Control Points Of Curve Research Articles

Improving mechanical properties of lattice structures using nonuniform hollow struts

In contrast to constant-strut lattices, the introduction of innovative strut designs has the potential to enhance the mechanical properties of lattice structures. This study presents a Bézier curve-based nonuniform section design for body-centered cubic lattices with hollow struts (BCCH). Periodic boundary conditions are applied to the unit cells, and a finite element (FE) numerical homogenization method is employed to assess their elastic properties. A comprehensive dataset is generated through the FE model, which is subsequently divided into training, validation, and testing sets. The coordinates of the Bézier curve control points serve as inputs to deep learning networks, which are trained on the training dataset. Relative density and elastic properties are treated as two distinct networks, with the validation set utilized to prevent overfitting. The objective function consists of two weighted components: one aims to maximize the relative Young's modulus, while the other ensures that the relative density achieves a specified value. An evolutionary algorithm is employed to optimize the objective function, with variations in the control point coordinates constrained to specific ranges. By leveraging the fast inference ability of the deep learning model, the stiffness and orientation-dependent mechanical properties can be efficiently tailored. Our results demonstrate that the optimized structures demonstrate superior stiffness (+92.8 %) and distributed stress field compared to the benchmark lattice. The design method also enables tailoring of specific mechanical properties, including isotropic elasticity. 3D-printed lattice designs were fabricated and compression tests confirmed agreement with simulation results in terms of stiffness. Additionally, the optimized designs exhibit superior strength (+99.6 %) and toughness compared to the benchmark lattices.

Research on the Application of Computer Big Data Technology in Smart Travel

This paper mainly focuses on the algorithms related to local path planning and path tracking control of unmanned vehicles in the process of obstacle avoidance. By introducing the temporal dimension as a reference, the perceptual results are projected onto the 3D spatio-temporal navigation map by combining the multi-target behavior prediction and other means; by increasing the temporal dimension, the static obstacles and dynamic obstacles are unified into the same parameter space. Under this parameter space, the front-end A* path search initializes the unified B spline curve control points, designs the trajectory cost function and performs nonlinear optimization to generate a spatio-temporal trajectory that satisfies the safety collision-free and vehicle motion constraints (speed and acceleration limits), thus transforming the decision and planning problem under the two-dimensional fence dynamic physical space into a static scene decision and planning problem under the three-dimensional spatio-temporal space. Through simulation verification, the whole process of the proposed trajectory planning method takes 51.27ms on average, which meets the driving requirements of driverless cars. In addition, by adjusting the search conditions of the A* algorithm, its overall planning efficiency is improved by 27.86% compared with the search speed of the traditional algorithm. The actual feeling and data results from the real vehicle experiments show its good tracking effect, which verifies the effectiveness and practicality of the algorithm proposed in this paper.

A Novel Method of Designing Random Rough Surface Considering Its Contact Force-Deformation Characteristic Requirement

Abstract The height probability distribution (HPD) of random rough surface topography has significant effect on its contact behaviors. In this paper, an optimization model to calculate the optimal HPD of random rough surface topography to make its contact force-deformation characteristic satisfy the given target force-deformation characteristic was established. In the solution to calculate the optimal HPD, using Bezier interpolation curve to represent the curve of HPD function and using the positions of the control points of Bezier interpolation curve as optimization variables were proposed. The solution was validated by numerical simulations implemented using MATLAB. The effect of the number of the control points on the minimum objective function value was investigated. Through analyzing the obtained result, we found the most appropriate number of the control points is 35. Comparison with the method using height parameters as optimization variables in literature was implemented. It was found that the proposed method is applicable to broader types of contact force-deformation characteristic requirements than the method using height parameters as optimization variables.

DPText-DETR: Towards Better Scene Text Detection with Dynamic Points in Transformer

Recently, Transformer-based methods, which predict polygon points or Bezier curve control points for localizing texts, are popular in scene text detection. However, these methods built upon detection transformer framework might achieve sub-optimal training efficiency and performance due to coarse positional query modeling. In addition, the point label form exploited in previous works implies the reading order of humans, which impedes the detection robustness from our observation. To address these challenges, this paper proposes a concise Dynamic Point Text DEtection TRansformer network, termed DPText-DETR. In detail, DPText-DETR directly leverages explicit point coordinates to generate position queries and dynamically updates them in a progressive way. Moreover, to improve the spatial inductive bias of non-local self-attention in Transformer, we present an Enhanced Factorized Self-Attention module which provides point queries within each instance with circular shape guidance. Furthermore, we design a simple yet effective positional label form to tackle the side effect of the previous form. To further evaluate the impact of different label forms on the detection robustness in real-world scenario, we establish an Inverse-Text test set containing 500 manually labeled images. Extensive experiments prove the high training efficiency, robustness, and state-of-the-art performance of our method on popular benchmarks. The code and the Inverse-Text test set are available at https://github.com/ymy-k/DPText-DETR.

Fairing-PIA: progressive-iterative approximation for fairing curve and surface generation

The fairing curves and surfaces are used extensively in geometric design, modeling, and industrial manufacturing. However, the majority of conventional fairing approaches, which lack sufficient parameters to improve fairness, are based on energy minimization problems. In this study, we develop a novel progressive-iterative approximation method for the fairing curve and surface generation (fairing-PIA). Fairing-PIA is an iteration method that can generate a series of curves (surfaces) by adjusting the control points of B-spline curves (surfaces). In fairing-PIA, each control point is endowed with an individual weight. Thus, the fairing-PIA has many parameters to optimize the shapes of curves and surfaces. Not only a fairing curve (surface) can be generated globally through fairing-PIA, but also the curve (surface) can be improved locally. Moreover, we prove the convergence of the developed fairing-PIA and show that the conventional energy minimization fairing model is a special case of fairing-PIA. Finally, numerical examples indicate that the proposed method is effective and efficient.

Predictive Assessment of Mycological State of Bulk-Stored Barley Using B-Splines in Conjunction with Genetic Algorithms

Postharvest grain preservation and storage can significantly affect the safety and nutritional value of cereal-based products. Negligence at this stage of the food processing chain can lead to mold development and mycotoxin accumulation, which pose considerable threats to the quality of harvested grain and, thus, to consumer health. Predictive models evaluating the risk associated with fungal activity constitute a promising solution for decision-making modules in advanced preservation management systems. In this study, an attempt was made to combine genetic algorithms and B-spline curves in order to develop a predictive model to assess the mycological state of malting barley grain stored at various temperatures (T = 12–30 °C) and water activity in grain (aw = 0.78–0.96). It was found that the B-spline curves consisting of four second-order polynomials were sufficient to approximate the datasets describing fungal growth in barley ecosystems stored under steady temperature and humidity conditions. Based on the designated structures of B-spline curves, a universal parameterized model covering the entire range of tested conditions was developed. In the model, the coordinates of the control points of B-spline curves were modulated by genetic algorithms using values of storage parameters (aw and T). A statistical assessment of model performance showed its high efficiency (R2 = 0.94, MAE = 0.21, RMSE = 0.28). As the proposed model is based on easily measurable on-line storage parameters, it could be used as an effective tool supporting modern systems of postharvest grain treatment.

Shape Reconstruction for Continuum Robot Based on Pythagorean Hodograph–Bézier Curve With IMU and Vision Sensors

The shape information is the key to realize real-time, accurate, and effective control of continuum robots. Traditional image processing method and start-to-end-point fitting method are combined. Inertial measurement unit (IMU) and camera are used to capture the end position and attitude information of continuum robot and do not rely on the acquisition of the global image to solve the problem of limited vision in a traditional image processing method. In addition, a new start-to-end-point fitting method is proposed, which is the Pythagorean hodograph—Bézier (PH-B) fitting method. The new method simplifies the solving steps of control points of fitting curve. The control points can be obtained only through the geometric relationship and do not need to rely on an optimization algorithm for iterative solution. This method has good shape fitting accuracy and applicability in the curvature range from 0° to 90° through the simulation analysis. A variety of experiments are designed to verify the results. The experimental results show that the maximum shape reconstruction error by the proposed method is about 2 mm. This proves the applicability of the PH-B method in the shape reconstruction of continuum robots.

Speed Adaptive Robot Trajectory Generation Based on Derivative Property of B-Spline Curve

In order to improve the safety of autonomous flight of quadrotor in three-dimensional complex environments, this paper proposes a speed adaptive motion planning method by limiting the distance between two adjacent control points based on the derivative property of B-Spline curve. First the initial B-Spline curve control points and the speed constraints based on derivative property are efficiently obtained by the front-end search that is divided into the shortest safe path search and reasonable step targeted expansion satisfying dynamic constraints. Then the back-end optimization assigns the corresponding safe flight corridor to the local trajectories according to the stage of the initial control points and uses MINVO basis ([1]) to limit the simplexes with minimum volume enclosing local trajectories. The trajectory generation is finally formulated as a Quadratically Constrained Quadratic Program (QCQP) which can be solved efficiently. Both simulations and real-world experiments validate the efficiency and performance of this method in generating safe, smooth, speed adaptive trajectories.

Adaptive Visual Servoing Shape Control of a Soft Robot Manipulator Using Bézier Curve Features

Soft continuum robot outperforms its rigid counterpart when executing in complicated environments thanks to its high dexterity of the redundant configuration. Shape control is regarded as a prerequisite to applications in unstructured environments. In this article, we develop an adaptive image-based visual servoing (IBVS) algorithm using an uncalibrated camera to realize visual shape control of the cable-driven soft manipulator. A Bézier curve is selected to be the feature providing shape information of the soft robot. An adaptive law is proposed to simultaneously solve the uncalibrated problem and to analytically model the motion of curve control points. The control algorithm is then designed with third-order Bézier curve being the image features, and theoretically proves its stability. The algorithm has been experimentally validated in the cable-driven soft continuum robot. The experiment results demonstrate rapid converging performance to C-type and S-type reference shapes.

BézierSeg: Parametric Shape Representation for Fast Object Segmentation in Medical Images.

Delineating the lesion area is an important task in image-based diagnosis. Pixel-wise classification is a popular approach to segmenting the region of interest. However, at fuzzy boundaries, such methods usually result in glitches, discontinuity or disconnection, inconsistent with the fact that lesions are solid and smooth. To overcome these problems and to provide an efficient, accurate, robust and concise solution that simplifies the whole segmentation pipeline in AI-assisted applications, we propose the BézierSeg model which outputs Bézier curves encompassing the region of interest. Directly modeling the contour with analytic equations ensures that the segmentation is connected and continuous, and that the boundary is smooth. In addition, it offers sub-pixel accuracy. Without loss of precision, the Bézier contour can be resampled and overlaid with images of any resolution. Moreover, clinicians can conveniently adjust the curve's control points to refine the result. Our experiments show that the proposed method runs in real time and achieves accuracy competitive with pixel-wise segmentation models.

Cognitive Granular-Based Path Planning and Tracking for Intelligent Vehicle with Multi-Segment Bezier Curve Stitching

Unmanned vehicles are currently facing many difficulties and challenges in improving safety performance when running in complex urban road traffic environments, such as low intelligence and poor comfort performance in the driving process. The real-time performance of vehicles and the comfort requirements of passengers in path planning and tracking control of unmanned vehicles have attracted more and more attentions. In this paper, in order to improve the real-time performance of the autonomous vehicle planning module and the comfort requirements of passengers that a local granular-based path planning method and tracking control based on multi-segment Bezier curve splicing and model predictive control theory are proposed. Especially, the maximum trajectory curvature satisfying ride comfort is regarded as an important constraint condition, and the corresponding curvature threshold is utilized to calculate the control points of Bezier curve. By using low-order interpolation curve splicing, the planning computation is reduced, and the real-time performance of planning is improved, compared with one-segment curve fitting method. Furthermore, the comfort performance of the planned path is reflected intuitively by the curvature information of the path. Finally, the effectiveness of the proposed control method is verified by the co-simulation platform built by MATLAB/Simulink and Carsim. The simulation results show that the path tracking effect of multi-segment Bezier curve fitting is better than that of high-order curve planning in terms of real-time performance and comfort.

BoolSurf

We port Boolean set operations between 2D shapes to surfaces of any genus, with any number of open boundaries. We combine shapes bounded by sets of freely intersecting loops, consisting of geodesic lines and cubic Bézier splines lying on a surface. We compute the arrangement of shapes directly on the surface and assign integer labels to the cells of such arrangement. Differently from the Euclidean case, some arrangements on a manifold may be inconsistent. We detect inconsistent arrangements and help the user to resolve them. Also, we extend to the manifold setting recent work on Boundary-Sampled Halfspaces, thus supporting operations more general than standard Booleans, which are well defined on inconsistent arrangements, too. Our implementation discretizes the input shapes into polylines at an arbitrary resolution, independent of the level of resolution of the underlying mesh. We resolve the arrangement inside each triangle of the mesh independently and combine the results to reconstruct both the boundaries and the interior of each cell in the arrangement. We reconstruct the control points of curves bounding cells, in order to free the result from discretization and provide an output in vector format. We support interactive usage, editing shapes consisting up to 100k line segments on meshes of up to 1M triangles.

Parametric PH Curves Model Based Kinematic Control of the Shape of Mobile Soft Manipulators in Unstructured Environment

Mobile soft continuum manipulator (MSCM) is more and more used in various applications of everyday life, such as logistics, farming, medical diagnosis, medical therapy, bakery, human collaboration, etc. However, the control of its shape remains a major challenge, especially when it is navigating in an unstructured environment. In this contribution, a kinematic-model-based shape control is designed in the space configuration for an MSCM, allowing its autonomous navigation in the presence of obstacles. For that purpose, the shape kinematic modeling is realized using a parametric spatial Pythagorean hodograph (PH) curve with a predefined length, whereas the artificial potential field algorithm acts on the control points of the PH curve for shape adaptation in presence of obstacles. The novelty of the proposed work resides in the use of parametric curve formalism to model the shape of an infinite degree of freedom mobile soft manipulator robot and its kinematic control by optimizing its bending potential energy during its motion. The shape optimization based on a minimal bending energy during the collision-free path is respecting a sliding mode strategy applied to the PH curve control points. Experimental results are obtained using a class of MSCM called RobotinoXT. These experiments show the advantages of using a reduced kinematic model based on PH curve to control the MSCM shape in dynamic motion.

Linear Tool Path-Smoothing Method in High-Speed Machining Based on Error Feasible Area and Curvature Optimization

Linear tool path is widely used in high-speed NC machining. However, the geometrical discontinuity of the corner between the linear tool paths will lead to fluctuations in speed, acceleration and jerk, which can excite machinery vibration and reduce the machining efficiency and surface quality. To solve these problems, a novel corner smoothing method based on error feasible area and curvature optimization is proposed in this paper. Compared with most traditional corner smoothing methods using higher-order curves with all control points lying in the straight segment and inside of the tool path, the proposed method constructs B-spline transition curves with smaller curvatures to smooth the corners by reasonably distributing the curve control points inside and outside the straight line segment of the tool path (i.e., error feasible area). Furthermore, the corner transition curve is optimized by the minimum curve curvature extreme to improve the smoothness of the corner transition curve and reduce fluctuation in the kinematic profiles while respecting the G3 continuity (i.e., curvature-smooth), transition length limits and the uniqueness of curvature extremum. Finally, the simulation results show that the proposed method can reduce the curvature value and improve the smoothness of the curve and the minimum transitional velocity of the corner, which means that it can enhance machining efficiency and weaken machining vibration. The feasibility and effectiveness of the method are also verified.

Optimization of parameters for FDM process with functional input based on LS-SVR

In recent years, fused deposition molding (FDM) has attracted much attention as one of the most common and promising 3D printing technologies. Forming accuracy is one of the most concerned quality characteristics in the FDM process and is influenced by many factors. Based on the fact that the temperature gradient affects the molding accuracy, this paper presents a method for optimizing the accuracy of fused deposition molded parts based on least square support vector regression (LS-SVR), which considers a functional input: the printing speed varies continuously in the printing process, thus reducing the temperature gradients. Some parameters that can affect the temperature and cooling of the part such as nozzle temperature, hotbed temperature, and filling rate are also included in the study. Integrating the characteristics of a functional input and the principle of experimental design, we propose to model the printing speed curve using a Bézier curve and use the curve control points together with the scalar inputs as the variables to be optimized. Then, the sample set is obtained experimentally using stratified Latin hypercube sampling for experimental point selection. The regression modeling of the sample data is performed using LS-SVR with an improved kernel function, where the kernel function is improved by the Fréchet distance. Finally, the entire model is optimized by means of the genetic algorithm. The results show that the dimensional accuracy of the parts is significantly optimized by the proposed method. A comparison with existing methods demonstrates the efficiency and practicality of the proposed method.

Solving Ordinary Differential Equations (ODEs) Using Least Square Method Based on Wang Ball Curves

Numerical methods are regularly established for the better approximate solutions of the ordinary differential equations (ODEs). The best approximate solution of ODEs can be obtained by error reduction between the approximate solution and exact solution. To improve the error accuracy, the representations of Wang Ball curves are proposed through the investigation of their control points by using the Least Square Method (LSM). The control points of Wang Ball curves are calculated by minimizing the residual function using LSM. The residual function is minimized by reducing the residual error where it is measured by the sum of the square of the residual function of the Wang Ball curve's control points. The approximate solution of ODEs is obtained by exploring and determining the control points of Wang Ball curves. Two numerical examples of initial value problem (IVP) and boundary value problem (BVP) are illustrated to demonstrate the proposed method in terms of error. The results of the numerical examples by using the proposed method show that the error accuracy is improved compared to the existing study of Bézier curves. Successfully, the convergence analysis is conducted with a two-point boundary value problem for the proposed method.

On approximation sine wave with the 5th and 7th order Bezier paths in plane

There are many studies to approximate to sine curve or sine wave. In this study, it has been examined the way how the sine wave can be written as any order Bezier curve. First, it has been written the 5th and the 7th degree Maclaurin series expansion of the parametric form of sine curve. Also, they are 5th and the 7th order Bezier paths, based on the control points with matrix form in E2. Hence it has been given the control points of the 5th and the 7th order Bezier curve based on the coefficients of the 5th and the 7th degree Maclaurin series expansion of the sine curves in three steps. Further it has been given the coefficients based on the control points of the 5th and the 7th order Bezier curve too.

Research on Fan Operation Evaluation and Error State Judgment Relying on Improved Neural Network and Intelligent Computing

Fan, as the most commonly used mechanical equipment, is widely used. In order to solve the problem of fan bearing fault diagnosis, this paper analyzes the main factors affecting fan spindle speed and power generation in operation. The input and output parameters of the performance prediction model are determined. The performance prediction model of wind turbine is established by using generalized regression neural network, and the smoothing factor of GRNN is optimized by comparing the prediction accuracy of the model. Based on this model, the sliding data window method is used to calculate the residual evaluation index of wind turbine speed and power in real time. When the evaluation index continuously exceeds the pre-set threshold, the abnormal state of wind turbine can be judged. In order to obtain wind turbine blades with better aerodynamic performance, a blade aerodynamic performance optimization method based on quantum heredity is proposed. The B é zier curve control point is used as the design variable to represent the continuous chord length and torsion angle distribution of the blade, the blade shape optimization model aiming at the maximum power is established, and the quantum genetic algorithm is used to optimize the chord length and torsion angle of the blade under different constraints. The optimization results of quantum genetic algorithm and classical genetic algorithm are compared and analyzed. Under the same parameters and boundary conditions, the proposed blade aerodynamic optimization method based on quantum genetic optimization is better than the classical genetic optimization method, and can obtain better blade aerodynamic shape and higher wind energy capture efficiency. This method makes up for the shortcomings of traditional fault diagnosis methods, improves the recognition rate of fault types and the accuracy of fault diagnosis, and the diagnosis effect is good.

Optimization of modular and helical coils applying genetic algorithm and fully-three-dimensional B-spline curves

A new numerical method for designing the external coils of a stellarator is presented. In this method, the shape of filamentary coils is expressed using fully three-dimensional B-spline curves that are not necessarily constrained on a winding surface. The control points of B-spline curves are optimized together with the coil position and current to minimize an objective function, which is defined using normal field components and engineering constraints. The genetic algorithm is employed to minimize the objective function for arbitrary combinations of modular, helical, and circular poloidal field coils without giving any specific initial guess of coil shapes. A new numerical code genetic optimizer using sequence of points for external coil is developed on the basis of this method, and successfully found optimized modular coils for the stellarators CFQS and Wendelstein 7-X. We also found a specific pattern of helical coil arrangement that can reproduce these optimized stellarators while creating divertor legs outside of the closed magnetic surfaces.

Estimating the Characteristic Curve of a Directional Control Valve in a Combined Multibody and Hydraulic System Using an Augmented Discrete Extended Kalman Filter.

The estimation of the parameters of a simulation model such that the model’s behaviour matches closely with reality can be a cumbersome task. This is due to the fact that a number of model parameters cannot be directly measured, and such parameters might change during the course of operation in a real system. Friction between different machine components is one example of these parameters. This can be due to a number of reasons, such as wear. Nevertheless, if one is able to accurately define all necessary parameters, essential information about the performance of the system machinery can be acquired. This information can be, in turn, utilised for product-specific tuning or predictive maintenance. To estimate parameters, the augmented discrete extended Kalman filter with a curve fitting method can be used, as demonstrated in this paper. In this study, the proposed estimation algorithm is applied to estimate the characteristic curves of a directional control valve in a four-bar mechanism actuated by a fluid power system. The mechanism is modelled by using the double-step semi-recursive multibody formulation, whereas the fluid power system under study is modelled by employing the lumped fluid theory. In practise, the characteristic curves of a directional control valve is described by three to six data control points of a third-order B-spline curve in the augmented discrete extended Kalman filter. The results demonstrate that the highly non-linear unknown characteristic curves can be estimated by using the proposed parameter estimation algorithm. It is also demonstrated that the root mean square error associated with the estimation of the characteristic curve is 0.08% with respect to the real model. In addition, all the errors in the estimated states and parameters of the system are within the 95% confidence interval. The estimation of the characteristic curve in a hydraulic valve can provide essential information for performance monitoring and maintenance applications.