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 ACC2017. pdf
- 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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