论文标题
CPL-SLAM：使用复杂的数字表示，有效且有效地正确正确的基于平面图的大满贯
CPL-SLAM: Efficient and Certifiably Correct Planar Graph-Based SLAM Using the Complex Number Representation
论文作者
论文摘要
在本文中，我们考虑了基于平面图的同时定位和映射（SLAM）的问题，该问题涉及自主剂的姿势和观察到的地标的位置。我们提出了CPL-SLAM，这是一种有效且证明正确的算法，可使用复杂的数字表示来求解基于平面图的SLAM。我们将基于平面图的SLAM制定并简化为单位络合物乘积的最大似然估计（MLE），并放松此非convex二次复杂的复杂优化问题，以凸出复杂的复杂的半决赛半决赛编程（SDP）。此外，我们将相应的复杂半芬矿编程简化为复杂斜面歧管上的Riemannian楼梯优化（RSO），可以用Riemannian Trust区域（RTR）方法解决。此外，我们证明只要噪声幅度低于一定阈值，SDP松弛和RSO简化就很紧。这项工作的功效是通过CPL-SLAM的应用以及与基于平面图的SLAM的现有最新方法的应用来验证的，这表明我们提出的算法能够确认基于平面的SLAM认证，并且在数值计算方面更有效，并且比现有状态的方法更有效，并且对测量噪声更强大。 CPL-SLAM的C ++代码可在https://github.com/murpheylab/cpl-slam上找到。
In this paper, 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 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 (MLE) 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 semidefinite programming to Riemannian staircase optimization (RSO) on the complex oblique manifold 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 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.
