三维位姿图优化问题的线性最小二乘初始化方法

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标题：A Linear Least Square Initialization Method for 3D Pose Graph Optimization Problem

作者：S. M. Nasiri, H. Moradi, Senior Member, IEEE, R. Hosseini

来源：2018 IEEE International Conference on Robotics and Automation (ICRA) May 21-25, 2018, Brisbane, Australia

编译：张宁

审核：颜青松，陈世浪

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摘要

姿态图优化（PGO）是机器人和机器视觉应用（如3D重建和3D SLAM）中出现的一个重要优化问题。位姿图的每个节点对应于方向和位置。PGO问题从节点之间的相对噪声观察中找到节点的方向和位置。最近的研究表明，众所周知的迭代PGO求解器需要良好的初始化才能收敛到良好的求解。然而，我们观察到最先进的初始化方法仅在低噪声问题中获得良好的初始化，并且它们在具有更多测量噪声的挑战性问题中失败。因此，迭代方法在高噪声问题中可能会收敛到不好的求解结果。

在本文中，提出了一种在PGO优化问题中获得方向的新方法。与其他众所周知的方法一样，初始位置是从最小二乘问题的结果中获得的。所提出的方法迭代地近似于当前估计的问题并将其转换为最小二乘问题。因此，该方法可以被视为迭代最小二乘法，其在计算上是高效的。仿真结果表明，所提出的初始化方法有助于最知名的迭代求解器在某些情况下获得更好的最优并显着优于其他求解器。

Abstract

Pose Graph Optimization (PGO) is an important optimization problem arising in robotics and machine vision applications like 3D reconstruction and 3D SLAM. Each node of pose graph corresponds to an orientation and a location. The PGO problem finds orientations and locations of the nodes from relative noisy observation between nodes. Recent investigations show that well-known iterative PGO solvers need good initialization to converge to good solutions. However, we observed that state-of-the-art initialization methods obtain good initialization only in low noise problems, and they fail in challenging problems having more measurement noise. Consequently, iterative methods may converge to bad solutions in high noise problems.

In this paper, a new method for obtaining orientations in the PGO optimization problem is presented. Like other well-known methods the initial locations are obtained from the result of a least-squares problem. The proposed method iteratively approximates the problem around current estimation and converts it to a least-squares problem. Therefore, the method can be seen as an iterative least-squares method which is computationally efficient. Simulation results show that the proposed initialization method helps the most well-known iterative solver to obtain better optima and significantly outperform other solvers in some cases.