Characterization of Spherical and Plane Curves Using Rotation Minimizing Frames

In this work, we study plane and spherical curves in Euclidean and Lorentz-Minkowski 3-spaces by employing rotation minimizing (RM) frames. By conveniently writing the curvature and torsion for a curve on a sphere, we show how to find the angle between the principal normal and an RM vector field for spherical curves. Later, we characterize plane and spherical curves as curves whose position vector lies, up to a translation, on a moving plane spanned by their unit tangent and an RM vector field. Finally, as an application, we characterize Bertrand curves as curves whose so-called natural mates are spherical.Comment: 8 pages. This version is an improvement of the previous one. In addition to a study of some properties of plane and spherical curves, it contains a characterization of Bertrand curves in terms of the so-called natural mate

Tracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow

We study the 6-dimensional dynamics -- position and orientation -- of a large sphere advected by a turbulent flow. The movement of the sphere is recorded with 2 high-speed cameras. Its orientation is tracked using a novel, efficient algorithm; it is based on the identification of possible orientation `candidates' at each time step, with the dynamics later obtained from maximization of a likelihood function. Analysis of the resulting linear and angular velocities and accelerations reveal a surprising intermittency for an object whose size lies in the integral range, close to the integral scale of the underlying turbulent flow

Volumetric Monitoring and Modeling of Indoor Air Pollutant Dispersion by the Use of 3D Particle Tracking Velocimetry

International audienc

Fast Object Learning and Dual-arm Coordination for Cluttered Stowing, Picking, and Packing

Robotic picking from cluttered bins is a demanding task, for which Amazon Robotics holds challenges. The 2017 Amazon Robotics Challenge (ARC) required stowing items into a storage system, picking specific items, and packing them into boxes. In this paper, we describe the entry of team NimbRo Picking. Our deep object perception pipeline can be quickly and efficiently adapted to new items using a custom turntable capture system and transfer learning. It produces high-quality item segments, on which grasp poses are found. A planning component coordinates manipulation actions between two robot arms, minimizing execution time. The system has been demonstrated successfully at ARC, where our team reached second places in both the picking task and the final stow-and-pick task. We also evaluate individual components.Comment: In: Proceedings of the International Conference on Robotics and Automation (ICRA) 201

HYPERSPECTRAL LINE-SCANNING MICROSCOPY FOR HIGH-SPEED MULTICOLOR QUANTUM DOT TRACKING

One of the challenges in studying protein interactions in live cells lies in the capacity to obtain both spatial and temporal information that is sufficient to extend existing knowledge of the dynamics and interactions, especially when tracking proteins at high density. Here we introduce a high-speed laser line-scanning hyperspectral microscope that is designed to track quantum dot labeled proteins at 27 frames/sec over an area of 28 um2 using 128 spectral channels spanning the range from 500 to 750 nm. This instrument simultaneously excites 8 species of quantum dots and employs a custom prism spectrometer and high speed EMCCD to obtain spectral information that is then used to distinguish and track individual probes at high density. These emitters are localized to within 10s of nm in each frame and reconstructed trajectories yield information of the protein dynamics and interactions. This manuscript describes the design, implementation, characterization, and application of a high-speed laser line-scanning hyperspectral microscope (HSM). The intended primary application is that of investigating the dynamics of transmembrane antibody receptors using quantum dot labeled immunoglobulin E (QD-IgE). Several additional examples demonstrate other advantages and applications of this method, including 3D hyperspectral imaging of live cells and hyperspectral superresolution imaging