5 research outputs found
Shonan Rotation Averaging: Global Optimality by Surfing
Shonan Rotation Averaging is a fast, simple, and elegant rotation averaging
algorithm that is guaranteed to recover globally optimal solutions under mild
assumptions on the measurement noise. Our method employs semidefinite
relaxation in order to recover provably globally optimal solutions of the
rotation averaging problem. In contrast to prior work, we show how to solve
large-scale instances of these relaxations using manifold minimization on (only
slightly) higher-dimensional rotation manifolds, re-using existing
high-performance (but local) structure-from-motion pipelines. Our method thus
preserves the speed and scalability of current SFM methods, while recovering
globally optimal solutions.Comment: 30 pages (paper + supplementary material). To appear at the European
Conference on Computer Vision (ECCV) 202
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
Rotation Coordinate Descent for Fast Globally Optimal Rotation Averaging
Under mild conditions on the noise level of the measurements, rotation
averaging satisfies strong duality, which enables global solutions to be
obtained via semidefinite programming (SDP) relaxation. However, generic
solvers for SDP are rather slow in practice, even on rotation averaging
instances of moderate size, thus developing specialised algorithms is vital. In
this paper, we present a fast algorithm that achieves global optimality called
rotation coordinate descent (RCD). Unlike block coordinate descent (BCD) which
solves SDP by updating the semidefinite matrix in a row-by-row fashion, RCD
directly maintains and updates all valid rotations throughout the iterations.
This obviates the need to store a large dense semidefinite matrix. We
mathematically prove the convergence of our algorithm and empirically show its
superior efficiency over state-of-the-art global methods on a variety of
problem configurations. Maintaining valid rotations also facilitates
incorporating local optimisation routines for further speed-ups. Moreover, our
algorithm is simple to implement; see supplementary material for a
demonstration program.Comment: Accepted to CVPR 2021 as an oral presentatio
Distributed Optimization in Sensor Network for Scalable Multi-Robot Relative State Estimation
Distance measurements demonstrate distinctive scalability when used for
relative state estimation in large-scale multi-robot systems. Despite the
attractiveness of distance measurements, multi-robot relative state estimation
based on distance measurements raises a tricky optimization problem, especially
in the context of large-scale systems. Motivated by this, we aim to develop
specialized computational techniques that enable robust and efficient
estimation when deploying distance measurements at scale. We first reveal the
commonality between the estimation problem and the one that finds realization
of a sensor network, from which we draw crucial lesson to inspire the proposed
methods. However, solving the latter problem in large-scale (still) requires
distributed optimization schemes with scalability natures, efficient
computational procedures, and fast convergence rates. Towards this goal, we
propose a complementary pair of distributed computational techniques with the
classical block coordinate descent (BCD) algorithm as a unified backbone. In
the first method, we treat Burer-Monteiro factorization as a rank-restricted
heuristic for rank-constrained semidefinite programming (SDP), where a
specialized BCD-type algorithm that analytically solve each block update
subproblem is employed. Although this method enables robust and (extremely)
fast recovery of estimates from initial guesses, it inevitably fails as the
initialization becomes disorganized. We therefore propose the second method,
derived from a convex formulation named anchored edge-based semidefinite
programming} (ESDP), to complement it, at the expense of a certain loss of
efficiency. This formulation is structurally decomposable so that BCD can be
naturally employed, where each subproblem is convex and (again) solved
exactly...Comment: Extended technical report (14 pages, 5 figures, 2 tables