Overlapping Schwarz Preconditioners for Pose-Graph SLAM in Robotics

TL;DR

This paper explores the use of additive overlapping Schwarz domain decomposition as an effective preconditioner for large linear systems in pose-graph SLAM, demonstrating scalability and structural analogy to PDE discretizations.

Contribution

It introduces a novel application of Schwarz preconditioners to pose-graph SLAM linear systems, showing their effectiveness and scalability in this context.

Findings

Preconditioned conjugate gradient method remains efficient regardless of problem size.

SLAM linear systems can be interpreted as finite element problems, enabling PDE-based preconditioning.

Numerical experiments confirm the scalability of the proposed preconditioner.

Abstract

We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph optimization back-end in Simultaneous Localization and Mapping (SLAM) in robotics. A brief introduction to both SLAM and domain decomposition preconditioners is given, followed by a description of the nonlinear least-squares formulation, its linearization, and the resulting matrix structure, making the paper accessible to readers without prior knowledge of either field. Numerical experiments for a simple model problem demonstrate the numerical scalability of the preconditioned conjugate gradient method to solve the linear systems resulting from Gauss--Newton linearization: Using the additive overlapping Schwarz preconditioner, the number of conjugate gradient iterations remains bounded independently of the problem size. We also show that a simplified SLAM problem can be interpreted as a finite element problem using linear elastic bars, highlighting the structural analogy to PDE discretizations and motivating the use of PDE-based preconditioners such as scalable domain decomposition preconditioners.