Continuous Curve Research Articles

Warehouse Path Planning Using Low-order Bézier Curves with Minimum-Time Optimization*

In this paper, low-order Bézier motion primitives are proposed for motion planning in corridor-constrained spaces, which is illustrated on a warehouse application. The proposed primitives are easily computed for given requirements (initial and final position, orientation and curvature). A new parametrization of the motion primitives is provided which allows an intuitive geometric interpretation. The combined path constructed from these primitives has a minimal number of turns, as third-order Bezier curves are used. At the same time, the combined path has continuous curvature. A path planning approach is proposed that finds the optimal combination of primitives that results in a minimum travel time while satisfying constraints on velocity, acceleration, and free space. To illustrate the applicability of the approach, a comparison with a typical predefined warehouse path and an existing advanced optimisation planner is provided and evaluated.

Optimal smooth polynomial lane change generation for autonomous racing

Online path re-planning is a crucial task for the control of autonomous vehicles, especially when driving at the handling limits in a dynamic environment. In this article, we propose a fast path planning algorithm meant for trajectory change scenarios, that is tailored to generate smooth reference paths. The proposed solution is based on a convex combination of the current and target paths, and guarantees heading and curvature continuity. Additionally, we complete the algorithm with a real-time compliant nonlinear program to generate nearly-time-optimal maneuvers. The proposed approach is tested on a driving simulator and compared against state-of-the-art solutions, which typically rely on numerical differentiation of path coordinates, often introducing inaccuracy and yielding inefficient or imprecise solutions.

Construction of 3D Motion Model Based on Simulation Algorithm

With the development of 3D technology, the construction of 3D motion model has become an important research issue in many fields, such as virtual reality, animation and robot vision. In this paper, a 3D motion model construction method based on simulation algorithm is proposed. Firstly, the gravity simulation algorithm is used to simulate the trajectory of the object, and the position data of multiple moments with numerical accuracy of 10cm are obtained. Then, the interpolation algorithm is used to interpolate these position data into continuous curves, and the object trajectory with 1cm accuracy is obtained. Finally, we integrate the obtained trajectory data with 3D modeling software to generate a 3D motion model with real motion effect. The experimental results show that this method has high accuracy and reliability in constructing 3D motion model, and is suitable for many fields.

Modeling discontinuous growth in reared Panulirus ornatus: A generalized additive model and Cox proportional hazard model approach.

Crustaceans exhibit discontinuous growth as they shed hard shells periodically. Fundamentally, the growth of crustaceans is typically assessed through two key components, length increase after molting (LI) and time intervals between consecutive molts (TI). In this article, we propose a unified likelihood approach that combines a generalized additive model and a Cox proportional hazard model to estimate the parameters of LI and TI separately in crustaceans. This approach captures the observed discontinuity in individuals, providing a comprehensive understanding of crustacean growth patterns. Our study focuses on 75 ornate rock lobsters (Panulirus ornatus) off the Torres Strait in northeastern Australia. Through a simulation study, we demonstrate the effectiveness of the proposed models in characterizing the discontinuity with a continuous growth curve at the population level.

Sequential Modeling by Leveraging Non-Uniform Distribution of Speech Emotion

The expression and perception of human emotions are not uniformly distributed over time. Therefore, tracking local changes of emotion within a segment can lead to better models for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">speech emotion recognition</i> (SER), even when the task is to provide a sentence-level prediction of the emotional content. A challenge to exploring local emotional changes within a sentence is that most existing emotional corpora only provide sentence-level annotations (i.e., one label per sentence). This labeling approach is not appropriate for leveraging the dynamic emotional trends within a sentence. We propose a framework that splits a sentence into a fixed number of chunks, generating chunk-level emotional patterns. The approach relies on emotion rankers to unveil the emotional pattern within a sentence, creating continuous emotional curves. Our approach trains the sentence-level SER model with a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sequence-to-sequence</i> formulation by leveraging the retrieved emotional curves. The proposed method achieves the best <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">concordance correlation coefficient</i> (CCC) prediction performance for arousal (0.7120), valence (0.3125), and dominance (0.6324) on the MSP-Podcast corpus. In addition, we validate the approach with experiments on the IEMOCAP and MSP-IMPROV databases. We further compare the retrieved curves with time-continuous emotional traces. The evaluation demonstrates that these retrieved chunk-label curves can effectively capture emotional trends within a sentence, displaying a time-consistency property that is similar to time-continuous traces annotated by human listeners. The proposed SER model learns meaningful, complementary, local information that contributes to the improvement of sentence-level predictions of emotional attributes.

COUNTABLE SPACES WITH PEANO PROPERTY

In 1890, Giuseppe Peano published an example of a continuous curve passing through every point of the square $[0,1]^2$. A curve with such properties is called a Peano curve. In fact, Peano constructed a continuous surjective mapping from the unit segment $[0,1]$ to the square $[0,1]^2$. Peano's research was motivated by one result of George Cantor that the set of points of a unit segment has the same cardinality as the set of points of a unit square.In 1890, Giuseppe Peano published an example of a continuous curve passing through every point of the square $[0,1]^2$. A curve with such properties is called a Peano curve. In fact, Peano constructed a continuous surjective mapping from the unit segment $[0,1]$ to the square $[0,1]^2$. Peano's research was motivated by one result of George Cantor that the set of points of a unit segment has the same cardinality as the set of points of a unit square. According to the Hahn-Mazurkevich theorem the Hausdorff topological space $X$ is a continuous image of a unit segment $[0,1]$ if and only if when $X$ is compact, metrizable, connected, locally connected and nonempty. The Hausdorff continuous image of a segment is called {\it Peano space} or {\it Peano continuum}. Sierpinski proved that a connected compact metric space $X$ is a Peano continuum if and only if for every $\varepsilon&gt;0$ the space $X$ can be covered by connected sets of the diameter $\le\varepsilon$. Therefore, naturally arises question about the investigation of disconnected metric spaces $X$ for which there is a continuous surjection between $X$ and $X^2$. Sierpinski characterized rational numbers as a metric countable space without isolated points. Hausdorff described irrational numbers as a metric, separable, completely metrizable, zero-dimensional and nowhere locally compact space. It follows, in particular, that the square $\mathbb Q^2$ is a continuous image of the set $\mathbb Q$ and the square of irrational numbers is a continuous image of the set of irrational numbers. Thus, it would be interesting to find a description of other disconnected subsets of the real line, except those that are homeomorphic to $\mathbb Q$ or $\mathbb R\setminus Q$. In this article we will focus on countable sets such that the set of isolated points of which may not be empty. The main result is the following (see Theorem 2): the square of a countable regular topological space $X$ is its continuous image if and only if $X$ is not compact.

A Remark on Tonelli’s Calculus of Variations

This paper provides a quite simple method of Tonelli’s calculus of variations with positive definite and superlinear Lagrangians. The result complements the classical literature of calculus of variations before Tonelli’s modern approach. Inspired by Euler’s spirit, the proposed method employs finite-dimensional approximation of the exact action functional, whose minimizer is easily found as a solution of Euler’s discretization of the exact Euler – Lagrange equation. The Euler – Cauchy polygonal line generated by the approximate minimizer converges to an exact smooth minimizing curve. This framework yields an elementary proof of the existence and regularity of minimizers within the family of smooth curves and hence, with a minor additional step, within the family of Lipschitz curves, without using modern functional analysis on absolutely continuous curves and lower semicontinuity of action functionals.

The optimization of continuous discount function through the continuous yield curve trajectories involving the parsimonious Nelson-siegel model

Yield curves which explain the variation in interest rates over varying maturities, provide important indicators with potentially useful implications on the investment choices, risk management strategies of financial institutions and fiscal policies of regulators. Accurately estimating the parsimonious parameters of the yield curve and modelling the discount function is highly important. The continuous forward rate function is a transformed discount function as a numerical device employed to obtain the price of a collection of bonds since the present value of a set of cash flows is computed by finding the product of these cash flows and the associated discount function. Nigeria’s bond market representing a major segment of the capital market and an important means of monetary transmission framework has suffered continuous liquidity problems. The lack of functional capital market instruments in form of government bonds has accounted for the poor performance of bond market. Consequently, this study intends to (i) Compute the discount function and (ii) Show its applications on life insurance offerings. This study analysed the term structure of interest rates using the Nigerian Eurobond which was collected for the years 2018 and 2019 from which the discount functions were constructed by adopting the continuous Nelson Siegel continuous function. A t-test conducted on the adjusted R2 on the model using Ordinary Least Square method after fixing the shape parameters was applied after computing the exponentially decaying factor. Computational evidence from the results reveals that the adjusted 𝑅square for 2018 and 2019 are 0.976and respectively0.986. This indicates that 97.6%of 2018 and 98.6% of the observed data can be explained by the Nelson-Siegel model of data using the estimated parameters for the two years and hence the result suggests a high level of accuracy confirming the degree to which the Nelson-Siegel yield curve parameters has estimated the illiquid Nigerian financial market.

Absolute Nodal Coordinate Formulation-Based Shape Sensing Approach for Large Deformation: Plane Beam

The inverse finite element method (IFEM) is currently one of the most studied methods in the field of shape sensing, in other words, the reconstruction of the displacement field of a structure from discrete strain measures. The current research is still insufficient in applying IFEM to flexible structures undergoing large deformation that are in increasing demand, especially in terms of computational efficiency. Hence, an element-by-element IFEM approach based on absolute nodal coordinate formulation (ANCF) is developed in the paper. Taking the plane beam as the object, a class of gradient-deficient ANCF plane beam element is introduced to provide a concise nonlinear nodal displacement/strain relationship. Similar to IFEM, the inverse ANCF (IANCF) plane beam element is obtained in the form of least-square formulation, which means IANCF describes the deformation reconstruction problem as a nonlinear optimization problem. Because the computational complexity of solving nonlinear optimization problems increases rapidly with the increase of the number of decision variables, an element-by-element solution algorithm that solves each element relatively independently is adopted, and the explicit iterative formula is given by the Newton method. Besides, a curvature continuity constraint is introduced to improve the well-posed-ness of this problem and the smoothness of the reconstructed shape. Through numerical analysis, IANCF exhibits remarkable accuracy in various deformation degrees and its insensitivity to the weight factors inherited from IFEM. In the experiment conducted with surface-mounted distributed optical fiber sensors, the effectiveness of IANCF for practical structures is verified.

Global bifurcation structure and some properties of steady periodic water waves with vorticity

This paper studies the classical water wave problem with vorticity described by the Euler equations with a free surface under the influence of gravity over a flat bottom. Based on fundamental work [5], we first obtain two continuous bifurcation curves which meet the laminar flow only one time by using the modified analytic bifurcation theorem. They are symmetric waves whose profiles are monotone between each crest and trough. Moreover, we show a connection between the concavity and convexity of wave profile and the monotonicity of the vertical velocity component v along the free surface. As an important application, we make up the missing major aspect on the behavior of v as mentioned in [4, Sect 4.4] for small amplitude waves. In addition, for favorable vorticity, we prove that the vertical displacement of water waves decreases with depth.

Path-planning algorithms for self-driving vehicles based on improved RRT-Connect

Abstract This study aims to solve path planning of intelligent vehicles in self-driving. In this study, an improved path-planning method combining constraints of the environment and vehicle is proposed. The algorithm designs a reasonable path cost function, then uses a heuristic guided search strategy to improve the speed and quality of path planning, and finally generates smooth and continuous curvature paths based on the path post-processing method focusing on the requirements of path smoothness. A simulation test shows that compared with the basic rapidly-exploring random tree (RRT), RRT-Connect and RRT* algorithms, the path length of the proposed algorithm can be reduced by 19.7%, 29.3% and 1% respectively, and the maximum planned path curvature of the proposed algorithm is 0.0796 m-1 and 0.1512 m-1 respectively, under the condition of a small amount of planning time. The algorithm can plan the more suitable driving path for intelligent vehicles in a complex environment.

Fractal Curves on Banach Algebras

Most of the fractal functions studied so far run through numerical values. Usually they are supported on sets of real numbers or in a complex field. This paper is devoted to the construction of fractal curves with values in abstract settings such as Banach spaces and algebras, with minimal conditions and structures, transcending in this way the numerical underlying scenario. This is performed via fixed point of an operator defined on a b-metric space of Banach-valued functions with domain on a real interval. The sets of images may provide uniparametric fractal collections of measures, operators or matrices, for instance. The defining operator is linked to a collection of maps (or iterated function system, and the conditions on these mappings determine the properties of the fractal function. In particular, it is possible to define continuous curves and fractal functions belonging to Bochner spaces of Banach-valued integrable functions. As residual result, we prove the existence of fractal functions coming from non-contractive operators as well. We provide new constructions of bases for Banach-valued maps, with a particular mention of spanning systems of functions valued on C*-algebras.

Integrated Approach Determines Formation-Water Salinity

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 22548, “Integrated Approach for Formation-Water-Salinity Determination,” by Tariq Alshaikhmubarak, SPE, and Laila Mira, SPE, Saudi Aramco, and Sherif Ghadiry, Schlumberger, et al. The paper has not been peer reviewed. Copyright 2022 International Petroleum Technology Conference. Reproduced by permission. _ In the complete paper, two methodologies are tested to achieve measurement of formation-water salinity. First, a novel dry-weight chlorine (DWCL) measurement from an advanced spectroscopy tool is used to estimate the formation salinity at the depth of investigation of the device. The second methodology uses a new downhole induction resistivity cell in the formation-tester tool. The chlorine measurement, along with the flowline-induction-resistivity measurement, helps enhance the quality of saturation evaluation for quick decision making during logging operations and acceleration of evaluation studies instead of waiting on laboratory results. Chlorine Work Flow The ability to quantify chlorine concentration can help derive formation salinity as a continuous curve. Because chlorine has a large capture cross section, it is possible to extract it from capture gamma ray spectra with acceptable uncertainty, but the real challenge is to split the total chlorine signal seen by the tool into formation chlorine signal and borehole contribution. The chlorine signal split is a fundamental step in this work flow, outlined in Fig. 1. Once the chlorine concentration in the formation is obtained—expressed as DWCL—several petrophysical applications are enabled. The first is computation of water volume assuming a known formation-water salinity. The second is computation of the sodium chloride (NaCl) equivalent salinity from an independent volume of water and DWCL. Finally, one can solve for the NaCl equivalent water salinity. Equations to achieve these steps are provided in the complete paper. Interpretation Considerations Capture spectroscopy measurements have a shallow depth of investigation (DOI) in the range of 8–10 in., which means sensitivity to mud-filtrate invasion in the volume of rock probed by the tool. The mud-filtrate invasion is controlled by several factors, including mud overbalance, formation exposure time to mud, formation porosity and permeability, and mudcake-formation process and efficiency. These factors must be considered when using the chlorine work flow to assess the effect of the invading water-based-mud (WBM) filtrate, which normally has a different salinity than the formation water. The main effect of oil-based-mud (OBM) filtrate invasion, assuming that only the oil phase is invading the formation, is a reduction of water volume at the measurement DOI, degrading the statistical precision of the DWCL and increasing the uncertainty in the computed salinity.

Personalization of IVF-ICSI workflow based on patient characteristics improves IVF laboratory outcomes and embryo ploidy by PGT-A

BackgroundIntracytoplasmic sperm injection (ICSI) has become a common method of fertilization in assisted reproduction worldwide. However, there are still gaps in knowledge of the ideal IVF-ICSI workflow including the optimal duration of time between induction of final oocyte maturation, oocyte denudation and ICSI. The aim of this study was to examine outcomes following different workflow protocols in IVF-ICSI procedures in blastocysts that have undergone undisturbed incubation and preimplantation genetic testing for aneuploidy (PGT-A) prior to transfer.MethodsRetrospective secondary analysis of 113 patients (179 IVF cycles, 713 embryos), all of whom have gone through IVF-ICSI and PGT-A using undisturbed culture. Predictive test variables were the length of time from: trigger to OPU, OPU to denudation, and denudation to ICSI. Outcome metrics assessed were: maturation, fertilization, blastulation and euploid rates. Generalized Estimated Equations Linear Model was used to examine the relationship between key elements of a given cycle and continuous outcomes and LOESS curves were used to determine the effect over time.ResultsIn a paired multi-regression analysis, where each patient served as its own control, delaying OPU in patients with unexplained infertility improved both maturation and blastulation rates (b = 29.7, p < 0.0001 and b = 9.1, p = 0.06, respectively). Longer incubation with cumulus cells (CCs) significantly correlated with improved ploidy rates among patients under 37, as well as among patients with unexplained infertility (r = 0.22 and 0.29, respectively), which was also evident in a multiple regression analysis (b = 6.73, p < 0.05), and in a paired analysis (b = 6.0, p < 0.05). Conversely, among patients with a leading infertility diagnosis of male factor, longer incubation of the denuded oocyte prior to ICSI resulted in a significantly higher euploid rate (b = 15.658, p < 0.0001).ConclusionsIn this study we have demonstrated that different IVF-ICSI workflows affect patients differently, depending on their primary infertility diagnosis. Thus, ideally, the IVF-ICSI workflow should be tailored to the individual patient based on the primary infertility diagnosis. This study contributes to our understanding surrounding the impact of IVF laboratory procedures and highlights the importance of not only tracking “classic” IVF outcomes (maturation, fertilization, blastulation rates), but highlights the importance that these procedures have on the ploidy of the embryo.

Smooth Planning for Manipulator with Multi-dimensional Actuator based on Quintic B-spline

In order to solve the impact problem of uneven velocity during continuous operation for manipulator with multi-dimensional actuator, a smooth planning scheme based on Quintic B-spline algorithm was proposed. Firstly, the physical model of multi-dimensional actuator and its working principle were introduced. At the same time, the motion of the output axis vertex in space was decomposed into three steps, which can make the position relationship between the points more intuitive and convenient for our study. Secondly, the characteristics of Quintic B-spline algorithm were analysed. In this step, the B-spline interpolation function was defined at first, and the basis function of polynomial of degree p was defined according to the relevant information and its characteristics were indicated. Then, we analysed the node sequence parameters. For Quintic B-spline algorithm, when the position sequence of the rotor running track was given, three conditions must be satisfied to uniquely determine the corresponding B-spline function, namely: node vector, control vertex and the degree p of the B-spline curve. On this basis, the boundary constraints and control vertices were solved, which was a very important step. By solving the control vertices of Quintic B-spline curve, a smooth and continuous angular displacement curve can be obtained. The addition of four boundary conditions greatly increases the controllability of the system, making the rotor can start and stop in any way within the constraint conditions, and the connection of each interpolation point is smooth and continuous. The Quintic B-spline algorithm interpolation curve was obtained by simulation based on the time-position sequence of the actuator interpolation points. The results of the interpolation curve verified the effectiveness of the Quintic B-spline algorithm. In addition, three continuous running planning conditions were designed for the same interpolation sequence of the rotor to verify the controllability of the algorithm to the angular velocity and angular acceleration of the rotor during operation. The simulation results show that the Quintic B-spline algorithm has strong controllability for the angular velocity of actuator, and can effectively alleviate the soft impact of the system. Finally, a smooth planning experimental platform with multi-dimensional actuator was built. By setting the same trajectory and different interpolation points, the proposed Quintic B-spline algorithm was compared with the existing S-shaped curve planning algorithm based on the improvement. The results show that the proposed scheme has high control accuracy and strong impact mitigation performance, which can provide a reference for other multi-dimensional actuator trajectory planning.

Three-Dimensional Dubins-Path-Guided Continuous Curvature Path Smoothing

This paper presents an efficient three-dimensional (3D) Dubins path design and a new continuous curvature path-smoothing algorithm. The proposed 3D Dubins path is a simple extension of the 2D path and serves as a reference path generator to guide the proposed smoothing algorithm. In the smoothing algorithm, the reference path is approximated by several cubic Bezier curves to generate a parametric path that simultaneously satisfies curvature continuity and maximum curvature requirements. The algorithm also provides a criterion to select a required number of Bezier curves to strictly meet the maximum curvature constraint. Therefore, our algorithm can be used for 3D path-following applications in many areas such as aerospace and robotics. The numerical simulation results show that the proposed algorithm produces a continuous curvature path that passes through all waypoints with a slight increase in path length compared with the original 3D Dubins reference path.

Numerical Simulation on Optimization of Process Parameters for Free Bending of Metal Tubes

Three-dimensional free bending is a new tube forming technology with continuous variable curvature. In order to improve the forming quality of tube, this paper studies the principle of three-dimensional free forming system and the numerical calculation of bending moment in detail, and it uses the finite element simulation to model the mechanism in the bending process. The simulation model is used to simulate the forming process of copper tube, and the influence of key process parameters on the forming process is analyzed,the shape of the inner cavity of the bending die and the gap between the tube and the bending die are studied, the distance between the bending die and the guide column is studied, the axial feed rate on the forming quality of tubular bending parts has also been studied. The optimum process parameters were determined by finite element simulation and analysis.

Geometry of planar curves intersecting many lines at a few points

The local Lipschitz property is shown for the graphs avoiding multiple point intersection with lines directed in a given cone. The assumption is much stronger than those of Marstrand’s well-known theorem, but the conclusion is much stronger too. Additionally, a continuous curve with a similar property is σ \sigma -finite with respect to Hausdorff length and an estimate on the Hausdorff measure of each “piece” is found.

A New Portfolio Optimization Model Under Tracking-Error Constraint with Linear Uncertainty Distributions.

Enhanced index tracking problem is the issue of selecting a tracking portfolio to outperform the benchmark return with a minimum tracking error. In this paper, we address the enhanced index tracking problem based on uncertainty theory where stock returns are treated as uncertain variables instead of random variables. First, we propose a nonlinear uncertain optimization model, i.e., uncertain mean-absolute downside deviation enhanced index tracking model. Then, we give the analytical solution of the proposed optimization model when stock returns take linear uncertainty distributions. Based on the solution, we find that tracking portfolio frontier is a continuous curve composed of at most n-1 different line segments. Furthermore, we give the condition that tracking portfolio return and risk increase with benchmark return and risk, respectively. Finally, we offer some experiments and show that our proposed model is effective in controlling the tracking error.

Minimal length multi-segment clothoid return paths for vehicles with turn rate constraints

Continuous curvature recovery paths are needed to accurately return a fixed wing autonomous vehicle with turn rate constraints back to a missions path in the correct direction after collision avoidance. Clothoid paths where curvature is linearly dependent to arc length can be used to make multi-segment splines with continuous curvature, but require optimization to ensure that the path is of minimal length while meeting curvature and sharpness limits. The present work considers the problem of returning a fixed wing aircraft back to its original path facing the correct direction after a leaving it during collision avoidance by presenting a method of optimizing a three segment clothoid spline to be of minimal length while meeting fixed wing turn rate constraints and targeting a path function. The impact of this work is enabling accurate path recovery after collision avoidance with minimal length paths that minimize the time spent off a missions planned route, giving better control over time of arrival for the planned route and more time to complete mission objectives.