Bezier Curves Research Articles

Ultra-compact and fabrication-tolerant multimode photonic jumpers based on dual Bezier curves.

Compact routing of multimode bus waveguides is of great significance for on-chip mode-division multiplexing (MDM) systems to realize high integration density and flexible layout. In this Letter, we propose and experimentally demonstrate a novel, to the best of our knowledge, multimode photonic jumper (MPJ) on a standard silicon-on-insulator (SOI) platform. It enables an ultra-compact connection between two parallel multimode waveguides (MWGs) with an arbitrary displacement. As a proof of concept, we describe two MPJs with displacements of 5.9 µm and 0.6 µm, each supporting three modes and featuring a longitudinal distance of around 14 µm. For both MPJs, the experimental results show insertion losses (ILs) below 0.086 dB and inter-modal cross talk (CT) below -17.6 dB over the wide wavelength range of 1525-1600 nm for all three modes.

A DTSD model based on PS-InSAR surface multi-type deformation monitoring of villages in the mining area

Evaluating building damage in mining areas using Interferometric Synthetic Aperture Radar (InSAR) has inherent challenges. This work presents a Delaunay Triangulation of Surface Deformation (DTSD) model that utilizes Permanent Scatter InSAR to analyze various types of deformations in villages. This model created a network of irregular triangles using Delaunay triangulation and PS points as the input. The calculation involved determining the inclination of triangular edges and the torsion of spatial Bezier curves fitted by these edges. The PS points' maximum inclination and curvature values were identified by solving over-determined equations. Results from a slurry injection mine in Huaibei, China, indicate that the various types of deformations in the neighboring communities were below 8 %, and the buildings experienced minimal damage. The DTSD model offers a theoretical framework for monitoring and assessing various types of surface deformation and designing essential zones for building protection.

Lattice optimization of fiber-reinforced polymer parts fabricated by additive manufacturing: the impact of Bezier curve order on mechanical properties

PurposeLattice structures are widely used for achieving optimal topology in additive manufacturing. However, the use of different lattices in a single design can result in stress concentrations at the transition points. This study aims to investigate the influence of Bezier curves on mechanical properties during the transformation from one lattice structure to another. It specifically focuses on the transition from a hexagonal to diamond lattice, using Bezier curves of various orders.Design/methodology/approachThe curves were designed by passing them through the same control points for different orders, such as third, fifth and seventh. The samples were sliced for 3D printing, and a tensile test was conducted. Young’s modulus and energy absorption abilities were measured to compare the mechanical properties of the models created with Bezier curves for the transformation between hexagonal and diamond models.FindingsThe analysis revealed a gradual change in mechanical properties from the hexagonal to the diamond lattice. Moreover, different orders of Bezier curves exhibited varying mechanical properties during the transformation between the two lattices. As the order of the Bezier curve increased, the mechanical properties smoothly changed from the hexagonal to diamond lattice. This prevented stress concentrations or mechanical behavior mismatch caused by sudden deformations at the transitions between the curves used in the design.Originality/valueThe study’s innovative use of Bezier curves of different orders to smoothly transformation between hexagonal and diamond lattices in additive manufacturing offers a practical solution to prevent stress concentrations and mechanical inconsistencies during such design transitions.

Shape optimization of annular transonic thrust nozzles via genetic algorithm and adjoint method

In this research, the idea of combining the genetic algorithm and adjoint method was proposed to leverage the benefits of both approaches to improve the accuracy of thrust nozzle shape optimization. Although the genetic algorithm can search the entire design space to approach the global optimum, its computational cost increases considerably with the number of design variables. Meanwhile, the adjoint method is unaffected by the design variables, but it cannot achieve the global optimum directly and relies on the initial guess geometry. To address these challenges, a genetic algorithm was initially employed to approximate the global optimal geometry of a thrust nozzle with a conical center body parameterized by a Bezier curve. A MATLAB code integrated the geometry parameterization, genetic algorithm, and Fluent R2 2021 flow solver. The resulting geometry was then considered as the initial guess for the adjoint method, which accurately achieved the final optimal geometry with increased control points. The genetic algorithm aimed to maximize the thrust coefficient as the objective function, while the adjoint solver aimed to minimize the axial velocity variance at the nozzle outlet as the cost function. Three distinct constraints were incorporated in the optimization process, and the influence of the center body shape on the results was thoroughly examined to consider all possible geometries throughout the optimization procedure. The findings revealed that the conical center body effectively adjusted the flow angle at the exit, significantly affecting the thrust force. Both optimization steps reduced the average velocity and increased the average pressure at the nozzle exit, enhanced the mass flow rate, and finally increased the thrust force. The genetic algorithm and adjoint method contributed to 3 % and 0.6 % increases, respectively, in the thrust force, resulting in a thrust coefficient of 96.15 % for the final optimized nozzle.

Analysis and optimization of the coupling effect for duct-rotor based on aerodynamic performance

The duct has the potential to provide additional thrust, which can enhance the overall aerodynamic performance of the system. Nonetheless, since the duct and the rotor interact with each other, it is crucial to consider their interaction while optimizing the system for improved performance. This paper presents a parameterization approach for the duct and rotor. Primarily, a rotor space characterization and parameter modeling method that utilizes Bezier curves, class functions/shape functions, and Bernstein polynomials is proposed. Next, the aerodynamic performance of different key factors of the duct-rotor system is calculated and analyzed using a numerical calculation method. The study found that the coupling effect of camber yf and chord length parameter Bc3 had a significant impact on the thrust coefficient, with a contribution rate of 7.3 %. Correspondingly, the coupling effect of camber yf and torsion angle parameter Ba3 had a great influence on the Figure of Merit (FM), with a contribution rate of 7.1 %. The thrust coefficient and FM of the rotor-duct system were optimized by taking the coupling effect into consideration, and the optimized ducted rotor was verified by experimental measurement. The test results shows that the high thrust case achieves a 25.60 % increase in thrust coefficient, while the high-FM case establishes an 8.89 % increase in the FM. This implies that the collaborative optimization based on the coupling effect of duct and rotor shape parameters can effectively improve the system's performance, such as thrust coefficient and Figure of Merit.

Obstacle avoidance motion planning for space redundant manipulator based on improved RRT algorithm

In addressing the challenge of obstacle-avoidance motion planning for space redundant manipulators operating in environments with obstacles, an improved method based on a rapidly exploring random tree (RRT) algorithm is proposed. The method first adopts a target probabilistic sampling strategy to enhance the target orientation. Secondly, an artificial potential field is constructed to steer the growth of the node tree in joint space. Subsequently, a collision detection model between the manipulator and obstacles is established based on the bounding capsule and bounding sphere in Cartesian space. Finally, the paths are pruned and smoothed with a cubic Bezier curve. The simulation results validate the method’s capacity to effectively plan a collision-free path for the space redundant manipulator and the joint motion trajectory is smooth.

Orca hydrofoil shape optimization using Bezier curve and Artificial Neural Network – Multiple objective Genetic Algorithm for low flow velocity

Tidal energy is a clean and predictable power source that is commonly harnessed by using horizontal axis tidal turbines. The power generating process of tidal turbines is influenced by various elements, one of which is the hydrofoil performance. This includes the lift coefficient, drag coefficient, and lift-to-drag ratio. This study introduces the utilization of the Orcinus Orca hydrofoil for horizontal axis tidal turbines. The Orcinus Orca geometry is obtained by modified the NACA0021 airfoil. Subsequently, Bezier curve parameterization is employed to make a smooth hydrofoil profile. The study further deploy an Artificial Neural Network coupled with a Multi-Objective Genetic Algorithm, specifically targeting optimization of the hydrofoil shape optimization at a low flow velocity, specifically at an inlet velocity of 0.5 m/s. The aim of this optimization is to augment the lift coefficient and diminish the drag coefficient in order to amplify the lift to drag ratio. The findings reveal a significant enhancement in performance, as the optimized Orcinus Orca hydrofoil exhibits a remarkable increase of 42.78 % and 27.93 % compared to the original Orcinus Orca and the Bezier-modified Orcinus Orca hydrofoils, respectively.

Multi-Domain Collaborative Task Allocation and Conflict Resolution in Unmanned Systems under Complex Constraints

Under the background that multi-domain collaborative tasks with complex constraints executed by heterogeneous unmanned systems, based on a consensus-based bundle algorithm, a consensus-based synergy algorithm is proposed to solve the distributed multi-domain collaborative task planning problem. First, a multi-domain collaborative task allocation model and score evaluation system are established by considering task resource requirement constraints, task timing constraints, and path threat constraints. Second, the time sequence constraints of collaborative tasks are transformed into elastic time window constraints. The bidding method based on collaborative constraints is used for task allocation, and the improved consistency conflict resolution principle is adopted to realize distributed multi-domain collaborative task allocation conflict resolution. Finally, the path planning is coupled to the task allocation process by using the Bezier curve path, and the results of multi-domain collaborative task allocation and path planning are obtained synchronously. Simulation results show that the proposed algorithm can effectively solve the problem of multi-domain collaborative task planning for heterogeneous unmanned systems.

A Time-History Contact Force Model of the Dynamic Load of AERORail Structures

This study proposes two curves that depict the vehicle–bridge contact force in a novel transportation system named AERORail, which is a lightweight cable-supported structure in which the rails and the prestressed cable form the load bearing system. Based on the contact force identified from a full-scale AERORail system, single and double-valley curves were obtained as the idealized contact force model for large- and small-span AERORail systems, respectively. This was achieved by utilizing the Bezier curves and the least squares method. The proposed curves were verified through a moving load model from a previous study under various spans and speeds. Moreover, the structural response of the AERORail structure under high-speed vehicle passing was explored using the idealized contact force model. The simulation results show that the proposed contact force model can predict the displacement response of 5 m and 15 m spans with a relative error of less than 5%, proving that the model can be used for dynamic analysis of AERORail.

Trajectory optimization of unmanned surface vehicle based on improved minimum snap

To solve the problem of path discontinuity and tracking difficulty in unmanned surface vehicle path planning, this paper introduces the Minimum Snap algorithm to optimize the trajectory, and makes some improvements to the Minimum Snap algorithm to address the problem of imperfect paths caused by uneven time allocation. The concept of a safe corridor is introduced to optimize the Minimum Snap algorithm. In response to the problem of excessive deviation from the reference value in some areas of the optimized path, a guidance function is added to make the path closer to the original trajectory. In the simulation, the proposed improved Minimum Snap is compared with Bezier curve and B-spline curve, the results show that the improved Minimum Snap can enable unmanned surface vehicle to complete turns and other actions with minimal energy consumption while driving safely, without experiencing severe acceleration and Jerk, laying the foundation for subsequent path tracking control.

Economical Design Perspective for Aircraft by Optimizing Airfoil S1223

Geographical positioning system based end computer control technology are utilized in the air modelling based dynamics models. Unmanned aircraft have the potential to significantly increase their coverage and flying precision. The observation area is effectively controlled if traditional continues pest control algorithms are used. Calculating the path phones take a long time. It is not ideal for aircraft control in real time, when Bezier curves are used to calculate the planning path point allow to minimize the calculation time in easiest way, but producing an expected target becomes difficult. When linear and circular interpolation devices which are frequently utilized in numerical, control system aid applied to the aircraft turning path control algorithm, the calculation time is reduced and the flight path becomes accurate as per objectives of this research discussed in section two. This paper combines flight course control and effects of flying speed an angle of attack on aircraft height to explain how the turning path control algorithm is implemented. The outcome results demonstrate that path control is accurate and the algorithm straight forward. Finally air photography and flight tests confirm the rationality of the design.

Optimize & Reduce: A Top-Down Approach for Image Vectorization

Vector image representation is a popular choice when editability and flexibility in resolution are desired. However, most images are only available in raster form, making raster-to-vector image conversion (vectorization) an important task. Classical methods for vectorization are either domain-specific or yield an abundance of shapes which limits editability and interpretability. Learning-based methods, that use differentiable rendering, have revolutionized vectorization, at the cost of poor generalization to out-of-training distribution domains, and optimization-based counterparts are either slow or produce non-editable and redundant shapes. In this work, we propose Optimize & Reduce (O&R), a top-down approach to vectorization that is both fast and domain-agnostic. O&R aims to attain a compact representation of input images by iteratively optimizing Bezier curve parameters and significantly reducing the number of shapes, using a devised importance measure. We contribute a benchmark of five datasets comprising images from a broad spectrum of image complexities - from emojis to natural-like images. Through extensive experiments on hundreds of images, we demonstrate that our method is domain agnostic and outperforms existing works in both reconstruction and perceptual quality for a fixed number of shapes. Moreover, we show that our algorithm is x10 faster than the state-of-the-art optimization-based method. Our code is publicly available: https://github.com/ajevnisek/optimize-and-reduce

Research on Ship Automatic Berthing Algorithm Based on Flow Matching and Velocity Matching

Addressing the automatic berthing task for vessels, this study introduces the Flow Matching Double Section Bezier Berth Method (FM-DSB) for handling downstream and upstream berthing instructions. By considering the orientation relationship between the direction of water flow and the berth, combined with berthing modes, the algorithm determines the vessel’s entry angle into the berth and plans the berthing path using double-section Bezier curves. Effective control of vessel speed post-path determination is essential. Therefore, based on the response of vessels to propeller inputs, this study introduces the Berthing Path Velocity Matching Method (BPVM). The BPVM ensures speed matching along the berthing path through analysis of vessel acceleration and deceleration capabilities. Subsequently, simulation experiments are conducted to validate the planning algorithm for both long-distance and short-distance berthing. Furthermore, the feasibility and effectiveness of the berthing path are verified using a dual-loop path tracker based on the planned results. Experimental outcomes illustrate the adaptability of the proposed algorithm in planning berthing paths that align with vessel motion characteristics, effectively guiding vessels into berths through the designed dual-loop control system.

Elastic properties of honeycombs with spline curve cell walls

In the ideal models, cell walls of honeycomb structures are perfect flat sheets or straight lines (viewed from out-of-plane projection), whereas most of the real honeycomb products contain curved cell walls due to the widely employed manufacturing processes. Moreover, some honeycomb products are made intentionally to have corrugated cell walls for an enhanced out-of-plane stability or an increase of structural stiffness. In the presented study, a relative new modeling method for the nonlinear cell walls of honeycomb structures is used. The method makes use of Bezier spline functions to describe the curved cell walls. Energy method and Castigliano's theorem are used to formulate the force-displacement relationship of a single cell wall, and the homogenized stiffness matrix is derived based on the proper boundary conditions of the cell walls. Analytical and experimental verification shows that the proposed model is very accurate and versatile in predicting the mechanical responses of different honeycomb geometries. Parametric studies are conducted, analytically and numerically, to examine the influence of the spline cell wall geometries on the honeycomb's effective in-plane properties and the out-of-plane stability. The study leads to the recommendation of a cell wall design strategy for maximizing the out-of-plane buckling resistance of honeycomb structures.

Novel Adaptive Path-Smoothening Optimization Method for Mobile Robots

A safe and smooth operating path is a prerequisite for mobile robots to accomplish tasks. Although the existing path optimization methods improve the smoothness of the planned path by introducing Bezier curve to locally optimize the path with regard to turning points, most of these methods manually select the position of control points and subjectively analyze the feasibility of the optimized path. It is argued unfavorably that it exhibits strong subjectivity and cumbersome selection process. To fill this gap, an adaptive path-smoothening optimization method is proposed in this study, which combines neural network, genetic algorithm, and Bezier curve to transform the path smoothing problem into an optimization problem. It rapidly determines the position of the optimal control point based on comprehension of constraints, e.g., path safety, curvature and kinematic restrains of the robot. The currently proposed method resolves the long-standing problems of strong subjectivity, cumbersome steps, and thus low efficiency in the selection process of control points, and lays the theoretical groundwork for smoothening the locus and path. To start with, according to the actual working conditions, the dataset corresponding to the position of the control point and the path deviation is constructed, and the neural network algorithm is used to solve the prediction model of the path deviation, so as to obtain the mapping relationship between the length and included angle of the control edge in the second-order Bezier curve and the path deviation. Subsequently, with reference to the prediction model of path deviation, a reliability evaluation function is formulated by comprehending multiple influential factors of mobile robot motion safety and path smoothness. The genetic algorithm is then introduced to detect the satisfactory control points in different environments. The currently proposed method is verified by experiments in different operating environments. The study results show that the currently proposed adaptive path-smoothening optimization method exhibits remarkably superior applicability and effectiveness compared to the currently prevailing methods. It demonstrates advantages of fast path planning, reduced path turning points, and desirable path smoothness. In addition, it can also ensure the safety of mobile robot along the planned path as availed by a pre-set criterion.

Trajectory Generation Method for Serial Robots in Hybrid Space Operations

The hybrid space of robots is divided into task space and joint space, with task space focused on trajectory-tracking accuracy, while joint space considers dynamic responsiveness and synchronization. Therefore, the robot-motion control systems need to effectively integrate both aspects, ensuring precision in task trajectory while promptly responding to unforeseen environmental events. Hence, this paper proposes an online trajectory-generation method for robots in both joint and task spaces. In task space, a planning approach is presented for high-precision NURBS curves. The global NURBS curve is segmented into several rational Bezier curves, establishing local coordinate systems for control points. This ensures that all local control points meet the chord error constraint, guaranteeing trajectory accuracy. To address the feed rate dynamic planning issue for segmented curves, an improved online S-shape feed-rate scheduling framework is introduced. This framework dynamically adjusts the current execution speed to meet task requirements. In joint space, an offline velocity planning based on a time synchronization scheme and a multi-dimensional synchronization technique based on the principle of spatial-coordinate system projection are proposed. Building upon the offline scheme, it allows for the modification of the target state for any sub-dimension during the motion process, with the remaining dimensions adapting accordingly. Simulation and experimentation demonstrate that the two proposed online trajectory generations for robot motion spaces, while ensuring task trajectory accuracy, effectively handle external unexpected events. They ensure joint synchronization and smoothness, carrying significant practical implications and application value for the stability of robot systems.

Comparison-Transfer Learning Based State-of-Health Estimation for Lithium-Ion Battery

Abstract Rapid and accurate estimation of the state of health of lithium-ion batteries is of great significance. This paper aims to address two issues faced when applying deep learning methods to estimate the health status of lithium-ion batteries: high data quality requirements and poor model generalizability. This paper proposes a comparison-transfer learning approach with cyclic synchronization to estimate the state of health of lithium-ion batteries. First, a cyclic synchronization method based on the Bezier curve fitting algorithm is introduced to synchronize the data obtained at different charge–discharge cycles of the lithium-ion battery, facilitating input to the model. Second, a comparison-transfer network using the Pearson correlation coefficient is proposed to transfer knowledge from the source dataset to predict the target dataset under different environmental temperatures. By training a pre-trained model on the source dataset and utilizing the correlation coefficient to analyze the similarity between the source and target datasets, the accumulated knowledge in the source dataset can be effectively utilized to enhance prediction performance on the target dataset. In the experiments, the proposed method is validated using the lithium-ion battery aging public datasets. The experimental results demonstrate that the proposed approach achieves superior prediction performance in the case of small-sample sizes, exhibiting higher accuracy and stability compared to traditional deep learning methods.

Detection of fatigue driving behavior based on facial expression

The scene environment in the cab is complex and changeable, which is easy to be disturbed by the changes of weather, light and other conditions, which brings many difficulties to the driver’s fatigue driving detection. This paper mainly analyzes the specific characteristics of the driving indoor environment, uses some technologies in the field of computer vision and image processing to improve the image quality, uses the Adaboost face detection algorithm based on Haar-like features, to detect and locate the driver’s face in the cockpit, and reduces the face detection area to determine whether the driver looks left and right or bowed. Then, on the basis of detecting the face, the method of gray scale integral projection is adopted to locate the eyes and the mouth, and the Bezier curve is used to fit the contour of the eyes and the mouth, and to judge the driver’s eye opening and the mouth opening by comprehensively analyzing the vertical and horizontal ratio. Later, ocular fatigue analysis was performed by using the PERCLOS(Percentage of Eyelid Closure over the Pupil over Time) criteria and by eyeblink frequency, and mouth fatigue analysis was also performed by the frequency of yawning.

Trajectory optimization with hybrid probabilistic roadmap approach to achieve time efficient navigation of unmanned vehicles in unstructured environment

PurposeThis paper aims to focus on solving the path optimization problem by modifying the probabilistic roadmap (PRM) technique as it suffers from the selection of the optimal number of nodes and deploy in free space for reliable trajectory planning.Design/methodology/approachTraditional PRM is modified by developing a decision-making strategy for the selection of optimal nodes w.r.t. the complexity of the environment and deploying the optimal number of nodes outside the closed segment. Subsequently, the generated trajectory is made smoother by implementing the modified Bezier curve technique, which selects an optimal number of control points near the sharp turns for the reliable convergence of the trajectory that reduces the sum of the robot’s turning angles.FindingsThe proposed technique is compared with state-of-the-art techniques that show the reduction of computational load by 12.46%, the number of sharp turns by 100%, the number of collisions by 100% and increase the velocity parameter by 19.91%.Originality/valueThe proposed adaptive technique provides a better solution for autonomous navigation of unmanned ground vehicles, transportation, warehouse applications, etc.

Optimization of multi-target continuous dynamic trajectory for unmanned aerial vehicles

In the problem of trajectory optimization for unmanned aerial vehicles (UAVs) passing through multiple target points, continuous velocity and acceleration in the process of optimization are essential for maintaining a feasible trajectory. This paper proposes a multi-segment holistic Bezier shaping method (MHBSM) for dynamic trajectory optimization. The MHBSM not only achieves holistic optimization of UAVs passing through a multi-target trajectory but also ensures high-order continuity at the junctions of trajectory segments. Unlike methods that generate non-dynamic trajectories by connecting arcs and straight lines (such as Dubins curves) without considering speed changes, MHBSM optimizes the trajectory while taking into account the dynamics of UAVs. The method optimizes the differential flat output space of a fixed-wing UAV dynamic model and transforms the dynamic optimization problem into a three-dimensional position optimization problem. The problem is then further transformed into an optimization of control points using the Bezier curve. The resulting trajectory satisfies the dynamic constraints. In comparison to the Gaussian pseudospectral method (GPM), MHBSM achieves similar optimization results with only a 2.58% difference, while requiring approximately 1.36% of the computational time on average. The MHBSM demonstrates excellent convergence performance while satisfying the constraints of continuous acceleration and obstacle avoidance.