CPL-SLAM: Efficient and Certifiably Correct Planar Graph-Based SLAM Using the Complex Number Representation
CPL-SLAM: Efficient and Certifiably Correct Planar Graph-Based SLAM Using the Complex Number Representation
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DOI：
10.1109/tro.2020.3006717
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发表时间：
2020-12-01
影响因子：
7.8
通讯作者：
Murphey, Todd
中科院分区：
文献类型：
--
作者：
Fan, Taosha;Wang, Hanlin;Murphey, Todd
在这篇文章中，我们考虑的问题，平面图为基础的同时定位和映射（SLAM），涉及到自主代理和观察到的地标的位置。我们提出了复杂的（CPL）-SLAM，一个有效的和可证明正确的算法来解决平面图为基础的SLAM使用复数表示。我们制定和简化平面图为单位复数的乘积的最大似然估计的SLAM，并放松这个非凸二次复杂的优化问题凸复半定规划（SDP）。此外，我们将相应的复SDP简化为复斜流形上的黎曼阶梯优化（RSO），可以用黎曼信赖域方法求解。此外，我们证明了SDP松弛和RSO简化是紧的，只要噪声幅度低于一定的阈值。通过CPL-SLAM的应用以及与现有的基于平面图的SLAM方法的比较，验证了本文算法的有效性，表明本文算法能够有效地求解基于平面图的SLAM问题，并且比现有的基于平面图的SLAM方法具有更高的数值计算效率和更强的测量噪声鲁棒性. CPL-SLAM的C++代码可在https://github.com/MurpheyLab/CPL-SLAM上获得。
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.