7 research outputs found
Improved Pose Graph Optimization for Planar Motions Using Riemannian Geometry on the Manifold of Dual Quaternions
We present a novel Riemannian approach for planar pose graph optimization
problems. By formulating the cost function based on the Riemannian metric on
the manifold of dual quaternions representing planar motions, the nonlinear
structure of the SE(2) group is inherently considered. To solve the on-manifold
least squares problem, a Riemannian Gauss-Newton method using the exponential
retraction is applied. The proposed Riemannian pose graph optimizer (RPG-Opt)
is further evaluated based on public planar pose graph data sets. Compared with
state-of-the-art frameworks, the proposed method gives equivalent accuracy and
better convergence robustness under large uncertainties of odometry
measurements.Comment: 7 pages. Submitted to 21st IFAC World Congress (IFAC 2020
Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC
We introduce Tempered Geodesic Markov Chain Monte Carlo (TG-MCMC) algorithm
for initializing pose graph optimization problems, arising in various scenarios
such as SFM (structure from motion) or SLAM (simultaneous localization and
mapping). TG-MCMC is first of its kind as it unites asymptotically global
non-convex optimization on the spherical manifold of quaternions with posterior
sampling, in order to provide both reliable initial poses and uncertainty
estimates that are informative about the quality of individual solutions. We
devise rigorous theoretical convergence guarantees for our method and
extensively evaluate it on synthetic and real benchmark datasets. Besides its
elegance in formulation and theory, we show that our method is robust to
missing data, noise and the estimated uncertainties capture intuitive
properties of the data.Comment: Published at NeurIPS 2018, 25 pages with supplement