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In this paper, we consider the problem of planar graph-based simultaneouslocalization and mapping (SLAM) that involves both poses of the autonomousagent and positions of observed landmarks. We present CPL-SLAM, an efficientand certifiably correct algorithm to solve planar graph-based SLAM using thecomplex number representation. We formulate and simplify planar graph-basedSLAM as the maximum likelihood estimation (MLE) on the product of unit complexnumbers, and relax this nonconvex quadratic complex optimization problem toconvex complex semidefinite programming (SDP). Furthermore, we simplify thecorresponding complex semidefinite programming to Riemannian staircaseoptimization (RSO) on the complex oblique manifold that can be solved with theRiemannian trust region (RTR) method. In addition, we prove that the SDPrelaxation and RSO simplification are tight as long as the noise magnitude isbelow a certain threshold. The efficacy of this work is validated throughapplications of CPL-SLAM and comparisons with existing state-of-the-art methodson planar graph-based SLAM, which indicates that our proposed algorithm iscapable of solving planar graph-based SLAM certifiably, and is more efficientin numerical computation and more robust to measurement noise than existingstate-of-the-art methods. The C++ code for CPL-SLAM is available athttps://github.com/MurpheyLab/CPL-SLAM.

CPL-SLAM: Efficient and Certifiably Correct Planar Graph-Based SLAM Using the Complex Number Representation