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An equilibrium point of a WIP (Wheeled Inverted Pendulum) with changing its center of gravity is derived and validated by various numerical simulations. Generally, the WIP has two equilibrium points which are unstable and stable one. The unstable one is interested in this study. To keep the WIP over the unstable equilibrium point, the WIP is consistently being adjusted. A state feedback controller for the WIP needs a control reference for the equilibrium point. The control reference can be obtained by studying an equilibrium point of the WIP based on statics. By using Lagrange method, this study is deriving dynamic equations of the WIP both with and without changing its center of gravity. Various numerical simulations are carried out to show the validation of the equilibrium point.

A Derivation of the Equilibrium Point for a Controller of a Wheeled Inverted Pendulum with Changing Its Center of Gravity