I am a master student that is trying to implement the funnels’s computation via SOS optimization but my resulting MathematicalProgram appears to be infeasible or to give not meaningful solutions.
I have watched the lecture 24 of the course “MIT 6.832 Underactuated Robotics (Spring 2022) “ about Feedback motion planning and I have found what I am trying to obtain.
In order to have a very useful help in my implementation I would like to ask if it is possible to get the code of this example. Has it been obtained via SOS optimization? Are there some implementation details that maybe are not in the papers?
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Federico Girlanda
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Unfortunately the funnel computation is not inside Drake yet. – Hongkai Dai May 18 '22 at 16:42
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Currently Drake doesn't have the code to compute the funnel through SOS. On the other hand we have the code to compute the region of attraction through SOS in https://github.com/RobotLocomotion/drake/blob/master/systems/analysis/region_of_attraction.h. You could consider to extend this code to computing the funnel.
There are quite some implementation details about Lyapunov analysis with sum-of-squares optimization. You could refer to this answer Numerical roundoff error in bilinear alternation leads to infeasibility for some implementation details.
Hongkai Dai
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First of all, I would like to thank you for the answer. \\ The code that I meant was the one that makes Tedrake obtain the result showed in the lesson. Is it possible to have it? \\ Unfortunately, I tried to implement the step-back in my bilinear optimization but the rho step is still failing. In order to make my problem more clear I want to share with you [my code](https://github.com/FedericoGirlanda/SOS-bilinear-alternation/blob/main/main.ipynb). It would be wonderful to have a feedback on it. – Federico Girlanda Jun 17 '22 at 13:40