A Homotopy method for Motion Planning


Slides presenting the method:

slides (v2)

slides (v1)

warning: this is a large PDF ~7MB — videos are visible using Acrobat reader, but not using Preview (on a Mac)


Some papers:

  • New Method for Motion Planning for Non-holonomic Systems using Partial Differential Equations, with S. Liu ACC2017pdf
  • Motion Planning for Non-holonomic Systems via the Heat Flow: theory and algorithms, with S. Liu (pdf) (2018)
  • Geometric Heat Flow and Motion Planning for Dynamic Systems, with S. Liu and Y. Fan (pdf) (2019)


The code below implements our motion planning method to find a trajectory that avoids obstacles for a unicycle. (Model in slide #1)

Sample code: unicycle_with_obstacle.m

To run the code, simply type the filename in the Matlab command window.

The code produces the following animations:

  • Homotopy from initial path to final path: video
  • Homotopy seen in x-y plane, and the trajectory of the unicycle with controls extracted using our method : video

Additional examples:

Car 180-turn in narrow street with bounded turning radius (model in slide #28): video

Car 180-turn in narrower street: video 

Car 90 degree turn in narrow streets: video

Car 90 degree turn in narrower streets: video



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