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

Recent Advances in Motion Analysis

The advances in the technology and methodology for human movement capture and analysis over the last decade have been remarkable. Besides acknowledged approaches for kinematic, dynamic, and electromyographic (EMG) analysis carried out in the laboratory, more recently developed devices, such as wearables, inertial measurement units, ambient sensors, and cameras or depth sensors, have been adopted on a wide scale. Furthermore, computational intelligence (CI) methods, such as artificial neural networks, have recently emerged as promising tools for the development and application of intelligent systems in motion analysis. Thus, the synergy of classic instrumentation and novel smart devices and techniques has created unique capabilities in the continuous monitoring of motor behaviors in different fields, such as clinics, sports, and ergonomics. However, real-time sensing, signal processing, human activity recognition, and characterization and interpretation of motion metrics and behaviors from sensor data still representing a challenging problem not only in laboratories but also at home and in the community. This book addresses open research issues related to the improvement of classic approaches and the development of novel technologies and techniques in the domain of motion analysis in all the various fields of application