外观
论文arXiv 2610.1465518 天前
位姿图优化的全局最优性
原文链接：Global Optimality of Pose Graph Optimization（arXiv 2610.14655 · 发布日期：2026-10-10）
Global Optimality of Pose Graph Optimization
本文研究PGO非凸优化景观，提出噪声显式界下的全局最优充分条件，并在多种随机数值仿真中验证。
核心要点
- PGO广泛用于机器人状态估计，但非凸且可能存在许多局部极小点。
- 构造包含全局极小点的吸引域，并显式刻画其半径受噪声控制。
- 利用一阶最优性条件，给出由噪声控制的局部极小点全局最优判据。
- 数值仿真在多种随机情形下验证理论，显示条件可有效认证PGO全局最优性。
验证范围与局限：验证限于多种随机情形下的数值仿真。
英文摘要 (Abstract)
Pose Graph Optimization (PGO) is a classical and widely applied problem in state estimation for robotics, playing a fundamental role in localization, mapping, and navigation. Yet, it is nonconvex in nature and may have many local minimizers, thus difficult to analyze. In this paper, we investigate the optimization landscape and establish a sufficient condition of global optimality for PGO. The ultimate goal of this paper is to theoretically confirm that the optimization landscape is benign and attractive around the global minimizer, if noise is smaller than an explicit and a priori bound. To reveal such an insight, this paper develops three main technical results. First, we identify a proper basin of attraction (BOA) containing global minimizer, and characterize its geometric property by showing that its radius is controlled by noise in an explicit way. Then, by exploring the first order optimality conditions of PGO, we prove that a local minimizer is globally optimal if a noise-controlled criterion is satisfied. Finally, by combining above two results, we prove that one and only one local minimizer exists in the BOA and this minimizer is globally optimal, when the noise is smaller than an explicit bound that can be verified a priori. Numerical simulations validate the proposed theory under various random cases, showing that the obtained conditions provide an effective criterion for certifying the global optimality of PGO.
作者：Shuan Ding, Ruishuang Chen, Mengfan Cao, Zaiyue Yang
来源
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