Rotation Representations and Their Conversions

A rigid body motion, which can be decomposed into rotation and translation, is essential for engineers and scientists who deal with moving systems in a space. While translation is as simple as vector addition, rotation is hard to understand because rotations are non-Euclidean, and there are many ways to represent them. Additionally, each representation comes with complex operations, and the conversions between different representations are not unique. Therefore, in this tutorial we review rotation representations which are widely used in industry and academia such as rotation matrices, Euler angles, rotation axis-angles, unit complex numbers, and unit quaternions. In particular, for better understanding we begin with rotations in a two dimensional space and extend them to a three dimensional space. In that context, we learn how to represent rotations in a two dimensional space with rotation angles and unit complex numbers, and extend them respectively to Euler angles and unit quaternions for rotations in a three dimensional space. The definitions and properties of mathematical entities used for representing rotations as well as the conversions between various rotation representations are summarized in tables for the reader’s later convenience.

View this article on IEEE Xplore

Design, Modeling, and Analysis of a 3-D Spiral Inductor With Magnetic Thin-Films for PwrSoC/PwrSiP DC-DC Converters

A solution architecture for monolithic system-on-chip (SoC) power conversion is in high demand to enable modern electronics with a reduced footprint and increased functionality. A promising solution is to reduce the microinductor size by using novel magnetically-enhanced 3-D design topologies. This work presents the design, modeling, and analysis of a 3-D spiral inductor with magnetic thin-films for power supply applications in the frequency range of 3–30 MHz. A closed-form analytical expression is derived for the inductance, including both the air- and magnetic-core contributions. To validate the air-core inductance model, we implement a 3-D spiral inductor on PCB. The theoretical calculation of air-core inductance is in good agreement with experimental data. To validate the inductance model of the magnetic-core, a 3-D spiral inductor is modeled with Ansys Maxwell electromagnetic field simulation software. A winding AC resistance model is additionally presented. We perform a design space exploration (DSE) to investigate the significance of the 3-D spiral inductor structure. Two important performance parameters are discussed: dc quality factor (Qdc) and ac quality factor (Qac) . Also, a 3-D spiral inductor structure with magnetic thin-films is characterized in Ansys Maxwell to estimate its potential, and a novel fabrication method is proposed to implement this inductor. The measured relative permeability ( μr ) and the magnetic loss tangent ( tan δ ) of Co-Zr-Ta-B magnetic thin-films, developed in-house, are used to simulate the proposed structure. The promising results of the DSE can be easily extended to improve the performance of other 3-D inductor topologies, such as the solenoid and the toroid. The numerical simulations reveal that the 3-D spiral inductor with magnetic thin-films has the potential to demonstrate a figure-of-merit (FOM) that is significantly higher than traditional inductors.

Published in the IEEE Magnetics Society Section of IEEE Access.

View this article on IEEE Xplore

The Cubli: Modeling and Nonlinear Attitude Control Utilizing Quaternions

This paper covers the modeling and nonlinear attitude control of the Cubli, a cube with three reaction wheels mounted on orthogonal faces that becomes a reaction wheel based 3D inverted pendulum when positioned in one of its vertices. The proposed approach utilizes quaternions instead of Euler angles as feedback control states. A nice advantage of quaternions, besides the usual arguments to avoid singularities and trigonometric functions, is that it allows working out quite complex dynamic equations completely by hand utilizing vector notation. Modeling is performed utilizing Lagrange equations and it is validated through computer simulations and Poinsot trajectories analysis. The derived nonlinear control law is based on feedback linearization technique, thus being time-invariant and equivalent to a linear one dynamically linearized at the given reference. Moreover, it is characterized by only three straightforward tuning parameters. Experimental results are presented.

View this article on IEEE Xplore

Rapid and Flexible 3D Printed Finger Prostheses With Soft Fingertips: Technique and Clinical Application

We present a method for fabricating passive finger prostheses with soft fingertips by utilizing 3D scanning and 3D printing with flexible filament. The proposed method uses multi-process printing at varying infill levels to provide soft fingertips to emulate biological fingers. The proposed method also enables rapid prototyping of finger prostheses, and the flexibility to change interphalangeal joint angles to fit the prostheses for different manipulation and occupational therapy tasks. The entire process of designing and fabricating the prostheses can be conducted in one day. The presented technique uses scan data of the intact side fingers to provide the shape and contour of the finger prostheses, while the socket is designed based on the scan data of the amputation side. The paper presents the developed technique and its clinical application. Experiments are conducted to measure the stiffness of the printed material at varying infill levels and the stiffness of the printed fingertips. The results are compared to measurements of biological fingertip stiffness from the literature. The clinical application includes two cases, one case with distal phalanx loss on the thumb, index, and middle fingers, and one case with distal and middle phalanx loss on the middle and ring fingers. Fitting was successful for both recipients and they were both able to use the prostheses successfully.

View this article on IEEE Xplore

The Internet of Federated Things (IoFT)

The Internet of Things (IoT) is on the verge of a major paradigm shift. In the IoT system of the future, IoFT, the “cloud” will be substituted by the “crowd” where model training is brought to the edge, allowing IoT devices to collaboratively extract knowledge and build smart analytics/models while keeping their personal data stored locally. This paradigm shift was set into motion by the tremendous increase in computational power on IoT devices and the recent advances in decentralized and privacy-preserving model training, coined as federated learning (FL). This article provides a vision for IoFT and a systematic overview of current efforts towards realizing this vision. Specifically, we first introduce the defining characteristics of IoFT and discuss FL data-driven approaches, opportunities, and challenges that allow decentralized inference within three dimensions: (i) a global model that maximizes utility across all IoT devices, (ii) a personalized model that borrows strengths across all devices yet retains its own model, (iii) a meta-learning model that quickly adapts to new devices or learning tasks. We end by describing the vision and challenges of IoFT in reshaping different industries through the lens of domain experts. Those industries include manufacturing, transportation, energy, healthcare, quality & reliability, business, and computing.

View this article on IEEE Xplore