Linear controller design for circular motion of unmanned bicycle

This paper deals with a dynamic modeling and linear control problem for the circular motion of an unmanned bicycle. It is well known that the bicycle control problem is quite complicated and challenging due to its nonlinearities, unstability and nonminimum phase steering behavior. In order to design a linear controller for the bicycle circular motion, a linear bicycle model of circular motion is derived from fully nonlinear differential equations. The first step is to find an equilibrium roll angle and steering angle given the under turning radius and an angular speed of rear wheel relative to a rear frame. Then at the second step, roll and steering control inputs which maintain equilibrium are calculated. Finally the linearized equations of the circular motion are derived from Lagrange's equations. Some simulation results on the LQ linear control for the circular motion are demonstrated to show the validity of the proposed approach.