Path Planning and Obstacle Avoidance for UAV in an Uncharted Environment

The growing industry of unmanned aerial vehicles (UAV) requires an efficient and robust algorithm to decide the path of the UAV and avoid obstacles. The study of pathfinding algorithms is ongoing research not just useful in the domain of drones, but in other fields like video games (AI pathfinding), terrain traversal (mapped, unmapped, areal, underwater, land, etc.), and industries that require robots to deliver packages. This paper proposes a new pathfinding algorithm that aims to solve the problem of pathfinding in unknown 2-dimensional terrain. Based on a system of assumptions and using the help of a set of sensors aboard the UAV, the algorithm navigates the UAV from a start point to an endpoint while avoiding any shape or size of obstacles in between. To avoid multiple different types of “infinite loop” situations where the UAV gets stuck around an obstacle, a priority-based selector for intermediate destinations is created. The algorithm is found to work effectively when simulated in Gazebo on Robot Operating System (ROS). Keywords: Path Planning, UAV, Obstacle Avoidance, Drone Navigation, Obstacle Detection, Uncharted Environment.

On the infinite loop spaces of algebraic cobordism and the motivic sphere

We obtain geometric models for the infinite loop spaces of the motivic spectra $\mathrm{MGL}$, $\mathrm{MSL}$, and $\mathbf{1}$ over a field. They are motivically equivalent to $\mathbb{Z}\times \mathrm{Hilb}_\infty^\mathrm{lci}(\mathbb{A}^\infty)^+$, $\mathbb{Z}\times \mathrm{Hilb}_\infty^\mathrm{or}(\mathbb{A}^\infty)^+$, and $\mathbb{Z}\times \mathrm{Hilb}_\infty^\mathrm{fr}(\mathbb{A}^\infty)^+$, respectively, where $\mathrm{Hilb}_d^\mathrm{lci}(\mathbb{A}^n)$ (resp. $\mathrm{Hilb}_d^\mathrm{or}(\mathbb{A}^n)$, $\mathrm{Hilb}_d^\mathrm{fr}(\mathbb{A}^n)$) is the Hilbert scheme of lci points (resp. oriented points, framed points) of degree $d$ in $\mathbb{A}^n$, and $+$ is Quillen's plus construction. Moreover, we show that the plus construction is redundant in positive characteristic. Comment: 13 pages. v5: published version; v4: final version, to appear in \'Epijournal G\'eom. Alg\'ebrique; v3: minor corrections; v2: added details in the moving lemma over finite fields

A New Reliability Ratio Weighted Bit Flipping Algorithm for Decoding LDPC Codes

In this study, we propose a “New Reliability Ratio Weighted Bit Flipping” (NRRWBF) algorithm for Low-Density Parity-Check (LDPC) codes. This algorithm improves the “Reliability Ratio Weighted Bit Flipping” (RRWBF) algorithm by modifying the reliability ratio. It surpasses the RRWBF in performance, reaching a 0.6 dB coding gain at a Binary Error Rate (BER) of 10−4 over the Additive White Gaussian Noise (AWGN) channel, and presents a significant reduction in the decoding complexity. Furthermore, we improved NRRWBF using the sum of the syndromes as a criterion to avoid the infinite loop. This will enable the decoder to attain a more efficient and effective decoding performance.

Medien zum Selbermachen Der Baumarkt als Ort des medialisierten Einkaufs seit den 1970er Jahren

Starting in the late 1960s and even more pronounced in the 70s, West-Germany saw an increasing number of hardware stores being founded. Since the idea behind the integrated Do-it-yourself-retail-store originated in the United States, it had to be adapted to suit Western-German circumstances. The problem that hardware-store owners faced right from the beginning, was, that the articles in their stores did not represent finished consumer goods, but rather goods that were meant to be turned into such by being used by the customer. Furthermore, until late in the 70s the products on offer were unfamiliar and in need of explanation to the German customers and therefore consulting intensive. In order to reduce the need for customer advisory, but still offer an attractive shopping experience and moreover to make clear, that the store offers not only products, but solutions to a range of different problems, the store owners, their franchise centers and their trade-association focused their efforts on the use of new technologies. It was the video technology that developed a leading role in this effort: By using this technology, stores were able to combine the offer of entertaining media, explanations to the usage of their products in action (which in turn reduced the need for customer advisory) and illustrations of the features of the DIY-products on offer. Starting in the mid-70s, this led to the production of films, which were shown on infinite loop in the hardware-stores.

Artificial Potential Field with Discrete Map Transformation for Feasible Indoor Path Planning

This work considers the path planning problem of personal mobility vehicle (PMV) for indoor navigation using the Artificial Potential Field (APF) method. The APF method sometimes suffers from an infinite loop problem during the planning phase when the goal is blocked by obstacles with certain characteristics. To address the issue, this study deploys the map augmentation method for replanning. When infinite loop situations occur, the map is transformed and the search for drivable path is initiated. The method successfully generates a feasible trajectory when the map is rotated at a certain angle. The scenario of successful planning is shown in the result.

Complete leading-order standard model corrections to quantum leptogenesis

Thermal leptogenesis, in the framework of the standard model with three additional heavy Majorana neutrinos, provides an attractive scenario to explain the observed baryon asymmetry in the universe. It is based on the out-of-equilibrium decay of Majorana neutrinos in a thermal bath of standard model particles, which in a fully quantum field theoretical formalism is obtained by solving Kadanoff-Baym equations. So far, the leading two-loop contributions from leptons and Higgs particles are included, but not yet gauge corrections. These enter at three-loop level but, in certain kinematical regimes, require a resummation to infinite loop order for a result to leading order in the gauge coupling. In this work, we apply such a resummation to the calculation of the lepton number density. The full result for the simplest “vanilla leptogenesis” scenario is by $$ \mathcal{O} $$ O (1) increased compared to that of quantum Boltzmann equations, and for the first time permits an estimate of all theoretical uncertainties. This step completes the quantum theory of leptogenesis and forms the basis for quantitative evaluations, as well as extensions to other scenarios.

SYMMETRIC MONOIDAL G-CATEGORIES AND THEIR STRICTIFICATION

We give an operadic definition of a genuine symmetric monoidal $G$-category, and we prove that its classifying space is a genuine $E_\infty $$G$-space. We do this by developing some very general categorical coherence theory. We combine results of Corner and Gurski, Power and Lack to develop a strictification theory for pseudoalgebras over operads and monads. It specializes to strictify genuine symmetric monoidal $G$-categories to genuine permutative $G$-categories. All of our work takes place in a general internal categorical framework that has many quite different specializations. When $G$ is a finite group, the theory here combines with previous work to generalize equivariant infinite loop space theory from strict space level input to considerably more general category level input. It takes genuine symmetric monoidal $G$-categories as input to an equivariant infinite loop space machine that gives genuine $\Omega $-$G$-spectra as output.

On the quotients of mapping class groups of surfaces by the Johnson subgroups

We study quotients of mapping class groups ${\Gamma _{g,1}}$ of oriented surfaces with one boundary component by the subgroups ${{\cal I}_{g,1}}(k)$ in the Johnson filtrations, and we show that the stable classifying spaces ${\mathbb {Z}} \times B{({\Gamma _\infty }/{{\cal I}_\infty }(k))^ + }$ after plus-construction are infinite loop spaces, fitting into a tower of infinite loop space maps that interpolates between the infinite loop spaces ${\mathbb {Z}} \times B\Gamma _\infty ^ + $ and ${\mathbb {Z}} \times B{({\Gamma _\infty }/{{\cal I}_\infty }(1))^ + } \simeq {\mathbb {Z}} \times B{\rm{Sp}}{({\mathbb {Z}})^ + }$ . We also show that for each level k of the Johnson filtration, the homology of these quotients with suitable systems of twisted coefficients stabilises as the genus of the surface goes to infinity.