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.

Offline decoupled path planning approach for effective coordination of multiple robots

Robotica ◽  
2009 ◽  
Vol 28 (4) ◽  
pp. 477-491 ◽  
Author(s):  
Shital S. Chiddarwar ◽  
N. Ramesh Babu
Keyword(s):  
Path Planning ◽  
Free Path ◽  
Minimum Distance ◽  
Degrees Of Freedom ◽  
Multiple Robots ◽  
A Algorithm ◽  
Two Phase ◽  
Six Degrees Of Freedom ◽  
Planning Approach ◽  
End Effectors

SUMMARYIn this paper, a decoupled offline path planning approach for determining the collision-free path of end effectors of multiple robots involved in coordinated manipulation is proposed. The proposed approach for decoupled path planning is a two-phase approach in which the path for coordinated manipulation is generated with a coupled interaction between collision checking and path planning techniques. Collision checking is done by modelling the links and environment of robot using swept sphere volume technique and utilizing minimum distance heuristic for interference check. While determining the path of the end effector of robots involved in coordinated manipulation, the obstacles present in the workspace are considered as static obstacles and the links of the robots are viewed as dynamic obstacles by the other robot. Coordination is done in offline mode by implementing replanning strategy which adopts incremental A* algorithm for searching the collision-free path. The effectiveness of proposed decoupled approach is demonstrated by considering two examples having multiple six degrees of freedom robots operating in 3D work cell environment with certain static obstacles.

Automatic Unstructured Mesh Generation Around Two-Dimensional Domains Described by B-Spline Curves

2001 ◽  
Author(s):  
Horacio Flórez Guzmán ◽  
Raúl Manzanilla Morillo
Keyword(s):  
Grid Generation ◽  
Computer Code ◽  
Two Dimensional ◽  
B Spline ◽  
Piecewise Polynomials ◽  
Spline Curves ◽  
Interpolation Problems ◽  
Interpolation Procedure ◽  
Definition Of ◽  
Unstructured Mesh Generation

Abstract A computer code for the generation of unstructured two-dimensional triangular meshes around arbitrary complex geometries has been developed. The code is based on Delaunay triangulation with an automatic point insertion scheme and a smoothing technique. The geometrical definition of the domain to be meshed is prescribed by means of B-spline curves obtained from two approaches of interest in Computer-Aided Geometric Design named inverse design and interpolation problems. The presented scheme is based on an interpolation procedure along a B-spline curve proposed by the author in a recent paper. This technique prevents that the resulting grid may overlap convex portions of the boundaries. The main goal is to study the possibility of extend the methodology of unstructured grid generation beginning with boundaries described by polylines to other in which they are prescribed by piecewise polynomials curves capable to drive more realistic problems. Several figures and examples from Computational Fluid Dynamics have been included to show the various steps of the algorithm. The results show that the code is able to solve the problem of automatic grid generation in a robust manner opening new perspectives for the development of a black-box grid generator.

scholarly journals Control point insertion for B-spline curves

1988 ◽  
Vol 38 (2) ◽  
pp. 307-313 ◽  
Author(s):  
Heinz H. Gonska ◽  
Andreas Röth
Keyword(s):  
User Interface ◽  
Control Point ◽  
Point Of View ◽  
Control Points ◽  
Natural User Interface ◽  
B Spline ◽  
Spline Curves

Inserting new knots into B-spline curves is a well-known technique in CAGD to gain extra flexibility for design purposes. However, from a user's point of view, the insertion of knots is somewhat unsatisfactory since the newly generated control points sometimes show up in unexpected locations. The aim of this note is to show that these problems can be circumvented by inserting the control vertices directly, thus also providing a more natural user interface.

B-SPLINE BASED STEREO FOR 3D RECONSTRUCTION OF LINE-LIKE OBJECTS USING AFFINE CAMERA MODEL

2001 ◽  
Vol 15 (02) ◽  
pp. 347-358 ◽  
Author(s):  
YIJUN XIAO ◽  
MINGYUE DING ◽  
JIAXIONG PENG
Keyword(s):  
Stereo Vision ◽  
Free Form ◽  
Control Points ◽  
Invariant Property ◽  
Affine Invariant ◽  
Camera Model ◽  
B Spline ◽  
Space Curves ◽  
Spline Curves ◽  
Affine Camera

This paper presents a novel curve based algorithm of stereo vision to reconstruct 3D line-like objects. B-spline approximations of 2D edge curves are selected as primitives for the reconstruction of their corresponding space curves so that, under the assumption of affine camera model, a 3D curve can be derived from reconstructing its control points according to the affine invariant property of B-Spline curves. The superiority of B-spline model in representing free-form curves gives good geometric properties of reconstruction results. Both theoretical analysis and experimental results demonstrate the validity of our approach.

scholarly journals Shape Designing Using Quadratic Trigonometric B-Spline Curves

2019 ◽  
Vol 3 (2) ◽  
pp. 36-49
Author(s):  
Amna Abdul Sittar ◽  
Abdul Majeed ◽  
Abd Rahni Mt Piah
Keyword(s):  
Shape Parameter ◽  
Control Points ◽  
B Spline ◽  
Spline Curves ◽  
Computer Aided ◽  
And Control

The B-spline curves, particularly trigonometric B-spline curves, have attained remarkable significance in the field of Computer Aided Geometric Designing (CAGD). Different researchers have developed different interpolants for shape designing using Ball, Bezier and ordinary B-spline. In this paper, quadratic trigonometric B-spline (piecewise) curve has been developed using a new basis for shape designing. The proposed method has one shape parameter which can be used to control and change the shape of objects. Different objects like flower, alphabet and vase have been designed using the proposed method. The effects of shape parameter and control points have been discussed also.

T-B Spline Curves with a Shape Parameter

2012 ◽  
Vol 241-244 ◽  
pp. 2144-2148
Author(s):  
Li Juan Chen ◽  
Ming Zhu Li
Keyword(s):  
Shape Parameter ◽  
Simple Structure ◽  
Control Points ◽  
Curve Segment ◽  
Closed Curves ◽  
B Spline ◽  
Spline Curve ◽  
Spline Curves

A T-B spline curves with a shape parameter λ is presented in this paper, which has simple structure and can be used to design curves. Analogous to the four B-spline curves, each curve segment is generated by five consecutive control points. For equidistant knots, the curves are C^2 continuous, but when the shape parameter λ equals to 0 , the curves are C^3 continuous. Moreover, this spline curve can be used to construct open and closed curves and can express ellipses conveniently.

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.

BEZIER AND B-SPLINE CURVES WITH KNOTS IN THE COMPLEX PLANE

Fractals ◽  
2011 ◽  
Vol 19 (01) ◽  
pp. 67-86 ◽  
Author(s):  
KONSTANTINOS I. TSIANOS ◽  
RON GOLDMAN
Keyword(s):  
Complex Domain ◽  
Polynomial Algorithms ◽  
Control Points ◽  
Knot Insertion ◽  
Real Numbers ◽  
Koch Curve ◽  
Natural Manner ◽  
B Spline ◽  
B Splines ◽  
Spline Curves

We extend some well known algorithms for planar Bezier and B-spline curves, including the de Casteljau subdivision algorithm for Bezier curves and several standard knot insertion procedures (Boehm's algorithm, the Oslo algorithm, and Schaefer's algorithm) for B-splines, from the real numbers to the complex domain. We then show how to apply these polynomial and piecewise polynomial algorithms in a complex variable to generate many well known fractal shapes such as the Sierpinski gasket, the Koch curve, and the C-curve. Thus these fractals also have Bezier and B-spline representations, albeit in the complex domain. These representations allow us to change the shape of a fractal in a natural manner by adjusting their complex Bezier and B-spline control points. We also construct natural parameterizations for these fractal shapes from their Bezier and B-spline representations.

Collision-Free Path Generation for Autonomous Manipulators Using Non-Uniform Rational B-Spline (NURBS) via Artificial Transformation

1992 ◽  
Author(s):  
N. Soni ◽  
A. Shirkhodaie ◽  
A. H. Soni
Keyword(s):  
Free Path ◽  
Target Position ◽  
Remote Detection ◽  
Path Generation ◽  
Control Points ◽  
B Spline ◽  
Full Size ◽  
B Splines ◽  
Small Increments ◽  
Crowded Environment

Abstract This paper presents an algorithm for collision free path planning of autonomous manipulators among obstacles. The algorithm uses powerful features of Non-Uniform Rational B-splines (NURBS) to determine the path of the manipulator in the complimentary space of the obstacles. Initially the algorithm artificially transforms the obstacles to point size. It then uses these point obstacles and start & target position of the manipulator as control points to determine a NURBS path which is the initial collision-free path. Obstacles are then iteratively increased in size by small increments. After each increment the new collision control points with obstacles are determined and a new collision-free NURBS path is generated to guide the manipulator through crowded obstacles. This procedure is continued till all the obstacles attain their full size and resulting path is maintained free of collision. The developed algorithm is most suited for manipulators facilitated with range sensors for remote detection of obstacles. The paper details the technique for obtaining a smooth collision-free path of a manipulator moving around a crowded environment with static obstacles.

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