2022/10/10 by Yulun Tian, Jonathan P. How, Tian, Yulun +1 · 1 citation
Computer Science · Engineering · #Distributed Control Multi-Agent Systems #FOS: Computer and information sciences #FOS: Mathematics #Indoor and Outdoor Localization Technologies #Optimization and Control (math.OC) #Robotics (cs.RO) #Robotics and Sensor-Based Localization
paper · pdf · doi:10.48550/arxiv.2210.05020
openalex publication_date 2022/10/10 · openalex created_date 2022/10/14 · openalex updated_date 2026/08/01
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.