In this papers, we derive a simple kinematic and dynamic formulation of an unmanned electric bicycle. We also check the controllability of the stabilization problem of bicycle. We propose a new control algorithm for the self stabilization of unmanned bicycle with bounded wheel speed and steering angle by using nonlinear control based on the sliding patch and stuck phenomena which was introduced by W. Ham. We also propose a sort of optimal control strategy for steering angle and driving wheel speed that make the length of bicycle`s path be the shortest. From the computer simulation results, we prove the validity of the proposed control algorithm.