Designing Sparse Reliable Pose-Graph SLAM: A Graph-Theoretic Approach

TL;DR

This paper introduces a novel graph-theoretic approach to designing sparse pose-graph SLAM problems by maximizing the weighted number of spanning trees, supported by new theoretical insights and approximation algorithms.

Contribution

It establishes the monotone log-submodularity of the weighted spanning trees and develops near-optimal algorithms with provable guarantees for sparse SLAM graph design.

Findings

Algorithms perform well on random graphs

Validated on real pose-graph SLAM dataset

Theoretical guarantees established for approximation methods

Abstract

In this paper, we aim to design sparse D-optimal (determinantoptimal) pose-graph SLAM problems through the synthesis of sparse graphs with the maximum weighted number of spanning trees. Characterizing graphs with the maximum number of spanning trees is an open problem in general. To tackle this problem, several new theoretical results are established in this paper, including the monotone log-submodularity of the weighted number of spanning trees. By exploiting these structures, we design a complementary pair of near-optimal efficient approximation algorithms with provable guarantees. Our theoretical results are validated using random graphs and a publicly available pose-graph SLAM dataset.