Group-$k$ consistent measurement set maximization via maximum clique over k-Uniform hypergraphs for robust multi-robot map merging

TL;DR

This paper introduces a unified graph-based approach for robust multi-robot map merging by maximizing consistent measurement sets using maximum clique algorithms on hypergraphs, improving outlier detection and computational efficiency.

Contribution

It generalizes the maximum clique approach to group-$k$ consistency in hypergraphs, enabling more robust outlier detection in multi-robot mapping.

Findings

Effective group-$k$ consistency checking reduces outlier influence.

Proposed algorithms outperform existing methods in multi-agent experiments.

Significant decrease in consistency check computations achieved.

Abstract

This paper unifies the theory of consistent-set maximization for robust outlier detection in a simultaneous localization and mapping framework. We first describe the notion of pairwise consistency before discussing how a consistency graph can be formed by evaluating pairs of measurements for consistency. Finding the largest set of consistent measurements is transformed into an instance of the maximum clique problem and can be solved relatively quickly using existing maximum-clique solvers. We then generalize our algorithm to check consistency on a group-$k$ basis by using a generalized notion of consistency and using generalized graphs. We also present modified maximum clique algorithms that function on generalized graphs to find the set of measurements that is internally group-$k$ consistent. We address the exponential nature of group-$k$ consistency and present methods that can substantially decrease the number of necessary checks performed when evaluating consistency. We extend our prior work to multi-agent systems in both simulation and hardware and provide a comparison with other state-of-the-art methods.