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sir-avinash / geometric-control-of-spherical-pendula

Geometric tracking controllers are developed for spherical single and double pendula, with almost global stability properties. The dynamics are coordinate-free, and evolve on manifolds that are products of S^2.
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Stability of Pendula #1

Open abdul-mannan-khan opened 7 years ago

abdul-mannan-khan commented 7 years ago

Dear Sir-Avinash,

First of all, please accept my deepest appreciation for uploading your wok. It is a great opportunity for the beginners. Thank You for that.

Secondly, I have one request if you could do something about it. Could you please attach the theoretical background of your work. It will help me understand it in a better way.

Thirdly, I notice that double pendulum simulations are being destabilized. Could yo please shed some light on it?

Your kind response will be very encouraging for the starters working in this domain.

Thank You.

Many Regards,

Dr. Abdul-Mannan

sir-avinash commented 7 years ago

Hi Abdul, A useful resource with regards to geometric modelling of rigid bodies is a book called "Global Formulations of Lagrangian and Hamiltonian Dynamics", by Taeyoung Lee, Melvin Leok and Harris McClamroch.

The geometric controller for the Spherical Pendulum is implemented from here: http://etd.gelman.gwu.edu/etd_11674/11674.pdf .

The double pendulum is still a work in progress, I still haven't figured out what the correct input vector field is in S^2. The dynamics are correct though. You may verify that by making the input zero and plotting energy. It should remain constant. Let me know otherwise.