Dynamic modeling and simulation of a bicycle stabilized by LQR control

In this paper, we present a new approach to mathematical modeling of the bicycle. It is based on the detailed nonlinear Whipple scientific description. We are focused on the state space representation which we use to solve the control law and we test the optimal linear quadratic control which finally gives satisfactory results. The article includes a several computer simulations of the single-track vehicle motion. We indicate when the bicycle is self-stable. The results are useful to make further research on the bicycle modelling.