40 research outputs found
Spectral Sparsification for Communication-Efficient Collaborative Rotation and Translation Estimation
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.Comment: Revised extended technical report (37 pages, 15 figures, 6 tables
Asynchronous and Parallel Distributed Pose Graph Optimization
We present Asynchronous Stochastic Parallel Pose Graph Optimization (ASAPP),
the first asynchronous algorithm for distributed pose graph optimization (PGO)
in multi-robot simultaneous localization and mapping. By enabling robots to
optimize their local trajectory estimates without synchronization, ASAPP offers
resiliency against communication delays and alleviates the need to wait for
stragglers in the network. Furthermore, ASAPP can be applied on the
rank-restricted relaxations of PGO, a crucial class of non-convex Riemannian
optimization problems that underlies recent breakthroughs on globally optimal
PGO. Under bounded delay, we establish the global first-order convergence of
ASAPP using a sufficiently small stepsize. The derived stepsize depends on the
worst-case delay and inherent problem sparsity, and furthermore matches known
result for synchronous algorithms when there is no delay. Numerical evaluations
on simulated and real-world datasets demonstrate favorable performance compared
to state-of-the-art synchronous approach, and show ASAPP's resilience against a
wide range of delays in practice.Comment: full paper with appendice