Generalized Proximal Methods for Pose Graph Optimization

TL;DR

This paper extends proximal optimization methods to non-convex pose graph problems, demonstrating convergence and accelerated rates, with practical validation in SLAM and sensor network localization.

Contribution

It introduces a generalized proximal framework for non-convex pose graph optimization with convergence guarantees and enhanced speed, suitable for distributed implementation.

Findings

Faster convergence to practical accuracy in SLAM and sensor localization

Methods are easily distributed and parallelized without efficiency loss

Proposed algorithms outperform existing techniques in speed

Abstract

In this paper, we generalize proximal methods that were originally designed for convex optimization on normed vector space to non-convex pose graph optimization (PGO) on special Euclidean groups, and show that our proposed generalized proximal methods for PGO converge to first-order critical points. Furthermore, we propose methods that significantly accelerate the rates of convergence almost without loss of any theoretical guarantees. In addition, our proposed methods can be easily distributed and parallelized with no compromise of efficiency. The efficacy of this work is validated through implementation on simultaneous localization and mapping (SLAM) and distributed 3D sensor network localization, which indicate that our proposed methods are a lot faster than existing techniques to converge to sufficient accuracy for practical use.