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
Volume	26
Issue number	4
DOIs	https://doi.org/10.1142/S0219199722500808
Publication status	Published - 2024 May 1

Keywords

Second-order parabolic equation
elastic flow
interpolation
path planning
spline

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1142/S0219199722500808

Cite this

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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.",

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