems
SP - 1904
EP - 1911
BT - 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2019
Y2 - 3 November 2019 through 8 November 2019
ER -