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.

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A Comprehensive Survey on Cooperative Intersection Management for Heterogeneous Connected Vehicles

Nowadays, with the advancement of technology, world is trending toward high mobility and dynamics. In this context, intersection management (IM) as one of the most crucial elements of the transportation sector demands high attention. Today, road entities including infrastructures, vulnerable road users (VRUs) such as motorcycles, moped, scooters, pedestrians, bicycles, and other types of vehicles such as trucks, buses, cars, emergency vehicles, and railway vehicles like trains or trams are able to communicate cooperatively using vehicle-to-everything (V2X) communications and provide traffic safety, efficiency, infotainment and ecological improvements. In this paper, we take into account different types of intersections in terms of signalized, semi-autonomous (hybrid) and autonomous intersections and conduct a comprehensive survey on various intersection management methods for heterogeneous connected vehicles (CVs). We consider heterogeneous classes of vehicles such as road and rail vehicles as well as VRUs including bicycles, scooters and motorcycles. All kinds of intersection goals, modeling, coordination architectures, scheduling policies are thoroughly discussed. Signalized and semi-autonomous intersections are assessed with respect to these parameters. We especially focus on autonomous intersection management (AIM) and categorize this section based on four major goals involving safety, efficiency, infotainment and environment. Each intersection goal provides an in-depth investigation on the corresponding literature from the aforementioned perspectives. Moreover, robustness and resiliency of IM are explored from diverse points of view encompassing sensors, information management and sharing, planning universal scheme, heterogeneous collaboration, vehicle classification, quality measurement, external factors, intersection types, localization faults, communication anomalies and channel optimization, synchronization, vehicle dynamics and model mismatch, model uncertainties, recovery, security and privacy.

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