Affine geometric heat flow and motion planning for dynamic systems

Shenyu Liu, Yinai Fan, Mohamed Ali Belabbas

Research output: Contribution to journalConference articlepeer-review


We present a new method for motion planning for control systems. The method aims to provide a natural computational framework in which a broad class of motion planning problems can be cast; including problems with holonomic and non-holonomic constraints, drift dynamics, obstacle constraints and constraints on the applied controls. The method, which finds its inspiration in recent work on the so-called geometric heat flows and curve shortening flows, relies on a hereby introduced partial differential equation, which we call the affine geometric heat flow, and evolves an arbitrary differentiable path joining initial to final state in configuration space to a path that meets the constraints imposed on the problem. From the path, controls to be applied on the system can be extracted. We provide conditions guaranteeing that the controls extracted will drive the system arbitrarily close to the desired final state, while meeting the imposed constraints and illustrate the method on three canonical examples.

Original languageEnglish (US)
Pages (from-to)168-173
Number of pages6
Issue number16
StatePublished - Sep 2019
Externally publishedYes
Event11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019 - Vienna, Austria
Duration: Sep 4 2019Sep 6 2019


  • Affine system with drift
  • Dubins car
  • Geometric control methods
  • Input constraints
  • Motion planning
  • Partial differential equations

ASJC Scopus subject areas

  • Control and Systems Engineering


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