Dear Khalil,

I suggest you to see links and attached files in topic.

- Path following for an omnidirectional mobile robot based on model ...

dl.acm.org/citation.cfm?id=1703477

- IEEE Xplore - Conference Table of Contents

ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6490927... -

- IEEE Xplore - Conference Table of Contents

ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=21827...p... -

-Conference Digest - ROBIO2016

robio2016.org/cms/wp-content/uploads/2016/11/robio2016_digest.

Best regards

Hello Khalil,

I would suggest the following tutorials:

http://robotics.itee.uq.edu.au/~metr4202/2014/tpl/t8-Week13-pendulum.pdf

https://www.control.isy.liu.se/student/tsrt19/ht2/file/invpendpmenglish.pdf

http://www.engr.usask.ca/classes/EE/480/Inverted%20Pendulum.pdf

Good luck!

Hello, Khalil,

I would suggest a general Lagrange dynamics approach, with generalized coordinates and forces. In the simplest model, assume rigid links of the pendulum, lumped masses and rotational inertia. A spherical joint has two angular degrees of freedom: zenith angle and azimuth. Derive the potential and kinetic energy of the entire system vs. the generalized coordinates and their derivatives, respectively. Then apply Lagrange method, and you will get a set of ordinary differential equations of motion. Good luck