Efficient robotic path planning algorithm based on artificial potential field

<span lang="EN-US">Path planning is crucial for a robot to be able to reach a target point safely to accomplish a given mission. In path planning, three essential criteria have to be considered namely path length, computational complexity and completeness. Among established path planning methods are voronoi diagram (VD), cell decomposition (CD), probability roadmap (PRM), visibility graph (VG) and potential field (PF). The above-mentioned methods could not fulfill all three criteria simultaneously which limits their application in optimal and real-time path planning. This paper proposes a path PF-based planning algorithm called dynamic artificial PF (DAPF). The proposed algorithm is capable of eliminating the local minima that frequently occurs in the conventional PF while fulfilling the criterion of path planning. DAPF also integrates path pruning to shorten the planned path. In order to evaluate its performance, DAPF has been simulated and compared with VG in terms of path length and computational complexity. It is found that DAPF is consistent in generating paths with low computation time in obstacle-rich environments compared to VG. The paths produced also are nearly optimal with respect to VG.</span>

An Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory

The improvement of overall uniformity and smoothness of spherical icosahedral grids, the basic framework of atmospheric models, is a key to reducing simulation errors. However, most of the existing grid optimization methods have optimized grid from different aspects and not improved overall uniformity and smoothness of grid at the same time, directly affecting the accuracy and stability of numerical simulation. Although a well-defined grid with more than 12 points cannot be constructed on a sphere, the area uniformity and the interval uniformity of the spherical grid can be traded off to enhance extremely the overall grid uniformity and smoothness. To solve this problem, an overall uniformity and smoothness optimization method of the spherical icosahedral grid is proposed based on the optimal transformation theory. The spherical cell decomposition method has been introduced to iteratively update the grid to minimize the spherical transportation cost, achieving an overall optimization of the spherical icosahedral grid. Experiments on the four optimized grids (the spring dynamics optimized grid, the Heikes and Randall optimized grid, the spherical centroidal Voronoi tessellations optimized grid and XU optimized grid) demonstrate that the grid area uniformity of our method has been raised by 22.60% of SPRG grid, −1.30% of HR grid, 38.30% of SCVT grid and 38.20% of XU grid, and the grid interval uniformity has been improved by 2.50% of SPRG grid, 2.80% of HR grid, 11.10% of SCVT grid and 11.00% of XU grid. Although the grid uniformity of the proposed method is similar with the HR grid, the smoothness of grid deformation has been enhanced by 79.32% of grid area and 24.07% of grid length. To some extent, the proposed method may be viewed as a novel optimization approach of the spherical icosahedral grid which can improve grid overall uniformity and smoothness of grid deformation.

The Composition of Saturated Vapor over 1-Butyl-3-methylimidazolium Tetrafluoroborate Ionic Liquid: A Multi-Technique Study of the Vaporization Process

A multi-technique approach based on Knudsen effusion mass spectrometry, gas phase chromatography, mass spectrometry, NMR and IR spectroscopy, thermal analysis, and quantum-chemical calculations was used to study the evaporation of 1-butyl-3-methylimidazolium tetrafluoroborate (BMImBF4). The saturated vapor over BMImBF4 was shown to have a complex composition which consisted of the neutral ion pairs (NIPs) [BMIm+][BF4−], imidazole-2-ylidene C8N2H14BF3, 1-methylimidazole C4N2H6, 1-butene C4H8, hydrogen fluoride HF, and boron trifluoride BF3. The vapor composition strongly depends on the evaporation conditions, shifting from congruent evaporation in the form of NIP under Langmuir conditions (open surface) to primary evaporation in the form of decomposition products under equilibrium conditions (Knudsen cell). Decomposition into imidazole-2-ylidene and HF is preferred. The vapor composition of BMImBF4 is temperature-depended as well: the fraction ratio of [BMIm+][BF4−] NIPs to decomposition products decreased by about a factor of three in the temperature range from 450 K to 510 K.

The Tutte polynomial and toric Nakajima quiver varieties

For a quiver $Q$ with underlying graph $\Gamma$ , we take $ {\mathcal {M}}$ an associated toric Nakajima quiver variety. In this article, we give a direct relation between a specialization of the Tutte polynomial of $\Gamma$ , the Kac polynomial of $Q$ and the Poincaré polynomial of $ {\mathcal {M}}$ . We do this by giving a cell decomposition of $ {\mathcal {M}}$ indexed by spanning trees of $\Gamma$ and ‘geometrizing’ the deletion and contraction operators on graphs. These relations have been previously established in Hausel–Sturmfels [6] and Crawley-Boevey–Van den Bergh [3], however the methods here are more hands-on.

Using coverage path planning methods for car park exploration

With the increasing number of vehicles on the roads, finding a free parking space has become a time-consuming problem. Traditional car parks are not equipped with occupancy sensors, so planning a systematic traversal of a car park can ease and shorten the search. Since car park exploration is similar to coverage path planning (CPP) problems, the core concepts of CPP algorithms can be used. This paper presents a method that divides maps into smaller cells using trapezoidal cell decomposition and then plans the traversal using wavefront algorithm core concepts. This method can be used for multi-storey car parks by planning the traversal of each floor separately and then the path from one floor to the next. Several alternative explorational paths can be generated by taking different personal preferences into account, such as the length of the driven route and the proximity to preferred locations. The planned traversals are compared by step number, the cell visitedness ratio, the number of visits to each cell and the cost function. The comparison of the methods is based on simulation results.

Fast and precise single-cell data analysis using a hierarchical autoencoder

A primary challenge in single-cell RNA sequencing (scRNA-seq) studies comes from the massive amount of data and the excess noise level. To address this challenge, we introduce an analysis framework, named single-cell Decomposition using Hierarchical Autoencoder (scDHA), that reliably extracts representative information of each cell. The scDHA pipeline consists of two core modules. The first module is a non-negative kernel autoencoder able to remove genes or components that have insignificant contributions to the part-based representation of the data. The second module is a stacked Bayesian autoencoder that projects the data onto a low-dimensional space (compressed). To diminish the tendency to overfit of neural networks, we repeatedly perturb the compressed space to learn a more generalized representation of the data. In an extensive analysis, we demonstrate that scDHA outperforms state-of-the-art techniques in many research sub-fields of scRNA-seq analysis, including cell segregation through unsupervised learning, visualization of transcriptome landscape, cell classification, and pseudo-time inference.

Effective Cylindrical Cell Decompositions for Restricted Sub-Pfaffian Sets

The o-minimal structure generated by the restricted Pfaffian functions, known as restricted sub-Pfaffian sets, admits a natural measure of complexity in terms of a format ${{\mathcal{F}}}$, recording information like the number of variables and quantifiers involved in the definition of the set, and a degree $D$, recording the degrees of the equations involved. Khovanskii and later Gabrielov and Vorobjov have established many effective estimates for the geometric complexity of sub-Pfaffian sets in terms of these parameters. It is often important in applications that these estimates are polynomial in $D$. Despite much research done in this area, it is still not known whether cell decomposition, the foundational operation of o-minimal geometry, preserves polynomial dependence on $D$. We slightly modify the usual notions of format and degree and prove that with these revised notions, this does in fact hold. As one consequence, we also obtain the first polynomial (in $D$) upper bounds for the sum of Betti numbers of sets defined using quantified formulas in the restricted sub-Pfaffian structure.

Effect of Fluoroethylene Carbonate Additive on the Initial Formation of Solid Electrolyte Interphase on Oxygen Functionalized Graphitic Anode in Lithium Ion Batteries

The formation of a solid electrolyte interphase (SEI) at the electrode/electrolyte interface substantially affects the stability and lifetime of lithium-ion batteries (LIBs). One of the methods to improve the lifetime of LIBs is by the inclusion of additive molecules to stabilize the SEI. To understand the effect of additive molecules on the initial stage of SEI formation, we compare the decomposition and oligomerization reactions of a fluoroethylene carbonate (FEC) additive on a range of oxygen functionalized graphitic anode to those of an ethylene carbonate (EC) organic electrolyte. A series of density functional theory (DFT) calculations augmented by ab-initio molecular dynamics (AIMD) simulations reveal that EC decomposition on an oxygen functionalized graphitic (1120) edge facet through an SN2 mechanism is spontaneous, even in an uncharged cell. Decomposition of EC through an SN2 reaction pathway results in alkoxide species regeneration which is responsible for continual oligomerization along the graphitic surface. In contrast, FEC prefers to decompose through an SN1 pathway, which does not promote alkoxide regeneration. The ability of FEC as an additive to suppress alkoxide regeneration results in a smaller and thinner SEI layer that is more flexible towards lithium intercalation during the charging/discharging process. In addition, the presence of different oxygen functional groups at the surface of graphite dictates the oligomerization products and LiF formation in the SEI.

Effect of Fluoroethylene Carbonate Additive on the Initial Formation of Solid Electrolyte Interphase on Oxygen Functionalized Graphitic Anode in Lithium Ion Batteries

The formation of a solid electrolyte interphase (SEI) at the electrode/electrolyte interface substantially affects the stability and lifetime of lithium-ion batteries (LIBs). One of the methods to improve the lifetime of LIBs is by the inclusion of additive molecules to stabilize the SEI. To understand the effect of additive molecules on the initial stage of SEI formation, we compare the decomposition and oligomerization reactions of a fluoroethylene carbonate (FEC) additive on a range of oxygen functionalized graphitic anode to those of an ethylene carbonate (EC) organic electrolyte. A series of density functional theory (DFT) calculations augmented by ab-initio molecular dynamics (AIMD) simulations reveal that EC decomposition on an oxygen functionalized graphitic (1120) edge facet through an SN2 mechanism is spontaneous, even in an uncharged cell. Decomposition of EC through an SN2 reaction pathway results in alkoxide species regeneration which is responsible for continual oligomerization along the graphitic surface. In contrast, FEC prefers to decompose through an SN1 pathway, which does not promote alkoxide regeneration. The ability of FEC as an additive to suppress alkoxide regeneration results in a smaller and thinner SEI layer that is more flexible towards lithium intercalation during the charging/discharging process. In addition, the presence of different oxygen functional groups at the surface of graphite dictates the oligomerization products and LiF formation in the SEI.