Efficient and Guaranteed Planar Pose Graph optimization Using the Complex Number Representation

Taosha Fan, Hanlin Wang, Michael Rubenstein, Todd Murphey

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

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 languageEnglish (US)
Title of host publication2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1904-1911
Number of pages8
ISBN (Electronic)9781728140049
DOIs
StatePublished - Nov 2019
Event2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2019 - Macau, China
Duration: Nov 3 2019Nov 8 2019

Publication series

NameIEEE International Conference on Intelligent Robots and Systems
ISSN (Print)2153-0858
ISSN (Electronic)2153-0866

Conference

Conference2019 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2019
Country/TerritoryChina
CityMacau
Period11/3/1911/8/19

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Computer Vision and Pattern Recognition
  • Computer Science Applications

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