Euclidean Distance Matrices: Essential Theory, Algorithms and Applications

Euclidean distance matrices (EDM) are matrices of squared distances between points. The definition is deceivingly simple: thanks to their many useful properties they have found applications in psychometrics, crystallography, machine learning, wireless sensor networks, acoustics, and more. Despite the usefulness of EDMs, they seem to be insufficiently known in the signal processing community. Our goal is to rectify this mishap in a concise tutorial. We review the fundamental properties of EDMs, such as rank or (non)definiteness. We show how various EDM properties can be used to design algorithms for completing and denoising distance data. Along the way, we demonstrate applications to microphone position calibration, ultrasound tomography, room reconstruction from echoes and phase retrieval. By spelling out the essential algorithms, we hope to fast-track the readers in applying EDMs to their own problems. Matlab code for all the described algorithms, and to generate the figures in the paper, is available online. Finally, we suggest directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine - change of title in the last revisio

A Software-Defined Multi-Element VLC Architecture

In the modern era of radio frequency (RF) spectrum crunch, visible light communication (VLC) is a recent and promising alternative technology that operates at the visible light spectrum. Thanks to its unlicensed and large bandwidth, VLC can deliver high throughput, better energy efficiency, and low cost data communications. In this article, a hybrid RF/VLC architecture is considered that can simultaneously provide light- ing and communication coverage across a room. Considered architecture involves a novel multi-element hemispherical bulb design, which can transmit multiple data streams over light emitting diode (LED) modules. Simulations considering various VLC transmitter configurations and topologies show that good link quality and high spatial reuse can be maintained in typical indoor communication scenarios

Automated sequence and motion planning for robotic spatial extrusion of 3D trusses

While robotic spatial extrusion has demonstrated a new and efficient means to fabricate 3D truss structures in architectural scale, a major challenge remains in automatically planning extrusion sequence and robotic motion for trusses with unconstrained topologies. This paper presents the first attempt in the field to rigorously formulate the extrusion sequence and motion planning (SAMP) problem, using a CSP encoding. Furthermore, this research proposes a new hierarchical planning framework to solve the extrusion SAMP problems that usually have a long planning horizon and 3D configuration complexity. By decoupling sequence and motion planning, the planning framework is able to efficiently solve the extrusion sequence, end-effector poses, joint configurations, and transition trajectories for spatial trusses with nonstandard topologies. This paper also presents the first detailed computation data to reveal the runtime bottleneck on solving SAMP problems, which provides insight and comparing baseline for future algorithmic development. Together with the algorithmic results, this paper also presents an open-source and modularized software implementation called Choreo that is machine-agnostic. To demonstrate the power of this algorithmic framework, three case studies, including real fabrication and simulation results, are presented.Comment: 24 pages, 16 figure

An anytime tree search algorithm for two-dimensional two- and three-staged guillotine packing problems

[libralesso_anytime_2020] proposed an anytime tree search algorithm for the 2018 ROADEF/EURO challenge glass cutting problem (https://www.roadef.org/challenge/2018/en/index.php). The resulting program was ranked first among 64 participants. In this article, we generalize it and show that it is not only effective for the specific problem it was originally designed for, but is also very competitive and even returns state-of-the-art solutions on a large variety of Cutting and Packing problems from the literature. We adapted the algorithm for two-dimensional Bin Packing, Multiple Knapsack, and Strip Packing Problems, with two- or three-staged exact or non-exact guillotine cuts, the orientation of the first cut being imposed or not, and with or without item rotation. The combination of efficiency, ability to provide good solutions fast, simplicity and versatility makes it particularly suited for industrial applications, which require quickly developing algorithms implementing several business-specific constraints. The algorithm is implemented in a new software package called PackingSolver

A proposed segmented precast concrete spherical cap: geometry, structural stability and construction

This study proposes the design and construction of a concrete spherical cap composed of uniformly-shaped precast doubly-curved panels based on spherical division techniques. A numerical structural analysis is conducted to study the failure behavior of the segmented structure and the capacity of the joints by using finite element modeling techniques to model the concrete material behavior, boundary conditions and intermediate joints of the precast panels. An experimental analysis is conducted to verify the capacity of the structure and the reliability of the modeling techniques, and to study the feasibility of the proposed panel prefabrication and assembly method. The results of this study demonstrate that the proposed precast system and connection design perform efficiently when compared to the monolithically-cast counterpart, particularly under uniform loading conditions. Additional insights on the properties and solution parameters of finite element modelling of concrete shell structures are presented based on the structural analysis of this work. The study concludes the ability of the proposed geometric design and construction method to enhance the prefabrication and construction efficiency with little effect on the structural capacity within the context of the selected geometry and conducted load tests, and recommends further parameters to study for design and construction optimization