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

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...

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Vydané v:IEEE transactions on robotics Ročník 36; číslo 6; s. 1719 - 1737
Hlavní autori: Fan, Taosha, Wang, Hanlin, Rubenstein, Michael, Murphey, Todd
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.12.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Algorithms
Autonomous agents
certifiably correct algorithms
Complex numbers
Maximum likelihood estimation
Noise measurement
Numerical analysis
Optimization
pose graph optimization
Representations
Robustness (mathematics)
Semidefinite programming
Simultaneous localization and mapping
ISSN:1552-3098, 1941-0468
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Shrnutí: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. The C++ code for CPL-SLAM is available at https://github.com/MurpheyLab/CPL-SLAM .
Bibliografia:ObjectType-Article-1
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ISSN:1552-3098
1941-0468
DOI:10.1109/TRO.2020.3006717