Control Points Of Bezier Curve Research Articles

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.

Investigation of improving the hydraulic turbine cascade performance using non-axisymmetric endwall contouring

Non-axisymmetric endwall contouring techniques have been widely applied in gas turbines; numerous papers and experimental studies have shown that it can significantly improve the overall performance of the turbine. This article first presents the non-axisymmetric endwall profile construction and optimization both for the rotor hub and shroud of a turbine drilling hydraulic cascade in the presence of an axisymmetric rotor, in order to improve the performance and investigate non-axisymmetric endwall contouring’s influence laws on a hydraulic cascade. Rotor cascade endwall design is studied by confining the axisymmetric variation near hub, shroud, and both endwalls. Endwall surface is parameterized with control points of Bezier curve, and control points are considered as design variables having a height constraint of 10%, 12%, or 15% span to move in radial coordinate. This methodology also combines Latin hypercube sampling with NSGA-II algorithm to obtain optimum solution. Computational fluid dynamics simulation results show that the non-axisymmetric endwall contouring technology applied to hub and shroud all realize an improvement in efficiency, while the NEW_S_15% has the best comprehensive performance and it causes an improvement of 1.52% in efficiency and 5.1% in torque. Off-design experiment shows that NEW_S_15% improves the output torque and efficiency as well even it deviates from design working condition, which proves valuableness of the non-axisymmetric endwall contouring technology.

Secondary shape optimization of topological boundary of cold plate channels

Secondary shape optimization for topological boundary is proposed to further improve heat dissipation performance of cold plates. Firstly, the topological boundaries obtained with topology optimization are fitted parametrically by Bezier curves. Here, considering the numerical complexity caused by Bezier curves characters, a simple process is introduced. Thereafter, three algorithms are proposed to formulate secondary shape optimization. The proposed algorithms can further qualitatively handle explicit geometry boundary through optimizing the coefficients of the established distance function or the control points of Bezier curves. The effectiveness of the proposed algorithms is subsequently verified by analyzing the 2D and 3D models given after topology optimization and the obtained results show that these approaches further provide well-performing cold plates design. These approaches provide a theoretical basis for engineering application and they are easy to be processed and implemented. The proposed approaches can be applied not only to the problem of conjugate heat transfer but also to the problems of pure heat conduction, continuum structure, even other more complicated engineering structures.

Construction of Optimal Bézier Splines

We consider a construction of a smooth curve by a set of interpolation nodes. The curve is constructed as a spline consisting of cubic Bezier curves. We show that if we require the continuity of the first and second derivatives, then such a spline is uniquely defined for any fixed parameterization of Bezier curves. The control points of Bezier curves are calculated as a solution of a system of linear equations with a four-diagonal band matrix. We consider various ways of parameterization of Bezier curves that make up a spline and their influence on its shape. The best spline is computed as a solution of an optimization problem: minimize the integral of the square of the second derivative with a fixed total transit time of a spline.

Intelligent Bézier curve-based path planning model using Chaotic Particle Swarm Optimization algorithm

Path planning algorithms have been used in different applications with the aim of finding a suitable collision-free path which satisfies some certain criteria such as the shortest path length and smoothness; thus, defining a suitable curve to describe path is essential. The main goal of these algorithms is to find the shortest and smooth path between the starting and target points. This paper makes use of a Bezier curve-based model for path planning. The control points of the Bezier curve significantly influence the length and smoothness of the path. In this paper, a novel Chaotic Particle Swarm Optimization (CPSO) algorithm has been proposed to optimize the control points of Bezier curve, and the proposed algorithm comes in two variants: CPSO-I and CPSO-II. Using the chosen control points, the optimum smooth path that minimizes the total distance between the starting and ending points is selected. To evaluate the CPSO algorithm, the results of the CPSO-I and CPSO-II algorithms are compared with the standard PSO algorithm. The experimental results proved that the proposed algorithm is capable of finding the optimal path. Moreover, the CPSO algorithm was tested against different numbers of control points and obstacles, and the CPSO algorithm achieved competitive results.