A second-order elastic flow for path planning in R2

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number2250080
JournalCommunications in Contemporary Mathematics
Publication statusAccepted/In press - 2023


  • elastic flow
  • interpolation
  • path planning
  • Second-order parabolic equation
  • spline

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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