Spectral Sparsification for Communication-Efficient Collaborative Rotation and Translation Estimation

TL;DR

This paper introduces spectral sparsification techniques for efficient communication in multi-robot rotation and translation estimation, improving convergence and robustness in collaborative SLAM and SfM tasks.

Contribution

It presents a novel spectral sparsification-based approach for distributed second-order optimization in multi-robot systems, with provable guarantees and robustness to outliers.

Findings

Achieves linear convergence rate in local optimization.

Reduces communication cost via spectral sparsification.

Demonstrates superior performance on real-world SLAM and SfM datasets.

Abstract

We propose fast and communication-efficient optimization algorithms for multi-robot rotation averaging and translation estimation problems that arise from collaborative simultaneous localization and mapping (SLAM), structure-from-motion (SfM), and camera network localization applications. Our methods are based on theoretical relations between the Hessians of the underlying Riemannian optimization problems and the Laplacians of suitably weighted graphs. We leverage these results to design a collaborative solver in which robots coordinate with a central server to perform approximate second-order optimization, by solving a Laplacian system at each iteration. Crucially, our algorithms permit robots to employ spectral sparsification to sparsify intermediate dense matrices before communication, and hence provide a mechanism to trade off accuracy with communication efficiency with provable guarantees. We perform rigorous theoretical analysis of our methods and prove that they enjoy (local) linear rate of convergence. Furthermore, we show that our methods can be combined with graduated non-convexity to achieve outlier-robust estimation. Extensive experiments on real-world SLAM and SfM scenarios demonstrate the superior convergence rate and communication efficiency of our methods.