Cpl-slam: Efficient and certifiably correct planar graph-based slam using the complex number representation

Taosha Fan, Hanlin Wang, Michael Rubenstein, Todd Murphey*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


In this article, we consider the problem of planar graph-based simultaneous localization and mapping (SLAM) that involves both poses of the autonomous agent and positions of observed landmarks. We present complex (CPL)-SLAM, an efficient and certifiably correct algorithm to solve planar graph-based SLAM using the complex number representation. We formulate and simplify planar graph-based SLAM as the maximum likelihood estimation on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to convex complex semidefinite programming (SDP). Furthermore, we simplify the corresponding complex SDP to Riemannian staircase optimization (RSO) on the complex oblique manifold that can be solved with the Riemannian trust region 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 applications of CPL-SLAM and comparisons with existing state-of-the-art methods on planar graph-based SLAM, which indicates that our proposed algorithm is capable of solving planar graph-based SLAM certifiably, and is more efficient in numerical computation and more robust to measurement noise than existing state-of-the-art methods.

Original languageEnglish (US)
Article number9143200
Pages (from-to)1719-1737
Number of pages19
JournalIEEE Transactions on Robotics
Issue number6
StatePublished - Dec 2020


  • certifiably correct algorithms
  • pose graph optimization
  • simultaneous localization and mapping

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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