A second-order elastic flow for path planning in R2

Chun Chi Lin; Yang Kai Lue; Dung The Tran

doi:10.1142/S0219199722500808

A second-order elastic flow for path planning in R2

Chun Chi Lin, Yang Kai Lue^*, Dung The Tran

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We provide an approach of elastic flow with dynamic conditions at the knot points to resolve the path planning problem in the plane. The elastic flow is set up by a second-order semilinear parabolic system with nonlocal lower-order terms. We prove the existence of classical global solutions to the elastic flow, whose asymptotic limits provide classical solutions to the path planning problem.

Original language	English
Article number	2250080
Journal	Communications in Contemporary Mathematics
DOIs	https://doi.org/10.1142/S0219199722500808
Publication status	Accepted/In press - 2023

Keywords

elastic flow
interpolation
path planning
Second-order parabolic equation
spline

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1142/S0219199722500808

Cite this

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title = "A second-order elastic flow for path planning in R2",

abstract = "We provide an approach of elastic flow with dynamic conditions at the knot points to resolve the path planning problem in the plane. The elastic flow is set up by a second-order semilinear parabolic system with nonlocal lower-order terms. We prove the existence of classical global solutions to the elastic flow, whose asymptotic limits provide classical solutions to the path planning problem.",

keywords = "elastic flow, interpolation, path planning, Second-order parabolic equation, spline",

author = "Lin, {Chun Chi} and Lue, {Yang Kai} and Tran, {Dung The}",

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AU - Lue, Yang Kai

AU - Tran, Dung The

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AB - We provide an approach of elastic flow with dynamic conditions at the knot points to resolve the path planning problem in the plane. The elastic flow is set up by a second-order semilinear parabolic system with nonlocal lower-order terms. We prove the existence of classical global solutions to the elastic flow, whose asymptotic limits provide classical solutions to the path planning problem.

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KW - interpolation

KW - path planning

KW - Second-order parabolic equation

KW - spline

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A second-order elastic flow for path planning in R2

Abstract

Keywords

ASJC Scopus subject areas

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