Derivation of nonlinear mathematical model of two-wheeled inverted pendulum

This paper begins with a useful presentation of known theoretical mechanics concepts for obtaining the equations of motion for systems of rigid bodies with and without non-holonomic constraints, using D'Alembert's principle. Then the equations of motion of a two-wheeled inverted pendulum on a flat surface with non-sliding wheels are obtained, by using the presented theory. Finally the nonlinear dynamical system is linearized and a linear state feedback control law for multi-input systems is obtained. The nonlinear system is simulated and stabilized using the linear control law.