Analysis of minima for geodesic and chordal cost for a minimal 2D pose-graph SLAM problem

2019/11/13 by Felix H. Kong, Kong, Felix H., Jiaheng Zhao +5
Computer Science · Engineering · Environmental Science · #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #Remote Sensing and LiDAR Applications #Robotics (cs.RO) #Robotics and Sensor-Based Localization

paper · pdf · doi:10.48550/arxiv.1911.05734

openalex publication_date 2019/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that for a minimal pose-graph problem, even in the ideal case of perfect measurements and spherical covariance, using the so-called "wrap function" when comparing angles results in multiple suboptimal local minima. We numerically estimate regions of attraction to these local minima for some numerical examples, and give evidence to show that they are of nonzero measure. In contrast, under the same assumptions, we show that the chordal distance representation of angle error has a unique minimum up to periodicity. For chordal cost, we also search for initial conditions that fail to converge to the global minimum, and find that this occurs with far fewer points than with geodesic cost.

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