Global Energy Fairing of B-Spline Curves in Path Planning Problems

2007 ◽  
Author(s):  
Alexander V. Pesterev ◽  
Lev B. Rapoport ◽  
Ruslan F. Gilimyanov
Keyword(s):  
Path Planning ◽  
Original Data ◽  
Moving Vehicle ◽  
B Spline ◽  
Spline Curves ◽  
Data Points ◽  
Set Of Points ◽  
First Time ◽  
Planning Problems ◽  
Third Derivative

The paper is concerned with path planning for mobile robots. Specifically, the discussion is related to the following problem: Given an ordered sequence of points on the plane, construct a path that fits these points and satisfies certain smoothness requirements. These requirements may be different in different problems and imply basically that the constructed path is to be realizable. Such a problem arises, e.g., when it is required to follow in an automated mode a path stored as a discrete set of points, which, e.g., were collected by a GPS receiver installed on a car when it followed this path for the first time. Due to errors inherent in the data points, the shape of the curve approximating the desired path turns out often inappropriate. The shape of the curve can be improved by applying the so-called fairing, which consists in moving the original data points with the aim to minimize some fairness criterion. Adequate small variations of the data points preserve the proximity of the resulting path to the original data points and make it fairer. In the paper, a new global fairing method is proposed. It reduces the problem of constructing a fair cubic B-spline curve to solving a quadratic programming problem with simple constraints. The fairing criterion is based on minimizing jumps of the spline third derivative. The discussion is illustrated by numerical examples of fairing two actual paths constructed by data points collected by a GPS/GLONASS receiver mounted on a moving vehicle.

Parametric Generation of Planing Hulls with NURBS Surfaces

2013 ◽  
Vol 57 (04) ◽  
pp. 241-261
Author(s):  
Francisco L. Perez-Arribas ◽  
Erno Peter-Cosma
Keyword(s):  
Maximum Deviation ◽  
Geometric Features ◽  
Surface Geometry ◽  
Orthogonal Projections ◽  
Parametric Generation ◽  
B Spline ◽  
Spline Curves ◽  
Hull Design ◽  
Data Points ◽  
Control Curves

This article presents a mathematical method for producing hard-chine ship hulls based on a set of numerical parameters that are directly related to the geometric features of the hull and uniquely define a hull form for this type of ship. The term planing hull is used generically to describe the majority of hard-chine boats being built today. This article is focused on unstepped, single-chine hulls. B-spline curves and surfaces were combined with constraints on the significant ship curves to produce the final hull design. The hard-chine hull geometry was modeled by decomposing the surface geometry into boundary curves, which were defined by design constraints or parameters. In planing hull design, these control curves are the center, chine, and sheer lines as well as their geometric features including position, slope, and, in the case of the chine, enclosed area and centroid. These geometric parameters have physical, hydrodynamic, and stability implications from the design point of view. The proposed method uses two-dimensional orthogonal projections of the control curves and then produces three-dimensional (3-D) definitions using B-spline fitting of the 3-D data points. The fitting considers maximum deviation from the curve to the data points and is based on an original selection of the parameterization. A net of B-spline curves (stations) is then created to match the previously defined 3-D boundaries. A final set of lofting surfaces of the previous B-spline curves produces the hull surface.

scholarly journals Measurement point sampling method for inspection of parts with free-form surfaces

2018 ◽  
Vol 10 (11) ◽  
pp. 168781401880957 ◽  
Author(s):  
Dezhong Zhao ◽  
Wenhu Wang ◽  
Jinhua Zhou ◽  
Ruisong Jiang ◽  
Kang Cui ◽  
...  
Keyword(s):  
Measurement Accuracy ◽  
Sampling Method ◽  
Free Form ◽  
Surface Inspection ◽  
B Spline ◽  
Spline Curves ◽  
Data Points ◽  
Manufacturing Accuracy ◽  
Method Of Measurement ◽  
Free Form Surfaces

Parts must be measured to evaluate the manufacturing accuracy in order to check whether their dimension is in expected tolerance. In engineering, parts with free-form surfaces are generally measured by high-precision coordinate-measuring machines. The measurement accuracy is usually improved by increasing the density of measurement points, which is time-consuming and costly. In this article, a novel sampling method of measurement points for free-form surface inspection is proposed. First, surface inspection is simplified into the inspection of a number of section curves of the surface. Second, B-spline curves constructed with an iterative method are employed to approximate these section curves. Subsequently, data points necessary to construct the B-spline curves are taken as the measurement points. Finally, the proposed method is compared with other two sampling methods. The results indicate that the proposed method greatly reduced the number of measurement points without decreasing the precision of surface modeling.

Fitting scattered data points with ball B-Spline curves using particle swarm optimization

2018 ◽  
Vol 72 ◽  
pp. 1-11 ◽  
Author(s):  
Zhongke Wu ◽  
Xingce Wang ◽  
Yan Fu ◽  
Junchen Shen ◽  
Qianqian Jiang ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Scattered Data ◽  
Swarm Optimization ◽  
B Spline ◽  
Spline Curves ◽  
Data Points

Collision-Free Path Planning by Using Nonperiodic B-Spline Curves

1993 ◽  
Vol 115 (3) ◽  
pp. 679-684 ◽  
Author(s):  
D. C. H. Yang
Keyword(s):  
Computational Complexity ◽  
Path Planning ◽  
Free Path ◽  
Computer Code ◽  
Control Points ◽  
B Spline ◽  
Spline Curves ◽  
End Effectors ◽  
Main Ideas ◽  
Fifth Order

This paper presents a method and an algorithm for the planning of collision-free paths through obstacles for robots end-effectors or autonomously guided vehicles. Fifth-order nonperiodic B-spline curves are chosen for this purpose. The main ideas are twofold: first, to avoid collision by moving around obstacles from the less blocking sides; and second, to assign two control points to all vertices of the control polygon. This method guarantees the generation of paths which have C3 continuity everywhere and satisfy the collision-free requirement. In addition, the obstacles can be of any shape, and the computational complexity and difficulty are relatively low. A computer code is developed for the implementation of this method. Case studies are given for illustration.

Collision-Free Path Planning by Using Non-Periodic B-Spline Curves

1990 ◽  
Author(s):  
D. C. H. Yang
Keyword(s):  
Computational Complexity ◽  
Path Planning ◽  
Computer Code ◽  
Control Points ◽  
A Algorithm ◽  
B Spline ◽  
Spline Curves ◽  
End Effectors ◽  
Main Ideas ◽  
Fifth Order

Abstract This paper presents a method and a algorithm for the planning of collision-free paths through obstacles for robots end-effectors or autonomously guided vehicles. Fifth-order non-periodic curves are chosen for this purpose. The main ideas are twofold: firstly, to avoid collision by moving around obstacles from the less blocking sides; and secondly, to assign two control points to all vertices of the control polygon. This method guarantees the generation of paths which have C3 continuity everywhere and satisfy the collision-free requirement. In addition, the obstacles can be of any shape, and the computational complexity and difficulty are relatively low. A computer code is developed for the implementation of this method. Cases study is given for illustration.

scholarly journals Physical-consistent behavior embodied in B-spline curves for robot path planning

2018 ◽  
Vol 51 (22) ◽  
pp. 306-311
Author(s):  
Davide Chiaravalli ◽  
Federico Califano ◽  
Luigi Biagiotti ◽  
Daniele De Gregorio ◽  
Claudio Melchiorri
Keyword(s):  
Path Planning ◽  
Robot Path Planning ◽  
B Spline ◽  
Spline Curves ◽  
Robot Path

scholarly journals A graph-based method for fitting planar B-spline curves with intersections

2015 ◽  
Vol 3 (1) ◽  
pp. 14-23 ◽  
Author(s):  
Pengbo Bo ◽  
Gongning Luo ◽  
Kuanquan Wang
Keyword(s):  
Shape Representation ◽  
Line Drawing ◽  
Weighted Graph ◽  
Point Clouds ◽  
Connected Components ◽  
Shape Information ◽  
B Spline ◽  
Spline Curves ◽  
Data Points ◽  
Shape Characteristics

Abstract The problem of fitting B-spline curves to planar point clouds is studied in this paper. A novel method is proposed to deal with the most challenging case where multiple intersecting curves or curves with self-intersection are necessary for shape representation. A method based on Delauney Triangulation of data points is developed to identify connected components which is also capable of removing outliers. A skeleton representation is utilized to represent the topological structure which is further used to create a weighted graph for deciding the merging of curve segments. Different to existing approaches which utilize local shape information near intersections, our method considers shape characteristics of curve segments in a larger scope and is thus capable of giving more satisfactory results. By fitting each group of data points with a B-spline curve, we solve the problems of curve structure reconstruction from point clouds, as well as the vectorization of simple line drawing images by drawing lines reconstruction.

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