Geometric Heat Flow Method for Legged Locomotion Planning

Yinai Fan, Shenyu Liu, Mohamed Ali Belabbas

Research output: Contribution to journalArticlepeer-review


We propose in this letter a motion planning method for legged robot locomotion based on Geometric Heat Flow framework. The task is challenging due to the hybrid nature of dynamics and contact constraints. We encode the hybrid dynamics and constraints into Riemannian inner product, and this inner product is defined so that short curves correspond to admissible motions for the system. We rely on the affine geometric heat flow to deform an arbitrary path connecting the desired initial and final states to this admissible motion. The method is able to automatically find the trajectory of robot's center of mass, feet contact positions and forces on uneven terrain.

Original languageEnglish (US)
Article number9127539
Pages (from-to)941-946
Number of pages6
JournalIEEE Control Systems Letters
Issue number3
StatePublished - Jul 2021


  • Motion planning
  • legged locomotion
  • nonlinear dynamical systems
  • trajectory optimization

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization


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