B-spline-to-Bezier conversion and applications on path planning

Ngoc Thinh Nguyen; Pranav Tej Gangavarapu; Floris Ernst

B-spline-to-Bezier conversion and applications on path planning

Ngoc Thinh Nguyen, Pranav Tej Gangavarapu, Floris Ernst

Institute of Robotics and Cognitive Systems

Abstract

In this paper, we present a new approach to calculate the B-spline-to-Bézler conversion matrix which converts the control points of a uniform B-spline curve into the control points of an equivalent Bézier curve. It takes into account the order of the curve intervals and hence can provide the conversion of the whole curve at once. The algorithm is implemented so that the computation time only increases proportionally with the number of control points until a constant value before getting saturated. Applications include but are not limited to the efficient usage in different optimal path planning algorithms for navigation in 2D non-convex polytopic region as being presented.

Original language	English
Title of host publication	2023 IEEE International Conference on Control, Decision and Information Technologies (CoDIT’23)
Number of pages	6
Publisher	IEEE
Publication date	2023
Pages	2643-2648
ISBN (Print)	2576-3547
ISBN (Electronic)	2576-3555
Publication status	Published - 2023

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Cite this

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title = "B-spline-to-Bezier conversion and applications on path planning",

abstract = "In this paper, we present a new approach to calculate the B-spline-to-B{\'e}zler conversion matrix which converts the control points of a uniform B-spline curve into the control points of an equivalent B{\'e}zier curve. It takes into account the order of the curve intervals and hence can provide the conversion of the whole curve at once. The algorithm is implemented so that the computation time only increases proportionally with the number of control points until a constant value before getting saturated. Applications include but are not limited to the efficient usage in different optimal path planning algorithms for navigation in 2D non-convex polytopic region as being presented.",

author = "Nguyen, {Ngoc Thinh} and Gangavarapu, {Pranav Tej} and Floris Ernst",

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AU - Nguyen, Ngoc Thinh

AU - Gangavarapu, Pranav Tej

AU - Ernst, Floris

PY - 2023

Y1 - 2023

N2 - In this paper, we present a new approach to calculate the B-spline-to-Bézler conversion matrix which converts the control points of a uniform B-spline curve into the control points of an equivalent Bézier curve. It takes into account the order of the curve intervals and hence can provide the conversion of the whole curve at once. The algorithm is implemented so that the computation time only increases proportionally with the number of control points until a constant value before getting saturated. Applications include but are not limited to the efficient usage in different optimal path planning algorithms for navigation in 2D non-convex polytopic region as being presented.

AB - In this paper, we present a new approach to calculate the B-spline-to-Bézler conversion matrix which converts the control points of a uniform B-spline curve into the control points of an equivalent Bézier curve. It takes into account the order of the curve intervals and hence can provide the conversion of the whole curve at once. The algorithm is implemented so that the computation time only increases proportionally with the number of control points until a constant value before getting saturated. Applications include but are not limited to the efficient usage in different optimal path planning algorithms for navigation in 2D non-convex polytopic region as being presented.

M3 - Conference contribution

SN - 2576-3547

SP - 2643

EP - 2648

BT - 2023 IEEE International Conference on Control, Decision and Information Technologies (CoDIT’23)

PB - IEEE

ER -